1,1,31,14,0.225000," ","int(1/(-b^2*x^2+a^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(b x +a \right)}{2 a b}-\frac{\ln \left(-b x +a \right)}{2 a b}$&$31$\\ norman&$\frac{\ln \left(b x +a \right)}{2 a b}-\frac{\ln \left(-b x +a \right)}{2 a b}$&$31$\\ risch&$\frac{\ln \left(b x +a \right)}{2 a b}-\frac{\ln \left(-b x +a \right)}{2 a b}$&$31$\\ \hline \end{longtable}"," ",0,"1/2*ln(b*x+a)/a/b-1/2/a/b*ln(-b*x+a)","B"
2,1,15,14,0.306000," ","int(1/(b^2*x^2+a^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(\frac{b x}{a}\right)}{a b}$&$15$\\ risch&$\frac{\arctan \left(\frac{b x}{a}\right)}{a b}$&$15$\\ \hline \end{longtable}"," ",0,"arctan(b*x/a)/a/b","A"
3,1,18,11,0.083000," ","int(sec(2*a*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(\sec \left(2 a x \right)+\tan \left(2 a x \right)\right)}{2 a}$&$18$\\ default&$\frac{\ln \left(\sec \left(2 a x \right)+\tan \left(2 a x \right)\right)}{2 a}$&$18$\\ norman&$-\frac{\ln \left(\tan \left(a x \right)-1\right)}{2 a}+\frac{\ln \left(\tan \left(a x \right)+1\right)}{2 a}$&$26$\\ risch&$\frac{\ln \left({\mathrm e}^{2 i a x}+i\right)}{2 a}-\frac{\ln \left({\mathrm e}^{2 i a x}-i\right)}{2 a}$&$32$\\ \hline \end{longtable}"," ",0,"1/2/a*ln(sec(2*a*x)+tan(2*a*x))","A"
4,1,8,7,0.082000," ","int(1/4/sin(1/3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{3 \ln \left(\tan \left(\frac{x}{6}\right)\right)}{4}$&$8$\\ derivativedivides&$\frac{3 \ln \left(\csc \left(\frac{x}{3}\right)-\cot \left(\frac{x}{3}\right)\right)}{4}$&$15$\\ default&$\frac{3 \ln \left(\csc \left(\frac{x}{3}\right)-\cot \left(\frac{x}{3}\right)\right)}{4}$&$15$\\ risch&$-\frac{3 \ln \left({\mathrm e}^{\frac{i x}{3}}+1\right)}{4}+\frac{3 \ln \left({\mathrm e}^{\frac{i x}{3}}-1\right)}{4}$&$22$\\ \hline \end{longtable}"," ",0,"3/4*ln(tan(1/6*x))","A"
5,1,21,11,0.253000," ","int(-1/cos(1/4*Pi+2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(\sec \left(\frac{\pi}{4}+2 x \right)+\tan \left(\frac{\pi}{4}+2 x \right)\right)}{2}$&$21$\\ default&$-\frac{\ln \left(\sec \left(\frac{\pi}{4}+2 x \right)+\tan \left(\frac{\pi}{4}+2 x \right)\right)}{2}$&$21$\\ norman&$\frac{\ln \left(\tan \left(\frac{\pi}{8}+x \right)-1\right)}{2}-\frac{\ln \left(\tan \left(\frac{\pi}{8}+x \right)+1\right)}{2}$&$24$\\ risch&$-\frac{\ln \left({\mathrm e}^{\frac{i \left(\pi +8 x \right)}{4}}+i\right)}{2}+\frac{\ln \left({\mathrm e}^{\frac{i \left(\pi +8 x \right)}{4}}-i\right)}{2}$&$32$\\ \hline \end{longtable}"," ",0,"-1/2*ln(sec(1/4*Pi+2*x)+tan(1/4*Pi+2*x))","A"
6,1,3,2,0.067000," ","int(sec(x)*tan(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\sec \left(x \right)$&$3$\\ default&$\sec \left(x \right)$&$3$\\ risch&$\frac{2 \,{\mathrm e}^{i x}}{1+{\mathrm e}^{2 i x}}$&$17$\\ \hline \end{longtable}"," ",0,"sec(x)","A"
7,1,5,4,0.030000," ","int(cot(x)*csc(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\csc \left(x \right)$&$5$\\ default&$-\csc \left(x \right)$&$5$\\ risch&$-\frac{2 i {\mathrm e}^{i x}}{{\mathrm e}^{2 i x}-1}$&$18$\\ \hline \end{longtable}"," ",0,"-csc(x)","A"
8,1,5,4,0.053000," ","int(tan(x)/sin(2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\tan \left(x \right)}{2}$&$5$\\ default&$\frac{\tan \left(x \right)}{2}$&$5$\\ norman&$\frac{\tan \left(x \right)}{2}$&$5$\\ risch&$\frac{i}{1+{\mathrm e}^{2 i x}}$&$13$\\ \hline \end{longtable}"," ",0,"1/2*tan(x)","A"
9,1,5,9,0.036000," ","int(1/(1+cos(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\tan \left(\frac{x}{2}\right)$&$5$\\ norman&$\tan \left(\frac{x}{2}\right)$&$5$\\ risch&$\frac{2 i}{{\mathrm e}^{i x}+1}$&$13$\\ \hline \end{longtable}"," ",0,"tan(1/2*x)","A"
10,1,9,12,0.037000," ","int(1/(1-cos(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{\tan \left(\frac{x}{2}\right)}$&$9$\\ norman&$-\frac{1}{\tan \left(\frac{x}{2}\right)}$&$9$\\ risch&$-\frac{2 i}{{\mathrm e}^{i x}-1}$&$13$\\ \hline \end{longtable}"," ",0,"-1/tan(1/2*x)","A"
11,1,13,12,0.073000," ","int(sin(x)/(a-b*cos(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(a -b \cos \left(x \right)\right)}{b}$&$13$\\ default&$\frac{\ln \left(a -b \cos \left(x \right)\right)}{b}$&$13$\\ risch&$-\frac{i x}{b}+\frac{\ln \left({\mathrm e}^{2 i x}-\frac{2 a \,{\mathrm e}^{i x}}{b}+1\right)}{b}$&$32$\\ norman&$\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+b \left(\tan^{2}\left(\frac{x}{2}\right)\right)+a -b \right)}{b}-\frac{\ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}{b}$&$42$\\ \hline \end{longtable}"," ",0,"ln(a-b*cos(x))/b","A"
12,1,16,15,0.130000," ","int(cos(x)/(a^2+b^2*sin(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\arctan \left(\frac{b \sin \left(x \right)}{a}\right)}{a b}$&$16$\\ default&$\frac{\arctan \left(\frac{b \sin \left(x \right)}{a}\right)}{a b}$&$16$\\ risch&$\frac{i \ln \left({\mathrm e}^{2 i x}-\frac{2 a \,{\mathrm e}^{i x}}{b}-1\right)}{2 b a}-\frac{i \ln \left({\mathrm e}^{2 i x}+\frac{2 a \,{\mathrm e}^{i x}}{b}-1\right)}{2 b a}$&$58$\\ \hline \end{longtable}"," ",0,"arctan(b*sin(x)/a)/a/b","A"
13,1,33,15,0.147000," ","int(cos(x)/(a^2-b^2*sin(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(-b \sin \left(x \right)+a \right)}{2 a b}+\frac{\ln \left(b \sin \left(x \right)+a \right)}{2 a b}$&$33$\\ default&$-\frac{\ln \left(-b \sin \left(x \right)+a \right)}{2 a b}+\frac{\ln \left(b \sin \left(x \right)+a \right)}{2 a b}$&$33$\\ norman&$-\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 b \tan \left(\frac{x}{2}\right)+a \right)}{2 a b}+\frac{\ln \left(a \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 b \tan \left(\frac{x}{2}\right)+a \right)}{2 a b}$&$54$\\ risch&$-\frac{\ln \left({\mathrm e}^{2 i x}-\frac{2 i a \,{\mathrm e}^{i x}}{b}-1\right)}{2 a b}+\frac{\ln \left({\mathrm e}^{2 i x}+\frac{2 i a \,{\mathrm e}^{i x}}{b}-1\right)}{2 a b}$&$58$\\ \hline \end{longtable}"," ",0,"-1/2/a/b*ln(-b*sin(x)+a)+1/2/a/b*ln(b*sin(x)+a)","B"
14,1,18,17,0.178000," ","int(sin(2*x)/(a^2+b^2*sin(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(a^{2}+b^{2} \left(\sin^{2}\left(x \right)\right)\right)}{b^{2}}$&$18$\\ default&$\frac{\ln \left(a^{2}+b^{2} \left(\sin^{2}\left(x \right)\right)\right)}{b^{2}}$&$18$\\ risch&$-\frac{2 i x}{b^{2}}+\frac{\ln \left({\mathrm e}^{4 i x}-\frac{2 \left(2 a^{2}+b^{2}\right) {\mathrm e}^{2 i x}}{b^{2}}+1\right)}{b^{2}}$&$40$\\ \hline \end{longtable}"," ",0,"ln(a^2+b^2*sin(x)^2)/b^2","A"
15,1,20,19,0.274000," ","int(sin(2*x)/(a^2-b^2*sin(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(a^{2}-b^{2} \left(\sin^{2}\left(x \right)\right)\right)}{b^{2}}$&$20$\\ default&$-\frac{\ln \left(a^{2}-b^{2} \left(\sin^{2}\left(x \right)\right)\right)}{b^{2}}$&$20$\\ risch&$\frac{2 i x}{b^{2}}-\frac{\ln \left({\mathrm e}^{4 i x}+\frac{2 \left(2 a^{2}-b^{2}\right) {\mathrm e}^{2 i x}}{b^{2}}+1\right)}{b^{2}}$&$43$\\ \hline \end{longtable}"," ",0,"-ln(a^2-b^2*sin(x)^2)/b^2","A"
16,1,19,18,0.156000," ","int(sin(2*x)/(a^2+b^2*cos(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(a^{2}+b^{2} \left(\cos^{2}\left(x \right)\right)\right)}{b^{2}}$&$19$\\ default&$-\frac{\ln \left(a^{2}+b^{2} \left(\cos^{2}\left(x \right)\right)\right)}{b^{2}}$&$19$\\ risch&$\frac{2 i x}{b^{2}}-\frac{\ln \left({\mathrm e}^{4 i x}+\frac{2 \left(2 a^{2}+b^{2}\right) {\mathrm e}^{2 i x}}{b^{2}}+1\right)}{b^{2}}$&$41$\\ \hline \end{longtable}"," ",0,"-ln(a^2+b^2*cos(x)^2)/b^2","A"
17,1,19,18,0.314000," ","int(sin(2*x)/(a^2-b^2*cos(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(a^{2}-b^{2} \left(\cos^{2}\left(x \right)\right)\right)}{b^{2}}$&$19$\\ default&$\frac{\ln \left(a^{2}-b^{2} \left(\cos^{2}\left(x \right)\right)\right)}{b^{2}}$&$19$\\ risch&$-\frac{2 i x}{b^{2}}+\frac{\ln \left({\mathrm e}^{4 i x}-\frac{2 \left(2 a^{2}-b^{2}\right) {\mathrm e}^{2 i x}}{b^{2}}+1\right)}{b^{2}}$&$42$\\ \hline \end{longtable}"," ",0,"ln(a^2-b^2*cos(x)^2)/b^2","A"
18,1,14,31,0.069000," ","int(1/(4-cos(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{3}\, \arctan \left(\frac{2 \tan \left(x \right) \sqrt{3}}{3}\right)}{6}$&$14$\\ risch&$\frac{i \sqrt{3}\, \ln \left({\mathrm e}^{2 i x}-4 \sqrt{3}-7\right)}{12}-\frac{i \sqrt{3}\, \ln \left({\mathrm e}^{2 i x}+4 \sqrt{3}-7\right)}{12}$&$40$\\ \hline \end{longtable}"," ",0,"1/6*3^(1/2)*arctan(2/3*tan(x)*3^(1/2))","A"
19,1,6,5,0.033000," ","int(exp(x)/(-1+exp(2*x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\arctanh \left({\mathrm e}^{x}\right)$&$6$\\ norman&$\frac{\ln \left(-1+{\mathrm e}^{x}\right)}{2}-\frac{\ln \left(1+{\mathrm e}^{x}\right)}{2}$&$16$\\ risch&$\frac{\ln \left(-1+{\mathrm e}^{x}\right)}{2}-\frac{\ln \left(1+{\mathrm e}^{x}\right)}{2}$&$16$\\ \hline \end{longtable}"," ",0,"-arctanh(exp(x))","A"
20,1,4,3,0.015000," ","int(1/x/ln(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\ln \left(\ln \left(x \right)\right)$&$4$\\ default&$\ln \left(\ln \left(x \right)\right)$&$4$\\ norman&$\ln \left(\ln \left(x \right)\right)$&$4$\\ risch&$\ln \left(\ln \left(x \right)\right)$&$4$\\ \hline \end{longtable}"," ",0,"ln(ln(x))","A"
21,1,4,3,0.025000," ","int(1/x/(1+ln(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\arctan \left(\ln \left(x \right)\right)$&$4$\\ default&$\arctan \left(\ln \left(x \right)\right)$&$4$\\ risch&$\frac{i \ln \left(\ln \left(x \right)+i\right)}{2}-\frac{i \ln \left(\ln \left(x \right)-i\right)}{2}$&$20$\\ \hline \end{longtable}"," ",0,"arctan(ln(x))","A"
22,1,8,9,0.020000," ","int(1/x/(1-ln(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$-\ln \left(-1+\ln \left(x \right)\right)$&$8$\\ risch&$-\ln \left(-1+\ln \left(x \right)\right)$&$8$\\ derivativedivides&$-\ln \left(1-\ln \left(x \right)\right)$&$10$\\ default&$-\ln \left(1-\ln \left(x \right)\right)$&$10$\\ \hline \end{longtable}"," ",0,"-ln(-1+ln(x))","A"
23,1,10,9,0.017000," ","int(1/x/(1+ln(x/a)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\ln \left(1+\ln \left(\frac{x}{a}\right)\right)$&$10$\\ default&$\ln \left(1+\ln \left(\frac{x}{a}\right)\right)$&$10$\\ norman&$\ln \left(1+\ln \left(\frac{x}{a}\right)\right)$&$10$\\ risch&$\ln \left(1+\ln \left(\frac{x}{a}\right)\right)$&$10$\\ \hline \end{longtable}"," ",0,"ln(1+ln(x/a))","A"
24,1,22,21,0.110000," ","int((1+x-x^(1/2))^2/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{1}{x}+x +3 \ln \left(x \right)+\frac{4}{\sqrt{x}}-4 \sqrt{x}$&$22$\\ default&$-\frac{1}{x}+x +3 \ln \left(x \right)+\frac{4}{\sqrt{x}}-4 \sqrt{x}$&$22$\\ trager&$\frac{\left(-1+x \right) \left(1+x \right)}{x}-\frac{4 \left(-1+x \right)}{\sqrt{x}}-3 \ln \left(\frac{1}{x}\right)$&$26$\\ \hline \end{longtable}"," ",0,"-1/x+x+3*ln(x)+4/x^(1/2)-4*x^(1/2)","A"
25,1,21,20,0.016000," ","int((2-x^(2/3))*(x+x^(1/2))/x^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{3 x^{\frac{2}{3}}}{2}-\frac{6 x^{\frac{7}{6}}}{7}+2 \ln \left(x \right)+4 \sqrt{x}$&$21$\\ default&$-\frac{3 x^{\frac{2}{3}}}{2}-\frac{6 x^{\frac{7}{6}}}{7}+2 \ln \left(x \right)+4 \sqrt{x}$&$21$\\ \hline \end{longtable}"," ",0,"-3/2*x^(2/3)-6/7*x^(7/6)+2*ln(x)+4*x^(1/2)","A"
26,1,11,10,0.292000," ","int((-1+2*x)/(3+2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x -2 \ln \left(3+2 x \right)$&$11$\\ norman&$x -2 \ln \left(3+2 x \right)$&$11$\\ meijerg&$-2 \ln \left(1+\frac{2 x}{3}\right)+x$&$11$\\ risch&$x -2 \ln \left(3+2 x \right)$&$11$\\ \hline \end{longtable}"," ",0,"x-2*ln(3+2*x)","A"
27,1,24,35,0.292000," ","int((-5+2*x)/(3*x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(3 x^{2}-2\right)}{3}+\frac{5 \sqrt{6}\, \arctanh \left(\frac{x \sqrt{6}}{2}\right)}{6}$&$24$\\ meijerg&$\frac{5 \sqrt{6}\, \arctanh \left(\frac{x \sqrt{2}\, \sqrt{3}}{2}\right)}{6}+\frac{\ln \left(1-\frac{3 x^{2}}{2}\right)}{3}$&$27$\\ risch&$\frac{\ln \left(3 x +\sqrt{6}\right)}{3}+\frac{5 \ln \left(3 x +\sqrt{6}\right) \sqrt{6}}{12}+\frac{\ln \left(3 x -\sqrt{6}\right)}{3}-\frac{5 \ln \left(3 x -\sqrt{6}\right) \sqrt{6}}{12}$&$52$\\ \hline \end{longtable}"," ",0,"1/3*ln(3*x^2-2)+5/6*6^(1/2)*arctanh(1/2*x*6^(1/2))","A"
28,1,24,23,0.262000," ","int((-5+2*x)/(3*x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(3 x^{2}+2\right)}{3}-\frac{5 \arctan \left(\frac{x \sqrt{6}}{2}\right) \sqrt{6}}{6}$&$24$\\ risch&$\frac{\ln \left(9 x^{2}+6\right)}{3}-\frac{5 \arctan \left(\frac{x \sqrt{6}}{2}\right) \sqrt{6}}{6}$&$24$\\ meijerg&$-\frac{5 \sqrt{6}\, \arctan \left(\frac{x \sqrt{2}\, \sqrt{3}}{2}\right)}{6}+\frac{\ln \left(1+\frac{3 x^{2}}{2}\right)}{3}$&$27$\\ \hline \end{longtable}"," ",0,"1/3*ln(3*x^2+2)-5/6*arctan(1/2*x*6^(1/2))*6^(1/2)","A"
29,1,14,13,0.098000," ","int(sin(1/4*x)*sin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sin \left(\frac{3 x}{4}\right)}{3}-\frac{2 \sin \left(\frac{5 x}{4}\right)}{5}$&$14$\\ risch&$\frac{2 \sin \left(\frac{3 x}{4}\right)}{3}-\frac{2 \sin \left(\frac{5 x}{4}\right)}{5}$&$14$\\ norman&$\frac{-\frac{8 \tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{8}\right)\right)}{15}+\frac{32 \left(\tan^{2}\left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{8}\right)}{15}+\frac{8 \tan \left(\frac{x}{2}\right)}{15}-\frac{32 \tan \left(\frac{x}{8}\right)}{15}}{\left(1+\tan^{2}\left(\frac{x}{8}\right)\right) \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}$&$59$\\ \hline \end{longtable}"," ",0,"2/3*sin(3/4*x)-2/5*sin(5/4*x)","A"
30,1,12,11,0.136000," ","int(cos(3*x)*cos(4*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sin \left(x \right)}{2}+\frac{\sin \left(7 x \right)}{14}$&$12$\\ risch&$\frac{\sin \left(x \right)}{2}+\frac{\sin \left(7 x \right)}{14}$&$12$\\ norman&$\frac{-\frac{8 \tan \left(2 x \right) \left(\tan^{2}\left(\frac{3 x}{2}\right)\right)}{7}+\frac{6 \left(\tan^{2}\left(2 x \right)\right) \tan \left(\frac{3 x}{2}\right)}{7}+\frac{8 \tan \left(2 x \right)}{7}-\frac{6 \tan \left(\frac{3 x}{2}\right)}{7}}{\left(1+\tan^{2}\left(\frac{3 x}{2}\right)\right) \left(1+\tan^{2}\left(2 x \right)\right)}$&$59$\\ \hline \end{longtable}"," ",0,"1/2*sin(x)+1/14*sin(7*x)","A"
31,1,20,21,0.125000," ","int(-tan(x)*tan(a-x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\arctan \left(\tan \left(x \right)\right)+\frac{\ln \left(1+\tan \left(x \right) \tan \left(a \right)\right)}{\tan \left(a \right)}$&$20$\\ default&$-\arctan \left(\tan \left(x \right)\right)+\frac{\ln \left(1+\tan \left(x \right) \tan \left(a \right)\right)}{\tan \left(a \right)}$&$20$\\ risch&$-x +\frac{i \ln \left({\mathrm e}^{2 i a}+{\mathrm e}^{2 i x}\right) {\mathrm e}^{2 i a}}{{\mathrm e}^{2 i a}-1}+\frac{i \ln \left({\mathrm e}^{2 i a}+{\mathrm e}^{2 i x}\right)}{{\mathrm e}^{2 i a}-1}-\frac{i \ln \left(1+{\mathrm e}^{2 i x}\right) {\mathrm e}^{2 i a}}{{\mathrm e}^{2 i a}-1}-\frac{i \ln \left(1+{\mathrm e}^{2 i x}\right)}{{\mathrm e}^{2 i a}-1}$&$103$\\ \hline \end{longtable}"," ",0,"-arctan(tan(x))+1/tan(a)*ln(1+tan(x)*tan(a))","A"
32,1,11,10,0.044000," ","int(sin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{2}-\frac{\cos \left(x \right) \sin \left(x \right)}{2}$&$11$\\ risch&$\frac{x}{2}-\frac{\sin \left(2 x \right)}{4}$&$11$\\ meijerg&$\frac{\sqrt{\pi}\, \left(\frac{2 x}{\sqrt{\pi}}-\frac{\sin \left(2 x \right)}{\sqrt{\pi}}\right)}{4}$&$22$\\ norman&$\frac{\tan^{3}\left(\frac{x}{2}\right)+x \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\frac{x}{2}+\frac{x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{2}-\tan \left(\frac{x}{2}\right)}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{2}}$&$45$\\ \hline \end{longtable}"," ",0,"1/2*x-1/2*cos(x)*sin(x)","A"
33,1,11,10,0.031000," ","int(cos(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{2}+\frac{\cos \left(x \right) \sin \left(x \right)}{2}$&$11$\\ risch&$\frac{x}{2}+\frac{\sin \left(2 x \right)}{4}$&$11$\\ norman&$\frac{x \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\frac{x}{2}-\left(\tan^{3}\left(\frac{x}{2}\right)\right)+\frac{x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{2}+\tan \left(\frac{x}{2}\right)}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{2}}$&$45$\\ \hline \end{longtable}"," ",0,"1/2*x+1/2*cos(x)*sin(x)","A"
34,1,7,6,0.040000," ","int(cos(x)^3*sin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(\cos^{4}\left(x \right)\right)}{4}$&$7$\\ default&$-\frac{\left(\cos^{4}\left(x \right)\right)}{4}$&$7$\\ risch&$-\frac{\cos \left(4 x \right)}{32}-\frac{\cos \left(2 x \right)}{8}$&$14$\\ norman&$\frac{2 \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{4}}$&$29$\\ meijerg&$\frac{\sqrt{\pi}\, \left(\frac{1}{\sqrt{\pi}}-\frac{\cos \left(2 x \right)}{\sqrt{\pi}}\right)}{8}+\frac{\sqrt{\pi}\, \left(\frac{1}{\sqrt{\pi}}-\frac{\cos \left(4 x \right)}{\sqrt{\pi}}\right)}{32}$&$38$\\ \hline \end{longtable}"," ",0,"-1/4*cos(x)^4","A"
35,1,32,11,0.406000," ","int(cos(x)^3/sin(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\cos^{4}\left(x \right)}{3 \sin \left(x \right)^{3}}+\frac{\cos^{4}\left(x \right)}{3 \sin \left(x \right)}+\frac{\left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}$&$32$\\ norman&$\frac{-\frac{1}{24}+\frac{3 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8}+\frac{3 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{8}-\frac{\left(\tan^{6}\left(\frac{x}{2}\right)\right)}{24}}{\tan \left(\frac{x}{2}\right)^{3}}$&$34$\\ risch&$\frac{2 i \left(3 \,{\mathrm e}^{5 i x}-2 \,{\mathrm e}^{3 i x}+3 \,{\mathrm e}^{i x}\right)}{3 \left({\mathrm e}^{2 i x}-1\right)^{3}}$&$35$\\ \hline \end{longtable}"," ",0,"-1/3/sin(x)^3*cos(x)^4+1/3/sin(x)*cos(x)^4+1/3*(2+cos(x)^2)*sin(x)","B"
36,1,15,7,0.286000," ","int(1/cos(x)^2/sin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{1}{\sin \left(x \right) \cos \left(x \right)}-2 \cot \left(x \right)$&$15$\\ risch&$-\frac{4 i}{\left(1+{\mathrm e}^{2 i x}\right) \left({\mathrm e}^{2 i x}-1\right)}$&$22$\\ norman&$\frac{\frac{1}{2}-3 \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\frac{\left(\tan^{4}\left(\frac{x}{2}\right)\right)}{2}}{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \tan \left(\frac{x}{2}\right)}$&$36$\\ \hline \end{longtable}"," ",0,"1/sin(x)/cos(x)-2*cot(x)","A"
37,1,17,10,0.023000," ","int(cot(3/4*x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-\frac{4}{3}-x \tan \left(\frac{3 x}{4}\right)}{\tan \left(\frac{3 x}{4}\right)}$&$17$\\ risch&$-x -\frac{8 i}{3 \left({\mathrm e}^{\frac{3 i x}{2}}-1\right)}$&$17$\\ derivativedivides&$-\frac{4 \cot \left(\frac{3 x}{4}\right)}{3}+\frac{2 \pi}{3}-\frac{4 \,\mathrm{arccot}\left(\cot \left(\frac{3 x}{4}\right)\right)}{3}$&$18$\\ default&$-\frac{4 \cot \left(\frac{3 x}{4}\right)}{3}+\frac{2 \pi}{3}-\frac{4 \,\mathrm{arccot}\left(\cot \left(\frac{3 x}{4}\right)\right)}{3}$&$18$\\ \hline \end{longtable}"," ",0,"(-4/3-x*tan(3/4*x))/tan(3/4*x)","A"
38,1,19,14,0.033000," ","int((1+tan(2*x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\tan \left(2 x \right)}{2}+\frac{\ln \left(1+\tan^{2}\left(2 x \right)\right)}{2}$&$19$\\ default&$\frac{\tan \left(2 x \right)}{2}+\frac{\ln \left(1+\tan^{2}\left(2 x \right)\right)}{2}$&$19$\\ norman&$\frac{\tan \left(2 x \right)}{2}+\frac{\ln \left(1+\tan^{2}\left(2 x \right)\right)}{2}$&$19$\\ risch&$2 i x +\frac{i}{{\mathrm e}^{4 i x}+1}-\ln \left({\mathrm e}^{4 i x}+1\right)$&$28$\\ \hline \end{longtable}"," ",0,"1/2*tan(2*x)+1/2*ln(1+tan(2*x)^2)","A"
39,1,11,10,0.054000," ","int((-cot(x)+tan(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-4 x -\cot \left(x \right)+\tan \left(x \right)$&$11$\\ norman&$\frac{-1+\tan^{2}\left(x \right)-4 x \tan \left(x \right)}{\tan \left(x \right)}$&$17$\\ risch&$-4 x -\frac{4 i}{\left(1+{\mathrm e}^{2 i x}\right) \left({\mathrm e}^{2 i x}-1\right)}$&$26$\\ \hline \end{longtable}"," ",0,"-4*x-cot(x)+tan(x)","A"
40,1,15,14,0.313000," ","int((-sec(x)+tan(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$2 \tan \left(x \right)-\frac{2}{\cos \left(x \right)}-x$&$15$\\ risch&$-x -\frac{4}{{\mathrm e}^{i x}+i}$&$17$\\ \hline \end{longtable}"," ",0,"2*tan(x)-2/cos(x)-x","A"
41,1,15,11,0.049000," ","int(sin(x)/(1+sin(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$x +\frac{2}{{\mathrm e}^{i x}+i}$&$15$\\ default&$2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)+\frac{2}{\tan \left(\frac{x}{2}\right)+1}$&$19$\\ norman&$\frac{x +x \tan \left(\frac{x}{2}\right)+x \left(\tan^{2}\left(\frac{x}{2}\right)\right)+x \left(\tan^{3}\left(\frac{x}{2}\right)\right)+2 \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}$&$53$\\ \hline \end{longtable}"," ",0,"x+2/(exp(I*x)+I)","C"
42,1,17,16,0.042000," ","int(cos(x)/(1-cos(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{\tan \left(\frac{x}{2}\right)}-2 \arctan \left(\tan \left(\frac{x}{2}\right)\right)$&$17$\\ risch&$-x -\frac{2 i}{{\mathrm e}^{i x}-1}$&$17$\\ norman&$\frac{-1-\left(\tan^{2}\left(\frac{x}{2}\right)\right)-x \tan \left(\frac{x}{2}\right)-x \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}$&$44$\\ \hline \end{longtable}"," ",0,"-1/tan(1/2*x)-2*arctan(tan(1/2*x))","A"
43,1,19,20,0.024000," ","int((-1+exp(1/2*x))^3/exp(1/2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&${\mathrm e}^{x}+3 x -6 \,{\mathrm e}^{\frac{x}{2}}+2 \,{\mathrm e}^{-\frac{x}{2}}$&$19$\\ derivativedivides&${\mathrm e}^{x}-6 \,{\mathrm e}^{\frac{x}{2}}+6 \ln \left({\mathrm e}^{\frac{x}{2}}\right)+2 \,{\mathrm e}^{-\frac{x}{2}}$&$29$\\ default&${\mathrm e}^{x}-6 \,{\mathrm e}^{\frac{x}{2}}+6 \ln \left({\mathrm e}^{\frac{x}{2}}\right)+2 \,{\mathrm e}^{-\frac{x}{2}}$&$29$\\ norman&$\left(2+{\mathrm e}^{\frac{3 x}{2}}-6 \,{\mathrm e}^{x}+3 x \,{\mathrm e}^{\frac{x}{2}}\right) {\mathrm e}^{-\frac{x}{2}}$&$31$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"exp(x)+3*x-6*exp(1/2*x)+2*exp(-1/2*x)","A"
44,1,14,17,0.314000," ","int(1/(x^2-6*x+5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(-5+x \right)}{4}-\frac{\ln \left(-1+x \right)}{4}$&$14$\\ norman&$\frac{\ln \left(-5+x \right)}{4}-\frac{\ln \left(-1+x \right)}{4}$&$14$\\ risch&$\frac{\ln \left(-5+x \right)}{4}-\frac{\ln \left(-1+x \right)}{4}$&$14$\\ \hline \end{longtable}"," ",0,"1/4*ln(-5+x)-1/4*ln(-1+x)","A"
45,1,11,10,0.032000," ","int(x^2/(x^6-6*x^3+13),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(\frac{x^{3}}{2}-\frac{3}{2}\right)}{6}$&$11$\\ risch&$\frac{\arctan \left(\frac{x^{3}}{2}-\frac{3}{2}\right)}{6}$&$11$\\ \hline \end{longtable}"," ",0,"1/6*arctan(1/2*x^3-3/2)","A"
46,1,29,39,0.398000," ","int((2+x)/(x^2-4*x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(x^{2}-4 x -1\right)}{2}-\frac{4 \sqrt{5}\, \arctanh \left(\frac{\left(2 x -4\right) \sqrt{5}}{10}\right)}{5}$&$29$\\ risch&$\frac{\ln \left(x -\sqrt{5}-2\right)}{2}+\frac{2 \ln \left(x -\sqrt{5}-2\right) \sqrt{5}}{5}+\frac{\ln \left(x -2+\sqrt{5}\right)}{2}-\frac{2 \ln \left(x -2+\sqrt{5}\right) \sqrt{5}}{5}$&$48$\\ \hline \end{longtable}"," ",0,"1/2*ln(x^2-4*x-1)-4/5*5^(1/2)*arctanh(1/10*(2*x-4)*5^(1/2))","A"
47,1,26,25,0.137000," ","int(1/(1+(1+x)^(1/3)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-3 \left(1+x \right)^{\frac{1}{3}}+\frac{3 \left(1+x \right)^{\frac{2}{3}}}{2}+3 \ln \left(1+\left(1+x \right)^{\frac{1}{3}}\right)$&$26$\\ trager&$-3 \left(1+x \right)^{\frac{1}{3}}+\frac{3 \left(1+x \right)^{\frac{2}{3}}}{2}+\ln \left(-3 \left(1+x \right)^{\frac{2}{3}}-3 \left(1+x \right)^{\frac{1}{3}}-x -2\right)$&$36$\\ default&$\ln \left(2+x \right)+\frac{3 \left(1+x \right)^{\frac{2}{3}}}{2}+2 \ln \left(1+\left(1+x \right)^{\frac{1}{3}}\right)-\ln \left(\left(1+x \right)^{\frac{2}{3}}-\left(1+x \right)^{\frac{1}{3}}+1\right)-3 \left(1+x \right)^{\frac{1}{3}}$&$47$\\ \hline \end{longtable}"," ",0,"-3*(1+x)^(1/3)+3/2*(1+x)^(2/3)+3*ln(1+(1+x)^(1/3))","A"
48,1,19,19,0.324000," ","int(1/(a*x+b)/x^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \arctan \left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b}}$&$19$\\ default&$\frac{2 \arctan \left(\frac{a \sqrt{x}}{\sqrt{a b}}\right)}{\sqrt{a b}}$&$19$\\ \hline \end{longtable}"," ",0,"2/(a*b)^(1/2)*arctan(a*x^(1/2)/(a*b)^(1/2))","A"
49,1,17,19,0.302000," ","int(x^3*(x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(x^{2}+1\right)^{\frac{3}{2}} \left(3 x^{2}-2\right)}{15}$&$17$\\ risch&$\frac{\left(3 x^{4}+x^{2}-2\right) \sqrt{x^{2}+1}}{15}$&$20$\\ trager&$\left(\frac{1}{5} x^{4}+\frac{1}{15} x^{2}-\frac{2}{15}\right) \sqrt{x^{2}+1}$&$21$\\ default&$\frac{x^{2} \left(x^{2}+1\right)^{\frac{3}{2}}}{5}-\frac{2 \left(x^{2}+1\right)^{\frac{3}{2}}}{15}$&$23$\\ meijerg&$-\frac{-\frac{8 \sqrt{\pi}}{15}+\frac{4 \sqrt{\pi}\, \left(x^{2}+1\right)^{\frac{3}{2}} \left(-3 x^{2}+2\right)}{15}}{4 \sqrt{\pi}}$&$31$\\ \hline \end{longtable}"," ",0,"1/15*(x^2+1)^(3/2)*(3*x^2-2)","A"
50,1,19,18,0.344000," ","int(x/(a^4-x^4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(\frac{x^{2}}{\sqrt{a^{4}-x^{4}}}\right)}{2}$&$19$\\ elliptic&$\frac{\arctan \left(\frac{x^{2}}{\sqrt{a^{4}-x^{4}}}\right)}{2}$&$19$\\ \hline \end{longtable}"," ",0,"1/2*arctan(x^2/(a^4-x^4)^(1/2))","A"
51,1,41,20,0.317000," ","int(1/x/(-a^2+x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(\frac{-2 a^{2}+2 \sqrt{-a^{2}}\, \sqrt{-a^{2}+x^{2}}}{x}\right)}{\sqrt{-a^{2}}}$&$41$\\ \hline \end{longtable}"," ",0,"-1/(-a^2)^(1/2)*ln((-2*a^2+2*(-a^2)^(1/2)*(-a^2+x^2)^(1/2))/x)","A"
52,1,37,21,0.315000," ","int(1/x/(a^2-x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(\frac{2 a^{2}+2 \sqrt{a^{2}}\, \sqrt{a^{2}-x^{2}}}{x}\right)}{\sqrt{a^{2}}}$&$37$\\ \hline \end{longtable}"," ",0,"-1/(a^2)^(1/2)*ln((2*a^2+2*(a^2)^(1/2)*(a^2-x^2)^(1/2))/x)","A"
53,1,35,19,0.308000," ","int(1/x/(a^2+x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(\frac{2 a^{2}+2 \sqrt{a^{2}}\, \sqrt{a^{2}+x^{2}}}{x}\right)}{\sqrt{a^{2}}}$&$35$\\ \hline \end{longtable}"," ",0,"-1/(a^2)^(1/2)*ln((2*a^2+2*(a^2)^(1/2)*(a^2+x^2)^(1/2))/x)","A"
54,1,7,6,0.289000," ","int(1/(-x^2+x+2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\arcsin \left(-\frac{1}{3}+\frac{2 x}{3}\right)$&$7$\\ trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x +\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{-x^{2}+x +2}\right)$&$37$\\ \hline \end{longtable}"," ",0,"arcsin(-1/3+2/3*x)","A"
55,1,15,16,0.403000," ","int(1/(3*x^2-4*x+5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{3}\, \arcsinh \left(\frac{3 \sqrt{11}\, \left(x -\frac{2}{3}\right)}{11}\right)}{3}$&$15$\\ trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-3 \RootOf \left(\textit{\_Z}^{2}-3\right) x +2 \RootOf \left(\textit{\_Z}^{2}-3\right)+3 \sqrt{3 x^{2}-4 x +5}\right)}{3}$&$42$\\ \hline \end{longtable}"," ",0,"1/3*3^(1/2)*arcsinh(3/11*11^(1/2)*(x-2/3))","A"
56,1,7,6,0.325000," ","int(1/(-x^2+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\arcsin \left(-1+2 x \right)$&$7$\\ meijerg&$2 \arcsin \left(\sqrt{x}\right)$&$7$\\ trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \sqrt{-x^{2}+x}+\RootOf \left(\textit{\_Z}^{2}+1\right)\right)$&$36$\\ \hline \end{longtable}"," ",0,"arcsin(-1+2*x)","A"
57,1,22,21,0.299000," ","int((1+2*x)/(-x^2+x+2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$2 \arcsin \left(-\frac{1}{3}+\frac{2 x}{3}\right)-2 \sqrt{-x^{2}+x +2}$&$22$\\ risch&$\frac{2 x^{2}-2 x -4}{\sqrt{-x^{2}+x +2}}+2 \arcsin \left(-\frac{1}{3}+\frac{2 x}{3}\right)$&$30$\\ trager&$-2 \sqrt{-x^{2}+x +2}+2 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}+1\right) x +\RootOf \left(\textit{\_Z}^{2}+1\right)+2 \sqrt{-x^{2}+x +2}\right)$&$51$\\ \hline \end{longtable}"," ",0,"2*arcsin(-1/3+2/3*x)-2*(-x^2+x+2)^(1/2)","A"
58,1,25,24,0.309000," ","int(1/x/(-x^2+x+2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctanh \left(\frac{\left(4+x \right) \sqrt{2}}{4 \sqrt{-x^{2}+x +2}}\right) \sqrt{2}}{2}$&$25$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-2\right) x +4 \sqrt{-x^{2}+x +2}-4 \RootOf \left(\textit{\_Z}^{2}-2\right)}{x}\right)}{2}$&$44$\\ \hline \end{longtable}"," ",0,"-1/2*arctanh(1/4*(4+x)*2^(1/2)/(-x^2+x+2)^(1/2))*2^(1/2)","A"
59,1,16,17,0.304000," ","int(1/(-2+x)/(-x^2+x+2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 \left(1+x \right)}{3 \sqrt{-x^{2}+x +2}}$&$16$\\ risch&$-\frac{2 \left(1+x \right)}{3 \sqrt{-x^{2}+x +2}}$&$16$\\ trager&$\frac{2 \sqrt{-x^{2}+x +2}}{3 \left(-2+x \right)}$&$18$\\ default&$\frac{2 \sqrt{-\left(-2+x \right)^{2}+6-3 x}}{3 \left(-2+x \right)}$&$22$\\ \hline \end{longtable}"," ",0,"-2/3*(1+x)/(-x^2+x+2)^(1/2)","A"
60,1,23,28,0.145000," ","int((2+3*sin(x))/(1-cos(x))/sin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\ln \left(\tan \left(\frac{x}{2}\right)\right)-\frac{3}{\tan \left(\frac{x}{2}\right)}-\frac{1}{2 \tan \left(\frac{x}{2}\right)^{2}}$&$23$\\ risch&$\frac{\left(\frac{1}{5}-\frac{3 i}{5}\right) \left(10 \,{\mathrm e}^{i x}-9+3 i\right)}{\left({\mathrm e}^{i x}-1\right)^{2}}-\ln \left({\mathrm e}^{i x}+1\right)+\ln \left({\mathrm e}^{i x}-1\right)$&$44$\\ norman&$\frac{-\frac{1}{2}-\frac{\left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2}-3 \left(\tan^{3}\left(\frac{x}{2}\right)\right)-3 \tan \left(\frac{x}{2}\right)}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)^{2}}+\ln \left(\tan \left(\frac{x}{2}\right)\right)$&$48$\\ \hline \end{longtable}"," ",0,"ln(tan(1/2*x))-3/tan(1/2*x)-1/2/tan(1/2*x)^2","A"
61,1,14,32,0.076000," ","int(1/(2+3*cos(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{10}\, \arctan \left(\frac{\tan \left(x \right) \sqrt{10}}{5}\right)}{10}$&$14$\\ risch&$\frac{i \sqrt{10}\, \ln \left({\mathrm e}^{2 i x}+\frac{2 \sqrt{10}}{3}+\frac{7}{3}\right)}{20}-\frac{i \sqrt{10}\, \ln \left({\mathrm e}^{2 i x}-\frac{2 \sqrt{10}}{3}+\frac{7}{3}\right)}{20}$&$40$\\ \hline \end{longtable}"," ",0,"1/10*10^(1/2)*arctan(1/5*tan(x)*10^(1/2))","A"
62,1,11,10,0.131000," ","int((1-tan(x))/sin(2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(\tan \left(x \right)\right)}{2}-\frac{\tan \left(x \right)}{2}$&$11$\\ norman&$\frac{\ln \left(\tan \left(x \right)\right)}{2}-\frac{\tan \left(x \right)}{2}$&$11$\\ risch&$-\frac{i}{1+{\mathrm e}^{2 i x}}-\frac{\ln \left(1+{\mathrm e}^{2 i x}\right)}{2}+\frac{\ln \left({\mathrm e}^{2 i x}-1\right)}{2}$&$34$\\ \hline \end{longtable}"," ",0,"1/2*ln(tan(x))-1/2*tan(x)","A"
63,1,4,9,0.041000," ","int((1+tan(x)^2)/(1-tan(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\arctanh \left(\tan \left(x \right)\right)$&$4$\\ default&$\arctanh \left(\tan \left(x \right)\right)$&$4$\\ norman&$-\frac{\ln \left(\tan \left(x \right)-1\right)}{2}+\frac{\ln \left(1+\tan \left(x \right)\right)}{2}$&$16$\\ risch&$\frac{\ln \left({\mathrm e}^{2 i x}+i\right)}{2}-\frac{\ln \left({\mathrm e}^{2 i x}-i\right)}{2}$&$24$\\ \hline \end{longtable}"," ",0,"arctanh(tan(x))","A"
64,1,15,14,0.061000," ","int((a^2-4*cos(x)^2)^(3/4)*sin(2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(a^{2}-4 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{7}{4}}}{7}$&$15$\\ default&$\frac{\left(a^{2}-4 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{7}{4}}}{7}$&$15$\\ \hline \end{longtable}"," ",0,"1/7*(a^2-4*cos(x)^2)^(7/4)","A"
65,1,15,14,0.126000," ","int(sin(2*x)/(a^2-4*sin(x)^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{3 \left(a^{2}-4 \left(\sin^{2}\left(x \right)\right)\right)^{\frac{2}{3}}}{8}$&$15$\\ default&$-\frac{3 \left(a^{2}-4 \left(\sin^{2}\left(x \right)\right)\right)^{\frac{2}{3}}}{8}$&$15$\\ \hline \end{longtable}"," ",0,"-3/8*(a^2-4*sin(x)^2)^(2/3)","A"
66,1,16,15,0.077000," ","int(1/(-1+a^(2*x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\arctan \left(\sqrt{-1+a^{2 x}}\right)}{\ln \left(a \right)}$&$16$\\ default&$\frac{\arctan \left(\sqrt{-1+a^{2 x}}\right)}{\ln \left(a \right)}$&$16$\\ \hline \end{longtable}"," ",0,"arctan((-1+a^(2*x))^(1/2))/ln(a)","A"
67,0,0,14,0.013000," ","int(exp(1/2*x)/(-1+exp(x))^(1/2),x)","\[\int \frac{{\mathrm e}^{\frac{x}{2}}}{\sqrt{-1+{\mathrm e}^{x}}}\, dx\]"," ",0,"int(exp(1/2*x)/(-1+exp(x))^(1/2),x)","F"
68,1,13,12,0.372000," ","int(arctan(x)^n/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\arctan \left(x \right)^{1+n}}{1+n}$&$13$\\ default&$\frac{\arctan \left(x \right)^{1+n}}{1+n}$&$13$\\ risch&$-\frac{i \left(-\ln \left(-i \left(x +i\right)\right)+\ln \left(-i \left(-x +i\right)\right)\right) \left(-\frac{i \left(-\ln \left(-i \left(x +i\right)\right)+\ln \left(-i \left(-x +i\right)\right)\right)}{2}\right)^{n}}{2 \left(1+n \right)}$&$56$\\ \hline \end{longtable}"," ",0,"arctan(x)^(1+n)/(1+n)","A"
69,1,38,34,0.252000," ","int(arcsin(x/a)^(3/2)/(a^2-x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \arcsin \left(\frac{x}{a}\right)^{\frac{5}{2}} a \sqrt{\frac{a^{2}-x^{2}}{a^{2}}}}{5 \sqrt{a^{2}-x^{2}}}$&$38$\\ \hline \end{longtable}"," ",0,"2/5*arcsin(x/a)^(5/2)*a/(a^2-x^2)^(1/2)*((a^2-x^2)/a^2)^(1/2)","A"
70,1,7,6,0.259000," ","int(1/arccos(x)^3/(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{1}{2 \arccos \left(x \right)^{2}}$&$7$\\ default&$\frac{1}{2 \arccos \left(x \right)^{2}}$&$7$\\ \hline \end{longtable}"," ",0,"1/2/arccos(x)^2","A"
71,1,23,22,0.014000," ","int(x*ln(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{2}}{4}-\frac{x^{2} \ln \left(x \right)}{2}+\frac{x^{2} \ln \left(x \right)^{2}}{2}$&$23$\\ norman&$\frac{x^{2}}{4}-\frac{x^{2} \ln \left(x \right)}{2}+\frac{x^{2} \ln \left(x \right)^{2}}{2}$&$23$\\ risch&$\frac{x^{2}}{4}-\frac{x^{2} \ln \left(x \right)}{2}+\frac{x^{2} \ln \left(x \right)^{2}}{2}$&$23$\\ \hline \end{longtable}"," ",0,"1/4*x^2-1/2*x^2*ln(x)+1/2*x^2*ln(x)^2","A"
72,1,11,13,0.016000," ","int(ln(x)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-\frac{1}{16}-\frac{\ln \left(x \right)}{4}}{x^{4}}$&$11$\\ default&$-\frac{1}{16 x^{4}}-\frac{\ln \left(x \right)}{4 x^{4}}$&$14$\\ risch&$-\frac{1}{16 x^{4}}-\frac{\ln \left(x \right)}{4 x^{4}}$&$14$\\ \hline \end{longtable}"," ",0,"(-1/16-1/4*ln(x))/x^4","A"
73,1,29,28,0.051000," ","int(x^2*ln((-1+x)/x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{3}-\frac{x^{2}}{6}-\frac{\ln \left(-1+x \right)}{3}+\frac{x^{3} \ln \left(\frac{-1+x}{x}\right)}{3}$&$29$\\ derivativedivides&$\frac{\ln \left(-\frac{1}{x}\right)}{3}-\frac{x}{3}-\frac{x^{2}}{6}+\frac{\ln \left(1-\frac{1}{x}\right) \left(1-\frac{1}{x}\right) \left(\left(1-\frac{1}{x}\right)^{2}+\frac{3}{x}\right) x^{3}}{3}$&$53$\\ default&$\frac{\ln \left(-\frac{1}{x}\right)}{3}-\frac{x}{3}-\frac{x^{2}}{6}+\frac{\ln \left(1-\frac{1}{x}\right) \left(1-\frac{1}{x}\right) \left(\left(1-\frac{1}{x}\right)^{2}+\frac{3}{x}\right) x^{3}}{3}$&$53$\\ \hline \end{longtable}"," ",0,"-1/3*x-1/6*x^2-1/3*ln(-1+x)+1/3*x^3*ln((-1+x)/x)","A"
74,1,17,15,0.297000," ","int(cos(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\frac{8}{3}+\cos^{4}\left(x \right)+\frac{4 \left(\cos^{2}\left(x \right)\right)}{3}\right) \sin \left(x \right)}{5}$&$17$\\ risch&$\frac{5 \sin \left(x \right)}{8}+\frac{\sin \left(5 x \right)}{80}+\frac{5 \sin \left(3 x \right)}{48}$&$18$\\ \hline \end{longtable}"," ",0,"1/5*(8/3+cos(x)^4+4/3*cos(x)^2)*sin(x)","A"
75,1,23,26,0.329000," ","int(cos(x)^4*sin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x}{16}-\frac{\sin \left(6 x \right)}{192}-\frac{\sin \left(4 x \right)}{64}+\frac{\sin \left(2 x \right)}{64}$&$23$\\ default&$-\frac{\left(\cos^{5}\left(x \right)\right) \sin \left(x \right)}{6}+\frac{\left(\cos^{3}\left(x \right)+\frac{3 \cos \left(x \right)}{2}\right) \sin \left(x \right)}{24}+\frac{x}{16}$&$26$\\ norman&$\frac{\frac{x}{16}+\frac{47 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{24}-\frac{13 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4}+\frac{13 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{4}-\frac{47 \left(\tan^{9}\left(\frac{x}{2}\right)\right)}{24}+\frac{\left(\tan^{11}\left(\frac{x}{2}\right)\right)}{8}+\frac{3 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8}+\frac{15 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{16}+\frac{5 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{4}+\frac{15 x \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{16}+\frac{3 x \left(\tan^{10}\left(\frac{x}{2}\right)\right)}{8}+\frac{x \left(\tan^{12}\left(\frac{x}{2}\right)\right)}{16}-\frac{\tan \left(\frac{x}{2}\right)}{8}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{6}}$&$116$\\ \hline \end{longtable}"," ",0,"1/16*x-1/192*sin(6*x)-1/64*sin(4*x)+1/64*sin(2*x)","A"
76,1,26,20,0.314000," ","int(1/sin(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\left(-\frac{\left(\csc^{3}\left(x \right)\right)}{4}-\frac{3 \csc \left(x \right)}{8}\right) \cot \left(x \right)+\frac{3 \ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{8}$&$26$\\ norman&$\frac{-\frac{1}{64}-\frac{\left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8}+\frac{\left(\tan^{6}\left(\frac{x}{2}\right)\right)}{8}+\frac{\left(\tan^{8}\left(\frac{x}{2}\right)\right)}{64}}{\tan \left(\frac{x}{2}\right)^{4}}+\frac{3 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{8}$&$42$\\ risch&$\frac{3 \,{\mathrm e}^{7 i x}-11 \,{\mathrm e}^{5 i x}-11 \,{\mathrm e}^{3 i x}+3 \,{\mathrm e}^{i x}}{4 \left({\mathrm e}^{2 i x}-1\right)^{4}}+\frac{3 \ln \left({\mathrm e}^{i x}-1\right)}{8}-\frac{3 \ln \left({\mathrm e}^{i x}+1\right)}{8}$&$62$\\ \hline \end{longtable}"," ",0,"(-1/4*csc(x)^3-3/8*csc(x))*cot(x)+3/8*ln(csc(x)-cot(x))","A"
77,1,18,17,0.044000," ","int(sin(x)/exp(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{{\mathrm e}^{-x} \cos \left(x \right)}{2}-\frac{{\mathrm e}^{-x} \sin \left(x \right)}{2}$&$18$\\ norman&$\frac{\left(-\frac{1}{2}+\frac{\left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2}-\tan \left(\frac{x}{2}\right)\right) {\mathrm e}^{-x}}{1+\tan^{2}\left(\frac{x}{2}\right)}$&$32$\\ risch&$-\frac{{\mathrm e}^{\left(-1+i\right) x}}{4}+\frac{i {\mathrm e}^{\left(-1+i\right) x}}{4}-\frac{{\mathrm e}^{\left(-1-i\right) x}}{4}-\frac{i {\mathrm e}^{\left(-1-i\right) x}}{4}$&$36$\\ \hline \end{longtable}"," ",0,"-1/2*exp(-x)*cos(x)-1/2*exp(-x)*sin(x)","A"
78,1,22,21,0.053000," ","int(exp(2*x)*sin(3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{3 \,{\mathrm e}^{2 x} \cos \left(3 x \right)}{13}+\frac{2 \,{\mathrm e}^{2 x} \sin \left(3 x \right)}{13}$&$22$\\ risch&$-\frac{3 \,{\mathrm e}^{\left(2+3 i\right) x}}{26}-\frac{i {\mathrm e}^{\left(2+3 i\right) x}}{13}-\frac{3 \,{\mathrm e}^{\left(2-3 i\right) x}}{26}+\frac{i {\mathrm e}^{\left(2-3 i\right) x}}{13}$&$36$\\ norman&$\frac{\frac{4 \,{\mathrm e}^{2 x} \tan \left(\frac{3 x}{2}\right)}{13}+\frac{3 \,{\mathrm e}^{2 x} \left(\tan^{2}\left(\frac{3 x}{2}\right)\right)}{13}-\frac{3 \,{\mathrm e}^{2 x}}{13}}{1+\tan^{2}\left(\frac{3 x}{2}\right)}$&$41$\\ \hline \end{longtable}"," ",0,"-3/13*exp(2*x)*cos(3*x)+2/13*exp(2*x)*sin(3*x)","A"
79,1,32,31,0.065000," ","int(a^x*cos(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{a^{x} \cos \left(x \right) \ln \left(a \right)}{1+\ln \left(a \right)^{2}}+\frac{a^{x} \sin \left(x \right)}{1+\ln \left(a \right)^{2}}$&$32$\\ norman&$\frac{\frac{\ln \left(a \right) {\mathrm e}^{x \ln \left(a \right)}}{1+\ln \left(a \right)^{2}}+\frac{2 \,{\mathrm e}^{x \ln \left(a \right)} \tan \left(\frac{x}{2}\right)}{1+\ln \left(a \right)^{2}}-\frac{\ln \left(a \right) {\mathrm e}^{x \ln \left(a \right)} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{1+\ln \left(a \right)^{2}}}{1+\tan^{2}\left(\frac{x}{2}\right)}$&$71$\\ \hline \end{longtable}"," ",0,"a^x*cos(x)*ln(a)/(1+ln(a)^2)+a^x*sin(x)/(1+ln(a)^2)","A"
80,1,14,13,0.036000," ","int(cos(ln(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline lookup&$\frac{x \cos \left(\ln \left(x \right)\right)}{2}+\frac{x \sin \left(\ln \left(x \right)\right)}{2}$&$14$\\ default&$\frac{x \cos \left(\ln \left(x \right)\right)}{2}+\frac{x \sin \left(\ln \left(x \right)\right)}{2}$&$14$\\ risch&$\left(\frac{1}{4}-\frac{i}{4}\right) x \,x^{i}+\left(\frac{1}{4}+\frac{i}{4}\right) x \,x^{-i}$&$22$\\ \hline \end{longtable}"," ",0,"1/2*x*cos(ln(x))+1/2*x*sin(ln(x))","A"
81,1,57,12,0.267000," ","int(ln(cos(x))*sec(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{x -x \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right) \ln \left(\frac{1-\left(\tan^{2}\left(\frac{x}{2}\right)\right)}{1+\tan^{2}\left(\frac{x}{2}\right)}\right)-2 \tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}$&$57$\\ default&$-4 i \left(\frac{\frac{{\mathrm e}^{2 i x} \ln \left(\left(1+{\mathrm e}^{2 i x}\right) {\mathrm e}^{-i x}\right)}{2}-\frac{1}{2}}{1+{\mathrm e}^{2 i x}}-\frac{\ln \left(1+{\mathrm e}^{2 i x}\right)}{4}+\frac{\ln \left(2\right)}{2+2 \,{\mathrm e}^{2 i x}}\right)$&$67$\\ risch&$-\frac{2 i \ln \left({\mathrm e}^{i x}\right)}{1+{\mathrm e}^{2 i x}}+\frac{\pi  \,\mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 i x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) \mathrm{csgn}\left(i \cos \left(x \right)\right)-\pi  \,\mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 i x}\right)\right) \mathrm{csgn}\left(i \cos \left(x \right)\right)^{2}-\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) \mathrm{csgn}\left(i \cos \left(x \right)\right)^{2}+\pi  \mathrm{csgn}\left(i \cos \left(x \right)\right)^{3}-i \ln \left(1+{\mathrm e}^{2 i x}\right) {\mathrm e}^{2 i x}-2 x \,{\mathrm e}^{2 i x}-2 i \ln \left(2\right)+i \ln \left(1+{\mathrm e}^{2 i x}\right)+2 i-2 x}{1+{\mathrm e}^{2 i x}}$&$156$\\ \hline \end{longtable}"," ",0,"(x-x*tan(1/2*x)^2-2*tan(1/2*x)*ln((1-tan(1/2*x)^2)/(1+tan(1/2*x)^2))-2*tan(1/2*x))/(tan(1/2*x)^2-1)","B"
82,1,20,13,0.029000," ","int(x*tan(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$x \tan \left(x \right)-\frac{x^{2}}{2}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{2}$&$20$\\ risch&$-\frac{x^{2}}{2}-2 i x +\frac{2 i x}{1+{\mathrm e}^{2 i x}}+\ln \left(1+{\mathrm e}^{2 i x}\right)$&$32$\\ \hline \end{longtable}"," ",0,"x*tan(x)-1/2*x^2-1/2*ln(1+tan(x)^2)","A"
83,1,21,20,0.010000," ","int(arcsin(x)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arcsin \left(x \right)}{x}-\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)$&$21$\\ \hline \end{longtable}"," ",0,"-arcsin(x)/x-arctanh(1/(-x^2+1)^(1/2))","A"
84,1,24,23,0.052000," ","int(arcsin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-2 x +x \arcsin \left(x \right)^{2}+2 \arcsin \left(x \right) \sqrt{-x^{2}+1}$&$24$\\ \hline \end{longtable}"," ",0,"-2*x+x*arcsin(x)^2+2*arcsin(x)*(-x^2+1)^(1/2)","A"
85,1,20,19,0.305000," ","int(x^2*arctan(x)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x \arctan \left(x \right)-\frac{\arctan \left(x \right)^{2}}{2}-\frac{\ln \left(x^{2}+1\right)}{2}$&$20$\\ risch&$\frac{\ln \left(i x +1\right)^{2}}{8}+\frac{i \left(-x +\frac{i \ln \left(-i x +1\right)}{2}\right) \ln \left(i x +1\right)}{2}+\frac{\ln \left(-i x +1\right)^{2}}{8}+\frac{i \ln \left(-i x +1\right) x}{2}-\frac{\ln \left(x^{2}+1\right)}{2}$&$67$\\ \hline \end{longtable}"," ",0,"x*arctan(x)-1/2*arctan(x)^2-1/2*ln(x^2+1)","A"
86,1,45,32,0.026000," ","int(arccos((x/(1+x))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x \arccos \left(\sqrt{\frac{x}{1+x}}\right)-\frac{\sqrt{x}\, \sqrt{\frac{1}{1+x}}\, \left(-\sqrt{x}+\arctan \left(\sqrt{x}\right)\right)}{\sqrt{\frac{x}{1+x}}}$&$45$\\ \hline \end{longtable}"," ",0,"x*arccos((x/(1+x))^(1/2))-1/(x/(1+x))^(1/2)*x^(1/2)*(1/(1+x))^(1/2)*(-x^(1/2)+arctan(x^(1/2)))","A"
87,1,21,21,0.252000," ","int((3*x^2+2*x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x^{4} \left(135 x^{3}+315 x^{2}+252 x +70\right)}{35}$&$21$\\ default&$2 x^{4}+\frac{36}{5} x^{5}+9 x^{6}+\frac{27}{7} x^{7}$&$22$\\ norman&$2 x^{4}+\frac{36}{5} x^{5}+9 x^{6}+\frac{27}{7} x^{7}$&$22$\\ risch&$2 x^{4}+\frac{36}{5} x^{5}+9 x^{6}+\frac{27}{7} x^{7}$&$22$\\ \hline \end{longtable}"," ",0,"1/35*x^4*(135*x^3+315*x^2+252*x+70)","A"
88,1,29,29,0.288000," ","int((-1+x)*(3*x^2+2*x-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x \left(45 x^{5}+18 x^{4}-105 x^{3}-20 x^{2}+75 x -30\right)}{30}$&$29$\\ default&$-x +\frac{5}{2} x^{2}-\frac{2}{3} x^{3}-\frac{7}{2} x^{4}+\frac{3}{5} x^{5}+\frac{3}{2} x^{6}$&$30$\\ norman&$-x +\frac{5}{2} x^{2}-\frac{2}{3} x^{3}-\frac{7}{2} x^{4}+\frac{3}{5} x^{5}+\frac{3}{2} x^{6}$&$30$\\ risch&$-x +\frac{5}{2} x^{2}-\frac{2}{3} x^{3}-\frac{7}{2} x^{4}+\frac{3}{5} x^{5}+\frac{3}{2} x^{6}$&$30$\\ \hline \end{longtable}"," ",0,"1/30*x*(45*x^5+18*x^4-105*x^3-20*x^2+75*x-30)","A"
89,1,29,23,0.325000," ","int(x^(-1+k)*(a+b*x^k)^n,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(a +b \,x^{k}\right) \left(a +b \,x^{k}\right)^{n}}{b \left(1+n \right) k}$&$29$\\ \hline \end{longtable}"," ",0,"(a+b*x^k)/b/(1+n)/k*(a+b*x^k)^n","A"
90,1,23,22,0.275000," ","int(x^3/(1+2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{8}-\frac{x^{2}}{8}+\frac{x^{3}}{6}-\frac{\ln \left(1+2 x \right)}{16}$&$23$\\ norman&$\frac{x}{8}-\frac{x^{2}}{8}+\frac{x^{3}}{6}-\frac{\ln \left(1+2 x \right)}{16}$&$23$\\ meijerg&$\frac{x \left(16 x^{2}-12 x +12\right)}{96}-\frac{\ln \left(1+2 x \right)}{16}$&$23$\\ risch&$\frac{x}{8}-\frac{x^{2}}{8}+\frac{x^{3}}{6}-\frac{\ln \left(1+2 x \right)}{16}$&$23$\\ \hline \end{longtable}"," ",0,"1/8*x-1/8*x^2+1/6*x^3-1/16*ln(1+2*x)","A"
91,1,27,26,0.282000," ","int(x^6/(3*x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{4 x}{27}-\frac{2 x^{3}}{27}+\frac{x^{5}}{15}-\frac{4 \arctan \left(\frac{x \sqrt{6}}{2}\right) \sqrt{6}}{81}$&$27$\\ risch&$\frac{4 x}{27}-\frac{2 x^{3}}{27}+\frac{x^{5}}{15}-\frac{4 \arctan \left(\frac{x \sqrt{6}}{2}\right) \sqrt{6}}{81}$&$27$\\ meijerg&$\frac{2 \sqrt{2}\, \sqrt{3}\, \left(\frac{x \sqrt{2}\, \sqrt{3}\, \left(\frac{189}{4} x^{4}-\frac{105}{2} x^{2}+105\right)}{105}-2 \arctan \left(\frac{x \sqrt{2}\, \sqrt{3}}{2}\right)\right)}{81}$&$43$\\ \hline \end{longtable}"," ",0,"4/27*x-2/27*x^3+1/15*x^5-4/81*arctan(1/2*x*6^(1/2))*6^(1/2)","A"
92,1,16,17,0.282000," ","int(1/(3*x^2-7*x+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(-1+3 x \right)}{5}+\frac{\ln \left(-2+x \right)}{5}$&$16$\\ norman&$-\frac{\ln \left(-1+3 x \right)}{5}+\frac{\ln \left(-2+x \right)}{5}$&$16$\\ risch&$-\frac{\ln \left(-1+3 x \right)}{5}+\frac{\ln \left(-2+x \right)}{5}$&$16$\\ \hline \end{longtable}"," ",0,"-1/5*ln(-1+3*x)+1/5*ln(-2+x)","A"
93,1,29,28,0.419000," ","int((-1+3*x)/(x^2-x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{3 \ln \left(x^{2}-x +1\right)}{2}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(-1+2 x \right) \sqrt{3}}{3}\right)}{3}$&$29$\\ risch&$\frac{3 \ln \left(4 x^{2}-4 x +4\right)}{2}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(-1+2 x \right) \sqrt{3}}{3}\right)}{3}$&$31$\\ \hline \end{longtable}"," ",0,"3/2*ln(x^2-x+1)+1/3*3^(1/2)*arctan(1/3*(-1+2*x)*3^(1/2))","A"
94,1,22,21,0.404000," ","int(x^2/(x^2+2*x+5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x -\frac{3 \arctan \left(\frac{1}{2}+\frac{x}{2}\right)}{2}-\ln \left(x^{2}+2 x +5\right)$&$22$\\ risch&$x -\frac{3 \arctan \left(\frac{1}{2}+\frac{x}{2}\right)}{2}-\ln \left(x^{2}+2 x +5\right)$&$22$\\ \hline \end{longtable}"," ",0,"x-3/2*arctan(1/2+1/2*x)-ln(x^2+2*x+5)","A"
95,1,39,38,0.411000," ","int((6*x^4-5*x^3+4*x^2)/(2*x^2-x+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x^{3}-\frac{x^{2}}{2}+\frac{\ln \left(2 x^{2}-x +1\right)}{4}+\frac{\sqrt{7}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{7}}{7}\right)}{14}$&$39$\\ risch&$x^{3}-\frac{x^{2}}{2}+\frac{\ln \left(16 x^{2}-8 x +8\right)}{4}+\frac{\sqrt{7}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{7}}{7}\right)}{14}$&$39$\\ \hline \end{longtable}"," ",0,"x^3-1/2*x^2+1/4*ln(2*x^2-x+1)+1/14*7^(1/2)*arctan(1/7*(4*x-1)*7^(1/2))","A"
96,1,18,19,0.028000," ","int((x^2+x-1)/(x^3+x^2-6*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(3+x \right)}{3}+\frac{\ln \left(x \right)}{6}+\frac{\ln \left(-2+x \right)}{2}$&$18$\\ norman&$\frac{\ln \left(3+x \right)}{3}+\frac{\ln \left(x \right)}{6}+\frac{\ln \left(-2+x \right)}{2}$&$18$\\ risch&$\frac{\ln \left(3+x \right)}{3}+\frac{\ln \left(x \right)}{6}+\frac{\ln \left(-2+x \right)}{2}$&$18$\\ \hline \end{longtable}"," ",0,"1/3*ln(3+x)+1/6*ln(x)+1/2*ln(-2+x)","A"
97,1,26,29,0.043000," ","int((11*a^2-7*a*x+5*x^2)/(-6*a^3+11*a^2*x-6*a*x^2+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-17 \ln \left(-2 a +x \right)+\frac{9 \ln \left(-a +x \right)}{2}+\frac{35 \ln \left(-3 a +x \right)}{2}$&$26$\\ default&$\frac{9 \ln \left(a -x \right)}{2}-17 \ln \left(2 a -x \right)+\frac{35 \ln \left(3 a -x \right)}{2}$&$30$\\ norman&$\frac{9 \ln \left(a -x \right)}{2}-17 \ln \left(2 a -x \right)+\frac{35 \ln \left(3 a -x \right)}{2}$&$30$\\ \hline \end{longtable}"," ",0,"-17*ln(-2*a+x)+9/2*ln(-a+x)+35/2*ln(-3*a+x)","A"
98,1,26,29,0.036000," ","int((x^2-x+2)/(x^4-5*x^2+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(-2+x \right)}{3}-\frac{2 \ln \left(2+x \right)}{3}-\frac{\ln \left(-1+x \right)}{3}+\frac{2 \ln \left(1+x \right)}{3}$&$26$\\ norman&$\frac{\ln \left(-2+x \right)}{3}-\frac{2 \ln \left(2+x \right)}{3}-\frac{\ln \left(-1+x \right)}{3}+\frac{2 \ln \left(1+x \right)}{3}$&$26$\\ risch&$\frac{\ln \left(-2+x \right)}{3}-\frac{2 \ln \left(2+x \right)}{3}-\frac{\ln \left(-1+x \right)}{3}+\frac{2 \ln \left(1+x \right)}{3}$&$26$\\ \hline \end{longtable}"," ",0,"1/3*ln(-2+x)-2/3*ln(2+x)-1/3*ln(-1+x)+2/3*ln(1+x)","A"
99,1,26,25,0.042000," ","int((2*x^2-5)/(x^4-5*x^2+6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctanh \left(\frac{x \sqrt{2}}{2}\right) \sqrt{2}}{2}-\frac{\arctanh \left(\frac{x \sqrt{3}}{3}\right) \sqrt{3}}{3}$&$26$\\ risch&$\frac{\sqrt{3}\, \ln \left(x -\sqrt{3}\right)}{6}-\frac{\sqrt{3}\, \ln \left(x +\sqrt{3}\right)}{6}+\frac{\sqrt{2}\, \ln \left(x -\sqrt{2}\right)}{4}-\frac{\sqrt{2}\, \ln \left(x +\sqrt{2}\right)}{4}$&$50$\\ \hline \end{longtable}"," ",0,"-1/2*arctanh(1/2*x*2^(1/2))*2^(1/2)-1/3*arctanh(1/3*x*3^(1/2))*3^(1/2)","A"
100,1,26,33,0.332000," ","int(1/(-4+x)/(-3+x)/(-2+x)/(-1+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(-2+x \right)}{2}+\frac{\ln \left(-4+x \right)}{6}-\frac{\ln \left(-3+x \right)}{2}-\frac{\ln \left(-1+x \right)}{6}$&$26$\\ norman&$\frac{\ln \left(-2+x \right)}{2}+\frac{\ln \left(-4+x \right)}{6}-\frac{\ln \left(-3+x \right)}{2}-\frac{\ln \left(-1+x \right)}{6}$&$26$\\ risch&$\frac{\ln \left(-2+x \right)}{2}+\frac{\ln \left(-4+x \right)}{6}-\frac{\ln \left(-3+x \right)}{2}-\frac{\ln \left(-1+x \right)}{6}$&$26$\\ \hline \end{longtable}"," ",0,"1/2*ln(-2+x)+1/6*ln(-4+x)-1/2*ln(-3+x)-1/6*ln(-1+x)","A"
101,1,17,25,0.299000," ","int((x^2+1)/(-1+x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{1-2 x}{\left(-1+x \right)^{2}}+\ln \left(-1+x \right)$&$17$\\ risch&$\frac{1-2 x}{\left(-1+x \right)^{2}}+\ln \left(-1+x \right)$&$17$\\ default&$-\frac{1}{\left(-1+x \right)^{2}}-\frac{2}{-1+x}+\ln \left(-1+x \right)$&$20$\\ meijerg&$-\frac{x \left(2-x \right)}{2 \left(1-x \right)^{2}}+\frac{x \left(-9 x +6\right)}{6 \left(1-x \right)^{2}}+\ln \left(1-x \right)$&$38$\\ \hline \end{longtable}"," ",0,"(1-2*x)/(-1+x)^2+ln(-1+x)","A"
102,1,33,32,0.281000," ","int(x^5/(3+x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-108 x +\frac{27 x^{2}}{2}-2 x^{3}+\frac{x^{4}}{4}+\frac{243}{3+x}+405 \ln \left(3+x \right)$&$33$\\ risch&$-108 x +\frac{27 x^{2}}{2}-2 x^{3}+\frac{x^{4}}{4}+\frac{243}{3+x}+405 \ln \left(3+x \right)$&$33$\\ norman&$\frac{-\frac{135}{2} x^{2}+\frac{15}{2} x^{3}-\frac{5}{4} x^{4}+\frac{1}{4} x^{5}+1215}{3+x}+405 \ln \left(3+x \right)$&$36$\\ meijerg&$-\frac{9 x \left(-\frac{1}{27} x^{4}+\frac{5}{27} x^{3}-\frac{10}{9} x^{2}+10 x +60\right)}{4 \left(1+\frac{x}{3}\right)}+405 \ln \left(1+\frac{x}{3}\right)$&$40$\\ \hline \end{longtable}"," ",0,"-108*x+27/2*x^2-2*x^3+1/4*x^4+243/(3+x)+405*ln(3+x)","A"
103,1,25,33,0.029000," ","int((5*x^3-2)/(x^4-8*x^3+18*x^2-27),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-\frac{407 x}{16}+\frac{955}{16}}{\left(-3+x \right)^{2}}+\frac{313 \ln \left(-3+x \right)}{64}+\frac{7 \ln \left(1+x \right)}{64}$&$25$\\ default&$-\frac{133}{8 \left(-3+x \right)^{2}}-\frac{407}{16 \left(-3+x \right)}+\frac{313 \ln \left(-3+x \right)}{64}+\frac{7 \ln \left(1+x \right)}{64}$&$28$\\ risch&$\frac{-\frac{407 x}{16}+\frac{955}{16}}{x^{2}-6 x +9}+\frac{313 \ln \left(-3+x \right)}{64}+\frac{7 \ln \left(1+x \right)}{64}$&$30$\\ \hline \end{longtable}"," ",0,"(-407/16*x+955/16)/(-3+x)^2+313/64*ln(-3+x)+7/64*ln(1+x)","A"
104,1,28,27,0.308000," ","int((x^3-6*x^2+3*x-9)/(3+x)^2/(4+x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{99}{3+x}+\frac{181}{4+x}+264 \ln \left(3+x \right)-263 \ln \left(4+x \right)$&$28$\\ norman&$\frac{280 x +939}{\left(4+x \right) \left(3+x \right)}+264 \ln \left(3+x \right)-263 \ln \left(4+x \right)$&$30$\\ risch&$\frac{280 x +939}{\left(4+x \right) \left(3+x \right)}+264 \ln \left(3+x \right)-263 \ln \left(4+x \right)$&$30$\\ \hline \end{longtable}"," ",0,"99/(3+x)+181/(4+x)+264*ln(3+x)-263*ln(4+x)","A"
105,1,31,33,0.354000," ","int((x^3+x^2+2)/x/(x^2-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-\frac{x}{2}-\frac{3}{2}}{x^{2}-1}+2 \ln \left(x \right)-\frac{3 \ln \left(-1+x \right)}{4}-\frac{5 \ln \left(1+x \right)}{4}$&$31$\\ risch&$\frac{-\frac{x}{2}-\frac{3}{2}}{x^{2}-1}+2 \ln \left(x \right)-\frac{3 \ln \left(-1+x \right)}{4}-\frac{5 \ln \left(1+x \right)}{4}$&$31$\\ default&$2 \ln \left(x \right)-\frac{1}{-1+x}-\frac{3 \ln \left(-1+x \right)}{4}+\frac{1}{2 x +2}-\frac{5 \ln \left(1+x \right)}{4}$&$32$\\ meijerg&$\frac{i \left(-\frac{i x}{-x^{2}+1}+i \arctanh \left(x \right)\right)}{2}+\frac{3 x^{2}}{-2 x^{2}+2}-\ln \left(-x^{2}+1\right)+1+2 \ln \left(x \right)+i \pi$&$71$\\ \hline \end{longtable}"," ",0,"(-1/2*x-3/2)/(x^2-1)+2*ln(x)-3/4*ln(-1+x)-5/4*ln(1+x)","A"
106,1,35,38,0.037000," ","int(1/(x^6-x^5-x^4+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{2 x^{2}}-\frac{1}{x}+2 \ln \left(x \right)-\frac{1}{2 \left(-1+x \right)}-\frac{7 \ln \left(-1+x \right)}{4}-\frac{\ln \left(1+x \right)}{4}$&$35$\\ norman&$\frac{\frac{1}{2}-\frac{3}{2} x^{2}+\frac{1}{2} x}{x^{2} \left(-1+x \right)}+2 \ln \left(x \right)-\frac{7 \ln \left(-1+x \right)}{4}-\frac{\ln \left(1+x \right)}{4}$&$37$\\ risch&$\frac{\frac{1}{2}-\frac{3}{2} x^{2}+\frac{1}{2} x}{x^{2} \left(-1+x \right)}+2 \ln \left(x \right)-\frac{7 \ln \left(-1+x \right)}{4}-\frac{\ln \left(1+x \right)}{4}$&$37$\\ \hline \end{longtable}"," ",0,"-1/2/x^2-1/x+2*ln(x)-1/2/(-1+x)-7/4*ln(-1+x)-1/4*ln(1+x)","A"
107,1,24,25,0.029000," ","int((x^4+1)/(x^3-x^2+x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x +\frac{x^{2}}{2}-\frac{\ln \left(x^{2}+1\right)}{2}-\arctan \left(x \right)+\ln \left(-1+x \right)$&$24$\\ risch&$x +\frac{x^{2}}{2}-\frac{\ln \left(x^{2}+1\right)}{2}-\arctan \left(x \right)+\ln \left(-1+x \right)$&$24$\\ \hline \end{longtable}"," ",0,"x+1/2*x^2-1/2*ln(x^2+1)-arctan(x)+ln(-1+x)","A"
108,1,22,21,0.322000," ","int(1/x/(1+x)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(x \right)}{2}+\ln \left(x \right)-\frac{\ln \left(1+x \right)}{2}-\frac{\ln \left(x^{2}+1\right)}{4}$&$22$\\ risch&$-\frac{\arctan \left(x \right)}{2}+\ln \left(x \right)-\frac{\ln \left(1+x \right)}{2}-\frac{\ln \left(x^{2}+1\right)}{4}$&$22$\\ \hline \end{longtable}"," ",0,"-1/2*arctan(x)+ln(x)-1/2*ln(1+x)-1/4*ln(x^2+1)","A"
109,1,26,17,0.038000," ","int(x^2/(x^4+x^2-2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(\frac{x \sqrt{2}}{2}\right) \sqrt{2}}{3}+\frac{\ln \left(-1+x \right)}{6}-\frac{\ln \left(1+x \right)}{6}$&$26$\\ risch&$\frac{\arctan \left(\frac{x \sqrt{2}}{2}\right) \sqrt{2}}{3}+\frac{\ln \left(-1+x \right)}{6}-\frac{\ln \left(1+x \right)}{6}$&$26$\\ \hline \end{longtable}"," ",0,"1/3*arctan(1/2*x*2^(1/2))*2^(1/2)+1/6*ln(-1+x)-1/6*ln(1+x)","A"
110,1,33,32,0.041000," ","int((x^3+4*x^2+6*x)/(x^4+2*x^3+3*x^2+4*x+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{1}{1+x}-\frac{\ln \left(1+x \right)}{3}+\frac{2 \ln \left(x^{2}+2\right)}{3}+\frac{4 \arctan \left(\frac{x \sqrt{2}}{2}\right) \sqrt{2}}{3}$&$33$\\ risch&$\frac{1}{1+x}-\frac{\ln \left(1+x \right)}{3}+\frac{2 \ln \left(x^{2}+2\right)}{3}+\frac{4 \arctan \left(\frac{x \sqrt{2}}{2}\right) \sqrt{2}}{3}$&$33$\\ \hline \end{longtable}"," ",0,"1/(1+x)-1/3*ln(1+x)+2/3*ln(x^2+2)+4/3*arctan(1/2*x*2^(1/2))*2^(1/2)","A"
111,1,35,36,0.317000," ","int(x/(1+x)/(1+2*x)^2/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{1}{\frac{5}{2}+5 x}-\frac{\ln \left(1+x \right)}{2}+\frac{16 \ln \left(1+2 x \right)}{25}-\frac{7 \ln \left(x^{2}+1\right)}{100}+\frac{\arctan \left(x \right)}{50}$&$35$\\ default&$\frac{2}{5 \left(1+2 x \right)}+\frac{\arctan \left(x \right)}{50}-\frac{\ln \left(1+x \right)}{2}+\frac{16 \ln \left(1+2 x \right)}{25}-\frac{7 \ln \left(x^{2}+1\right)}{100}$&$37$\\ \hline \end{longtable}"," ",0,"1/5/(1/2+x)-1/2*ln(1+x)+16/25*ln(1+2*x)-7/100*ln(x^2+1)+1/50*arctan(x)","A"
112,1,33,39,0.362000," ","int((3*x^2+x-2)/(-1+x)^3/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{5 x}{2}+2}{\left(-1+x \right)^{2}}-\frac{3 \ln \left(-1+x \right)}{2}+\frac{3 \ln \left(4 x^{2}+4\right)}{4}-\arctan \left(x \right)$&$33$\\ default&$\frac{3 \ln \left(x^{2}+1\right)}{4}-\arctan \left(x \right)-\frac{1}{2 \left(-1+x \right)^{2}}-\frac{5}{2 \left(-1+x \right)}-\frac{3 \ln \left(-1+x \right)}{2}$&$34$\\ \hline \end{longtable}"," ",0,"(-5/2*x+2)/(-1+x)^2-3/2*ln(-1+x)+3/4*ln(4*x^2+4)-arctan(x)","A"
113,1,54,53,0.050000," ","int(1/(x^4+x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(x^{2}+x +1\right)}{4}+\frac{\arctan \left(\frac{\left(1+2 x \right) \sqrt{3}}{3}\right) \sqrt{3}}{6}-\frac{\ln \left(x^{2}-x +1\right)}{4}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(-1+2 x \right) \sqrt{3}}{3}\right)}{6}$&$54$\\ risch&$\frac{\ln \left(4 x^{2}+4 x +4\right)}{4}+\frac{\arctan \left(\frac{\left(1+2 x \right) \sqrt{3}}{3}\right) \sqrt{3}}{6}-\frac{\ln \left(4 x^{2}-4 x +4\right)}{4}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(-1+2 x \right) \sqrt{3}}{3}\right)}{6}$&$60$\\ \hline \end{longtable}"," ",0,"1/4*ln(x^2+x+1)+1/6*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2)-1/4*ln(x^2-x+1)+1/6*3^(1/2)*arctan(1/3*(-1+2*x)*3^(1/2))","A"
114,1,46,39,0.341000," ","int((2*x^3+3)/(x^5-9*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(x^{2}+3\right)}{12}+\frac{\arctan \left(\frac{x \sqrt{3}}{3}\right) \sqrt{3}}{3}-\frac{\ln \left(x \right)}{3}+\frac{\ln \left(x^{2}-3\right)}{12}-\frac{\arctanh \left(\frac{x \sqrt{3}}{3}\right) \sqrt{3}}{3}$&$46$\\ meijerg&$\frac{\ln \left(1-\frac{x^{4}}{9}\right)}{12}-\frac{\ln \left(x \right)}{3}+\frac{\ln \left(3\right)}{6}-\frac{i \pi}{12}+\frac{x^{3} \sqrt{3}\, \left(\ln \left(1-\frac{\sqrt{3}\, \left(x^{4}\right)^{\frac{1}{4}}}{3}\right)-\ln \left(1+\frac{\sqrt{3}\, \left(x^{4}\right)^{\frac{1}{4}}}{3}\right)+2 \arctan \left(\frac{\sqrt{3}\, \left(x^{4}\right)^{\frac{1}{4}}}{3}\right)\right)}{6 \left(x^{4}\right)^{\frac{3}{4}}}$&$79$\\ risch&$-\frac{\ln \left(x \right)}{3}+\frac{\ln \left(4 x^{2}+12\right)}{12}+\frac{\arctan \left(\frac{x \sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{\ln \left(2 x -2 \sqrt{3}\right)}{12}+\frac{\ln \left(2 x -2 \sqrt{3}\right) \sqrt{3}}{6}+\frac{\ln \left(2 x +2 \sqrt{3}\right)}{12}-\frac{\ln \left(2 x +2 \sqrt{3}\right) \sqrt{3}}{6}$&$82$\\ \hline \end{longtable}"," ",0,"1/12*ln(x^2+3)+1/3*arctan(1/3*x*3^(1/2))*3^(1/2)-1/3*ln(x)+1/12*ln(x^2-3)-1/3*arctanh(1/3*x*3^(1/2))*3^(1/2)","A"
115,1,38,46,0.427000," ","int((5*x^3+8*x-20)/(-4+x)^3/(x^2-4*x+8),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{41 x}{4}+\frac{81}{4}}{\left(-4+x \right)^{2}}+\frac{45 \ln \left(x^{2}-4 x +8\right)}{32}+\frac{3 \arctan \left(-1+\frac{x}{2}\right)}{16}-\frac{45 \ln \left(-4+x \right)}{16}$&$38$\\ default&$\frac{45 \ln \left(x^{2}-4 x +8\right)}{32}+\frac{3 \arctan \left(-1+\frac{x}{2}\right)}{16}-\frac{83}{4 \left(-4+x \right)^{2}}-\frac{41}{4 \left(-4+x \right)}-\frac{45 \ln \left(-4+x \right)}{16}$&$41$\\ \hline \end{longtable}"," ",0,"(-41/4*x+81/4)/(-4+x)^2+45/32*ln(x^2-4*x+8)+3/16*arctan(-1+1/2*x)-45/16*ln(-4+x)","A"
116,1,36,35,0.318000," ","int(1/(x^2+1)/(x^2+2)/(x^2+3)/(x^2+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(\frac{x}{2}\right)}{12}+\frac{\arctan \left(x \right)}{6}-\frac{\arctan \left(\frac{x \sqrt{2}}{2}\right) \sqrt{2}}{4}+\frac{\arctan \left(\frac{x \sqrt{3}}{3}\right) \sqrt{3}}{6}$&$36$\\ risch&$-\frac{\arctan \left(\frac{x}{2}\right)}{12}+\frac{\arctan \left(x \right)}{6}-\frac{\arctan \left(\frac{x \sqrt{2}}{2}\right) \sqrt{2}}{4}+\frac{\arctan \left(\frac{x \sqrt{3}}{3}\right) \sqrt{3}}{6}$&$36$\\ \hline \end{longtable}"," ",0,"-1/12*arctan(1/2*x)+1/6*arctan(x)-1/4*arctan(1/2*x*2^(1/2))*2^(1/2)+1/6*arctan(1/3*x*3^(1/2))*3^(1/2)","A"
117,1,34,33,0.283000," ","int(x/(x^2+1)/(x^2+2)/(x^2+3)/(x^2+4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(x^{2}+1\right)}{12}-\frac{\ln \left(x^{2}+2\right)}{4}+\frac{\ln \left(x^{2}+3\right)}{4}-\frac{\ln \left(x^{2}+4\right)}{12}$&$34$\\ norman&$\frac{\ln \left(x^{2}+1\right)}{12}-\frac{\ln \left(x^{2}+2\right)}{4}+\frac{\ln \left(x^{2}+3\right)}{4}-\frac{\ln \left(x^{2}+4\right)}{12}$&$34$\\ risch&$\frac{\ln \left(x^{2}+1\right)}{12}-\frac{\ln \left(x^{2}+2\right)}{4}+\frac{\ln \left(x^{2}+3\right)}{4}-\frac{\ln \left(x^{2}+4\right)}{12}$&$34$\\ \hline \end{longtable}"," ",0,"1/12*ln(x^2+1)-1/4*ln(x^2+2)+1/4*ln(x^2+3)-1/12*ln(x^2+4)","A"
118,1,41,49,0.296000," ","int(1/(a^3+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\ln \left(a +x \right)}{3 a^{2}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{4} \textit{\_Z}^{2}+a^{2} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(\textit{\_R} \,a^{3}+x \right)\right)}{3}$&$41$\\ default&$\frac{-\frac{\ln \left(a^{2}-a x +x^{2}\right)}{2}+\sqrt{3}\, \arctan \left(\frac{\left(2 x -a \right) \sqrt{3}}{3 a}\right)}{3 a^{2}}+\frac{\ln \left(a +x \right)}{3 a^{2}}$&$51$\\ \hline \end{longtable}"," ",0,"1/3*ln(a+x)/a^2+1/3*sum(_R*ln(_R*a^3+x),_R=RootOf(_Z^2*a^4+_Z*a^2+1))","C"
119,1,51,49,0.280000," ","int(x/(a^3+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\frac{\ln \left(a^{2}-a x +x^{2}\right)}{2}+\sqrt{3}\, \arctan \left(\frac{\left(2 x -a \right) \sqrt{3}}{3 a}\right)}{3 a}-\frac{\ln \left(a +x \right)}{3 a}$&$51$\\ risch&$\frac{\ln \left(4 a^{2}-4 a x +4 x^{2}\right)}{6 a}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -a \right) \sqrt{3}}{3 a}\right)}{3 a}-\frac{\ln \left(a +x \right)}{3 a}$&$56$\\ \hline \end{longtable}"," ",0,"1/3/a*(1/2*ln(a^2-a*x+x^2)+3^(1/2)*arctan(1/3*(2*x-a)*3^(1/2)/a))-1/3*ln(a+x)/a","A"
120,1,11,10,0.262000," ","int(x^2/(a^3+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(a^{3}+x^{3}\right)}{3}$&$11$\\ default&$\frac{\ln \left(a^{3}+x^{3}\right)}{3}$&$11$\\ risch&$\frac{\ln \left(a^{3}+x^{3}\right)}{3}$&$11$\\ norman&$\frac{\ln \left(a +x \right)}{3}+\frac{\ln \left(a^{2}-a x +x^{2}\right)}{3}$&$22$\\ \hline \end{longtable}"," ",0,"1/3*ln(a^3+x^3)","A"
121,1,21,20,0.272000," ","int(1/x/(a^3+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\ln \left(x \right)}{a^{3}}-\frac{\ln \left(a^{3}+x^{3}\right)}{3 a^{3}}$&$21$\\ default&$-\frac{\ln \left(a^{2}-a x +x^{2}\right)}{3 a^{3}}+\frac{\ln \left(x \right)}{a^{3}}-\frac{\ln \left(a +x \right)}{3 a^{3}}$&$34$\\ norman&$-\frac{\ln \left(a^{2}-a x +x^{2}\right)}{3 a^{3}}+\frac{\ln \left(x \right)}{a^{3}}-\frac{\ln \left(a +x \right)}{3 a^{3}}$&$34$\\ \hline \end{longtable}"," ",0,"ln(x)/a^3-1/3*ln(a^3+x^3)/a^3","A"
122,1,60,57,0.278000," ","int(1/x^2/(a^3+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{-\frac{\ln \left(a^{2}-a x +x^{2}\right)}{2}-\sqrt{3}\, \arctan \left(\frac{\left(2 x -a \right) \sqrt{3}}{3 a}\right)}{3 a^{4}}-\frac{1}{a^{3} x}+\frac{\ln \left(a +x \right)}{3 a^{4}}$&$60$\\ risch&$-\frac{1}{a^{3} x}+\frac{\ln \left(-a -x \right)}{3 a^{4}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{8} \textit{\_Z}^{2}+a^{4} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(\left(-4 \textit{\_R}^{3} a^{12}+3\right) x -a^{9} \textit{\_R}^{2}\right)\right)}{3}$&$67$\\ \hline \end{longtable}"," ",0,"1/3/a^4*(-1/2*ln(a^2-a*x+x^2)-3^(1/2)*arctan(1/3*(2*x-a)*3^(1/2)/a))-1/a^3/x+1/3*ln(a+x)/a^4","A"
123,1,60,57,0.303000," ","int(1/x^3/(a^3+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\frac{\ln \left(a^{2}-a x +x^{2}\right)}{2}-\sqrt{3}\, \arctan \left(\frac{\left(2 x -a \right) \sqrt{3}}{3 a}\right)}{3 a^{5}}-\frac{\ln \left(a +x \right)}{3 a^{5}}-\frac{1}{2 a^{3} x^{2}}$&$60$\\ risch&$-\frac{1}{2 a^{3} x^{2}}+\frac{\ln \left(4 a^{2}-4 a x +4 x^{2}\right)}{6 a^{5}}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -a \right) \sqrt{3}}{3 a}\right)}{3 a^{5}}-\frac{\ln \left(a +x \right)}{3 a^{5}}$&$64$\\ \hline \end{longtable}"," ",0,"1/3/a^5*(1/2*ln(a^2-a*x+x^2)-3^(1/2)*arctan(1/3*(2*x-a)*3^(1/2)/a))-1/3*ln(a+x)/a^5-1/2/a^3/x^2","A"
124,1,34,29,0.270000," ","int(1/x^4/(a^3+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{1}{3 a^{3} x^{3}}-\frac{\ln \left(x \right)}{a^{6}}+\frac{\ln \left(-a^{3}-x^{3}\right)}{3 a^{6}}$&$34$\\ default&$\frac{\ln \left(a^{2}-a x +x^{2}\right)}{3 a^{6}}-\frac{1}{3 a^{3} x^{3}}-\frac{\ln \left(x \right)}{a^{6}}+\frac{\ln \left(a +x \right)}{3 a^{6}}$&$43$\\ norman&$\frac{\ln \left(a^{2}-a x +x^{2}\right)}{3 a^{6}}-\frac{1}{3 a^{3} x^{3}}-\frac{\ln \left(x \right)}{a^{6}}+\frac{\ln \left(a +x \right)}{3 a^{6}}$&$43$\\ \hline \end{longtable}"," ",0,"-1/3/a^3/x^3-ln(x)/a^6+1/3/a^6*ln(-a^3-x^3)","A"
125,1,66,64,0.284000," ","int(1/x^5/(a^3+x^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\frac{\ln \left(a^{2}-a x +x^{2}\right)}{2}+\sqrt{3}\, \arctan \left(\frac{\left(2 x -a \right) \sqrt{3}}{3 a}\right)}{3 a^{7}}-\frac{1}{4 a^{3} x^{4}}+\frac{1}{a^{6} x}-\frac{\ln \left(a +x \right)}{3 a^{7}}$&$66$\\ risch&$\frac{\frac{x^{3}}{a^{6}}-\frac{1}{4 a^{3}}}{x^{4}}-\frac{\ln \left(a +x \right)}{3 a^{7}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{14} \textit{\_Z}^{2}-a^{7} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(\left(-4 \textit{\_R}^{3} a^{21}-3\right) x +a^{15} \textit{\_R}^{2}\right)\right)}{3}$&$72$\\ \hline \end{longtable}"," ",0,"1/3/a^7*(1/2*ln(a^2-a*x+x^2)+3^(1/2)*arctan(1/3*(2*x-a)*3^(1/2)/a))-1/4/a^3/x^4+1/a^6/x-1/3*ln(a+x)/a^7","A"
126,0,0,40,0.029000," ","int(1/(x^m)/(a^3+x^3),x)","\[\int \frac{x^{-m}}{a^{3}+x^{3}}\, dx\]"," ",0,"int(1/(x^m)/(a^3+x^3),x)","F"
127,1,33,23,0.278000," ","int(1/(a^4-x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(\frac{x}{a}\right)}{2 a^{3}}+\frac{\ln \left(a +x \right)}{4 a^{3}}-\frac{\ln \left(a -x \right)}{4 a^{3}}$&$33$\\ risch&$\frac{\arctan \left(\frac{x}{a}\right)}{2 a^{3}}-\frac{\ln \left(-a +x \right)}{4 a^{3}}+\frac{\ln \left(a +x \right)}{4 a^{3}}$&$33$\\ \hline \end{longtable}"," ",0,"1/2*arctan(x/a)/a^3+1/4*ln(a+x)/a^3-1/4/a^3*ln(a-x)","A"
128,1,30,13,0.335000," ","int(x/(a^4-x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(a^{2}+x^{2}\right)}{4 a^{2}}-\frac{\ln \left(a^{2}-x^{2}\right)}{4 a^{2}}$&$30$\\ risch&$-\frac{\ln \left(-a^{2}+x^{2}\right)}{4 a^{2}}+\frac{\ln \left(a^{2}+x^{2}\right)}{4 a^{2}}$&$30$\\ norman&$-\frac{\ln \left(a -x \right)}{4 a^{2}}-\frac{\ln \left(a +x \right)}{4 a^{2}}+\frac{\ln \left(a^{2}+x^{2}\right)}{4 a^{2}}$&$35$\\ \hline \end{longtable}"," ",0,"1/4/a^2*ln(a^2+x^2)-1/4/a^2*ln(a^2-x^2)","B"
129,1,23,22,0.316000," ","int(1/x/(a^4-x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\ln \left(x \right)}{a^{4}}-\frac{\ln \left(-a^{4}+x^{4}\right)}{4 a^{4}}$&$23$\\ default&$-\frac{\ln \left(a^{2}+x^{2}\right)}{4 a^{4}}+\frac{\ln \left(x \right)}{a^{4}}-\frac{\ln \left(a +x \right)}{4 a^{4}}-\frac{\ln \left(a -x \right)}{4 a^{4}}$&$41$\\ norman&$-\frac{\ln \left(a^{2}+x^{2}\right)}{4 a^{4}}+\frac{\ln \left(x \right)}{a^{4}}-\frac{\ln \left(a +x \right)}{4 a^{4}}-\frac{\ln \left(a -x \right)}{4 a^{4}}$&$41$\\ \hline \end{longtable}"," ",0,"ln(x)/a^4-1/4/a^4*ln(-a^4+x^4)","A"
130,1,41,31,0.275000," ","int(1/x^2/(a^4-x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(\frac{x}{a}\right)}{2 a^{5}}-\frac{1}{a^{4} x}+\frac{\ln \left(a +x \right)}{4 a^{5}}-\frac{\ln \left(a -x \right)}{4 a^{5}}$&$41$\\ risch&$-\frac{1}{a^{4} x}-\frac{\ln \left(-a +x \right)}{4 a^{5}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{10} \textit{\_Z}^{2}+1\right)}{\sum}\textit{\_R} \ln \left(\left(5 \textit{\_R}^{4} a^{20}-4\right) x +a^{16} \textit{\_R}^{3}\right)\right)}{4}+\frac{\ln \left(a +x \right)}{4 a^{5}}$&$68$\\ \hline \end{longtable}"," ",0,"-1/2*arctan(x/a)/a^5-1/a^4/x+1/4*ln(a+x)/a^5-1/4/a^5*ln(a-x)","A"
131,1,42,22,0.270000," ","int(1/x^3/(a^4-x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{1}{2 a^{4} x^{2}}-\frac{\ln \left(a^{2}-x^{2}\right)}{4 a^{6}}+\frac{\ln \left(-a^{2}-x^{2}\right)}{4 a^{6}}$&$42$\\ default&$\frac{\ln \left(a^{2}+x^{2}\right)}{4 a^{6}}-\frac{\ln \left(a +x \right)}{4 a^{6}}-\frac{\ln \left(a -x \right)}{4 a^{6}}-\frac{1}{2 a^{4} x^{2}}$&$43$\\ norman&$\frac{\ln \left(a^{2}+x^{2}\right)}{4 a^{6}}-\frac{\ln \left(a +x \right)}{4 a^{6}}-\frac{\ln \left(a -x \right)}{4 a^{6}}-\frac{1}{2 a^{4} x^{2}}$&$43$\\ \hline \end{longtable}"," ",0,"-1/2/a^4/x^2-1/4/a^6*ln(a^2-x^2)+1/4/a^6*ln(-a^2-x^2)","A"
132,1,41,31,0.280000," ","int(1/x^4/(a^4-x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(\frac{x}{a}\right)}{2 a^{7}}-\frac{1}{3 a^{4} x^{3}}+\frac{\ln \left(a +x \right)}{4 a^{7}}-\frac{\ln \left(a -x \right)}{4 a^{7}}$&$41$\\ risch&$-\frac{1}{3 a^{4} x^{3}}-\frac{\ln \left(a -x \right)}{4 a^{7}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{14} \textit{\_Z}^{2}+1\right)}{\sum}\textit{\_R} \ln \left(\left(-5 \textit{\_R}^{4} a^{28}+4\right) x -a^{8} \textit{\_R} \right)\right)}{4}+\frac{\ln \left(-a -x \right)}{4 a^{7}}$&$71$\\ \hline \end{longtable}"," ",0,"1/2*arctan(x/a)/a^7-1/3/a^4/x^3+1/4*ln(a+x)/a^7-1/4/a^7*ln(a-x)","A"
133,0,0,39,0.034000," ","int(1/(x^m)/(a^4-x^4),x)","\[\int \frac{x^{-m}}{a^{4}-x^{4}}\, dx\]"," ",0,"int(1/(x^m)/(a^4-x^4),x)","F"
134,1,14,13,0.289000," ","int(x/(a^4+x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(\frac{x^{2}}{a^{2}}\right)}{2 a^{2}}$&$14$\\ risch&$\frac{\arctan \left(\frac{x^{2}}{a^{2}}\right)}{2 a^{2}}$&$14$\\ \hline \end{longtable}"," ",0,"1/2*arctan(x^2/a^2)/a^2","A"
135,1,24,85,0.271000," ","int(x^2/(a^4+x^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}+a^{4}\right)}{\sum}\frac{\ln \left(x -\textit{\_R} \right)}{\textit{\_R}}\right)}{4}$&$24$\\ default&$\frac{\sqrt{2}\, \left(\ln \left(\frac{x^{2}-\left(a^{4}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{a^{4}}}{x^{2}+\left(a^{4}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{a^{4}}}\right)+2 \arctan \left(\frac{\sqrt{2}\, x}{\left(a^{4}\right)^{\frac{1}{4}}}+1\right)+2 \arctan \left(\frac{\sqrt{2}\, x}{\left(a^{4}\right)^{\frac{1}{4}}}-1\right)\right)}{8 \left(a^{4}\right)^{\frac{1}{4}}}$&$85$\\ \hline \end{longtable}"," ",0,"1/4*sum(1/_R*ln(x-_R),_R=RootOf(_Z^4+a^4))","C"
136,1,55,149,0.361000," ","int(1/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{16} \textit{\_Z}^{4}+a^{12} \textit{\_Z}^{3}+a^{8} \textit{\_Z}^{2}+a^{4} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(\textit{\_R} \,a^{5}+x \right)\right)}{5}+\frac{\ln \left(a +x \right)}{5 a^{4}}$&$55$\\ default&$\frac{\ln \left(a +x \right)}{5 a^{4}}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}+\textit{\_Z}^{2} a^{2}-a^{3} \textit{\_Z} +a^{4}\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+2 \textit{\_R}^{2} a -3 \textit{\_R} \,a^{2}+4 a^{3}\right) \ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}}}{5 a^{4}}$&$101$\\ \hline \end{longtable}"," ",0,"1/5*sum(_R*ln(_R*a^5+x),_R=RootOf(_Z^4*a^16+_Z^3*a^12+_Z^2*a^8+_Z*a^4+1))+1/5*ln(a+x)/a^4","C"
137,1,60,149,0.346000," ","int(x/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\ln \left(a +x \right)}{5 a^{3}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{12} \textit{\_Z}^{4}-a^{9} \textit{\_Z}^{3}+a^{6} \textit{\_Z}^{2}-a^{3} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(-a^{10} \textit{\_R}^{3}+x \right)\right)}{5}$&$60$\\ default&$-\frac{\ln \left(a +x \right)}{5 a^{3}}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}+\textit{\_Z}^{2} a^{2}-a^{3} \textit{\_Z} +a^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{3}-2 \textit{\_R}^{2} a +3 \textit{\_R} \,a^{2}+a^{3}\right) \ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}}}{5 a^{3}}$&$97$\\ \hline \end{longtable}"," ",0,"-1/5*ln(a+x)/a^3+1/5*sum(_R*ln(-_R^3*a^10+x),_R=RootOf(_Z^4*a^12-_Z^3*a^9+_Z^2*a^6-_Z*a^3+1))","C"
138,1,58,149,0.349000," ","int(x^2/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\ln \left(a +x \right)}{5 a^{2}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{8} \textit{\_Z}^{4}+a^{6} \textit{\_Z}^{3}+a^{4} \textit{\_Z}^{2}+a^{2} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(x \,\textit{\_R}^{3} a^{5}+1\right)\right)}{5}$&$58$\\ default&$\frac{\ln \left(a +x \right)}{5 a^{2}}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}+\textit{\_Z}^{2} a^{2}-a^{3} \textit{\_Z} +a^{4}\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+2 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}\right) \ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}}}{5 a^{2}}$&$101$\\ \hline \end{longtable}"," ",0,"1/5*ln(a+x)/a^2+1/5*sum(_R*ln(_R^3*a^5*x+1),_R=RootOf(_Z^4*a^8+_Z^3*a^6+_Z^2*a^4+_Z*a^2+1))","C"
139,1,73,149,0.319000," ","int(x^3/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\ln \left(a +x \right)}{5 a}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{4} \textit{\_Z}^{4}-a^{3} \textit{\_Z}^{3}+\textit{\_Z}^{2} a^{2}-a \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(\textit{\_R}^{3} a^{4}-\textit{\_R}^{2} a^{3}+\textit{\_R} \,a^{2}-a +x \right)\right)}{5}$&$73$\\ default&$-\frac{\ln \left(a +x \right)}{5 a}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}+\textit{\_Z}^{2} a^{2}-a^{3} \textit{\_Z} +a^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{3}+3 \textit{\_R}^{2} a -2 \textit{\_R} \,a^{2}+a^{3}\right) \ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}}}{5 a}$&$97$\\ \hline \end{longtable}"," ",0,"-1/5*ln(a+x)/a+1/5*sum(_R*ln(_R^3*a^4-_R^2*a^3+_R*a^2-a+x),_R=RootOf(_Z^4*a^4-_Z^3*a^3+_Z^2*a^2-_Z*a+1))","C"
140,1,11,10,0.338000," ","int(x^4/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(a^{5}+x^{5}\right)}{5}$&$11$\\ default&$\frac{\ln \left(a^{5}+x^{5}\right)}{5}$&$11$\\ risch&$\frac{\ln \left(a^{5}+x^{5}\right)}{5}$&$11$\\ norman&$\frac{\ln \left(a +x \right)}{5}+\frac{\ln \left(a^{4}-a^{3} x +a^{2} x^{2}-a \,x^{3}+x^{4}\right)}{5}$&$37$\\ \hline \end{longtable}"," ",0,"1/5*ln(a^5+x^5)","A"
141,1,21,20,0.314000," ","int(1/x/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\ln \left(x \right)}{a^{5}}-\frac{\ln \left(a^{5}+x^{5}\right)}{5 a^{5}}$&$21$\\ default&$\frac{\ln \left(x \right)}{a^{5}}-\frac{\ln \left(a +x \right)}{5 a^{5}}-\frac{\ln \left(a^{4}-a^{3} x +a^{2} x^{2}-a \,x^{3}+x^{4}\right)}{5 a^{5}}$&$49$\\ norman&$\frac{\ln \left(x \right)}{a^{5}}-\frac{\ln \left(a +x \right)}{5 a^{5}}-\frac{\ln \left(a^{4}-a^{3} x +a^{2} x^{2}-a \,x^{3}+x^{4}\right)}{5 a^{5}}$&$49$\\ \hline \end{longtable}"," ",0,"ln(x)/a^5-1/5*ln(a^5+x^5)/a^5","A"
142,1,76,157,0.362000," ","int(1/x^2/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{1}{a^{5} x}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{24} \textit{\_Z}^{4}+a^{18} \textit{\_Z}^{3}+a^{12} \textit{\_Z}^{2}+a^{6} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(\left(6 \textit{\_R}^{5} a^{30}-5\right) x +a^{25} \textit{\_R}^{4}\right)\right)}{5}+\frac{\ln \left(a +x \right)}{5 a^{6}}$&$76$\\ default&$-\frac{1}{a^{5} x}+\frac{\ln \left(a +x \right)}{5 a^{6}}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}+\textit{\_Z}^{2} a^{2}-a^{3} \textit{\_Z} +a^{4}\right)}{\sum}\frac{\left(-\textit{\_R}^{3}-3 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}\right) \ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}}}{5 a^{6}}$&$109$\\ \hline \end{longtable}"," ",0,"-1/a^5/x+1/5*sum(_R*ln((6*_R^5*a^30-5)*x+a^25*_R^4),_R=RootOf(_Z^4*a^24+_Z^3*a^18+_Z^2*a^12+_Z*a^6+1))+1/5*ln(a+x)/a^6","C"
143,1,78,157,0.349000," ","int(1/x^3/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{1}{2 a^{5} x^{2}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{28} \textit{\_Z}^{4}-a^{21} \textit{\_Z}^{3}+a^{14} \textit{\_Z}^{2}-a^{7} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(\left(-6 \textit{\_R}^{5} a^{35}-5\right) x +a^{15} \textit{\_R}^{2}\right)\right)}{5}-\frac{\ln \left(a +x \right)}{5 a^{7}}$&$78$\\ default&$-\frac{\ln \left(a +x \right)}{5 a^{7}}-\frac{1}{2 a^{5} x^{2}}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}+\textit{\_Z}^{2} a^{2}-a^{3} \textit{\_Z} +a^{4}\right)}{\sum}\frac{\left(\textit{\_R}^{3}-2 \textit{\_R}^{2} a -2 \textit{\_R} \,a^{2}+a^{3}\right) \ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}}}{5 a^{7}}$&$105$\\ \hline \end{longtable}"," ",0,"-1/2/a^5/x^2+1/5*sum(_R*ln((-6*_R^5*a^35-5)*x+a^15*_R^2),_R=RootOf(_Z^4*a^28-_Z^3*a^21+_Z^2*a^14-_Z*a^7+1))-1/5*ln(a+x)/a^7","C"
144,1,81,157,0.367000," ","int(1/x^4/(a^5+x^5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{1}{3 a^{5} x^{3}}+\frac{\ln \left(-a -x \right)}{5 a^{8}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(a^{32} \textit{\_Z}^{4}+a^{24} \textit{\_Z}^{3}+a^{16} \textit{\_Z}^{2}+a^{8} \textit{\_Z} +1\right)}{\sum}\textit{\_R} \ln \left(\left(-6 \textit{\_R}^{5} a^{40}+5\right) x -a^{25} \textit{\_R}^{3}\right)\right)}{5}$&$81$\\ default&$-\frac{1}{3 a^{5} x^{3}}+\frac{\ln \left(a +x \right)}{5 a^{8}}+\frac{\munderset{\textit{\_R} =\RootOf \left(\textit{\_Z}^{4}-a \,\textit{\_Z}^{3}+\textit{\_Z}^{2} a^{2}-a^{3} \textit{\_Z} +a^{4}\right)}{\sum}\frac{\left(-\textit{\_R}^{3}+2 \textit{\_R}^{2} a -3 \textit{\_R} \,a^{2}-a^{3}\right) \ln \left(x -\textit{\_R} \right)}{4 \textit{\_R}^{3}-3 \textit{\_R}^{2} a +2 \textit{\_R} \,a^{2}-a^{3}}}{5 a^{8}}$&$109$\\ \hline \end{longtable}"," ",0,"-1/3/a^5/x^3+1/5/a^8*ln(-a-x)+1/5*sum(_R*ln((-6*_R^5*a^40+5)*x-a^25*_R^3),_R=RootOf(_Z^4*a^32+_Z^3*a^24+_Z^2*a^16+_Z*a^8+1))","C"
145,0,0,40,0.035000," ","int(1/(x^m)/(a^5+x^5),x)","\[\int \frac{x^{-m}}{a^{5}+x^{5}}\, dx\]"," ",0,"int(1/(x^m)/(a^5+x^5),x)","F"
146,1,10,27,0.283000," ","int((x^4+1)/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\arctan \left(x \right)+\frac{\arctan \left(x^{3}\right)}{3}$&$10$\\ default&$\frac{2 \arctan \left(x \right)}{3}+\frac{\arctan \left(2 x -\sqrt{3}\right)}{3}+\frac{\arctan \left(2 x +\sqrt{3}\right)}{3}$&$28$\\ meijerg&$\frac{x^{5} \sqrt{3}\, \ln \left(1-\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{6}}+\left(x^{6}\right)^{\frac{1}{3}}\right)}{12 \left(x^{6}\right)^{\frac{5}{6}}}+\frac{x^{5} \arctan \left(\frac{\left(x^{6}\right)^{\frac{1}{6}}}{2-\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{6}}}\right)}{6 \left(x^{6}\right)^{\frac{5}{6}}}+\frac{x^{5} \arctan \left(\left(x^{6}\right)^{\frac{1}{6}}\right)}{3 \left(x^{6}\right)^{\frac{5}{6}}}-\frac{x^{5} \sqrt{3}\, \ln \left(1+\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{6}}+\left(x^{6}\right)^{\frac{1}{3}}\right)}{12 \left(x^{6}\right)^{\frac{5}{6}}}+\frac{x^{5} \arctan \left(\frac{\left(x^{6}\right)^{\frac{1}{6}}}{2+\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{6}}}\right)}{6 \left(x^{6}\right)^{\frac{5}{6}}}-\frac{x \sqrt{3}\, \ln \left(1-\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{6}}+\left(x^{6}\right)^{\frac{1}{3}}\right)}{12 \left(x^{6}\right)^{\frac{1}{6}}}+\frac{x \arctan \left(\frac{\left(x^{6}\right)^{\frac{1}{6}}}{2-\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{6}}}\right)}{6 \left(x^{6}\right)^{\frac{1}{6}}}+\frac{x \arctan \left(\left(x^{6}\right)^{\frac{1}{6}}\right)}{3 \left(x^{6}\right)^{\frac{1}{6}}}+\frac{x \sqrt{3}\, \ln \left(1+\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{6}}+\left(x^{6}\right)^{\frac{1}{3}}\right)}{12 \left(x^{6}\right)^{\frac{1}{6}}}+\frac{x \arctan \left(\frac{\left(x^{6}\right)^{\frac{1}{6}}}{2+\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{6}}}\right)}{6 \left(x^{6}\right)^{\frac{1}{6}}}$&$274$\\ \hline \end{longtable}"," ",0,"arctan(x)+1/3*arctan(x^3)","A"
147,1,44,51,0.426000," ","int(1/(x^2+3*x+5)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{6}{121} x^{3}+\frac{27}{121} x^{2}+\frac{68}{121} x +\frac{123}{242}}{\left(x^{2}+3 x +5\right)^{2}}+\frac{12 \arctan \left(\frac{\left(3+2 x \right) \sqrt{11}}{11}\right) \sqrt{11}}{1331}$&$44$\\ default&$\frac{3+2 x}{22 \left(x^{2}+3 x +5\right)^{2}}+\frac{\frac{9}{121}+\frac{6 x}{121}}{x^{2}+3 x +5}+\frac{12 \arctan \left(\frac{\left(3+2 x \right) \sqrt{11}}{11}\right) \sqrt{11}}{1331}$&$52$\\ \hline \end{longtable}"," ",0,"(6/121*x^3+27/121*x^2+68/121*x+123/242)/(x^2+3*x+5)^2+12/1331*arctan(1/11*(3+2*x)*11^(1/2))*11^(1/2)","A"
148,1,28,35,0.275000," ","int((x^4+x^2+1)/(x^2+1)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\frac{7}{16} x^{5}+\frac{5}{6} x^{3}+\frac{9}{16} x}{\left(x^{2}+1\right)^{3}}+\frac{7 \arctan \left(x \right)}{16}$&$28$\\ risch&$\frac{\frac{7}{16} x^{5}+\frac{5}{6} x^{3}+\frac{9}{16} x}{\left(x^{2}+1\right)^{3}}+\frac{7 \arctan \left(x \right)}{16}$&$28$\\ meijerg&$\frac{x \left(15 x^{4}+40 x^{2}+33\right)}{48 \left(x^{2}+1\right)^{3}}+\frac{7 \arctan \left(x \right)}{16}-\frac{x \left(-15 x^{4}+40 x^{2}+15\right)}{240 \left(x^{2}+1\right)^{3}}-\frac{x \left(-3 x^{4}-8 x^{2}+3\right)}{48 \left(x^{2}+1\right)^{3}}$&$72$\\ \hline \end{longtable}"," ",0,"(7/16*x^5+5/6*x^3+9/16*x)/(x^2+1)^3+7/16*arctan(x)","A"
149,1,103,81,0.591000," ","int((A*x+B)/(a*x^2+2*b*x+c)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-2 A b +2 B a \right) x +2 b B -2 A c}{\left(4 a c -4 b^{2}\right) \left(a \,x^{2}+2 b x +c \right)}+\frac{\left(-2 A b +2 B a \right) \arctan \left(\frac{2 a x +2 b}{2 \sqrt{a c -b^{2}}}\right)}{\left(4 a c -4 b^{2}\right) \sqrt{a c -b^{2}}}$&$103$\\ risch&$\frac{-\frac{\left(A b -B a \right) x}{2 \left(a c -b^{2}\right)}-\frac{A c -b B}{2 \left(a c -b^{2}\right)}}{a \,x^{2}+2 b x +c}+\frac{\ln \left(\left(-a^{2} c +a \,b^{2}\right) x -\left(-a c +b^{2}\right)^{\frac{3}{2}}-a b c +b^{3}\right) A b}{4 \left(-a c +b^{2}\right)^{\frac{3}{2}}}-\frac{\ln \left(\left(-a^{2} c +a \,b^{2}\right) x -\left(-a c +b^{2}\right)^{\frac{3}{2}}-a b c +b^{3}\right) B a}{4 \left(-a c +b^{2}\right)^{\frac{3}{2}}}-\frac{\ln \left(\left(a^{2} c -a \,b^{2}\right) x -\left(-a c +b^{2}\right)^{\frac{3}{2}}+a b c -b^{3}\right) A b}{4 \left(-a c +b^{2}\right)^{\frac{3}{2}}}+\frac{\ln \left(\left(a^{2} c -a \,b^{2}\right) x -\left(-a c +b^{2}\right)^{\frac{3}{2}}+a b c -b^{3}\right) B a}{4 \left(-a c +b^{2}\right)^{\frac{3}{2}}}$&$262$\\ \hline \end{longtable}"," ",0,"((-2*A*b+2*B*a)*x+2*b*B-2*A*c)/(4*a*c-4*b^2)/(a*x^2+2*b*x+c)+(-2*A*b+2*B*a)/(4*a*c-4*b^2)/(a*c-b^2)^(1/2)*arctan(1/2*(2*a*x+2*b)/(a*c-b^2)^(1/2))","A"
150,1,35,34,0.397000," ","int((5*x^3-27*x^2+55*x-41)/(x^2-4*x+5)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{1-x}{x^{2}-4 x +5}+2 \arctan \left(-2+x \right)+\frac{5 \ln \left(x^{2}-4 x +5\right)}{2}$&$35$\\ risch&$\frac{1-x}{x^{2}-4 x +5}+2 \arctan \left(-2+x \right)+\frac{5 \ln \left(x^{2}-4 x +5\right)}{2}$&$35$\\ \hline \end{longtable}"," ",0,"(1-x)/(x^2-4*x+5)+2*arctan(-2+x)+5/2*ln(x^2-4*x+5)","A"
151,1,41,46,0.292000," ","int(1/(x^3-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x}{3 \left(x^{3}-1\right)}-\frac{2 \ln \left(-1+x \right)}{9}+\frac{\ln \left(x^{2}+x +1\right)}{9}+\frac{2 \sqrt{3}\, \arctan \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{9}$&$41$\\ default&$\frac{-1+x}{9 x^{2}+9 x +9}+\frac{\ln \left(x^{2}+x +1\right)}{9}+\frac{2 \arctan \left(\frac{\left(1+2 x \right) \sqrt{3}}{3}\right) \sqrt{3}}{9}-\frac{1}{9 \left(-1+x \right)}-\frac{2 \ln \left(-1+x \right)}{9}$&$53$\\ meijerg&$-\frac{\left(-1\right)^{\frac{2}{3}} \left(\frac{3 x \left(-1\right)^{\frac{1}{3}}}{-3 x^{3}+3}-\frac{2 x \left(-1\right)^{\frac{1}{3}} \left(\ln \left(1-\left(x^{3}\right)^{\frac{1}{3}}\right)-\frac{\ln \left(1+\left(x^{3}\right)^{\frac{1}{3}}+\left(x^{3}\right)^{\frac{2}{3}}\right)}{2}-\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(x^{3}\right)^{\frac{1}{3}}}{2+\left(x^{3}\right)^{\frac{1}{3}}}\right)\right)}{3 \left(x^{3}\right)^{\frac{1}{3}}}\right)}{3}$&$86$\\ \hline \end{longtable}"," ",0,"-1/3*x/(x^3-1)-2/9*ln(-1+x)+1/9*ln(x^2+x+1)+2/9*3^(1/2)*arctan(2/3*(1/2+x)*3^(1/2))","A"
152,1,29,30,0.273000," ","int((3*x^4+4)/x^2/(x^2+1)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{4}{x}-\frac{\frac{25}{8} x^{3}+\frac{39}{8} x}{\left(x^{2}+1\right)^{2}}-\frac{57 \arctan \left(x \right)}{8}$&$29$\\ risch&$\frac{-\frac{57}{8} x^{4}-\frac{103}{8} x^{2}-4}{\left(x^{2}+1\right)^{2} x}-\frac{57 \arctan \left(x \right)}{8}$&$29$\\ meijerg&$-\frac{15 x^{4}+25 x^{2}+8}{2 x \left(x^{2}+1\right)^{2}}-\frac{57 \arctan \left(x \right)}{8}-\frac{x \left(-3 x^{2}+3\right)}{8 \left(x^{2}+1\right)^{2}}$&$47$\\ \hline \end{longtable}"," ",0,"-4/x-(25/8*x^3+39/8*x)/(x^2+1)^2-57/8*arctan(x)","A"
153,1,39,40,0.277000," ","int(x/(x^6+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\ln \left(x^{2}+1\right)}{6}-\frac{\ln \left(x^{4}-x^{2}+1\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{2 \left(x^{2}-\frac{1}{2}\right) \sqrt{3}}{3}\right)}{6}$&$39$\\ default&$-\frac{\ln \left(x^{4}-x^{2}+1\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{6}+\frac{\ln \left(x^{2}+1\right)}{6}$&$41$\\ meijerg&$\frac{x^{2} \ln \left(1+\left(x^{6}\right)^{\frac{1}{3}}\right)}{6 \left(x^{6}\right)^{\frac{1}{3}}}-\frac{x^{2} \ln \left(1-\left(x^{6}\right)^{\frac{1}{3}}+\left(x^{6}\right)^{\frac{2}{3}}\right)}{12 \left(x^{6}\right)^{\frac{1}{3}}}+\frac{x^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(x^{6}\right)^{\frac{1}{3}}}{2-\left(x^{6}\right)^{\frac{1}{3}}}\right)}{6 \left(x^{6}\right)^{\frac{1}{3}}}$&$80$\\ \hline \end{longtable}"," ",0,"1/6*ln(x^2+1)-1/12*ln(x^4-x^2+1)+1/6*3^(1/2)*arctan(2/3*(x^2-1/2)*3^(1/2))","A"
154,1,14,13,0.303000," ","int((-1+x^(-1+n))/(-n*x+x^n),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\ln \left(-n x +x^{n}\right)}{n}$&$14$\\ norman&$\frac{\ln \left(n x -{\mathrm e}^{n \ln \left(x \right)}\right)}{n}$&$17$\\ \hline \end{longtable}"," ",0,"ln(-n*x+x^n)/n","A"
155,1,35,34,0.033000," ","int(x^3/(3*x^4-2*x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(3 x^{4}-2 x^{2}+1\right)}{12}+\frac{\sqrt{2}\, \arctan \left(\frac{\left(6 x^{2}-2\right) \sqrt{2}}{4}\right)}{12}$&$35$\\ risch&$\frac{\ln \left(9 x^{4}-6 x^{2}+3\right)}{12}+\frac{\sqrt{2}\, \arctan \left(\frac{\left(3 x^{2}-1\right) \sqrt{2}}{2}\right)}{12}$&$35$\\ \hline \end{longtable}"," ",0,"1/12*ln(3*x^4-2*x^2+1)+1/12*2^(1/2)*arctan(1/4*(6*x^2-2)*2^(1/2))","A"
156,1,25,26,0.026000," ","int(x^5/(3*x^4+x^2-4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{2}}{6}-\frac{8 \ln \left(3 x^{2}+4\right)}{63}+\frac{\ln \left(x^{2}-1\right)}{14}$&$25$\\ risch&$\frac{x^{2}}{6}-\frac{8 \ln \left(3 x^{2}+4\right)}{63}+\frac{\ln \left(x^{2}-1\right)}{14}$&$25$\\ norman&$\frac{x^{2}}{6}+\frac{\ln \left(-1+x \right)}{14}+\frac{\ln \left(1+x \right)}{14}-\frac{8 \ln \left(3 x^{2}+4\right)}{63}$&$29$\\ \hline \end{longtable}"," ",0,"1/6*x^2-8/63*ln(3*x^2+4)+1/14*ln(x^2-1)","A"
157,1,18,21,0.029000," ","int(x^2/(x^6-10*x^3+9),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(x^{3}-9\right)}{24}-\frac{\ln \left(x^{3}-1\right)}{24}$&$18$\\ risch&$\frac{\ln \left(x^{3}-9\right)}{24}-\frac{\ln \left(x^{3}-1\right)}{24}$&$18$\\ norman&$-\frac{\ln \left(-1+x \right)}{24}+\frac{\ln \left(x^{3}-9\right)}{24}-\frac{\ln \left(x^{2}+x +1\right)}{24}$&$25$\\ \hline \end{longtable}"," ",0,"1/24*ln(x^3-9)-1/24*ln(x^3-1)","A"
158,1,22,34,0.293000," ","int((x^3-4*x^2+1)/(-2+x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-2 x^{2}+10 x -\frac{29}{3}}{\left(-2+x \right)^{3}}+\ln \left(-2+x \right)$&$22$\\ risch&$\frac{-2 x^{2}+10 x -\frac{29}{3}}{\left(-2+x \right)^{3}}+\ln \left(-2+x \right)$&$22$\\ default&$\frac{2}{\left(-2+x \right)^{2}}+\frac{7}{3 \left(-2+x \right)^{3}}+\ln \left(-2+x \right)-\frac{2}{-2+x}$&$27$\\ meijerg&$\frac{x \left(\frac{1}{4} x^{2}-\frac{3}{2} x +3\right)}{48 \left(1-\frac{x}{2}\right)^{3}}+\frac{x \left(\frac{11}{2} x^{2}-15 x +12\right)}{24 \left(1-\frac{x}{2}\right)^{3}}+\ln \left(1-\frac{x}{2}\right)-\frac{x^{3}}{12 \left(1-\frac{x}{2}\right)^{3}}$&$60$\\ \hline \end{longtable}"," ",0,"(-2*x^2+10*x-29/3)/(-2+x)^3+ln(-2+x)","A"
159,1,22,37,0.288000," ","int(x^3/(-1+x)^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-\frac{1}{8} x^{3}+\frac{1}{24} x^{2}-\frac{1}{120} x +\frac{1}{1320}}{\left(-1+x \right)^{11}}$&$22$\\ risch&$\frac{-\frac{1}{8} x^{3}+\frac{1}{24} x^{2}-\frac{1}{120} x +\frac{1}{1320}}{\left(-1+x \right)^{11}}$&$22$\\ gosper&$-\frac{165 x^{3}-55 x^{2}+11 x -1}{1320 \left(-1+x \right)^{11}}$&$23$\\ default&$-\frac{1}{8 \left(-1+x \right)^{8}}-\frac{3}{10 \left(-1+x \right)^{10}}-\frac{1}{11 \left(-1+x \right)^{11}}-\frac{1}{3 \left(-1+x \right)^{9}}$&$30$\\ meijerg&$\frac{x^{4} \left(-x^{7}+11 x^{6}-55 x^{5}+165 x^{4}-330 x^{3}+462 x^{2}-462 x +330\right)}{1320 \left(1-x \right)^{11}}$&$48$\\ \hline \end{longtable}"," ",0,"1/(-1+x)^11*(-1/8*x^3+1/24*x^2-1/120*x+1/1320)","A"
160,1,34,45,0.263000," ","int((x^4-3*x)/(1+2*x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{3}+\frac{9}{8} x^{2}+\frac{23}{24} x +\frac{49}{384}}{\left(1+2 x \right)^{4}}+\frac{\ln \left(1+2 x \right)}{32}$&$34$\\ norman&$\frac{-\frac{37}{12} x^{3}-\frac{31}{16} x^{2}-\frac{1}{16} x -\frac{49}{24} x^{4}}{\left(1+2 x \right)^{4}}+\frac{\ln \left(1+2 x \right)}{32}$&$37$\\ default&$-\frac{25}{128 \left(1+2 x \right)^{4}}+\frac{7}{24 \left(1+2 x \right)^{3}}-\frac{3}{32 \left(1+2 x \right)^{2}}+\frac{1}{8+16 x}+\frac{\ln \left(1+2 x \right)}{32}$&$46$\\ meijerg&$-\frac{x \left(1000 x^{3}+1040 x^{2}+420 x +60\right)}{960 \left(1+2 x \right)^{4}}+\frac{\ln \left(1+2 x \right)}{32}-\frac{x^{2} \left(4 x^{2}+8 x +6\right)}{4 \left(1+2 x \right)^{4}}$&$57$\\ \hline \end{longtable}"," ",0,"16*(1/16*x^3+9/128*x^2+23/384*x+49/6144)/(1+2*x)^4+1/32*ln(1+2*x)","A"
161,1,35,28,0.286000," ","int(1/(-1+x)^2/(1+x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{8 \left(-1+x \right)}-\frac{3 \ln \left(-1+x \right)}{16}-\frac{1}{8 \left(1+x \right)^{2}}-\frac{1}{4 \left(1+x \right)}+\frac{3 \ln \left(1+x \right)}{16}$&$35$\\ norman&$\frac{-\frac{3}{8} x -\frac{3}{8} x^{2}+\frac{1}{4}}{\left(-1+x \right) \left(1+x \right)^{2}}-\frac{3 \ln \left(-1+x \right)}{16}+\frac{3 \ln \left(1+x \right)}{16}$&$35$\\ risch&$\frac{-\frac{3}{8} x -\frac{3}{8} x^{2}+\frac{1}{4}}{\left(-1+x \right) \left(1+x \right)^{2}}-\frac{3 \ln \left(-1+x \right)}{16}+\frac{3 \ln \left(1+x \right)}{16}$&$35$\\ \hline \end{longtable}"," ",0,"-1/8/(-1+x)-3/16*ln(-1+x)-1/8/(1+x)^2-1/4/(1+x)+3/16*ln(1+x)","A"
162,1,28,27,0.312000," ","int(1/(5-6*x)^2/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{25 x}+\frac{12 \ln \left(x \right)}{125}-\frac{6}{25 \left(-5+6 x \right)}-\frac{12 \ln \left(-5+6 x \right)}{125}$&$28$\\ risch&$\frac{-\frac{12 x}{25}+\frac{1}{5}}{x \left(-5+6 x \right)}+\frac{12 \ln \left(x \right)}{125}-\frac{12 \ln \left(-5+6 x \right)}{125}$&$31$\\ norman&$\frac{\frac{1}{5}-\frac{72 x^{2}}{125}}{x \left(-5+6 x \right)}+\frac{12 \ln \left(x \right)}{125}-\frac{12 \ln \left(-5+6 x \right)}{125}$&$32$\\ meijerg&$\frac{108 x}{625 \left(3-\frac{18 x}{5}\right)}-\frac{12 \ln \left(1-\frac{6 x}{5}\right)}{125}+\frac{6}{125}+\frac{12 \ln \left(x \right)}{125}+\frac{12 \ln \left(2\right)}{125}+\frac{12 \ln \left(3\right)}{125}-\frac{12 \ln \left(5\right)}{125}+\frac{12 i \pi}{125}-\frac{1}{25 x}$&$46$\\ \hline \end{longtable}"," ",0,"-1/25/x+12/125*ln(x)-6/25/(-5+6*x)-12/125*ln(-5+6*x)","A"
163,1,40,53,0.288000," ","int(1/(x^2-2*x-3)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{\frac{3}{128} x^{3}-\frac{9}{128} x^{2}-\frac{11}{128} x +\frac{17}{128}}{\left(x^{2}-2 x -3\right)^{2}}+\frac{3 \ln \left(-3+x \right)}{512}-\frac{3 \ln \left(1+x \right)}{512}$&$40$\\ risch&$\frac{\frac{3}{128} x^{3}-\frac{9}{128} x^{2}-\frac{11}{128} x +\frac{17}{128}}{\left(x^{2}-2 x -3\right)^{2}}+\frac{3 \ln \left(-3+x \right)}{512}-\frac{3 \ln \left(1+x \right)}{512}$&$40$\\ default&$-\frac{1}{128 \left(-3+x \right)^{2}}+\frac{3}{256 \left(-3+x \right)}+\frac{3 \ln \left(-3+x \right)}{512}+\frac{1}{128 \left(1+x \right)^{2}}+\frac{3}{256 \left(1+x \right)}-\frac{3 \ln \left(1+x \right)}{512}$&$42$\\ \hline \end{longtable}"," ",0,"(3/128*x^3-9/128*x^2-11/128*x+17/128)/(x^2-2*x-3)^2+3/512*ln(-3+x)-3/512*ln(1+x)","A"
164,1,36,39,0.366000," ","int(1/(x^2-4*x+13)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{1}{216} x^{3}-\frac{1}{36} x^{2}+\frac{1}{8} x -\frac{19}{108}}{\left(x^{2}-4 x +13\right)^{2}}+\frac{\arctan \left(-\frac{2}{3}+\frac{x}{3}\right)}{648}$&$36$\\ default&$\frac{2 x -4}{72 \left(x^{2}-4 x +13\right)^{2}}+\frac{2 x -4}{432 x^{2}-1728 x +5616}+\frac{\arctan \left(-\frac{2}{3}+\frac{x}{3}\right)}{648}$&$44$\\ \hline \end{longtable}"," ",0,"(1/216*x^3-1/36*x^2+1/8*x-19/108)/(x^2-4*x+13)^2+1/648*arctan(-2/3+1/3*x)","A"
165,1,45,48,0.310000," ","int(1/(2+x)^3/(3+x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{10 x^{4}+105 x^{3}+\frac{1225}{3} x^{2}+\frac{4175}{6} x +\frac{2627}{6}}{\left(2+x \right)^{2} \left(3+x \right)^{3}}+10 \ln \left(2+x \right)-10 \ln \left(3+x \right)$&$45$\\ risch&$\frac{10 x^{4}+105 x^{3}+\frac{1225}{3} x^{2}+\frac{4175}{6} x +\frac{2627}{6}}{\left(2+x \right)^{2} \left(3+x \right)^{3}}+10 \ln \left(2+x \right)-10 \ln \left(3+x \right)$&$45$\\ default&$-\frac{1}{2 \left(2+x \right)^{2}}+\frac{4}{2+x}+\frac{1}{3 \left(3+x \right)^{3}}+\frac{3}{2 \left(3+x \right)^{2}}+\frac{6}{3+x}+10 \ln \left(2+x \right)-10 \ln \left(3+x \right)$&$49$\\ \hline \end{longtable}"," ",0,"(10*x^4+105*x^3+1225/3*x^2+4175/6*x+2627/6)/(2+x)^2/(3+x)^3+10*ln(2+x)-10*ln(3+x)","A"
166,1,32,31,0.378000," ","int(x^6/(x^2-2)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$4 x +\frac{x^{3}}{3}-\frac{2 x}{x^{2}-2}-5 \arctanh \left(\frac{x \sqrt{2}}{2}\right) \sqrt{2}$&$32$\\ risch&$\frac{x^{3}}{3}+4 x -\frac{2 x}{x^{2}-2}+\frac{5 \sqrt{2}\, \ln \left(x -\sqrt{2}\right)}{2}-\frac{5 \sqrt{2}\, \ln \left(x +\sqrt{2}\right)}{2}$&$44$\\ meijerg&$i \sqrt{2}\, \left(-\frac{i x \sqrt{2}\, \left(-\frac{7}{2} x^{4}-35 x^{2}+105\right)}{42 \left(-\frac{x^{2}}{2}+1\right)}+5 i \arctanh \left(\frac{x \sqrt{2}}{2}\right)\right)$&$46$\\ \hline \end{longtable}"," ",0,"4*x+1/3*x^3-2*x/(x^2-2)-5*arctanh(1/2*x*2^(1/2))*2^(1/2)","A"
167,1,31,46,0.268000," ","int(x^8/(x^2+4)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$x +\frac{\frac{29}{4} x^{5}+\frac{136}{3} x^{3}+76 x}{\left(x^{2}+4\right)^{3}}-\frac{35 \arctan \left(\frac{x}{2}\right)}{8}$&$31$\\ default&$x -\frac{16 \left(-\frac{29}{64} x^{5}-\frac{17}{6} x^{3}-\frac{19}{4} x \right)}{\left(x^{2}+4\right)^{3}}-\frac{35 \arctan \left(\frac{x}{2}\right)}{8}$&$32$\\ meijerg&$\frac{x \left(\frac{9}{4} x^{6}+\frac{693}{16} x^{4}+210 x^{2}+315\right)}{144 \left(\frac{x^{2}}{4}+1\right)^{3}}-\frac{35 \arctan \left(\frac{x}{2}\right)}{8}$&$37$\\ \hline \end{longtable}"," ",0,"x+(29/4*x^5+136/3*x^3+76*x)/(x^2+4)^3-35/8*arctan(1/2*x)","A"
168,1,34,36,0.512000," ","int((-4+7*x)/(3*x^2+2*x+5)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{19 x}{84}-\frac{13}{28}}{x^{2}+\frac{2}{3} x +\frac{5}{3}}-\frac{19 \arctan \left(\frac{\left(1+3 x \right) \sqrt{14}}{14}\right) \sqrt{14}}{392}$&$34$\\ default&$\frac{-38 x -78}{168 x^{2}+112 x +280}-\frac{19 \sqrt{14}\, \arctan \left(\frac{\left(6 x +2\right) \sqrt{14}}{28}\right)}{392}$&$37$\\ \hline \end{longtable}"," ",0,"(-19/84*x-13/28)/(x^2+2/3*x+5/3)-19/392*arctan(1/14*(1+3*x)*14^(1/2))*14^(1/2)","A"
169,1,37,36,0.353000," ","int((5-4*x)/(3*x^2-4*x-2)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{14 x -36}{40 \left(3 x^{2}-4 x -2\right)}+\frac{7 \sqrt{10}\, \arctanh \left(\frac{\left(6 x -4\right) \sqrt{10}}{20}\right)}{200}$&$37$\\ risch&$\frac{-\frac{7 x}{60}+\frac{3}{10}}{x^{2}-\frac{4}{3} x -\frac{2}{3}}+\frac{7 \sqrt{10}\, \ln \left(3 x -2+\sqrt{10}\right)}{400}-\frac{7 \sqrt{10}\, \ln \left(3 x -2-\sqrt{10}\right)}{400}$&$48$\\ \hline \end{longtable}"," ",0,"-1/40*(14*x-36)/(3*x^2-4*x-2)+7/200*10^(1/2)*arctanh(1/20*(6*x-4)*10^(1/2))","A"
170,1,27,31,0.269000," ","int(x^5/(x^4+1)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{x^{2} \left(-3 x^{4}+3\right)}{48 \left(x^{4}+1\right)^{2}}+\frac{\arctan \left(x^{2}\right)}{16}$&$27$\\ risch&$\frac{\frac{1}{16} x^{6}-\frac{1}{16} x^{2}}{\left(x^{4}+1\right)^{2}}+\frac{\arctan \left(x^{2}\right)}{16}$&$27$\\ default&$\frac{\frac{1}{8} x^{6}-\frac{1}{8} x^{2}}{2 \left(x^{4}+1\right)^{2}}+\frac{\arctan \left(x^{2}\right)}{16}$&$28$\\ \hline \end{longtable}"," ",0,"-1/48*x^2*(-3*x^4+3)/(x^4+1)^2+1/16*arctan(x^2)","A"
171,1,29,28,0.256000," ","int(x*(x^2+1)^3/(x^4+2*x^2+2)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{1}{4 x^{4}+8 x^{2}+8}+\frac{\ln \left(x^{4}+2 x^{2}+2\right)}{4}$&$29$\\ norman&$\frac{1}{4 x^{4}+8 x^{2}+8}+\frac{\ln \left(x^{4}+2 x^{2}+2\right)}{4}$&$29$\\ risch&$\frac{1}{4 x^{4}+8 x^{2}+8}+\frac{\ln \left(x^{4}+2 x^{2}+2\right)}{4}$&$29$\\ \hline \end{longtable}"," ",0,"1/4/(x^4+2*x^2+2)+1/4*ln(x^4+2*x^2+2)","A"
172,1,12,11,0.258000," ","int(x^3/(a^4+x^4)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{1}{8 \left(a^{4}+x^{4}\right)^{2}}$&$12$\\ derivativedivides&$-\frac{1}{8 \left(a^{4}+x^{4}\right)^{2}}$&$12$\\ default&$-\frac{1}{8 \left(a^{4}+x^{4}\right)^{2}}$&$12$\\ norman&$-\frac{1}{8 \left(a^{4}+x^{4}\right)^{2}}$&$12$\\ risch&$-\frac{1}{8 \left(a^{4}+x^{4}\right)^{2}}$&$12$\\ \hline \end{longtable}"," ",0,"-1/8/(a^4+x^4)^2","A"
173,1,45,48,0.268000," ","int(1/x/(a^4+x^4)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{\frac{3}{8 a^{4}}+\frac{x^{4}}{4 a^{8}}}{\left(a^{4}+x^{4}\right)^{2}}+\frac{\ln \left(x \right)}{a^{12}}-\frac{\ln \left(a^{4}+x^{4}\right)}{4 a^{12}}$&$45$\\ risch&$\frac{\frac{3}{8 a^{4}}+\frac{x^{4}}{4 a^{8}}}{\left(a^{4}+x^{4}\right)^{2}}+\frac{\ln \left(x \right)}{a^{12}}-\frac{\ln \left(a^{4}+x^{4}\right)}{4 a^{12}}$&$45$\\ default&$-\frac{-\frac{a^{4}}{2 \left(a^{4}+x^{4}\right)}+\frac{\ln \left(a^{4}+x^{4}\right)}{2}-\frac{a^{8}}{4 \left(a^{4}+x^{4}\right)^{2}}}{2 a^{12}}+\frac{\ln \left(x \right)}{a^{12}}$&$52$\\ \hline \end{longtable}"," ",0,"(3/8/a^4+1/4/a^8*x^4)/(a^4+x^4)^2+ln(x)/a^12-1/4*ln(a^4+x^4)/a^12","A"
174,1,75,127,0.282000," ","int(1/x^2/(a^4+x^4)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{45 x^{8}}{32 a^{12}}-\frac{81 x^{4}}{32 a^{8}}-\frac{1}{a^{4}}}{x \left(a^{4}+x^{4}\right)^{2}}+\frac{45 \left(\munderset{\textit{\_R} =\RootOf \left(a^{52} \textit{\_Z}^{4}+1\right)}{\sum}\textit{\_R} \ln \left(\left(5 \textit{\_R}^{4} a^{52}+4\right) x +\textit{\_R}^{3} a^{40}\right)\right)}{128}$&$75$\\ default&$-\frac{\frac{\frac{17}{32} a^{4} x^{3}+\frac{13}{32} x^{7}}{\left(a^{4}+x^{4}\right)^{2}}+\frac{45 \sqrt{2}\, \left(\ln \left(\frac{x^{2}-\left(a^{4}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{a^{4}}}{x^{2}+\left(a^{4}\right)^{\frac{1}{4}} x \sqrt{2}+\sqrt{a^{4}}}\right)+2 \arctan \left(\frac{\sqrt{2}\, x}{\left(a^{4}\right)^{\frac{1}{4}}}+1\right)+2 \arctan \left(\frac{\sqrt{2}\, x}{\left(a^{4}\right)^{\frac{1}{4}}}-1\right)\right)}{256 \left(a^{4}\right)^{\frac{1}{4}}}}{a^{12}}-\frac{1}{a^{12} x}$&$124$\\ \hline \end{longtable}"," ",0,"(-45/32/a^12*x^8-81/32/a^8*x^4-1/a^4)/x/(a^4+x^4)^2+45/128*sum(_R*ln((5*_R^4*a^52+4)*x+_R^3*a^40),_R=RootOf(_Z^4*a^52+1))","C"
175,1,53,56,0.289000," ","int(1/x^3/(a^4+x^4)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\frac{\frac{9}{8} a^{4} x^{2}+\frac{7}{8} x^{6}}{\left(a^{4}+x^{4}\right)^{2}}+\frac{15 \arctan \left(\frac{x^{2}}{a^{2}}\right)}{8 a^{2}}}{2 a^{12}}-\frac{1}{2 a^{12} x^{2}}$&$53$\\ risch&$\frac{-\frac{15 x^{8}}{16 a^{12}}-\frac{25 x^{4}}{16 a^{8}}-\frac{1}{2 a^{4}}}{x^{2} \left(a^{4}+x^{4}\right)^{2}}+\frac{15 \left(\munderset{\textit{\_R} =\RootOf \left(a^{28} \textit{\_Z}^{2}+1\right)}{\sum}\textit{\_R} \ln \left(\left(-5 \textit{\_R}^{2} a^{28}-4\right) x^{2}-a^{16} \textit{\_R} \right)\right)}{32}$&$76$\\ \hline \end{longtable}"," ",0,"-1/2/a^12*((9/8*a^4*x^2+7/8*x^6)/(a^4+x^4)^2+15/8*arctan(x^2/a^2)/a^2)-1/2/a^12/x^2","A"
176,1,29,33,0.262000," ","int(x^14/(2*x^5+3)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{\frac{3 x^{5}}{10}+\frac{27}{80}}{\left(2 x^{5}+3\right)^{2}}+\frac{\ln \left(2 x^{5}+3\right)}{40}$&$29$\\ risch&$\frac{\frac{3 x^{5}}{10}+\frac{27}{80}}{\left(2 x^{5}+3\right)^{2}}+\frac{\ln \left(2 x^{5}+3\right)}{40}$&$30$\\ meijerg&$-\frac{x^{5} \left(6 x^{5}+6\right)}{360 \left(1+\frac{2 x^{5}}{3}\right)^{2}}+\frac{\ln \left(1+\frac{2 x^{5}}{3}\right)}{40}$&$33$\\ default&$-\frac{9}{80 \left(2 x^{5}+3\right)^{2}}+\frac{3}{20 \left(2 x^{5}+3\right)}+\frac{\ln \left(2 x^{5}+3\right)}{40}$&$34$\\ \hline \end{longtable}"," ",0,"(3/10*x^5+27/80)/(2*x^5+3)^2+1/40*ln(2*x^5+3)","A"
177,1,47,225,0.273000," ","int(x^6/(2*x^5+3)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{1}{75} x^{7}-\frac{3}{100} x^{2}}{\left(2 x^{5}+3\right)^{2}}+\frac{\left(\munderset{\textit{\_R} =\RootOf \left(2 \textit{\_Z}^{5}+3\right)}{\sum}\frac{\ln \left(x -\textit{\_R} \right)}{\textit{\_R}^{3}}\right)}{500}$&$47$\\ meijerg&$\frac{108^{\frac{4}{5}} \left(-\frac{x^{2} 2^{\frac{2}{5}} 3^{\frac{3}{5}} \left(-\frac{28 x^{5}}{3}+21\right)}{105 \left(1+\frac{2 x^{5}}{3}\right)^{2}}+\frac{2 \,108^{\frac{1}{5}} x^{2} \left(-\frac{2^{\frac{3}{5}} 3^{\frac{2}{5}} \ln \left(1+\frac{2^{\frac{1}{5}} 3^{\frac{4}{5}} \left(x^{5}\right)^{\frac{1}{5}}}{3}\right)}{2 \left(x^{5}\right)^{\frac{2}{5}}}-\frac{2^{\frac{3}{5}} 3^{\frac{2}{5}} \cos \left(\frac{2 \pi}{5}\right) \ln \left(1-\frac{2 \cos \left(\frac{\pi}{5}\right) 2^{\frac{1}{5}} 3^{\frac{4}{5}} \left(x^{5}\right)^{\frac{1}{5}}}{3}+\frac{2^{\frac{2}{5}} 3^{\frac{3}{5}} \left(x^{5}\right)^{\frac{2}{5}}}{3}\right)}{2 \left(x^{5}\right)^{\frac{2}{5}}}+\frac{72^{\frac{1}{5}} \arctan \left(\frac{\sin \left(\frac{\pi}{5}\right) 2^{\frac{1}{5}} 3^{\frac{4}{5}} \left(x^{5}\right)^{\frac{1}{5}}}{3-\cos \left(\frac{\pi}{5}\right) 2^{\frac{1}{5}} 3^{\frac{4}{5}} \left(x^{5}\right)^{\frac{1}{5}}}\right) \sin \left(\frac{2 \pi}{5}\right)}{\left(x^{5}\right)^{\frac{2}{5}}}+\frac{2^{\frac{3}{5}} 3^{\frac{2}{5}} \cos \left(\frac{\pi}{5}\right) \ln \left(1+\frac{2 \cos \left(\frac{2 \pi}{5}\right) 2^{\frac{1}{5}} 3^{\frac{4}{5}} \left(x^{5}\right)^{\frac{1}{5}}}{3}+\frac{2^{\frac{2}{5}} 3^{\frac{3}{5}} \left(x^{5}\right)^{\frac{2}{5}}}{3}\right)}{2 \left(x^{5}\right)^{\frac{2}{5}}}-\frac{72^{\frac{1}{5}} \arctan \left(\frac{\sin \left(\frac{2 \pi}{5}\right) 2^{\frac{1}{5}} 3^{\frac{4}{5}} \left(x^{5}\right)^{\frac{1}{5}}}{3+\cos \left(\frac{2 \pi}{5}\right) 2^{\frac{1}{5}} 3^{\frac{4}{5}} \left(x^{5}\right)^{\frac{1}{5}}}\right) \sin \left(\frac{\pi}{5}\right)}{\left(x^{5}\right)^{\frac{2}{5}}}\right)}{25}\right)}{6480}$&$277$\\ default&$\frac{\frac{1}{75} x^{7}-\frac{3}{100} x^{2}}{\left(2 x^{5}+3\right)^{2}}+\frac{48^{\frac{2}{5}} \ln \left(48^{\frac{1}{5}}+2 x \right)}{150 \left(5+\sqrt{5}\right) \left(\sqrt{5}-5\right)}+\frac{48^{\frac{2}{5}} \ln \left(x \sqrt{5}\, 48^{\frac{1}{5}}-x 48^{\frac{1}{5}}+48^{\frac{2}{5}}+4 x^{2}\right) \sqrt{5}}{12000}+\frac{48^{\frac{2}{5}} \ln \left(x \sqrt{5}\, 48^{\frac{1}{5}}-x 48^{\frac{1}{5}}+48^{\frac{2}{5}}+4 x^{2}\right)}{12000}-\frac{48^{\frac{3}{5}} \sqrt{5}\, \arctan \left(\frac{\sqrt{5}\, 48^{\frac{1}{5}}}{\sqrt{10 \,48^{\frac{2}{5}}+2 \sqrt{5}\, 48^{\frac{2}{5}}}}-\frac{48^{\frac{1}{5}}}{\sqrt{10 \,48^{\frac{2}{5}}+2 \sqrt{5}\, 48^{\frac{2}{5}}}}+\frac{8 x}{\sqrt{10 \,48^{\frac{2}{5}}+2 \sqrt{5}\, 48^{\frac{2}{5}}}}\right)}{1500 \sqrt{10 \,48^{\frac{2}{5}}+2 \sqrt{5}\, 48^{\frac{2}{5}}}}-\frac{48^{\frac{2}{5}} \ln \left(-x \sqrt{5}\, 48^{\frac{1}{5}}+48^{\frac{2}{5}}-x 48^{\frac{1}{5}}+4 x^{2}\right) \sqrt{5}}{12000}+\frac{48^{\frac{2}{5}} \ln \left(-x \sqrt{5}\, 48^{\frac{1}{5}}+48^{\frac{2}{5}}-x 48^{\frac{1}{5}}+4 x^{2}\right)}{12000}+\frac{48^{\frac{3}{5}} \arctan \left(-\frac{\sqrt{5}\, 48^{\frac{1}{5}}}{\sqrt{10 \,48^{\frac{2}{5}}-2 \sqrt{5}\, 48^{\frac{2}{5}}}}-\frac{48^{\frac{1}{5}}}{\sqrt{10 \,48^{\frac{2}{5}}-2 \sqrt{5}\, 48^{\frac{2}{5}}}}+\frac{8 x}{\sqrt{10 \,48^{\frac{2}{5}}-2 \sqrt{5}\, 48^{\frac{2}{5}}}}\right) \sqrt{5}}{1500 \sqrt{10 \,48^{\frac{2}{5}}-2 \sqrt{5}\, 48^{\frac{2}{5}}}}$&$354$\\ \hline \end{longtable}"," ",0,"4*(1/300*x^7-3/400*x^2)/(2*x^5+3)^2+1/500*sum(1/_R^3*ln(x-_R),_R=RootOf(2*_Z^5+3))","C"
178,1,39,46,0.280000," ","int(9/5/x^2/(-2*x^2+3)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{8 \left(\frac{7}{16} x^{3}-\frac{27}{32} x \right)}{15 \left(2 x^{2}-3\right)^{2}}+\frac{\arctanh \left(\frac{x \sqrt{6}}{3}\right) \sqrt{6}}{24}-\frac{1}{15 x}$&$39$\\ meijerg&$\frac{i \sqrt{6}\, \left(\frac{i \sqrt{6}\, \left(\frac{20}{3} x^{4}-\frac{50}{3} x^{2}+8\right)}{4 x \left(-\frac{2 x^{2}}{3}+1\right)^{2}}-\frac{15 i \arctanh \left(\frac{x \sqrt{2}\, \sqrt{3}}{3}\right)}{2}\right)}{180}$&$51$\\ risch&$\frac{-\frac{1}{2} x^{4}+\frac{5}{4} x^{2}-\frac{3}{5}}{\left(2 x^{2}-3\right)^{2} x}+\frac{\sqrt{6}\, \ln \left(x +\frac{\sqrt{6}}{2}\right)}{48}-\frac{\sqrt{6}\, \ln \left(x -\frac{\sqrt{6}}{2}\right)}{48}$&$54$\\ \hline \end{longtable}"," ",0,"-8/15*(7/16*x^3-27/32*x)/(2*x^2-3)^2+1/24*arctanh(1/3*x*6^(1/2))*6^(1/2)-1/15/x","A"
179,1,29,30,0.000000," ","int((3*x^4+4)/x^2/(x^2+1)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{4}{x}-\frac{\frac{25}{8} x^{3}+\frac{39}{8} x}{\left(x^{2}+1\right)^{2}}-\frac{57 \arctan \left(x \right)}{8}$&$29$\\ risch&$\frac{-\frac{57}{8} x^{4}-\frac{103}{8} x^{2}-4}{\left(x^{2}+1\right)^{2} x}-\frac{57 \arctan \left(x \right)}{8}$&$29$\\ meijerg&$-\frac{15 x^{4}+25 x^{2}+8}{2 x \left(x^{2}+1\right)^{2}}-\frac{57 \arctan \left(x \right)}{8}-\frac{x \left(-3 x^{2}+3\right)}{8 \left(x^{2}+1\right)^{2}}$&$47$\\ \hline \end{longtable}"," ",0,"-4/x-(25/8*x^3+39/8*x)/(x^2+1)^2-57/8*arctan(x)","A"
180,1,31,36,0.032000," ","int((-x^4+5*x^3+6*x^2-3*x+5)/(x^5-x^4-2*x^3+2*x^2+x-1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\ln \left(-1+x \right)-\frac{3}{2 \left(-1+x \right)^{2}}-\frac{2}{-1+x}+\frac{1}{1+x}-2 \ln \left(1+x \right)$&$31$\\ norman&$\frac{-x^{2}-\frac{7}{2} x +\frac{3}{2}}{\left(-1+x \right)^{2} \left(1+x \right)}-2 \ln \left(1+x \right)+\ln \left(-1+x \right)$&$33$\\ risch&$\frac{-x^{2}-\frac{7}{2} x +\frac{3}{2}}{x^{3}-x^{2}-x +1}-2 \ln \left(1+x \right)+\ln \left(-1+x \right)$&$38$\\ \hline \end{longtable}"," ",0,"ln(-1+x)-3/2/(-1+x)^2-2/(-1+x)+1/(1+x)-2*ln(1+x)","A"
181,1,54,53,0.313000," ","int((x^2+1)/x/(x^3+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{x^{2}}{3}+\frac{1}{3}}{x^{3}+1}-\frac{5 \ln \left(4 x^{2}-4 x +4\right)}{18}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(-1+2 x \right) \sqrt{3}}{3}\right)}{9}-\frac{4 \ln \left(1+x \right)}{9}+\ln \left(x \right)$&$54$\\ default&$\ln \left(x \right)-\frac{-1-x}{9 \left(x^{2}-x +1\right)}-\frac{5 \ln \left(x^{2}-x +1\right)}{18}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(-1+2 x \right) \sqrt{3}}{3}\right)}{9}+\frac{2}{9 \left(1+x \right)}-\frac{4 \ln \left(1+x \right)}{9}$&$61$\\ meijerg&$\frac{x^{2}}{3 x^{3}+3}-\frac{x^{2} \ln \left(1+\left(x^{3}\right)^{\frac{1}{3}}\right)}{9 \left(x^{3}\right)^{\frac{2}{3}}}+\frac{x^{2} \ln \left(1-\left(x^{3}\right)^{\frac{1}{3}}+\left(x^{3}\right)^{\frac{2}{3}}\right)}{18 \left(x^{3}\right)^{\frac{2}{3}}}+\frac{x^{2} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(x^{3}\right)^{\frac{1}{3}}}{2-\left(x^{3}\right)^{\frac{1}{3}}}\right)}{9 \left(x^{3}\right)^{\frac{2}{3}}}-\frac{2 x^{3}}{3 \left(2 x^{3}+2\right)}-\frac{\ln \left(x^{3}+1\right)}{3}+\frac{1}{3}+\ln \left(x \right)$&$118$\\ \hline \end{longtable}"," ",0,"(1/3*x^2+1/3)/(x^3+1)-5/18*ln(4*x^2-4*x+4)+1/9*3^(1/2)*arctan(1/3*(-1+2*x)*3^(1/2))-4/9*ln(1+x)+ln(x)","A"
182,1,54,54,0.398000," ","int((x^2-3*x-2)/(1+x)^2/(x^2+x+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{-\frac{5 x}{3}-\frac{7}{3}}{x^{2}+x +1}+\frac{\ln \left(x^{2}+x +1\right)}{2}-\frac{25 \arctan \left(\frac{\left(1+2 x \right) \sqrt{3}}{3}\right) \sqrt{3}}{9}-\frac{2}{1+x}-\ln \left(1+x \right)$&$54$\\ risch&$\frac{-\frac{11}{3} x^{2}-6 x -\frac{13}{3}}{\left(x^{2}+x +1\right) \left(1+x \right)}-\ln \left(1+x \right)+\frac{\ln \left(625 x^{2}+625 x +625\right)}{2}-\frac{25 \sqrt{3}\, \arctan \left(\frac{2 \left(25 x +\frac{25}{2}\right) \sqrt{3}}{75}\right)}{9}$&$61$\\ \hline \end{longtable}"," ",0,"(-5/3*x-7/3)/(x^2+x+1)+1/2*ln(x^2+x+1)-25/9*arctan(1/3*(1+2*x)*3^(1/2))*3^(1/2)-2/(1+x)-ln(1+x)","A"
183,1,32,35,0.320000," ","int(1/(1-4*x)^3/(2-3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{12 x}{25}-\frac{1}{50}}{\left(4 x -1\right)^{2}}+\frac{9 \ln \left(-2+3 x \right)}{125}-\frac{9 \ln \left(4 x -1\right)}{125}$&$32$\\ norman&$\frac{\frac{8}{25} x +\frac{8}{25} x^{2}}{\left(4 x -1\right)^{2}}+\frac{9 \ln \left(-2+3 x \right)}{125}-\frac{9 \ln \left(4 x -1\right)}{125}$&$35$\\ default&$\frac{9 \ln \left(-2+3 x \right)}{125}+\frac{1}{10 \left(4 x -1\right)^{2}}+\frac{3}{25 \left(4 x -1\right)}-\frac{9 \ln \left(4 x -1\right)}{125}$&$36$\\ \hline \end{longtable}"," ",0,"16*(3/100*x-1/800)/(4*x-1)^2+9/125*ln(-2+3*x)-9/125*ln(4*x-1)","A"
184,1,19,23,0.289000," ","int(x^3/(-5*x^2+2)^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{15 x^{2}-1}{750 \left(5 x^{2}-2\right)^{6}}$&$19$\\ risch&$\frac{\frac{x^{2}}{50}-\frac{1}{750}}{\left(5 x^{2}-2\right)^{6}}$&$19$\\ default&$\frac{1}{150 \left(5 x^{2}-2\right)^{6}}+\frac{1}{250 \left(5 x^{2}-2\right)^{5}}$&$24$\\ norman&$\frac{-\frac{25}{32} x^{10}-\frac{5}{12} x^{6}+\frac{1}{8} x^{4}+\frac{25}{32} x^{8}+\frac{125}{384} x^{12}}{\left(5 x^{2}-2\right)^{6}}$&$37$\\ meijerg&$\frac{x^{4} \left(\frac{625}{16} x^{8}-\frac{375}{4} x^{6}+\frac{375}{4} x^{4}-50 x^{2}+15\right)}{7680 \left(1-\frac{5 x^{2}}{2}\right)^{6}}$&$37$\\ \hline \end{longtable}"," ",0,"1/750*(15*x^2-1)/(5*x^2-2)^6","A"
185,1,35,38,0.280000," ","int(x^7/(-5*x^2+2)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x^{2}}{250}+\frac{\frac{6 x^{2}}{125}-\frac{2}{125}}{\left(5 x^{2}-2\right)^{2}}-\frac{3 \ln \left(5 x^{2}-2\right)}{625}$&$35$\\ norman&$\frac{-\frac{6}{125} x^{2}+\frac{9}{50} x^{4}-\frac{1}{10} x^{6}}{\left(5 x^{2}-2\right)^{2}}-\frac{3 \ln \left(5 x^{2}-2\right)}{625}$&$38$\\ meijerg&$-\frac{x^{2} \left(25 x^{4}-45 x^{2}+12\right)}{1000 \left(1-\frac{5 x^{2}}{2}\right)^{2}}-\frac{3 \ln \left(1-\frac{5 x^{2}}{2}\right)}{625}$&$38$\\ default&$-\frac{x^{2}}{250}+\frac{6}{625 \left(5 x^{2}-2\right)}+\frac{2}{625 \left(5 x^{2}-2\right)^{2}}-\frac{3 \ln \left(5 x^{2}-2\right)}{625}$&$39$\\ \hline \end{longtable}"," ",0,"-1/250*x^2+25*(6/3125*x^2-2/3125)/(5*x^2-2)^2-3/625*ln(5*x^2-2)","A"
186,1,35,34,0.282000," ","int(1/(-2+x)^3/(1+x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{18 \left(-2+x \right)^{2}}+\frac{2}{27 \left(-2+x \right)}+\frac{1}{27+27 x}+\frac{\ln \left(-2+x \right)}{27}-\frac{\ln \left(1+x \right)}{27}$&$35$\\ norman&$\frac{\frac{1}{9} x^{2}-\frac{5}{18} x -\frac{1}{18}}{\left(-2+x \right)^{2} \left(1+x \right)}+\frac{\ln \left(-2+x \right)}{27}-\frac{\ln \left(1+x \right)}{27}$&$35$\\ risch&$\frac{\frac{1}{9} x^{2}-\frac{5}{18} x -\frac{1}{18}}{\left(-2+x \right)^{2} \left(1+x \right)}+\frac{\ln \left(-2+x \right)}{27}-\frac{\ln \left(1+x \right)}{27}$&$35$\\ \hline \end{longtable}"," ",0,"-1/18/(-2+x)^2+2/27/(-2+x)+1/27/(1+x)+1/27*ln(-2+x)-1/27*ln(1+x)","A"
187,1,45,48,0.002000," ","int(1/(2+x)^3/(3+x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{10 x^{4}+105 x^{3}+\frac{1225}{3} x^{2}+\frac{4175}{6} x +\frac{2627}{6}}{\left(2+x \right)^{2} \left(3+x \right)^{3}}+10 \ln \left(2+x \right)-10 \ln \left(3+x \right)$&$45$\\ risch&$\frac{10 x^{4}+105 x^{3}+\frac{1225}{3} x^{2}+\frac{4175}{6} x +\frac{2627}{6}}{\left(2+x \right)^{2} \left(3+x \right)^{3}}+10 \ln \left(2+x \right)-10 \ln \left(3+x \right)$&$45$\\ default&$-\frac{1}{2 \left(2+x \right)^{2}}+\frac{4}{2+x}+\frac{1}{3 \left(3+x \right)^{3}}+\frac{3}{2 \left(3+x \right)^{2}}+\frac{6}{3+x}+10 \ln \left(2+x \right)-10 \ln \left(3+x \right)$&$49$\\ \hline \end{longtable}"," ",0,"(10*x^4+105*x^3+1225/3*x^2+4175/6*x+2627/6)/(2+x)^2/(3+x)^3+10*ln(2+x)-10*ln(3+x)","A"
188,1,33,32,0.000000," ","int(x^5/(3+x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-108 x +\frac{27 x^{2}}{2}-2 x^{3}+\frac{x^{4}}{4}+\frac{243}{3+x}+405 \ln \left(3+x \right)$&$33$\\ risch&$-108 x +\frac{27 x^{2}}{2}-2 x^{3}+\frac{x^{4}}{4}+\frac{243}{3+x}+405 \ln \left(3+x \right)$&$33$\\ norman&$\frac{-\frac{135}{2} x^{2}+\frac{15}{2} x^{3}-\frac{5}{4} x^{4}+\frac{1}{4} x^{5}+1215}{3+x}+405 \ln \left(3+x \right)$&$36$\\ meijerg&$-\frac{9 x \left(-\frac{1}{27} x^{4}+\frac{5}{27} x^{3}-\frac{10}{9} x^{2}+10 x +60\right)}{4 \left(1+\frac{x}{3}\right)}+405 \ln \left(1+\frac{x}{3}\right)$&$40$\\ \hline \end{longtable}"," ",0,"-108*x+27/2*x^2-2*x^3+1/4*x^4+243/(3+x)+405*ln(3+x)","A"
189,1,38,38,0.016000," ","int((c1*x+b1)*(c*x^2+2*b*x+a),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{c \mathit{c1} \,x^{4}}{4}+\left(\frac{2 b \mathit{c1}}{3}+\frac{\mathit{b1} c}{3}\right) x^{3}+\left(\frac{a \mathit{c1}}{2}+b \mathit{b1} \right) x^{2}+a \mathit{b1} x$&$38$\\ default&$a \mathit{b1} x +\frac{\left(a \mathit{c1} +2 b \mathit{b1} \right) x^{2}}{2}+\frac{\left(2 b \mathit{c1} +\mathit{b1} c \right) x^{3}}{3}+\frac{c \mathit{c1} \,x^{4}}{4}$&$39$\\ gosper&$\frac{1}{4} c \mathit{c1} \,x^{4}+\frac{2}{3} x^{3} b \mathit{c1} +\frac{1}{3} x^{3} \mathit{b1} c +\frac{1}{2} x^{2} a \mathit{c1} +x^{2} b \mathit{b1} +a \mathit{b1} x$&$40$\\ risch&$\frac{1}{4} c \mathit{c1} \,x^{4}+\frac{2}{3} x^{3} b \mathit{c1} +\frac{1}{3} x^{3} \mathit{b1} c +\frac{1}{2} x^{2} a \mathit{c1} +x^{2} b \mathit{b1} +a \mathit{b1} x$&$40$\\ \hline \end{longtable}"," ",0,"1/4*c*c1*x^4+(2/3*b*c1+1/3*b1*c)*x^3+(1/2*a*c1+b*b1)*x^2+a*b1*x","A"
190,1,89,86,0.321000," ","int((c1*x+b1)*(c*x^2+2*b*x+a)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{c^{2} \mathit{c1} \,x^{6}}{6}+\left(\frac{4}{5} \mathit{c1} b c +\frac{1}{5} \mathit{b1} \,c^{2}\right) x^{5}+\left(\frac{1}{2} a c \mathit{c1} +b^{2} \mathit{c1} +b \mathit{b1} c \right) x^{4}+\left(\frac{4}{3} a b \mathit{c1} +\frac{2}{3} a \mathit{b1} c +\frac{4}{3} b^{2} \mathit{b1} \right) x^{3}+\left(\frac{1}{2} \mathit{c1} \,a^{2}+2 \mathit{b1} a b \right) x^{2}+a^{2} \mathit{b1} x$&$89$\\ default&$\frac{c^{2} \mathit{c1} \,x^{6}}{6}+\frac{\left(4 \mathit{c1} b c +\mathit{b1} \,c^{2}\right) x^{5}}{5}+\frac{\left(4 b \mathit{b1} c +\mathit{c1} \left(2 a c +4 b^{2}\right)\right) x^{4}}{4}+\frac{\left(\mathit{b1} \left(2 a c +4 b^{2}\right)+4 a b \mathit{c1} \right) x^{3}}{3}+\frac{\left(\mathit{c1} \,a^{2}+4 \mathit{b1} a b \right) x^{2}}{2}+a^{2} \mathit{b1} x$&$95$\\ gosper&$\frac{1}{6} c^{2} \mathit{c1} \,x^{6}+\frac{4}{5} x^{5} \mathit{c1} b c +\frac{1}{5} x^{5} \mathit{b1} \,c^{2}+\frac{1}{2} x^{4} a c \mathit{c1} +x^{4} b^{2} \mathit{c1} +x^{4} b \mathit{b1} c +\frac{4}{3} x^{3} a b \mathit{c1} +\frac{2}{3} x^{3} a \mathit{b1} c +\frac{4}{3} x^{3} b^{2} \mathit{b1} +\frac{1}{2} x^{2} \mathit{c1} \,a^{2}+2 x^{2} \mathit{b1} a b +a^{2} \mathit{b1} x$&$99$\\ risch&$\frac{1}{6} c^{2} \mathit{c1} \,x^{6}+\frac{4}{5} x^{5} \mathit{c1} b c +\frac{1}{5} x^{5} \mathit{b1} \,c^{2}+\frac{1}{2} x^{4} a c \mathit{c1} +x^{4} b^{2} \mathit{c1} +x^{4} b \mathit{b1} c +\frac{4}{3} x^{3} a b \mathit{c1} +\frac{2}{3} x^{3} a \mathit{b1} c +\frac{4}{3} x^{3} b^{2} \mathit{b1} +\frac{1}{2} x^{2} \mathit{c1} \,a^{2}+2 x^{2} \mathit{b1} a b +a^{2} \mathit{b1} x$&$99$\\ \hline \end{longtable}"," ",0,"1/6*c^2*c1*x^6+(4/5*c1*b*c+1/5*b1*c^2)*x^5+(1/2*a*c*c1+b^2*c1+b*b1*c)*x^4+(4/3*a*b*c1+2/3*a*b1*c+4/3*b^2*b1)*x^3+(1/2*c1*a^2+2*b1*a*b)*x^2+a^2*b1*x","A"
191,1,165,155,0.301000," ","int((c1*x+b1)*(c*x^2+2*b*x+a)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{c^{3} \mathit{c1} \,x^{8}}{8}+\left(\frac{6}{7} \mathit{c1} b \,c^{2}+\frac{1}{7} \mathit{b1} \,c^{3}\right) x^{7}+\left(\frac{1}{2} a \,c^{2} \mathit{c1} +2 b^{2} c \mathit{c1} +\mathit{b1} b \,c^{2}\right) x^{6}+\left(\frac{12}{5} a b c \mathit{c1} +\frac{3}{5} a \mathit{b1} \,c^{2}+\frac{8}{5} b^{3} \mathit{c1} +\frac{12}{5} b^{2} \mathit{b1} c \right) x^{5}+\left(\frac{3}{4} a^{2} c \mathit{c1} +3 a \,b^{2} \mathit{c1} +3 a b \mathit{b1} c +2 b^{3} \mathit{b1} \right) x^{4}+\left(2 \mathit{c1} \,a^{2} b +a^{2} \mathit{b1} c +4 a \,b^{2} \mathit{b1} \right) x^{3}+\left(\frac{1}{2} \mathit{c1} \,a^{3}+3 \mathit{b1} \,a^{2} b \right) x^{2}+a^{3} \mathit{b1} x$&$165$\\ gosper&$\frac{1}{8} c^{3} \mathit{c1} \,x^{8}+\frac{6}{7} x^{7} \mathit{c1} b \,c^{2}+\frac{1}{7} x^{7} \mathit{b1} \,c^{3}+\frac{1}{2} x^{6} a \,c^{2} \mathit{c1} +2 x^{6} b^{2} c \mathit{c1} +x^{6} \mathit{b1} b \,c^{2}+\frac{12}{5} x^{5} a b c \mathit{c1} +\frac{3}{5} x^{5} a \mathit{b1} \,c^{2}+\frac{8}{5} x^{5} b^{3} \mathit{c1} +\frac{12}{5} x^{5} b^{2} \mathit{b1} c +\frac{3}{4} x^{4} a^{2} c \mathit{c1} +3 x^{4} a \,b^{2} \mathit{c1} +3 x^{4} a b \mathit{b1} c +2 x^{4} b^{3} \mathit{b1} +2 a^{2} b \mathit{c1} \,x^{3}+a^{2} \mathit{b1} c \,x^{3}+4 a \,b^{2} \mathit{b1} \,x^{3}+\frac{1}{2} x^{2} \mathit{c1} \,a^{3}+3 x^{2} \mathit{b1} \,a^{2} b +a^{3} \mathit{b1} x$&$189$\\ risch&$\frac{1}{8} c^{3} \mathit{c1} \,x^{8}+\frac{6}{7} x^{7} \mathit{c1} b \,c^{2}+\frac{1}{7} x^{7} \mathit{b1} \,c^{3}+\frac{1}{2} x^{6} a \,c^{2} \mathit{c1} +2 x^{6} b^{2} c \mathit{c1} +x^{6} \mathit{b1} b \,c^{2}+\frac{12}{5} x^{5} a b c \mathit{c1} +\frac{3}{5} x^{5} a \mathit{b1} \,c^{2}+\frac{8}{5} x^{5} b^{3} \mathit{c1} +\frac{12}{5} x^{5} b^{2} \mathit{b1} c +\frac{3}{4} x^{4} a^{2} c \mathit{c1} +3 x^{4} a \,b^{2} \mathit{c1} +3 x^{4} a b \mathit{b1} c +2 x^{4} b^{3} \mathit{b1} +2 a^{2} b \mathit{c1} \,x^{3}+a^{2} \mathit{b1} c \,x^{3}+4 a \,b^{2} \mathit{b1} \,x^{3}+\frac{1}{2} x^{2} \mathit{c1} \,a^{3}+3 x^{2} \mathit{b1} \,a^{2} b +a^{3} \mathit{b1} x$&$189$\\ default&$\frac{c^{3} \mathit{c1} \,x^{8}}{8}+\frac{\left(6 \mathit{c1} b \,c^{2}+\mathit{b1} \,c^{3}\right) x^{7}}{7}+\frac{\left(6 \mathit{b1} b \,c^{2}+\mathit{c1} \left(c^{2} a +8 b^{2} c +c \left(2 a c +4 b^{2}\right)\right)\right) x^{6}}{6}+\frac{\left(\mathit{b1} \left(c^{2} a +8 b^{2} c +c \left(2 a c +4 b^{2}\right)\right)+\mathit{c1} \left(8 a b c +2 b \left(2 a c +4 b^{2}\right)\right)\right) x^{5}}{5}+\frac{\left(\mathit{b1} \left(8 a b c +2 b \left(2 a c +4 b^{2}\right)\right)+\mathit{c1} \left(a \left(2 a c +4 b^{2}\right)+8 b^{2} a +a^{2} c \right)\right) x^{4}}{4}+\frac{\left(\mathit{b1} \left(a \left(2 a c +4 b^{2}\right)+8 b^{2} a +a^{2} c \right)+6 \mathit{c1} \,a^{2} b \right) x^{3}}{3}+\frac{\left(\mathit{c1} \,a^{3}+6 \mathit{b1} \,a^{2} b \right) x^{2}}{2}+a^{3} \mathit{b1} x$&$237$\\ \hline \end{longtable}"," ",0,"1/8*c^3*c1*x^8+(6/7*c1*b*c^2+1/7*b1*c^3)*x^7+(1/2*a*c^2*c1+2*b^2*c*c1+b1*b*c^2)*x^6+(12/5*a*b*c*c1+3/5*a*b1*c^2+8/5*b^3*c1+12/5*b^2*b1*c)*x^5+(3/4*a^2*c*c1+3*a*b^2*c1+3*a*b*b1*c+2*b^3*b1)*x^4+(2*a^2*b*c1+a^2*b1*c+4*a*b^2*b1)*x^3+(1/2*c1*a^3+3*b1*a^2*b)*x^2+a^3*b1*x","A"
192,1,264,247,0.302000," ","int((c1*x+b1)*(c*x^2+2*b*x+a)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{c^{4} \mathit{c1} \,x^{10}}{10}+\left(\frac{8}{9} \mathit{c1} b \,c^{3}+\frac{1}{9} \mathit{b1} \,c^{4}\right) x^{9}+\left(\frac{1}{2} a \,c^{3} \mathit{c1} +3 b^{2} c^{2} \mathit{c1} +\mathit{b1} b \,c^{3}\right) x^{8}+\left(\frac{24}{7} a b \,c^{2} \mathit{c1} +\frac{4}{7} a \mathit{b1} \,c^{3}+\frac{32}{7} b^{3} c \mathit{c1} +\frac{24}{7} b^{2} \mathit{b1} \,c^{2}\right) x^{7}+\left(a^{2} c^{2} \mathit{c1} +8 a \,b^{2} c \mathit{c1} +4 a b \mathit{b1} \,c^{2}+\frac{8}{3} b^{4} \mathit{c1} +\frac{16}{3} b^{3} \mathit{b1} c \right) x^{6}+\left(\frac{24}{5} a^{2} b c \mathit{c1} +\frac{6}{5} a^{2} \mathit{b1} \,c^{2}+\frac{32}{5} a \,b^{3} \mathit{c1} +\frac{48}{5} a \,b^{2} \mathit{b1} c +\frac{16}{5} b^{4} \mathit{b1} \right) x^{5}+\left(a^{3} c \mathit{c1} +6 a^{2} b^{2} \mathit{c1} +6 a^{2} b \mathit{b1} c +8 a \,b^{3} \mathit{b1} \right) x^{4}+\left(\frac{8}{3} \mathit{c1} \,a^{3} b +\frac{4}{3} a^{3} \mathit{b1} c +8 a^{2} b^{2} \mathit{b1} \right) x^{3}+\left(\frac{1}{2} \mathit{c1} \,a^{4}+4 \mathit{b1} \,a^{3} b \right) x^{2}+a^{4} \mathit{b1} x$&$264$\\ gosper&$\frac{1}{2} x^{2} \mathit{c1} \,a^{4}+\frac{8}{3} x^{6} b^{4} \mathit{c1} +\frac{16}{5} x^{5} b^{4} \mathit{b1} +\frac{1}{9} x^{9} \mathit{b1} \,c^{4}+\frac{1}{10} c^{4} \mathit{c1} \,x^{10}+\frac{4}{3} x^{3} a^{3} \mathit{b1} c +8 x^{3} a^{2} b^{2} \mathit{b1} +4 x^{2} \mathit{b1} \,a^{3} b +a^{3} c \mathit{c1} \,x^{4}+6 a^{2} b^{2} \mathit{c1} \,x^{4}+8 a \,b^{3} \mathit{b1} \,x^{4}+\frac{6}{5} x^{5} a^{2} \mathit{b1} \,c^{2}+\frac{32}{5} x^{5} a \,b^{3} \mathit{c1} +\frac{8}{3} x^{3} \mathit{c1} \,a^{3} b +\frac{8}{9} x^{9} \mathit{c1} b \,c^{3}+\frac{1}{2} x^{8} a \,c^{3} \mathit{c1} +3 x^{8} b^{2} c^{2} \mathit{c1} +x^{8} \mathit{b1} b \,c^{3}+\frac{4}{7} x^{7} a \mathit{b1} \,c^{3}+\frac{32}{7} x^{7} b^{3} c \mathit{c1} +\frac{24}{7} x^{7} b^{2} \mathit{b1} \,c^{2}+x^{6} a^{2} c^{2} \mathit{c1} +\frac{16}{3} x^{6} b^{3} \mathit{b1} c +a^{4} \mathit{b1} x +6 a^{2} b \mathit{b1} c \,x^{4}+\frac{24}{5} x^{5} a^{2} b c \mathit{c1} +\frac{48}{5} x^{5} a \,b^{2} \mathit{b1} c +8 x^{6} a \,b^{2} c \mathit{c1} +4 x^{6} a b \mathit{b1} \,c^{2}+\frac{24}{7} x^{7} a b \,c^{2} \mathit{c1}$&$308$\\ risch&$\frac{1}{2} x^{2} \mathit{c1} \,a^{4}+\frac{8}{3} x^{6} b^{4} \mathit{c1} +\frac{16}{5} x^{5} b^{4} \mathit{b1} +\frac{1}{9} x^{9} \mathit{b1} \,c^{4}+\frac{1}{10} c^{4} \mathit{c1} \,x^{10}+\frac{4}{3} x^{3} a^{3} \mathit{b1} c +8 x^{3} a^{2} b^{2} \mathit{b1} +4 x^{2} \mathit{b1} \,a^{3} b +a^{3} c \mathit{c1} \,x^{4}+6 a^{2} b^{2} \mathit{c1} \,x^{4}+8 a \,b^{3} \mathit{b1} \,x^{4}+\frac{6}{5} x^{5} a^{2} \mathit{b1} \,c^{2}+\frac{32}{5} x^{5} a \,b^{3} \mathit{c1} +\frac{8}{3} x^{3} \mathit{c1} \,a^{3} b +\frac{8}{9} x^{9} \mathit{c1} b \,c^{3}+\frac{1}{2} x^{8} a \,c^{3} \mathit{c1} +3 x^{8} b^{2} c^{2} \mathit{c1} +x^{8} \mathit{b1} b \,c^{3}+\frac{4}{7} x^{7} a \mathit{b1} \,c^{3}+\frac{32}{7} x^{7} b^{3} c \mathit{c1} +\frac{24}{7} x^{7} b^{2} \mathit{b1} \,c^{2}+x^{6} a^{2} c^{2} \mathit{c1} +\frac{16}{3} x^{6} b^{3} \mathit{b1} c +a^{4} \mathit{b1} x +6 a^{2} b \mathit{b1} c \,x^{4}+\frac{24}{5} x^{5} a^{2} b c \mathit{c1} +\frac{48}{5} x^{5} a \,b^{2} \mathit{b1} c +8 x^{6} a \,b^{2} c \mathit{c1} +4 x^{6} a b \mathit{b1} \,c^{2}+\frac{24}{7} x^{7} a b \,c^{2} \mathit{c1}$&$308$\\ default&$\frac{c^{4} \mathit{c1} \,x^{10}}{10}+\frac{\left(8 \mathit{c1} b \,c^{3}+\mathit{b1} \,c^{4}\right) x^{9}}{9}+\frac{\left(8 \mathit{b1} b \,c^{3}+\mathit{c1} \left(2 \left(2 a c +4 b^{2}\right) c^{2}+16 b^{2} c^{2}\right)\right) x^{8}}{8}+\frac{\left(\mathit{b1} \left(2 \left(2 a c +4 b^{2}\right) c^{2}+16 b^{2} c^{2}\right)+\mathit{c1} \left(8 a b \,c^{2}+8 \left(2 a c +4 b^{2}\right) b c \right)\right) x^{7}}{7}+\frac{\left(\mathit{b1} \left(8 a b \,c^{2}+8 \left(2 a c +4 b^{2}\right) b c \right)+\mathit{c1} \left(2 a^{2} c^{2}+32 a \,b^{2} c +\left(2 a c +4 b^{2}\right)^{2}\right)\right) x^{6}}{6}+\frac{\left(\mathit{b1} \left(2 a^{2} c^{2}+32 a \,b^{2} c +\left(2 a c +4 b^{2}\right)^{2}\right)+\mathit{c1} \left(8 a^{2} b c +8 a b \left(2 a c +4 b^{2}\right)\right)\right) x^{5}}{5}+\frac{\left(\mathit{b1} \left(8 a^{2} b c +8 a b \left(2 a c +4 b^{2}\right)\right)+\mathit{c1} \left(2 a^{2} \left(2 a c +4 b^{2}\right)+16 a^{2} b^{2}\right)\right) x^{4}}{4}+\frac{\left(\mathit{b1} \left(2 a^{2} \left(2 a c +4 b^{2}\right)+16 a^{2} b^{2}\right)+8 \mathit{c1} \,a^{3} b \right) x^{3}}{3}+\frac{\left(\mathit{c1} \,a^{4}+8 \mathit{b1} \,a^{3} b \right) x^{2}}{2}+a^{4} \mathit{b1} x$&$363$\\ \hline \end{longtable}"," ",0,"1/10*c^4*c1*x^10+(8/9*c1*b*c^3+1/9*b1*c^4)*x^9+(1/2*a*c^3*c1+3*b^2*c^2*c1+b1*b*c^3)*x^8+(24/7*a*b*c^2*c1+4/7*a*b1*c^3+32/7*b^3*c*c1+24/7*b^2*b1*c^2)*x^7+(a^2*c^2*c1+8*a*b^2*c*c1+4*a*b*b1*c^2+8/3*b^4*c1+16/3*b^3*b1*c)*x^6+(24/5*a^2*b*c*c1+6/5*a^2*b1*c^2+32/5*a*b^3*c1+48/5*a*b^2*b1*c+16/5*b^4*b1)*x^5+(a^3*c*c1+6*a^2*b^2*c1+6*a^2*b*b1*c+8*a*b^3*b1)*x^4+(8/3*c1*a^3*b+4/3*a^3*b1*c+8*a^2*b^2*b1)*x^3+(1/2*c1*a^4+4*b1*a^3*b)*x^2+a^4*b1*x","A"
193,0,0,147,0.074000," ","int((c1*x+b1)*(c*x^2+2*b*x+a)^n,x)","\[\int \left(\mathit{c1} x +\mathit{b1} \right) \left(c \,x^{2}+2 b x +a \right)^{n}\, dx\]"," ",0,"int((c1*x+b1)*(c*x^2+2*b*x+a)^n,x)","F"
194,1,63,59,0.347000," ","int((c1*x+b1)/(c*x^2+2*b*x+a),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\mathit{c1} \ln \left(c \,x^{2}+2 b x +a \right)}{2 c}+\frac{\left(\mathit{b1} -\frac{\mathit{c1} b}{c}\right) \arctan \left(\frac{2 c x +2 b}{2 \sqrt{a c -b^{2}}}\right)}{\sqrt{a c -b^{2}}}$&$63$\\ risch&$\frac{\ln \left(-a b c \mathit{c1} +a \mathit{b1} \,c^{2}+b^{3} \mathit{c1} -b^{2} \mathit{b1} c -\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, c x -\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, b \right) a \mathit{c1}}{2 a c -2 b^{2}}-\frac{\ln \left(-a b c \mathit{c1} +a \mathit{b1} \,c^{2}+b^{3} \mathit{c1} -b^{2} \mathit{b1} c -\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, c x -\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, b \right) b^{2} \mathit{c1}}{2 c \left(a c -b^{2}\right)}+\frac{\ln \left(-a b c \mathit{c1} +a \mathit{b1} \,c^{2}+b^{3} \mathit{c1} -b^{2} \mathit{b1} c -\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, c x -\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, b \right) \sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}}{2 c \left(a c -b^{2}\right)}+\frac{\ln \left(-a b c \mathit{c1} +a \mathit{b1} \,c^{2}+b^{3} \mathit{c1} -b^{2} \mathit{b1} c +\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, c x +\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, b \right) a \mathit{c1}}{2 a c -2 b^{2}}-\frac{\ln \left(-a b c \mathit{c1} +a \mathit{b1} \,c^{2}+b^{3} \mathit{c1} -b^{2} \mathit{b1} c +\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, c x +\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, b \right) b^{2} \mathit{c1}}{2 c \left(a c -b^{2}\right)}-\frac{\ln \left(-a b c \mathit{c1} +a \mathit{b1} \,c^{2}+b^{3} \mathit{c1} -b^{2} \mathit{b1} c +\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, c x +\sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}\, b \right) \sqrt{-\left(b \mathit{c1} -\mathit{b1} c \right)^{2} \left(a c -b^{2}\right)}}{2 c \left(a c -b^{2}\right)}$&$618$\\ \hline \end{longtable}"," ",0,"1/2*c1*ln(c*x^2+2*b*x+a)/c+(b1-c1*b/c)/(a*c-b^2)^(1/2)*arctan(1/2*(2*c*x+2*b)/(a*c-b^2)^(1/2))","A"
195,1,103,82,0.345000," ","int((c1*x+b1)/(c*x^2+2*b*x+a)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-2 b \mathit{c1} +2 \mathit{b1} c \right) x +2 b \mathit{b1} -2 a \mathit{c1}}{\left(4 a c -4 b^{2}\right) \left(c \,x^{2}+2 b x +a \right)}+\frac{\left(-2 b \mathit{c1} +2 \mathit{b1} c \right) \arctan \left(\frac{2 c x +2 b}{2 \sqrt{a c -b^{2}}}\right)}{\left(4 a c -4 b^{2}\right) \sqrt{a c -b^{2}}}$&$103$\\ risch&$\frac{-\frac{\left(b \mathit{c1} -\mathit{b1} c \right) x}{2 \left(a c -b^{2}\right)}-\frac{a \mathit{c1} -b \mathit{b1}}{2 \left(a c -b^{2}\right)}}{c \,x^{2}+2 b x +a}+\frac{\ln \left(\left(-c^{2} a +b^{2} c \right) x -\left(-a c +b^{2}\right)^{\frac{3}{2}}-a b c +b^{3}\right) b \mathit{c1}}{4 \left(-a c +b^{2}\right)^{\frac{3}{2}}}-\frac{\ln \left(\left(-c^{2} a +b^{2} c \right) x -\left(-a c +b^{2}\right)^{\frac{3}{2}}-a b c +b^{3}\right) \mathit{b1} c}{4 \left(-a c +b^{2}\right)^{\frac{3}{2}}}-\frac{\ln \left(\left(c^{2} a -b^{2} c \right) x -\left(-a c +b^{2}\right)^{\frac{3}{2}}+a b c -b^{3}\right) b \mathit{c1}}{4 \left(-a c +b^{2}\right)^{\frac{3}{2}}}+\frac{\ln \left(\left(c^{2} a -b^{2} c \right) x -\left(-a c +b^{2}\right)^{\frac{3}{2}}+a b c -b^{3}\right) \mathit{b1} c}{4 \left(-a c +b^{2}\right)^{\frac{3}{2}}}$&$262$\\ \hline \end{longtable}"," ",0,"((-2*b*c1+2*b1*c)*x+2*b*b1-2*a*c1)/(4*a*c-4*b^2)/(c*x^2+2*b*x+a)+(-2*b*c1+2*b1*c)/(4*a*c-4*b^2)/(a*c-b^2)^(1/2)*arctan(1/2*(2*c*x+2*b)/(a*c-b^2)^(1/2))","A"
196,1,155,121,0.351000," ","int((c1*x+b1)/(c*x^2+2*b*x+a)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-2 b \mathit{c1} +2 \mathit{b1} c \right) x +2 b \mathit{b1} -2 a \mathit{c1}}{2 \left(4 a c -4 b^{2}\right) \left(c \,x^{2}+2 b x +a \right)^{2}}+\frac{3 \left(-2 b \mathit{c1} +2 \mathit{b1} c \right) \left(\frac{2 c x +2 b}{\left(4 a c -4 b^{2}\right) \left(c \,x^{2}+2 b x +a \right)}+\frac{2 c \arctan \left(\frac{2 c x +2 b}{2 \sqrt{a c -b^{2}}}\right)}{\left(4 a c -4 b^{2}\right) \sqrt{a c -b^{2}}}\right)}{2 \left(4 a c -4 b^{2}\right)}$&$155$\\ risch&$\frac{-\frac{3 c^{2} \left(b \mathit{c1} -\mathit{b1} c \right) x^{3}}{8 \left(a^{2} c^{2}-2 a \,b^{2} c +b^{4}\right)}-\frac{9 b c \left(b \mathit{c1} -\mathit{b1} c \right) x^{2}}{8 \left(a^{2} c^{2}-2 a \,b^{2} c +b^{4}\right)}-\frac{\left(5 a c +4 b^{2}\right) \left(b \mathit{c1} -\mathit{b1} c \right) x}{8 \left(a^{2} c^{2}-2 a \,b^{2} c +b^{4}\right)}-\frac{2 a^{2} c \mathit{c1} +a \,b^{2} \mathit{c1} -5 a b \mathit{b1} c +2 b^{3} \mathit{b1}}{8 \left(a^{2} c^{2}-2 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{2}+2 b x +a \right)^{2}}-\frac{3 c \ln \left(\left(a^{2} c^{3}-2 a \,b^{2} c^{2}+b^{4} c \right) x -\left(-a c +b^{2}\right)^{\frac{5}{2}}+a^{2} b \,c^{2}-2 a \,b^{3} c +b^{5}\right) b \mathit{c1}}{16 \left(-a c +b^{2}\right)^{\frac{5}{2}}}+\frac{3 c^{2} \ln \left(\left(a^{2} c^{3}-2 a \,b^{2} c^{2}+b^{4} c \right) x -\left(-a c +b^{2}\right)^{\frac{5}{2}}+a^{2} b \,c^{2}-2 a \,b^{3} c +b^{5}\right) \mathit{b1}}{16 \left(-a c +b^{2}\right)^{\frac{5}{2}}}+\frac{3 c \ln \left(\left(-a^{2} c^{3}+2 a \,b^{2} c^{2}-b^{4} c \right) x -\left(-a c +b^{2}\right)^{\frac{5}{2}}-a^{2} b \,c^{2}+2 a \,b^{3} c -b^{5}\right) b \mathit{c1}}{16 \left(-a c +b^{2}\right)^{\frac{5}{2}}}-\frac{3 c^{2} \ln \left(\left(-a^{2} c^{3}+2 a \,b^{2} c^{2}-b^{4} c \right) x -\left(-a c +b^{2}\right)^{\frac{5}{2}}-a^{2} b \,c^{2}+2 a \,b^{3} c -b^{5}\right) \mathit{b1}}{16 \left(-a c +b^{2}\right)^{\frac{5}{2}}}$&$473$\\ \hline \end{longtable}"," ",0,"1/2*((-2*b*c1+2*b1*c)*x+2*b*b1-2*a*c1)/(4*a*c-4*b^2)/(c*x^2+2*b*x+a)^2+3/2*(-2*b*c1+2*b1*c)/(4*a*c-4*b^2)*((2*c*x+2*b)/(4*a*c-4*b^2)/(c*x^2+2*b*x+a)+2*c/(4*a*c-4*b^2)/(a*c-b^2)^(1/2)*arctan(1/2*(2*c*x+2*b)/(a*c-b^2)^(1/2)))","A"
197,1,206,162,0.375000," ","int((c1*x+b1)/(c*x^2+2*b*x+a)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-2 b \mathit{c1} +2 \mathit{b1} c \right) x +2 b \mathit{b1} -2 a \mathit{c1}}{3 \left(4 a c -4 b^{2}\right) \left(c \,x^{2}+2 b x +a \right)^{3}}+\frac{5 \left(-2 b \mathit{c1} +2 \mathit{b1} c \right) \left(\frac{2 c x +2 b}{2 \left(4 a c -4 b^{2}\right) \left(c \,x^{2}+2 b x +a \right)^{2}}+\frac{3 c \left(\frac{2 c x +2 b}{\left(4 a c -4 b^{2}\right) \left(c \,x^{2}+2 b x +a \right)}+\frac{2 c \arctan \left(\frac{2 c x +2 b}{2 \sqrt{a c -b^{2}}}\right)}{\left(4 a c -4 b^{2}\right) \sqrt{a c -b^{2}}}\right)}{4 a c -4 b^{2}}\right)}{3 \left(4 a c -4 b^{2}\right)}$&$206$\\ risch&$\frac{-\frac{5 c^{4} \left(b \mathit{c1} -\mathit{b1} c \right) x^{5}}{16 \left(c^{3} a^{3}-3 b^{2} c^{2} a^{2}+3 b^{4} c a -b^{6}\right)}-\frac{25 c^{3} \left(b \mathit{c1} -\mathit{b1} c \right) b \,x^{4}}{16 \left(c^{3} a^{3}-3 b^{2} c^{2} a^{2}+3 b^{4} c a -b^{6}\right)}-\frac{5 \left(4 a c +11 b^{2}\right) c^{2} \left(b \mathit{c1} -\mathit{b1} c \right) x^{3}}{24 \left(c^{3} a^{3}-3 b^{2} c^{2} a^{2}+3 b^{4} c a -b^{6}\right)}-\frac{5 b \left(4 a c +b^{2}\right) c \left(b \mathit{c1} -\mathit{b1} c \right) x^{2}}{8 \left(c^{3} a^{3}-3 b^{2} c^{2} a^{2}+3 b^{4} c a -b^{6}\right)}-\frac{\left(11 a^{2} b \,c^{2} \mathit{c1} -11 a^{2} \mathit{b1} \,c^{3}+18 a \,b^{3} c \mathit{c1} -18 a \,b^{2} \mathit{b1} \,c^{2}-4 b^{5} \mathit{c1} +4 b^{4} \mathit{b1} c \right) x}{16 \left(c^{3} a^{3}-3 b^{2} c^{2} a^{2}+3 b^{4} c a -b^{6}\right)}-\frac{8 a^{3} c^{2} \mathit{c1} +9 a^{2} b^{2} c \mathit{c1} -33 a^{2} b \mathit{b1} \,c^{2}-2 a \,b^{4} \mathit{c1} +26 a \,b^{3} \mathit{b1} c -8 b^{5} \mathit{b1}}{48 \left(c^{3} a^{3}-3 b^{2} c^{2} a^{2}+3 b^{4} c a -b^{6}\right)}}{\left(c \,x^{2}+2 b x +a \right)^{3}}+\frac{5 c^{2} \ln \left(\left(-a^{3} c^{4}+3 a^{2} b^{2} c^{3}-3 a \,b^{4} c^{2}+b^{6} c \right) x -\left(-a c +b^{2}\right)^{\frac{7}{2}}-a^{3} b \,c^{3}+3 a^{2} b^{3} c^{2}-3 a \,b^{5} c +b^{7}\right) b \mathit{c1}}{32 \left(-a c +b^{2}\right)^{\frac{7}{2}}}-\frac{5 c^{3} \ln \left(\left(-a^{3} c^{4}+3 a^{2} b^{2} c^{3}-3 a \,b^{4} c^{2}+b^{6} c \right) x -\left(-a c +b^{2}\right)^{\frac{7}{2}}-a^{3} b \,c^{3}+3 a^{2} b^{3} c^{2}-3 a \,b^{5} c +b^{7}\right) \mathit{b1}}{32 \left(-a c +b^{2}\right)^{\frac{7}{2}}}-\frac{5 c^{2} \ln \left(\left(a^{3} c^{4}-3 a^{2} b^{2} c^{3}+3 a \,b^{4} c^{2}-b^{6} c \right) x -\left(-a c +b^{2}\right)^{\frac{7}{2}}+a^{3} b \,c^{3}-3 a^{2} b^{3} c^{2}+3 a \,b^{5} c -b^{7}\right) b \mathit{c1}}{32 \left(-a c +b^{2}\right)^{\frac{7}{2}}}+\frac{5 c^{3} \ln \left(\left(a^{3} c^{4}-3 a^{2} b^{2} c^{3}+3 a \,b^{4} c^{2}-b^{6} c \right) x -\left(-a c +b^{2}\right)^{\frac{7}{2}}+a^{3} b \,c^{3}-3 a^{2} b^{3} c^{2}+3 a \,b^{5} c -b^{7}\right) \mathit{b1}}{32 \left(-a c +b^{2}\right)^{\frac{7}{2}}}$&$792$\\ \hline \end{longtable}"," ",0,"1/3*((-2*b*c1+2*b1*c)*x+2*b*b1-2*a*c1)/(4*a*c-4*b^2)/(c*x^2+2*b*x+a)^3+5/3*(-2*b*c1+2*b1*c)/(4*a*c-4*b^2)*(1/2*(2*c*x+2*b)/(4*a*c-4*b^2)/(c*x^2+2*b*x+a)^2+3*c/(4*a*c-4*b^2)*((2*c*x+2*b)/(4*a*c-4*b^2)/(c*x^2+2*b*x+a)+2*c/(4*a*c-4*b^2)/(a*c-b^2)^(1/2)*arctan(1/2*(2*c*x+2*b)/(a*c-b^2)^(1/2))))","A"
198,0,0,157,0.069000," ","int((c1*x+b1)/((c*x^2+2*b*x+a)^n),x)","\[\int \left(\mathit{c1} x +\mathit{b1} \right) \left(c \,x^{2}+2 b x +a \right)^{-n}\, dx\]"," ",0,"int((c1*x+b1)/((c*x^2+2*b*x+a)^n),x)","F"
199,1,31,37,0.293000," ","int(x/(2*x^2+6*x+3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(2 x^{2}+6 x +3\right)}{4}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(4 x +6\right) \sqrt{3}}{6}\right)}{2}$&$31$\\ risch&$\frac{\ln \left(3+2 x +\sqrt{3}\right)}{4}+\frac{\ln \left(3+2 x +\sqrt{3}\right) \sqrt{3}}{4}+\frac{\ln \left(3+2 x -\sqrt{3}\right)}{4}-\frac{\ln \left(3+2 x -\sqrt{3}\right) \sqrt{3}}{4}$&$56$\\ \hline \end{longtable}"," ",0,"1/4*ln(2*x^2+6*x+3)+1/2*3^(1/2)*arctanh(1/6*(4*x+6)*3^(1/2))","A"
200,1,56,55,0.300000," ","int((-3+2*x)/(2*x^2+6*x+3)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{-24 x -30}{24 \left(2 x^{2}+6 x +3\right)^{2}}-\frac{4 x +6}{4 \left(2 x^{2}+6 x +3\right)}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(4 x +6\right) \sqrt{3}}{6}\right)}{3}$&$56$\\ risch&$\frac{-2 x^{3}-9 x^{2}-11 x -\frac{13}{4}}{\left(2 x^{2}+6 x +3\right)^{2}}+\frac{\ln \left(3+2 x +\sqrt{3}\right) \sqrt{3}}{6}-\frac{\ln \left(3+2 x -\sqrt{3}\right) \sqrt{3}}{6}$&$61$\\ \hline \end{longtable}"," ",0,"-1/24*(-24*x-30)/(2*x^2+6*x+3)^2-1/4*(4*x+6)/(2*x^2+6*x+3)+1/3*3^(1/2)*arctanh(1/6*(4*x+6)*3^(1/2))","A"
201,1,28,30,0.289000," ","int((-1+x)/(x^2+5*x+4)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{5}{9 \left(4+x \right)}-\frac{7 \ln \left(4+x \right)}{27}+\frac{2}{9 \left(1+x \right)}+\frac{7 \ln \left(1+x \right)}{27}$&$28$\\ norman&$\frac{\frac{7 x}{9}+\frac{13}{9}}{x^{2}+5 x +4}+\frac{7 \ln \left(1+x \right)}{27}-\frac{7 \ln \left(4+x \right)}{27}$&$30$\\ risch&$\frac{\frac{7 x}{9}+\frac{13}{9}}{x^{2}+5 x +4}+\frac{7 \ln \left(1+x \right)}{27}-\frac{7 \ln \left(4+x \right)}{27}$&$30$\\ \hline \end{longtable}"," ",0,"5/9/(4+x)-7/27*ln(4+x)+2/9/(1+x)+7/27*ln(1+x)","A"
202,1,60,81,0.290000," ","int(1/(x^2+3*x+2)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{4098 x +\frac{9730}{3} x^{5}+\frac{32942}{3} x^{3}+70 x^{7}+735 x^{6}+9093 x^{2}+\frac{15575}{2} x^{4}+\frac{3105}{4}}{\left(x^{2}+3 x +2\right)^{4}}+70 \ln \left(1+x \right)-70 \ln \left(2+x \right)$&$60$\\ risch&$\frac{4098 x +\frac{9730}{3} x^{5}+\frac{32942}{3} x^{3}+70 x^{7}+735 x^{6}+9093 x^{2}+\frac{15575}{2} x^{4}+\frac{3105}{4}}{\left(x^{2}+3 x +2\right)^{4}}+70 \ln \left(1+x \right)-70 \ln \left(2+x \right)$&$60$\\ default&$\frac{1}{4 \left(2+x \right)^{4}}+\frac{5}{3 \left(2+x \right)^{3}}+\frac{15}{2 \left(2+x \right)^{2}}+\frac{35}{2+x}-70 \ln \left(2+x \right)-\frac{1}{4 \left(1+x \right)^{4}}+\frac{5}{3 \left(1+x \right)^{3}}-\frac{15}{2 \left(1+x \right)^{2}}+\frac{35}{1+x}+70 \ln \left(1+x \right)$&$70$\\ \hline \end{longtable}"," ",0,"(4098*x+9730/3*x^5+32942/3*x^3+70*x^7+735*x^6+9093*x^2+15575/2*x^4+3105/4)/(x^2+3*x+2)^4+70*ln(1+x)-70*ln(2+x)","A"
203,1,62,66,0.429000," ","int(1/x^3/(2*x^2-6*x+7)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{4 \left(\frac{63 x}{20}-\frac{287}{20}\right)}{2401 \left(x^{2}-3 x +\frac{7}{2}\right)}-\frac{40 \ln \left(2 x^{2}-6 x +7\right)}{2401}+\frac{234 \sqrt{5}\, \arctan \left(\frac{\left(4 x -6\right) \sqrt{5}}{10}\right)}{60025}-\frac{1}{98 x^{2}}-\frac{12}{343 x}+\frac{80 \ln \left(x \right)}{2401}$&$62$\\ risch&$\frac{-\frac{138}{1715} x^{3}+\frac{407}{1715} x^{2}-\frac{9}{49} x -\frac{1}{14}}{x^{2} \left(2 x^{2}-6 x +7\right)}-\frac{40 \ln \left(4 x^{2}-12 x +14\right)}{2401}+\frac{234 \sqrt{5}\, \arctan \left(\frac{\left(-3+2 x \right) \sqrt{5}}{5}\right)}{60025}+\frac{80 \ln \left(x \right)}{2401}$&$67$\\ \hline \end{longtable}"," ",0,"-4/2401*(63/20*x-287/20)/(x^2-3*x+7/2)-40/2401*ln(2*x^2-6*x+7)+234/60025*5^(1/2)*arctan(1/10*(4*x-6)*5^(1/2))-1/98/x^2-12/343/x+80/2401*ln(x)","A"
204,1,60,96,0.291000," ","int(x^9/(x^2+3*x+2)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-229950 x^{3}-85880 x -67824 x^{5}-15350 x^{6}-1458 x^{7}-\frac{651951}{4} x^{4}-\frac{571502}{3} x^{2}-\frac{48820}{3}}{\left(x^{2}+3 x +2\right)^{4}}-1471 \ln \left(1+x \right)+1472 \ln \left(2+x \right)$&$60$\\ risch&$\frac{-229950 x^{3}-85880 x -67824 x^{5}-15350 x^{6}-1458 x^{7}-\frac{651951}{4} x^{4}-\frac{571502}{3} x^{2}-\frac{48820}{3}}{\left(x^{2}+3 x +2\right)^{4}}-1471 \ln \left(1+x \right)+1472 \ln \left(2+x \right)$&$60$\\ default&$-\frac{128}{\left(2+x \right)^{4}}-\frac{256}{3 \left(2+x \right)^{3}}-\frac{384}{\left(2+x \right)^{2}}-\frac{1024}{2+x}+1472 \ln \left(2+x \right)+\frac{1}{4 \left(1+x \right)^{4}}-\frac{14}{3 \left(1+x \right)^{3}}+\frac{48}{\left(1+x \right)^{2}}-\frac{434}{1+x}-1471 \ln \left(1+x \right)$&$70$\\ \hline \end{longtable}"," ",0,"(-229950*x^3-85880*x-67824*x^5-15350*x^6-1458*x^7-651951/4*x^4-571502/3*x^2-48820/3)/(x^2+3*x+2)^4-1471*ln(1+x)+1472*ln(2+x)","A"
205,1,64,96,0.299000," ","int((1+2*x)^2/(2*x^2+5*x+3)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{173600 x^{6}+\frac{1428116}{3} x +19840 x^{7}+\frac{1939360}{3} x^{5}+1624648 x^{3}+\frac{3552290}{3} x^{2}+\frac{3983500}{3} x^{4}+\frac{325799}{4}}{\left(2 x^{2}+5 x +3\right)^{4}}+2480 \ln \left(1+x \right)-2480 \ln \left(3+2 x \right)$&$64$\\ risch&$\frac{173600 x^{6}+\frac{1428116}{3} x +19840 x^{7}+\frac{1939360}{3} x^{5}+1624648 x^{3}+\frac{3552290}{3} x^{2}+\frac{3983500}{3} x^{4}+\frac{325799}{4}}{\left(2 x^{2}+5 x +3\right)^{4}}+2480 \ln \left(1+x \right)-2480 \ln \left(3+2 x \right)$&$65$\\ default&$\frac{16}{\left(3+2 x \right)^{4}}+\frac{256}{3 \left(3+2 x \right)^{3}}+\frac{328}{\left(3+2 x \right)^{2}}+\frac{1360}{3+2 x}-2480 \ln \left(3+2 x \right)-\frac{1}{4 \left(1+x \right)^{4}}+\frac{14}{3 \left(1+x \right)^{3}}-\frac{52}{\left(1+x \right)^{2}}+\frac{560}{1+x}+2480 \ln \left(1+x \right)$&$80$\\ \hline \end{longtable}"," ",0,"(173600*x^6+1428116/3*x+19840*x^7+1939360/3*x^5+1624648*x^3+3552290/3*x^2+3983500/3*x^4+325799/4)/(2*x^2+5*x+3)^4+2480*ln(1+x)-2480*ln(3+2*x)","A"
206,1,35,34,0.256000," ","int((-b*x^2+a)^3/x^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{a^{3}}{6 x^{6}}+\frac{3 a^{2} b}{4 x^{4}}-\frac{3 a \,b^{2}}{2 x^{2}}-b^{3} \ln \left(x \right)$&$35$\\ norman&$\frac{-\frac{1}{6} a^{3}+\frac{3}{4} a^{2} b \,x^{2}-\frac{3}{2} b^{2} a \,x^{4}}{x^{6}}-b^{3} \ln \left(x \right)$&$37$\\ risch&$\frac{-\frac{1}{6} a^{3}+\frac{3}{4} a^{2} b \,x^{2}-\frac{3}{2} b^{2} a \,x^{4}}{x^{6}}-b^{3} \ln \left(x \right)$&$37$\\ \hline \end{longtable}"," ",0,"-1/6*a^3/x^6+3/4*a^2*b/x^4-3/2*a*b^2/x^2-b^3*ln(x)","A"
207,1,55,73,0.293000," ","int(x^13/(a^4+x^4)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{5 a^{8} x^{2}}{256}-\frac{55 a^{4} x^{6}}{768}-\frac{73 x^{10}}{768}+\frac{5 x^{14}}{256 a^{4}}}{\left(a^{4}+x^{4}\right)^{4}}+\frac{5 \arctan \left(\frac{x^{2}}{a^{2}}\right)}{256 a^{6}}$&$55$\\ default&$\frac{\frac{5 x^{14}}{128 a^{4}}-\frac{73 x^{10}}{384}-\frac{55 a^{4} x^{6}}{384}-\frac{5 a^{8} x^{2}}{128}}{2 \left(a^{4}+x^{4}\right)^{4}}+\frac{5 \arctan \left(\frac{x^{2}}{a^{2}}\right)}{256 a^{6}}$&$56$\\ \hline \end{longtable}"," ",0,"(-5/256*a^8*x^2-55/768*a^4*x^6-73/768*x^10+5/256/a^4*x^14)/(a^4+x^4)^4+5/256*arctan(x^2/a^2)/a^6","A"
208,1,32,31,0.293000," ","int(x^(3/2)*(x^2+1)*(-x+2*x^(1/2))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{8 x^{\frac{7}{2}}}{7}-x^{4}+\frac{2 x^{\frac{9}{2}}}{9}+\frac{8 x^{\frac{11}{2}}}{11}-\frac{2 x^{6}}{3}+\frac{2 x^{\frac{13}{2}}}{13}$&$32$\\ default&$\frac{8 x^{\frac{7}{2}}}{7}-x^{4}+\frac{2 x^{\frac{9}{2}}}{9}+\frac{8 x^{\frac{11}{2}}}{11}-\frac{2 x^{6}}{3}+\frac{2 x^{\frac{13}{2}}}{13}$&$32$\\ trager&$-\frac{\left(2 x^{5}+2 x^{4}+5 x^{3}+5 x^{2}+5 x +5\right) \left(-1+x \right)}{3}+\frac{2 x^{\frac{7}{2}} \left(693 x^{3}+3276 x^{2}+1001 x +5148\right)}{9009}$&$52$\\ \hline \end{longtable}"," ",0,"8/7*x^(7/2)-x^4+2/9*x^(9/2)+8/11*x^(11/2)-2/3*x^6+2/13*x^(13/2)","A"
209,1,32,31,0.286000," ","int((-3*x^(3/5)+x^(3/2))^2*(-1/3*x^(2/3)+4*x^(3/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{45 x^{\frac{43}{15}}}{43}+\frac{360 x^{\frac{37}{10}}}{37}+\frac{60 x^{\frac{113}{30}}}{113}-\frac{120 x^{\frac{23}{5}}}{23}-\frac{x^{\frac{14}{3}}}{14}+\frac{8 x^{\frac{11}{2}}}{11}$&$32$\\ default&$-\frac{45 x^{\frac{43}{15}}}{43}+\frac{360 x^{\frac{37}{10}}}{37}+\frac{60 x^{\frac{113}{30}}}{113}-\frac{120 x^{\frac{23}{5}}}{23}-\frac{x^{\frac{14}{3}}}{14}+\frac{8 x^{\frac{11}{2}}}{11}$&$32$\\ \hline \end{longtable}"," ",0,"-45/43*x^(43/15)+360/37*x^(37/10)+60/113*x^(113/30)-120/23*x^(23/5)-1/14*x^(14/3)+8/11*x^(11/2)","A"
210,1,19,18,0.083000," ","int(1/(1+(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-2 \ln \left(1+\sqrt{1+x}\right)+2 \sqrt{1+x}$&$19$\\ trager&$2 \sqrt{1+x}-\ln \left(2 \sqrt{1+x}+2+x \right)$&$22$\\ default&$2 \sqrt{1+x}+\ln \left(-1+\sqrt{1+x}\right)-\ln \left(1+\sqrt{1+x}\right)-\ln \left(x \right)$&$31$\\ meijerg&$\frac{-4 \sqrt{\pi}+4 \sqrt{\pi}\, \sqrt{1+x}-4 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{1+x}}{2}\right)}{2 \sqrt{\pi}}$&$37$\\ \hline \end{longtable}"," ",0,"-2*ln(1+(1+x)^(1/2))+2*(1+x)^(1/2)","A"
211,1,13,11,0.022000," ","int(x/(1+(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(1+x \right)^{\frac{3}{2}}}{3}-1-x$&$13$\\ default&$\frac{2 \left(1+x \right)^{\frac{3}{2}}}{3}-1-x$&$13$\\ trager&$-x +\left(\frac{2}{3}+\frac{2 x}{3}\right) \sqrt{1+x}$&$16$\\ meijerg&$\frac{-\frac{\sqrt{\pi}\, \left(12 x +8\right)}{6}+\frac{\sqrt{\pi}\, \left(8+8 x \right) \sqrt{1+x}}{6}}{2 \sqrt{\pi}}$&$32$\\ \hline \end{longtable}"," ",0,"2/3*(1+x)^(3/2)-1-x","A"
212,1,21,21,0.273000," ","int((1+(1+x)^(1/2))/(-1+(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$1+x +4 \sqrt{1+x}+4 \ln \left(-1+\sqrt{1+x}\right)$&$21$\\ default&$1+x +4 \sqrt{1+x}+4 \ln \left(-1+\sqrt{1+x}\right)$&$21$\\ trager&$-1+x +4 \sqrt{1+x}+2 \ln \left(2 \sqrt{1+x}-2-x \right)$&$26$\\ \hline \end{longtable}"," ",0,"1+x+4*(1+x)^(1/2)+4*ln(-1+(1+x)^(1/2))","A"
213,1,26,27,0.045000," ","int(1/((1+x)^(2/3)-(1+x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$3 \left(1+x \right)^{\frac{1}{3}}+6 \left(1+x \right)^{\frac{1}{6}}+6 \ln \left(\left(1+x \right)^{\frac{1}{6}}-1\right)$&$26$\\ default&$6 \left(1+x \right)^{\frac{1}{6}}+3 \left(1+x \right)^{\frac{1}{3}}+\ln \left(x \right)+2 \ln \left(\left(1+x \right)^{\frac{1}{6}}-1\right)-\ln \left(\left(1+x \right)^{\frac{1}{3}}+\left(1+x \right)^{\frac{1}{6}}+1\right)-2 \ln \left(1+\left(1+x \right)^{\frac{1}{6}}\right)+\ln \left(\left(1+x \right)^{\frac{1}{3}}-\left(1+x \right)^{\frac{1}{6}}+1\right)-\ln \left(1+\sqrt{1+x}\right)+\ln \left(-1+\sqrt{1+x}\right)+2 \ln \left(\left(1+x \right)^{\frac{1}{3}}-1\right)-\ln \left(\left(1+x \right)^{\frac{2}{3}}+\left(1+x \right)^{\frac{1}{3}}+1\right)$&$111$\\ \hline \end{longtable}"," ",0,"3*(1+x)^(1/3)+6*(1+x)^(1/6)+6*ln((1+x)^(1/6)-1)","A"
214,1,17,19,0.299000," ","int((1+x^(1/4))^(1/3)/x^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$2 \sqrt{x}\, \hypergeom \left(\left[-\frac{1}{3}, 2\right], \left[3\right], -x^{\frac{1}{4}}\right)$&$17$\\ derivativedivides&$-3 \left(1+x^{\frac{1}{4}}\right)^{\frac{4}{3}}+\frac{12 \left(1+x^{\frac{1}{4}}\right)^{\frac{7}{3}}}{7}$&$20$\\ default&$-3 \left(1+x^{\frac{1}{4}}\right)^{\frac{4}{3}}+\frac{12 \left(1+x^{\frac{1}{4}}\right)^{\frac{7}{3}}}{7}$&$20$\\ \hline \end{longtable}"," ",0,"2*x^(1/2)*hypergeom([-1/3,2],[3],-x^(1/4))","C"
215,1,30,36,0.301000," ","int(1/x^3/(1+x)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{15 x^{2}+5 x -2}{4 \sqrt{1+x}\, x^{2}}-\frac{15 \arctanh \left(\sqrt{1+x}\right)}{4}$&$30$\\ trager&$\frac{15 x^{2}+5 x -2}{4 \sqrt{1+x}\, x^{2}}-\frac{15 \ln \left(\frac{2 \sqrt{1+x}+2+x}{x}\right)}{8}$&$39$\\ derivativedivides&$\frac{2}{\sqrt{1+x}}+\frac{1}{8 \left(1+\sqrt{1+x}\right)^{2}}+\frac{7}{8 \left(1+\sqrt{1+x}\right)}-\frac{15 \ln \left(1+\sqrt{1+x}\right)}{8}-\frac{1}{8 \left(-1+\sqrt{1+x}\right)^{2}}+\frac{7}{8 \left(-1+\sqrt{1+x}\right)}+\frac{15 \ln \left(-1+\sqrt{1+x}\right)}{8}$&$73$\\ default&$\frac{2}{\sqrt{1+x}}+\frac{1}{8 \left(1+\sqrt{1+x}\right)^{2}}+\frac{7}{8 \left(1+\sqrt{1+x}\right)}-\frac{15 \ln \left(1+\sqrt{1+x}\right)}{8}-\frac{1}{8 \left(-1+\sqrt{1+x}\right)^{2}}+\frac{7}{8 \left(-1+\sqrt{1+x}\right)}+\frac{15 \ln \left(-1+\sqrt{1+x}\right)}{8}$&$73$\\ meijerg&$\frac{\frac{\sqrt{\pi}\, \left(-47 x^{2}-24 x +8\right)}{16 x^{2}}-\frac{\sqrt{\pi}\, \left(-60 x^{2}-20 x +8\right)}{16 x^{2} \sqrt{1+x}}-\frac{15 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{1+x}}{2}\right)}{4}+\frac{15 \left(\frac{47}{30}-2 \ln \left(2\right)+\ln \left(x \right)\right) \sqrt{\pi}}{8}-\frac{\sqrt{\pi}}{2 x^{2}}+\frac{3 \sqrt{\pi}}{2 x}}{\sqrt{\pi}}$&$92$\\ \hline \end{longtable}"," ",0,"1/4*(15*x^2+5*x-2)/(1+x)^(1/2)/x^2-15/4*arctanh((1+x)^(1/2))","A"
216,1,59,86,0.332000," ","int(1/(1-x)^(7/2)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{45045 x^{6}-105105 x^{5}+69069 x^{4}-6435 x^{3}-1430 x^{2}-520 x -240}{960 x^{4} \sqrt{1-x}\, \left(-1+x \right)^{2}}-\frac{3003 \arctanh \left(\sqrt{1-x}\right)}{64}$&$59$\\ trager&$-\frac{\left(45045 x^{6}-105105 x^{5}+69069 x^{4}-6435 x^{3}-1430 x^{2}-520 x -240\right) \sqrt{1-x}}{960 \left(-1+x \right)^{3} x^{4}}+\frac{3003 \ln \left(\frac{-2+x +2 \sqrt{1-x}}{x}\right)}{128}$&$68$\\ meijerg&$\frac{\frac{\sqrt{\pi}\, \left(-329177 x^{4}+110880 x^{3}+30240 x^{2}+8960 x +1920\right)}{7680 x^{4}}-\frac{\sqrt{\pi}\, \left(-180180 x^{6}+420420 x^{5}-276276 x^{4}+25740 x^{3}+5720 x^{2}+2080 x +960\right)}{3840 x^{4} \left(1-x \right)^{\frac{5}{2}}}-\frac{3003 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{1-x}}{2}\right)}{64}+\frac{3003 \left(\frac{329177}{180180}-2 \ln \left(2\right)+\ln \left(x \right)+i \pi \right) \sqrt{\pi}}{128}-\frac{\sqrt{\pi}}{4 x^{4}}-\frac{7 \sqrt{\pi}}{6 x^{3}}-\frac{63 \sqrt{\pi}}{16 x^{2}}-\frac{231 \sqrt{\pi}}{16 x}}{\sqrt{\pi}}$&$146$\\ derivativedivides&$-\frac{1}{64 \left(\sqrt{1-x}-1\right)^{4}}+\frac{17}{96 \left(\sqrt{1-x}-1\right)^{3}}-\frac{159}{128 \left(\sqrt{1-x}-1\right)^{2}}+\frac{1083}{128 \left(\sqrt{1-x}-1\right)}+\frac{3003 \ln \left(\sqrt{1-x}-1\right)}{128}+\frac{2}{5 \left(1-x \right)^{\frac{5}{2}}}+\frac{10}{3 \left(1-x \right)^{\frac{3}{2}}}+\frac{30}{\sqrt{1-x}}+\frac{1}{64 \left(\sqrt{1-x}+1\right)^{4}}+\frac{17}{96 \left(\sqrt{1-x}+1\right)^{3}}+\frac{159}{128 \left(\sqrt{1-x}+1\right)^{2}}+\frac{1083}{128 \left(\sqrt{1-x}+1\right)}-\frac{3003 \ln \left(\sqrt{1-x}+1\right)}{128}$&$157$\\ default&$-\frac{1}{64 \left(\sqrt{1-x}-1\right)^{4}}+\frac{17}{96 \left(\sqrt{1-x}-1\right)^{3}}-\frac{159}{128 \left(\sqrt{1-x}-1\right)^{2}}+\frac{1083}{128 \left(\sqrt{1-x}-1\right)}+\frac{3003 \ln \left(\sqrt{1-x}-1\right)}{128}+\frac{2}{5 \left(1-x \right)^{\frac{5}{2}}}+\frac{10}{3 \left(1-x \right)^{\frac{3}{2}}}+\frac{30}{\sqrt{1-x}}+\frac{1}{64 \left(\sqrt{1-x}+1\right)^{4}}+\frac{17}{96 \left(\sqrt{1-x}+1\right)^{3}}+\frac{159}{128 \left(\sqrt{1-x}+1\right)^{2}}+\frac{1083}{128 \left(\sqrt{1-x}+1\right)}-\frac{3003 \ln \left(\sqrt{1-x}+1\right)}{128}$&$157$\\ \hline \end{longtable}"," ",0,"1/960*(45045*x^6-105105*x^5+69069*x^4-6435*x^3-1430*x^2-520*x-240)/x^4/(1-x)^(1/2)/(-1+x)^2-3003/64*arctanh((1-x)^(1/2))","A"
217,1,85,75,0.536000," ","int(1/(-1+x)^(2/3)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{2}{3}} \left(\frac{308 \Gamma \left(\frac{2}{3}\right) x \hypergeom \left(\left[1, 1, \frac{17}{3}\right], \left[2, 6\right], x\right)}{729}+\frac{110 \left(\frac{877}{1320}+\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+\ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)}{243}-\frac{\Gamma \left(\frac{2}{3}\right)}{4 x^{4}}-\frac{2 \Gamma \left(\frac{2}{3}\right)}{9 x^{3}}-\frac{5 \Gamma \left(\frac{2}{3}\right)}{18 x^{2}}-\frac{40 \Gamma \left(\frac{2}{3}\right)}{81 x}\right)}{\Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(-1+x \right)^{\frac{2}{3}}}$&$85$\\ risch&$\frac{220 x^{4}-88 x^{3}-33 x^{2}-18 x -81}{324 x^{4} \left(-1+x \right)^{\frac{2}{3}}}+\frac{110 \left(-\mathrm{signum}\left(-1+x \right)\right)^{\frac{2}{3}} \left(\frac{2 \Gamma \left(\frac{2}{3}\right) x \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], x\right)}{3}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+\ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{243 \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(-1+x \right)^{\frac{2}{3}}}$&$87$\\ derivativedivides&$-\frac{-75 \left(-1+x \right)^{\frac{7}{3}}+190 \left(-1+x \right)^{2}-350 \left(-1+x \right)^{\frac{5}{3}}+\frac{1157 \left(-1+x \right)^{\frac{4}{3}}}{4}+\frac{149}{4}-138 x -116 \left(-1+x \right)^{\frac{2}{3}}+137 \left(-1+x \right)^{\frac{1}{3}}}{243 \left(\left(-1+x \right)^{\frac{2}{3}}-\left(-1+x \right)^{\frac{1}{3}}+1\right)^{4}}-\frac{55 \ln \left(\left(-1+x \right)^{\frac{2}{3}}-\left(-1+x \right)^{\frac{1}{3}}+1\right)}{243}+\frac{110 \sqrt{3}\, \arctan \left(\frac{\left(2 \left(-1+x \right)^{\frac{1}{3}}-1\right) \sqrt{3}}{3}\right)}{243}-\frac{1}{324 \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)^{4}}-\frac{5}{243 \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)^{3}}-\frac{20}{243 \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)^{2}}-\frac{25}{81 \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)}+\frac{110 \ln \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)}{243}$&$158$\\ default&$-\frac{-75 \left(-1+x \right)^{\frac{7}{3}}+190 \left(-1+x \right)^{2}-350 \left(-1+x \right)^{\frac{5}{3}}+\frac{1157 \left(-1+x \right)^{\frac{4}{3}}}{4}+\frac{149}{4}-138 x -116 \left(-1+x \right)^{\frac{2}{3}}+137 \left(-1+x \right)^{\frac{1}{3}}}{243 \left(\left(-1+x \right)^{\frac{2}{3}}-\left(-1+x \right)^{\frac{1}{3}}+1\right)^{4}}-\frac{55 \ln \left(\left(-1+x \right)^{\frac{2}{3}}-\left(-1+x \right)^{\frac{1}{3}}+1\right)}{243}+\frac{110 \sqrt{3}\, \arctan \left(\frac{\left(2 \left(-1+x \right)^{\frac{1}{3}}-1\right) \sqrt{3}}{3}\right)}{243}-\frac{1}{324 \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)^{4}}-\frac{5}{243 \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)^{3}}-\frac{20}{243 \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)^{2}}-\frac{25}{81 \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)}+\frac{110 \ln \left(1+\left(-1+x \right)^{\frac{1}{3}}\right)}{243}$&$158$\\ trager&$\frac{\left(220 x^{3}+132 x^{2}+99 x +81\right) \left(-1+x \right)^{\frac{1}{3}}}{324 x^{4}}+\frac{110 \ln \left(\frac{144 \left(-1+x \right)^{\frac{2}{3}} \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)+4608 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)^{2} x +144 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right) \left(-1+x \right)^{\frac{1}{3}}-9216 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)^{2}+144 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right) x +3 \left(-1+x \right)^{\frac{1}{3}}-192 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)+x -1}{x}\right)}{243}-\frac{110 \ln \left(-\frac{144 \left(-1+x \right)^{\frac{2}{3}} \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)+2304 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)^{2} x +3 \left(-1+x \right)^{\frac{2}{3}}-4608 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)^{2}+96 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right) x +3 \left(-1+x \right)^{\frac{1}{3}}-240 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)-2}{x}\right)}{243}-\frac{1760 \ln \left(-\frac{144 \left(-1+x \right)^{\frac{2}{3}} \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)+2304 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)^{2} x +3 \left(-1+x \right)^{\frac{2}{3}}-4608 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)^{2}+96 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right) x +3 \left(-1+x \right)^{\frac{1}{3}}-240 \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)-2}{x}\right) \RootOf \left(2304 \textit{\_Z}^{2}+48 \textit{\_Z} +1\right)}{81}$&$349$\\ \hline \end{longtable}"," ",0,"1/GAMMA(2/3)/signum(-1+x)^(2/3)*(-signum(-1+x))^(2/3)*(308/729*GAMMA(2/3)*x*hypergeom([1,1,17/3],[2,6],x)+110/243*(877/1320+1/6*Pi*3^(1/2)-3/2*ln(3)+ln(x)+I*Pi)*GAMMA(2/3)-1/4*GAMMA(2/3)/x^4-2/9*GAMMA(2/3)/x^3-5/18*GAMMA(2/3)/x^2-40/81*GAMMA(2/3)/x)","C"
218,1,39,34,0.164000," ","int(((1-x)/(1+x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{-1+x}{1+x}}\, \left(1+x \right) \left(\sqrt{-x^{2}+1}+\arcsin \left(x \right)\right)}{\sqrt{-\left(1+x \right) \left(-1+x \right)}}$&$39$\\ risch&$\left(1+x \right) \sqrt{-\frac{-1+x}{1+x}}-\frac{\arcsin \left(x \right) \sqrt{-\frac{-1+x}{1+x}}\, \sqrt{-\left(1+x \right) \left(-1+x \right)}}{-1+x}$&$49$\\ trager&$\left(1+x \right) \sqrt{-\frac{-1+x}{1+x}}+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-\frac{-1+x}{1+x}}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-\frac{-1+x}{1+x}}+x \right)$&$67$\\ \hline \end{longtable}"," ",0,"(-(-1+x)/(1+x))^(1/2)*(1+x)/(-(1+x)*(-1+x))^(1/2)*((-x^2+1)^(1/2)+arcsin(x))","A"
219,1,195,80,0.102000," ","int(x*((-a+x)/(b-x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(a -3 b -2 x \right) \left(b -x \right) \sqrt{-\frac{a -x}{b -x}}\, \sqrt{-\left(a -x \right) \left(b -x \right)}}{4 \sqrt{-\left(-a +x \right) \left(-b +x \right)}}+\frac{\left(\frac{\arctan \left(\frac{x -\frac{a}{2}-\frac{b}{2}}{\sqrt{-x^{2}+\left(a +b \right) x -a b}}\right) a b}{4}+\frac{\arctan \left(\frac{x -\frac{a}{2}-\frac{b}{2}}{\sqrt{-x^{2}+\left(a +b \right) x -a b}}\right) a^{2}}{8}-\frac{3 \arctan \left(\frac{x -\frac{a}{2}-\frac{b}{2}}{\sqrt{-x^{2}+\left(a +b \right) x -a b}}\right) b^{2}}{8}\right) \sqrt{-\frac{a -x}{b -x}}\, \sqrt{-\left(a -x \right) \left(b -x \right)}}{a -x}$&$195$\\ default&$\frac{\sqrt{-\frac{a -x}{b -x}}\, \left(b -x \right) \left(\arctan \left(\frac{a -2 x +b}{2 \sqrt{-a b +a x +b x -x^{2}}}\right) a^{2}+2 b \arctan \left(\frac{a -2 x +b}{2 \sqrt{-a b +a x +b x -x^{2}}}\right) a -3 \arctan \left(\frac{a -2 x +b}{2 \sqrt{-a b +a x +b x -x^{2}}}\right) b^{2}+2 \sqrt{-a b +a x +b x -x^{2}}\, a -6 \sqrt{-a b +a x +b x -x^{2}}\, b -4 \sqrt{-a b +a x +b x -x^{2}}\, x \right)}{8 \sqrt{-\left(a -x \right) \left(b -x \right)}}$&$196$\\ \hline \end{longtable}"," ",0,"1/4*(a-3*b-2*x)*(b-x)/(-(-a+x)*(-b+x))^(1/2)*(-(a-x)/(b-x))^(1/2)*(-(a-x)*(b-x))^(1/2)+(1/4*arctan((x-1/2*a-1/2*b)/(-x^2+(a+b)*x-a*b)^(1/2))*a*b+1/8*arctan((x-1/2*a-1/2*b)/(-x^2+(a+b)*x-a*b)^(1/2))*a^2-3/8*arctan((x-1/2*a-1/2*b)/(-x^2+(a+b)*x-a*b)^(1/2))*b^2)*(-(a-x)/(b-x))^(1/2)*(-(a-x)*(b-x))^(1/2)/(a-x)","B"
220,1,64,36,0.402000," ","int((-5+x)^(1/2)*(3+x)^(1/2)/(-1+x)/(x^2-25),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-5+x}\, \sqrt{3+x}\, \left(\sqrt{5}\, \arctanh \left(\frac{\left(5+3 x \right) \sqrt{5}}{5 \sqrt{x^{2}-2 x -15}}\right)-5 \arctan \left(\frac{4}{\sqrt{x^{2}-2 x -15}}\right)\right)}{30 \sqrt{x^{2}-2 x -15}}$&$64$\\ \hline \end{longtable}"," ",0,"1/30*(-5+x)^(1/2)*(3+x)^(1/2)*(5^(1/2)*arctanh(1/5*(5+3*x)*5^(1/2)/(x^2-2*x-15)^(1/2))-5*arctan(4/(x^2-2*x-15)^(1/2)))/(x^2-2*x-15)^(1/2)","A"
221,0,0,219,0.044000," ","int(x^2*(-x^2+1)^(1/4)*(1+x)^(1/2)/(1-x)^(1/2)/((1-x)^(1/2)-(1+x)^(1/2)),x)","\[\int \frac{x^{2} \left(-x^{2}+1\right)^{\frac{1}{4}} \sqrt{1+x}}{\sqrt{1-x}\, \left(\sqrt{1-x}-\sqrt{1+x}\right)}\, dx\]"," ",0,"int(x^2*(-x^2+1)^(1/4)*(1+x)^(1/2)/(1-x)^(1/2)/((1-x)^(1/2)-(1+x)^(1/2)),x)","F"
222,0,0,219,0.039000," ","int(x*(1+x)^(2/3)*(1-x)^(1/2)/(-(1-x)^(5/6)*(1+x)^(1/3)+(1-x)^(2/3)*(1+x)^(1/2)),x)","\[\int \frac{x \left(1+x \right)^{\frac{2}{3}} \sqrt{1-x}}{-\left(1-x \right)^{\frac{5}{6}} \left(1+x \right)^{\frac{1}{3}}+\left(1-x \right)^{\frac{2}{3}} \sqrt{1+x}}\, dx\]"," ",0,"int(x*(1+x)^(2/3)*(1-x)^(1/2)/(-(1-x)^(5/6)*(1+x)^(1/3)+(1-x)^(2/3)*(1+x)^(1/2)),x)","F"
223,1,22,21,0.043000," ","int(1/((-1+x)^4*(1+x)^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{3 \left(-1+x \right) \left(1+x \right)}{2 \left(\left(-1+x \right)^{4} \left(1+x \right)^{2}\right)^{\frac{1}{3}}}$&$22$\\ risch&$-\frac{3 \left(-1+x \right) \left(1+x \right)}{2 \left(\left(-1+x \right)^{4} \left(1+x \right)^{2}\right)^{\frac{1}{3}}}$&$22$\\ trager&$-\frac{3 \left(x^{6}-2 x^{5}-x^{4}+4 x^{3}-x^{2}-2 x +1\right)^{\frac{2}{3}}}{2 \left(1+x \right) \left(-1+x \right)^{3}}$&$43$\\ \hline \end{longtable}"," ",0,"-3/2*(-1+x)*(1+x)/((-1+x)^4*(1+x)^2)^(1/3)","A"
224,1,22,21,0.061000," ","int(1/((-1+x)^3*(2+x)^5)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{4 \left(-1+x \right) \left(2+x \right)}{3 \left(\left(-1+x \right)^{3} \left(2+x \right)^{5}\right)^{\frac{1}{4}}}$&$22$\\ risch&$\frac{4 \left(-1+x \right) \left(2+x \right)}{3 \left(\left(-1+x \right)^{3} \left(2+x \right)^{5}\right)^{\frac{1}{4}}}$&$22$\\ trager&$\frac{4 \left(x^{8}+7 x^{7}+13 x^{6}-11 x^{5}-50 x^{4}-8 x^{3}+64 x^{2}+16 x -32\right)^{\frac{3}{4}}}{3 \left(-1+x \right)^{2} \left(2+x \right)^{4}}$&$53$\\ \hline \end{longtable}"," ",0,"4/3*(-1+x)*(2+x)/((-1+x)^3*(2+x)^5)^(1/4)","A"
225,1,27,45,0.049000," ","int(1/((-1+x)^7*(1+x)^2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{3 \left(1+x \right) \left(-1+x \right) \left(3 x -5\right)}{16 \left(\left(-1+x \right)^{7} \left(1+x \right)^{2}\right)^{\frac{1}{3}}}$&$27$\\ risch&$\frac{3 \left(-1+x \right) \left(3 x^{2}-2 x -5\right)}{16 \left(\left(-1+x \right)^{7} \left(1+x \right)^{2}\right)^{\frac{1}{3}}}$&$29$\\ trager&$\frac{3 \left(3 x -5\right) \left(x^{9}-5 x^{8}+8 x^{7}-14 x^{5}+14 x^{4}-8 x^{2}+5 x -1\right)^{\frac{2}{3}}}{16 \left(-1+x \right)^{6} \left(1+x \right)}$&$53$\\ \hline \end{longtable}"," ",0,"3/16*(1+x)*(-1+x)*(3*x-5)/((-1+x)^7*(1+x)^2)^(1/3)","A"
226,1,370,57,0.445000," ","int(1/((-1+x)^2*(1+x))^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(\frac{4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}-3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x -4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +x^{2}+2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}-1}{-1+x}\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x^{2}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x +3 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}-5 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x^{2}+6 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x -3 \left(x^{3}-x^{2}-x +1\right)^{\frac{2}{3}}+3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}} x +2 x^{2}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)-3 \left(x^{3}-x^{2}-x +1\right)^{\frac{1}{3}}-4 x +2}{-1+x}\right)$&$370$\\ \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^3-x^2-x+1)^(1/3)*x+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^3-x^2-x+1)^(1/3)*x+2*x^2-RootOf(_Z^2-_Z+1)-3*(x^3-x^2-x+1)^(1/3)-4*x+2)/(-1+x))","C"
227,1,86,95,0.236000," ","int((1/x+x)/((-2+x)*(1+x)^3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{4 \left(-2+x \right) \left(1+x \right)}{3 \sqrt{\left(-2+x \right) \left(1+x \right)^{3}}}+\frac{\left(\ln \left(-\frac{1}{2}+x +\sqrt{x^{2}-x -2}\right)+\frac{\sqrt{2}\, \arctan \left(\frac{\left(-4-x \right) \sqrt{2}}{4 \sqrt{x^{2}-x -2}}\right)}{2}\right) \left(1+x \right) \sqrt{\left(1+x \right) \left(-2+x \right)}}{\sqrt{\left(-2+x \right) \left(1+x \right)^{3}}}$&$86$\\ default&$\frac{\left(-3 \sqrt{2}\, \arctan \left(\frac{\left(4+x \right) \sqrt{2}}{4 \sqrt{x^{2}-x -2}}\right) x +6 \ln \left(-\frac{1}{2}+x +\sqrt{x^{2}-x -2}\right) x -3 \sqrt{2}\, \arctan \left(\frac{\left(4+x \right) \sqrt{2}}{4 \sqrt{x^{2}-x -2}}\right)+6 \ln \left(-\frac{1}{2}+x +\sqrt{x^{2}-x -2}\right)-8 \sqrt{x^{2}-x -2}\right) \sqrt{\left(1+x \right) \left(-2+x \right)}}{6 \sqrt{\left(-2+x \right) \left(1+x \right)^{3}}}$&$118$\\ trager&$-\frac{4 \sqrt{x^{4}+x^{3}-3 x^{2}-5 x -2}}{3 \left(1+x \right)^{2}}+\ln \left(\frac{2 x^{2}+2 \sqrt{x^{4}+x^{3}-3 x^{2}-5 x -2}+x -1}{1+x}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+5 \RootOf \left(\textit{\_Z}^{2}+2\right) x +4 \sqrt{x^{4}+x^{3}-3 x^{2}-5 x -2}+4 \RootOf \left(\textit{\_Z}^{2}+2\right)}{x \left(1+x \right)}\right)}{2}$&$128$\\ \hline \end{longtable}"," ",0,"-4/3*(-2+x)*(1+x)/((-2+x)*(1+x)^3)^(1/2)+(ln(-1/2+x+(x^2-x-2)^(1/2))+1/2*2^(1/2)*arctan(1/4*(-4-x)*2^(1/2)/(x^2-x-2)^(1/2)))/((-2+x)*(1+x)^3)^(1/2)*(1+x)*((1+x)*(-2+x))^(1/2)","A"
228,1,1247,127,4.797000," ","int(((-1+x)^2*(1+x))^(1/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(\left(-1+x \right)^{2} \left(1+x \right)\right)^{\frac{1}{3}}}{x}+\frac{\left(-\frac{\ln \left(-\frac{-157880368143+288529720857 x +4262769939861 x^{5}-2841846626574 x^{3}+4262769939861 x^{4}-2395436537574 x^{2}+334666315224 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{5}+65021838093 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+52300823301 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+2933694720 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{5}-223110876816 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{3}-477460395840 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}-266744567736 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x +334666315224 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{4}+2933694720 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{4}-1955796480 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{3}-21459433600 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}-19612292480 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x +1030402198152 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x^{3}-5266768885533 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{4}+343467399384 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x^{2}-3511179257022 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{3}-114489133128 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x +2340786171348 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{2}+390131028558 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x -12395048712 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)-108655360 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2}-195065514279 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}-38163044376 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-1755589628511 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x^{3}+1412122229127 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{4}-585196542837 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x^{2}+941414819418 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{3}+195065514279 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x -627609879612 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{2}-104601646602 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x}{x \left(1+x \right)}\right)}{3}+\frac{\RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \ln \left(-\frac{33401336760+117256110840 x -901836092520 x^{5}+601224061680 x^{3}-901836092520 x^{4}+685078835760 x^{2}-1454977597671 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{5}-65021838093 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}-12721014792 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+14285122848 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{5}+969985065114 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{3}+1047579629778 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}+131482623837 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -1454977597671 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{4}+14285122848 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{4}-9523415232 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{3}-104493028240 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}-95498691632 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x -4236366687381 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x^{3}+5266768885533 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{4}-1412122229127 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x^{2}+3511179257022 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{3}+470707409709 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x -2340786171348 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{2}-390131028558 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x +53888059173 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)-529078624 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2}+195065514279 \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}}+156902469903 \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}}+1755589628511 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x^{3}-343467399384 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{4}+585196542837 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x^{2}-228978266256 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{3}-195065514279 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{2}{3}} x +152652177504 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x^{2}+25442029584 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}+x^{2}-x -1\right)^{\frac{1}{3}} x}{x \left(1+x \right)}\right)}{9}\right) \left(\left(-1+x \right)^{2} \left(1+x \right)\right)^{\frac{1}{3}} \left(\left(-1+x \right) \left(1+x \right)^{2}\right)^{\frac{1}{3}}}{\left(-1+x \right) \left(1+x \right)}$&$1247$\\ trager&$\text{Expression too large to display}$&$2057$\\ \hline \end{longtable}"," ",0,"-((-1+x)^2*(1+x))^(1/3)/x+(-1/3*ln(-(-157880368143+288529720857*x+4262769939861*x^5-2841846626574*x^3+4262769939861*x^4-2395436537574*x^2-108655360*RootOf(_Z^2-3*_Z+9)^2-12395048712*RootOf(_Z^2-3*_Z+9)+2933694720*RootOf(_Z^2-3*_Z+9)^2*x^4-1955796480*RootOf(_Z^2-3*_Z+9)^2*x^3-21459433600*RootOf(_Z^2-3*_Z+9)^2*x^2-19612292480*RootOf(_Z^2-3*_Z+9)^2*x+334666315224*RootOf(_Z^2-3*_Z+9)*x^5+1030402198152*(x^3+x^2-x-1)^(2/3)*x^3-5266768885533*(x^3+x^2-x-1)^(1/3)*x^4+343467399384*(x^3+x^2-x-1)^(2/3)*x^2-3511179257022*(x^3+x^2-x-1)^(1/3)*x^3+65021838093*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)-114489133128*(x^3+x^2-x-1)^(2/3)*x+2340786171348*(x^3+x^2-x-1)^(1/3)*x^2+52300823301*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)+390131028558*(x^3+x^2-x-1)^(1/3)*x+2933694720*RootOf(_Z^2-3*_Z+9)^2*x^5-195065514279*(x^3+x^2-x-1)^(1/3)-38163044376*(x^3+x^2-x-1)^(2/3)-1755589628511*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)*x^3+1412122229127*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x^4-585196542837*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)*x^2+941414819418*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x^3+195065514279*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)*x-627609879612*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x^2-104601646602*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x-223110876816*RootOf(_Z^2-3*_Z+9)*x^3-477460395840*RootOf(_Z^2-3*_Z+9)*x^2-266744567736*RootOf(_Z^2-3*_Z+9)*x+334666315224*RootOf(_Z^2-3*_Z+9)*x^4)/x/(1+x))+1/9*RootOf(_Z^2-3*_Z+9)*ln(-(33401336760+117256110840*x-901836092520*x^5+601224061680*x^3-901836092520*x^4+685078835760*x^2-529078624*RootOf(_Z^2-3*_Z+9)^2+53888059173*RootOf(_Z^2-3*_Z+9)+14285122848*RootOf(_Z^2-3*_Z+9)^2*x^4-9523415232*RootOf(_Z^2-3*_Z+9)^2*x^3-104493028240*RootOf(_Z^2-3*_Z+9)^2*x^2-95498691632*RootOf(_Z^2-3*_Z+9)^2*x-1454977597671*RootOf(_Z^2-3*_Z+9)*x^5-4236366687381*(x^3+x^2-x-1)^(2/3)*x^3+5266768885533*(x^3+x^2-x-1)^(1/3)*x^4-1412122229127*(x^3+x^2-x-1)^(2/3)*x^2+3511179257022*(x^3+x^2-x-1)^(1/3)*x^3-65021838093*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)+470707409709*(x^3+x^2-x-1)^(2/3)*x-2340786171348*(x^3+x^2-x-1)^(1/3)*x^2-12721014792*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)-390131028558*(x^3+x^2-x-1)^(1/3)*x+14285122848*RootOf(_Z^2-3*_Z+9)^2*x^5+195065514279*(x^3+x^2-x-1)^(1/3)+156902469903*(x^3+x^2-x-1)^(2/3)+1755589628511*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)*x^3-343467399384*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x^4+585196542837*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)*x^2-228978266256*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x^3-195065514279*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(2/3)*x+152652177504*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x^2+25442029584*RootOf(_Z^2-3*_Z+9)*(x^3+x^2-x-1)^(1/3)*x+969985065114*RootOf(_Z^2-3*_Z+9)*x^3+1047579629778*RootOf(_Z^2-3*_Z+9)*x^2+131482623837*RootOf(_Z^2-3*_Z+9)*x-1454977597671*RootOf(_Z^2-3*_Z+9)*x^4)/x/(1+x)))*((-1+x)^2*(1+x))^(1/3)*((-1+x)*(1+x)^2)^(1/3)/(-1+x)/(1+x)","C"
229,1,26,33,0.326000," ","int(1/(x^2-2*x-3)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{x^{3}-3 x^{2}-3 x +5}{24 \left(x^{2}-2 x -3\right)^{\frac{3}{2}}}$&$26$\\ risch&$\frac{x^{3}-3 x^{2}-3 x +5}{24 \left(x^{2}-2 x -3\right)^{\frac{3}{2}}}$&$26$\\ gosper&$\frac{\left(1+x \right) \left(-3+x \right) \left(x^{3}-3 x^{2}-3 x +5\right)}{24 \left(x^{2}-2 x -3\right)^{\frac{5}{2}}}$&$32$\\ default&$-\frac{2 x -2}{24 \left(x^{2}-2 x -3\right)^{\frac{3}{2}}}+\frac{2 x -2}{48 \sqrt{x^{2}-2 x -3}}$&$36$\\ \hline \end{longtable}"," ",0,"1/24*(x^3-3*x^2-3*x+5)/(x^2-2*x-3)^(3/2)","A"
230,1,35,34,0.142000," ","int(1/(x^3-5*x^2+3*x+9)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\ln \left(\frac{x^{2}+4 \sqrt{x^{3}-5 x^{2}+3 x +9}+2 x -15}{\left(-3+x \right)^{2}}\right)}{2}$&$35$\\ default&$\frac{\left(-3+x \right) \sqrt{1+x}\, \left(\ln \left(\sqrt{1+x}-2\right)-\ln \left(\sqrt{1+x}+2\right)\right)}{2 \sqrt{x^{3}-5 x^{2}+3 x +9}}$&$45$\\ \hline \end{longtable}"," ",0,"-1/2*ln((x^2+4*(x^3-5*x^2+3*x+9)^(1/2)+2*x-15)/(-3+x)^2)","A"
231,1,71,117,0.113000," ","int(1/(x^3-5*x^2+3*x+9)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{15 x^{2}-70 x +43}{256 \left(-3+x \right) \sqrt{\left(1+x \right) \left(-3+x \right)^{2}}}+\frac{\left(-\frac{15 \ln \left(\sqrt{1+x}+2\right)}{1024}+\frac{15 \ln \left(\sqrt{1+x}-2\right)}{1024}\right) \sqrt{1+x}\, \left(-3+x \right)}{\sqrt{\left(1+x \right) \left(-3+x \right)^{2}}}$&$71$\\ trager&$\frac{\left(15 x^{2}-70 x +43\right) \sqrt{x^{3}-5 x^{2}+3 x +9}}{256 \left(-3+x \right)^{3} \left(1+x \right)}+\frac{15 \ln \left(\frac{-x^{2}+4 \sqrt{x^{3}-5 x^{2}+3 x +9}-2 x +15}{\left(-3+x \right)^{2}}\right)}{1024}$&$75$\\ default&$\frac{\left(-3+x \right)^{3} \left(1+x \right) \left(15 \left(1+x \right)^{\frac{5}{2}} \ln \left(\sqrt{1+x}-2\right)-15 \left(1+x \right)^{\frac{5}{2}} \ln \left(\sqrt{1+x}+2\right)-120 \left(1+x \right)^{\frac{3}{2}} \ln \left(\sqrt{1+x}-2\right)+120 \left(1+x \right)^{\frac{3}{2}} \ln \left(\sqrt{1+x}+2\right)+240 \ln \left(\sqrt{1+x}-2\right) \sqrt{1+x}-240 \ln \left(\sqrt{1+x}+2\right) \sqrt{1+x}+60 x^{2}-280 x +172\right)}{1024 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{3}{2}} \left(\sqrt{1+x}-2\right)^{2} \left(\sqrt{1+x}+2\right)^{2}}$&$144$\\ \hline \end{longtable}"," ",0,"1/256*(15*x^2-70*x+43)/(-3+x)/((1+x)*(-3+x)^2)^(1/2)+(-15/1024*ln((1+x)^(1/2)+2)+15/1024*ln((1+x)^(1/2)-2))/((1+x)*(-3+x)^2)^(1/2)*(1+x)^(1/2)*(-3+x)","A"
232,1,672,65,0.470000," ","int(1/(x^3-5*x^2+3*x+9)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \ln \left(-\frac{20 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}-60 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x +27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{2}{3}}+27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}} x -33 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}-81 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}}-6 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -216 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{2}{3}}-216 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}} x -36 x^{2}+315 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)+648 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}}+360 x -756}{-3+x}\right)}{3}-\frac{\ln \left(-\frac{20 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}-60 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x -27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}} x -87 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}+81 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}}+366 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -135 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{2}{3}}-135 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}} x +45 x^{2}-315 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)+405 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}}-198 x +189}{-3+x}\right) \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)}{3}+\ln \left(-\frac{20 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x^{2}-60 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)^{2} x -27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{2}{3}}-27 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}} x -87 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x^{2}+81 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}}+366 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right) x -135 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{2}{3}}-135 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}} x +45 x^{2}-315 \RootOf \left(\textit{\_Z}^{2}-3 \textit{\_Z} +9\right)+405 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}}-198 x +189}{-3+x}\right)$&$672$\\ \hline \end{longtable}"," ",0,"1/3*RootOf(_Z^2-3*_Z+9)*ln(-(20*RootOf(_Z^2-3*_Z+9)^2*x^2-60*RootOf(_Z^2-3*_Z+9)^2*x+27*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(2/3)+27*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(1/3)*x-33*RootOf(_Z^2-3*_Z+9)*x^2-81*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(1/3)-6*RootOf(_Z^2-3*_Z+9)*x-216*(x^3-5*x^2+3*x+9)^(2/3)-216*(x^3-5*x^2+3*x+9)^(1/3)*x-36*x^2+315*RootOf(_Z^2-3*_Z+9)+648*(x^3-5*x^2+3*x+9)^(1/3)+360*x-756)/(-3+x))-1/3*ln(-(20*RootOf(_Z^2-3*_Z+9)^2*x^2-60*RootOf(_Z^2-3*_Z+9)^2*x-27*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(2/3)-27*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(1/3)*x-87*RootOf(_Z^2-3*_Z+9)*x^2+81*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(1/3)+366*RootOf(_Z^2-3*_Z+9)*x-135*(x^3-5*x^2+3*x+9)^(2/3)-135*(x^3-5*x^2+3*x+9)^(1/3)*x+45*x^2-315*RootOf(_Z^2-3*_Z+9)+405*(x^3-5*x^2+3*x+9)^(1/3)-198*x+189)/(-3+x))*RootOf(_Z^2-3*_Z+9)+ln(-(20*RootOf(_Z^2-3*_Z+9)^2*x^2-60*RootOf(_Z^2-3*_Z+9)^2*x-27*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(2/3)-27*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(1/3)*x-87*RootOf(_Z^2-3*_Z+9)*x^2+81*RootOf(_Z^2-3*_Z+9)*(x^3-5*x^2+3*x+9)^(1/3)+366*RootOf(_Z^2-3*_Z+9)*x-135*(x^3-5*x^2+3*x+9)^(2/3)-135*(x^3-5*x^2+3*x+9)^(1/3)*x+45*x^2-315*RootOf(_Z^2-3*_Z+9)+405*(x^3-5*x^2+3*x+9)^(1/3)-198*x+189)/(-3+x))","C"
233,1,20,25,0.031000," ","int(1/(x^3-5*x^2+3*x+9)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 \left(-3+x \right) \left(1+x \right)}{4 \left(\left(1+x \right) \left(-3+x \right)^{2}\right)^{\frac{2}{3}}}$&$20$\\ trager&$-\frac{3 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{1}{3}}}{4 \left(-3+x \right)}$&$23$\\ gosper&$-\frac{3 \left(1+x \right) \left(-3+x \right)}{4 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{2}{3}}}$&$24$\\ \hline \end{longtable}"," ",0,"-3/4/((1+x)*(-3+x)^2)^(2/3)*(-3+x)*(1+x)","A"
234,1,29,80,0.042000," ","int(1/(x^3-5*x^2+3*x+9)^(4/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\frac{27}{320} x^{2}-\frac{63}{160} x +\frac{87}{320}}{\left(-3+x \right) \left(\left(1+x \right) \left(-3+x \right)^{2}\right)^{\frac{1}{3}}}$&$29$\\ gosper&$\frac{3 \left(1+x \right) \left(-3+x \right) \left(9 x^{2}-42 x +29\right)}{320 \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{4}{3}}}$&$34$\\ trager&$\frac{3 \left(9 x^{2}-42 x +29\right) \left(x^{3}-5 x^{2}+3 x +9\right)^{\frac{2}{3}}}{320 \left(-3+x \right)^{3} \left(1+x \right)}$&$38$\\ \hline \end{longtable}"," ",0,"3/320*(9*x^2-42*x+29)/(-3+x)/((1+x)*(-3+x)^2)^(1/3)","A"
235,1,15,16,0.359000," ","int(1/(-2*x^2+3*x+4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{2}\, \arcsin \left(\frac{4 \sqrt{41}\, \left(x -\frac{3}{4}\right)}{41}\right)}{2}$&$15$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-4 \RootOf \left(\textit{\_Z}^{2}+2\right) x +3 \RootOf \left(\textit{\_Z}^{2}+2\right)+4 \sqrt{-2 x^{2}+3 x +4}\right)}{2}$&$42$\\ \hline \end{longtable}"," ",0,"1/2*2^(1/2)*arcsin(4/41*41^(1/2)*(x-3/4))","A"
236,1,5,4,0.316000," ","int(1/(-x^2+4*x-3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\arcsin \left(-2+x \right)$&$5$\\ trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{2}+1\right) x +2 \RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{-x^{2}+4 x -3}\right)$&$39$\\ \hline \end{longtable}"," ",0,"arcsin(-2+x)","A"
237,1,12,11,0.292000," ","int(1/(-3*x^2-5*x-2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arcsin \left(5+6 x \right) \sqrt{3}}{3}$&$12$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(-6 \RootOf \left(\textit{\_Z}^{2}+3\right) x -5 \RootOf \left(\textit{\_Z}^{2}+3\right)+6 \sqrt{-3 x^{2}-5 x -2}\right)}{3}$&$42$\\ \hline \end{longtable}"," ",0,"1/3*arcsin(5+6*x)*3^(1/2)","A"
238,1,29,21,0.290000," ","int(1/(x^2+4)/(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{5}\, \arctan \left(\frac{\sqrt{5}\, \sqrt{-x^{2}+1}\, x}{2 x^{2}-2}\right)}{10}$&$29$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+5\right) \ln \left(-\frac{9 \RootOf \left(\textit{\_Z}^{2}+5\right) x^{2}-20 \sqrt{-x^{2}+1}\, x -4 \RootOf \left(\textit{\_Z}^{2}+5\right)}{x^{2}+4}\right)}{20}$&$51$\\ \hline \end{longtable}"," ",0,"-1/10*5^(1/2)*arctan(1/2*5^(1/2)*(-x^2+1)^(1/2)/(x^2-1)*x)","A"
239,1,22,21,0.287000," ","int(1/(x^2+4)/(4*x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctanh \left(\frac{x \sqrt{15}}{2 \sqrt{4 x^{2}+1}}\right) \sqrt{15}}{30}$&$22$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-15\right) \ln \left(\frac{31 \RootOf \left(\textit{\_Z}^{2}-15\right) x^{2}+60 \sqrt{4 x^{2}+1}\, x +4 \RootOf \left(\textit{\_Z}^{2}-15\right)}{x^{2}+4}\right)}{60}$&$50$\\ \hline \end{longtable}"," ",0,"1/30*arctanh(1/2*x*15^(1/2)/(4*x^2+1)^(1/2))*15^(1/2)","A"
240,1,49,20,0.301000," ","int(x/(-x^2+3)/(-x^2+5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-7 \RootOf \left(\textit{\_Z}^{2}-2\right)+4 \sqrt{-x^{2}+5}}{x^{2}-3}\right)}{4}$&$49$\\ default&$\frac{\sqrt{2}\, \arctanh \left(\frac{\left(4+2 \sqrt{3}\, \left(x +\sqrt{3}\right)\right) \sqrt{2}}{4 \sqrt{-\left(x +\sqrt{3}\right)^{2}+2 \sqrt{3}\, \left(x +\sqrt{3}\right)+2}}\right)}{4}+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(4-2 \sqrt{3}\, \left(x -\sqrt{3}\right)\right) \sqrt{2}}{4 \sqrt{-\left(x -\sqrt{3}\right)^{2}-2 \sqrt{3}\, \left(x -\sqrt{3}\right)+2}}\right)}{4}$&$100$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*x^2-7*RootOf(_Z^2-2)+4*(-x^2+5)^(1/2))/(x^2-3))","C"
241,1,48,20,0.303000," ","int(x/(-x^2+5)/(-x^2+3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}-\RootOf \left(\textit{\_Z}^{2}+2\right)-4 \sqrt{-x^{2}+3}}{x^{2}-5}\right)}{4}$&$48$\\ default&$-\frac{\sqrt{2}\, \arctan \left(\frac{\left(-4+2 \sqrt{5}\, \left(x +\sqrt{5}\right)\right) \sqrt{2}}{4 \sqrt{-\left(x +\sqrt{5}\right)^{2}+2 \sqrt{5}\, \left(x +\sqrt{5}\right)-2}}\right)}{4}-\frac{\sqrt{2}\, \arctan \left(\frac{\left(-4-2 \sqrt{5}\, \left(x -\sqrt{5}\right)\right) \sqrt{2}}{4 \sqrt{-\left(x -\sqrt{5}\right)^{2}-2 \sqrt{5}\, \left(x -\sqrt{5}\right)-2}}\right)}{4}$&$100$\\ \hline \end{longtable}"," ",0,"1/4*RootOf(_Z^2+2)*ln((RootOf(_Z^2+2)*x^2-RootOf(_Z^2+2)-4*(-x^2+3)^(1/2))/(x^2-5))","C"
242,1,70,31,0.282000," ","int(1/(x^4-1)/(x^2+2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(\frac{x}{\sqrt{x^{2}+2}}\right)}{2}-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(4+2 x \right) \sqrt{3}}{6 \sqrt{\left(-1+x \right)^{2}+1+2 x}}\right)}{12}+\frac{\sqrt{3}\, \arctanh \left(\frac{\left(4-2 x \right) \sqrt{3}}{6 \sqrt{\left(1+x \right)^{2}+1-2 x}}\right)}{12}$&$70$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{2}+3 \sqrt{x^{2}+2}\, x -\RootOf \left(\textit{\_Z}^{2}-3\right)}{\left(1+x \right) \left(-1+x \right)}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\sqrt{x^{2}+2}\, x +\RootOf \left(\textit{\_Z}^{2}+1\right)}{x^{2}+1}\right)}{4}$&$86$\\ \hline \end{longtable}"," ",0,"-1/2*arctan(x/(x^2+2)^(1/2))-1/12*3^(1/2)*arctanh(1/6*(4+2*x)*3^(1/2)/((-1+x)^2+1+2*x)^(1/2))+1/12*3^(1/2)*arctanh(1/6*(4-2*x)*3^(1/2)/((1+x)^2+1-2*x)^(1/2))","B"
243,1,49,48,0.425000," ","int(x/(x^2-1)/(x^2+2*x+4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{7}\, \arctanh \left(\frac{\left(10+4 x \right) \sqrt{7}}{14 \sqrt{\left(-1+x \right)^{2}+3+4 x}}\right)}{14}-\frac{\sqrt{3}\, \arctanh \left(\frac{\sqrt{3}}{\sqrt{\left(1+x \right)^{2}+3}}\right)}{6}$&$49$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-7\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}-7\right) x +7 \sqrt{x^{2}+2 x +4}-5 \RootOf \left(\textit{\_Z}^{2}-7\right)}{-1+x}\right)}{14}-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{\sqrt{x^{2}+2 x +4}+\RootOf \left(\textit{\_Z}^{2}-3\right)}{1+x}\right)}{6}$&$80$\\ \hline \end{longtable}"," ",0,"-1/14*7^(1/2)*arctanh(1/14*(10+4*x)*7^(1/2)/((-1+x)^2+3+4*x)^(1/2))-1/6*3^(1/2)*arctanh(3^(1/2)/((1+x)^2+3)^(1/2))","A"
244,1,69,64,0.581000," ","int(1/(x^3-8)/(x^2+2*x+5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctanh \left(\sqrt{x^{2}+2 x +5}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(2 x +2\right)}{6 \sqrt{x^{2}+2 x +5}}\right)}{12}-\frac{\sqrt{13}\, \arctanh \left(\frac{\left(14+6 x \right) \sqrt{13}}{26 \sqrt{\left(-2+x \right)^{2}+1+6 x}}\right)}{156}$&$69$\\ trager&$\RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \ln \left(-\frac{-2880 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2} x +126 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \sqrt{x^{2}+2 x +5}+306 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x -8 \sqrt{x^{2}+2 x +5}+570 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)-7 x -19}{12 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x -x -2}\right)+\frac{\ln \left(\frac{5760 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2} x +252 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \sqrt{x^{2}+2 x +5}-348 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x -5 \sqrt{x^{2}+2 x +5}+1140 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)+3 x -57}{6 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x +1}\right)}{12}-\ln \left(\frac{5760 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)^{2} x +252 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) \sqrt{x^{2}+2 x +5}-348 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x -5 \sqrt{x^{2}+2 x +5}+1140 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)+3 x -57}{6 \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right) x +1}\right) \RootOf \left(144 \textit{\_Z}^{2}-12 \textit{\_Z} +1\right)-\frac{\RootOf \left(\textit{\_Z}^{2}-13\right) \ln \left(-\frac{3 \RootOf \left(\textit{\_Z}^{2}-13\right) x +13 \sqrt{x^{2}+2 x +5}+7 \RootOf \left(\textit{\_Z}^{2}-13\right)}{-2+x}\right)}{156}$&$388$\\ \hline \end{longtable}"," ",0,"1/12*arctanh((x^2+2*x+5)^(1/2))-1/12*3^(1/2)*arctan(1/6*3^(1/2)/(x^2+2*x+5)^(1/2)*(2*x+2))-1/156*13^(1/2)*arctanh(1/26*(14+6*x)*13^(1/2)/((-2+x)^2+1+6*x)^(1/2))","A"
245,1,53,52,0.750000," ","int(x/(x^2+x+4)/(4*x^2+4*x+5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(\frac{\sqrt{4 x^{2}+4 x +5}\, \sqrt{11}}{11}\right) \sqrt{11}}{11}-\frac{\sqrt{165}\, \arctanh \left(\frac{\sqrt{165}\, \left(8 x +4\right)}{60 \sqrt{4 x^{2}+4 x +5}}\right)}{165}$&$53$\\ trager&$\RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right) \ln \left(-\frac{3524400 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{5} x +111270 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{3} x -41385 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{3}+3420 \sqrt{4 x^{2}+4 x +5}\, \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{2}+754 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right) x -899 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)+52 \sqrt{4 x^{2}+4 x +5}}{165 x \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{2}+3 x -4}\right)+\frac{165 \ln \left(-\frac{8276400 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{5} x +385770 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{3} x +97185 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{3}-9405 \sqrt{4 x^{2}+4 x +5}\, \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{2}+3784 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right) x +1364 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)-256 \sqrt{4 x^{2}+4 x +5}}{165 x \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{2}+4 x +4}\right) \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{3}}{4}+\frac{7 \ln \left(-\frac{8276400 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{5} x +385770 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{3} x +97185 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{3}-9405 \sqrt{4 x^{2}+4 x +5}\, \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{2}+3784 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right) x +1364 \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)-256 \sqrt{4 x^{2}+4 x +5}}{165 x \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)^{2}+4 x +4}\right) \RootOf \left(27225 \textit{\_Z}^{4}+1155 \textit{\_Z}^{2}+16\right)}{4}$&$516$\\ \hline \end{longtable}"," ",0,"1/11*arctan(1/11*(4*x^2+4*x+5)^(1/2)*11^(1/2))*11^(1/2)-1/165*165^(1/2)*arctanh(1/60*165^(1/2)*(8*x+4)/(4*x^2+4*x+5)^(1/2))","A"
246,1,128,46,0.724000," ","int((3+x)/(x^2+1)/(x^2+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\frac{\left(-1+x \right)^{2}}{\left(-1-x \right)^{2}}+3}\, \sqrt{2}\, \left(\arctanh \left(\frac{\sqrt{\frac{\left(-1+x \right)^{2}}{\left(-1-x \right)^{2}}+3}\, \sqrt{2}}{2}\right)-2 \arctan \left(\frac{\sqrt{2}\, \left(-1+x \right)}{\sqrt{\frac{\left(-1+x \right)^{2}}{\left(-1-x \right)^{2}}+3}\, \left(-1-x \right)}\right)\right)}{\sqrt{\frac{\frac{\left(-1+x \right)^{2}}{\left(-1-x \right)^{2}}+3}{\left(1+\frac{-1+x}{-1-x}\right)^{2}}}\, \left(1+\frac{-1+x}{-1-x}\right)}$&$128$\\ trager&$-\frac{2 \ln \left(\frac{-12 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{5} x -172 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{3} x +320 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{2} \sqrt{x^{2}+x +1}+40 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{3}+217 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right) x +960 \sqrt{x^{2}+x +1}+620 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)}{2 x \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{2}+3 x -4}\right) \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{3}}{5}-\frac{6 \ln \left(\frac{-12 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{5} x -172 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{3} x +320 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{2} \sqrt{x^{2}+x +1}+40 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{3}+217 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right) x +960 \sqrt{x^{2}+x +1}+620 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)}{2 x \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{2}+3 x -4}\right) \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)}{5}-\RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right) \ln \left(-\frac{-12 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{4} x -92 x \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{2}+64 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right) \sqrt{x^{2}+x +1}-40 \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{2}-175 x -140}{2 x \RootOf \left(4 \textit{\_Z}^{4}+12 \textit{\_Z}^{2}+25\right)^{2}+3 x +4}\right)$&$452$\\ \hline \end{longtable}"," ",0,"((-1+x)^2/(-1-x)^2+3)^(1/2)*2^(1/2)*(arctanh(1/2*((-1+x)^2/(-1-x)^2+3)^(1/2)*2^(1/2))-2*arctan(2^(1/2)/((-1+x)^2/(-1-x)^2+3)^(1/2)*(-1+x)/(-1-x)))/(((-1+x)^2/(-1-x)^2+3)/(1+(-1+x)/(-1-x))^2)^(1/2)/(1+(-1+x)/(-1-x))","B"
247,1,158,53,0.954000," ","int((1+2*x)/(3*x^2+4*x+4)/(x^2+6*x-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{-\frac{6 \left(-2+x \right)^{2}}{\left(-1-x \right)^{2}}+15}\, \left(4 \sqrt{7}\, \arctanh \left(\frac{\sqrt{-\frac{6 \left(-2+x \right)^{2}}{\left(-1-x \right)^{2}}+15}\, \sqrt{7}}{21}\right)-5 \sqrt{14}\, \arctan \left(\frac{\sqrt{14}\, \sqrt{-\frac{6 \left(-2+x \right)^{2}}{\left(-1-x \right)^{2}}+15}\, \left(-2+x \right)}{4 \left(\frac{2 \left(-2+x \right)^{2}}{\left(-1-x \right)^{2}}-5\right) \left(-1-x \right)}\right)\right)}{84 \sqrt{-\frac{3 \left(\frac{2 \left(-2+x \right)^{2}}{\left(-1-x \right)^{2}}-5\right)}{\left(1+\frac{-2+x}{-1-x}\right)^{2}}}\, \left(1+\frac{-2+x}{-1-x}\right)}$&$158$\\ trager&$\RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right) \ln \left(-\frac{1568802816 x \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{5}+6019776 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{3} x +39686976 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{3}+3171168 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{2} \sqrt{x^{2}+6 x -1}+5768 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right) x +73542 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)+50611 \sqrt{x^{2}+6 x -1}}{2016 x \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{2}-3 x -40}\right)-\frac{672 \ln \left(\frac{159860736 x \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{5}+2221632 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{3} x -4044096 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{3}+352352 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{2} \sqrt{x^{2}+6 x -1}-2340 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right) x +3978 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)+319 \sqrt{x^{2}+6 x -1}}{2016 x \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{2}+37 x +40}\right) \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{3}}{11}-\frac{34 \ln \left(\frac{159860736 x \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{5}+2221632 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{3} x -4044096 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{3}+352352 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{2} \sqrt{x^{2}+6 x -1}-2340 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right) x +3978 \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)+319 \sqrt{x^{2}+6 x -1}}{2016 x \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)^{2}+37 x +40}\right) \RootOf \left(451584 \textit{\_Z}^{4}+7616 \textit{\_Z}^{2}+121\right)}{33}$&$502$\\ \hline \end{longtable}"," ",0,"-1/84*(-6*(-2+x)^2/(-1-x)^2+15)^(1/2)*(4*7^(1/2)*arctanh(1/21*(-6*(-2+x)^2/(-1-x)^2+15)^(1/2)*7^(1/2))-5*14^(1/2)*arctan(1/4*14^(1/2)*(-6*(-2+x)^2/(-1-x)^2+15)^(1/2)/(2*(-2+x)^2/(-1-x)^2-5)*(-2+x)/(-1-x)))/(-3*(2*(-2+x)^2/(-1-x)^2-5)/(1+(-2+x)/(-1-x))^2)^(1/2)/(1+(-2+x)/(-1-x))","B"
248,1,192,64,0.465000," ","int((A*x+B)/(5*x^2-18*x+17)/(10*x^2-22*x+13)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}\, \sqrt{35}\, \left(\arctanh \left(\frac{2 \sqrt{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}\, \sqrt{35}}{35}\right) A -4 \arctan \left(\frac{\sqrt{35}\, \left(-2+x \right)}{\sqrt{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}\, \left(1-x \right)}\right) A +\arctanh \left(\frac{2 \sqrt{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}\, \sqrt{35}}{35}\right) B -2 \arctan \left(\frac{\sqrt{35}\, \left(-2+x \right)}{\sqrt{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}\, \left(1-x \right)}\right) B \right)}{70 \sqrt{\frac{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}{\left(1+\frac{-2+x}{1-x}\right)^{2}}}\, \left(1+\frac{-2+x}{1-x}\right)}$&$192$\\ \hline \end{longtable}"," ",0,"1/70*((-2+x)^2/(1-x)^2+9)^(1/2)*35^(1/2)*(arctanh(2/35*((-2+x)^2/(1-x)^2+9)^(1/2)*35^(1/2))*A-4*arctan(35^(1/2)/((-2+x)^2/(1-x)^2+9)^(1/2)*(-2+x)/(1-x))*A+arctanh(2/35*((-2+x)^2/(1-x)^2+9)^(1/2)*35^(1/2))*B-2*arctan(35^(1/2)/((-2+x)^2/(1-x)^2+9)^(1/2)*(-2+x)/(1-x))*B)/(((-2+x)^2/(1-x)^2+9)/(1+(-2+x)/(1-x))^2)^(1/2)/(1+(-2+x)/(1-x))","B"
249,1,82,28,0.361000," ","int((-2+x)/(5*x^2-18*x+17)/(10*x^2-22*x+13)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-35\right) \ln \left(-\frac{75 \RootOf \left(\textit{\_Z}^{2}-35\right) x^{2}-158 \RootOf \left(\textit{\_Z}^{2}-35\right) x +140 \sqrt{10 x^{2}-22 x +13}\, x +87 \RootOf \left(\textit{\_Z}^{2}-35\right)-140 \sqrt{10 x^{2}-22 x +13}}{5 x^{2}-18 x +17}\right)}{140}$&$82$\\ default&$-\frac{\sqrt{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}\, \sqrt{35}\, \arctanh \left(\frac{2 \sqrt{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}\, \sqrt{35}}{35}\right)}{70 \sqrt{\frac{\frac{\left(-2+x \right)^{2}}{\left(1-x \right)^{2}}+9}{\left(1+\frac{-2+x}{1-x}\right)^{2}}}\, \left(1+\frac{-2+x}{1-x}\right)}$&$94$\\ \hline \end{longtable}"," ",0,"-1/140*RootOf(_Z^2-35)*ln(-(75*RootOf(_Z^2-35)*x^2-158*RootOf(_Z^2-35)*x+140*(10*x^2-22*x+13)^(1/2)*x+87*RootOf(_Z^2-35)-140*(10*x^2-22*x+13)^(1/2))/(5*x^2-18*x+17))","C"
250,1,40,50,0.306000," ","int(x^4*(-x^2+5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x \left(8 x^{4}-10 x^{2}-75\right) \left(x^{2}-5\right)}{48 \sqrt{-x^{2}+5}}+\frac{125 \arcsin \left(\frac{x \sqrt{5}}{5}\right)}{16}$&$40$\\ default&$-\frac{x^{3} \left(-x^{2}+5\right)^{\frac{3}{2}}}{6}-\frac{5 x \left(-x^{2}+5\right)^{\frac{3}{2}}}{8}+\frac{25 x \sqrt{-x^{2}+5}}{16}+\frac{125 \arcsin \left(\frac{x \sqrt{5}}{5}\right)}{16}$&$49$\\ meijerg&$\frac{125 i \left(\frac{i \sqrt{\pi}\, x \sqrt{5}\, \left(-\frac{8}{5} x^{4}+2 x^{2}+15\right) \sqrt{-\frac{x^{2}}{5}+1}}{300}-\frac{i \sqrt{\pi}\, \arcsin \left(\frac{x \sqrt{5}}{5}\right)}{4}\right)}{4 \sqrt{\pi}}$&$52$\\ trager&$\frac{x \left(8 x^{4}-10 x^{2}-75\right) \sqrt{-x^{2}+5}}{48}+\frac{125 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-x^{2}+5}+x \right)}{16}$&$53$\\ \hline \end{longtable}"," ",0,"-1/48*x*(8*x^4-10*x^2-75)*(x^2-5)/(-x^2+5)^(1/2)+125/16*arcsin(1/5*x*5^(1/2))","A"
251,1,25,37,0.325000," ","int(1/x^6/(x^2+2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{\sqrt{x^{2}+2}\, \left(2 x^{4}-2 x^{2}+3\right)}{30 x^{5}}$&$25$\\ trager&$-\frac{\sqrt{x^{2}+2}\, \left(2 x^{4}-2 x^{2}+3\right)}{30 x^{5}}$&$25$\\ meijerg&$-\frac{\sqrt{2}\, \left(\frac{2}{3} x^{4}-\frac{2}{3} x^{2}+1\right) \sqrt{1+\frac{x^{2}}{2}}}{10 x^{5}}$&$30$\\ risch&$-\frac{2 x^{6}+2 x^{4}-x^{2}+6}{30 x^{5} \sqrt{x^{2}+2}}$&$30$\\ default&$-\frac{\sqrt{x^{2}+2}}{10 x^{5}}+\frac{\sqrt{x^{2}+2}}{15 x^{3}}-\frac{\sqrt{x^{2}+2}}{15 x}$&$38$\\ \hline \end{longtable}"," ",0,"-1/30*(x^2+2)^(1/2)*(2*x^4-2*x^2+3)/x^5","A"
252,1,25,37,0.276000," ","int(1/(2*x^2+3)^(7/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x \left(32 x^{4}+120 x^{2}+135\right)}{405 \left(2 x^{2}+3\right)^{\frac{5}{2}}}$&$25$\\ trager&$\frac{x \left(32 x^{4}+120 x^{2}+135\right)}{405 \left(2 x^{2}+3\right)^{\frac{5}{2}}}$&$25$\\ risch&$\frac{x \left(32 x^{4}+120 x^{2}+135\right)}{405 \left(2 x^{2}+3\right)^{\frac{5}{2}}}$&$25$\\ meijerg&$\frac{\sqrt{3}\, x \left(\frac{32}{9} x^{4}+\frac{40}{3} x^{2}+15\right)}{1215 \left(1+\frac{2 x^{2}}{3}\right)^{\frac{5}{2}}}$&$28$\\ default&$\frac{x}{15 \left(2 x^{2}+3\right)^{\frac{5}{2}}}+\frac{4 x}{135 \left(2 x^{2}+3\right)^{\frac{3}{2}}}+\frac{8 x}{405 \sqrt{2 x^{2}+3}}$&$38$\\ \hline \end{longtable}"," ",0,"1/405*x*(32*x^4+120*x^2+135)/(2*x^2+3)^(5/2)","A"
253,1,328,10,0.069000," ","int(x/(1+x^2+a*(x^2+1)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{\left(x -\sqrt{\left(a -1\right) \left(1+a \right)}\right)^{2}+2 \sqrt{\left(a -1\right) \left(1+a \right)}\, \left(x -\sqrt{\left(a -1\right) \left(1+a \right)}\right)+a^{2}}}{2 a}+\frac{a \ln \left(\frac{2 a^{2}+2 \sqrt{\left(a -1\right) \left(1+a \right)}\, \left(x -\sqrt{\left(a -1\right) \left(1+a \right)}\right)+2 \sqrt{a^{2}}\, \sqrt{\left(x -\sqrt{\left(a -1\right) \left(1+a \right)}\right)^{2}+2 \sqrt{\left(a -1\right) \left(1+a \right)}\, \left(x -\sqrt{\left(a -1\right) \left(1+a \right)}\right)+a^{2}}}{x -\sqrt{\left(a -1\right) \left(1+a \right)}}\right)}{2 \sqrt{a^{2}}}+\frac{\sqrt{x^{2}+1}}{a}-\frac{\sqrt{\left(x +\sqrt{\left(a -1\right) \left(1+a \right)}\right)^{2}-2 \sqrt{\left(a -1\right) \left(1+a \right)}\, \left(x +\sqrt{\left(a -1\right) \left(1+a \right)}\right)+a^{2}}}{2 a}+\frac{a \ln \left(\frac{2 a^{2}-2 \sqrt{\left(a -1\right) \left(1+a \right)}\, \left(x +\sqrt{\left(a -1\right) \left(1+a \right)}\right)+2 \sqrt{a^{2}}\, \sqrt{\left(x +\sqrt{\left(a -1\right) \left(1+a \right)}\right)^{2}-2 \sqrt{\left(a -1\right) \left(1+a \right)}\, \left(x +\sqrt{\left(a -1\right) \left(1+a \right)}\right)+a^{2}}}{x +\sqrt{\left(a -1\right) \left(1+a \right)}}\right)}{2 \sqrt{a^{2}}}+\frac{\ln \left(-a^{2}+x^{2}+1\right)}{2}$&$328$\\ \hline \end{longtable}"," ",0,"-1/2/a*((x-((a-1)*(1+a))^(1/2))^2+2*((a-1)*(1+a))^(1/2)*(x-((a-1)*(1+a))^(1/2))+a^2)^(1/2)+1/2*a/(a^2)^(1/2)*ln((2*a^2+2*((a-1)*(1+a))^(1/2)*(x-((a-1)*(1+a))^(1/2))+2*(a^2)^(1/2)*((x-((a-1)*(1+a))^(1/2))^2+2*((a-1)*(1+a))^(1/2)*(x-((a-1)*(1+a))^(1/2))+a^2)^(1/2))/(x-((a-1)*(1+a))^(1/2)))+1/a*(x^2+1)^(1/2)-1/2/a*((x+((a-1)*(1+a))^(1/2))^2-2*((a-1)*(1+a))^(1/2)*(x+((a-1)*(1+a))^(1/2))+a^2)^(1/2)+1/2*a/(a^2)^(1/2)*ln((2*a^2-2*((a-1)*(1+a))^(1/2)*(x+((a-1)*(1+a))^(1/2))+2*(a^2)^(1/2)*((x+((a-1)*(1+a))^(1/2))^2-2*((a-1)*(1+a))^(1/2)*(x+((a-1)*(1+a))^(1/2))+a^2)^(1/2))/(x+((a-1)*(1+a))^(1/2)))+1/2*ln(-a^2+x^2+1)","B"
254,1,11,10,0.349000," ","int((x^2-x+1)/(x^2+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\arcsinh \left(x \right)+\frac{1}{\sqrt{x^{2}+1}}$&$11$\\ risch&$\arcsinh \left(x \right)+\frac{1}{\sqrt{x^{2}+1}}$&$11$\\ trager&$\frac{1}{\sqrt{x^{2}+1}}-\ln \left(x -\sqrt{x^{2}+1}\right)$&$23$\\ meijerg&$\frac{x}{\sqrt{x^{2}+1}}+\frac{-\frac{\sqrt{\pi}\, x}{\sqrt{x^{2}+1}}+\sqrt{\pi}\, \arcsinh \left(x \right)}{\sqrt{\pi}}-\frac{\sqrt{\pi}-\frac{\sqrt{\pi}}{\sqrt{x^{2}+1}}}{\sqrt{\pi}}$&$56$\\ \hline \end{longtable}"," ",0,"arcsinh(x)+1/(x^2+1)^(1/2)","A"
255,1,23,22,0.276000," ","int((x^2+1)^(1/2)/(x^2+2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\arcsinh \left(x \right)-\frac{\arctanh \left(\frac{x \sqrt{2}}{2 \sqrt{x^{2}+1}}\right) \sqrt{2}}{2}$&$23$\\ trager&$-\ln \left(x -\sqrt{x^{2}+1}\right)+\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-4 x \sqrt{x^{2}+1}+2 \RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{2}+2}\right)}{4}$&$64$\\ \hline \end{longtable}"," ",0,"arcsinh(x)-1/2*arctanh(1/2*x*2^(1/2)/(x^2+1)^(1/2))*2^(1/2)","A"
256,1,38,37,0.283000," ","int(1/(x^2+2)^2/(x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 \arctanh \left(\frac{x \sqrt{2}}{2 \sqrt{x^{2}+1}}\right) \sqrt{2}}{8}-\frac{x \sqrt{x^{2}+1}}{4 \left(x^{2}+2\right)}$&$38$\\ default&$\frac{x}{4 \sqrt{x^{2}+1}\, \left(\frac{x^{2}}{x^{2}+1}-2\right)}+\frac{3 \arctanh \left(\frac{x \sqrt{2}}{2 \sqrt{x^{2}+1}}\right) \sqrt{2}}{8}$&$46$\\ trager&$-\frac{x \sqrt{x^{2}+1}}{4 \left(x^{2}+2\right)}-\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{3 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{2}-4 x \sqrt{x^{2}+1}+2 \RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{2}+2}\right)}{16}$&$67$\\ \hline \end{longtable}"," ",0,"3/8*arctanh(1/2*x*2^(1/2)/(x^2+1)^(1/2))*2^(1/2)-1/4*x*(x^2+1)^(1/2)/(x^2+2)","A"
257,1,64,30,0.313000," ","int(x^2/(x^2-6)/(x^2-2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(x -\sqrt{x^{2}-2}\right)-\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(-\frac{5 \RootOf \left(\textit{\_Z}^{2}-6\right) x^{2}+12 \sqrt{x^{2}-2}\, x -6 \RootOf \left(\textit{\_Z}^{2}-6\right)}{x^{2}-6}\right)}{4}$&$64$\\ default&$\ln \left(x +\sqrt{x^{2}-2}\right)-\frac{\sqrt{6}\, \arctanh \left(\frac{8+2 \sqrt{6}\, \left(x -\sqrt{6}\right)}{4 \sqrt{\left(x -\sqrt{6}\right)^{2}+2 \sqrt{6}\, \left(x -\sqrt{6}\right)+4}}\right)}{4}+\frac{\sqrt{6}\, \arctanh \left(\frac{8-2 \sqrt{6}\, \left(x +\sqrt{6}\right)}{4 \sqrt{\left(x +\sqrt{6}\right)^{2}-2 \sqrt{6}\, \left(x +\sqrt{6}\right)+4}}\right)}{4}$&$100$\\ \hline \end{longtable}"," ",0,"-ln(x-(x^2-2)^(1/2))-1/4*RootOf(_Z^2-6)*ln(-(5*RootOf(_Z^2-6)*x^2+12*(x^2-2)^(1/2)*x-6*RootOf(_Z^2-6))/(x^2-6))","C"
258,1,53,39,0.309000," ","int((x^2+5)/(x^2+1)^2/(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{x \left(x^{2}-1\right)}{\left(x^{2}+1\right) \sqrt{-x^{2}+1}}-2 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{-x^{2}+1}\, x}{x^{2}-1}\right)$&$53$\\ trager&$\frac{x \sqrt{-x^{2}+1}}{x^{2}+1}+\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{-3 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{2}+4 \sqrt{-x^{2}+1}\, x +\RootOf \left(\textit{\_Z}^{2}+2\right)}{x^{2}+1}\right)$&$66$\\ default&$-2 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{-x^{2}+1}\, x}{x^{2}-1}\right)-\frac{\sqrt{-x^{2}+1}\, x}{2 \left(x^{2}-1\right) \left(\frac{\left(-x^{2}+1\right) x^{2}}{\left(x^{2}-1\right)^{2}}+\frac{1}{2}\right)}$&$70$\\ \hline \end{longtable}"," ",0,"-x*(x^2-1)/(x^2+1)/(-x^2+1)^(1/2)-2*2^(1/2)*arctan(2^(1/2)*(-x^2+1)^(1/2)/(x^2-1)*x)","A"
259,1,82,66,0.920000," ","int((4*x-(-x^2+1)^(1/2))/(5+(-x^2+1)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{25 \arctan \left(\frac{x \sqrt{6}}{12}\right) \sqrt{6}}{12}+10 \ln \left(x^{2}+24\right)-x +5 \arcsin \left(x \right)+\frac{25 \sqrt{6}\, \arctan \left(\frac{5 \sqrt{6}\, \sqrt{-x^{2}+1}\, x}{12 \left(x^{2}-1\right)}\right)}{12}-4 \sqrt{-x^{2}+1}+20 \arctanh \left(\frac{\sqrt{-x^{2}+1}}{5}\right)$&$82$\\ trager&$-x -4 \sqrt{-x^{2}+1}+5 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \ln \left(\frac{-25 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)^{2} \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) x -24 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)^{2} x +49 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) \sqrt{-x^{2}+1}+100 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)^{2} x -8 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) x -96 x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)^{2}-196 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \sqrt{-x^{2}+1}+196 \sqrt{-x^{2}+1}\, \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-5 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)+441 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) x +392 x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-834 \sqrt{-x^{2}+1}+20 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)-20 \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)+68 x +85}{x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-4 x -5}\right)-5 \ln \left(-\frac{25 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)^{2} \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) x -24 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)^{2} x +49 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) \sqrt{-x^{2}+1}-100 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)^{2} x +392 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) x -96 x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)^{2}-196 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \sqrt{-x^{2}+1}+196 \sqrt{-x^{2}+1}\, \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-5 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-1159 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) x +1144 x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-734 \sqrt{-x^{2}+1}+20 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)-20 \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-2940 x +75}{x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-4 x -5}\right) \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)-5 \ln \left(\frac{24 \sqrt{-x^{2}+1}\, \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-96 \sqrt{-x^{2}+1}+25 x}{x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-4 x -5}\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-40 \ln \left(-\frac{25 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)^{2} \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) x -24 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)^{2} x +49 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) \sqrt{-x^{2}+1}-100 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)^{2} x +392 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right) x -96 x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)^{2}-196 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \sqrt{-x^{2}+1}+196 \sqrt{-x^{2}+1}\, \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-5 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-1159 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right) x +1144 x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-734 \sqrt{-x^{2}+1}+20 \RootOf \left(\textit{\_Z}^{2}+8 \textit{\_Z} +17\right)-20 \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-2940 x +75}{x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-4 x -5}\right)+40 \ln \left(\frac{24 \sqrt{-x^{2}+1}\, \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-96 \sqrt{-x^{2}+1}+25 x}{x \RootOf \left(24 \textit{\_Z}^{2}-192 \textit{\_Z} +409\right)-4 x -5}\right)$&$1033$\\ \hline \end{longtable}"," ",0,"25/12*arctan(1/12*x*6^(1/2))*6^(1/2)+10*ln(x^2+24)-x+5*arcsin(x)+25/12*6^(1/2)*arctan(5/12*6^(1/2)*(-x^2+1)^(1/2)/(x^2-1)*x)-4*(-x^2+1)^(1/2)+20*arctanh(1/5*(-x^2+1)^(1/2))","A"
260,1,654,99,0.048000," ","int(x^2*(2-(x^2+1)^(1/2))/(1-x^3+(x^2+1)^(3/2))/(x^2+1)^(1/2),x)","\[-\frac{x^{2}}{6}+\frac{8 x}{9}-\frac{7 \ln \left(3 x^{2}+2 x +3\right)}{54}+\frac{4 \sqrt{2}\, \arctan \left(\frac{\left(6 x +2\right) \sqrt{2}}{8}\right)}{27}-\frac{41 \arcsinh \left(x \right)}{54}-\frac{\sqrt{2}\, \sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\, \left(-\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\, \left(1+x \right)}{2 \left(\frac{\left(1+x \right)^{2}}{\left(1-x \right)^{2}}+1\right) \left(1-x \right)}\right)+5 \arctanh \left(\sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\right)\right)}{12 \sqrt{\frac{\frac{\left(1+x \right)^{2}}{\left(1-x \right)^{2}}+1}{\left(1+\frac{1+x}{1-x}\right)^{2}}}\, \left(1+\frac{1+x}{1-x}\right)}+\frac{3 \sqrt{2}\, \sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\, \left(-\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\, \left(1+x \right)}{2 \left(\frac{\left(1+x \right)^{2}}{\left(1-x \right)^{2}}+1\right) \left(1-x \right)}\right)+\arctanh \left(\sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\right)\right)}{8 \sqrt{\frac{\frac{\left(1+x \right)^{2}}{\left(1-x \right)^{2}}+1}{\left(1+\frac{1+x}{1-x}\right)^{2}}}\, \left(1+\frac{1+x}{1-x}\right)}-\frac{x \sqrt{x^{2}+1}}{6}+\frac{8 \sqrt{x^{2}+1}}{9}+\frac{\sqrt{2}\, \sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\, \left(13 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\, \left(1+x \right)}{2 \left(\frac{\left(1+x \right)^{2}}{\left(1-x \right)^{2}}+1\right) \left(1-x \right)}\right)+43 \arctanh \left(\sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\right)\right)}{216 \sqrt{\frac{\frac{\left(1+x \right)^{2}}{\left(1-x \right)^{2}}+1}{\left(1+\frac{1+x}{1-x}\right)^{2}}}\, \left(1+\frac{1+x}{1-x}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\, \left(-11 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\, \left(1+x \right)}{2 \left(\frac{\left(1+x \right)^{2}}{\left(1-x \right)^{2}}+1\right) \left(1-x \right)}\right)+\arctanh \left(\sqrt{\frac{2 \left(1+x \right)^{2}}{\left(1-x \right)^{2}}+2}\right)\right)}{36 \sqrt{\frac{\frac{\left(1+x \right)^{2}}{\left(1-x \right)^{2}}+1}{\left(1+\frac{1+x}{1-x}\right)^{2}}}\, \left(1+\frac{1+x}{1-x}\right)}\]"," ",0,"-1/6*x^2+8/9*x-7/54*ln(3*x^2+2*x+3)+4/27*2^(1/2)*arctan(1/8*(6*x+2)*2^(1/2))-41/54*arcsinh(x)-1/12*2^(1/2)*(2*(1+x)^2/(1-x)^2+2)^(1/2)*(-2^(1/2)*arctan(1/2*2^(1/2)*(2*(1+x)^2/(1-x)^2+2)^(1/2)/((1+x)^2/(1-x)^2+1)*(1+x)/(1-x))+5*arctanh((2*(1+x)^2/(1-x)^2+2)^(1/2)))/(((1+x)^2/(1-x)^2+1)/(1+(1+x)/(1-x))^2)^(1/2)/(1+(1+x)/(1-x))+3/8*2^(1/2)*(2*(1+x)^2/(1-x)^2+2)^(1/2)*(-2^(1/2)*arctan(1/2*2^(1/2)*(2*(1+x)^2/(1-x)^2+2)^(1/2)/((1+x)^2/(1-x)^2+1)*(1+x)/(1-x))+arctanh((2*(1+x)^2/(1-x)^2+2)^(1/2)))/(((1+x)^2/(1-x)^2+1)/(1+(1+x)/(1-x))^2)^(1/2)/(1+(1+x)/(1-x))-1/6*x*(x^2+1)^(1/2)+8/9*(x^2+1)^(1/2)+1/216*2^(1/2)*(2*(1+x)^2/(1-x)^2+2)^(1/2)*(13*2^(1/2)*arctan(1/2*2^(1/2)*(2*(1+x)^2/(1-x)^2+2)^(1/2)/((1+x)^2/(1-x)^2+1)*(1+x)/(1-x))+43*arctanh((2*(1+x)^2/(1-x)^2+2)^(1/2)))/(((1+x)^2/(1-x)^2+1)/(1+(1+x)/(1-x))^2)^(1/2)/(1+(1+x)/(1-x))-1/36*2^(1/2)*(2*(1+x)^2/(1-x)^2+2)^(1/2)*(-11*2^(1/2)*arctan(1/2*2^(1/2)*(2*(1+x)^2/(1-x)^2+2)^(1/2)/((1+x)^2/(1-x)^2+1)*(1+x)/(1-x))+arctanh((2*(1+x)^2/(1-x)^2+2)^(1/2)))/(((1+x)^2/(1-x)^2+1)/(1+(1+x)/(1-x))^2)^(1/2)/(1+(1+x)/(1-x))","B"
261,1,60,54,0.306000," ","int(x*(2*r*x-x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(3 r^{2}+r x -2 x^{2}\right) x \left(2 r -x \right)}{6 \sqrt{-x \left(-2 r +x \right)}}+\frac{r^{3} \arctan \left(\frac{x -r}{\sqrt{2 r x -x^{2}}}\right)}{2}$&$60$\\ default&$-\frac{\left(2 r x -x^{2}\right)^{\frac{3}{2}}}{3}+r \left(-\frac{\left(2 r -2 x \right) \sqrt{2 r x -x^{2}}}{4}+\frac{r^{2} \arctan \left(\frac{x -r}{\sqrt{2 r x -x^{2}}}\right)}{2}\right)$&$64$\\ \hline \end{longtable}"," ",0,"-1/6*(3*r^2+r*x-2*x^2)*x*(2*r-x)/(-x*(-2*r+x))^(1/2)+1/2*r^3*arctan((x-r)/(2*r*x-x^2)^(1/2))","A"
262,1,69,73,0.291000," ","int(x^2*(2*r*x-x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(15 r^{3}+5 r^{2} x +2 r \,x^{2}-6 x^{3}\right) x \left(2 r -x \right)}{24 \sqrt{-x \left(-2 r +x \right)}}+\frac{5 r^{4} \arctan \left(\frac{x -r}{\sqrt{2 r x -x^{2}}}\right)}{8}$&$69$\\ default&$-\frac{x \left(2 r x -x^{2}\right)^{\frac{3}{2}}}{4}+\frac{5 r \left(-\frac{\left(2 r x -x^{2}\right)^{\frac{3}{2}}}{3}+r \left(-\frac{\left(2 r -2 x \right) \sqrt{2 r x -x^{2}}}{4}+\frac{r^{2} \arctan \left(\frac{x -r}{\sqrt{2 r x -x^{2}}}\right)}{2}\right)\right)}{4}$&$83$\\ \hline \end{longtable}"," ",0,"-1/24*(15*r^3+5*r^2*x+2*r*x^2-6*x^3)*x*(2*r-x)/(-x*(-2*r+x))^(1/2)+5/8*r^4*arctan((x-r)/(2*r*x-x^2)^(1/2))","A"
263,1,77,93,0.286000," ","int(x^3*(2*r*x-x^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\left(105 r^{4}+35 r^{3} x +14 r^{2} x^{2}+6 r \,x^{3}-24 x^{4}\right) x \left(2 r -x \right)}{120 \sqrt{-x \left(-2 r +x \right)}}+\frac{7 r^{5} \arctan \left(\frac{x -r}{\sqrt{2 r x -x^{2}}}\right)}{8}$&$77$\\ default&$-\frac{x^{2} \left(2 r x -x^{2}\right)^{\frac{3}{2}}}{5}+\frac{7 r \left(-\frac{x \left(2 r x -x^{2}\right)^{\frac{3}{2}}}{4}+\frac{5 r \left(-\frac{\left(2 r x -x^{2}\right)^{\frac{3}{2}}}{3}+r \left(-\frac{\left(2 r -2 x \right) \sqrt{2 r x -x^{2}}}{4}+\frac{r^{2} \arctan \left(\frac{x -r}{\sqrt{2 r x -x^{2}}}\right)}{2}\right)\right)}{4}\right)}{5}$&$104$\\ \hline \end{longtable}"," ",0,"-1/120*(105*r^4+35*r^3*x+14*r^2*x^2+6*r*x^3-24*x^4)*x*(2*r-x)/(-x*(-2*r+x))^(1/2)+7/8*r^5*arctan((x-r)/(2*r*x-x^2)^(1/2))","A"
264,1,42,38,0.296000," ","int(1/(x^2-1)/(x^2+2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{3}\, \arctanh \left(\frac{\left(2+4 x \right) \sqrt{3}}{6 \sqrt{\left(-1+x \right)^{2}-1+4 x}}\right)}{6}+\frac{\arctan \left(\frac{1}{\sqrt{\left(1+x \right)^{2}-1}}\right)}{2}$&$42$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}-3\right) x +3 \sqrt{x^{2}+2 x}-\RootOf \left(\textit{\_Z}^{2}-3\right)}{-1+x}\right)}{6}-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+1\right)+\sqrt{x^{2}+2 x}}{1+x}\right)}{2}$&$77$\\ \hline \end{longtable}"," ",0,"-1/6*3^(1/2)*arctanh(1/6*(2+4*x)*3^(1/2)/((-1+x)^2-1+4*x)^(1/2))+1/2*arctan(1/((1+x)^2-1)^(1/2))","A"
265,1,56,64,0.290000," ","int((-2+3*x)/(1+x)^3/(-x^2+2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x \left(-2+x \right) \left(9+4 x \right)}{6 \left(1+x \right)^{2} \sqrt{-x \left(-2+x \right)}}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(-2+4 x \right) \sqrt{3}}{6 \sqrt{-\left(1+x \right)^{2}+1+4 x}}\right)}{6}$&$56$\\ trager&$-\frac{\left(9+4 x \right) \sqrt{-x^{2}+2 x}}{6 \left(1+x \right)^{2}}+\frac{\RootOf \left(\textit{\_Z}^{2}+3\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+3\right) x +3 \sqrt{-x^{2}+2 x}-\RootOf \left(\textit{\_Z}^{2}+3\right)}{1+x}\right)}{6}$&$71$\\ default&$-\frac{5 \sqrt{-\left(1+x \right)^{2}+1+4 x}}{6 \left(1+x \right)^{2}}-\frac{2 \sqrt{-\left(1+x \right)^{2}+1+4 x}}{3 \left(1+x \right)}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(-2+4 x \right) \sqrt{3}}{6 \sqrt{-\left(1+x \right)^{2}+1+4 x}}\right)}{6}$&$74$\\ \hline \end{longtable}"," ",0,"1/6*x*(-2+x)*(9+4*x)/(1+x)^2/(-x*(-2+x))^(1/2)-1/6*3^(1/2)*arctan(1/6*(-2+4*x)*3^(1/2)/(-(1+x)^2+1+4*x)^(1/2))","A"
266,1,10,11,0.353000," ","int(1/(x^2+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)$&$10$\\ trager&$-\ln \left(2 \sqrt{x^{2}+x +1}-1-2 x \right)$&$19$\\ \hline \end{longtable}"," ",0,"arcsinh(2/3*(1/2+x)*3^(1/2))","A"
267,1,33,42,0.348000," ","int(x^3/(x^2+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(8 x^{2}-10 x -1\right) \sqrt{x^{2}+x +1}}{24}+\frac{7 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{16}$&$33$\\ trager&$\left(\frac{1}{3} x^{2}-\frac{5}{12} x -\frac{1}{24}\right) \sqrt{x^{2}+x +1}-\frac{7 \ln \left(2 \sqrt{x^{2}+x +1}-1-2 x \right)}{16}$&$39$\\ default&$\frac{x^{2} \sqrt{x^{2}+x +1}}{3}-\frac{5 x \sqrt{x^{2}+x +1}}{12}-\frac{\sqrt{x^{2}+x +1}}{24}+\frac{7 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{16}$&$47$\\ \hline \end{longtable}"," ",0,"1/24*(8*x^2-10*x-1)*(x^2+x+1)^(1/2)+7/16*arcsinh(2/3*(1/2+x)*3^(1/2))","A"
268,1,16,15,0.338000," ","int(1/(x^2+x+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\frac{4 x}{3}+\frac{2}{3}}{\sqrt{x^{2}+x +1}}$&$16$\\ default&$\frac{\frac{4 x}{3}+\frac{2}{3}}{\sqrt{x^{2}+x +1}}$&$16$\\ trager&$\frac{\frac{4 x}{3}+\frac{2}{3}}{\sqrt{x^{2}+x +1}}$&$16$\\ risch&$\frac{\frac{4 x}{3}+\frac{2}{3}}{\sqrt{x^{2}+x +1}}$&$16$\\ \hline \end{longtable}"," ",0,"2/3*(1+2*x)/(x^2+x+1)^(1/2)","A"
269,1,14,13,0.348000," ","int(x/(x^2+x+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{2 \left(2+x \right)}{3 \sqrt{x^{2}+x +1}}$&$14$\\ trager&$-\frac{2 \left(2+x \right)}{3 \sqrt{x^{2}+x +1}}$&$14$\\ risch&$-\frac{2 \left(2+x \right)}{3 \sqrt{x^{2}+x +1}}$&$14$\\ default&$-\frac{1}{\sqrt{x^{2}+x +1}}-\frac{1+2 x}{3 \sqrt{x^{2}+x +1}}$&$27$\\ \hline \end{longtable}"," ",0,"-2/3*(2+x)/(x^2+x+1)^(1/2)","A"
270,1,33,45,0.348000," ","int(x^3/(x^2+x+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x^{2}+7 x +5}{3 \sqrt{x^{2}+x +1}}-\frac{3 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{2}$&$33$\\ trager&$\frac{3 x^{2}+7 x +5}{3 \sqrt{x^{2}+x +1}}+\frac{3 \ln \left(2 \sqrt{x^{2}+x +1}-1-2 x \right)}{2}$&$40$\\ default&$\frac{x^{2}}{\sqrt{x^{2}+x +1}}+\frac{3 x}{2 \sqrt{x^{2}+x +1}}+\frac{5}{4 \sqrt{x^{2}+x +1}}+\frac{\frac{5}{12}+\frac{5 x}{6}}{\sqrt{x^{2}+x +1}}-\frac{3 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{2}$&$61$\\ \hline \end{longtable}"," ",0,"1/3*(3*x^2+7*x+5)/(x^2+x+1)^(1/2)-3/2*arcsinh(2/3*(1/2+x)*3^(1/2))","A"
271,1,38,50,0.352000," ","int(x^2*(x^2+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(48 x^{3}+8 x^{2}+14 x -37\right) \sqrt{x^{2}+x +1}}{192}+\frac{3 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{128}$&$38$\\ trager&$\left(\frac{1}{4} x^{3}+\frac{1}{24} x^{2}+\frac{7}{96} x -\frac{37}{192}\right) \sqrt{x^{2}+x +1}-\frac{3 \ln \left(2 \sqrt{x^{2}+x +1}-1-2 x \right)}{128}$&$44$\\ default&$\frac{x \left(x^{2}+x +1\right)^{\frac{3}{2}}}{4}-\frac{5 \left(x^{2}+x +1\right)^{\frac{3}{2}}}{24}+\frac{\left(1+2 x \right) \sqrt{x^{2}+x +1}}{64}+\frac{3 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{128}$&$49$\\ \hline \end{longtable}"," ",0,"1/192*(48*x^3+8*x^2+14*x-37)*(x^2+x+1)^(1/2)+3/128*arcsinh(2/3*(1/2+x)*3^(1/2))","A"
272,1,38,44,0.348000," ","int((x^2+x+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(16 x^{3}+24 x^{2}+42 x +17\right) \sqrt{x^{2}+x +1}}{64}+\frac{27 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{128}$&$38$\\ default&$\frac{\left(1+2 x \right) \left(x^{2}+x +1\right)^{\frac{3}{2}}}{8}+\frac{9 \left(1+2 x \right) \sqrt{x^{2}+x +1}}{64}+\frac{27 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{128}$&$43$\\ trager&$\left(\frac{1}{4} x^{3}+\frac{3}{8} x^{2}+\frac{21}{32} x +\frac{17}{64}\right) \sqrt{x^{2}+x +1}+\frac{27 \ln \left(1+2 x +2 \sqrt{x^{2}+x +1}\right)}{128}$&$44$\\ \hline \end{longtable}"," ",0,"1/64*(16*x^3+24*x^2+42*x+17)*(x^2+x+1)^(1/2)+27/128*arcsinh(2/3*(1/2+x)*3^(1/2))","A"
273,1,48,59,0.348000," ","int((x^2+x+1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(256 x^{5}+640 x^{4}+1264 x^{3}+1256 x^{2}+1142 x +383\right) \sqrt{x^{2}+x +1}}{1536}+\frac{135 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{1024}$&$48$\\ trager&$\left(\frac{1}{6} x^{5}+\frac{5}{12} x^{4}+\frac{79}{96} x^{3}+\frac{157}{192} x^{2}+\frac{571}{768} x +\frac{383}{1536}\right) \sqrt{x^{2}+x +1}-\frac{135 \ln \left(2 \sqrt{x^{2}+x +1}-1-2 x \right)}{1024}$&$54$\\ default&$\frac{\left(1+2 x \right) \left(x^{2}+x +1\right)^{\frac{5}{2}}}{12}+\frac{5 \left(1+2 x \right) \left(x^{2}+x +1\right)^{\frac{3}{2}}}{64}+\frac{45 \left(1+2 x \right) \sqrt{x^{2}+x +1}}{512}+\frac{135 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{1024}$&$58$\\ \hline \end{longtable}"," ",0,"1/1536*(256*x^5+640*x^4+1264*x^3+1256*x^2+1142*x+383)*(x^2+x+1)^(1/2)+135/1024*arcsinh(2/3*(1/2+x)*3^(1/2))","A"
274,1,31,30,0.346000," ","int(1/x^2/(x^2+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)}{2}-\frac{\sqrt{x^{2}+x +1}}{x}$&$31$\\ risch&$\frac{\arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)}{2}-\frac{\sqrt{x^{2}+x +1}}{x}$&$31$\\ trager&$-\frac{\sqrt{x^{2}+x +1}}{x}+\frac{\ln \left(\frac{2 \sqrt{x^{2}+x +1}+2+x}{x}\right)}{2}$&$35$\\ \hline \end{longtable}"," ",0,"1/2*arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))-(x^2+x+1)^(1/2)/x","A"
275,1,42,43,0.355000," ","int(1/x^3/(x^2+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(-2+3 x \right) \sqrt{x^{2}+x +1}}{4 x^{2}}-\frac{\ln \left(\frac{-2-x +2 \sqrt{x^{2}+x +1}}{x}\right)}{8}$&$42$\\ risch&$\frac{3 x^{3}+x^{2}+x -2}{4 x^{2} \sqrt{x^{2}+x +1}}+\frac{\arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)}{8}$&$42$\\ default&$\frac{\arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)}{8}-\frac{\sqrt{x^{2}+x +1}}{2 x^{2}}+\frac{3 \sqrt{x^{2}+x +1}}{4 x}$&$44$\\ \hline \end{longtable}"," ",0,"1/4*(-2+3*x)/x^2*(x^2+x+1)^(1/2)-1/8*ln((-2-x+2*(x^2+x+1)^(1/2))/x)","A"
276,1,41,48,0.355000," ","int(1/x^2/(x^2+x+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{5 x^{2}+7 x +3}{3 x \sqrt{x^{2}+x +1}}+\frac{3 \arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)}{2}$&$41$\\ trager&$-\frac{5 x^{2}+7 x +3}{3 x \sqrt{x^{2}+x +1}}-\frac{3 \ln \left(\frac{-2-x +2 \sqrt{x^{2}+x +1}}{x}\right)}{2}$&$47$\\ default&$-\frac{1}{x \sqrt{x^{2}+x +1}}-\frac{3}{2 \sqrt{x^{2}+x +1}}-\frac{5 \left(1+2 x \right)}{6 \sqrt{x^{2}+x +1}}+\frac{3 \arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)}{2}$&$56$\\ \hline \end{longtable}"," ",0,"-1/3*(5*x^2+7*x+3)/x/(x^2+x+1)^(1/2)+3/2*arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))","A"
277,1,46,61,0.351000," ","int(1/x^3/(x^2+x+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{37 x^{3}+23 x^{2}+15 x -6}{12 \sqrt{x^{2}+x +1}\, x^{2}}-\frac{3 \arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)}{8}$&$46$\\ trager&$\frac{37 x^{3}+23 x^{2}+15 x -6}{12 \sqrt{x^{2}+x +1}\, x^{2}}+\frac{3 \ln \left(\frac{-2-x +2 \sqrt{x^{2}+x +1}}{x}\right)}{8}$&$52$\\ default&$-\frac{1}{2 x^{2} \sqrt{x^{2}+x +1}}+\frac{5}{4 x \sqrt{x^{2}+x +1}}+\frac{3}{8 \sqrt{x^{2}+x +1}}+\frac{\frac{37}{24}+\frac{37 x}{12}}{\sqrt{x^{2}+x +1}}-\frac{3 \arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)}{8}$&$69$\\ \hline \end{longtable}"," ",0,"1/12*(37*x^3+23*x^2+15*x-6)/(x^2+x+1)^(1/2)/x^2-3/8*arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))","A"
278,1,22,18,0.355000," ","int(1/(1+x)/(x^2+x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\arctanh \left(\frac{1-x}{2 \sqrt{\left(1+x \right)^{2}-x}}\right)$&$22$\\ trager&$-\ln \left(\frac{2 \sqrt{x^{2}+x +1}+1-x}{1+x}\right)$&$25$\\ \hline \end{longtable}"," ",0,"-arctanh(1/2*(1-x)/((1+x)^2-x)^(1/2))","A"
279,1,69,66,0.416000," ","int(1/(x^3-x)/(x^2+2*x+4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctanh \left(\frac{8+2 x}{4 \sqrt{x^{2}+2 x +4}}\right)}{2}-\frac{\sqrt{7}\, \arctanh \left(\frac{\left(10+4 x \right) \sqrt{7}}{14 \sqrt{\left(-1+x \right)^{2}+3+4 x}}\right)}{14}-\frac{\sqrt{3}\, \arctanh \left(\frac{\sqrt{3}}{\sqrt{\left(1+x \right)^{2}+3}}\right)}{6}$&$69$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-7\right) \ln \left(\frac{-2 \RootOf \left(\textit{\_Z}^{2}-7\right) x +7 \sqrt{x^{2}+2 x +4}-5 \RootOf \left(\textit{\_Z}^{2}-7\right)}{-1+x}\right)}{14}-\frac{\ln \left(\frac{-4-x +2 \sqrt{x^{2}+2 x +4}}{x}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(\frac{-\RootOf \left(\textit{\_Z}^{2}-3\right)+\sqrt{x^{2}+2 x +4}}{1+x}\right)}{6}$&$105$\\ \hline \end{longtable}"," ",0,"1/2*arctanh(1/4*(8+2*x)/(x^2+2*x+4)^(1/2))-1/14*7^(1/2)*arctanh(1/14*(10+4*x)*7^(1/2)/((-1+x)^2+3+4*x)^(1/2))-1/6*3^(1/2)*arctanh(3^(1/2)/((1+x)^2+3)^(1/2))","A"
280,1,56,54,0.382000," ","int((x^2+2*x+4)^(1/2)/(-1+x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{\sqrt{x^{2}+2 x +4}}{-1+x}+\arcsinh \left(\frac{\left(1+x \right) \sqrt{3}}{3}\right)-\frac{2 \sqrt{7}\, \arctanh \left(\frac{\left(10+4 x \right) \sqrt{7}}{14 \sqrt{\left(-1+x \right)^{2}+3+4 x}}\right)}{7}$&$56$\\ trager&$-\frac{\sqrt{x^{2}+2 x +4}}{-1+x}+\ln \left(1+x +\sqrt{x^{2}+2 x +4}\right)+\frac{2 \RootOf \left(\textit{\_Z}^{2}-7\right) \ln \left(-\frac{-2 \RootOf \left(\textit{\_Z}^{2}-7\right) x +7 \sqrt{x^{2}+2 x +4}-5 \RootOf \left(\textit{\_Z}^{2}-7\right)}{-1+x}\right)}{7}$&$79$\\ default&$-\frac{\left(\left(-1+x \right)^{2}+3+4 x \right)^{\frac{3}{2}}}{7 \left(-1+x \right)}+\frac{2 \sqrt{\left(-1+x \right)^{2}+3+4 x}}{7}+\arcsinh \left(\frac{\left(1+x \right) \sqrt{3}}{3}\right)-\frac{2 \sqrt{7}\, \arctanh \left(\frac{\left(10+4 x \right) \sqrt{7}}{14 \sqrt{\left(-1+x \right)^{2}+3+4 x}}\right)}{7}+\frac{\left(2 x +2\right) \sqrt{\left(-1+x \right)^{2}+3+4 x}}{14}$&$91$\\ \hline \end{longtable}"," ",0,"-1/(-1+x)*(x^2+2*x+4)^(1/2)+arcsinh(1/3*(1+x)*3^(1/2))-2/7*7^(1/2)*arctanh(1/14*(10+4*x)*7^(1/2)/((-1+x)^2+3+4*x)^(1/2))","A"
281,1,64,63,0.715000," ","int((3+2*x)/(x^2+2*x+3)^2/(x^2+2*x+4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(-3+x \right) \sqrt{x^{2}+2 x +4}}{4 x^{2}+8 x +12}+\arctanh \left(\sqrt{x^{2}+2 x +4}\right)-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \left(2 x +2\right)}{4 \sqrt{x^{2}+2 x +4}}\right)}{8}$&$64$\\ default&$-\frac{1}{2 \left(\sqrt{x^{2}+2 x +4}-1\right)}-\frac{\ln \left(\sqrt{x^{2}+2 x +4}-1\right)}{2}-\frac{1}{2 \left(\sqrt{x^{2}+2 x +4}+1\right)}+\frac{\ln \left(\sqrt{x^{2}+2 x +4}+1\right)}{2}+\frac{\frac{3}{4}+\frac{3 x}{4}}{\sqrt{x^{2}+2 x +4}\, \left(\frac{\left(1+x \right)^{2}}{x^{2}+2 x +4}+2\right)}-\frac{\arctan \left(\frac{\left(1+x \right) \sqrt{2}}{2 \sqrt{x^{2}+2 x +4}}\right) \sqrt{2}}{8}$&$123$\\ trager&$\frac{\left(-3+x \right) \sqrt{x^{2}+2 x +4}}{4 x^{2}+8 x +12}-3 \ln \left(\frac{48384 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)^{2} x +960 \sqrt{x^{2}+2 x +4}\, \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)-15312 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right) x -143 \sqrt{x^{2}+2 x +4}+3696 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)+1210 x -605}{48 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right) x -7 x +3}\right) \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)+3 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right) \ln \left(-\frac{-16128 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)^{2} x +320 \sqrt{x^{2}+2 x +4}\, \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)+5648 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right) x -59 \sqrt{x^{2}+2 x +4}+1232 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)-494 x -209}{16 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right) x -3 x -1}\right)+\ln \left(\frac{48384 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)^{2} x +960 \sqrt{x^{2}+2 x +4}\, \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)-15312 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right) x -143 \sqrt{x^{2}+2 x +4}+3696 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right)+1210 x -605}{48 \RootOf \left(384 \textit{\_Z}^{2}-128 \textit{\_Z} +11\right) x -7 x +3}\right)$&$372$\\ \hline \end{longtable}"," ",0,"1/4*(-3+x)/(x^2+2*x+3)*(x^2+2*x+4)^(1/2)+arctanh((x^2+2*x+4)^(1/2))-1/8*2^(1/2)*arctan(1/4*2^(1/2)/(x^2+2*x+4)^(1/2)*(2*x+2))","A"
282,1,21,30,0.338000," ","int((2*x^3+3*x^2)/(2*x^2+x-3)/(x^2+2*x-3)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(-3+2 x \right) \left(3+x \right)}{2 \sqrt{x^{2}+2 x -3}}$&$21$\\ trager&$\frac{\left(-3+2 x \right) \sqrt{x^{2}+2 x -3}}{2 x -2}$&$23$\\ risch&$\frac{2 x^{2}+3 x -9}{2 \sqrt{x^{2}+2 x -3}}$&$23$\\ default&$\sqrt{x^{2}+2 x -3}-\frac{\sqrt{\left(-1+x \right)^{2}-4+4 x}}{2 \left(-1+x \right)}$&$31$\\ \hline \end{longtable}"," ",0,"1/2*(-3+2*x)*(3+x)/(x^2+2*x-3)^(1/2)","A"
283,1,63,70,2.706000," ","int((x^4+1)/(x^2+x+1)/(x^2+x+2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(2 x -7\right) \sqrt{x^{2}+x +2}}{4}-\frac{\arcsinh \left(\frac{2 \sqrt{7}\, \left(\frac{1}{2}+x \right)}{7}\right)}{8}-\arctanh \left(\sqrt{x^{2}+x +2}\right)+\frac{\arctan \left(\frac{\left(1+2 x \right) \sqrt{3}}{3 \sqrt{x^{2}+x +2}}\right) \sqrt{3}}{3}$&$63$\\ default&$\frac{x \sqrt{x^{2}+x +2}}{2}-\frac{7 \sqrt{x^{2}+x +2}}{4}-\frac{\arcsinh \left(\frac{2 \sqrt{7}\, \left(\frac{1}{2}+x \right)}{7}\right)}{8}-\arctanh \left(\sqrt{x^{2}+x +2}\right)+\frac{\arctan \left(\frac{\left(1+2 x \right) \sqrt{3}}{3 \sqrt{x^{2}+x +2}}\right) \sqrt{3}}{3}$&$69$\\ trager&$\left(\frac{x}{2}-\frac{7}{4}\right) \sqrt{x^{2}+x +2}+\frac{\ln \left(\frac{119439007666026577658978862131641122955470355864 x -1547697292817558076095613967756493895336593544 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{7}-34406958119166765379202600686515679522775898 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{9}-408428037511035132158259563133572071702902093 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{8}-15578368508457466770335635637334282174776498052 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}+92867550610519727468293762800988464367923626556 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{4}+212792550384822375335114880746026740201438299184 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{3}+273186779333881661281495026943233632964832014864 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{2}-70797359348887984486272050254218036232928952 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{9}-979164562034479840429835479647785236680079548 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{8}-4788386803733240523480198798685975575347417184 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{7}-8466366722931133143875003385747183129791862600 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{6}+10087853194776611638959898784312956615330359960 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{5}+130122211413585191690424618867539965108616302212 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{2}+196657319548613971516945068585949038000971514228 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x -338148427546681507680571202357084317563591216 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{6}+15251938730635387772703465424126946970054792756 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{5}+61460684890082525267083167131316588242892347214 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{4}+114720586388952785990125336776140922456177253704 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{3}+77433073972677421673765677678710388152097321464 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x -3249432473630521638596853264962745579360405280 x^{7}-5270431261764271464385323331931230871412749376 x^{5}+97982488562224055418949456789552431477293304320 x^{3}-8168630465209889786412283012903312887099029104 x^{6}+31249267089218217898695235629549587705149988912 x^{4}+143128220092880680254710157516723345620115609552 x^{2}-36399766591903565523888587932723614181739944 x^{9}-571567717666758708366024893119100951344256660 x^{8}-15659202392168100756065522907306187543554274712 \sqrt{x^{2}+x +2}-80541634539772649096117881567690437759482687424 x \sqrt{x^{2}+x +2}+22145439835415776771931821181847880189581078124+553367855612862471389197899373472979050440128 \sqrt{x^{2}+x +2}\, x^{7}+2940584159547113642125204402878116918693453152 \sqrt{x^{2}+x +2}\, x^{6}+6474570049250822753745477662601749042350206336 \sqrt{x^{2}+x +2}\, x^{5}-1383100890638304327135314702231314502897488800 \sqrt{x^{2}+x +2}\, x^{4}-33106204550783809819500749413074566530756750912 \sqrt{x^{2}+x +2}\, x^{3}-77646952763997029322699085858555023816147693024 \sqrt{x^{2}+x +2}\, x^{2}+36399766811592879989652699602324316481006504 \sqrt{x^{2}+x +2}\, x^{8}+22031124286478773119250323350247573703566656514 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)+34406958283933751228525684438716206247225818 \sqrt{x^{2}+x +2}\, \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{8}+391224574382993408807496237955864608039304224 \sqrt{x^{2}+x +2}\, \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{7}+70797359678421956184918217758619089681828792 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}\, x^{8}+1336858636074842185280660610444399489138966480 \sqrt{x^{2}+x +2}\, \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{6}+943765914223119166864375404851776970759195232 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}\, x^{7}-542193641294841347379235514772028707324385008 \sqrt{x^{2}+x +2}\, \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{5}+4269200061821671816190368251302777197688034672 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}\, x^{6}-16916019799735424659186697666206970777890289580 \sqrt{x^{2}+x +2}\, \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{4}+5896140866636764872731802925206074249112002208 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}\, x^{5}-49560907705036167058886144826155835342301569264 \sqrt{x^{2}+x +2}\, \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{3}-18379755789404327250773521187737912806531548280 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}\, x^{4}-78323227078274890647304119940633201714527981192 \sqrt{x^{2}+x +2}\, \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x^{2}-82753380069385375793447165943111704847470171136 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}\, x^{3}-54753673104174503511706603527633757903688747520 \sqrt{x^{2}+x +2}\, \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)^{2} x -155975768722135705403328647704719793841721488256 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}\, x^{2}-135163654996251933645966015919960738916686168224 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) \sqrt{x^{2}+x +2}\, x}{\left(3 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x +4 x +2\right)^{8}}\right)}{8}-\frac{\ln \left(\frac{\RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{2}+\RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x +4 x \sqrt{x^{2}+x +2}+x^{2}-5 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)+2 \sqrt{x^{2}+x +2}+x -5}{x^{2}+x +1}\right) \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)}{2}-\ln \left(\frac{\RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x^{2}+\RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right) x +4 x \sqrt{x^{2}+x +2}+x^{2}-5 \RootOf \left(3 \textit{\_Z}^{2}+6 \textit{\_Z} +4\right)+2 \sqrt{x^{2}+x +2}+x -5}{x^{2}+x +1}\right)$&$1101$\\ \hline \end{longtable}"," ",0,"1/4*(2*x-7)*(x^2+x+2)^(1/2)-1/8*arcsinh(2/7*7^(1/2)*(1/2+x))-arctanh((x^2+x+2)^(1/2))+1/3*arctan(1/3*(1+2*x)*3^(1/2)/(x^2+x+2)^(1/2))*3^(1/2)","A"
284,1,38,46,0.371000," ","int(1/(x^2+2*x+4)^(7/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{8 x^{5}+40 x^{4}+140 x^{3}+260 x^{2}+355 x +203}{405 \left(x^{2}+2 x +4\right)^{\frac{5}{2}}}$&$38$\\ trager&$\frac{8 x^{5}+40 x^{4}+140 x^{3}+260 x^{2}+355 x +203}{405 \left(x^{2}+2 x +4\right)^{\frac{5}{2}}}$&$38$\\ risch&$\frac{8 x^{5}+40 x^{4}+140 x^{3}+260 x^{2}+355 x +203}{405 \left(x^{2}+2 x +4\right)^{\frac{5}{2}}}$&$38$\\ default&$\frac{2 x +2}{30 \left(x^{2}+2 x +4\right)^{\frac{5}{2}}}+\frac{\frac{4}{135}+\frac{4 x}{135}}{\left(x^{2}+2 x +4\right)^{\frac{3}{2}}}+\frac{\frac{8}{405}+\frac{8 x}{405}}{\sqrt{x^{2}+2 x +4}}$&$53$\\ \hline \end{longtable}"," ",0,"1/405*(8*x^5+40*x^4+140*x^3+260*x^2+355*x+203)/(x^2+2*x+4)^(5/2)","A"
285,1,30,39,0.307000," ","int(1/(3*x^2+8*x+1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{54 x^{3}+216 x^{2}+171 x -28}{507 \left(3 x^{2}+8 x +1\right)^{\frac{3}{2}}}$&$30$\\ trager&$\frac{54 x^{3}+216 x^{2}+171 x -28}{507 \left(3 x^{2}+8 x +1\right)^{\frac{3}{2}}}$&$30$\\ risch&$\frac{54 x^{3}+216 x^{2}+171 x -28}{507 \left(3 x^{2}+8 x +1\right)^{\frac{3}{2}}}$&$30$\\ default&$-\frac{6 x +8}{78 \left(3 x^{2}+8 x +1\right)^{\frac{3}{2}}}+\frac{6 x +8}{169 \sqrt{3 x^{2}+8 x +1}}$&$40$\\ \hline \end{longtable}"," ",0,"1/507*(54*x^3+216*x^2+171*x-28)/(3*x^2+8*x+1)^(3/2)","A"
286,1,30,39,0.389000," ","int(1/(-3*x^2+4*x+5)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{54 x^{3}-108 x^{2}-99 x +98}{1083 \left(-3 x^{2}+4 x +5\right)^{\frac{3}{2}}}$&$30$\\ default&$-\frac{-6 x +4}{114 \left(-3 x^{2}+4 x +5\right)^{\frac{3}{2}}}-\frac{-6 x +4}{361 \sqrt{-3 x^{2}+4 x +5}}$&$40$\\ trager&$-\frac{\left(54 x^{3}-108 x^{2}-99 x +98\right) \sqrt{-3 x^{2}+4 x +5}}{1083 \left(3 x^{2}-4 x -5\right)^{2}}$&$42$\\ risch&$\frac{54 x^{3}-108 x^{2}-99 x +98}{1083 \left(3 x^{2}-4 x -5\right) \sqrt{-3 x^{2}+4 x +5}}$&$42$\\ \hline \end{longtable}"," ",0,"-1/1083*(54*x^3-108*x^2-99*x+98)/(-3*x^2+4*x+5)^(3/2)","A"
287,1,40,27,0.137000," ","int(1/(1+(x^2+2*x+2)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(\left(1+x \right)^{2}+1\right)^{\frac{3}{2}}}{1+x}+\left(1+x \right) \sqrt{\left(1+x \right)^{2}+1}+\arcsinh \left(1+x \right)+\frac{1}{1+x}$&$40$\\ trager&$-\frac{x}{1+x}-\frac{\sqrt{x^{2}+2 x +2}}{1+x}-\ln \left(\sqrt{x^{2}+2 x +2}-1-x \right)$&$45$\\ \hline \end{longtable}"," ",0,"-1/(1+x)*((1+x)^2+1)^(3/2)+(1+x)*((1+x)^2+1)^(1/2)+arcsinh(1+x)+1/(1+x)","A"
288,1,52,38,0.122000," ","int(1/(x+(x^2+x+1)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\sqrt{\left(1+x \right)^{2}-x}-\frac{\arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{2}-\arctanh \left(\frac{1-x}{2 \sqrt{\left(1+x \right)^{2}-x}}\right)-x +\ln \left(1+x \right)$&$52$\\ trager&$\sqrt{x^{2}+x +1}-x -\frac{\ln \left(\frac{2 x^{2} \sqrt{x^{2}+x +1}+2 x^{3}+8 \sqrt{x^{2}+x +1}\, x +9 x^{2}+14 \sqrt{x^{2}+x +1}+12 x +13}{\left(1+x \right)^{4}}\right)}{2}$&$71$\\ \hline \end{longtable}"," ",0,"((1+x)^2-x)^(1/2)-1/2*arcsinh(2/3*(1/2+x)*3^(1/2))-arctanh(1/2*(1-x)/((1+x)^2-x)^(1/2))-x+ln(1+x)","A"
289,1,55,60,0.069000," ","int(x^2/(1+2*x+2*(x^2+x+1)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\left(2+3 x \right) x^{3}}{18}+\frac{\left(\frac{1}{2} x^{3}+\frac{1}{12} x^{2}+\frac{7}{48} x -\frac{37}{96}\right) \sqrt{x^{2}+x +1}}{3}-\frac{\ln \left(2 \sqrt{x^{2}+x +1}-1-2 x \right)}{64}$&$55$\\ default&$-\frac{x^{3}}{9}-\frac{x^{4}}{6}+\frac{x \left(x^{2}+x +1\right)^{\frac{3}{2}}}{6}-\frac{5 \left(x^{2}+x +1\right)^{\frac{3}{2}}}{36}+\frac{\left(1+2 x \right) \sqrt{x^{2}+x +1}}{96}+\frac{\arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{64}$&$59$\\ \hline \end{longtable}"," ",0,"-1/18*(2+3*x)*x^3+1/3*(1/2*x^3+1/12*x^2+7/48*x-37/96)*(x^2+x+1)^(1/2)-1/64*ln(2*(x^2+x+1)^(1/2)-1-2*x)","A"
290,1,80,67,0.385000," ","int((-3*x+(x^2+x+1)^(1/2))/(-1+(x^2+x+1)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-4 \ln \left(1+x \right)+\ln \left(x \right)+x -4 \sqrt{\left(1+x \right)^{2}-x}+\frac{5 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{2}+4 \arctanh \left(\frac{1-x}{2 \sqrt{\left(1+x \right)^{2}-x}}\right)+\sqrt{x^{2}+x +1}-\arctanh \left(\frac{2+x}{2 \sqrt{x^{2}+x +1}}\right)$&$80$\\ trager&$-1+x -3 \sqrt{x^{2}+x +1}+\frac{\ln \left(\frac{-8-96 x +5493060 x^{7}+1790544 x^{5}-1526 x^{3}+3865870 x^{6}+445596 x^{4}-507 x^{2}+4224608 x^{9}+8448 x^{14}+5593140 x^{8}+458 x^{2} \sqrt{x^{2}+x +1}+8 \sqrt{x^{2}+x +1}+2392341 x^{10}+308624 x^{12}+512 x^{15}+64992 x^{13}+1008642 x^{11}+92 \sqrt{x^{2}+x +1}\, x +512 \sqrt{x^{2}+x +1}\, x^{14}+8192 \sqrt{x^{2}+x +1}\, x^{13}+60704 \sqrt{x^{2}+x +1}\, x^{12}+275296 \sqrt{x^{2}+x +1}\, x^{11}+849754 \sqrt{x^{2}+x +1}\, x^{10}+1875388 \sqrt{x^{2}+x +1}\, x^{9}+3018000 \sqrt{x^{2}+x +1}\, x^{8}+3530640 \sqrt{x^{2}+x +1}\, x^{7}+2914860 \sqrt{x^{2}+x +1}\, x^{6}+1571080 \sqrt{x^{2}+x +1}\, x^{5}+450424 \sqrt{x^{2}+x +1}\, x^{4}+1264 \sqrt{x^{2}+x +1}\, x^{3}}{\left(1+x \right)^{16}}\right)}{2}$&$288$\\ \hline \end{longtable}"," ",0,"-4*ln(1+x)+ln(x)+x-4*((1+x)^2-x)^(1/2)+5/2*arcsinh(2/3*(1/2+x)*3^(1/2))+4*arctanh(1/2*(1-x)/((1+x)^2-x)^(1/2))+(x^2+x+1)^(1/2)-arctanh(1/2*(2+x)/(x^2+x+1)^(1/2))","A"
291,1,140,127,0.027000," ","int((1+x)/(-(x^2+x+1)^(1/2)+(x^2+2*x+4)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-2 \sqrt{\left(3+x \right)^{2}-5 x -8}+\frac{43 \arcsinh \left(\frac{2 \left(\frac{1}{2}+x \right) \sqrt{3}}{3}\right)}{8}+2 \sqrt{7}\, \arctanh \left(\frac{\left(-1-5 x \right) \sqrt{7}}{14 \sqrt{\left(3+x \right)^{2}-5 x -8}}\right)-2 \sqrt{\left(3+x \right)^{2}-4 x -5}+\frac{11 \arcsinh \left(\frac{\left(1+x \right) \sqrt{3}}{3}\right)}{2}+2 \sqrt{7}\, \arctanh \left(\frac{\left(2-4 x \right) \sqrt{7}}{14 \sqrt{\left(3+x \right)^{2}-4 x -5}}\right)+\frac{\left(1+2 x \right) \sqrt{x^{2}+x +1}}{4}+\frac{\left(2 x +2\right) \sqrt{x^{2}+2 x +4}}{4}$&$140$\\ \hline \end{longtable}"," ",0,"-2*((3+x)^2-5*x-8)^(1/2)+43/8*arcsinh(2/3*(1/2+x)*3^(1/2))+2*7^(1/2)*arctanh(1/14*(-1-5*x)*7^(1/2)/((3+x)^2-5*x-8)^(1/2))-2*((3+x)^2-4*x-5)^(1/2)+11/2*arcsinh(1/3*(1+x)*3^(1/2))+2*7^(1/2)*arctanh(1/14*(2-4*x)*7^(1/2)/((3+x)^2-4*x-5)^(1/2))+1/4*(1+2*x)*(x^2+x+1)^(1/2)+1/4*(2*x+2)*(x^2+2*x+4)^(1/2)","A"
292,1,30,29,0.319000," ","int(1/x^3/(-1+x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \arctan \left(\sqrt{-1+x}\right)}{4}+\frac{\sqrt{-1+x}}{2 x^{2}}+\frac{3 \sqrt{-1+x}}{4 x}$&$30$\\ default&$\frac{3 \arctan \left(\sqrt{-1+x}\right)}{4}+\frac{\sqrt{-1+x}}{2 x^{2}}+\frac{3 \sqrt{-1+x}}{4 x}$&$30$\\ risch&$\frac{3 x^{2}-x -2}{4 x^{2} \sqrt{-1+x}}+\frac{3 \arctan \left(\sqrt{-1+x}\right)}{4}$&$30$\\ trager&$\frac{\left(2+3 x \right) \sqrt{-1+x}}{4 x^{2}}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{2 \RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-1+x}+x -2}{x}\right)}{8}$&$46$\\ meijerg&$\frac{\sqrt{-\mathrm{signum}\left(-1+x \right)}\, \left(\frac{\sqrt{\pi}\, \left(-7 x^{2}+8 x +8\right)}{16 x^{2}}-\frac{\sqrt{\pi}\, \left(12 x +8\right) \sqrt{1-x}}{16 x^{2}}-\frac{3 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{1-x}}{2}\right)}{4}+\frac{3 \left(\frac{7}{6}-2 \ln \left(2\right)+\ln \left(x \right)+i \pi \right) \sqrt{\pi}}{8}-\frac{\sqrt{\pi}}{2 x^{2}}-\frac{\sqrt{\pi}}{2 x}\right)}{\sqrt{\pi}\, \sqrt{\mathrm{signum}\left(-1+x \right)}}$&$108$\\ \hline \end{longtable}"," ",0,"3/4*arctan((-1+x)^(1/2))+1/2*(-1+x)^(1/2)/x^2+3/4*(-1+x)^(1/2)/x","A"
293,1,12,11,0.034000," ","int(1/(1-3/x)^(4/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{1}{\left(1-\frac{3}{x}\right)^{\frac{1}{3}}}$&$12$\\ default&$-\frac{1}{\left(1-\frac{3}{x}\right)^{\frac{1}{3}}}$&$12$\\ risch&$-\frac{1}{\left(\frac{-3+x}{x}\right)^{\frac{1}{3}}}$&$12$\\ gosper&$-\frac{-3+x}{x \left(\frac{-3+x}{x}\right)^{\frac{4}{3}}}$&$18$\\ trager&$-\frac{x \left(-\frac{3-x}{x}\right)^{\frac{2}{3}}}{-3+x}$&$21$\\ \hline \end{longtable}"," ",0,"-1/(1-3/x)^(1/3)","A"
294,1,67,60,0.605000," ","int((-1+3*x)^(4/3)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{4 \mathrm{signum}\left(-\frac{1}{3}+x \right)^{\frac{4}{3}} \left(-\frac{3 \Gamma \left(\frac{2}{3}\right) x \hypergeom \left(\left[\frac{2}{3}, 1, 1\right], \left[2, 3\right], 3 x \right)}{2}+3 \left(2+\frac{\pi  \sqrt{3}}{6}-\frac{\ln \left(3\right)}{2}+\ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)+\frac{3 \Gamma \left(\frac{2}{3}\right)}{4 x}\right)}{3 \Gamma \left(\frac{2}{3}\right) \left(-\mathrm{signum}\left(-\frac{1}{3}+x \right)\right)^{\frac{4}{3}}}$&$67$\\ derivativedivides&$9 \left(-1+3 x \right)^{\frac{1}{3}}-\frac{1}{1+\left(-1+3 x \right)^{\frac{1}{3}}}-4 \ln \left(1+\left(-1+3 x \right)^{\frac{1}{3}}\right)+\frac{1+\left(-1+3 x \right)^{\frac{1}{3}}}{\left(-1+3 x \right)^{\frac{2}{3}}-\left(-1+3 x \right)^{\frac{1}{3}}+1}+2 \ln \left(\left(-1+3 x \right)^{\frac{2}{3}}-\left(-1+3 x \right)^{\frac{1}{3}}+1\right)-4 \sqrt{3}\, \arctan \left(\frac{\left(2 \left(-1+3 x \right)^{\frac{1}{3}}-1\right) \sqrt{3}}{3}\right)$&$109$\\ default&$9 \left(-1+3 x \right)^{\frac{1}{3}}-\frac{1}{1+\left(-1+3 x \right)^{\frac{1}{3}}}-4 \ln \left(1+\left(-1+3 x \right)^{\frac{1}{3}}\right)+\frac{1+\left(-1+3 x \right)^{\frac{1}{3}}}{\left(-1+3 x \right)^{\frac{2}{3}}-\left(-1+3 x \right)^{\frac{1}{3}}+1}+2 \ln \left(\left(-1+3 x \right)^{\frac{2}{3}}-\left(-1+3 x \right)^{\frac{1}{3}}+1\right)-4 \sqrt{3}\, \arctan \left(\frac{\left(2 \left(-1+3 x \right)^{\frac{1}{3}}-1\right) \sqrt{3}}{3}\right)$&$109$\\ risch&$\frac{\left(-1+3 x \right)^{\frac{1}{3}}}{x}+\frac{\left(-\frac{4 \left(-1+3 x \right)^{\frac{2}{3}} \left(-\mathrm{signum}\left(-\frac{1}{3}+x \right)\right)^{\frac{2}{3}} \left(2 \Gamma \left(\frac{2}{3}\right) x \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], 3 x \right)+\left(\frac{\pi  \sqrt{3}}{6}-\frac{\ln \left(3\right)}{2}+\ln \left(x \right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{\left(\left(-1+3 x \right)^{2}\right)^{\frac{1}{3}} \Gamma \left(\frac{2}{3}\right) \mathrm{signum}\left(-\frac{1}{3}+x \right)^{\frac{2}{3}}}+\frac{9 \left(-1+3 x \right)^{\frac{2}{3}} \left(-\mathrm{signum}\left(-\frac{1}{3}+x \right)\right)^{\frac{2}{3}} x \hypergeom \left(\left[\frac{2}{3}, 1\right], \left[2\right], 3 x \right)}{\left(\left(-1+3 x \right)^{2}\right)^{\frac{1}{3}} \mathrm{signum}\left(-\frac{1}{3}+x \right)^{\frac{2}{3}}}\right) \left(\left(-1+3 x \right)^{2}\right)^{\frac{1}{3}}}{\left(-1+3 x \right)^{\frac{2}{3}}}$&$146$\\ trager&$\frac{\left(1+9 x \right) \left(-1+3 x \right)^{\frac{1}{3}}}{x}-4 \ln \left(\frac{\left(-1+3 x \right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +\left(-1+3 x \right)^{\frac{1}{3}}}{x}\right)+4 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \ln \left(-\frac{\left(-1+3 x \right)^{\frac{2}{3}} \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2} x -\left(-1+3 x \right)^{\frac{2}{3}}+\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) \left(-1+3 x \right)^{\frac{1}{3}}-\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)^{2}-2 \RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right) x +\RootOf \left(\textit{\_Z}^{2}-\textit{\_Z} +1\right)}{x}\right)$&$195$\\ \hline \end{longtable}"," ",0,"-4/3/GAMMA(2/3)*signum(-1/3+x)^(4/3)/(-signum(-1/3+x))^(4/3)*(-3/2*GAMMA(2/3)*x*hypergeom([2/3,1,1],[2,3],3*x)+3*(2+1/6*Pi*3^(1/2)-1/2*ln(3)+ln(x)+I*Pi)*GAMMA(2/3)+3/4*GAMMA(2/3)/x)","C"
295,1,18,28,0.300000," ","int((4-3*x)^(4/3)*x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{4 \,2^{\frac{2}{3}} x^{3} \hypergeom \left(\left[-\frac{4}{3}, 3\right], \left[4\right], \frac{3 x}{4}\right)}{3}$&$18$\\ gosper&$-\frac{\left(35 x^{2}+28 x +16\right) \left(4-3 x \right)^{\frac{7}{3}}}{455}$&$20$\\ derivativedivides&$-\frac{16 \left(4-3 x \right)^{\frac{7}{3}}}{63}+\frac{4 \left(4-3 x \right)^{\frac{10}{3}}}{45}-\frac{\left(4-3 x \right)^{\frac{13}{3}}}{117}$&$29$\\ default&$-\frac{16 \left(4-3 x \right)^{\frac{7}{3}}}{63}+\frac{4 \left(4-3 x \right)^{\frac{10}{3}}}{45}-\frac{\left(4-3 x \right)^{\frac{13}{3}}}{117}$&$29$\\ trager&$\left(-\frac{9}{13} x^{4}+\frac{84}{65} x^{3}-\frac{32}{455} x^{2}-\frac{64}{455} x -\frac{256}{455}\right) \left(4-3 x \right)^{\frac{1}{3}}$&$29$\\ risch&$\frac{\left(315 x^{4}-588 x^{3}+32 x^{2}+64 x +256\right) \left(-4+3 x \right)}{455 \left(4-3 x \right)^{\frac{2}{3}}}$&$35$\\ \hline \end{longtable}"," ",0,"4/3*2^(2/3)*x^3*hypergeom([-4/3,3],[4],3/4*x)","C"
296,1,53,36,0.307000," ","int((1-2*x^(1/3))^(3/4)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$4 \left(1-2 x^{\frac{1}{3}}\right)^{\frac{3}{4}}+3 \ln \left(\left(1-2 x^{\frac{1}{3}}\right)^{\frac{1}{4}}-1\right)-3 \ln \left(\left(1-2 x^{\frac{1}{3}}\right)^{\frac{1}{4}}+1\right)+6 \arctan \left(\left(1-2 x^{\frac{1}{3}}\right)^{\frac{1}{4}}\right)$&$53$\\ default&$4 \left(1-2 x^{\frac{1}{3}}\right)^{\frac{3}{4}}+3 \ln \left(\left(1-2 x^{\frac{1}{3}}\right)^{\frac{1}{4}}-1\right)-3 \ln \left(\left(1-2 x^{\frac{1}{3}}\right)^{\frac{1}{4}}+1\right)+6 \arctan \left(\left(1-2 x^{\frac{1}{3}}\right)^{\frac{1}{4}}\right)$&$53$\\ meijerg&$-\frac{9 \sqrt{2}\, \Gamma \left(\frac{3}{4}\right) \left(\frac{2 \pi  \sqrt{2}\, x^{\frac{1}{3}} \hypergeom \left(\left[\frac{1}{4}, 1, 1\right], \left[2, 2\right], 2 x^{\frac{1}{3}}\right)}{\Gamma \left(\frac{3}{4}\right)}-\frac{4 \left(\frac{4}{3}-2 \ln \left(2\right)-\frac{\pi}{2}+\frac{\ln \left(x \right)}{3}+i \pi \right) \pi  \sqrt{2}}{3 \Gamma \left(\frac{3}{4}\right)}\right)}{8 \pi}$&$65$\\ \hline \end{longtable}"," ",0,"4*(1-2*x^(1/3))^(3/4)+3*ln((1-2*x^(1/3))^(1/4)-1)-3*ln((1-2*x^(1/3))^(1/4)+1)+6*arctan((1-2*x^(1/3))^(1/4))","A"
297,1,20,45,0.290000," ","int(x/(3-2*x^(1/2))^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3^{\frac{1}{4}} x^{2} \hypergeom \left(\left[\frac{3}{4}, 4\right], \left[5\right], \frac{2 \sqrt{x}}{3}\right)}{6}$&$20$\\ derivativedivides&$-\frac{27 \left(3-2 \sqrt{x}\right)^{\frac{1}{4}}}{2}+\frac{27 \left(3-2 \sqrt{x}\right)^{\frac{5}{4}}}{10}-\frac{\left(3-2 \sqrt{x}\right)^{\frac{9}{4}}}{2}+\frac{\left(3-2 \sqrt{x}\right)^{\frac{13}{4}}}{26}$&$46$\\ default&$-\frac{27 \left(3-2 \sqrt{x}\right)^{\frac{1}{4}}}{2}+\frac{27 \left(3-2 \sqrt{x}\right)^{\frac{5}{4}}}{10}-\frac{\left(3-2 \sqrt{x}\right)^{\frac{9}{4}}}{2}+\frac{\left(3-2 \sqrt{x}\right)^{\frac{13}{4}}}{26}$&$46$\\ \hline \end{longtable}"," ",0,"1/6*3^(1/4)*x^2*hypergeom([3/4,4],[5],2/3*x^(1/2))","C"
298,1,85,132,0.316000," ","int((-1+2*x^(1/2))^(5/4)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{5 \mathrm{signum}\left(-1+2 \sqrt{x}\right)^{\frac{5}{4}} \left(\frac{\Gamma \left(\frac{3}{4}\right) \sqrt{x}\, \hypergeom \left(\left[1, 1, \frac{7}{4}\right], \left[2, 4\right], 2 \sqrt{x}\right)}{4}+\frac{\left(-2 \ln \left(2\right)+\frac{\pi}{2}-\frac{3}{2}+\frac{\ln \left(x \right)}{2}+i \pi \right) \Gamma \left(\frac{3}{4}\right)}{2}-\frac{2 \Gamma \left(\frac{3}{4}\right)}{5 x}+\frac{2 \Gamma \left(\frac{3}{4}\right)}{\sqrt{x}}\right)}{2 \Gamma \left(\frac{3}{4}\right) \left(-\mathrm{signum}\left(-1+2 \sqrt{x}\right)\right)^{\frac{5}{4}}}$&$85$\\ derivativedivides&$\frac{-\frac{9 \left(-1+2 \sqrt{x}\right)^{\frac{5}{4}}}{4}-\frac{5 \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}}{4}}{x}+\frac{5 \sqrt{2}\, \left(\ln \left(\frac{1+\sqrt{2}\, \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}+\sqrt{-1+2 \sqrt{x}}}{1-\sqrt{2}\, \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}+\sqrt{-1+2 \sqrt{x}}}\right)+2 \arctan \left(1+\sqrt{2}\, \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}\right)+2 \arctan \left(-1+\sqrt{2}\, \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}\right)\right)}{8}$&$125$\\ default&$\frac{-\frac{9 \left(-1+2 \sqrt{x}\right)^{\frac{5}{4}}}{4}-\frac{5 \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}}{4}}{x}+\frac{5 \sqrt{2}\, \left(\ln \left(\frac{1+\sqrt{2}\, \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}+\sqrt{-1+2 \sqrt{x}}}{1-\sqrt{2}\, \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}+\sqrt{-1+2 \sqrt{x}}}\right)+2 \arctan \left(1+\sqrt{2}\, \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}\right)+2 \arctan \left(-1+\sqrt{2}\, \left(-1+2 \sqrt{x}\right)^{\frac{1}{4}}\right)\right)}{8}$&$125$\\ \hline \end{longtable}"," ",0,"5/2/GAMMA(3/4)*signum(-1+2*x^(1/2))^(5/4)/(-signum(-1+2*x^(1/2)))^(5/4)*(1/4*GAMMA(3/4)*x^(1/2)*hypergeom([1,1,7/4],[2,4],2*x^(1/2))+1/2*(-2*ln(2)+1/2*Pi-3/2+1/2*ln(x)+I*Pi)*GAMMA(3/4)-2/5*GAMMA(3/4)/x+2*GAMMA(3/4)/x^(1/2))","C"
299,1,10,9,0.285000," ","int(x^6*(x^7+1)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{3 \left(x^{7}+1\right)^{\frac{4}{3}}}{28}$&$10$\\ default&$\frac{3 \left(x^{7}+1\right)^{\frac{4}{3}}}{28}$&$10$\\ risch&$\frac{3 \left(x^{7}+1\right)^{\frac{4}{3}}}{28}$&$10$\\ trager&$\left(\frac{3}{28}+\frac{3 x^{7}}{28}\right) \left(x^{7}+1\right)^{\frac{1}{3}}$&$16$\\ meijerg&$\frac{x^{7} \hypergeom \left(\left[-\frac{1}{3}, 1\right], \left[2\right], -x^{7}\right)}{7}$&$17$\\ gosper&$\frac{3 \left(1+x \right) \left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x +1\right) \left(x^{7}+1\right)^{\frac{1}{3}}}{28}$&$37$\\ \hline \end{longtable}"," ",0,"3/28*(x^7+1)^(4/3)","A"
300,1,10,9,0.272000," ","int(x^6/(x^7+1)^(5/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{3}{14 \left(x^{7}+1\right)^{\frac{2}{3}}}$&$10$\\ default&$-\frac{3}{14 \left(x^{7}+1\right)^{\frac{2}{3}}}$&$10$\\ trager&$-\frac{3}{14 \left(x^{7}+1\right)^{\frac{2}{3}}}$&$10$\\ risch&$-\frac{3}{14 \left(x^{7}+1\right)^{\frac{2}{3}}}$&$10$\\ meijerg&$\frac{x^{7} \hypergeom \left(\left[1, \frac{5}{3}\right], \left[2\right], -x^{7}\right)}{7}$&$17$\\ gosper&$-\frac{3 \left(1+x \right) \left(x^{6}-x^{5}+x^{4}-x^{3}+x^{2}-x +1\right)}{14 \left(x^{7}+1\right)^{\frac{5}{3}}}$&$37$\\ \hline \end{longtable}"," ",0,"-3/14/(x^7+1)^(2/3)","A"
301,1,74,43,9.787000," ","int(1/x/(2*x^7-27)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{\left(-\mathrm{signum}\left(-1+\frac{2 x^{7}}{27}\right)\right)^{\frac{2}{3}} \left(\frac{4 \Gamma \left(\frac{2}{3}\right) x^{7} \hypergeom \left(\left[1, 1, \frac{5}{3}\right], \left[2, 2\right], \frac{2 x^{7}}{27}\right)}{81}+\left(\frac{\pi  \sqrt{3}}{6}-\frac{9 \ln \left(3\right)}{2}+7 \ln \left(x \right)+\ln \left(2\right)+i \pi \right) \Gamma \left(\frac{2}{3}\right)\right)}{63 \mathrm{signum}\left(-1+\frac{2 x^{7}}{27}\right)^{\frac{2}{3}} \Gamma \left(\frac{2}{3}\right)}$&$74$\\ trager&$-\frac{\ln \left(-\frac{3421730148318 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)^{2} x^{7}-279878182758 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right) x^{7}-7423011100 x^{7}+1660604640093 \left(2 x^{7}-27\right)^{\frac{2}{3}} \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)-3421730148318 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)^{2}-4981813920279 \left(2 x^{7}-27\right)^{\frac{1}{3}} \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)+38988042624 \left(2 x^{7}-27\right)^{\frac{2}{3}}+14565249522135 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)-116964127872 \left(2 x^{7}-27\right)^{\frac{1}{3}}+308648801538}{x^{7}}\right)}{63}-\frac{\ln \left(-\frac{3421730148318 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)^{2} x^{7}-279878182758 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right) x^{7}-7423011100 x^{7}+1660604640093 \left(2 x^{7}-27\right)^{\frac{2}{3}} \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)-3421730148318 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)^{2}-4981813920279 \left(2 x^{7}-27\right)^{\frac{1}{3}} \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)+38988042624 \left(2 x^{7}-27\right)^{\frac{2}{3}}+14565249522135 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)-116964127872 \left(2 x^{7}-27\right)^{\frac{1}{3}}+308648801538}{x^{7}}\right) \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)}{7}+\frac{\RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right) \ln \left(-\frac{757355840490254039191854 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)^{2} x^{7}+48949965800622396478998 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right) x^{7}-24206310434198416909112 x^{7}-347409114848503477844697 \left(2 x^{7}-27\right)^{\frac{2}{3}} \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)-757355840490254039191854 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)^{2}+1042227344545510433534091 \left(2 x^{7}-27\right)^{\frac{1}{3}} \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)+56201354332314412587237 \left(2 x^{7}-27\right)^{\frac{2}{3}}-3210832682579892860512479 \RootOf \left(81 \textit{\_Z}^{2}+9 \textit{\_Z} +1\right)-168604062996943237761711 \left(2 x^{7}-27\right)^{\frac{1}{3}}+496462116886011762183999}{x^{7}}\right)}{7}$&$453$\\ \hline \end{longtable}"," ",0,"1/63/signum(-1+2/27*x^7)^(2/3)*(-signum(-1+2/27*x^7))^(2/3)*(4/81*GAMMA(2/3)*x^7*hypergeom([1,1,5/3],[2,2],2/27*x^7)+(1/6*Pi*3^(1/2)-9/2*ln(3)+7*ln(x)+ln(2)+I*Pi)*GAMMA(2/3))/GAMMA(2/3)","C"
302,1,76,53,9.886000," ","int((x^7+1)^(2/3)/x^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(\frac{\pi  \sqrt{3}\, x^{7} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 3\right], -x^{7}\right)}{9 \Gamma \left(\frac{2}{3}\right)}-\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}-1+7 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}+\frac{\pi  \sqrt{3}}{\Gamma \left(\frac{2}{3}\right) x^{7}}\right)}{21 \pi}$&$76$\\ risch&$-\frac{\left(x^{7}+1\right)^{\frac{2}{3}}}{7 x^{7}}+\frac{\sqrt{3}\, \Gamma \left(\frac{2}{3}\right) \left(-\frac{2 \pi  \sqrt{3}\, x^{7} \hypergeom \left(\left[1, 1, \frac{4}{3}\right], \left[2, 2\right], -x^{7}\right)}{9 \Gamma \left(\frac{2}{3}\right)}+\frac{2 \left(-\frac{\pi  \sqrt{3}}{6}-\frac{3 \ln \left(3\right)}{2}+7 \ln \left(x \right)\right) \pi  \sqrt{3}}{3 \Gamma \left(\frac{2}{3}\right)}\right)}{21 \pi}$&$76$\\ trager&$-\frac{\left(x^{7}+1\right)^{\frac{2}{3}}}{7 x^{7}}+\frac{2 \ln \left(-\frac{3914010 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{7}-2502441 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{7}-71266 x^{7}+6095754 \left(x^{7}+1\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-3914010 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-770175 \left(x^{7}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+1775193 \left(x^{7}+1\right)^{\frac{2}{3}}-6630249 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2031918 \left(x^{7}+1\right)^{\frac{1}{3}}-178165}{x^{7}}\right)}{21}+\frac{2 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) \ln \left(\frac{320697 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2} x^{7}+1625367 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right) x^{7}+1304670 x^{7}+6095754 \left(x^{7}+1\right)^{\frac{2}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-320697 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)^{2}-5325579 \left(x^{7}+1\right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)+256725 \left(x^{7}+1\right)^{\frac{2}{3}}-877074 \RootOf \left(9 \textit{\_Z}^{2}+3 \textit{\_Z} +1\right)-2031918 \left(x^{7}+1\right)^{\frac{1}{3}}+1739560}{x^{7}}\right)}{7}$&$294$\\ \hline \end{longtable}"," ",0,"-1/21/Pi*3^(1/2)*GAMMA(2/3)*(1/9*Pi*3^(1/2)/GAMMA(2/3)*x^7*hypergeom([1,1,4/3],[2,3],-x^7)-2/3*(-1/6*Pi*3^(1/2)-3/2*ln(3)-1+7*ln(x))*Pi*3^(1/2)/GAMMA(2/3)+Pi*3^(1/2)/GAMMA(2/3)/x^7)","C"
303,1,20,55,3.743000," ","int((4*x^4+3)^(1/4)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3^{\frac{1}{4}} \hypergeom \left(\left[-\frac{1}{4}, -\frac{1}{4}\right], \left[\frac{3}{4}\right], -\frac{4 x^{4}}{3}\right)}{x}$&$20$\\ risch&$-\frac{\left(4 x^{4}+3\right)^{\frac{1}{4}}}{x}+\frac{4 \,3^{\frac{1}{4}} x^{3} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -\frac{4 x^{4}}{3}\right)}{9}$&$35$\\ trager&$-\frac{\left(4 x^{4}+3\right)^{\frac{1}{4}}}{x}-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(4 \RootOf \left(\textit{\_Z}^{2}-2\right) \sqrt{4 x^{4}+3}\, x^{2}+8 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}-4 \left(4 x^{4}+3\right)^{\frac{3}{4}} x -8 x^{3} \left(4 x^{4}+3\right)^{\frac{1}{4}}+3 \RootOf \left(\textit{\_Z}^{2}-2\right)\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(4 \RootOf \left(\textit{\_Z}^{2}+2\right) \sqrt{4 x^{4}+3}\, x^{2}-8 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}-4 \left(4 x^{4}+3\right)^{\frac{3}{4}} x +8 x^{3} \left(4 x^{4}+3\right)^{\frac{1}{4}}-3 \RootOf \left(\textit{\_Z}^{2}+2\right)\right)}{4}$&$166$\\ \hline \end{longtable}"," ",0,"-3^(1/4)/x*hypergeom([-1/4,-1/4],[3/4],-4/3*x^4)","C"
304,1,19,69,3.406000," ","int(x^2*(4*x^4+3)^(5/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$3^{\frac{1}{4}} x^{3} \hypergeom \left(\left[-\frac{5}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -\frac{4 x^{4}}{3}\right)$&$19$\\ risch&$\frac{x^{3} \left(16 x^{4}+27\right) \left(4 x^{4}+3\right)^{\frac{1}{4}}}{32}+\frac{5 \,3^{\frac{1}{4}} x^{3} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -\frac{4 x^{4}}{3}\right)}{32}$&$42$\\ trager&$\frac{x^{3} \left(16 x^{4}+27\right) \left(4 x^{4}+3\right)^{\frac{1}{4}}}{32}+\frac{45 \RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(4 \RootOf \left(\textit{\_Z}^{2}+2\right) \sqrt{4 x^{4}+3}\, x^{2}-8 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}+4 \left(4 x^{4}+3\right)^{\frac{3}{4}} x -8 x^{3} \left(4 x^{4}+3\right)^{\frac{1}{4}}-3 \RootOf \left(\textit{\_Z}^{2}+2\right)\right)}{512}+\frac{45 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-2 \RootOf \left(\textit{\_Z}^{2}-2\right) \left(4 x^{4}+3\right)^{\frac{3}{4}} x -4 \left(4 x^{4}+3\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}-2\right) x^{3}-4 \sqrt{4 x^{4}+3}\, x^{2}-8 x^{4}-3\right)}{512}$&$166$\\ \hline \end{longtable}"," ",0,"3^(1/4)*x^3*hypergeom([-5/4,3/4],[7/4],-4/3*x^4)","C"
305,1,20,69,3.325000," ","int(x^6*(4*x^4+3)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3^{\frac{1}{4}} x^{7} \hypergeom \left(\left[-\frac{1}{4}, \frac{7}{4}\right], \left[\frac{11}{4}\right], -\frac{4 x^{4}}{3}\right)}{7}$&$20$\\ risch&$\frac{x^{3} \left(16 x^{4}+3\right) \left(4 x^{4}+3\right)^{\frac{1}{4}}}{128}-\frac{3 \,3^{\frac{1}{4}} x^{3} \hypergeom \left(\left[\frac{3}{4}, \frac{3}{4}\right], \left[\frac{7}{4}\right], -\frac{4 x^{4}}{3}\right)}{128}$&$42$\\ trager&$\frac{x^{3} \left(16 x^{4}+3\right) \left(4 x^{4}+3\right)^{\frac{1}{4}}}{128}+\frac{27 \RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-4 \RootOf \left(\textit{\_Z}^{2}-2\right) \sqrt{4 x^{4}+3}\, x^{2}-8 \RootOf \left(\textit{\_Z}^{2}-2\right) x^{4}+4 \left(4 x^{4}+3\right)^{\frac{3}{4}} x +8 x^{3} \left(4 x^{4}+3\right)^{\frac{1}{4}}-3 \RootOf \left(\textit{\_Z}^{2}-2\right)\right)}{2048}+\frac{27 \RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-4 \RootOf \left(\textit{\_Z}^{2}+2\right) \sqrt{4 x^{4}+3}\, x^{2}+8 \RootOf \left(\textit{\_Z}^{2}+2\right) x^{4}+4 \left(4 x^{4}+3\right)^{\frac{3}{4}} x -8 x^{3} \left(4 x^{4}+3\right)^{\frac{1}{4}}+3 \RootOf \left(\textit{\_Z}^{2}+2\right)\right)}{2048}$&$173$\\ \hline \end{longtable}"," ",0,"1/7*3^(1/4)*x^7*hypergeom([-1/4,7/4],[11/4],-4/3*x^4)","C"
306,1,15,74,3.229000," ","int((x*(-x^2+1))^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$\frac{3 x^{\frac{4}{3}} \hypergeom \left(\left[-\frac{1}{3}, \frac{2}{3}\right], \left[\frac{5}{3}\right], x^{2}\right)}{4}$&$15$\\ trager&$\frac{x \left(-x^{3}+x \right)^{\frac{1}{3}}}{2}-\frac{\ln \left(4959 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}-6768 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-x^{3}+x \right)^{\frac{2}{3}}-22833 \left(-x^{3}+x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -17718 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+7611 \left(-x^{3}+x \right)^{\frac{2}{3}}+5355 x \left(-x^{3}+x \right)^{\frac{1}{3}}-19836 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}-1705 x^{2}+9711 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)+1085\right)}{6}+\frac{\RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \ln \left(-6354 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2} x^{2}+6768 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) \left(-x^{3}+x \right)^{\frac{2}{3}}-16065 \left(-x^{3}+x \right)^{\frac{1}{3}} \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x -20715 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right) x^{2}+5355 \left(-x^{3}+x \right)^{\frac{2}{3}}+7611 x \left(-x^{3}+x \right)^{\frac{1}{3}}+25416 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)^{2}+1550 x^{2}+4494 \RootOf \left(9 \textit{\_Z}^{2}-3 \textit{\_Z} +1\right)-465\right)}{2}$&$305$\\ 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)}$&$786$\\ \hline \end{longtable}"," ",0,"3/4*x^(4/3)*hypergeom([-1/3,2/3],[5/3],x^2)","C"
307,1,51,82,0.286000," ","int(((1+x^(1/3))*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{3 \left(\frac{\sqrt{\pi}\, x^{\frac{1}{6}} \left(-1152 x^{\frac{4}{3}}-144 x +168 x^{\frac{2}{3}}-210 x^{\frac{1}{3}}+315\right) \sqrt{1+x^{\frac{1}{3}}}}{2880}-\frac{7 \sqrt{\pi}\, \arcsinh \left(x^{\frac{1}{6}}\right)}{64}\right)}{2 \sqrt{\pi}}$&$51$\\ derivativedivides&$\frac{\sqrt{\left(1+x^{\frac{1}{3}}\right) x}\, \left(768 x^{\frac{2}{3}} \left(x^{\frac{2}{3}}+x^{\frac{1}{3}}\right)^{\frac{3}{2}}-672 x^{\frac{1}{3}} \left(x^{\frac{2}{3}}+x^{\frac{1}{3}}\right)^{\frac{3}{2}}+560 \left(x^{\frac{2}{3}}+x^{\frac{1}{3}}\right)^{\frac{3}{2}}-420 \sqrt{x^{\frac{2}{3}}+x^{\frac{1}{3}}}\, x^{\frac{1}{3}}+105 \ln \left(\frac{1}{2}+x^{\frac{1}{3}}+\sqrt{x^{\frac{2}{3}}+x^{\frac{1}{3}}}\right)-210 \sqrt{x^{\frac{2}{3}}+x^{\frac{1}{3}}}\right)}{1280 x^{\frac{1}{3}} \sqrt{\left(1+x^{\frac{1}{3}}\right) x^{\frac{1}{3}}}}$&$108$\\ default&$\frac{\sqrt{\left(1+x^{\frac{1}{3}}\right) x}\, \left(768 x^{\frac{2}{3}} \left(x^{\frac{2}{3}}+x^{\frac{1}{3}}\right)^{\frac{3}{2}}-672 x^{\frac{1}{3}} \left(x^{\frac{2}{3}}+x^{\frac{1}{3}}\right)^{\frac{3}{2}}+560 \left(x^{\frac{2}{3}}+x^{\frac{1}{3}}\right)^{\frac{3}{2}}-420 \sqrt{x^{\frac{2}{3}}+x^{\frac{1}{3}}}\, x^{\frac{1}{3}}+105 \ln \left(\frac{1}{2}+x^{\frac{1}{3}}+\sqrt{x^{\frac{2}{3}}+x^{\frac{1}{3}}}\right)-210 \sqrt{x^{\frac{2}{3}}+x^{\frac{1}{3}}}\right)}{1280 x^{\frac{1}{3}} \sqrt{\left(1+x^{\frac{1}{3}}\right) x^{\frac{1}{3}}}}$&$108$\\ \hline \end{longtable}"," ",0,"-3/2/Pi^(1/2)*(1/2880*Pi^(1/2)*x^(1/6)*(-1152*x^(4/3)-144*x+168*x^(2/3)-210*x^(1/3)+315)*(1+x^(1/3))^(1/2)-7/64*Pi^(1/2)*arcsinh(x^(1/6)))","A"
308,1,58,27,0.299000," ","int(x^3/(x^4-1)/(2*x^8+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{2 \RootOf \left(\textit{\_Z}^{2}-3\right) x^{4}+\RootOf \left(\textit{\_Z}^{2}-3\right)+3 \sqrt{2 x^{8}+1}}{\left(-1+x \right) \left(1+x \right) \left(x^{2}+1\right)}\right)}{12}$&$58$\\ \hline \end{longtable}"," ",0,"-1/12*RootOf(_Z^2-3)*ln(-(2*RootOf(_Z^2-3)*x^4+RootOf(_Z^2-3)+3*(2*x^8+1)^(1/2))/(-1+x)/(1+x)/(x^2+1))","C"
309,1,47,47,0.355000," ","int(x^9*(x^10+x^5+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\left(\frac{1}{15} x^{10}+\frac{1}{60} x^{5}+\frac{1}{24}\right) \sqrt{x^{10}+x^{5}+1}-\frac{3 \ln \left(2 x^{5}+2 \sqrt{x^{10}+x^{5}+1}+1\right)}{80}$&$47$\\ risch&$\frac{\left(8 x^{10}+2 x^{5}+5\right) \sqrt{x^{10}+x^{5}+1}}{120}+\frac{3 \ln \left(-2 x^{5}+2 \sqrt{x^{10}+x^{5}+1}-1\right)}{80}$&$48$\\ \hline \end{longtable}"," ",0,"(1/15*x^10+1/60*x^5+1/24)*(x^10+x^5+1)^(1/2)-3/80*ln(2*x^5+2*(x^10+x^5+1)^(1/2)+1)","A"
310,1,52,57,0.223000," ","int(1/x^5/(x^4+2*x^2+4)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\left(3 x^{2}-4\right) \sqrt{x^{4}+2 x^{2}+4}}{64 x^{4}}+\frac{\ln \left(\frac{x^{2}+2 \sqrt{x^{4}+2 x^{2}+4}+4}{x^{2}}\right)}{128}$&$52$\\ default&$-\frac{\sqrt{x^{4}+2 x^{2}+4}}{16 x^{4}}+\frac{3 \sqrt{x^{4}+2 x^{2}+4}}{64 x^{2}}+\frac{\arctanh \left(\frac{2 x^{2}+8}{4 \sqrt{x^{4}+2 x^{2}+4}}\right)}{128}$&$60$\\ risch&$\frac{3 x^{6}+2 x^{4}+4 x^{2}-16}{64 x^{4} \sqrt{x^{4}+2 x^{2}+4}}+\frac{\arctanh \left(\frac{2 x^{2}+8}{4 \sqrt{x^{4}+2 x^{2}+4}}\right)}{128}$&$60$\\ elliptic&$-\frac{\sqrt{x^{4}+2 x^{2}+4}}{16 x^{4}}+\frac{3 \sqrt{x^{4}+2 x^{2}+4}}{64 x^{2}}+\frac{\arctanh \left(\frac{2 x^{2}+8}{4 \sqrt{x^{4}+2 x^{2}+4}}\right)}{128}$&$60$\\ \hline \end{longtable}"," ",0,"1/64*(3*x^2-4)/x^4*(x^4+2*x^2+4)^(1/2)+1/128*ln((x^2+2*(x^4+2*x^2+4)^(1/2)+4)/x^2)","A"
311,1,27,19,0.203000," ","int((x^2-1)/x/(x^4+3*x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\ln \left(\frac{-x^{2}+\sqrt{x^{4}+3 x^{2}+1}-1}{x}\right)$&$27$\\ default&$\frac{\ln \left(\frac{3}{2}+x^{2}+\sqrt{x^{4}+3 x^{2}+1}\right)}{2}+\frac{\arctanh \left(\frac{3 x^{2}+2}{2 \sqrt{x^{4}+3 x^{2}+1}}\right)}{2}$&$46$\\ elliptic&$\frac{\ln \left(\frac{3}{2}+x^{2}+\sqrt{x^{4}+3 x^{2}+1}\right)}{2}+\frac{\arctanh \left(\frac{3 x^{2}+2}{2 \sqrt{x^{4}+3 x^{2}+1}}\right)}{2}$&$46$\\ \hline \end{longtable}"," ",0,"-ln((-x^2+(x^4+3*x^2+1)^(1/2)-1)/x)","A"
312,1,14,13,0.310000," ","int((2*x^3-3*x)*(x^4-3*x^2)^(3/5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{5 \left(x^{4}-3 x^{2}\right)^{\frac{8}{5}}}{16}$&$14$\\ gosper&$\frac{5 \left(x^{4}-3 x^{2}\right)^{\frac{3}{5}} x^{2} \left(x^{2}-3\right)}{16}$&$22$\\ trager&$\frac{5 \left(x^{4}-3 x^{2}\right)^{\frac{3}{5}} x^{2} \left(x^{2}-3\right)}{16}$&$22$\\ risch&$\frac{5 x^{2} \left(x^{2} \left(x^{2}-3\right)\right)^{\frac{3}{5}} \left(x^{2}-3\right)}{16}$&$22$\\ meijerg&$\frac{5 \,3^{\frac{3}{5}} \mathrm{signum}\left(-1+\frac{x^{2}}{3}\right)^{\frac{3}{5}} x^{\frac{26}{5}} \hypergeom \left(\left[-\frac{3}{5}, \frac{13}{5}\right], \left[\frac{18}{5}\right], \frac{x^{2}}{3}\right)}{13 \left(-\mathrm{signum}\left(-1+\frac{x^{2}}{3}\right)\right)^{\frac{3}{5}}}-\frac{15 \,3^{\frac{3}{5}} \mathrm{signum}\left(-1+\frac{x^{2}}{3}\right)^{\frac{3}{5}} x^{\frac{16}{5}} \hypergeom \left(\left[-\frac{3}{5}, \frac{8}{5}\right], \left[\frac{13}{5}\right], \frac{x^{2}}{3}\right)}{16 \left(-\mathrm{signum}\left(-1+\frac{x^{2}}{3}\right)\right)^{\frac{3}{5}}}$&$84$\\ \hline \end{longtable}"," ",0,"5/16*(x^4-3*x^2)^(8/5)","A"
313,1,116,34,0.353000," ","int((-2*x^5+3*x^8-x^2*(3*x^3-1)^(2/3))/(3*x^3-1)^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline meijerg&$-\frac{\left(-\mathrm{signum}\left(3 x^{3}-1\right)\right)^{\frac{3}{4}} x^{6} \hypergeom \left(\left[\frac{3}{4}, 2\right], \left[3\right], 3 x^{3}\right)}{3 \mathrm{signum}\left(3 x^{3}-1\right)^{\frac{3}{4}}}+\frac{\left(-\mathrm{signum}\left(3 x^{3}-1\right)\right)^{\frac{3}{4}} x^{9} \hypergeom \left(\left[\frac{3}{4}, 3\right], \left[4\right], 3 x^{3}\right)}{3 \mathrm{signum}\left(3 x^{3}-1\right)^{\frac{3}{4}}}-\frac{\left(-\mathrm{signum}\left(3 x^{3}-1\right)\right)^{\frac{1}{12}} x^{3} \hypergeom \left(\left[\frac{1}{12}, 1\right], \left[2\right], 3 x^{3}\right)}{3 \mathrm{signum}\left(3 x^{3}-1\right)^{\frac{1}{12}}}$&$116$\\ \hline \end{longtable}"," ",0,"-1/3/signum(3*x^3-1)^(3/4)*(-signum(3*x^3-1))^(3/4)*x^6*hypergeom([3/4,2],[3],3*x^3)+1/3/signum(3*x^3-1)^(3/4)*(-signum(3*x^3-1))^(3/4)*x^9*hypergeom([3/4,3],[4],3*x^3)-1/3/signum(3*x^3-1)^(1/12)*(-signum(3*x^3-1))^(1/12)*x^3*hypergeom([1/12,1],[2],3*x^3)","C"
314,1,902,59,2.738000," ","int(1/(x^3-1)/(x^3+2)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\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) \ln \left(-\frac{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} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{3}+12 \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}+15 \left(x^{3}+2\right)^{\frac{2}{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)^{2} x +45 \left(x^{3}+2\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}+7 \left(x^{3}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{2}+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}+16 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{3}+21 x \left(x^{3}+2\right)^{\frac{2}{3}}+18 \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)+8 \RootOf \left(\textit{\_Z}^{3}-9\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right)-\frac{\ln \left(\frac{-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} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{3}+9 \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}+15 \left(x^{3}+2\right)^{\frac{2}{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)^{2} x +45 \left(x^{3}+2\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}-2 \left(x^{3}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{2}+9 \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 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{3}-6 x \left(x^{3}+2\right)^{\frac{2}{3}}+18 \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)-6 \RootOf \left(\textit{\_Z}^{3}-9\right)}{\left(-1+x \right) \left(x^{2}+x +1\right)}\right) \RootOf \left(\textit{\_Z}^{3}-9\right)}{9}-\ln \left(\frac{-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} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{3}+9 \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}+15 \left(x^{3}+2\right)^{\frac{2}{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)^{2} x +45 \left(x^{3}+2\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}-2 \left(x^{3}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-9\right)^{2} x^{2}+9 \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 \RootOf \left(\textit{\_Z}^{3}-9\right) x^{3}-6 x \left(x^{3}+2\right)^{\frac{2}{3}}+18 \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)-6 \RootOf \left(\textit{\_Z}^{3}-9\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)$&$902$\\ \hline \end{longtable}"," ",0,"RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*ln(-(27*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+12*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3+15*(x^3+2)^(2/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*x+45*(x^3+2)^(1/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*x^2+7*(x^3+2)^(1/3)*RootOf(_Z^3-9)^2*x^2+36*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3+16*RootOf(_Z^3-9)*x^3+21*x*(x^3+2)^(2/3)+18*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)+8*RootOf(_Z^3-9))/(-1+x)/(x^2+x+1))-1/9*ln((-27*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+9*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3+15*(x^3+2)^(2/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*x+45*(x^3+2)^(1/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*x^2-2*(x^3+2)^(1/3)*RootOf(_Z^3-9)^2*x^2+9*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-3*RootOf(_Z^3-9)*x^3-6*x*(x^3+2)^(2/3)+18*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)-6*RootOf(_Z^3-9))/(-1+x)/(x^2+x+1))*RootOf(_Z^3-9)-ln((-27*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+9*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3+15*(x^3+2)^(2/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*x+45*(x^3+2)^(1/3)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*x^2-2*(x^3+2)^(1/3)*RootOf(_Z^3-9)^2*x^2+9*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-3*RootOf(_Z^3-9)*x^3-6*x*(x^3+2)^(2/3)+18*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)-6*RootOf(_Z^3-9))/(-1+x)/(x^2+x+1))*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)","C"
315,1,150,104,1.335000," ","int(1/(x^4+1)/(x^4+2)^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$-\frac{\RootOf \left(\textit{\_Z}^{4}+1\right) \ln \left(\frac{\sqrt{x^{4}+2}\, \RootOf \left(\textit{\_Z}^{4}+1\right)^{3} x^{2}-\left(x^{4}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}+\left(x^{4}+2\right)^{\frac{3}{4}} x -\RootOf \left(\textit{\_Z}^{4}+1\right)}{x^{4}+1}\right)}{4}+\frac{\RootOf \left(\textit{\_Z}^{4}+1\right)^{3} \ln \left(\frac{\left(x^{4}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+1\right)^{2} x^{3}-\sqrt{x^{4}+2}\, \RootOf \left(\textit{\_Z}^{4}+1\right) x^{2}+\left(x^{4}+2\right)^{\frac{3}{4}} x +\RootOf \left(\textit{\_Z}^{4}+1\right)^{3}}{x^{4}+1}\right)}{4}$&$150$\\ \hline \end{longtable}"," ",0,"-1/4*RootOf(_Z^4+1)*ln(((x^4+2)^(1/2)*RootOf(_Z^4+1)^3*x^2-(x^4+2)^(1/4)*RootOf(_Z^4+1)^2*x^3+(x^4+2)^(3/4)*x-RootOf(_Z^4+1))/(x^4+1))+1/4*RootOf(_Z^4+1)^3*ln(((x^4+2)^(1/4)*RootOf(_Z^4+1)^2*x^3-(x^4+2)^(1/2)*RootOf(_Z^4+1)*x^2+(x^4+2)^(3/4)*x+RootOf(_Z^4+1)^3)/(x^4+1))","C"
316,1,29,48,1.633000," ","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&$\frac{x \left(x^{3}+2\right)^{\frac{2}{3}}}{3}+\frac{5 \ln \left(-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}+6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}-8 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+3 x \left(x^{3}+2\right)^{\frac{2}{3}}-4 x^{3}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-4\right)}{9}+\frac{10 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \ln \left(4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)^{2} x^{3}-6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{2}{3}} x +6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right) x^{3}+3 \left(x^{3}+2\right)^{\frac{1}{3}} x^{2}-2 x^{3}-4 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} +1\right)-4\right)}{9}$&$226$\\ \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"
317,1,228,56,2.832000," ","int((x^4+1)^(3/4)/(x^4+2)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(x^{4}+1\right)^{\frac{3}{4}} x}{8 x^{4}+16}+\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}-4 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{x^{4}+2}\right)}{64}+\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}+3 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{4}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x +2 \RootOf \left(\textit{\_Z}^{4}-2\right)}{x^{4}+2}\right)}{64}$&$228$\\ trager&$\frac{\left(x^{4}+1\right)^{\frac{3}{4}} x}{8 x^{4}+16}-\frac{3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{2}-2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) x^{4}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{x^{4}+2}\right)}{64}-\frac{3 \RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(-\frac{-2 \sqrt{x^{4}+1}\, \RootOf \left(\textit{\_Z}^{4}-2\right)^{3} x^{2}+2 \left(x^{4}+1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2} x^{3}-3 \RootOf \left(\textit{\_Z}^{4}-2\right) x^{4}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 \RootOf \left(\textit{\_Z}^{4}-2\right)}{x^{4}+2}\right)}{64}$&$229$\\ \hline \end{longtable}"," ",0,"1/8*x*(x^4+1)^(3/4)/(x^4+2)+3/64*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln((2*(x^4+1)^(1/2)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4-2)^2*x^3-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4-4*(x^4+1)^(3/4)*x-2*RootOf(_Z^2+RootOf(_Z^4-2)^2))/(x^4+2))+3/64*RootOf(_Z^4-2)*ln(-(2*(x^4+1)^(1/2)*RootOf(_Z^4-2)^3*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4-2)^2*x^3+3*RootOf(_Z^4-2)*x^4+4*(x^4+1)^(3/4)*x+2*RootOf(_Z^4-2))/(x^4+2))","C"
318,1,23,36,0.324000," ","int((x^5-2)^2/(x^5+3)^(16/5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x \left(97 x^{10}+462 x^{5}+1188\right)}{891 \left(x^{5}+3\right)^{\frac{11}{5}}}$&$23$\\ trager&$\frac{x \left(97 x^{10}+462 x^{5}+1188\right)}{891 \left(x^{5}+3\right)^{\frac{11}{5}}}$&$23$\\ risch&$\frac{x \left(97 x^{10}+462 x^{5}+1188\right)}{891 \left(x^{5}+3\right)^{\frac{11}{5}}}$&$23$\\ meijerg&$\frac{4 \,3^{\frac{4}{5}} x \left(\frac{25}{9} x^{10}+\frac{55}{3} x^{5}+33\right)}{2673 \left(1+\frac{x^{5}}{3}\right)^{\frac{11}{5}}}+\frac{3^{\frac{4}{5}} x^{11}}{891 \left(1+\frac{x^{5}}{3}\right)^{\frac{11}{5}}}-\frac{2 \,3^{\frac{4}{5}} x^{6} \left(11+\frac{5 x^{5}}{3}\right)}{2673 \left(1+\frac{x^{5}}{3}\right)^{\frac{11}{5}}}$&$70$\\ \hline \end{longtable}"," ",0,"1/891*x*(97*x^10+462*x^5+1188)/(x^5+3)^(11/5)","A"
319,1,2501,71,13.602000," ","int(1/(x^3+3*x^2+3*x)/(x^3+3*x^2+3*x+3)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\text{Expression too large to display}$&$2501$\\ \hline \end{longtable}"," ",0,"1/9*RootOf(_Z^3-9)*ln(-(5486785533*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x+1732189959*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x-4041776571*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3+15322002984*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(2/3)*x+6809512275*(x^3+3*x^2+3*x+3)^(2/3)-10200674203*RootOf(_Z^3-9)*x^3-30602022609*RootOf(_Z^3-9)*x^2-32311070361*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-12802499577*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2-53038926819*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)+1732189959*RootOf(_Z^3-9)^3*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2+5486785533*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*x^2-96933211083*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2-96933211083*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x-16744502937*RootOf(_Z^3-9)-30602022609*RootOf(_Z^3-9)*x+2837496903*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)+6809512275*(x^3+3*x^2+3*x+3)^(2/3)*x+1828928511*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+577396653*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3+15322002984*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(2/3)+2837496903*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x^2+5674993806*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x-20428536825*RootOf(_Z^3-9)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(1/3)-20428536825*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x^2-40857073650*RootOf(_Z^3-9)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(1/3)*x)/x/(x^2+3*x+3))-1/9*ln(-(10102924098*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x+1732189959*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x-4041776571*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3-15322002984*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(2/3)*x-8512490709*(x^3+3*x^2+3*x+3)^(2/3)+10778070856*RootOf(_Z^3-9)*x^3+32334212568*RootOf(_Z^3-9)*x^2+62862638832*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-23573489562*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2+74088110052*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)+1732189959*RootOf(_Z^3-9)^3*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2+10102924098*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*x^2+188587916496*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2+188587916496*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x+12702726366*RootOf(_Z^3-9)+32334212568*RootOf(_Z^3-9)*x-2269837425*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)-8512490709*(x^3+3*x^2+3*x+3)^(2/3)*x+3367641366*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+577396653*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3-15322002984*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(2/3)-2269837425*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x^2-4539674850*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x+25537472127*RootOf(_Z^3-9)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(1/3)+25537472127*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x^2+51074944254*RootOf(_Z^3-9)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(1/3)*x)/x/(x^2+3*x+3))*RootOf(_Z^3-9)-ln(-(10102924098*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x+1732189959*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x-4041776571*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3-15322002984*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(2/3)*x-8512490709*(x^3+3*x^2+3*x+3)^(2/3)+10778070856*RootOf(_Z^3-9)*x^3+32334212568*RootOf(_Z^3-9)*x^2+62862638832*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-23573489562*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2+74088110052*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)+1732189959*RootOf(_Z^3-9)^3*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2+10102924098*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*x^2+188587916496*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2+188587916496*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x+12702726366*RootOf(_Z^3-9)+32334212568*RootOf(_Z^3-9)*x-2269837425*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)-8512490709*(x^3+3*x^2+3*x+3)^(2/3)*x+3367641366*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+577396653*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3-15322002984*RootOf(_Z^3-9)^2*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(2/3)-2269837425*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x^2-4539674850*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x+25537472127*RootOf(_Z^3-9)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(1/3)+25537472127*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x^2+51074944254*RootOf(_Z^3-9)*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*(x^3+3*x^2+3*x+3)^(1/3)*x)/x/(x^2+3*x+3))*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)","C"
320,1,22,18,0.321000," ","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&$-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) x +\sqrt{x^{4}+1}}{x^{2}+1}\right)}{2}$&$34$\\ 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*arctan(1/2/x*2^(1/2)*(x^4+1)^(1/2))*2^(1/2)","A"
321,1,22,18,0.301000," ","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/x*2^(1/2)*(x^4+1)^(1/2))*2^(1/2)","A"
322,1,18,14,0.297000," ","int((x^2+1)/x/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}+\frac{\arcsinh \left(x^{2}\right)}{2}$&$18$\\ trager&$\ln \left(\frac{x^{2}+\sqrt{x^{4}+1}-1}{x}\right)$&$18$\\ elliptic&$-\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}+\frac{\arcsinh \left(x^{2}\right)}{2}$&$18$\\ meijerg&$\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{-2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{x^{4}+1}}{2}\right)+\left(-2 \ln \left(2\right)+4 \ln \left(x \right)\right) \sqrt{\pi}}{4 \sqrt{\pi}}$&$44$\\ \hline \end{longtable}"," ",0,"-1/2*arctanh(1/(x^4+1)^(1/2))+1/2*arcsinh(x^2)","A"
323,1,18,14,0.289000," ","int((x^2-1)/x/(x^4+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}$&$18$\\ elliptic&$\frac{\arcsinh \left(x^{2}\right)}{2}+\frac{\arctanh \left(\frac{1}{\sqrt{x^{4}+1}}\right)}{2}$&$18$\\ trager&$-\ln \left(\frac{-x^{2}+\sqrt{x^{4}+1}-1}{x}\right)$&$22$\\ meijerg&$\frac{\arcsinh \left(x^{2}\right)}{2}-\frac{-2 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{x^{4}+1}}{2}\right)+\left(-2 \ln \left(2\right)+4 \ln \left(x \right)\right) \sqrt{\pi}}{4 \sqrt{\pi}}$&$44$\\ \hline \end{longtable}"," ",0,"1/2*arcsinh(x^2)+1/2*arctanh(1/(x^4+1)^(1/2))","A"
324,1,31,21,0.556000," ","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&$\frac{\arctanh \left(\frac{\sqrt{x^{4}+x^{2}+1}\, \sqrt{2}\, \sqrt{6}}{6 x}\right) \sqrt{6}\, \sqrt{2}}{6}$&$31$\\ trager&$\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}-3\right) x +\sqrt{x^{4}+x^{2}+1}}{\left(1+x \right) \left(-1+x \right)}\right)}{3}$&$41$\\ default&$-\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , \frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}$&$184$\\ \hline \end{longtable}"," ",0,"1/6*arctanh(1/6*(x^4+x^2+1)^(1/2)*2^(1/2)/x*6^(1/2))*6^(1/2)*2^(1/2)","A"
325,1,18,13,0.487000," ","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&$-\arctan \left(\frac{\sqrt{x^{4}+x^{2}+1}}{x}\right)$&$18$\\ trager&$\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) x -\sqrt{x^{4}+x^{2}+1}}{x^{2}+1}\right)$&$39$\\ default&$-\frac{2 \sqrt{1-\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) x^{2}}\, \sqrt{1-\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{2}}\, \EllipticF \left(\frac{x \sqrt{-2+2 i \sqrt{3}}}{2}, \frac{\sqrt{-2+2 i \sqrt{3}}}{2}\right)}{\sqrt{-2+2 i \sqrt{3}}\, \sqrt{x^{4}+x^{2}+1}}+\frac{2 \sqrt{1+\frac{x^{2}}{2}-\frac{i x^{2} \sqrt{3}}{2}}\, \sqrt{1+\frac{x^{2}}{2}+\frac{i x^{2} \sqrt{3}}{2}}\, \EllipticPi \left(\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, x , -\frac{1}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \frac{\sqrt{-\frac{1}{2}-\frac{i \sqrt{3}}{2}}}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-\frac{1}{2}+\frac{i \sqrt{3}}{2}}\, \sqrt{x^{4}+x^{2}+1}}$&$188$\\ \hline \end{longtable}"," ",0,"-arctan(1/x*(x^4+x^2+1)^(1/2))","A"
326,1,15,14,0.079000," ","int((x^4-1)/x^2/(x^4+x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{x^{4}+x^{2}+1}}{x}$&$15$\\ trager&$\frac{\sqrt{x^{4}+x^{2}+1}}{x}$&$15$\\ risch&$\frac{\sqrt{x^{4}+x^{2}+1}}{x}$&$15$\\ elliptic&$\frac{\sqrt{x^{4}+x^{2}+1}}{x}$&$15$\\ gosper&$\frac{\left(x^{2}+x +1\right) \left(x^{2}-x +1\right)}{\sqrt{x^{4}+x^{2}+1}\, x}$&$29$\\ \hline \end{longtable}"," ",0,"1/x*(x^4+x^2+1)^(1/2)","A"
327,1,247419,66,0.386000," ","int((-x^2+1)/(2*a*x+x^2+1)/(2*a*x^3+x^4+2*b*x^2+2*a*x+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$247419$\\ elliptic&$\text{Expression too large to display}$&$258804$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
328,0,0,18,0.023000," ","int(1/(x^4+1)/(-x^2+(x^4+1)^(1/2))^(1/2),x)","\[\int \frac{1}{\left(x^{4}+1\right) \sqrt{-x^{2}+\sqrt{x^{4}+1}}}\, dx\]"," ",0,"int(1/(x^4+1)/(-x^2+(x^4+1)^(1/2))^(1/2),x)","F"
329,0,0,22,0.033000," ","int(1/(1+x^(2*n))/(-x^2+(1+x^(2*n))^(1/n))^(1/2),x)","\[\int \frac{1}{\left(1+x^{2 n}\right) \sqrt{-x^{2}+\left(1+x^{2 n}\right)^{\frac{1}{n}}}}\, dx\]"," ",0,"int(1/(1+x^(2*n))/(-x^2+(1+x^(2*n))^(1/n))^(1/2),x)","F"
330,1,11,10,0.030000," ","int(cos(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{2}+\frac{\cos \left(x \right) \sin \left(x \right)}{2}$&$11$\\ risch&$\frac{x}{2}+\frac{\sin \left(2 x \right)}{4}$&$11$\\ norman&$\frac{x \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\frac{x}{2}-\left(\tan^{3}\left(\frac{x}{2}\right)\right)+\frac{x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{2}+\tan \left(\frac{x}{2}\right)}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{2}}$&$45$\\ \hline \end{longtable}"," ",0,"1/2*x+1/2*cos(x)*sin(x)","A"
331,1,11,9,0.302000," ","int(cos(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}$&$11$\\ risch&$\frac{3 \sin \left(x \right)}{4}+\frac{\sin \left(3 x \right)}{12}$&$12$\\ \hline \end{longtable}"," ",0,"1/3*(2+cos(x)^2)*sin(x)","A"
332,1,17,18,0.311000," ","int(sin(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x}{8}+\frac{\sin \left(4 x \right)}{32}-\frac{\sin \left(2 x \right)}{4}$&$17$\\ default&$-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{4}+\frac{3 x}{8}$&$18$\\ norman&$\frac{\frac{3 x}{8}-\frac{11 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{4}+\frac{11 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4}+\frac{3 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{4}+\frac{3 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2}+\frac{9 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{4}+\frac{3 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{2}+\frac{3 x \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{8}-\frac{3 \tan \left(\frac{x}{2}\right)}{4}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{4}}$&$82$\\ \hline \end{longtable}"," ",0,"3/8*x+1/32*sin(4*x)-1/4*sin(2*x)","A"
333,1,23,26,0.323000," ","int(cos(x)^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{5 x}{16}+\frac{\sin \left(6 x \right)}{192}+\frac{3 \sin \left(4 x \right)}{64}+\frac{15 \sin \left(2 x \right)}{64}$&$23$\\ default&$\frac{\left(\cos^{5}\left(x \right)+\frac{5 \left(\cos^{3}\left(x \right)\right)}{4}+\frac{15 \cos \left(x \right)}{8}\right) \sin \left(x \right)}{6}+\frac{5 x}{16}$&$24$\\ norman&$\frac{\frac{5 x}{16}-\frac{5 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{24}+\frac{15 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4}-\frac{15 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{4}+\frac{5 \left(\tan^{9}\left(\frac{x}{2}\right)\right)}{24}-\frac{11 \left(\tan^{11}\left(\frac{x}{2}\right)\right)}{8}+\frac{15 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{8}+\frac{75 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{16}+\frac{25 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{4}+\frac{75 x \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{16}+\frac{15 x \left(\tan^{10}\left(\frac{x}{2}\right)\right)}{8}+\frac{5 x \left(\tan^{12}\left(\frac{x}{2}\right)\right)}{16}+\frac{11 \tan \left(\frac{x}{2}\right)}{8}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{6}}$&$116$\\ \hline \end{longtable}"," ",0,"5/16*x+1/192*sin(6*x)+3/64*sin(4*x)+15/64*sin(2*x)","A"
334,1,29,34,0.355000," ","int(sin(x)^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{35 x}{128}+\frac{\sin \left(8 x \right)}{1024}-\frac{\sin \left(6 x \right)}{96}+\frac{7 \sin \left(4 x \right)}{128}-\frac{7 \sin \left(2 x \right)}{32}$&$29$\\ default&$-\frac{\left(\sin^{7}\left(x \right)+\frac{7 \left(\sin^{5}\left(x \right)\right)}{6}+\frac{35 \left(\sin^{3}\left(x \right)\right)}{24}+\frac{35 \sin \left(x \right)}{16}\right) \cos \left(x \right)}{8}+\frac{35 x}{128}$&$30$\\ norman&$\frac{\frac{35 x}{128}-\frac{35 \tan \left(\frac{x}{2}\right)}{64}+\frac{1225 x \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{64}+\frac{245 x \left(\tan^{10}\left(\frac{x}{2}\right)\right)}{16}+\frac{245 x \left(\tan^{12}\left(\frac{x}{2}\right)\right)}{32}+\frac{245 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{16}-\frac{805 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{192}+\frac{35 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{16}+\frac{245 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{32}+\frac{35 x \left(\tan^{14}\left(\frac{x}{2}\right)\right)}{16}+\frac{35 x \left(\tan^{16}\left(\frac{x}{2}\right)\right)}{128}+\frac{805 \left(\tan^{13}\left(\frac{x}{2}\right)\right)}{192}+\frac{35 \left(\tan^{15}\left(\frac{x}{2}\right)\right)}{64}-\frac{2681 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{192}-\frac{5053 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{192}+\frac{5053 \left(\tan^{9}\left(\frac{x}{2}\right)\right)}{192}+\frac{2681 \left(\tan^{11}\left(\frac{x}{2}\right)\right)}{192}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{8}}$&$150$\\ \hline \end{longtable}"," ",0,"35/128*x+1/1024*sin(8*x)-1/96*sin(6*x)+7/128*sin(4*x)-7/32*sin(2*x)","A"
335,1,15,14,0.337000," ","int(cos(1/4*Pi+1/2*x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x}{8}+\frac{\cos \left(x \right)}{2}-\frac{\sin \left(2 x \right)}{16}$&$15$\\ derivativedivides&$\frac{\left(\cos^{3}\left(\frac{\pi}{4}+\frac{x}{2}\right)+\frac{3 \cos \left(\frac{\pi}{4}+\frac{x}{2}\right)}{2}\right) \sin \left(\frac{\pi}{4}+\frac{x}{2}\right)}{2}+\frac{3 \pi}{16}+\frac{3 x}{8}$&$39$\\ default&$\frac{\left(\cos^{3}\left(\frac{\pi}{4}+\frac{x}{2}\right)+\frac{3 \cos \left(\frac{\pi}{4}+\frac{x}{2}\right)}{2}\right) \sin \left(\frac{\pi}{4}+\frac{x}{2}\right)}{2}+\frac{3 \pi}{16}+\frac{3 x}{8}$&$39$\\ norman&$\frac{\frac{3 x}{8}-\frac{3 \left(\tan^{3}\left(\frac{\pi}{8}+\frac{x}{4}\right)\right)}{2}+\frac{3 \left(\tan^{5}\left(\frac{\pi}{8}+\frac{x}{4}\right)\right)}{2}-\frac{5 \left(\tan^{7}\left(\frac{\pi}{8}+\frac{x}{4}\right)\right)}{2}+\frac{3 x \left(\tan^{2}\left(\frac{\pi}{8}+\frac{x}{4}\right)\right)}{2}+\frac{9 x \left(\tan^{4}\left(\frac{\pi}{8}+\frac{x}{4}\right)\right)}{4}+\frac{3 x \left(\tan^{6}\left(\frac{\pi}{8}+\frac{x}{4}\right)\right)}{2}+\frac{3 x \left(\tan^{8}\left(\frac{\pi}{8}+\frac{x}{4}\right)\right)}{8}+\frac{5 \tan \left(\frac{\pi}{8}+\frac{x}{4}\right)}{2}}{\left(1+\tan^{2}\left(\frac{\pi}{8}+\frac{x}{4}\right)\right)^{4}}$&$118$\\ \hline \end{longtable}"," ",0,"3/8*x+1/2*cos(x)-1/16*sin(2*x)","A"
336,1,22,23,0.540000," ","int(-cos(5/12*Pi+3*x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\sin \left(\frac{\pi}{4}+9 x \right)}{36}-\frac{\sin \left(\frac{5 \pi}{12}+3 x \right)}{4}$&$22$\\ derivativedivides&$-\frac{\left(2+\cos^{2}\left(\frac{5 \pi}{12}+3 x \right)\right) \sin \left(\frac{5 \pi}{12}+3 x \right)}{9}$&$23$\\ default&$-\frac{\left(2+\cos^{2}\left(\frac{5 \pi}{12}+3 x \right)\right) \sin \left(\frac{5 \pi}{12}+3 x \right)}{9}$&$23$\\ norman&$\frac{-\frac{4 \left(\tan^{3}\left(\frac{5 \pi}{24}+\frac{3 x}{2}\right)\right)}{9}-\frac{2 \left(\tan^{5}\left(\frac{5 \pi}{24}+\frac{3 x}{2}\right)\right)}{3}-\frac{2 \tan \left(\frac{5 \pi}{24}+\frac{3 x}{2}\right)}{3}}{\left(1+\tan^{2}\left(\frac{5 \pi}{24}+\frac{3 x}{2}\right)\right)^{3}}$&$51$\\ \hline \end{longtable}"," ",0,"1/36*sin(1/4*Pi+9*x)-1/4*sin(5/12*Pi+3*x)","A"
337,1,18,17,0.310000," ","int(1/sin(x)^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\left(-\frac{8}{15}-\frac{\left(\csc^{4}\left(x \right)\right)}{5}-\frac{4 \left(\csc^{2}\left(x \right)\right)}{15}\right) \cot \left(x \right)$&$18$\\ risch&$-\frac{16 i \left(10 \,{\mathrm e}^{4 i x}-5 \,{\mathrm e}^{2 i x}+1\right)}{15 \left({\mathrm e}^{2 i x}-1\right)^{5}}$&$29$\\ norman&$\frac{-\frac{1}{160}-\frac{5 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{96}-\frac{5 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{16}+\frac{5 \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{16}+\frac{5 \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{96}+\frac{\left(\tan^{10}\left(\frac{x}{2}\right)\right)}{160}}{\tan \left(\frac{x}{2}\right)^{5}}$&$50$\\ \hline \end{longtable}"," ",0,"(-8/15-1/5*csc(x)^4-4/15*csc(x)^2)*cot(x)","A"
338,1,32,28,0.360000," ","int(csc(x)^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\left(-\frac{\left(\csc^{5}\left(x \right)\right)}{6}-\frac{5 \left(\csc^{3}\left(x \right)\right)}{24}-\frac{5 \csc \left(x \right)}{16}\right) \cot \left(x \right)+\frac{5 \ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{16}$&$32$\\ norman&$\frac{-\frac{1}{384}-\frac{3 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{128}-\frac{15 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{128}+\frac{15 \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{128}+\frac{3 \left(\tan^{10}\left(\frac{x}{2}\right)\right)}{128}+\frac{\left(\tan^{12}\left(\frac{x}{2}\right)\right)}{384}}{\tan \left(\frac{x}{2}\right)^{6}}+\frac{5 \ln \left(\tan \left(\frac{x}{2}\right)\right)}{16}$&$58$\\ risch&$\frac{15 \,{\mathrm e}^{11 i x}-85 \,{\mathrm e}^{9 i x}+198 \,{\mathrm e}^{7 i x}+198 \,{\mathrm e}^{5 i x}-85 \,{\mathrm e}^{3 i x}+15 \,{\mathrm e}^{i x}}{24 \left({\mathrm e}^{2 i x}-1\right)^{6}}-\frac{5 \ln \left({\mathrm e}^{i x}+1\right)}{16}+\frac{5 \ln \left({\mathrm e}^{i x}-1\right)}{16}$&$76$\\ \hline \end{longtable}"," ",0,"(-1/6*csc(x)^5-5/24*csc(x)^3-5/16*csc(x))*cot(x)+5/16*ln(csc(x)-cot(x))","A"
339,1,37,33,0.333000," ","int(1/cos(x)^12,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\left(-\frac{256}{693}-\frac{\left(\sec^{10}\left(x \right)\right)}{11}-\frac{10 \left(\sec^{8}\left(x \right)\right)}{99}-\frac{80 \left(\sec^{6}\left(x \right)\right)}{693}-\frac{32 \left(\sec^{4}\left(x \right)\right)}{231}-\frac{128 \left(\sec^{2}\left(x \right)\right)}{693}\right) \tan \left(x \right)$&$37$\\ risch&$\frac{512 i \left(462 \,{\mathrm e}^{10 i x}+330 \,{\mathrm e}^{8 i x}+165 \,{\mathrm e}^{6 i x}+55 \,{\mathrm e}^{4 i x}+11 \,{\mathrm e}^{2 i x}+1\right)}{693 \left(1+{\mathrm e}^{2 i x}\right)^{11}}$&$50$\\ \hline \end{longtable}"," ",0,"-(-256/693-1/11*sec(x)^10-10/99*sec(x)^8-80/693*sec(x)^6-32/231*sec(x)^4-128/693*sec(x)^2)*tan(x)","A"
340,1,40,30,0.651000," ","int(1/cos(1/4*Pi+3*x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\sec \left(\frac{\pi}{4}+3 x \right) \tan \left(\frac{\pi}{4}+3 x \right)}{6}+\frac{\ln \left(\sec \left(\frac{\pi}{4}+3 x \right)+\tan \left(\frac{\pi}{4}+3 x \right)\right)}{6}$&$40$\\ default&$\frac{\sec \left(\frac{\pi}{4}+3 x \right) \tan \left(\frac{\pi}{4}+3 x \right)}{6}+\frac{\ln \left(\sec \left(\frac{\pi}{4}+3 x \right)+\tan \left(\frac{\pi}{4}+3 x \right)\right)}{6}$&$40$\\ norman&$\frac{\frac{\left(\tan^{3}\left(\frac{\pi}{8}+\frac{3 x}{2}\right)\right)}{3}+\frac{\tan \left(\frac{\pi}{8}+\frac{3 x}{2}\right)}{3}}{\left(\tan^{2}\left(\frac{\pi}{8}+\frac{3 x}{2}\right)-1\right)^{2}}-\frac{\ln \left(\tan \left(\frac{\pi}{8}+\frac{3 x}{2}\right)-1\right)}{6}+\frac{\ln \left(\tan \left(\frac{\pi}{8}+\frac{3 x}{2}\right)+1\right)}{6}$&$66$\\ risch&$-\frac{i \left(\left(-1\right)^{\frac{3}{4}} {\mathrm e}^{9 i x}-\left(-1\right)^{\frac{1}{4}} {\mathrm e}^{3 i x}\right)}{3 \left(i {\mathrm e}^{6 i x}+1\right)^{2}}+\frac{\ln \left({\mathrm e}^{\frac{i \left(\pi +12 x \right)}{4}}+i\right)}{6}-\frac{\ln \left({\mathrm e}^{\frac{i \left(\pi +12 x \right)}{4}}-i\right)}{6}$&$67$\\ \hline \end{longtable}"," ",0,"1/6*sec(1/4*Pi+3*x)*tan(1/4*Pi+3*x)+1/6*ln(sec(1/4*Pi+3*x)+tan(1/4*Pi+3*x))","A"
341,1,19,18,0.043000," ","int(tan(x)^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$-x +\tan \left(x \right)-\frac{\left(\tan^{3}\left(x \right)\right)}{3}+\frac{\left(\tan^{5}\left(x \right)\right)}{5}$&$19$\\ derivativedivides&$\frac{\left(\tan^{5}\left(x \right)\right)}{5}-\frac{\left(\tan^{3}\left(x \right)\right)}{3}+\tan \left(x \right)-\arctan \left(\tan \left(x \right)\right)$&$21$\\ default&$\frac{\left(\tan^{5}\left(x \right)\right)}{5}-\frac{\left(\tan^{3}\left(x \right)\right)}{3}+\tan \left(x \right)-\arctan \left(\tan \left(x \right)\right)$&$21$\\ risch&$-x +\frac{2 i \left(45 \,{\mathrm e}^{8 i x}+90 \,{\mathrm e}^{6 i x}+140 \,{\mathrm e}^{4 i x}+70 \,{\mathrm e}^{2 i x}+23\right)}{15 \left(1+{\mathrm e}^{2 i x}\right)^{5}}$&$47$\\ \hline \end{longtable}"," ",0,"-x+tan(x)-1/3*tan(x)^3+1/5*tan(x)^5","A"
342,1,26,16,0.058000," ","int(1/tan(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{2}-\frac{1}{4 \tan \left(x \right)^{4}}+\ln \left(\tan \left(x \right)\right)+\frac{1}{2 \tan \left(x \right)^{2}}$&$26$\\ default&$-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{2}-\frac{1}{4 \tan \left(x \right)^{4}}+\ln \left(\tan \left(x \right)\right)+\frac{1}{2 \tan \left(x \right)^{2}}$&$26$\\ norman&$\frac{-\frac{1}{4}+\frac{\left(\tan^{2}\left(x \right)\right)}{2}}{\tan \left(x \right)^{4}}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{2}+\ln \left(\tan \left(x \right)\right)$&$27$\\ risch&$-i x -\frac{4 \left({\mathrm e}^{6 i x}-{\mathrm e}^{4 i x}+{\mathrm e}^{2 i x}\right)}{\left({\mathrm e}^{2 i x}-1\right)^{4}}+\ln \left({\mathrm e}^{2 i x}-1\right)$&$43$\\ \hline \end{longtable}"," ",0,"-1/2*ln(1+tan(x)^2)-1/4/tan(x)^4+ln(tan(x))+1/2/tan(x)^2","A"
343,1,38,24,0.045000," ","int(cot(1/4*Pi+1/3*x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\left(\cot^{3}\left(\frac{\pi}{4}+\frac{x}{3}\right)\right)+3 \cot \left(\frac{\pi}{4}+\frac{x}{3}\right)-\frac{3 \pi}{2}+3 \,\mathrm{arccot}\left(\cot \left(\frac{\pi}{4}+\frac{x}{3}\right)\right)$&$38$\\ default&$-\left(\cot^{3}\left(\frac{\pi}{4}+\frac{x}{3}\right)\right)+3 \cot \left(\frac{\pi}{4}+\frac{x}{3}\right)-\frac{3 \pi}{2}+3 \,\mathrm{arccot}\left(\cot \left(\frac{\pi}{4}+\frac{x}{3}\right)\right)$&$38$\\ norman&$\frac{-1+x \left(\tan^{3}\left(\frac{\pi}{4}+\frac{x}{3}\right)\right)+3 \left(\tan^{2}\left(\frac{\pi}{4}+\frac{x}{3}\right)\right)}{\tan \left(\frac{\pi}{4}+\frac{x}{3}\right)^{3}}$&$38$\\ risch&$x +\frac{4 i \left(-3 \,{\mathrm e}^{\frac{4 i x}{3}}-3 i {\mathrm e}^{\frac{2 i x}{3}}+2\right)}{\left({\mathrm e}^{\frac{i \left(3 \pi +4 x \right)}{6}}-1\right)^{3}}$&$38$\\ \hline \end{longtable}"," ",0,"-cot(1/4*Pi+1/3*x)^3+3*cot(1/4*Pi+1/3*x)-3/2*Pi+3*arccot(cot(1/4*Pi+1/3*x))","A"
344,1,35,44,0.320000," ","int(cos(x)^6*sin(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x}{256}+\frac{\sin \left(10 x \right)}{5120}+\frac{\sin \left(8 x \right)}{2048}-\frac{\sin \left(6 x \right)}{1024}-\frac{\sin \left(4 x \right)}{256}+\frac{\sin \left(2 x \right)}{512}$&$35$\\ default&$-\frac{\left(\cos^{7}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{10}-\frac{3 \left(\cos^{7}\left(x \right)\right) \sin \left(x \right)}{80}+\frac{\left(\cos^{5}\left(x \right)+\frac{5 \left(\cos^{3}\left(x \right)\right)}{4}+\frac{15 \cos \left(x \right)}{8}\right) \sin \left(x \right)}{160}+\frac{3 x}{256}$&$42$\\ \hline \end{longtable}"," ",0,"3/256*x+1/5120*sin(10*x)+1/2048*sin(8*x)-1/1024*sin(6*x)-1/256*sin(4*x)+1/512*sin(2*x)","A"
345,1,38,25,0.053000," ","int(cos(x)^6*sin(x)^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(\cos^{7}\left(x \right)\right) \left(\sin^{6}\left(x \right)\right)}{13}-\frac{6 \left(\sin^{4}\left(x \right)\right) \left(\cos^{7}\left(x \right)\right)}{143}-\frac{8 \left(\sin^{2}\left(x \right)\right) \left(\cos^{7}\left(x \right)\right)}{429}-\frac{16 \left(\cos^{7}\left(x \right)\right)}{3003}$&$38$\\ risch&$-\frac{5 \cos \left(x \right)}{1024}+\frac{\cos \left(13 x \right)}{53248}-\frac{\cos \left(11 x \right)}{45056}-\frac{\cos \left(9 x \right)}{6144}+\frac{3 \cos \left(7 x \right)}{14336}+\frac{3 \cos \left(5 x \right)}{4096}-\frac{5 \cos \left(3 x \right)}{4096}$&$42$\\ \hline \end{longtable}"," ",0,"-1/13*cos(x)^7*sin(x)^6-6/143*sin(x)^4*cos(x)^7-8/429*sin(x)^2*cos(x)^7-16/3003*cos(x)^7","A"
346,1,37,36,0.067000," ","int(sin(x)^11/cos(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(\sin^{10}\left(x \right)\right)}{10}-\frac{\left(\sin^{8}\left(x \right)\right)}{8}-\frac{\left(\sin^{6}\left(x \right)\right)}{6}-\frac{\left(\sin^{4}\left(x \right)\right)}{4}-\frac{\left(\sin^{2}\left(x \right)\right)}{2}-\ln \left(\cos \left(x \right)\right)$&$37$\\ risch&$i x +\frac{281 \,{\mathrm e}^{2 i x}}{1024}+\frac{281 \,{\mathrm e}^{-2 i x}}{1024}-\ln \left(1+{\mathrm e}^{2 i x}\right)+\frac{\cos \left(10 x \right)}{5120}-\frac{3 \cos \left(8 x \right)}{1024}+\frac{67 \cos \left(6 x \right)}{3072}-\frac{29 \cos \left(4 x \right)}{256}$&$54$\\ \hline \end{longtable}"," ",0,"-1/10*sin(x)^10-1/8*sin(x)^8-1/6*sin(x)^6-1/4*sin(x)^4-1/2*sin(x)^2-ln(cos(x))","A"
347,1,38,33,0.326000," ","int(1/cos(x)^6/sin(x)^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{512 i \left(10 \,{\mathrm e}^{8 i x}-5 \,{\mathrm e}^{4 i x}+1\right)}{15 \left({\mathrm e}^{2 i x}-1\right)^{5} \left(1+{\mathrm e}^{2 i x}\right)^{5}}$&$38$\\ default&$\frac{1}{5 \sin \left(x \right)^{5} \cos \left(x \right)^{5}}-\frac{2}{5 \sin \left(x \right)^{5} \cos \left(x \right)^{3}}+\frac{16}{15 \sin \left(x \right)^{3} \cos \left(x \right)^{3}}-\frac{32}{15 \sin \left(x \right)^{3} \cos \left(x \right)}+\frac{128}{15 \sin \left(x \right) \cos \left(x \right)}-\frac{256 \cot \left(x \right)}{15}$&$56$\\ \hline \end{longtable}"," ",0,"-512/15*I*(10*exp(8*I*x)-5*exp(4*I*x)+1)/(exp(2*I*x)-1)^5/(1+exp(2*I*x))^5","C"
348,1,11,18,0.049000," ","int(cos(x)^2*sin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x}{8}-\frac{\sin \left(4 x \right)}{32}$&$11$\\ default&$\frac{x}{8}+\frac{\cos \left(x \right) \sin \left(x \right)}{8}-\frac{\left(\cos^{3}\left(x \right)\right) \sin \left(x \right)}{4}$&$19$\\ norman&$\frac{\frac{x}{8}+\frac{7 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{4}-\frac{7 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4}+\frac{\left(\tan^{7}\left(\frac{x}{2}\right)\right)}{4}+\frac{x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2}+\frac{3 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{4}+\frac{x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{2}+\frac{x \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{8}-\frac{\tan \left(\frac{x}{2}\right)}{4}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{4}}$&$82$\\ \hline \end{longtable}"," ",0,"1/8*x-1/32*sin(4*x)","A"
349,1,17,36,0.335000," ","int(cos(x)^4*sin(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x}{128}+\frac{\sin \left(8 x \right)}{1024}-\frac{\sin \left(4 x \right)}{128}$&$17$\\ default&$-\frac{\left(\cos^{5}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{8}-\frac{\left(\cos^{5}\left(x \right)\right) \sin \left(x \right)}{16}+\frac{\left(\cos^{3}\left(x \right)+\frac{3 \cos \left(x \right)}{2}\right) \sin \left(x \right)}{64}+\frac{3 x}{128}$&$36$\\ norman&$\frac{\frac{3 x}{128}-\frac{3 \tan \left(\frac{x}{2}\right)}{64}+\frac{105 x \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{64}+\frac{21 x \left(\tan^{10}\left(\frac{x}{2}\right)\right)}{16}+\frac{21 x \left(\tan^{12}\left(\frac{x}{2}\right)\right)}{32}+\frac{21 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{16}-\frac{23 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{64}+\frac{3 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{16}+\frac{21 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{32}+\frac{3 x \left(\tan^{14}\left(\frac{x}{2}\right)\right)}{16}+\frac{3 x \left(\tan^{16}\left(\frac{x}{2}\right)\right)}{128}+\frac{23 \left(\tan^{13}\left(\frac{x}{2}\right)\right)}{64}+\frac{3 \left(\tan^{15}\left(\frac{x}{2}\right)\right)}{64}+\frac{333 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{64}-\frac{671 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{64}+\frac{671 \left(\tan^{9}\left(\frac{x}{2}\right)\right)}{64}-\frac{333 \left(\tan^{11}\left(\frac{x}{2}\right)\right)}{64}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{8}}$&$150$\\ \hline \end{longtable}"," ",0,"3/128*x+1/1024*sin(8*x)-1/128*sin(4*x)","A"
350,1,23,54,0.309000," ","int(cos(x)^6*sin(x)^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{5 x}{1024}-\frac{\sin \left(12 x \right)}{24576}+\frac{3 \sin \left(8 x \right)}{8192}-\frac{15 \sin \left(4 x \right)}{8192}$&$23$\\ default&$-\frac{\left(\cos^{7}\left(x \right)\right) \left(\sin^{5}\left(x \right)\right)}{12}-\frac{\left(\cos^{7}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{24}-\frac{\left(\cos^{7}\left(x \right)\right) \sin \left(x \right)}{64}+\frac{\left(\cos^{5}\left(x \right)+\frac{5 \left(\cos^{3}\left(x \right)\right)}{4}+\frac{15 \cos \left(x \right)}{8}\right) \sin \left(x \right)}{384}+\frac{5 x}{1024}$&$52$\\ \hline \end{longtable}"," ",0,"5/1024*x-1/24576*sin(12*x)+3/8192*sin(8*x)-15/8192*sin(4*x)","A"
351,1,29,72,0.315000," ","int(cos(x)^8*sin(x)^8,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{35 x}{32768}+\frac{\sin \left(16 x \right)}{524288}-\frac{\sin \left(12 x \right)}{49152}+\frac{7 \sin \left(8 x \right)}{65536}-\frac{7 \sin \left(4 x \right)}{16384}$&$29$\\ default&$-\frac{\left(\cos^{9}\left(x \right)\right) \left(\sin^{7}\left(x \right)\right)}{16}-\frac{\left(\cos^{9}\left(x \right)\right) \left(\sin^{5}\left(x \right)\right)}{32}-\frac{5 \left(\cos^{9}\left(x \right)\right) \left(\sin^{3}\left(x \right)\right)}{384}-\frac{\left(\cos^{9}\left(x \right)\right) \sin \left(x \right)}{256}+\frac{\left(\cos^{7}\left(x \right)+\frac{7 \left(\cos^{5}\left(x \right)\right)}{6}+\frac{35 \left(\cos^{3}\left(x \right)\right)}{24}+\frac{35 \cos \left(x \right)}{16}\right) \sin \left(x \right)}{2048}+\frac{35 x}{32768}$&$68$\\ \hline \end{longtable}"," ",0,"35/32768*x+1/524288*sin(16*x)-1/49152*sin(12*x)+7/65536*sin(8*x)-7/16384*sin(4*x)","A"
352,0,0,52,0.026000," ","int(cos(x)^(2*m)*sin(x)^(2*m),x)","\[\int \left(\cos^{2 m}\left(x \right)\right) \left(\sin^{2 m}\left(x \right)\right)\, dx\]"," ",0,"int(cos(x)^(2*m)*sin(x)^(2*m),x)","F"
353,1,25,24,0.094000," ","int(1/cos(1/4*Pi+2*x)/sin(1/4*Pi+2*x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{1}{4 \sin \left(\frac{\pi}{4}+2 x \right)^{2}}+\frac{\ln \left(\tan \left(\frac{\pi}{4}+2 x \right)\right)}{2}$&$25$\\ default&$-\frac{1}{4 \sin \left(\frac{\pi}{4}+2 x \right)^{2}}+\frac{\ln \left(\tan \left(\frac{\pi}{4}+2 x \right)\right)}{2}$&$25$\\ risch&$\frac{i {\mathrm e}^{4 i x}}{\left(i {\mathrm e}^{4 i x}-1\right)^{2}}+\frac{\ln \left(i {\mathrm e}^{4 i x}-1\right)}{2}-\frac{\ln \left(i {\mathrm e}^{4 i x}+1\right)}{2}$&$48$\\ norman&$\frac{-\frac{1}{16}-\frac{\left(\tan^{4}\left(\frac{\pi}{8}+x \right)\right)}{16}}{\tan \left(\frac{\pi}{8}+x \right)^{2}}+\frac{\ln \left(\tan \left(\frac{\pi}{8}+x \right)\right)}{2}-\frac{\ln \left(\tan \left(\frac{\pi}{8}+x \right)-1\right)}{2}-\frac{\ln \left(\tan \left(\frac{\pi}{8}+x \right)+1\right)}{2}$&$54$\\ \hline \end{longtable}"," ",0,"-1/4/sin(1/4*Pi+2*x)^2+1/2*ln(tan(1/4*Pi+2*x))","A"
354,1,11,6,0.060000," ","int(sec(x)^2*tan(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sin^{3}\left(x \right)}{3 \cos \left(x \right)^{3}}$&$11$\\ risch&$-\frac{2 i \left(3 \,{\mathrm e}^{4 i x}+1\right)}{3 \left(1+{\mathrm e}^{2 i x}\right)^{3}}$&$22$\\ \hline \end{longtable}"," ",0,"1/3*sin(x)^3/cos(x)^3","A"
355,1,32,9,0.310000," ","int(cot(x)^3*csc(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\cos^{4}\left(x \right)}{3 \sin \left(x \right)^{3}}+\frac{\cos^{4}\left(x \right)}{3 \sin \left(x \right)}+\frac{\left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}$&$32$\\ risch&$\frac{2 i \left(3 \,{\mathrm e}^{5 i x}-2 \,{\mathrm e}^{3 i x}+3 \,{\mathrm e}^{i x}\right)}{3 \left({\mathrm e}^{2 i x}-1\right)^{3}}$&$35$\\ \hline \end{longtable}"," ",0,"-1/3/sin(x)^3*cos(x)^4+1/3/sin(x)*cos(x)^4+1/3*(2+cos(x)^2)*sin(x)","B"
356,1,7,6,0.061000," ","int(sec(x)^3*tan(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(\sec^{3}\left(x \right)\right)}{3}$&$7$\\ default&$\frac{\left(\sec^{3}\left(x \right)\right)}{3}$&$7$\\ risch&$\frac{8 \,{\mathrm e}^{3 i x}}{3 \left(1+{\mathrm e}^{2 i x}\right)^{3}}$&$17$\\ \hline \end{longtable}"," ",0,"1/3*sec(x)^3","A"
357,1,36,20,0.076000," ","int(cot(x)^2*csc(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\cos^{3}\left(x \right)}{4 \sin \left(x \right)^{4}}-\frac{\cos^{3}\left(x \right)}{8 \sin \left(x \right)^{2}}-\frac{\cos \left(x \right)}{8}-\frac{\ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{8}$&$36$\\ risch&$-\frac{{\mathrm e}^{7 i x}+7 \,{\mathrm e}^{5 i x}+7 \,{\mathrm e}^{3 i x}+{\mathrm e}^{i x}}{4 \left({\mathrm e}^{2 i x}-1\right)^{4}}+\frac{\ln \left({\mathrm e}^{i x}+1\right)}{8}-\frac{\ln \left({\mathrm e}^{i x}-1\right)}{8}$&$58$\\ \hline \end{longtable}"," ",0,"-1/4*cos(x)^3/sin(x)^4-1/8/sin(x)^2*cos(x)^3-1/8*cos(x)-1/8*ln(csc(x)-cot(x))","A"
358,1,22,13,0.070000," ","int(cos(x)^3/sin(x)^7,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\cos^{4}\left(x \right)}{6 \sin \left(x \right)^{6}}-\frac{\cos^{4}\left(x \right)}{12 \sin \left(x \right)^{4}}$&$22$\\ norman&$\frac{-\frac{1}{384}+\frac{3 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{128}+\frac{3 \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{128}-\frac{\left(\tan^{12}\left(\frac{x}{2}\right)\right)}{384}}{\tan \left(\frac{x}{2}\right)^{6}}$&$34$\\ risch&$\frac{4 \,{\mathrm e}^{8 i x}+\frac{8 \,{\mathrm e}^{6 i x}}{3}+4 \,{\mathrm e}^{4 i x}}{\left({\mathrm e}^{2 i x}-1\right)^{6}}$&$34$\\ \hline \end{longtable}"," ",0,"-1/6/sin(x)^6*cos(x)^4-1/12/sin(x)^4*cos(x)^4","A"
359,1,49,19,0.203000," ","int(sec(x)^(3/2)*tan(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\frac{32 \left(\sin^{8}\left(\frac{x}{2}\right)\right)}{3}-\frac{64 \left(\sin^{6}\left(\frac{x}{2}\right)\right)}{3}+\frac{96 \left(\sin^{4}\left(\frac{x}{2}\right)\right)}{7}-\frac{64 \left(\sin^{2}\left(\frac{x}{2}\right)\right)}{21}+\frac{64}{231}}{\left(-2 \left(\sin^{2}\left(\frac{x}{2}\right)\right)+1\right)^{\frac{11}{2}}}$&$49$\\ \hline \end{longtable}"," ",0,"32/231/(-2*sin(1/2*x)^2+1)^(11/2)*(77*sin(1/2*x)^8-154*sin(1/2*x)^6+99*sin(1/2*x)^4-22*sin(1/2*x)^2+2)","B"
360,1,26,13,0.499000," ","int(sec(x)^4*tan(x)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(4 \left(\cos^{2}\left(x \right)\right)+5\right) \sin \left(x \right) \left(\frac{\sin \left(x \right)}{\cos \left(x \right)}\right)^{\frac{3}{2}}}{45 \cos \left(x \right)^{3}}$&$26$\\ \hline \end{longtable}"," ",0,"2/45*(4*cos(x)^2+5)*sin(x)*(sin(x)/cos(x))^(3/2)/cos(x)^3","A"
361,1,52,30,0.094000," ","int(cot(x)^4*csc(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\cos^{5}\left(x \right)}{6 \sin \left(x \right)^{6}}-\frac{\cos^{5}\left(x \right)}{24 \sin \left(x \right)^{4}}+\frac{\cos^{5}\left(x \right)}{48 \sin \left(x \right)^{2}}+\frac{\left(\cos^{3}\left(x \right)\right)}{48}+\frac{\cos \left(x \right)}{16}+\frac{\ln \left(\csc \left(x \right)-\cot \left(x \right)\right)}{16}$&$52$\\ risch&$\frac{3 \,{\mathrm e}^{11 i x}+47 \,{\mathrm e}^{9 i x}+78 \,{\mathrm e}^{7 i x}+78 \,{\mathrm e}^{5 i x}+47 \,{\mathrm e}^{3 i x}+3 \,{\mathrm e}^{i x}}{24 \left({\mathrm e}^{2 i x}-1\right)^{6}}-\frac{\ln \left({\mathrm e}^{i x}+1\right)}{16}+\frac{\ln \left({\mathrm e}^{i x}-1\right)}{16}$&$76$\\ \hline \end{longtable}"," ",0,"-1/6/sin(x)^6*cos(x)^5-1/24/sin(x)^4*cos(x)^5+1/48/sin(x)^2*cos(x)^5+1/48*cos(x)^3+1/16*cos(x)+1/16*ln(csc(x)-cot(x))","A"
362,1,76,50,0.561000," ","int(sec(1/4*Pi+1/2*x)^3*tan(1/4*Pi+1/2*x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\sin^{3}\left(\frac{\pi}{4}+\frac{x}{2}\right)}{2 \cos \left(\frac{\pi}{4}+\frac{x}{2}\right)^{4}}+\frac{\sin^{3}\left(\frac{\pi}{4}+\frac{x}{2}\right)}{4 \cos \left(\frac{\pi}{4}+\frac{x}{2}\right)^{2}}+\frac{\sin \left(\frac{\pi}{4}+\frac{x}{2}\right)}{4}-\frac{\ln \left(\sec \left(\frac{\pi}{4}+\frac{x}{2}\right)+\tan \left(\frac{\pi}{4}+\frac{x}{2}\right)\right)}{4}$&$76$\\ default&$\frac{\sin^{3}\left(\frac{\pi}{4}+\frac{x}{2}\right)}{2 \cos \left(\frac{\pi}{4}+\frac{x}{2}\right)^{4}}+\frac{\sin^{3}\left(\frac{\pi}{4}+\frac{x}{2}\right)}{4 \cos \left(\frac{\pi}{4}+\frac{x}{2}\right)^{2}}+\frac{\sin \left(\frac{\pi}{4}+\frac{x}{2}\right)}{4}-\frac{\ln \left(\sec \left(\frac{\pi}{4}+\frac{x}{2}\right)+\tan \left(\frac{\pi}{4}+\frac{x}{2}\right)\right)}{4}$&$76$\\ risch&$\frac{i \left(-\left(-1\right)^{\frac{3}{4}} {\mathrm e}^{\frac{7 i x}{2}}+7 \left(-1\right)^{\frac{1}{4}} {\mathrm e}^{\frac{5 i x}{2}}+7 \left(-1\right)^{\frac{3}{4}} {\mathrm e}^{\frac{3 i x}{2}}-\left(-1\right)^{\frac{1}{4}} {\mathrm e}^{\frac{i x}{2}}\right)}{2 \left(i {\mathrm e}^{i x}+1\right)^{4}}+\frac{\ln \left({\mathrm e}^{\frac{i \left(\pi +2 x \right)}{4}}-i\right)}{4}-\frac{\ln \left({\mathrm e}^{\frac{i \left(\pi +2 x \right)}{4}}+i\right)}{4}$&$88$\\ \hline \end{longtable}"," ",0,"1/2*sin(1/4*Pi+1/2*x)^3/cos(1/4*Pi+1/2*x)^4+1/4*sin(1/4*Pi+1/2*x)^3/cos(1/4*Pi+1/2*x)^2+1/4*sin(1/4*Pi+1/2*x)-1/4*ln(sec(1/4*Pi+1/2*x)+tan(1/4*Pi+1/2*x))","A"
363,1,210,80,0.565000," ","int((1+cot(x)^3)*(a*sec(x)^2-sin(2*x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \left(\cos^{8}\left(x \right)\right)}{\sin \left(x \right)^{2}}+2 \left(\cos^{6}\left(x \right)\right)+\cos^{4}\left(x \right)+2 \left(\cos^{2}\left(x \right)\right)+4 \ln \left(\sin \left(x \right)\right)-\frac{4 \left(\cos^{7}\left(x \right)\right)}{\sin \left(x \right)}-4 \left(\cos^{5}\left(x \right)+\frac{5 \left(\cos^{3}\left(x \right)\right)}{4}+\frac{15 \cos \left(x \right)}{8}\right) \sin \left(x \right)+\frac{x}{2}-\frac{2 \left(\cos^{6}\left(x \right)\right)}{\sin \left(x \right)^{2}}+\frac{8 \left(\cos^{5}\left(x \right)\right)}{\sin \left(x \right)}+8 \left(\cos^{3}\left(x \right)+\frac{3 \cos \left(x \right)}{2}\right) \sin \left(x \right)-4 a \left(-\frac{\left(\cot^{2}\left(x \right)\right)}{2}-\ln \left(\sin \left(x \right)\right)\right)-4 a \left(-\cot \left(x \right)-x \right)-4 \cot \left(x \right)-\frac{4 a}{\sin \left(x \right)^{2}}+a^{2} \left(-\frac{1}{2 \sin \left(x \right)^{2}}+\ln \left(\tan \left(x \right)\right)\right)-a^{2} \left(\frac{1}{\sin \left(x \right) \cos \left(x \right)}-2 \cot \left(x \right)\right)-4 a \left(-\frac{1}{2 \sin \left(x \right)^{2}}+\ln \left(\tan \left(x \right)\right)\right)+a^{2} \left(\frac{1}{3 \sin \left(x \right) \cos \left(x \right)^{3}}+\frac{4}{3 \sin \left(x \right) \cos \left(x \right)}-\frac{8 \cot \left(x \right)}{3}\right)$&$210$\\ risch&$\frac{x}{2}-4 i x a +4 a x +\frac{i {\mathrm e}^{4 i x}}{16}+\frac{{\mathrm e}^{4 i x}}{16}-\frac{i {\mathrm e}^{-4 i x}}{16}+\frac{3 \,{\mathrm e}^{2 i x}}{4}+\frac{3 \,{\mathrm e}^{-2 i x}}{4}+\frac{{\mathrm e}^{-4 i x}}{16}-4 i x +\frac{2 a \left(12 i {\mathrm e}^{8 i x}+3 a \,{\mathrm e}^{8 i x}+6 i a \,{\mathrm e}^{6 i x}+24 i {\mathrm e}^{6 i x}+9 a \,{\mathrm e}^{6 i x}-10 i a \,{\mathrm e}^{4 i x}+9 a \,{\mathrm e}^{4 i x}+2 i a \,{\mathrm e}^{2 i x}-24 i {\mathrm e}^{2 i x}+3 a \,{\mathrm e}^{2 i x}+2 i a -12 i\right)}{3 \left({\mathrm e}^{2 i x}-1\right)^{2} \left(1+{\mathrm e}^{2 i x}\right)^{3}}+\ln \left({\mathrm e}^{2 i x}-1\right) a^{2}+4 \ln \left({\mathrm e}^{2 i x}-1\right)-\ln \left(1+{\mathrm e}^{2 i x}\right) a^{2}+4 \ln \left(1+{\mathrm e}^{2 i x}\right) a$&$219$\\ \hline \end{longtable}"," ",0,"2/sin(x)^2*cos(x)^8+2*cos(x)^6+cos(x)^4+2*cos(x)^2+4*ln(sin(x))-4/sin(x)*cos(x)^7-4*(cos(x)^5+5/4*cos(x)^3+15/8*cos(x))*sin(x)+1/2*x-2/sin(x)^2*cos(x)^6+8/sin(x)*cos(x)^5+8*(cos(x)^3+3/2*cos(x))*sin(x)-4*a*(-1/2*cot(x)^2-ln(sin(x)))-4*a*(-cot(x)-x)-4*cot(x)-4*a/sin(x)^2+a^2*(-1/2/sin(x)^2+ln(tan(x)))-a^2*(1/sin(x)/cos(x)-2*cot(x))-4*a*(-1/2/sin(x)^2+ln(tan(x)))+a^2*(1/3/sin(x)/cos(x)^3+4/3/sin(x)/cos(x)-8/3*cot(x))","B"
364,1,55,56,0.380000," ","int((4-3*cos(x))*(1-1/2*sin(x))^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{227 x}{32}+\frac{19 \cos \left(x \right)}{2}-\frac{531 \sin \left(x \right)}{128}-\frac{3 \sin \left(5 x \right)}{1280}+\frac{3 \cos \left(4 x \right)}{64}+\frac{\sin \left(4 x \right)}{128}-\frac{\cos \left(3 x \right)}{6}+\frac{99 \sin \left(3 x \right)}{256}-\frac{27 \cos \left(2 x \right)}{16}-\frac{25 \sin \left(2 x \right)}{16}$&$55$\\ default&$\frac{227 x}{32}+8 \cos \left(x \right)-3 \cos \left(x \right) \sin \left(x \right)+\frac{2 \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}-\frac{\left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{16}-3 \sin \left(x \right)-3 \left(\cos^{2}\left(x \right)\right)-\frac{3 \left(\sin^{3}\left(x \right)\right)}{2}+\frac{3 \left(\sin^{4}\left(x \right)\right)}{8}-\frac{3 \left(\sin^{5}\left(x \right)\right)}{80}$&$66$\\ norman&$\frac{-29 \left(\tan^{8}\left(\frac{x}{2}\right)\right)-\frac{57 \left(\tan^{10}\left(\frac{x}{2}\right)\right)}{5}+\frac{97 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{3}+\frac{128 \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{3}+\frac{227 x}{32}-\frac{391 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{8}-\frac{306 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{5}-\frac{185 \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{8}+\frac{3 \left(\tan^{9}\left(\frac{x}{2}\right)\right)}{16}+\frac{1135 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{32}+\frac{1135 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{16}+\frac{1135 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{16}+\frac{1135 x \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{32}+\frac{227 x \left(\tan^{10}\left(\frac{x}{2}\right)\right)}{32}-\frac{195 \tan \left(\frac{x}{2}\right)}{16}+\frac{109}{15}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{5}}$&$132$\\ \hline \end{longtable}"," ",0,"227/32*x+19/2*cos(x)-531/128*sin(x)-3/1280*sin(5*x)+3/64*cos(4*x)+1/128*sin(4*x)-1/6*cos(3*x)+99/256*sin(3*x)-27/16*cos(2*x)-25/16*sin(2*x)","A"
365,1,35,31,0.064000," ","int((1/2-3*cot(x))*(3-2*cot(x))^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-8 \left(\cot^{3}\left(x \right)\right)+56 \left(\cot^{2}\left(x \right)\right)-156 \cot \left(x \right)-2 \ln \left(\cot^{2}\left(x \right)+1\right)+\frac{285 \pi}{4}-\frac{285 \,\mathrm{arccot}\left(\cot \left(x \right)\right)}{2}$&$35$\\ default&$-8 \left(\cot^{3}\left(x \right)\right)+56 \left(\cot^{2}\left(x \right)\right)-156 \cot \left(x \right)-2 \ln \left(\cot^{2}\left(x \right)+1\right)+\frac{285 \pi}{4}-\frac{285 \,\mathrm{arccot}\left(\cot \left(x \right)\right)}{2}$&$35$\\ norman&$\frac{-8-156 \left(\tan^{2}\left(x \right)\right)-\frac{285 x \left(\tan^{3}\left(x \right)\right)}{2}+56 \tan \left(x \right)}{\tan \left(x \right)^{3}}+4 \ln \left(\tan \left(x \right)\right)-2 \ln \left(1+\tan^{2}\left(x \right)\right)$&$40$\\ risch&$-\frac{285 x}{2}-4 i x +\frac{\left(-\frac{224}{1873}-\frac{264 i}{1873}\right) \left(1873 \,{\mathrm e}^{4 i x}-1260 i {\mathrm e}^{2 i x}-3358 \,{\mathrm e}^{2 i x}+1221+1036 i\right)}{\left({\mathrm e}^{2 i x}-1\right)^{3}}+4 \ln \left({\mathrm e}^{2 i x}-1\right)$&$58$\\ \hline \end{longtable}"," ",0,"-8*cot(x)^3+56*cot(x)^2-156*cot(x)-2*ln(cot(x)^2+1)+285/4*Pi-285/2*arccot(cot(x))","A"
366,1,21,14,0.333000," ","int(cos(5*x)/cos(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$16 x -5 \left(-\frac{2}{3}-\frac{\left(\sec^{2}\left(x \right)\right)}{3}\right) \tan \left(x \right)-20 \tan \left(x \right)$&$21$\\ risch&$16 x -\frac{20 i \left(6 \,{\mathrm e}^{4 i x}+9 \,{\mathrm e}^{2 i x}+5\right)}{3 \left(1+{\mathrm e}^{2 i x}\right)^{3}}$&$33$\\ \hline \end{longtable}"," ",0,"16*x-5*(-2/3-1/3*sec(x)^2)*tan(x)-20*tan(x)","A"
367,1,22,10,0.327000," ","int(cos(4*x)/cos(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\ln \left(\sec \left(x \right)+\tan \left(x \right)\right)+\frac{8 \left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{3}-8 \sin \left(x \right)$&$22$\\ risch&$i {\mathrm e}^{i x}-i {\mathrm e}^{-i x}+\ln \left({\mathrm e}^{i x}+i\right)-\ln \left({\mathrm e}^{i x}-i\right)+\frac{2 \sin \left(3 x \right)}{3}$&$44$\\ \hline \end{longtable}"," ",0,"ln(sec(x)+tan(x))+8/3*(2+cos(x)^2)*sin(x)-8*sin(x)","B"
368,1,14,13,0.123000," ","int(cos(x)*cos(4*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sin \left(3 x \right)}{6}+\frac{\sin \left(5 x \right)}{10}$&$14$\\ risch&$\frac{\sin \left(3 x \right)}{6}+\frac{\sin \left(5 x \right)}{10}$&$14$\\ norman&$\frac{-\frac{8 \tan \left(2 x \right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{15}+\frac{2 \left(\tan^{2}\left(2 x \right)\right) \tan \left(\frac{x}{2}\right)}{15}+\frac{8 \tan \left(2 x \right)}{15}-\frac{2 \tan \left(\frac{x}{2}\right)}{15}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \left(1+\tan^{2}\left(2 x \right)\right)}$&$59$\\ \hline \end{longtable}"," ",0,"1/6*sin(3*x)+1/10*sin(5*x)","A"
369,1,31,20,0.364000," ","int(cos(4*x)/cos(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\left(-\frac{\left(\sec^{3}\left(x \right)\right)}{4}-\frac{3 \sec \left(x \right)}{8}\right) \tan \left(x \right)+\frac{35 \ln \left(\sec \left(x \right)+\tan \left(x \right)\right)}{8}-4 \sec \left(x \right) \tan \left(x \right)$&$31$\\ risch&$\frac{i \left(29 \,{\mathrm e}^{7 i x}+21 \,{\mathrm e}^{5 i x}-21 \,{\mathrm e}^{3 i x}-29 \,{\mathrm e}^{i x}\right)}{4 \left(1+{\mathrm e}^{2 i x}\right)^{4}}+\frac{35 \ln \left({\mathrm e}^{i x}+i\right)}{8}-\frac{35 \ln \left({\mathrm e}^{i x}-i\right)}{8}$&$65$\\ \hline \end{longtable}"," ",0,"-(-1/4*sec(x)^3-3/8*sec(x))*tan(x)+35/8*ln(sec(x)+tan(x))-4*sec(x)*tan(x)","A"
370,1,29,28,0.153000," ","int(cos(x)^4*cos(4*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{16}+\frac{\sin \left(2 x \right)}{8}+\frac{3 \sin \left(4 x \right)}{32}+\frac{\sin \left(6 x \right)}{24}+\frac{\sin \left(8 x \right)}{128}$&$29$\\ risch&$\frac{x}{16}+\frac{\sin \left(2 x \right)}{8}+\frac{3 \sin \left(4 x \right)}{32}+\frac{\sin \left(6 x \right)}{24}+\frac{\sin \left(8 x \right)}{128}$&$29$\\ \hline \end{longtable}"," ",0,"1/16*x+1/8*sin(2*x)+3/32*sin(4*x)+1/24*sin(6*x)+1/128*sin(8*x)","A"
371,1,35,18,0.143000," ","int(cos(5*x)/sin(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{5}{4 \sin \left(x \right)^{4}}+\frac{5 \left(\cos^{4}\left(x \right)\right)}{\sin \left(x \right)^{4}}-4 \left(\cot^{4}\left(x \right)\right)+8 \left(\cot^{2}\left(x \right)\right)+16 \ln \left(\sin \left(x \right)\right)$&$35$\\ risch&$-16 i x -\frac{4 \left(6 \,{\mathrm e}^{6 i x}-11 \,{\mathrm e}^{4 i x}+6 \,{\mathrm e}^{2 i x}\right)}{\left({\mathrm e}^{2 i x}-1\right)^{4}}+16 \ln \left({\mathrm e}^{2 i x}-1\right)$&$49$\\ \hline \end{longtable}"," ",0,"-5/4/sin(x)^4+5/sin(x)^4*cos(x)^4-4*cot(x)^4+8*cot(x)^2+16*ln(sin(x))","A"
372,1,19,12,0.133000," ","int(sin(4*x)/sin(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2}{\sin \left(x \right)^{2}}-4 \left(\cot^{2}\left(x \right)\right)-8 \ln \left(\sin \left(x \right)\right)$&$19$\\ risch&$8 i x +\frac{8 \,{\mathrm e}^{2 i x}}{\left({\mathrm e}^{2 i x}-1\right)^{2}}-8 \ln \left({\mathrm e}^{2 i x}-1\right)$&$32$\\ \hline \end{longtable}"," ",0,"2/sin(x)^2-4*cot(x)^2-8*ln(sin(x))","A"
373,1,35,50,0.264000," ","int(cos(x)/sin(x)/(2+sin(2*x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(1+\tan \left(x \right)+\tan^{2}\left(x \right)\right)}{4}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \tan \left(x \right)+1\right) \sqrt{3}}{3}\right)}{6}+\frac{\ln \left(\tan \left(x \right)\right)}{2}$&$35$\\ risch&$-\frac{\ln \left({\mathrm e}^{2 i x}-i \sqrt{3}+2 i\right)}{4}+\frac{i \ln \left({\mathrm e}^{2 i x}-i \sqrt{3}+2 i\right) \sqrt{3}}{12}-\frac{\ln \left({\mathrm e}^{2 i x}+i \sqrt{3}+2 i\right)}{4}-\frac{i \ln \left({\mathrm e}^{2 i x}+i \sqrt{3}+2 i\right) \sqrt{3}}{12}+\frac{\ln \left({\mathrm e}^{2 i x}-1\right)}{2}$&$88$\\ \hline \end{longtable}"," ",0,"-1/4*ln(1+tan(x)+tan(x)^2)-1/6*3^(1/2)*arctan(1/3*(2*tan(x)+1)*3^(1/2))+1/2*ln(tan(x))","A"
374,1,27,9,0.149000," ","int(cos(x)^2/cos(3*x)/sin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(1+\cos \left(x \right)\right)}{2}-\frac{\ln \left(4 \left(\cos^{2}\left(x \right)\right)-3\right)}{2}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{2}$&$27$\\ risch&$\ln \left({\mathrm e}^{2 i x}-1\right)-\frac{\ln \left({\mathrm e}^{4 i x}-{\mathrm e}^{2 i x}+1\right)}{2}$&$27$\\ \hline \end{longtable}"," ",0,"1/2*ln(1+cos(x))-1/2*ln(4*cos(x)^2-3)+1/2*ln(-1+cos(x))","B"
375,1,12,7,0.125000," ","int(sin(2*x)/(cos(x)^4+sin(x)^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\arctan \left(2 \left(\cos^{2}\left(x \right)\right)-1\right)$&$12$\\ default&$-\arctan \left(2 \left(\cos^{2}\left(x \right)\right)-1\right)$&$12$\\ risch&$-\frac{i \ln \left({\mathrm e}^{4 i x}+2 i {\mathrm e}^{2 i x}+1\right)}{2}+\frac{i \ln \left({\mathrm e}^{4 i x}-2 i {\mathrm e}^{2 i x}+1\right)}{2}$&$40$\\ \hline \end{longtable}"," ",0,"-arctan(2*cos(x)^2-1)","A"
376,1,43,41,0.206000," ","int(1/(4+sin(x)+cos(x)*3^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{52 \arctan \left(\frac{26 \tan \left(\frac{x}{2}\right)+2 \sqrt{3}+8}{16 \sqrt{3}+12}\right)}{\left(\sqrt{3}-4\right) \left(16 \sqrt{3}+12\right)}$&$43$\\ risch&$-\frac{i \sqrt{3}\, \ln \left(-\frac{i \sqrt{3}}{2}-\frac{3}{2}+i+\sqrt{3}+{\mathrm e}^{i x}\right)}{6}+\frac{i \sqrt{3}\, \ln \left({\mathrm e}^{i x}+\frac{3}{2}+i+\sqrt{3}+\frac{i \sqrt{3}}{2}\right)}{6}$&$52$\\ \hline \end{longtable}"," ",0,"-52/(3^(1/2)-4)/(16*3^(1/2)+12)*arctan((26*tan(1/2*x)+2*3^(1/2)+8)/(16*3^(1/2)+12))","A"
377,1,20,29,0.125000," ","int(1/(3+4*cos(x)+4*sin(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \sqrt{23}\, \arctanh \left(\frac{\left(2 \tan \left(\frac{x}{2}\right)-8\right) \sqrt{23}}{46}\right)}{23}$&$20$\\ risch&$\frac{\sqrt{23}\, \ln \left({\mathrm e}^{i x}+\frac{3}{8}+\frac{3 i}{8}-\frac{\sqrt{23}}{8}+\frac{i \sqrt{23}}{8}\right)}{23}-\frac{\sqrt{23}\, \ln \left({\mathrm e}^{i x}+\frac{3}{8}+\frac{3 i}{8}+\frac{\sqrt{23}}{8}-\frac{i \sqrt{23}}{8}\right)}{23}$&$54$\\ \hline \end{longtable}"," ",0,"2/23*23^(1/2)*arctanh(1/46*(2*tan(1/2*x)-8)*23^(1/2))","A"
378,1,8,23,0.096000," ","int(1/(4-3*cos(x)^2+5*sin(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(3 \tan \left(x \right)\right)}{3}$&$8$\\ risch&$-\frac{i \ln \left({\mathrm e}^{2 i x}-\frac{1}{2}\right)}{6}+\frac{i \ln \left({\mathrm e}^{2 i x}-2\right)}{6}$&$24$\\ \hline \end{longtable}"," ",0,"1/3*arctan(3*tan(x))","A"
379,1,31,22,0.213000," ","int(1/(4+4*cot(x)+tan(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{3 \ln \left(1+\tan^{2}\left(x \right)\right)}{50}+\frac{4 \arctan \left(\tan \left(x \right)\right)}{25}+\frac{2}{5 \left(2+\tan \left(x \right)\right)}-\frac{3 \ln \left(2+\tan \left(x \right)\right)}{25}$&$31$\\ norman&$\frac{\frac{8 x}{25}+\frac{4 x \tan \left(x \right)}{25}+\frac{2}{5}}{2+\tan \left(x \right)}-\frac{3 \ln \left(2+\tan \left(x \right)\right)}{25}+\frac{3 \ln \left(1+\tan^{2}\left(x \right)\right)}{50}$&$35$\\ risch&$\frac{4 x}{25}+\frac{3 i x}{25}+\frac{16}{25 \left(5 \,{\mathrm e}^{2 i x}+3+4 i\right)}-\frac{12 i}{25 \left(5 \,{\mathrm e}^{2 i x}+3+4 i\right)}-\frac{3 \ln \left({\mathrm e}^{2 i x}+\frac{3}{5}+\frac{4 i}{5}\right)}{25}$&$52$\\ \hline \end{longtable}"," ",0,"3/50*ln(1+tan(x)^2)+4/25*arctan(tan(x))+2/5/(2+tan(x))-3/25*ln(2+tan(x))","A"
380,1,39,55,0.220000," ","int(1/(2*sec(x)+sin(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{1+4 \tan \left(x \right)}{30+15 \tan \left(x \right)+30 \left(\tan^{2}\left(x \right)\right)}+\frac{8 \sqrt{15}\, \arctan \left(\frac{\left(1+4 \tan \left(x \right)\right) \sqrt{15}}{15}\right)}{225}$&$39$\\ risch&$\frac{\left(\frac{8}{3615}-\frac{2 i}{241}\right) \left(241 \,{\mathrm e}^{2 i x}-15+4 i\right)}{{\mathrm e}^{4 i x}+8 i {\mathrm e}^{2 i x}-1}+\frac{4 i \sqrt{15}\, \ln \left({\mathrm e}^{2 i x}+i \sqrt{15}+4 i\right)}{225}-\frac{4 i \sqrt{15}\, \ln \left({\mathrm e}^{2 i x}-i \sqrt{15}+4 i\right)}{225}$&$76$\\ \hline \end{longtable}"," ",0,"1/15*(1+4*tan(x))/(2+tan(x)+2*tan(x)^2)+8/225*15^(1/2)*arctan(1/15*(1+4*tan(x))*15^(1/2))","A"
381,1,29,43,0.138000," ","int(1/(cos(x)+2*sec(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\tan \left(x \right)}{18+12 \left(\tan^{2}\left(x \right)\right)}+\frac{\sqrt{6}\, \arctan \left(\frac{\tan \left(x \right) \sqrt{6}}{3}\right)}{36}$&$29$\\ risch&$\frac{i \left(5 \,{\mathrm e}^{2 i x}+1\right)}{3 \,{\mathrm e}^{4 i x}+30 \,{\mathrm e}^{2 i x}+3}+\frac{i \sqrt{6}\, \ln \left({\mathrm e}^{2 i x}+2 \sqrt{6}+5\right)}{72}-\frac{i \sqrt{6}\, \ln \left({\mathrm e}^{2 i x}-2 \sqrt{6}+5\right)}{72}$&$68$\\ \hline \end{longtable}"," ",0,"1/6*tan(x)/(3+2*tan(x)^2)+1/36*6^(1/2)*arctan(1/3*tan(x)*6^(1/2))","A"
382,1,45,34,0.102000," ","int((5-tan(x)-6*tan(x)^2)/(1+3*tan(x))^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{14 \ln \left(1+\tan^{2}\left(x \right)\right)}{125}-\frac{67 \arctan \left(\tan \left(x \right)\right)}{250}-\frac{7}{10 \left(1+3 \tan \left(x \right)\right)^{2}}-\frac{29}{50 \left(1+3 \tan \left(x \right)\right)}-\frac{28 \ln \left(1+3 \tan \left(x \right)\right)}{125}$&$45$\\ default&$\frac{14 \ln \left(1+\tan^{2}\left(x \right)\right)}{125}-\frac{67 \arctan \left(\tan \left(x \right)\right)}{250}-\frac{7}{10 \left(1+3 \tan \left(x \right)\right)^{2}}-\frac{29}{50 \left(1+3 \tan \left(x \right)\right)}-\frac{28 \ln \left(1+3 \tan \left(x \right)\right)}{125}$&$45$\\ risch&$-\frac{67 x}{250}+\frac{28 i x}{125}+\frac{\left(-\frac{36}{24125}-\frac{621 i}{48250}\right) \left(965 \,{\mathrm e}^{2 i x}-324+768 i\right)}{\left(5 \,{\mathrm e}^{2 i x}-4+3 i\right)^{2}}-\frac{28 \ln \left({\mathrm e}^{2 i x}-\frac{4}{5}+\frac{3 i}{5}\right)}{125}$&$49$\\ norman&$\frac{\frac{297 \tan \left(x \right)}{50}+\frac{288 \left(\tan^{2}\left(x \right)\right)}{25}-\frac{67 x}{250}-\frac{201 x \tan \left(x \right)}{125}-\frac{603 x \left(\tan^{2}\left(x \right)\right)}{250}}{\left(1+3 \tan \left(x \right)\right)^{2}}-\frac{28 \ln \left(1+3 \tan \left(x \right)\right)}{125}+\frac{14 \ln \left(1+\tan^{2}\left(x \right)\right)}{125}$&$55$\\ \hline \end{longtable}"," ",0,"14/125*ln(1+tan(x)^2)-67/250*arctan(tan(x))-7/10/(1+3*tan(x))^2-29/50/(1+3*tan(x))-28/125*ln(1+3*tan(x))","A"
383,1,20,7,0.149000," ","int(cos(x)^2/cos(3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(2 \sin \left(x \right)-1\right)}{4}+\frac{\ln \left(1+2 \sin \left(x \right)\right)}{4}$&$20$\\ risch&$\frac{\ln \left(i {\mathrm e}^{i x}+{\mathrm e}^{2 i x}-1\right)}{4}-\frac{\ln \left(-i {\mathrm e}^{i x}+{\mathrm e}^{2 i x}-1\right)}{4}$&$38$\\ \hline \end{longtable}"," ",0,"-1/4*ln(2*sin(x)-1)+1/4*ln(1+2*sin(x))","B"
384,1,13,12,0.115000," ","int(sin(x)/cos(2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctanh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{2}$&$13$\\ risch&$\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 i x}+\sqrt{2}\, {\mathrm e}^{i x}+1\right)}{4}-\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 i x}-\sqrt{2}\, {\mathrm e}^{i x}+1\right)}{4}$&$47$\\ \hline \end{longtable}"," ",0,"1/2*arctanh(cos(x)*2^(1/2))*2^(1/2)","A"
385,1,21,13,0.136000," ","int(sin(x)^2/cos(2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(\tan \left(x \right)-1\right)}{4}-\frac{\arctan \left(\tan \left(x \right)\right)}{2}+\frac{\ln \left(1+\tan \left(x \right)\right)}{4}$&$21$\\ risch&$-\frac{x}{2}-\frac{\ln \left({\mathrm e}^{2 i x}-i\right)}{4}+\frac{\ln \left({\mathrm e}^{2 i x}+i\right)}{4}$&$27$\\ \hline \end{longtable}"," ",0,"-1/4*ln(tan(x)-1)-1/2*arctan(tan(x))+1/4*ln(1+tan(x))","A"
386,1,18,17,0.138000," ","int(sin(x)^3/cos(3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(\cos \left(x \right)\right)}{3}-\frac{\ln \left(4 \left(\cos^{2}\left(x \right)\right)-3\right)}{24}$&$18$\\ risch&$-\frac{i x}{4}+\frac{\ln \left(1+{\mathrm e}^{2 i x}\right)}{3}-\frac{\ln \left({\mathrm e}^{4 i x}-{\mathrm e}^{2 i x}+1\right)}{24}$&$33$\\ \hline \end{longtable}"," ",0,"1/3*ln(cos(x))-1/24*ln(4*cos(x)^2-3)","A"
387,1,27,17,0.137000," ","int(cos(x)/sin(3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\ln \left({\mathrm e}^{2 i x}-1\right)}{3}-\frac{\ln \left({\mathrm e}^{4 i x}+{\mathrm e}^{2 i x}+1\right)}{6}$&$27$\\ default&$\frac{\ln \left(1+\cos \left(x \right)\right)}{6}+\frac{\ln \left(-1+\cos \left(x \right)\right)}{6}-\frac{\ln \left(2 \cos \left(x \right)-1\right)}{6}-\frac{\ln \left(2 \cos \left(x \right)+1\right)}{6}$&$34$\\ \hline \end{longtable}"," ",0,"1/3*ln(exp(2*I*x)-1)-1/6*ln(exp(4*I*x)+exp(2*I*x)+1)","C"
388,1,28,18,0.168000," ","int(sin(x)/sin(4*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(1+\sin \left(x \right)\right)}{8}+\frac{\ln \left(-1+\sin \left(x \right)\right)}{8}+\frac{\arctanh \left(\sin \left(x \right) \sqrt{2}\right) \sqrt{2}}{4}$&$28$\\ risch&$\frac{\ln \left({\mathrm e}^{i x}-i\right)}{4}-\frac{\ln \left({\mathrm e}^{i x}+i\right)}{4}+\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 i x}+i \sqrt{2}\, {\mathrm e}^{i x}-1\right)}{8}-\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 i x}-i \sqrt{2}\, {\mathrm e}^{i x}-1\right)}{8}$&$72$\\ \hline \end{longtable}"," ",0,"-1/8*ln(1+sin(x))+1/8*ln(-1+sin(x))+1/4*arctanh(sin(x)*2^(1/2))*2^(1/2)","A"
389,1,28,18,0.190000," ","int(sin(x)^3/sin(4*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(-1+\sin \left(x \right)\right)}{8}-\frac{\ln \left(1+\sin \left(x \right)\right)}{8}+\frac{\arctanh \left(\sin \left(x \right) \sqrt{2}\right) \sqrt{2}}{8}$&$28$\\ risch&$-\frac{\ln \left({\mathrm e}^{i x}+i\right)}{4}+\frac{\ln \left({\mathrm e}^{i x}-i\right)}{4}-\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 i x}-i \sqrt{2}\, {\mathrm e}^{i x}-1\right)}{16}+\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 i x}+i \sqrt{2}\, {\mathrm e}^{i x}-1\right)}{16}$&$72$\\ \hline \end{longtable}"," ",0,"1/8*ln(-1+sin(x))-1/8*ln(1+sin(x))+1/8*arctanh(sin(x)*2^(1/2))*2^(1/2)","A"
390,1,22,14,0.161000," ","int((1+sin(2*x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\sin \left(2 x \right)-1\right) \sqrt{1+\sin \left(2 x \right)}}{\cos \left(2 x \right)}$&$22$\\ \hline \end{longtable}"," ",0,"(sin(2*x)-1)*(1+sin(2*x))^(1/2)/cos(2*x)","A"
391,1,31,15,0.148000," ","int((1-sin(2*x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(\sin \left(2 x \right)-1\right) \left(1+\sin \left(2 x \right)\right)}{\cos \left(2 x \right) \sqrt{1-\sin \left(2 x \right)}}$&$31$\\ \hline \end{longtable}"," ",0,"-(sin(2*x)-1)*(1+sin(2*x))/cos(2*x)/(1-sin(2*x))^(1/2)","A"
392,1,9,23,0.093000," ","int(1/(1+cos(2*x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{2}\, \mathrm{am}^{-1}\left(x | 1\right)}{2}$&$9$\\ risch&$-\frac{\sqrt{2}\, \ln \left({\mathrm e}^{i x}-i\right) \cos \left(x \right)}{\sqrt{\left(1+{\mathrm e}^{2 i x}\right)^{2} {\mathrm e}^{-2 i x}}}+\frac{\sqrt{2}\, \ln \left({\mathrm e}^{i x}+i\right) \cos \left(x \right)}{\sqrt{\left(1+{\mathrm e}^{2 i x}\right)^{2} {\mathrm e}^{-2 i x}}}$&$67$\\ \hline \end{longtable}"," ",0,"1/2*2^(1/2)*InverseJacobiAM(x,1)","C"
393,1,17,25,0.137000," ","int(1/(1-cos(2*x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sin \left(x \right) \arctanh \left(\cos \left(x \right)\right) \sqrt{2}}{\sqrt{2-2 \cos \left(2 x \right)}}$&$17$\\ risch&$\frac{\sqrt{2}\, \ln \left({\mathrm e}^{i x}-1\right) \sin \left(x \right)}{\sqrt{-\left({\mathrm e}^{2 i x}-1\right)^{2} {\mathrm e}^{-2 i x}}}-\frac{\sqrt{2}\, \ln \left({\mathrm e}^{i x}+1\right) \sin \left(x \right)}{\sqrt{-\left({\mathrm e}^{2 i x}-1\right)^{2} {\mathrm e}^{-2 i x}}}$&$67$\\ \hline \end{longtable}"," ",0,"-1/2*sin(x)*arctanh(cos(x))*2^(1/2)/(sin(x)^2)^(1/2)","A"
394,1,52,42,0.138000," ","int(1/(1-cos(3*x))^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(\frac{\cos \left(\frac{3 x}{2}\right)}{2}+\frac{\left(\ln \left(1+\cos \left(\frac{3 x}{2}\right)\right)-\ln \left(\cos \left(\frac{3 x}{2}\right)-1\right)\right) \left(\sin^{2}\left(\frac{3 x}{2}\right)\right)}{4}\right) \sqrt{2}}{3 \sin \left(\frac{3 x}{2}\right) \sqrt{2-2 \cos \left(3 x \right)}}$&$52$\\ \hline \end{longtable}"," ",0,"-1/6*(1/2*cos(3/2*x)+1/4*(ln(1+cos(3/2*x))-ln(cos(3/2*x)-1))*sin(3/2*x)^2)/sin(3/2*x)*2^(1/2)/(sin(3/2*x)^2)^(1/2)","A"
395,1,47,49,0.153000," ","int((1-sin(2/3*x))^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(-1+\sin \left(\frac{2 x}{3}\right)\right) \left(\sin \left(\frac{2 x}{3}\right)+1\right) \left(3 \left(\sin^{2}\left(\frac{2 x}{3}\right)\right)-14 \sin \left(\frac{2 x}{3}\right)+43\right)}{5 \cos \left(\frac{2 x}{3}\right) \sqrt{1-\sin \left(\frac{2 x}{3}\right)}}$&$47$\\ \hline \end{longtable}"," ",0,"-1/5*(-1+sin(2/3*x))*(sin(2/3*x)+1)*(3*sin(2/3*x)^2-14*sin(2/3*x)+43)/cos(2/3*x)/(1-sin(2/3*x))^(1/2)","A"
396,1,31,41,0.481000," ","int(cos(x)*(-cos(x)^2+2*(1+2*sin(x))^(1/4))/(1+2*sin(x))^(3/2),x)","\[\frac{\sin^{2}\left(x \right)-2 \sin \left(x \right)-12 \left(1+2 \sin \left(x \right)\right)^{\frac{1}{4}}+1}{3 \sqrt{1+2 \sin \left(x \right)}}\]"," ",0,"1/3/(1+2*sin(x))^(1/2)*(sin(x)^2-2*sin(x)-12*(1+2*sin(x))^(1/4)+1)","A"
397,1,49,70,0.119000," ","int(tan(x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline lookup&$\frac{\left(\sqrt{\tan}\left(x \right)\right) \cos \left(x \right) \sqrt{2}\, \arccos \left(\cos \left(x \right)-\sin \left(x \right)\right)}{2 \sqrt{\cos \left(x \right) \sin \left(x \right)}}-\frac{\sqrt{2}\, \ln \left(\cos \left(x \right)+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right) \cos \left(x \right)+\sin \left(x \right)\right)}{2}$&$49$\\ default&$\frac{\left(\sqrt{\tan}\left(x \right)\right) \cos \left(x \right) \sqrt{2}\, \arccos \left(\cos \left(x \right)-\sin \left(x \right)\right)}{2 \sqrt{\cos \left(x \right) \sin \left(x \right)}}-\frac{\sqrt{2}\, \ln \left(\cos \left(x \right)+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right) \cos \left(x \right)+\sin \left(x \right)\right)}{2}$&$49$\\ derivativedivides&$\frac{\sqrt{2}\, \left(\ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)+\tan \left(x \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)+\tan \left(x \right)}\right)+2 \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)\right)+2 \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)\right)\right)}{4}$&$62$\\ \hline \end{longtable}"," ",0,"1/2*tan(x)^(1/2)/(cos(x)*sin(x))^(1/2)*cos(x)*2^(1/2)*arccos(cos(x)-sin(x))-1/2*2^(1/2)*ln(cos(x)+2^(1/2)*tan(x)^(1/2)*cos(x)+sin(x))","A"
398,1,53,44,0.105000," ","int(1/tan(5*x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(1-\left(\tan^{\frac{2}{3}}\left(5 x \right)\right)+\tan^{\frac{4}{3}}\left(5 x \right)\right)}{20}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \left(\tan^{\frac{2}{3}}\left(5 x \right)\right)-1\right) \sqrt{3}}{3}\right)}{10}+\frac{\ln \left(1+\tan^{\frac{2}{3}}\left(5 x \right)\right)}{10}$&$53$\\ default&$-\frac{\ln \left(1-\left(\tan^{\frac{2}{3}}\left(5 x \right)\right)+\tan^{\frac{4}{3}}\left(5 x \right)\right)}{20}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 \left(\tan^{\frac{2}{3}}\left(5 x \right)\right)-1\right) \sqrt{3}}{3}\right)}{10}+\frac{\ln \left(1+\tan^{\frac{2}{3}}\left(5 x \right)\right)}{10}$&$53$\\ \hline \end{longtable}"," ",0,"-1/20*ln(1-tan(5*x)^(2/3)+tan(5*x)^(4/3))+1/10*3^(1/2)*arctan(1/3*(2*tan(5*x)^(2/3)-1)*3^(1/2))+1/10*ln(1+tan(5*x)^(2/3))","A"
399,1,130,69,0.227000," ","int(1/(4+3*tan(2*x))^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{13 \sqrt{2}\, \ln \left(9+3 \tan \left(2 x \right)-3 \sqrt{4+3 \tan \left(2 x \right)}\, \sqrt{2}\right)}{1000}+\frac{9 \sqrt{2}\, \arctan \left(\frac{\left(2 \sqrt{4+3 \tan \left(2 x \right)}-3 \sqrt{2}\right) \sqrt{2}}{2}\right)}{500}+\frac{13 \sqrt{2}\, \ln \left(9+3 \tan \left(2 x \right)+3 \sqrt{4+3 \tan \left(2 x \right)}\, \sqrt{2}\right)}{1000}+\frac{9 \sqrt{2}\, \arctan \left(\frac{\left(2 \sqrt{4+3 \tan \left(2 x \right)}+3 \sqrt{2}\right) \sqrt{2}}{2}\right)}{500}-\frac{3}{25 \sqrt{4+3 \tan \left(2 x \right)}}$&$130$\\ default&$-\frac{13 \sqrt{2}\, \ln \left(9+3 \tan \left(2 x \right)-3 \sqrt{4+3 \tan \left(2 x \right)}\, \sqrt{2}\right)}{1000}+\frac{9 \sqrt{2}\, \arctan \left(\frac{\left(2 \sqrt{4+3 \tan \left(2 x \right)}-3 \sqrt{2}\right) \sqrt{2}}{2}\right)}{500}+\frac{13 \sqrt{2}\, \ln \left(9+3 \tan \left(2 x \right)+3 \sqrt{4+3 \tan \left(2 x \right)}\, \sqrt{2}\right)}{1000}+\frac{9 \sqrt{2}\, \arctan \left(\frac{\left(2 \sqrt{4+3 \tan \left(2 x \right)}+3 \sqrt{2}\right) \sqrt{2}}{2}\right)}{500}-\frac{3}{25 \sqrt{4+3 \tan \left(2 x \right)}}$&$130$\\ \hline \end{longtable}"," ",0,"-13/1000*2^(1/2)*ln(9+3*tan(2*x)-3*(4+3*tan(2*x))^(1/2)*2^(1/2))+9/500*2^(1/2)*arctan(1/2*(2*(4+3*tan(2*x))^(1/2)-3*2^(1/2))*2^(1/2))+13/1000*2^(1/2)*ln(9+3*tan(2*x)+3*(4+3*tan(2*x))^(1/2)*2^(1/2))+9/500*2^(1/2)*arctan(1/2*(2*(4+3*tan(2*x))^(1/2)+3*2^(1/2))*2^(1/2))-3/25/(4+3*tan(2*x))^(1/2)","A"
400,1,219,30,0.770000," ","int((-(4-3*tan(x))^(1/2)+3*tan(x))/cos(x)^2/(4-3*tan(x))^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(-1+\cos \left(x \right)\right)^{2} \left(1+\cos \left(x \right)\right)^{2} \left(16 \sqrt{\frac{4 \cos \left(x \right)-3 \sin \left(x \right)}{\cos \left(x \right)}}\, \cos \left(x \right)+4 \cos \left(x \right) \ln \left(-\frac{-2+2 \cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)+4 \cos \left(x \right) \ln \left(-\frac{-2 \sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-4 \cos \left(x \right) \ln \left(-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}\right)-4 \cos \left(x \right) \ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)-6 \sin \left(x \right) \sqrt{\frac{4 \cos \left(x \right)-3 \sin \left(x \right)}{\cos \left(x \right)}}-3 \sin \left(x \right) \ln \left(-\frac{-2+2 \cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)-3 \sin \left(x \right) \ln \left(-\frac{-2 \sin \left(x \right)-1+\cos \left(x \right)}{\sin \left(x \right)}\right)+3 \sin \left(x \right) \ln \left(-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}\right)+3 \sin \left(x \right) \ln \left(-\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}\right)\right)}{3 \left(4 \cos \left(x \right)-3 \sin \left(x \right)\right) \sin \left(x \right)^{4}}$&$219$\\ \hline \end{longtable}"," ",0,"1/3*(-1+cos(x))^2*(1+cos(x))^2*(16*((4*cos(x)-3*sin(x))/cos(x))^(1/2)*cos(x)+4*cos(x)*ln(-(-2+2*cos(x)+sin(x))/sin(x))+4*cos(x)*ln(-(-2*sin(x)-1+cos(x))/sin(x))-4*cos(x)*ln(-(-1+cos(x)-sin(x))/sin(x))-4*cos(x)*ln(-(-1+cos(x)+sin(x))/sin(x))-6*sin(x)*((4*cos(x)-3*sin(x))/cos(x))^(1/2)-3*sin(x)*ln(-(-2+2*cos(x)+sin(x))/sin(x))-3*sin(x)*ln(-(-2*sin(x)-1+cos(x))/sin(x))+3*sin(x)*ln(-(-1+cos(x)-sin(x))/sin(x))+3*sin(x)*ln(-(-1+cos(x)+sin(x))/sin(x)))/(4*cos(x)-3*sin(x))/sin(x)^4","B"
401,1,94,68,0.075000," ","int(tan(x)/(-1+tan(x)^(1/2))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\arctan \left(\tan \left(x \right)\right)}{2}-\frac{\sqrt{2}\, \left(\ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)+\tan \left(x \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)+\tan \left(x \right)}\right)+2 \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)\right)+2 \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)\right)\right)}{4}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{4}-\frac{1}{-1+\sqrt{\tan}\left(x \right)}+\ln \left(-1+\sqrt{\tan}\left(x \right)\right)$&$94$\\ default&$-\frac{\arctan \left(\tan \left(x \right)\right)}{2}-\frac{\sqrt{2}\, \left(\ln \left(\frac{1-\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)+\tan \left(x \right)}{1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)+\tan \left(x \right)}\right)+2 \arctan \left(1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)\right)+2 \arctan \left(-1+\sqrt{2}\, \left(\sqrt{\tan}\left(x \right)\right)\right)\right)}{4}-\frac{\ln \left(1+\tan^{2}\left(x \right)\right)}{4}-\frac{1}{-1+\sqrt{\tan}\left(x \right)}+\ln \left(-1+\sqrt{\tan}\left(x \right)\right)$&$94$\\ \hline \end{longtable}"," ",0,"-1/2*arctan(tan(x))-1/4*2^(1/2)*(ln((1-2^(1/2)*tan(x)^(1/2)+tan(x))/(1+2^(1/2)*tan(x)^(1/2)+tan(x)))+2*arctan(1+2^(1/2)*tan(x)^(1/2))+2*arctan(-1+2^(1/2)*tan(x)^(1/2)))-1/4*ln(1+tan(x)^2)-1/(-1+tan(x)^(1/2))+ln(-1+tan(x)^(1/2))","A"
402,1,266,25,0.183000," ","int(sin(x)/sin(2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \left(2 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-\sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+2 \left(\tan^{4}\left(\frac{x}{2}\right)\right)-2 \left(\tan^{2}\left(\frac{x}{2}\right)\right)\right)}{2 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}$&$266$\\ \hline \end{longtable}"," ",0,"-1/2*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)*(2*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^2-(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^2+2*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))-(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))+2*tan(1/2*x)^4-2*tan(1/2*x)^2)/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)/(1+tan(1/2*x)^2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
403,1,98,25,0.184000," ","int(cos(x)/sin(2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)}{\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}$&$98$\\ \hline \end{longtable}"," ",0,"(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))","C"
404,1,171,35,0.170000," ","int(sin(x)*sin(2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)+2 \left(\tan^{3}\left(\frac{x}{2}\right)\right)-2 \tan \left(\frac{x}{2}\right)\right)}{\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)}$&$171$\\ \hline \end{longtable}"," ",0,"(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)*((tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^2+(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))+2*tan(1/2*x)^3-2*tan(1/2*x))/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)/(1+tan(1/2*x)^2)","C"
405,1,442,35,0.309000," ","int((cos(x)-sin(x))*sin(2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \left(-3 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)+4 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)+4 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \left(\tan^{4}\left(\frac{x}{2}\right)\right)-3 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}+4 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-2 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{3}\left(\frac{x}{2}\right)\right)+4 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \tan \left(\frac{x}{2}\right)\right)}{\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}}$&$442$\\ \hline \end{longtable}"," ",0,"(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)*(-3*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2+4*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^2+4*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*tan(1/2*x)^4-3*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)+4*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))-2*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^3+4*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*tan(1/2*x)^2+2*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x))/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)/(1+tan(1/2*x)^2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)/(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)","C"
406,1,510,47,0.237000," ","int(sin(x)^7/sin(2*x)^(7/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \left(5 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{14}\left(\frac{x}{2}\right)\right)+35 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{12}\left(\frac{x}{2}\right)\right)+10 \left(\tan^{15}\left(\frac{x}{2}\right)\right)+105 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{10}\left(\frac{x}{2}\right)\right)+66 \left(\tan^{13}\left(\frac{x}{2}\right)\right)+175 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{8}\left(\frac{x}{2}\right)\right)-1014 \left(\tan^{11}\left(\frac{x}{2}\right)\right)+175 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{6}\left(\frac{x}{2}\right)\right)+2002 \left(\tan^{9}\left(\frac{x}{2}\right)\right)+105 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{x}{2}\right)\right)-2002 \left(\tan^{7}\left(\frac{x}{2}\right)\right)+35 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)+1014 \left(\tan^{5}\left(\frac{x}{2}\right)\right)+5 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-66 \left(\tan^{3}\left(\frac{x}{2}\right)\right)-10 \tan \left(\frac{x}{2}\right)\right)}{2688 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{7} \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}$&$510$\\ \hline \end{longtable}"," ",0,"1/2688*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)*(5*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^14+35*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^12+10*tan(1/2*x)^15+105*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^10+66*tan(1/2*x)^13+175*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^8-1014*tan(1/2*x)^11+175*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^6+2002*tan(1/2*x)^9+105*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^4-2002*tan(1/2*x)^7+35*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^2+1014*tan(1/2*x)^5+5*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))-66*tan(1/2*x)^3-10*tan(1/2*x))/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)/(1+tan(1/2*x)^2)^7/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
407,1,1108,47,0.263000," ","int(cos(x)^7/sin(2*x)^(7/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(192 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{6}\left(\frac{x}{2}\right)\right)-96 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{6}\left(\frac{x}{2}\right)\right)-\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{10}\left(\frac{x}{2}\right)\right)-384 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{4}\left(\frac{x}{2}\right)\right)+192 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{4}\left(\frac{x}{2}\right)\right)+96 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \left(\tan^{8}\left(\frac{x}{2}\right)\right)+3 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{8}\left(\frac{x}{2}\right)\right)+48 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{8}\left(\frac{x}{2}\right)\right)+192 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-96 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-192 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \left(\tan^{6}\left(\frac{x}{2}\right)\right)+14 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{6}\left(\frac{x}{2}\right)\right)-144 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{6}\left(\frac{x}{2}\right)\right)+96 \left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}+14 \left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}+144 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{4}\left(\frac{x}{2}\right)\right)+3 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-48 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\right)}{160 \tan \left(\frac{x}{2}\right)^{3} \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}$&$1108$\\ \hline \end{longtable}"," ",0,"1/160*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)/tan(1/2*x)^3*(192*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^6-96*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^6-(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^10-384*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^4+192*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^4+96*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*tan(1/2*x)^8+3*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^8+48*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^8+192*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-96*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-192*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*tan(1/2*x)^6+14*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^6-144*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^6+96*tan(1/2*x)^4*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)+14*tan(1/2*x)^4*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)+144*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^4+3*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-48*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2))/(tan(1/2*x)^2-1)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)/(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)/(tan(1/2*x)-1)/(tan(1/2*x)+1)","C"
408,1,508,12,0.267000," ","int(sin(2*x)^(3/2)/sin(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(96 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-48 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{6}\left(\frac{x}{2}\right)\right)+28 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{4}\left(\frac{x}{2}\right)\right)+40 \left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}+\left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}-28 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\right)}{5 \tan \left(\frac{x}{2}\right)^{3} \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}}$&$508$\\ \hline \end{longtable}"," ",0,"1/5*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)/tan(1/2*x)^3*(96*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-48*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^6+28*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^4+40*tan(1/2*x)^4*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)+tan(1/2*x)^4*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)-28*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2+(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2))/(tan(1/2*x)^3-tan(1/2*x))^(1/2)/(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)","C"
409,1,286,23,0.211000," ","int(1/cos(x)^3/sin(2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \left(5 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{6}\left(\frac{x}{2}\right)\right)+15 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{4}\left(\frac{x}{2}\right)\right)-14 \left(\tan^{7}\left(\frac{x}{2}\right)\right)+15 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 \left(\tan^{5}\left(\frac{x}{2}\right)\right)+5 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right)-2 \left(\tan^{3}\left(\frac{x}{2}\right)\right)+14 \tan \left(\frac{x}{2}\right)\right)}{12 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{3} \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}$&$286$\\ \hline \end{longtable}"," ",0,"1/12*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)*(5*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^6+15*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^4-14*tan(1/2*x)^7+15*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)^2+2*tan(1/2*x)^5+5*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))-2*tan(1/2*x)^3+14*tan(1/2*x))/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)/(1+tan(1/2*x)^2)^3/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
410,1,121,21,0.161000," ","int(1/sin(x)/sin(2*x)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(\tan^{2}\left(\frac{x}{2}\right)-1\right) \left(2 \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \tan \left(\frac{x}{2}\right)-\left(\tan^{4}\left(\frac{x}{2}\right)\right)+1\right)}{12 \tan \left(\frac{x}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}$&$121$\\ \hline \end{longtable}"," ",0,"-1/12*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)^2-1)/tan(1/2*x)*(2*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*tan(1/2*x)-tan(1/2*x)^4+1)/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
411,1,761,52,0.606000," ","int(cos(x)^3*(cos(2*x)-3*tan(x))/(sin(x)^2-sin(2*x))/sin(2*x)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-\frac{\tan \left(\frac{x}{2}\right)}{\tan^{2}\left(\frac{x}{2}\right)-1}}\, \left(932 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-3024 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-2 \tan \left(\frac{x}{2}\right)+2}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticE \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, \frac{\sqrt{2}}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)+24 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{6}\left(\frac{x}{2}\right)\right)+3 \sqrt{2}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \left(\munderset{\underline{\hspace{1.25 ex}}\alpha  =\RootOf \left(\textit{\_Z}^{4}+\textit{\_Z}^{3}+2 \textit{\_Z}^{2}-\textit{\_Z} +1\right)}{\sum}\frac{\left(34 \underline{\hspace{1.25 ex}}\alpha^{3}+13 \underline{\hspace{1.25 ex}}\alpha^{2}+34 \underline{\hspace{1.25 ex}}\alpha  -21\right) \left(\underline{\hspace{1.25 ex}}\alpha^{3}+2 \underline{\hspace{1.25 ex}}\alpha  -3\right) \sqrt{\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-\tan \left(\frac{x}{2}\right)+1}\, \sqrt{-\tan \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{\tan \left(\frac{x}{2}\right)+1}, -\frac{1}{4} \underline{\hspace{1.25 ex}}\alpha^{3}-\frac{1}{2} \underline{\hspace{1.25 ex}}\alpha  +\frac{3}{4}, \frac{\sqrt{2}}{2}\right)}{\sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}}\right) \left(\tan^{2}\left(\frac{x}{2}\right)\right)+200 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{5}\left(\frac{x}{2}\right)\right)-24 \left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}-1920 \left(\tan^{4}\left(\frac{x}{2}\right)\right) \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}-552 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{4}\left(\frac{x}{2}\right)\right)-24 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)+552 \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \left(\tan^{2}\left(\frac{x}{2}\right)\right)-200 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \tan \left(\frac{x}{2}\right) \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}+24 \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan^{2}\left(\frac{x}{2}\right)-1\right)}\right)}{3840 \tan \left(\frac{x}{2}\right)^{3} \sqrt{\tan \left(\frac{x}{2}\right) \left(\tan \left(\frac{x}{2}\right)-1\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}\, \sqrt{\tan^{3}\left(\frac{x}{2}\right)-\tan \left(\frac{x}{2}\right)}}$&$761$\\ \hline \end{longtable}"," ",0,"1/3840*(-tan(1/2*x)/(tan(1/2*x)^2-1))^(1/2)/tan(1/2*x)^3*(932*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticF((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-3024*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)+1)^(1/2)*(-2*tan(1/2*x)+2)^(1/2)*(-tan(1/2*x))^(1/2)*EllipticE((tan(1/2*x)+1)^(1/2),1/2*2^(1/2))*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2+24*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^6+3*2^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*sum((34*_alpha^3+13*_alpha^2+34*_alpha-21)*(_alpha^3+2*_alpha-3)*(tan(1/2*x)+1)^(1/2)*(-tan(1/2*x)+1)^(1/2)*(-tan(1/2*x))^(1/2)/(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*EllipticPi((tan(1/2*x)+1)^(1/2),-1/4*_alpha^3-1/2*_alpha+3/4,1/2*2^(1/2)),_alpha=RootOf(_Z^4+_Z^3+2*_Z^2-_Z+1))*tan(1/2*x)^2+200*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^5-24*tan(1/2*x)^4*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)-1920*tan(1/2*x)^4*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)-552*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^4-24*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2+552*(tan(1/2*x)^3-tan(1/2*x))^(1/2)*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)^2-200*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*tan(1/2*x)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2)+24*(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)*(tan(1/2*x)*(tan(1/2*x)^2-1))^(1/2))/(tan(1/2*x)*(tan(1/2*x)-1)*(tan(1/2*x)+1))^(1/2)/(tan(1/2*x)^3-tan(1/2*x))^(1/2)","C"
412,1,16,15,0.358000," ","int((sin(x)/cos(x)^5)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \cos \left(x \right) \sin \left(x \right) \sqrt{\frac{\sin \left(x \right)}{\cos \left(x \right)^{5}}}}{3}$&$16$\\ \hline \end{longtable}"," ",0,"2/3*cos(x)*sin(x)*(sin(x)/cos(x)^5)^(1/2)","A"
413,1,318,73,0.510000," ","int((sin(x)^5/cos(x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{32}\, \left(-1+\cos \left(x \right)\right) \left(-3 i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}+3 i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}-3 \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}-3 \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}+2 \left(\cos^{2}\left(x \right)\right) \sqrt{2}-2 \cos \left(x \right) \sqrt{2}\right) \left(1+\cos \left(x \right)\right)^{2} \sqrt{\frac{\sin^{5}\left(x \right)}{\cos \left(x \right)}}}{32 \sin \left(x \right)^{5}}$&$318$\\ \hline \end{longtable}"," ",0,"-1/32*32^(1/2)*(-1+cos(x))*(-3*I*EllipticPi((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*(-(-1+cos(x)-sin(x))/sin(x))^(1/2)+3*I*EllipticPi((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*(-(-1+cos(x)-sin(x))/sin(x))^(1/2)-3*EllipticPi((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((-1+cos(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*(-(-1+cos(x)-sin(x))/sin(x))^(1/2)-3*EllipticPi((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((-1+cos(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*(-(-1+cos(x)-sin(x))/sin(x))^(1/2)+2*cos(x)^2*2^(1/2)-2*cos(x)*2^(1/2))*(1+cos(x))^2*(sin(x)^5/cos(x))^(1/2)/sin(x)^5","C"
414,0,0,39,0.511000," ","int((sin(x)^2/cos(x)^14)^(1/3),x)","\[\int \left(\frac{\sin^{2}\left(x \right)}{\cos \left(x \right)^{14}}\right)^{\frac{1}{3}}\, dx\]"," ",0,"int((sin(x)^2/cos(x)^14)^(1/3),x)","F"
415,0,0,60,0.441000," ","int(1/(cos(x)^11*sin(x)^13)^(1/4),x)","\[\int \frac{1}{\left(\left(\cos^{11}\left(x \right)\right) \left(\sin^{13}\left(x \right)\right)\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(1/(cos(x)^11*sin(x)^13)^(1/4),x)","F"
416,1,247,92,0.755000," ","int((cos(2*x)-sin(2*x)^(1/2))/(cos(x)^3*sin(x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 \cos \left(x \right) \sin \left(x \right)}{\sqrt{\left(\cos^{3}\left(x \right)\right) \sin \left(x \right)}}+\frac{2 \sqrt{2}\, \cos \left(x \right) \sqrt{\cos \left(x \right) \sin \left(x \right)}\, \arctanh \left(\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)}{\sqrt{\left(\cos^{3}\left(x \right)\right) \sin \left(x \right)}}-\frac{\sqrt{2}\, \left(i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-i \EllipticPi \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)-2 \EllipticF \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right)+\EllipticPi \left(\sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right)\right) \cos \left(x \right) \sqrt{-\frac{-1+\cos \left(x \right)-\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{-1+\cos \left(x \right)+\sin \left(x \right)}{\sin \left(x \right)}}\, \sqrt{\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}}\, \left(\sin^{2}\left(x \right)\right)}{\left(-1+\cos \left(x \right)\right) \sqrt{\left(\cos^{3}\left(x \right)\right) \sin \left(x \right)}}$&$247$\\ \hline \end{longtable}"," ",0,"-2*cos(x)*sin(x)/(cos(x)^3*sin(x))^(1/2)+2*2^(1/2)*cos(x)*(cos(x)*sin(x))^(1/2)*arctanh((-1+cos(x))/sin(x))/(cos(x)^3*sin(x))^(1/2)-2^(1/2)*(I*EllipticPi((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))-I*EllipticPi((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2))-2*EllipticF((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2*2^(1/2))+EllipticPi((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2-1/2*I,1/2*2^(1/2))+EllipticPi((-(-1+cos(x)-sin(x))/sin(x))^(1/2),1/2+1/2*I,1/2*2^(1/2)))*cos(x)*(-(-1+cos(x)-sin(x))/sin(x))^(1/2)*((-1+cos(x)+sin(x))/sin(x))^(1/2)*((-1+cos(x))/sin(x))^(1/2)*sin(x)^2/(-1+cos(x))/(cos(x)^3*sin(x))^(1/2)","C"
417,1,22964,298,4.602000," ","int((-2*sin(2*x)+(cos(x)*sin(x)^3)^(1/2))/(-(cos(x)^3*sin(x))^(1/2)+tan(x)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$22964$\\ \hline \end{longtable}"," ",0,"result too large to display","C"
418,0,0,99,1.316000," ","int(((sin(x)/cos(x)^7)^(1/3)-3*tan(x))/(cos(x)^5*sin(x))^(2/3),x)","\[\int \frac{\left(\frac{\sin \left(x \right)}{\cos \left(x \right)^{7}}\right)^{\frac{1}{3}}-3 \tan \left(x \right)}{\left(\left(\cos^{5}\left(x \right)\right) \sin \left(x \right)\right)^{\frac{2}{3}}}\, dx\]"," ",0,"int(((sin(x)/cos(x)^7)^(1/3)-3*tan(x))/(cos(x)^5*sin(x))^(2/3),x)","F"
419,1,56,55,0.082000," ","int((1+2*cos(x)^2)^(5/2)*sin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{5 \cos \left(x \right) \left(1+2 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{24}-\frac{\cos \left(x \right) \left(1+2 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}{6}-\frac{5 \arcsinh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{32}-\frac{5 \cos \left(x \right) \sqrt{1+2 \left(\cos^{2}\left(x \right)\right)}}{16}$&$56$\\ default&$-\frac{5 \cos \left(x \right) \left(1+2 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}{24}-\frac{\cos \left(x \right) \left(1+2 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}{6}-\frac{5 \arcsinh \left(\cos \left(x \right) \sqrt{2}\right) \sqrt{2}}{32}-\frac{5 \cos \left(x \right) \sqrt{1+2 \left(\cos^{2}\left(x \right)\right)}}{16}$&$56$\\ \hline \end{longtable}"," ",0,"-5/24*cos(x)*(1+2*cos(x)^2)^(3/2)-1/6*cos(x)*(1+2*cos(x)^2)^(5/2)-5/32*arcsinh(cos(x)*2^(1/2))*2^(1/2)-5/16*cos(x)*(1+2*cos(x)^2)^(1/2)","A"
420,1,103,53,0.227000," ","int(cos(x)*(5*cos(x)^2+sin(x)^2)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\left(4 \left(\cos^{2}\left(x \right)\right)+1\right) \left(\sin^{2}\left(x \right)\right)}\, \left(512 \sqrt{-4 \left(\sin^{4}\left(x \right)\right)+5 \left(\sin^{2}\left(x \right)\right)}\, \left(\sin^{4}\left(x \right)\right)-2080 \sqrt{-4 \left(\sin^{4}\left(x \right)\right)+5 \left(\sin^{2}\left(x \right)\right)}\, \left(\sin^{2}\left(x \right)\right)+3300 \sqrt{-4 \left(\sin^{4}\left(x \right)\right)+5 \left(\sin^{2}\left(x \right)\right)}+1875 \arcsin \left(-1+\frac{8 \left(\sin^{2}\left(x \right)\right)}{5}\right)\right)}{192 \sin \left(x \right) \sqrt{4 \left(\cos^{2}\left(x \right)\right)+1}}$&$103$\\ \hline \end{longtable}"," ",0,"1/192*((4*cos(x)^2+1)*sin(x)^2)^(1/2)*(512*(-4*sin(x)^4+5*sin(x)^2)^(1/2)*sin(x)^4-2080*(-4*sin(x)^4+5*sin(x)^2)^(1/2)*sin(x)^2+3300*(-4*sin(x)^4+5*sin(x)^2)^(1/2)+1875*arcsin(-1+8/5*sin(x)^2))/sin(x)/(4*cos(x)^2+1)^(1/2)","A"
421,1,82,46,0.222000," ","int(cos(x)*(-cos(x)^2-5*sin(x)^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\left(4 \left(\cos^{2}\left(x \right)\right)-5\right) \left(\sin^{2}\left(x \right)\right)}\, \left(-32 \sqrt{-4 \left(\sin^{4}\left(x \right)\right)-\left(\sin^{2}\left(x \right)\right)}\, \left(\sin^{2}\left(x \right)\right)-20 \sqrt{-4 \left(\sin^{4}\left(x \right)\right)-\left(\sin^{2}\left(x \right)\right)}+3 \arcsin \left(8 \left(\sin^{2}\left(x \right)\right)+1\right)\right)}{32 \sin \left(x \right) \sqrt{4 \left(\cos^{2}\left(x \right)\right)-5}}$&$82$\\ \hline \end{longtable}"," ",0,"1/32*((4*cos(x)^2-5)*sin(x)^2)^(1/2)*(-32*(-4*sin(x)^4-sin(x)^2)^(1/2)*sin(x)^2-20*(-4*sin(x)^4-sin(x)^2)^(1/2)+3*arcsin(8*sin(x)^2+1))/sin(x)/(4*cos(x)^2-5)^(1/2)","A"
422,1,44,43,0.134000," ","int(sin(x)/(5*cos(x)^2-2*sin(x)^2)^(7/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\cos \left(x \right)}{10 \left(-2+7 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}-\frac{\cos \left(x \right)}{15 \left(-2+7 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{\cos \left(x \right)}{15 \sqrt{-2+7 \left(\cos^{2}\left(x \right)\right)}}$&$44$\\ default&$\frac{\cos \left(x \right)}{10 \left(-2+7 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{5}{2}}}-\frac{\cos \left(x \right)}{15 \left(-2+7 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{\cos \left(x \right)}{15 \sqrt{-2+7 \left(\cos^{2}\left(x \right)\right)}}$&$44$\\ \hline \end{longtable}"," ",0,"1/10*cos(x)/(-2+7*cos(x)^2)^(5/2)-1/15*cos(x)/(-2+7*cos(x)^2)^(3/2)+1/15*cos(x)/(-2+7*cos(x)^2)^(1/2)","A"
423,1,58,28,0.284000," ","int(cos(x)*cos(2*x)/(2-5*sin(x)^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{20 \arcsin \left(\frac{\sin \left(x \right) \sqrt{10}}{2}\right) \sqrt{5}\, \left(\cos^{2}\left(x \right)\right)+5 \sin \left(x \right) \sqrt{5 \left(\cos^{2}\left(x \right)\right)-3}-12 \arcsin \left(\frac{\sin \left(x \right) \sqrt{10}}{2}\right) \sqrt{5}}{250 \left(\cos^{2}\left(x \right)\right)-150}$&$58$\\ \hline \end{longtable}"," ",0,"1/50/(5*cos(x)^2-3)*(20*arcsin(1/2*sin(x)*10^(1/2))*5^(1/2)*cos(x)^2+5*sin(x)*(5*cos(x)^2-3)^(1/2)-12*arcsin(1/2*sin(x)*10^(1/2))*5^(1/2))","B"
424,1,53,36,0.230000," ","int(sin(5*x)/(5*cos(x)^2+9*sin(x)^2)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{4 \left(\cos^{3}\left(x \right)\right)}{3 \left(9-4 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{214 \cos \left(x \right)}{243 \sqrt{9-4 \left(\cos^{2}\left(x \right)\right)}}-\frac{\arcsin \left(\frac{2 \cos \left(x \right)}{3}\right)}{2}+\frac{26 \cos \left(x \right)}{27 \left(9-4 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}$&$53$\\ default&$-\frac{4 \left(\cos^{3}\left(x \right)\right)}{3 \left(9-4 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{214 \cos \left(x \right)}{243 \sqrt{9-4 \left(\cos^{2}\left(x \right)\right)}}-\frac{\arcsin \left(\frac{2 \cos \left(x \right)}{3}\right)}{2}+\frac{26 \cos \left(x \right)}{27 \left(9-4 \left(\cos^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}$&$53$\\ \hline \end{longtable}"," ",0,"-4/3*cos(x)^3/(9-4*cos(x)^2)^(3/2)+214/243*cos(x)/(9-4*cos(x)^2)^(1/2)-1/2*arcsin(2/3*cos(x))+26/27*cos(x)/(9-4*cos(x)^2)^(3/2)","A"
425,1,46,37,0.144000," ","int(cos(x)*cos(2*x)*sin(3*x)/(-5+4*sin(x)^2)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(\cos^{4}\left(x \right)\right)}{\left(-4 \left(\cos^{2}\left(x \right)\right)-1\right)^{\frac{3}{2}}}+\frac{7 \left(\cos^{2}\left(x \right)\right)}{2 \left(-4 \left(\cos^{2}\left(x \right)\right)-1\right)^{\frac{3}{2}}}+\frac{1}{2 \left(-4 \left(\cos^{2}\left(x \right)\right)-1\right)^{\frac{3}{2}}}$&$46$\\ default&$\frac{2 \left(\cos^{4}\left(x \right)\right)}{\left(-4 \left(\cos^{2}\left(x \right)\right)-1\right)^{\frac{3}{2}}}+\frac{7 \left(\cos^{2}\left(x \right)\right)}{2 \left(-4 \left(\cos^{2}\left(x \right)\right)-1\right)^{\frac{3}{2}}}+\frac{1}{2 \left(-4 \left(\cos^{2}\left(x \right)\right)-1\right)^{\frac{3}{2}}}$&$46$\\ \hline \end{longtable}"," ",0,"2*cos(x)^4/(-4*cos(x)^2-1)^(3/2)+7/2*cos(x)^2/(-4*cos(x)^2-1)^(3/2)+1/2/(-4*cos(x)^2-1)^(3/2)","A"
426,1,131,92,0.435000," ","int((-2*cos(x)^3*(-1+sin(x))+cos(2*x)*sin(x))/sin(x)^2/(-5+sin(x)^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-2 \ln \left(\sin \left(x \right)+\sqrt{-5+\sin^{2}\left(x \right)}\right)+2 \sqrt{-5+\sin^{2}\left(x \right)}+\frac{2 \sqrt{5}\, \arctan \left(\frac{\sqrt{5}}{\sqrt{-5+\sin^{2}\left(x \right)}}\right)}{5}+\frac{2 \sqrt{-5+\sin^{2}\left(x \right)}}{5 \sin \left(x \right)}-\frac{\sqrt{\left(-5+\sin^{2}\left(x \right)\right) \left(\cos^{2}\left(x \right)\right)}\, \left(-\sqrt{5}\, \arctan \left(\frac{\left(3 \left(\sin^{2}\left(x \right)\right)-5\right) \sqrt{5}}{5 \sqrt{-\left(\cos^{4}\left(x \right)\right)-4 \left(\cos^{2}\left(x \right)\right)}}\right)-10 \arcsin \left(1+\frac{\left(\cos^{2}\left(x \right)\right)}{2}\right)\right)}{10 \cos \left(x \right) \sqrt{-5+\sin^{2}\left(x \right)}}$&$131$\\ \hline \end{longtable}"," ",0,"-2*ln(sin(x)+(-5+sin(x)^2)^(1/2))+2*(-5+sin(x)^2)^(1/2)+2/5*5^(1/2)*arctan(5^(1/2)/(-5+sin(x)^2)^(1/2))+2/5*(-5+sin(x)^2)^(1/2)/sin(x)-1/10*((-5+sin(x)^2)*cos(x)^2)^(1/2)*(-5^(1/2)*arctan(1/5*(3*sin(x)^2-5)*5^(1/2)/(-cos(x)^4-4*cos(x)^2)^(1/2))-10*arcsin(1+1/2*cos(x)^2))/cos(x)/(-5+sin(x)^2)^(1/2)","A"
427,0,0,84,180.000000," ","int(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x)","\[\int \frac{\cos \left(3 x \right)}{-\sqrt{-1+8 \left(\cos^{2}\left(x \right)\right)}+\sqrt{3 \left(\cos^{2}\left(x \right)\right)-\left(\sin^{2}\left(x \right)\right)}}\, dx\]"," ",0,"int(cos(3*x)/(-(-1+8*cos(x)^2)^(1/2)+(3*cos(x)^2-sin(x)^2)^(1/2)),x)","F"
428,1,38,25,0.250000," ","int((2-3*sin(x)^2)^(3/5)*sin(4*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{5 \left(3 \left(\cos^{2}\left(x \right)\right)-1\right)^{\frac{8}{5}}}{12}-\frac{20 \left(\frac{1}{2}+\frac{3 \cos \left(2 x \right)}{2}\right)^{\frac{13}{5}}}{117}-\frac{5 \left(\frac{1}{2}+\frac{3 \cos \left(2 x \right)}{2}\right)^{\frac{8}{5}}}{18}$&$38$\\ \hline \end{longtable}"," ",0,"5/12*(3*cos(x)^2-1)^(8/5)-20/117*(1/2+3/2*cos(2*x))^(13/5)-5/18*(1/2+3/2*cos(2*x))^(8/5)","A"
429,1,62,23,0.157000," ","int(cos(x)*cos(2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{\left(2 \left(\cos^{2}\left(x \right)\right)-1\right) \left(\sin^{2}\left(x \right)\right)}\, \left(-\sqrt{2}\, \arcsin \left(4 \left(\sin^{2}\left(x \right)\right)-1\right)-4 \sqrt{-2 \left(\sin^{4}\left(x \right)\right)+\sin^{2}\left(x \right)}\right)}{8 \sin \left(x \right) \sqrt{2 \left(\cos^{2}\left(x \right)\right)-1}}$&$62$\\ \hline \end{longtable}"," ",0,"-1/8*((2*cos(x)^2-1)*sin(x)^2)^(1/2)*(-2^(1/2)*arcsin(4*sin(x)^2-1)-4*(-2*sin(x)^4+sin(x)^2)^(1/2))/sin(x)/(2*cos(x)^2-1)^(1/2)","B"
430,1,55,39,0.130000," ","int(cos(2*x)^(3/2)*sin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(\cos^{3}\left(x \right)\right) \sqrt{2 \left(\cos^{2}\left(x \right)\right)-1}}{2}+\frac{5 \cos \left(x \right) \sqrt{2 \left(\cos^{2}\left(x \right)\right)-1}}{8}-\frac{3 \ln \left(\cos \left(x \right) \sqrt{2}+\sqrt{2 \left(\cos^{2}\left(x \right)\right)-1}\right) \sqrt{2}}{16}$&$55$\\ \hline \end{longtable}"," ",0,"-1/2*cos(x)^3*(2*cos(x)^2-1)^(1/2)+5/8*cos(x)*(2*cos(x)^2-1)^(1/2)-3/16*ln(cos(x)*2^(1/2)+(2*cos(x)^2-1)^(1/2))*2^(1/2)","A"
431,1,39,12,0.184000," ","int(sin(x)/cos(2*x)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{-2 \left(\sin^{2}\left(x \right)\right)+1}\, \cos \left(x \right) \left(4 \left(\sin^{2}\left(x \right)\right)-1\right)}{12 \left(\sin^{4}\left(x \right)\right)-12 \left(\sin^{2}\left(x \right)\right)+3}$&$39$\\ \hline \end{longtable}"," ",0,"1/3/(4*sin(x)^4-4*sin(x)^2+1)*(-2*sin(x)^2+1)^(1/2)*cos(x)*(4*sin(x)^2-1)","B"
432,1,100,37,0.206000," ","int(cos(2*x)^(3/2)/cos(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{\left(2 \left(\cos^{2}\left(x \right)\right)-1\right) \left(\sin^{2}\left(x \right)\right)}\, \left(4 \sqrt{2}\, \arcsin \left(4 \left(\cos^{2}\left(x \right)\right)-3\right) \left(\cos^{2}\left(x \right)\right)-5 \arctan \left(\frac{3 \left(\cos^{2}\left(x \right)\right)-2}{2 \sqrt{-2 \left(\sin^{4}\left(x \right)\right)+\sin^{2}\left(x \right)}}\right) \left(\cos^{2}\left(x \right)\right)+2 \sqrt{-2 \left(\sin^{4}\left(x \right)\right)+\sin^{2}\left(x \right)}\right)}{4 \cos \left(x \right)^{2} \sin \left(x \right) \sqrt{2 \left(\cos^{2}\left(x \right)\right)-1}}$&$100$\\ \hline \end{longtable}"," ",0,"-1/4*((2*cos(x)^2-1)*sin(x)^2)^(1/2)*(4*2^(1/2)*arcsin(4*cos(x)^2-3)*cos(x)^2-5*arctan(1/2*(3*cos(x)^2-2)/(-2*sin(x)^4+sin(x)^2)^(1/2))*cos(x)^2+2*(-2*sin(x)^4+sin(x)^2)^(1/2))/cos(x)^2/sin(x)/(2*cos(x)^2-1)^(1/2)","B"
433,1,180,65,0.407000," ","int((3*sin(x)^3-cos(x)*sin(4*x))/cos(2*x)^(7/2)/csc(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{120 \ln \left(\cos \left(x \right) \sqrt{2}+\sqrt{-2 \left(\sin^{2}\left(x \right)\right)+1}\right) \sqrt{2}\, \left(\sin^{6}\left(x \right)\right)+338 \sqrt{-2 \left(\sin^{2}\left(x \right)\right)+1}\, \cos \left(x \right) \left(\sin^{4}\left(x \right)\right)-180 \ln \left(\cos \left(x \right) \sqrt{2}+\sqrt{-2 \left(\sin^{2}\left(x \right)\right)+1}\right) \sqrt{2}\, \left(\sin^{4}\left(x \right)\right)-276 \sqrt{-2 \left(\sin^{2}\left(x \right)\right)+1}\, \left(\sin^{2}\left(x \right)\right) \cos \left(x \right)+90 \ln \left(\cos \left(x \right) \sqrt{2}+\sqrt{-2 \left(\sin^{2}\left(x \right)\right)+1}\right) \sqrt{2}\, \left(\sin^{2}\left(x \right)\right)+58 \sqrt{-2 \left(\sin^{2}\left(x \right)\right)+1}\, \cos \left(x \right)-15 \ln \left(\cos \left(x \right) \sqrt{2}+\sqrt{-2 \left(\sin^{2}\left(x \right)\right)+1}\right) \sqrt{2}}{30 \left(8 \left(\sin^{6}\left(x \right)\right)-12 \left(\sin^{4}\left(x \right)\right)+6 \left(\sin^{2}\left(x \right)\right)-1\right)}$&$180$\\ \hline \end{longtable}"," ",0,"-1/30/(8*sin(x)^6-12*sin(x)^4+6*sin(x)^2-1)*(120*ln(cos(x)*2^(1/2)+(-2*sin(x)^2+1)^(1/2))*2^(1/2)*sin(x)^6+338*(-2*sin(x)^2+1)^(1/2)*cos(x)*sin(x)^4-180*ln(cos(x)*2^(1/2)+(-2*sin(x)^2+1)^(1/2))*2^(1/2)*sin(x)^4-276*(-2*sin(x)^2+1)^(1/2)*sin(x)^2*cos(x)+90*ln(cos(x)*2^(1/2)+(-2*sin(x)^2+1)^(1/2))*2^(1/2)*sin(x)^2+58*(-2*sin(x)^2+1)^(1/2)*cos(x)-15*ln(cos(x)*2^(1/2)+(-2*sin(x)^2+1)^(1/2))*2^(1/2))","B"
434,1,754,54,0.700000," ","int((4-5*sec(x)^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{i \left(-70 i \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{2}\, \sqrt{5}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{-9-4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -\frac{1}{9+4 \sqrt{5}}, \frac{\sqrt{-9+4 \sqrt{5}}}{\sqrt{-9-4 \sqrt{5}}}\right)+64 i \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{2}\, \sqrt{5}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{-9-4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{9+4 \sqrt{5}}, \frac{\sqrt{-9+4 \sqrt{5}}}{\sqrt{-9-4 \sqrt{5}}}\right)+3 i \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{2}\, \sqrt{5}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right) \left(\sqrt{5}+2\right)}{\sin \left(x \right)}, 9-4 \sqrt{5}\right)-140 i \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{2}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{-9-4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -\frac{1}{9+4 \sqrt{5}}, \frac{\sqrt{-9+4 \sqrt{5}}}{\sqrt{-9-4 \sqrt{5}}}\right)+128 i \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{2}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{-9-4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{9+4 \sqrt{5}}, \frac{\sqrt{-9+4 \sqrt{5}}}{\sqrt{-9-4 \sqrt{5}}}\right)+6 i \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{2}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right) \left(\sqrt{5}+2\right)}{\sin \left(x \right)}, 9-4 \sqrt{5}\right)+80 \left(\cos^{3}\left(x \right)\right) \sqrt{5}+180 \left(\cos^{3}\left(x \right)\right)-80 \left(\cos^{2}\left(x \right)\right) \sqrt{5}-180 \left(\cos^{2}\left(x \right)\right)-100 \cos \left(x \right) \sqrt{5}-225 \cos \left(x \right)+100 \sqrt{5}+225\right) \cos \left(x \right) \sin \left(x \right) \left(\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}{2 \left(\sqrt{5}+2\right) \sqrt{-9-4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right) \left(4 \left(\cos^{2}\left(x \right)\right)-5\right)^{2}}$&$754$\\ \hline \end{longtable}"," ",0,"-1/2*I/(5^(1/2)+2)/(-9-4*5^(1/2))^(1/2)*(-70*I*cos(x)^2*sin(x)*2^(1/2)*5^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*EllipticPi((-9-4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),-1/(9+4*5^(1/2)),(-9+4*5^(1/2))^(1/2)/(-9-4*5^(1/2))^(1/2))+64*I*cos(x)^2*sin(x)*2^(1/2)*5^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*EllipticPi((-9-4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),1/(9+4*5^(1/2)),(-9+4*5^(1/2))^(1/2)/(-9-4*5^(1/2))^(1/2))+3*I*cos(x)^2*sin(x)*2^(1/2)*5^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*EllipticF(I*(-1+cos(x))*(5^(1/2)+2)/sin(x),9-4*5^(1/2))-140*I*cos(x)^2*sin(x)*2^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*EllipticPi((-9-4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),-1/(9+4*5^(1/2)),(-9+4*5^(1/2))^(1/2)/(-9-4*5^(1/2))^(1/2))+128*I*cos(x)^2*sin(x)*2^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*EllipticPi((-9-4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),1/(9+4*5^(1/2)),(-9+4*5^(1/2))^(1/2)/(-9-4*5^(1/2))^(1/2))+6*I*cos(x)^2*sin(x)*2^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*EllipticF(I*(-1+cos(x))*(5^(1/2)+2)/sin(x),9-4*5^(1/2))+80*cos(x)^3*5^(1/2)+180*cos(x)^3-80*cos(x)^2*5^(1/2)-180*cos(x)^2-100*cos(x)*5^(1/2)-225*cos(x)+100*5^(1/2)+225)*cos(x)*sin(x)*((4*cos(x)^2-5)/cos(x)^2)^(3/2)/(-1+cos(x))/(4*cos(x)^2-5)^2","C"
435,1,473,32,0.686000," ","int(1/(4-5*sec(x)^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{i \left(4 \left(\cos^{2}\left(x \right)\right)-5\right) \left(2 i \sin \left(x \right) \sqrt{2}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \sqrt{5}\, \EllipticPi \left(\frac{\sqrt{-9-4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{9+4 \sqrt{5}}, \frac{\sqrt{-9+4 \sqrt{5}}}{\sqrt{-9-4 \sqrt{5}}}\right)-i \sin \left(x \right) \sqrt{2}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \sqrt{5}\, \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right) \left(\sqrt{5}+2\right)}{\sin \left(x \right)}, 9-4 \sqrt{5}\right)+4 i \sin \left(x \right) \sqrt{2}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \EllipticPi \left(\frac{\sqrt{-9-4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{9+4 \sqrt{5}}, \frac{\sqrt{-9+4 \sqrt{5}}}{\sqrt{-9-4 \sqrt{5}}}\right)-2 i \sin \left(x \right) \sqrt{2}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right) \left(\sqrt{5}+2\right)}{\sin \left(x \right)}, 9-4 \sqrt{5}\right)+20 \cos \left(x \right) \sqrt{5}+45 \cos \left(x \right)-20 \sqrt{5}-45\right) \sin \left(x \right)}{4 \sqrt{-9-4 \sqrt{5}}\, \left(\sqrt{5}+2\right) \left(-1+\cos \left(x \right)\right) \cos \left(x \right)^{3} \left(\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}$&$473$\\ \hline \end{longtable}"," ",0,"-1/4*I/(-9-4*5^(1/2))^(1/2)/(5^(1/2)+2)*(4*cos(x)^2-5)*(2*I*sin(x)*2^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*5^(1/2)*EllipticPi((-9-4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),1/(9+4*5^(1/2)),(-9+4*5^(1/2))^(1/2)/(-9-4*5^(1/2))^(1/2))-I*sin(x)*2^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*5^(1/2)*EllipticF(I*(-1+cos(x))*(5^(1/2)+2)/sin(x),9-4*5^(1/2))+4*I*sin(x)*2^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*EllipticPi((-9-4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),1/(9+4*5^(1/2)),(-9+4*5^(1/2))^(1/2)/(-9-4*5^(1/2))^(1/2))-2*I*sin(x)*2^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*EllipticF(I*(-1+cos(x))*(5^(1/2)+2)/sin(x),9-4*5^(1/2))+20*cos(x)*5^(1/2)+45*cos(x)-20*5^(1/2)-45)*sin(x)/(-1+cos(x))/cos(x)^3/((4*cos(x)^2-5)/cos(x)^2)^(3/2)","C"
436,1,975,74,1.140000," ","int((-2*cot(x)^2+sin(x))/(1+5*tan(x)^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{i \left(6 i \cos \left(x \right) \sin \left(x \right) \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}\, \arctanh \left(\frac{\sqrt{-16}\, \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{2 \sin \left(x \right)^{2} \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)+4 i \cos \left(x \right) \sin \left(x \right) \sqrt{2}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right) \left(-2+\sqrt{5}\right)}{\sin \left(x \right)}, 9+4 \sqrt{5}\right)-3 i \sin \left(x \right) \arctanh \left(\frac{\sqrt{-16}\, \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{2 \sin \left(x \right)^{2} \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}}\right) \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sqrt{5}-3 i \cos \left(x \right) \sqrt{5}\, \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right) \arctanh \left(\frac{\sqrt{-16}\, \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{2 \sin \left(x \right)^{2} \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)-8 i \cos \left(x \right) \sqrt{2}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sin \left(x \right) \EllipticPi \left(\frac{\sqrt{-9+4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -\frac{1}{-9+4 \sqrt{5}}, \frac{\sqrt{-9-4 \sqrt{5}}}{\sqrt{-9+4 \sqrt{5}}}\right)-3 \cos \left(x \right) \sqrt{5}\, \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right) \arctan \left(\frac{2 \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)^{2} \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)-8 i \sqrt{2}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sin \left(x \right) \EllipticPi \left(\frac{\sqrt{-9+4 \sqrt{5}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -\frac{1}{-9+4 \sqrt{5}}, \frac{\sqrt{-9-4 \sqrt{5}}}{\sqrt{-9+4 \sqrt{5}}}\right)+4 i \sqrt{2}\, \sqrt{\frac{2 \cos \left(x \right) \sqrt{5}-4 \cos \left(x \right)-2 \sqrt{5}+5}{1+\cos \left(x \right)}}\, \sqrt{-\frac{2 \left(2 \cos \left(x \right) \sqrt{5}+4 \cos \left(x \right)-2 \sqrt{5}-5\right)}{1+\cos \left(x \right)}}\, \sin \left(x \right) \EllipticF \left(\frac{i \left(-1+\cos \left(x \right)\right) \left(-2+\sqrt{5}\right)}{\sin \left(x \right)}, 9+4 \sqrt{5}\right)+2 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \sqrt{5}+6 \cos \left(x \right) \sin \left(x \right) \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}\, \arctan \left(\frac{2 \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)^{2} \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)-3 \sin \left(x \right) \arctan \left(\frac{2 \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)^{2} \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}}\right) \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sqrt{5}+6 i \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right) \arctanh \left(\frac{\sqrt{-16}\, \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{2 \sin \left(x \right)^{2} \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}}\right)-4 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right)-164 \left(\cos^{2}\left(x \right)\right) \sqrt{5}+6 \arctan \left(\frac{2 \cos \left(x \right) \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)^{2} \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}}\right) \sqrt{-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right)+328 \left(\cos^{2}\left(x \right)\right)-5 \sin \left(x \right) \sqrt{5}+10 \sin \left(x \right)+180 \sqrt{5}-360\right) \left(\cos^{3}\left(x \right)\right) \left(-\frac{4 \left(\cos^{2}\left(x \right)\right)-5}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}{8 \sqrt{-9+4 \sqrt{5}}\, \left(\sqrt{5}+2\right)^{2} \left(-2+\sqrt{5}\right)^{2} \left(4 \left(\cos^{2}\left(x \right)\right)-5\right)^{2} \sin \left(x \right)}$&$975$\\ \hline \end{longtable}"," ",0,"1/8*I/(-9+4*5^(1/2))^(1/2)/(5^(1/2)+2)^2/(-2+5^(1/2))^2/(4*cos(x)^2-5)^2*(-8*I*2^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*sin(x)*EllipticPi((-9+4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),-1/(-9+4*5^(1/2)),(-9-4*5^(1/2))^(1/2)/(-9+4*5^(1/2))^(1/2))-3*I*sin(x)*arctanh(1/2*(-16)^(1/2)*cos(x)*(-1+cos(x))/sin(x)^2/(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2))*(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2)*5^(1/2)+4*I*cos(x)*sin(x)*2^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*EllipticF(I*(-1+cos(x))*(-2+5^(1/2))/sin(x),9+4*5^(1/2))-8*I*cos(x)*2^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*sin(x)*EllipticPi((-9+4*5^(1/2))^(1/2)*(-1+cos(x))/sin(x),-1/(-9+4*5^(1/2)),(-9-4*5^(1/2))^(1/2)/(-9+4*5^(1/2))^(1/2))+6*I*(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2)*sin(x)*arctanh(1/2*(-16)^(1/2)*cos(x)*(-1+cos(x))/sin(x)^2/(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2))-3*cos(x)*5^(1/2)*(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2)*sin(x)*arctan(2*cos(x)*(-1+cos(x))/sin(x)^2/(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2))-3*I*cos(x)*5^(1/2)*(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2)*sin(x)*arctanh(1/2*(-16)^(1/2)*cos(x)*(-1+cos(x))/sin(x)^2/(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2))+6*I*cos(x)*sin(x)*(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2)*arctanh(1/2*(-16)^(1/2)*cos(x)*(-1+cos(x))/sin(x)^2/(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2))+2*cos(x)^2*sin(x)*5^(1/2)+6*cos(x)*sin(x)*(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2)*arctan(2*cos(x)*(-1+cos(x))/sin(x)^2/(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2))-3*sin(x)*arctan(2*cos(x)*(-1+cos(x))/sin(x)^2/(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2))*(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2)*5^(1/2)+4*I*2^(1/2)*((2*cos(x)*5^(1/2)-4*cos(x)-2*5^(1/2)+5)/(1+cos(x)))^(1/2)*(-2*(2*cos(x)*5^(1/2)+4*cos(x)-2*5^(1/2)-5)/(1+cos(x)))^(1/2)*sin(x)*EllipticF(I*(-1+cos(x))*(-2+5^(1/2))/sin(x),9+4*5^(1/2))-4*cos(x)^2*sin(x)-164*cos(x)^2*5^(1/2)+6*arctan(2*cos(x)*(-1+cos(x))/sin(x)^2/(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2))*(-(4*cos(x)^2-5)/(1+cos(x))^2)^(1/2)*sin(x)+328*cos(x)^2-5*sin(x)*5^(1/2)+10*sin(x)+180*5^(1/2)-360)*cos(x)^3*(-(4*cos(x)^2-5)/cos(x)^2)^(3/2)/sin(x)","C"
437,1,64,31,0.763000," ","int((-3+cos(2*x))/cos(x)^4/(4-cot(x)^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(5 \left(\cos^{2}\left(x \right)\right)+2\right) \sqrt{-\frac{5 \left(\cos^{2}\left(x \right)\right)-4}{\sin \left(x \right)^{2}}}\, \sin \left(x \right) \sqrt{4}}{12 \cos \left(x \right)^{3}}+\frac{\sqrt{4}\, \sin \left(x \right) \sqrt{-\frac{5 \left(\cos^{2}\left(x \right)\right)-4}{\sin \left(x \right)^{2}}}}{4 \cos \left(x \right)}$&$64$\\ \hline \end{longtable}"," ",0,"-1/12*(5*cos(x)^2+2)*(-(5*cos(x)^2-4)/sin(x)^2)^(1/2)*sin(x)*4^(1/2)/cos(x)^3+1/4*4^(1/2)*sin(x)*(-(5*cos(x)^2-4)/sin(x)^2)^(1/2)/cos(x)","B"
438,1,1615,55,0.906000," ","int((3+sin(x)^2)*tan(x)^3/(-2+cos(x)^2)/(5-4*sec(x)^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\text{Expression too large to display}$&$1615$\\ \hline \end{longtable}"," ",0,"-3/5/(-5+2*5^(1/2))/(5+2*5^(1/2))/(-6+2*5^(1/2)+2^(1/2))/(-6+2*5^(1/2)-2^(1/2))/(6+2*5^(1/2)+2^(1/2))/(2*3^(1/2)+6^(1/2))/(6+2*5^(1/2)-2^(1/2))/(2*3^(1/2)-6^(1/2))*(5*cos(x)^2-4)*(50*cos(x)*3^(1/2)*2^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)+6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)+10*cos(x)+4*2^(1/2)+4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))+50*cos(x)*3^(1/2)*2^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)-6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)-10*cos(x)+4*2^(1/2)-4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))-25*cos(x)*2^(1/2)*6^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)+6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)+10*cos(x)+4*2^(1/2)+4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))+25*cos(x)*2^(1/2)*6^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)-6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)-10*cos(x)+4*2^(1/2)-4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))+100*cos(x)*3^(1/2)*arctanh(1/2/(2*3^(1/2)+6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)+10*cos(x)+4*2^(1/2)+4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)-100*cos(x)*3^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)-6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)-10*cos(x)+4*2^(1/2)-4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))+72*cos(x)*5^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2*5^(1/2)*cos(x)*4^(1/2)*(-1+cos(x))/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))-50*cos(x)*6^(1/2)*arctanh(1/2/(2*3^(1/2)+6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)+10*cos(x)+4*2^(1/2)+4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)-50*cos(x)*6^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)-6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)-10*cos(x)+4*2^(1/2)-4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))+50*3^(1/2)*2^(1/2)*arctanh(1/2/(2*3^(1/2)+6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)+10*cos(x)+4*2^(1/2)+4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)+50*3^(1/2)*2^(1/2)*arctanh(1/2/(2*3^(1/2)-6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)-10*cos(x)+4*2^(1/2)-4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)-25*2^(1/2)*6^(1/2)*arctanh(1/2/(2*3^(1/2)+6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)+10*cos(x)+4*2^(1/2)+4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)+25*2^(1/2)*6^(1/2)*arctanh(1/2/(2*3^(1/2)-6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)-10*cos(x)+4*2^(1/2)-4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)+100*3^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)+6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)+10*cos(x)+4*2^(1/2)+4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))-100*3^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)-6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)-10*cos(x)+4*2^(1/2)-4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))+72*5^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2*5^(1/2)*cos(x)*4^(1/2)*(-1+cos(x))/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))-50*6^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)+6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)+10*cos(x)+4*2^(1/2)+4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))-50*6^(1/2)*((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2)*arctanh(1/2/(2*3^(1/2)-6^(1/2))*4^(1/2)*(-1+cos(x))*(5*cos(x)*2^(1/2)-10*cos(x)+4*2^(1/2)-4)/sin(x)^2/((5*cos(x)^2-4)/(1+cos(x))^2)^(1/2))-240*cos(x))/cos(x)^3/((5*cos(x)^2-4)/cos(x)^2)^(3/2)","B"
439,1,117,45,0.968000," ","int((sec(x)^2-3*(4*sec(x)^2+5*tan(x)^2)^(1/2)*tan(x))/sin(x)^2/(4*sec(x)^2+5*tan(x)^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{6 \left(\cos^{3}\left(x \right)\right) \sin \left(x \right) \left(-\frac{5 \left(\cos^{2}\left(x \right)\right)-9}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)-3 \left(\cos^{3}\left(x \right)\right) \sin \left(x \right) \left(-\frac{5 \left(\cos^{2}\left(x \right)\right)-9}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}} \ln \left(-\frac{5 \left(\cos^{2}\left(x \right)\right)-9}{\left(1+\cos \left(x \right)\right)^{2}}\right)+25 \left(\cos^{4}\left(x \right)\right)-80 \left(\cos^{2}\left(x \right)\right)+63}{8 \cos \left(x \right)^{3} \sin \left(x \right) \left(-\frac{5 \left(\cos^{2}\left(x \right)\right)-9}{\cos \left(x \right)^{2}}\right)^{\frac{3}{2}}}$&$117$\\ \hline \end{longtable}"," ",0,"-1/8*(6*cos(x)^3*sin(x)*(-(5*cos(x)^2-9)/cos(x)^2)^(3/2)*ln(-(-1+cos(x))/sin(x))-3*cos(x)^3*sin(x)*(-(5*cos(x)^2-9)/cos(x)^2)^(3/2)*ln(-(5*cos(x)^2-9)/(1+cos(x))^2)+25*cos(x)^4-80*cos(x)^2+63)/cos(x)^3/sin(x)/(-(5*cos(x)^2-9)/cos(x)^2)^(3/2)","B"
440,1,61,52,0.080000," ","int(tan(x)*(1+5*tan(x)^2)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$5 \left(\tan^{4}\left(x \right)\right) \sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}-\frac{14 \left(\tan^{2}\left(x \right)\right) \sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}{3}+\frac{223 \sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}{15}-32 \arctan \left(\frac{\sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}{2}\right)$&$61$\\ default&$5 \left(\tan^{4}\left(x \right)\right) \sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}-\frac{14 \left(\tan^{2}\left(x \right)\right) \sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}{3}+\frac{223 \sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}{15}-32 \arctan \left(\frac{\sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}{2}\right)$&$61$\\ \hline \end{longtable}"," ",0,"5*tan(x)^4*(1+5*tan(x)^2)^(1/2)-14/3*tan(x)^2*(1+5*tan(x)^2)^(1/2)+223/15*(1+5*tan(x)^2)^(1/2)-32*arctan(1/2*(1+5*tan(x)^2)^(1/2))","A"
441,1,41,40,0.087000," ","int(tan(x)/(1+5*tan(x)^2)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\arctan \left(\frac{\sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}{2}\right)}{32}+\frac{1}{16 \sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}-\frac{1}{12 \left(1+5 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}$&$41$\\ default&$\frac{\arctan \left(\frac{\sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}{2}\right)}{32}+\frac{1}{16 \sqrt{1+5 \left(\tan^{2}\left(x \right)\right)}}-\frac{1}{12 \left(1+5 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}$&$41$\\ \hline \end{longtable}"," ",0,"1/32*arctan(1/2*(1+5*tan(x)^2)^(1/2))+1/16/(1+5*tan(x)^2)^(1/2)-1/12/(1+5*tan(x)^2)^(3/2)","A"
442,0,0,110,0.049000," ","int(tan(x)/(a^3+b^3*tan(x)^2)^(1/3),x)","\[\int \frac{\tan \left(x \right)}{\left(a^{3}+b^{3} \left(\tan^{2}\left(x \right)\right)\right)^{\frac{1}{3}}}\, dx\]"," ",0,"int(tan(x)/(a^3+b^3*tan(x)^2)^(1/3),x)","F"
443,0,0,58,0.039000," ","int(tan(x)*(1-7*tan(x)^2)^(2/3),x)","\[\int \tan \left(x \right) \left(1-7 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{2}{3}}\, dx\]"," ",0,"int(tan(x)*(1-7*tan(x)^2)^(2/3),x)","F"
444,0,0,48,0.046000," ","int(cot(x)/(a^4+b^4*csc(x)^2)^(1/4),x)","\[\int \frac{\cot \left(x \right)}{\left(a^{4}+b^{4} \left(\csc^{2}\left(x \right)\right)\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(cot(x)/(a^4+b^4*csc(x)^2)^(1/4),x)","F"
445,0,0,50,0.049000," ","int(cot(x)/(a^4-b^4*csc(x)^2)^(1/4),x)","\[\int \frac{\cot \left(x \right)}{\left(a^{4}-b^{4} \left(\csc^{2}\left(x \right)\right)\right)^{\frac{1}{4}}}\, dx\]"," ",0,"int(cot(x)/(a^4-b^4*csc(x)^2)^(1/4),x)","F"
446,0,0,108,180.000000," ","int(tan(x)*((1-3*sec(x)^2)^(1/3)*sin(x)^2+3*tan(x)^2)/cos(x)^2/(1-3*sec(x)^2)^(5/6)/(1-(1-3*sec(x)^2)^(1/2)),x)","\[\int \frac{\tan \left(x \right) \left(\left(1-3 \left(\sec^{2}\left(x \right)\right)\right)^{\frac{1}{3}} \left(\sin^{2}\left(x \right)\right)+3 \left(\tan^{2}\left(x \right)\right)\right)}{\cos \left(x \right)^{2} \left(1-3 \left(\sec^{2}\left(x \right)\right)\right)^{\frac{5}{6}} \left(1-\sqrt{1-3 \left(\sec^{2}\left(x \right)\right)}\right)}\, dx\]"," ",0,"int(tan(x)*((1-3*sec(x)^2)^(1/3)*sin(x)^2+3*tan(x)^2)/cos(x)^2/(1-3*sec(x)^2)^(5/6)/(1-(1-3*sec(x)^2)^(1/2)),x)","F"
447,1,559,78,1.023000," ","int((-cos(2*x)+2*tan(x)^2)/cos(x)^2/(tan(x)*tan(2*x))^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{2}\, \sqrt{4}\, \left(-1+\cos \left(x \right)\right)^{2} \left(-48 \left(\cos^{4}\left(x \right)\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \cos \left(x \right) \sqrt{4}\, \left(-1+\cos \left(x \right)\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right)^{2}}\right)+22 \left(\cos^{4}\left(x \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}-168 \left(\cos^{4}\left(x \right)\right) \ln \left(-\frac{4 \left(\left(\cos^{2}\left(x \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}-2 \left(\cos^{2}\left(x \right)\right)+\cos \left(x \right)-\sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}+1\right)}{\sin \left(x \right)^{2}}\right)+33 \left(\cos^{4}\left(x \right)\right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(x \right)\right)-3 \cos \left(x \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right)^{2}}\right)+201 \left(\cos^{4}\left(x \right)\right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(x \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}-2 \left(\cos^{2}\left(x \right)\right)+\cos \left(x \right)-\sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}+1\right)}{\sin \left(x \right)^{2}}\right)+48 \left(\cos^{3}\left(x \right)\right) \sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \cos \left(x \right) \sqrt{4}\, \left(-1+\cos \left(x \right)\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right)^{2}}\right)+168 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{4 \left(\left(\cos^{2}\left(x \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}-2 \left(\cos^{2}\left(x \right)\right)+\cos \left(x \right)-\sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}+1\right)}{\sin \left(x \right)^{2}}\right)-33 \left(\cos^{3}\left(x \right)\right) \arctanh \left(\frac{\sqrt{4}\, \left(2 \left(\cos^{2}\left(x \right)\right)-3 \cos \left(x \right)+1\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right)^{2}}\right)-201 \left(\cos^{3}\left(x \right)\right) \ln \left(-\frac{2 \left(\left(\cos^{2}\left(x \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}-2 \left(\cos^{2}\left(x \right)\right)+\cos \left(x \right)-\sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}+1\right)}{\sin \left(x \right)^{2}}\right)-36 \left(\cos^{2}\left(x \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}+8 \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\right)}{96 \cos \left(x \right)^{3} \sin \left(x \right)^{3} \left(\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}\right)^{\frac{3}{2}} \left(\frac{\sin^{2}\left(x \right)}{2 \left(\cos^{2}\left(x \right)\right)-1}\right)^{\frac{3}{2}}}$&$559$\\ \hline \end{longtable}"," ",0,"-1/96*2^(1/2)*4^(1/2)*(-1+cos(x))^2*(-48*cos(x)^4*2^(1/2)*arctanh(1/2*2^(1/2)*cos(x)*4^(1/2)*(-1+cos(x))/((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)/sin(x)^2)+22*cos(x)^4*((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)-168*cos(x)^4*ln(-4*(cos(x)^2*((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)-2*cos(x)^2+cos(x)-((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)+1)/sin(x)^2)+33*cos(x)^4*arctanh(1/2*4^(1/2)*(2*cos(x)^2-3*cos(x)+1)/((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)/sin(x)^2)+201*cos(x)^4*ln(-2*(cos(x)^2*((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)-2*cos(x)^2+cos(x)-((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)+1)/sin(x)^2)+48*cos(x)^3*2^(1/2)*arctanh(1/2*2^(1/2)*cos(x)*4^(1/2)*(-1+cos(x))/((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)/sin(x)^2)+168*cos(x)^3*ln(-4*(cos(x)^2*((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)-2*cos(x)^2+cos(x)-((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)+1)/sin(x)^2)-33*cos(x)^3*arctanh(1/2*4^(1/2)*(2*cos(x)^2-3*cos(x)+1)/((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)/sin(x)^2)-201*cos(x)^3*ln(-2*(cos(x)^2*((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)-2*cos(x)^2+cos(x)-((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)+1)/sin(x)^2)-36*cos(x)^2*((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)+8*((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2))/cos(x)^3/sin(x)^3/((2*cos(x)^2-1)/(1+cos(x))^2)^(3/2)/(sin(x)^2/(2*cos(x)^2-1))^(3/2)","B"
448,1,127,99,0.511000," ","int(tan(x)/(a^3-b^3*cos(x)^n)^(4/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\frac{\ln \left(a -\left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{1}{3}}\right)}{a^{4}}+\frac{-\frac{\ln \left(a^{2}+a \left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{1}{3}}+\left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{2}{3}}\right)}{2}+\sqrt{3}\, \arctan \left(\frac{\left(a +2 \left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{1}{3}}\right) \sqrt{3}}{3 a}\right)}{a^{4}}+\frac{3}{a^{3} \left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{1}{3}}}}{n}$&$127$\\ default&$-\frac{\frac{\ln \left(a -\left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{1}{3}}\right)}{a^{4}}+\frac{-\frac{\ln \left(a^{2}+a \left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{1}{3}}+\left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{2}{3}}\right)}{2}+\sqrt{3}\, \arctan \left(\frac{\left(a +2 \left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{1}{3}}\right) \sqrt{3}}{3 a}\right)}{a^{4}}+\frac{3}{a^{3} \left(a^{3}-b^{3} \left(\cos^{n}\left(x \right)\right)\right)^{\frac{1}{3}}}}{n}$&$127$\\ \hline \end{longtable}"," ",0,"-1/n*(1/a^4*ln(a-(a^3-b^3*cos(x)^n)^(1/3))+1/a^4*(-1/2*ln(a^2+a*(a^3-b^3*cos(x)^n)^(1/3)+(a^3-b^3*cos(x)^n)^(2/3))+3^(1/2)*arctan(1/3*(a+2*(a^3-b^3*cos(x)^n)^(1/3))/a*3^(1/2)))+3/a^3/(a^3-b^3*cos(x)^n)^(1/3))","A"
449,0,0,74,0.170000," ","int((1+2*cos(x)^9)^(5/6)*tan(x),x)","\[\int \left(1+2 \left(\cos^{9}\left(x \right)\right)\right)^{\frac{5}{6}} \tan \left(x \right)\, dx\]"," ",0,"int((1+2*cos(x)^9)^(5/6)*tan(x),x)","F"
450,0,0,37,0.962000," ","int(cot(x)*sin(x)^9/(2-5*sin(x)^3)^(4/3),x)","\[\int \frac{\cot \left(x \right) \left(\sin^{9}\left(x \right)\right)}{\left(2-5 \left(\sin^{3}\left(x \right)\right)\right)^{\frac{4}{3}}}\, dx\]"," ",0,"int(cot(x)*sin(x)^9/(2-5*sin(x)^3)^(4/3),x)","F"
451,1,26,16,0.099000," ","int(tan(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{3 \left(1-8 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{1}{3}}}{16}-\frac{3 \left(1-8 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{2}{3}}}{32}$&$26$\\ default&$-\frac{3 \left(1-8 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{1}{3}}}{16}-\frac{3 \left(1-8 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{2}{3}}}{32}$&$26$\\ \hline \end{longtable}"," ",0,"-3/16*(1-8*tan(x)^2)^(1/3)-3/32*(1-8*tan(x)^2)^(2/3)","A"
452,0,0,23,0.778000," ","int(cot(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x)","\[\int \frac{\cot \left(x \right) \left(1+\left(1-8 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{1}{3}}\right)}{\cos \left(x \right)^{2} \left(1-8 \left(\tan^{2}\left(x \right)\right)\right)^{\frac{2}{3}}}\, dx\]"," ",0,"int(cot(x)*(1+(1-8*tan(x)^2)^(1/3))/cos(x)^2/(1-8*tan(x)^2)^(2/3),x)","F"
453,0,0,81,1.085000," ","int((5*cos(x)^2-(-1+5*sin(x)^2)^(1/2))*tan(x)/(-1+5*sin(x)^2)^(1/4)/(2+(-1+5*sin(x)^2)^(1/2)),x)","\[\int \frac{\left(5 \left(\cos^{2}\left(x \right)\right)-\sqrt{-1+5 \left(\sin^{2}\left(x \right)\right)}\right) \tan \left(x \right)}{\left(-1+5 \left(\sin^{2}\left(x \right)\right)\right)^{\frac{1}{4}} \left(2+\sqrt{-1+5 \left(\sin^{2}\left(x \right)\right)}\right)}\, dx\]"," ",0,"int((5*cos(x)^2-(-1+5*sin(x)^2)^(1/2))*tan(x)/(-1+5*sin(x)^2)^(1/4)/(2+(-1+5*sin(x)^2)^(1/2)),x)","F"
454,0,0,17,0.260000," ","int(cos(x)^4*cos(2*x)^(2/3)*tan(x),x)","\[\int \left(\cos^{4}\left(x \right)\right) \left(\cos^{\frac{2}{3}}\left(2 x \right)\right) \tan \left(x \right)\, dx\]"," ",0,"int(cos(x)^4*cos(2*x)^(2/3)*tan(x),x)","F"
455,0,0,77,0.442000," ","int(sin(x)^6*tan(x)/cos(2*x)^(3/4),x)","\[\int \frac{\left(\sin^{6}\left(x \right)\right) \tan \left(x \right)}{\cos \left(2 x \right)^{\frac{3}{4}}}\, dx\]"," ",0,"int(sin(x)^6*tan(x)/cos(2*x)^(3/4),x)","F"
456,1,88,15,0.430000," ","int((tan(x)*tan(2*x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{4}\, \sqrt{\frac{1-\left(\cos^{2}\left(x \right)\right)}{2 \left(\cos^{2}\left(x \right)\right)-1}}\, \sin \left(x \right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\, \arctanh \left(\frac{\sqrt{2}\, \cos \left(x \right) \sqrt{4}\, \left(-1+\cos \left(x \right)\right)}{2 \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\left(1+\cos \left(x \right)\right)^{2}}}\, \sin \left(x \right)^{2}}\right)}{2 \left(-1+\cos \left(x \right)\right)}$&$88$\\ \hline \end{longtable}"," ",0,"-1/2*4^(1/2)*((1-cos(x)^2)/(2*cos(x)^2-1))^(1/2)*sin(x)*((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)*arctanh(1/2*2^(1/2)*cos(x)*4^(1/2)*(-1+cos(x))/((2*cos(x)^2-1)/(1+cos(x))^2)^(1/2)/sin(x)^2)/(-1+cos(x))","B"
457,1,242,26,0.763000," ","int((cot(2*x)/cot(x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{2}\, \left(4 \EllipticPi \left(\frac{\sqrt{3+2 \sqrt{2}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, -\frac{1}{3+2 \sqrt{2}}, \frac{\sqrt{3-2 \sqrt{2}}}{\sqrt{3+2 \sqrt{2}}}\right)-2 \EllipticPi \left(\frac{\sqrt{3+2 \sqrt{2}}\, \left(-1+\cos \left(x \right)\right)}{\sin \left(x \right)}, \frac{1}{3+2 \sqrt{2}}, \frac{\sqrt{3-2 \sqrt{2}}}{\sqrt{3+2 \sqrt{2}}}\right)-\EllipticF \left(\frac{\left(-1+\cos \left(x \right)\right) \left(1+\sqrt{2}\right)}{\sin \left(x \right)}, 3-2 \sqrt{2}\right)\right) \left(2+\sqrt{2}\right) \cos \left(x \right) \left(\sin^{2}\left(x \right)\right) \sqrt{\frac{2 \left(\cos^{2}\left(x \right)\right)-1}{\cos \left(x \right)^{2}}}\, \sqrt{-\frac{2 \left(\cos \left(x \right) \sqrt{2}-\sqrt{2}-2 \cos \left(x \right)+1\right)}{1+\cos \left(x \right)}}\, \sqrt{\frac{\cos \left(x \right) \sqrt{2}-\sqrt{2}+2 \cos \left(x \right)-1}{1+\cos \left(x \right)}}}{2 \sqrt{3+2 \sqrt{2}}\, \left(1+\sqrt{2}\right) \left(-1+\cos \left(x \right)\right) \left(2 \left(\cos^{2}\left(x \right)\right)-1\right)}$&$242$\\ \hline \end{longtable}"," ",0,"1/2*2^(1/2)/(3+2*2^(1/2))^(1/2)/(1+2^(1/2))*(4*EllipticPi((3+2*2^(1/2))^(1/2)*(-1+cos(x))/sin(x),-1/(3+2*2^(1/2)),(3-2*2^(1/2))^(1/2)/(3+2*2^(1/2))^(1/2))-2*EllipticPi((3+2*2^(1/2))^(1/2)*(-1+cos(x))/sin(x),1/(3+2*2^(1/2)),(3-2*2^(1/2))^(1/2)/(3+2*2^(1/2))^(1/2))-EllipticF((-1+cos(x))*(1+2^(1/2))/sin(x),3-2*2^(1/2)))*(2+2^(1/2))*cos(x)*sin(x)^2*((2*cos(x)^2-1)/cos(x)^2)^(1/2)*(-2*(cos(x)*2^(1/2)-2^(1/2)-2*cos(x)+1)/(1+cos(x)))^(1/2)*((cos(x)*2^(1/2)-2^(1/2)+2*cos(x)-1)/(1+cos(x)))^(1/2)/(-1+cos(x))/(2*cos(x)^2-1)","C"
458,1,24,23,0.315000," ","int(1/x^5/(x^2+5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{20 x^{4}}+\frac{1}{50 x^{2}}+\frac{\ln \left(x \right)}{125}-\frac{\ln \left(x^{2}+5\right)}{250}$&$24$\\ norman&$\frac{-\frac{1}{20}+\frac{x^{2}}{50}}{x^{4}}+\frac{\ln \left(x \right)}{125}-\frac{\ln \left(x^{2}+5\right)}{250}$&$25$\\ risch&$\frac{-\frac{1}{20}+\frac{x^{2}}{50}}{x^{4}}+\frac{\ln \left(x \right)}{125}-\frac{\ln \left(x^{2}+5\right)}{250}$&$25$\\ meijerg&$-\frac{\ln \left(1+\frac{x^{2}}{5}\right)}{250}+\frac{\ln \left(x \right)}{125}-\frac{\ln \left(5\right)}{250}-\frac{1}{20 x^{4}}+\frac{1}{50 x^{2}}$&$30$\\ \hline \end{longtable}"," ",0,"-1/20/x^4+1/50/x^2+1/125*ln(x)-1/250*ln(x^2+5)","A"
459,1,29,28,0.322000," ","int(1/x^6/(x^2+5),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{25 x^{5}}+\frac{1}{75 x^{3}}-\frac{1}{125 x}-\frac{\arctan \left(\frac{x \sqrt{5}}{5}\right) \sqrt{5}}{625}$&$29$\\ risch&$\frac{-\frac{1}{125} x^{4}+\frac{1}{75} x^{2}-\frac{1}{25}}{x^{5}}-\frac{\arctan \left(\frac{x \sqrt{5}}{5}\right) \sqrt{5}}{625}$&$30$\\ meijerg&$\frac{\sqrt{5}\, \left(-\frac{2 \sqrt{5}}{x}+\frac{10 \sqrt{5}}{3 x^{3}}-\frac{10 \sqrt{5}}{x^{5}}-2 \arctan \left(\frac{x \sqrt{5}}{5}\right)\right)}{1250}$&$40$\\ \hline \end{longtable}"," ",0,"-1/25/x^5+1/75/x^3-1/125/x-1/625*arctan(1/5*x*5^(1/2))*5^(1/2)","A"
460,1,34,48,0.349000," ","int(1/x/(x^2-4)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{-\frac{1}{128} x^{4}+\frac{5}{64} x^{2}-\frac{11}{48}}{\left(x^{2}-4\right)^{3}}+\frac{\ln \left(x \right)}{256}-\frac{\ln \left(x^{2}-4\right)}{512}$&$34$\\ norman&$\frac{-\frac{1}{128} x^{4}+\frac{5}{64} x^{2}-\frac{11}{48}}{\left(x^{2}-4\right)^{3}}+\frac{\ln \left(x \right)}{256}-\frac{\ln \left(-2+x \right)}{512}-\frac{\ln \left(2+x \right)}{512}$&$38$\\ meijerg&$\frac{x^{2} \left(\frac{11}{16} x^{4}-\frac{27}{4} x^{2}+18\right)}{12288 \left(1-\frac{x^{2}}{4}\right)^{3}}-\frac{\ln \left(1-\frac{x^{2}}{4}\right)}{512}+\frac{11}{3072}+\frac{\ln \left(x \right)}{256}-\frac{\ln \left(2\right)}{256}+\frac{i \pi}{512}$&$51$\\ default&$\frac{\ln \left(x \right)}{256}-\frac{1}{1536 \left(-2+x \right)^{3}}+\frac{3}{2048 \left(-2+x \right)^{2}}-\frac{11}{4096 \left(-2+x \right)}-\frac{\ln \left(-2+x \right)}{512}+\frac{1}{1536 \left(2+x \right)^{3}}+\frac{3}{2048 \left(2+x \right)^{2}}+\frac{11}{4096 \left(2+x \right)}-\frac{\ln \left(2+x \right)}{512}$&$60$\\ \hline \end{longtable}"," ",0,"(-1/128*x^4+5/64*x^2-11/48)/(x^2-4)^3+1/256*ln(x)-1/512*ln(x^2-4)","A"
461,1,35,37,0.334000," ","int(1/x/(x^2-2)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{3 x^{2}-8}{12 \left(x^{2}-2\right)^{\frac{3}{2}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}}{\sqrt{x^{2}-2}}\right)}{8}$&$35$\\ default&$-\frac{1}{6 \left(x^{2}-2\right)^{\frac{3}{2}}}+\frac{1}{4 \sqrt{x^{2}-2}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}}{\sqrt{x^{2}-2}}\right)}{8}$&$37$\\ trager&$\frac{3 x^{2}-8}{12 \left(x^{2}-2\right)^{\frac{3}{2}}}-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(\frac{\sqrt{x^{2}-2}-\RootOf \left(\textit{\_Z}^{2}+2\right)}{x}\right)}{8}$&$47$\\ meijerg&$\frac{\sqrt{2}\, \left(-\mathrm{signum}\left(-1+\frac{x^{2}}{2}\right)\right)^{\frac{5}{2}} \left(-2 \sqrt{\pi}+\frac{\sqrt{\pi}\, \left(-6 x^{2}+16\right)}{8 \left(-\frac{x^{2}}{2}+1\right)^{\frac{3}{2}}}-\frac{3 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{-\frac{x^{2}}{2}+1}}{2}\right)}{2}+\frac{3 \left(\frac{8}{3}-3 \ln \left(2\right)+2 \ln \left(x \right)+i \pi \right) \sqrt{\pi}}{4}\right)}{12 \sqrt{\pi}\, \mathrm{signum}\left(-1+\frac{x^{2}}{2}\right)^{\frac{5}{2}}}$&$96$\\ \hline \end{longtable}"," ",0,"1/12*(3*x^2-8)/(x^2-2)^(3/2)-1/8*2^(1/2)*arctan(2^(1/2)/(x^2-2)^(1/2))","A"
462,1,46,46,0.349000," ","int((x^2-10)^(5/2)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(x^{2}-10\right)^{\frac{5}{2}}}{5}-\frac{10 \left(x^{2}-10\right)^{\frac{3}{2}}}{3}+100 \sqrt{x^{2}-10}+100 \sqrt{10}\, \arctan \left(\frac{\sqrt{10}}{\sqrt{x^{2}-10}}\right)$&$46$\\ trager&$\left(\frac{1}{5} x^{4}-\frac{22}{3} x^{2}+\frac{460}{3}\right) \sqrt{x^{2}-10}-100 \RootOf \left(\textit{\_Z}^{2}+10\right) \ln \left(\frac{\sqrt{x^{2}-10}+\RootOf \left(\textit{\_Z}^{2}+10\right)}{x}\right)$&$49$\\ meijerg&$-\frac{375 \sqrt{2}\, \sqrt{5}\, \mathrm{signum}\left(-1+\frac{x^{2}}{10}\right)^{\frac{5}{2}} \left(\frac{368 \sqrt{\pi}}{225}-\frac{4 \sqrt{\pi}\, \left(\frac{3}{25} x^{4}-\frac{22}{5} x^{2}+92\right) \sqrt{1-\frac{x^{2}}{10}}}{225}+\frac{16 \sqrt{\pi}\, \ln \left(\frac{1}{2}+\frac{\sqrt{1-\frac{x^{2}}{10}}}{2}\right)}{15}-\frac{8 \left(\frac{46}{15}-3 \ln \left(2\right)+2 \ln \left(x \right)-\ln \left(5\right)+i \pi \right) \sqrt{\pi}}{15}\right)}{4 \sqrt{\pi}\, \left(-\mathrm{signum}\left(-1+\frac{x^{2}}{10}\right)\right)^{\frac{5}{2}}}$&$108$\\ \hline \end{longtable}"," ",0,"1/5*(x^2-10)^(5/2)-10/3*(x^2-10)^(3/2)+100*(x^2-10)^(1/2)+100*10^(1/2)*arctan(10^(1/2)/(x^2-10)^(1/2))","A"
463,1,15,14,0.012000," ","int(x^(1+2*n),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x^{2+2 n}}{2+2 n}$&$15$\\ default&$\frac{x^{2+2 n}}{2+2 n}$&$16$\\ risch&$\frac{x \,x^{1+2 n}}{2+2 n}$&$16$\\ norman&$\frac{x \,{\mathrm e}^{\left(1+2 n \right) \ln \left(x \right)}}{2+2 n}$&$18$\\ \hline \end{longtable}"," ",0,"1/2*x^(2+2*n)/(1+n)","A"
464,1,30,38,0.328000," ","int(x^7/(x^2-5)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-75 x^{2}+\frac{1}{2} x^{6}+\frac{1125}{4}}{\left(x^{2}-5\right)^{2}}+\frac{15 \ln \left(x^{2}-5\right)}{2}$&$30$\\ risch&$\frac{x^{2}}{2}+\frac{-\frac{75 x^{2}}{2}+\frac{625}{4}}{\left(x^{2}-5\right)^{2}}+\frac{15 \ln \left(x^{2}-5\right)}{2}$&$30$\\ default&$\frac{x^{2}}{2}-\frac{125}{4 \left(x^{2}-5\right)^{2}}-\frac{75}{2 \left(x^{2}-5\right)}+\frac{15 \ln \left(x^{2}-5\right)}{2}$&$33$\\ meijerg&$\frac{x^{2} \left(\frac{4}{25} x^{4}-\frac{18}{5} x^{2}+12\right)}{8 \left(-\frac{x^{2}}{5}+1\right)^{2}}+\frac{15 \ln \left(-\frac{x^{2}}{5}+1\right)}{2}$&$38$\\ \hline \end{longtable}"," ",0,"(-75*x^2+1/2*x^6+1125/4)/(x^2-5)^2+15/2*ln(x^2-5)","A"
465,1,21,34,0.335000," ","int((3*x^5-4*x^3)/(x^2-1)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{-\frac{3}{4} x^{4}+\frac{7}{6} x^{2}-\frac{7}{24}}{\left(x^{2}-1\right)^{4}}$&$21$\\ risch&$\frac{-\frac{3}{4} x^{4}+\frac{7}{6} x^{2}-\frac{7}{24}}{\left(x^{2}-1\right)^{4}}$&$21$\\ gosper&$-\frac{18 x^{4}-28 x^{2}+7}{24 \left(x^{2}-1\right)^{4}}$&$22$\\ meijerg&$-\frac{x^{6} \left(-x^{2}+4\right)}{8 \left(-x^{2}+1\right)^{4}}+\frac{x^{4} \left(x^{4}-4 x^{2}+6\right)}{6 \left(-x^{2}+1\right)^{4}}$&$47$\\ default&$\frac{1}{128 \left(-1+x \right)^{4}}-\frac{11}{192 \left(-1+x \right)^{3}}-\frac{27}{256 \left(-1+x \right)^{2}}+\frac{27}{256 \left(-1+x \right)}+\frac{1}{128 \left(1+x \right)^{4}}+\frac{11}{192 \left(1+x \right)^{3}}-\frac{27}{256 \left(1+x \right)^{2}}-\frac{27}{256 \left(1+x \right)}$&$58$\\ \hline \end{longtable}"," ",0,"(-3/4*x^4+7/6*x^2-7/24)/(x^2-1)^4","A"
466,1,17,19,0.293000," ","int(x^3*(x^2+1)^(9/14),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{7 \left(x^{2}+1\right)^{\frac{23}{14}} \left(23 x^{2}-14\right)}{851}$&$17$\\ meijerg&$\frac{x^{4} \hypergeom \left(\left[-\frac{9}{14}, 2\right], \left[3\right], -x^{2}\right)}{4}$&$17$\\ trager&$\left(\frac{7}{37} x^{4}+\frac{63}{851} x^{2}-\frac{98}{851}\right) \left(x^{2}+1\right)^{\frac{9}{14}}$&$21$\\ risch&$\frac{7 \left(x^{2}+1\right)^{\frac{9}{14}} \left(23 x^{4}+9 x^{2}-14\right)}{851}$&$22$\\ \hline \end{longtable}"," ",0,"7/851*(x^2+1)^(23/14)*(23*x^2-14)","A"
467,1,22,28,0.326000," ","int(x^5/(x^2-4)^(13/6),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline trager&$\frac{\frac{3}{5} x^{4}-\frac{144}{5} x^{2}+\frac{3456}{35}}{\left(x^{2}-4\right)^{\frac{7}{6}}}$&$22$\\ risch&$\frac{\frac{3}{5} x^{4}-\frac{144}{5} x^{2}+\frac{3456}{35}}{\left(x^{2}-4\right)^{\frac{7}{6}}}$&$22$\\ gosper&$\frac{3 \left(-2+x \right) \left(2+x \right) \left(7 x^{4}-336 x^{2}+1152\right)}{35 \left(x^{2}-4\right)^{\frac{13}{6}}}$&$28$\\ meijerg&$\frac{2^{\frac{2}{3}} \left(-\mathrm{signum}\left(-1+\frac{x^{2}}{4}\right)\right)^{\frac{13}{6}} x^{6} \hypergeom \left(\left[\frac{13}{6}, 3\right], \left[4\right], \frac{x^{2}}{4}\right)}{192 \mathrm{signum}\left(-1+\frac{x^{2}}{4}\right)^{\frac{13}{6}}}$&$42$\\ \hline \end{longtable}"," ",0,"3/35*(7*x^4-336*x^2+1152)/(x^2-4)^(7/6)","A"
468,1,20,25,0.295000," ","int(1/(2*x^2+1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x \left(4 x^{2}+3\right)}{3 \left(2 x^{2}+1\right)^{\frac{3}{2}}}$&$20$\\ trager&$\frac{x \left(4 x^{2}+3\right)}{3 \left(2 x^{2}+1\right)^{\frac{3}{2}}}$&$20$\\ meijerg&$\frac{x \left(4 x^{2}+3\right)}{3 \left(2 x^{2}+1\right)^{\frac{3}{2}}}$&$20$\\ risch&$\frac{x \left(4 x^{2}+3\right)}{3 \left(2 x^{2}+1\right)^{\frac{3}{2}}}$&$20$\\ default&$\frac{x}{3 \left(2 x^{2}+1\right)^{\frac{3}{2}}}+\frac{2 x}{3 \sqrt{2 x^{2}+1}}$&$26$\\ \hline \end{longtable}"," ",0,"1/3*x*(4*x^2+3)/(2*x^2+1)^(3/2)","A"
469,1,23,33,0.389000," ","int(1/(x^2-2*x-1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x^{3}-3 x^{2}+2}{6 \left(x^{2}-2 x -1\right)^{\frac{3}{2}}}$&$23$\\ trager&$\frac{x^{3}-3 x^{2}+2}{6 \left(x^{2}-2 x -1\right)^{\frac{3}{2}}}$&$23$\\ risch&$\frac{x^{3}-3 x^{2}+2}{6 \left(x^{2}-2 x -1\right)^{\frac{3}{2}}}$&$23$\\ default&$-\frac{2 x -2}{12 \left(x^{2}-2 x -1\right)^{\frac{3}{2}}}+\frac{2 x -2}{12 \sqrt{x^{2}-2 x -1}}$&$36$\\ \hline \end{longtable}"," ",0,"1/6*(x^3-3*x^2+2)/(x^2-2*x-1)^(3/2)","A"
470,1,23,35,0.343000," ","int(1/x^4/(x^2-8)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{x^{4}-4 x^{2}-8}{192 x^{3} \sqrt{x^{2}-8}}$&$23$\\ trager&$-\frac{x^{4}-4 x^{2}-8}{192 x^{3} \sqrt{x^{2}-8}}$&$23$\\ risch&$-\frac{x^{4}-4 x^{2}-8}{192 x^{3} \sqrt{x^{2}-8}}$&$23$\\ default&$\frac{1}{24 x^{3} \sqrt{x^{2}-8}}+\frac{1}{48 x \sqrt{x^{2}-8}}-\frac{x}{192 \sqrt{x^{2}-8}}$&$36$\\ meijerg&$-\frac{\sqrt{2}\, \left(-\mathrm{signum}\left(-1+\frac{x^{2}}{8}\right)\right)^{\frac{3}{2}} \left(-\frac{1}{8} x^{4}+\frac{1}{2} x^{2}+1\right)}{96 \mathrm{signum}\left(-1+\frac{x^{2}}{8}\right)^{\frac{3}{2}} x^{3} \sqrt{1-\frac{x^{2}}{8}}}$&$52$\\ \hline \end{longtable}"," ",0,"-1/192*(x^4-4*x^2-8)/x^3/(x^2-8)^(1/2)","A"
471,1,16,16,0.291000," ","int((x^2+5)^2/x^(13/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\frac{3}{2} x^{4}-\frac{15}{2} x^{2}-\frac{15}{2}}{x^{\frac{10}{3}}}$&$16$\\ trager&$\frac{\frac{3}{2} x^{4}-\frac{15}{2} x^{2}-\frac{15}{2}}{x^{\frac{10}{3}}}$&$16$\\ risch&$\frac{\frac{3}{2} x^{4}-\frac{15}{2} x^{2}-\frac{15}{2}}{x^{\frac{10}{3}}}$&$16$\\ derivativedivides&$-\frac{15}{2 x^{\frac{10}{3}}}-\frac{15}{2 x^{\frac{4}{3}}}+\frac{3 x^{\frac{2}{3}}}{2}$&$17$\\ default&$-\frac{15}{2 x^{\frac{10}{3}}}-\frac{15}{2 x^{\frac{4}{3}}}+\frac{3 x^{\frac{2}{3}}}{2}$&$17$\\ \hline \end{longtable}"," ",0,"3/2*(x^4-5*x^2-5)/x^(10/3)","A"
472,1,47,46,0.327000," ","int(1/x^7/(x^2+1)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{6 x^{6}}+\frac{3}{4 x^{4}}-\frac{3}{x^{2}}-\frac{1}{4 \left(x^{2}+1\right)^{2}}-\frac{2}{x^{2}+1}-10 \ln \left(x \right)+5 \ln \left(x^{2}+1\right)$&$47$\\ norman&$\frac{-\frac{1}{6}-5 x^{8}-\frac{15}{2} x^{6}+\frac{5}{12} x^{2}-\frac{5}{3} x^{4}}{x^{6} \left(x^{2}+1\right)^{2}}-10 \ln \left(x \right)+5 \ln \left(x^{2}+1\right)$&$47$\\ risch&$\frac{-\frac{1}{6}-5 x^{8}-\frac{15}{2} x^{6}+\frac{5}{12} x^{2}-\frac{5}{3} x^{4}}{x^{6} \left(x^{2}+1\right)^{2}}-10 \ln \left(x \right)+5 \ln \left(x^{2}+1\right)$&$47$\\ meijerg&$\frac{x^{2} \left(9 x^{2}+10\right)}{4 \left(x^{2}+1\right)^{2}}+5 \ln \left(x^{2}+1\right)-\frac{9}{4}-10 \ln \left(x \right)-\frac{1}{6 x^{6}}+\frac{3}{4 x^{4}}-\frac{3}{x^{2}}$&$49$\\ \hline \end{longtable}"," ",0,"-1/6/x^6+3/4/x^4-3/x^2-1/4/(x^2+1)^2-2/(x^2+1)-10*ln(x)+5*ln(x^2+1)","A"
473,1,22,19,0.281000," ","int(((x^2+2)/x^2)^(7/9)/(x^2+2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{9 x \left(\frac{x^{2}+2}{x^{2}}\right)^{\frac{7}{9}}}{10 \sqrt{x^{2}+2}}$&$22$\\ risch&$-\frac{9 x \left(\frac{x^{2}+2}{x^{2}}\right)^{\frac{7}{9}}}{10 \sqrt{x^{2}+2}}$&$22$\\ \hline \end{longtable}"," ",0,"-9/10*x/(x^2+2)^(1/2)*((x^2+2)/x^2)^(7/9)","A"
474,1,28,36,0.352000," ","int(x^4/(-x^2+10^(1/2))^(9/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x^{5} \left(-2 x^{2}+7 \sqrt{10}\right)}{350 \left(-x^{2}+\sqrt{10}\right)^{\frac{7}{2}}}$&$28$\\ meijerg&$\frac{10^{\frac{3}{4}} x^{5} \left(-\frac{\sqrt{2}\, \sqrt{5}\, x^{2}}{5}+7\right)}{35000 \left(1-\frac{\sqrt{10}\, x^{2}}{10}\right)^{\frac{7}{2}}}$&$34$\\ risch&$\frac{2 x^{7}-7 \sqrt{10}\, x^{5}}{350 \left(x^{2}-\sqrt{10}\right)^{3} \sqrt{-x^{2}+\sqrt{10}}}$&$39$\\ trager&$-\frac{2 \sqrt{10}\, \left(\sqrt{10}\, x^{2}-35\right) x^{5} \sqrt{-x^{2}+\sqrt{10}}}{35 \left(\sqrt{10}\, x^{2}-10\right)^{4}}$&$40$\\ default&$\frac{x^{3}}{4 \left(-x^{2}+\sqrt{10}\right)^{\frac{7}{2}}}-\frac{3 \sqrt{10}\, \left(\frac{x}{6 \left(-x^{2}+\sqrt{10}\right)^{\frac{7}{2}}}-\frac{\sqrt{10}\, \left(\frac{x \sqrt{10}}{70 \left(-x^{2}+\sqrt{10}\right)^{\frac{7}{2}}}+\frac{3 \sqrt{10}\, \left(\frac{x \sqrt{10}}{50 \left(-x^{2}+\sqrt{10}\right)^{\frac{5}{2}}}+\frac{2 \sqrt{10}\, \left(\frac{x \sqrt{10}}{30 \left(-x^{2}+\sqrt{10}\right)^{\frac{3}{2}}}+\frac{x}{15 \sqrt{-x^{2}+\sqrt{10}}}\right)}{25}\right)}{35}\right)}{6}\right)}{4}$&$121$\\ \hline \end{longtable}"," ",0,"1/350*x^5*(-2*x^2+7*10^(1/2))/(-x^2+10^(1/2))^(7/2)","A"
475,1,22,21,0.314000," ","int(x^2/(-x^2+3)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\arcsin \left(\frac{x \sqrt{3}}{3}\right)+\frac{x}{\sqrt{-x^{2}+3}}$&$22$\\ risch&$-\arcsin \left(\frac{x \sqrt{3}}{3}\right)+\frac{x}{\sqrt{-x^{2}+3}}$&$22$\\ meijerg&$\frac{i \left(-\frac{i \sqrt{\pi}\, x \sqrt{3}}{3 \sqrt{-\frac{x^{2}}{3}+1}}+i \sqrt{\pi}\, \arcsin \left(\frac{x \sqrt{3}}{3}\right)\right)}{\sqrt{\pi}}$&$40$\\ trager&$-\frac{x \sqrt{-x^{2}+3}}{x^{2}-3}+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{2}+1\right) \sqrt{-x^{2}+3}+x \right)$&$48$\\ \hline \end{longtable}"," ",0,"-arcsin(1/3*x*3^(1/2))+x/(-x^2+3)^(1/2)","A"
476,1,32,32,0.326000," ","int((-x^2+25)^(3/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{4 x^{4}-125 x^{2}+625}{3 x^{3} \sqrt{-x^{2}+25}}+\arcsin \left(\frac{x}{5}\right)$&$32$\\ meijerg&$-\frac{3 i \left(-\frac{1000 i \sqrt{\pi}\, \left(-\frac{4 x^{2}}{25}+1\right) \sqrt{-\frac{x^{2}}{25}+1}}{9 x^{3}}+\frac{8 i \sqrt{\pi}\, \arcsin \left(\frac{x}{5}\right)}{3}\right)}{8 \sqrt{\pi}}$&$43$\\ trager&$\frac{\left(4 x^{2}-25\right) \sqrt{-x^{2}+25}}{3 x^{3}}+\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{2}+1\right) x +\sqrt{-x^{2}+25}\right)$&$50$\\ default&$-\frac{\left(-x^{2}+25\right)^{\frac{5}{2}}}{75 x^{3}}+\frac{2 \left(-x^{2}+25\right)^{\frac{5}{2}}}{1875 x}+\frac{2 x \left(-x^{2}+25\right)^{\frac{3}{2}}}{1875}+\frac{\sqrt{-x^{2}+25}\, x}{25}+\arcsin \left(\frac{x}{5}\right)$&$58$\\ \hline \end{longtable}"," ",0,"-1/3*(4*x^4-125*x^2+625)/x^3/(-x^2+25)^(1/2)+arcsin(1/5*x)","A"
477,1,25,37,0.314000," ","int(1/(-2*x^2+1)^(7/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{x \left(32 x^{4}-40 x^{2}+15\right)}{15 \left(-2 x^{2}+1\right)^{\frac{5}{2}}}$&$25$\\ meijerg&$\frac{x \left(32 x^{4}-40 x^{2}+15\right)}{15 \left(-2 x^{2}+1\right)^{\frac{5}{2}}}$&$25$\\ trager&$-\frac{\left(32 x^{4}-40 x^{2}+15\right) x \sqrt{-2 x^{2}+1}}{15 \left(2 x^{2}-1\right)^{3}}$&$34$\\ risch&$\frac{x \left(32 x^{4}-40 x^{2}+15\right)}{15 \left(2 x^{2}-1\right)^{2} \sqrt{-2 x^{2}+1}}$&$34$\\ default&$\frac{x}{5 \left(-2 x^{2}+1\right)^{\frac{5}{2}}}+\frac{4 x}{15 \left(-2 x^{2}+1\right)^{\frac{3}{2}}}+\frac{8 x}{15 \sqrt{-2 x^{2}+1}}$&$38$\\ \hline \end{longtable}"," ",0,"1/15*x*(32*x^4-40*x^2+15)/(-2*x^2+1)^(5/2)","A"
478,1,28,35,0.443000," ","int(1/(-x^2+6*x-7)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{x^{3}-9 x^{2}+24 x -18}{6 \left(-x^{2}+6 x -7\right)^{\frac{3}{2}}}$&$28$\\ trager&$-\frac{\left(x^{3}-9 x^{2}+24 x -18\right) \sqrt{-x^{2}+6 x -7}}{6 \left(x^{2}-6 x +7\right)^{2}}$&$38$\\ risch&$\frac{x^{3}-9 x^{2}+24 x -18}{6 \left(x^{2}-6 x +7\right) \sqrt{-x^{2}+6 x -7}}$&$38$\\ default&$-\frac{-2 x +6}{12 \left(-x^{2}+6 x -7\right)^{\frac{3}{2}}}-\frac{-2 x +6}{12 \sqrt{-x^{2}+6 x -7}}$&$40$\\ \hline \end{longtable}"," ",0,"-1/6*(x^3-9*x^2+24*x-18)/(-x^2+6*x-7)^(3/2)","A"
479,1,33,32,0.363000," ","int((-2*x^2-2*x+1)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x -3 x^{2}+2 x^{3}+4 x^{4}-\frac{12}{5} x^{5}-4 x^{6}-\frac{8}{7} x^{7}$&$33$\\ norman&$x -3 x^{2}+2 x^{3}+4 x^{4}-\frac{12}{5} x^{5}-4 x^{6}-\frac{8}{7} x^{7}$&$33$\\ risch&$x -3 x^{2}+2 x^{3}+4 x^{4}-\frac{12}{5} x^{5}-4 x^{6}-\frac{8}{7} x^{7}$&$33$\\ gosper&$-\frac{x \left(40 x^{6}+140 x^{5}+84 x^{4}-140 x^{3}-70 x^{2}+105 x -35\right)}{35}$&$34$\\ \hline \end{longtable}"," ",0,"x-3*x^2+2*x^3+4*x^4-12/5*x^5-4*x^6-8/7*x^7","A"
480,1,30,29,0.363000," ","int((-1+5*x)*(x^2-x-1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-x +\frac{3}{2} x^{2}+\frac{11}{3} x^{3}-\frac{3}{4} x^{4}-\frac{11}{5} x^{5}+\frac{5}{6} x^{6}$&$30$\\ default&$-x +\frac{3}{2} x^{2}+\frac{11}{3} x^{3}-\frac{3}{4} x^{4}-\frac{11}{5} x^{5}+\frac{5}{6} x^{6}$&$30$\\ norman&$-x +\frac{3}{2} x^{2}+\frac{11}{3} x^{3}-\frac{3}{4} x^{4}-\frac{11}{5} x^{5}+\frac{5}{6} x^{6}$&$30$\\ risch&$-x +\frac{3}{2} x^{2}+\frac{11}{3} x^{3}-\frac{3}{4} x^{4}-\frac{11}{5} x^{5}+\frac{5}{6} x^{6}$&$30$\\ \hline \end{longtable}"," ",0,"-x+3/2*x^2+11/3*x^3-3/4*x^4-11/5*x^5+5/6*x^6","A"
481,1,30,39,0.447000," ","int((1+3*x)/(2*x^2-8*x+1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{8 x^{3}-48 x^{2}+54 x -1}{42 \left(2 x^{2}-8 x +1\right)^{\frac{3}{2}}}$&$30$\\ trager&$\frac{8 x^{3}-48 x^{2}+54 x -1}{42 \left(2 x^{2}-8 x +1\right)^{\frac{3}{2}}}$&$30$\\ risch&$\frac{8 x^{3}-48 x^{2}+54 x -1}{42 \left(2 x^{2}-8 x +1\right)^{\frac{3}{2}}}$&$30$\\ default&$-\frac{4 x -8}{12 \left(2 x^{2}-8 x +1\right)^{\frac{3}{2}}}+\frac{4 x -8}{42 \sqrt{2 x^{2}-8 x +1}}-\frac{1}{2 \left(2 x^{2}-8 x +1\right)^{\frac{3}{2}}}$&$54$\\ \hline \end{longtable}"," ",0,"1/42*(8*x^3-48*x^2+54*x-1)/(2*x^2-8*x+1)^(3/2)","A"
482,1,30,37,0.395000," ","int((8*x^3-8*x-1)/(-4*x^2+2*x+1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{488 x^{3}-216 x^{2}-156 x -27}{75 \left(-4 x^{2}+2 x +1\right)^{\frac{3}{2}}}$&$30$\\ trager&$\frac{\left(488 x^{3}-216 x^{2}-156 x -27\right) \sqrt{-4 x^{2}+2 x +1}}{75 \left(4 x^{2}-2 x -1\right)^{2}}$&$42$\\ risch&$-\frac{488 x^{3}-216 x^{2}-156 x -27}{75 \left(4 x^{2}-2 x -1\right) \sqrt{-4 x^{2}+2 x +1}}$&$42$\\ default&$\frac{2 x^{2}}{\left(-4 x^{2}+2 x +1\right)^{\frac{3}{2}}}-\frac{x}{4 \left(-4 x^{2}+2 x +1\right)^{\frac{3}{2}}}-\frac{49}{48 \left(-4 x^{2}+2 x +1\right)^{\frac{3}{2}}}+\frac{\frac{61}{240}-\frac{61 x}{60}}{\left(-4 x^{2}+2 x +1\right)^{\frac{3}{2}}}+\frac{\frac{61}{150}-\frac{122 x}{75}}{\sqrt{-4 x^{2}+2 x +1}}$&$86$\\ \hline \end{longtable}"," ",0,"1/75*(488*x^3-216*x^2-156*x-27)/(-4*x^2+2*x+1)^(3/2)","A"
483,1,56,65,0.383000," ","int(x^2*cos(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{5 x \cos \left(x \right)}{4}+\frac{5 \left(x^{2}-2\right) \sin \left(x \right)}{8}+\frac{x \cos \left(5 x \right)}{200}+\frac{\left(25 x^{2}-2\right) \sin \left(5 x \right)}{2000}+\frac{5 x \cos \left(3 x \right)}{72}+\frac{5 \left(9 x^{2}-2\right) \sin \left(3 x \right)}{432}$&$56$\\ default&$\frac{x^{2} \left(\frac{8}{3}+\cos^{4}\left(x \right)+\frac{4 \left(\cos^{2}\left(x \right)\right)}{3}\right) \sin \left(x \right)}{5}-\frac{16 \sin \left(x \right)}{15}+\frac{16 x \cos \left(x \right)}{15}+\frac{2 x \left(\cos^{5}\left(x \right)\right)}{25}-\frac{2 \left(\frac{8}{3}+\cos^{4}\left(x \right)+\frac{4 \left(\cos^{2}\left(x \right)\right)}{3}\right) \sin \left(x \right)}{125}+\frac{8 x \left(\cos^{3}\left(x \right)\right)}{45}-\frac{8 \left(2+\cos^{2}\left(x \right)\right) \sin \left(x \right)}{135}$&$70$\\ \hline \end{longtable}"," ",0,"5/4*x*cos(x)+5/8*(x^2-2)*sin(x)+1/200*x*cos(5*x)+1/2000*(25*x^2-2)*sin(5*x)+5/72*x*cos(3*x)+5/432*(9*x^2-2)*sin(3*x)","A"
484,1,50,59,0.380000," ","int(x^3*sin(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\left(-\frac{3}{4} x^{3}+\frac{9}{2} x \right) \cos \left(x \right)+\frac{9 \left(x^{2}-2\right) \sin \left(x \right)}{4}+\left(\frac{1}{12} x^{3}-\frac{1}{18} x \right) \cos \left(3 x \right)-\frac{\left(9 x^{2}-2\right) \sin \left(3 x \right)}{108}$&$50$\\ default&$-\frac{x^{3} \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{3}+2 x^{2} \sin \left(x \right)-\frac{40 \sin \left(x \right)}{9}+4 x \cos \left(x \right)+\frac{x^{2} \left(\sin^{3}\left(x \right)\right)}{3}+\frac{2 x \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{9}-\frac{2 \left(\sin^{3}\left(x \right)\right)}{27}$&$57$\\ norman&$\frac{\frac{40 x}{9}-\frac{2 x^{3}}{3}-\frac{496 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{27}-\frac{80 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{9}+\frac{16 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{3}-\frac{16 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{3}-\frac{40 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{9}+4 x^{2} \tan \left(\frac{x}{2}\right)+\frac{32 x^{2} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3}+4 x^{2} \left(\tan^{5}\left(\frac{x}{2}\right)\right)-2 x^{3} \left(\tan^{2}\left(\frac{x}{2}\right)\right)+2 x^{3} \left(\tan^{4}\left(\frac{x}{2}\right)\right)+\frac{2 x^{3} \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{3}-\frac{80 \tan \left(\frac{x}{2}\right)}{9}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{3}}$&$134$\\ \hline \end{longtable}"," ",0,"(-3/4*x^3+9/2*x)*cos(x)+9/4*(x^2-2)*sin(x)+(1/12*x^3-1/18*x)*cos(3*x)-1/108*(9*x^2-2)*sin(3*x)","A"
485,1,67,83,0.415000," ","int(x^2*sin(x)^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{5 x^{3}}{48}-\frac{x \cos \left(6 x \right)}{576}-\frac{\left(18 x^{2}-1\right) \sin \left(6 x \right)}{3456}+\frac{3 x \cos \left(4 x \right)}{128}+\frac{3 \left(8 x^{2}-1\right) \sin \left(4 x \right)}{512}-\frac{15 x \cos \left(2 x \right)}{64}-\frac{15 \left(2 x^{2}-1\right) \sin \left(2 x \right)}{128}$&$67$\\ default&$x^{2} \left(-\frac{\left(\sin^{5}\left(x \right)+\frac{5 \left(\sin^{3}\left(x \right)\right)}{4}+\frac{15 \sin \left(x \right)}{8}\right) \cos \left(x \right)}{6}+\frac{5 x}{16}\right)+\frac{x \left(\sin^{6}\left(x \right)\right)}{18}+\frac{\left(\sin^{5}\left(x \right)+\frac{5 \left(\sin^{3}\left(x \right)\right)}{4}+\frac{15 \sin \left(x \right)}{8}\right) \cos \left(x \right)}{108}+\frac{115 x}{1152}+\frac{5 x \left(\sin^{4}\left(x \right)\right)}{48}+\frac{5 \left(\sin^{3}\left(x \right)+\frac{3 \sin \left(x \right)}{2}\right) \cos \left(x \right)}{192}-\frac{5 x \left(\cos^{2}\left(x \right)\right)}{16}+\frac{5 \cos \left(x \right) \sin \left(x \right)}{32}-\frac{5 x^{3}}{24}$&$96$\\ \hline \end{longtable}"," ",0,"5/48*x^3-1/576*x*cos(6*x)-1/3456*(18*x^2-1)*sin(6*x)+3/128*x*cos(4*x)+3/512*(8*x^2-1)*sin(4*x)-15/64*x*cos(2*x)-15/128*(2*x^2-1)*sin(2*x)","A"
486,1,32,34,0.378000," ","int(x^2*cos(x)*sin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{2} \left(\sin^{3}\left(x \right)\right)}{3}+\frac{2 x \left(2+\sin^{2}\left(x \right)\right) \cos \left(x \right)}{9}-\frac{2 \left(\sin^{3}\left(x \right)\right)}{27}-\frac{4 \sin \left(x \right)}{9}$&$32$\\ risch&$\frac{x \cos \left(x \right)}{2}+\frac{\left(x^{2}-2\right) \sin \left(x \right)}{4}-\frac{x \cos \left(3 x \right)}{18}-\frac{\left(9 x^{2}-2\right) \sin \left(3 x \right)}{108}$&$36$\\ norman&$\frac{\frac{4 x}{9}-\frac{64 \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{27}-\frac{8 \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{9}+\frac{4 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{3}-\frac{4 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{3}-\frac{4 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{9}+\frac{8 x^{2} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{3}-\frac{8 \tan \left(\frac{x}{2}\right)}{9}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{3}}$&$76$\\ \hline \end{longtable}"," ",0,"1/3*x^2*sin(x)^3+2/9*x*(2+sin(x)^2)*cos(x)-2/27*sin(x)^3-4/9*sin(x)","A"
487,1,60,27,0.073000," ","int(x*cos(x)^4/sin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{3 x^{2}}{4}+\frac{i \left(2 x +i\right) {\mathrm e}^{2 i x}}{16}-\frac{i \left(-i+2 x \right) {\mathrm e}^{-2 i x}}{16}-2 i x -\frac{2 i x}{{\mathrm e}^{2 i x}-1}+\ln \left({\mathrm e}^{2 i x}-1\right)$&$60$\\ norman&$\frac{-\frac{\tan \left(\frac{x}{2}\right)}{2}-\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right)}{2}-\frac{x}{2}-\frac{3 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2}+\frac{3 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{2}+\frac{x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{2}-\frac{3 x^{2} \tan \left(\frac{x}{2}\right)}{4}-\frac{3 x^{2} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{2}-\frac{3 x^{2} \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{4}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{2} \tan \left(\frac{x}{2}\right)}-\ln \left(1+\tan^{2}\left(\frac{x}{2}\right)\right)+\ln \left(\tan \left(\frac{x}{2}\right)\right)$&$111$\\ \hline \end{longtable}"," ",0,"-3/4*x^2+1/16*I*(2*x+I)*exp(2*I*x)-1/16*I*(-I+2*x)*exp(-2*I*x)-2*I*x-2*I*x/(exp(2*I*x)-1)+ln(exp(2*I*x)-1)","C"
488,1,76,24,0.103000," ","int(x*sin(x)^3/cos(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{\frac{2 x}{3}-\frac{\left(\tan^{5}\left(\frac{x}{2}\right)\right)}{3}-2 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)-2 x \left(\tan^{4}\left(\frac{x}{2}\right)\right)+\frac{2 x \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{3}+\frac{\tan \left(\frac{x}{2}\right)}{3}}{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right)^{3}}-\frac{5 \ln \left(\tan \left(\frac{x}{2}\right)-1\right)}{6}+\frac{5 \ln \left(\tan \left(\frac{x}{2}\right)+1\right)}{6}$&$76$\\ risch&$-\frac{6 x \,{\mathrm e}^{5 i x}+4 x \,{\mathrm e}^{3 i x}-i {\mathrm e}^{5 i x}+6 x \,{\mathrm e}^{i x}+i {\mathrm e}^{i x}}{3 \left(1+{\mathrm e}^{2 i x}\right)^{3}}-\frac{5 \ln \left({\mathrm e}^{i x}-i\right)}{6}+\frac{5 \ln \left({\mathrm e}^{i x}+i\right)}{6}$&$76$\\ \hline \end{longtable}"," ",0,"(2/3*x-1/3*tan(1/2*x)^5-2*x*tan(1/2*x)^2-2*x*tan(1/2*x)^4+2/3*x*tan(1/2*x)^6+1/3*tan(1/2*x))/(tan(1/2*x)^2-1)^3-5/6*ln(tan(1/2*x)-1)+5/6*ln(tan(1/2*x)+1)","B"
489,1,13,12,0.341000," ","int(x*sin(x)/cos(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{2 \cos \left(x \right)^{2}}-\frac{\tan \left(x \right)}{2}$&$13$\\ risch&$\frac{2 x \,{\mathrm e}^{2 i x}-i {\mathrm e}^{2 i x}-i}{\left(1+{\mathrm e}^{2 i x}\right)^{2}}$&$30$\\ norman&$\frac{\tan^{3}\left(\frac{x}{2}\right)+x \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\frac{x}{2}+\frac{x \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{2}-\tan \left(\frac{x}{2}\right)}{\left(\tan^{2}\left(\frac{x}{2}\right)-1\right)^{2}}$&$45$\\ \hline \end{longtable}"," ",0,"1/2*x/cos(x)^2-1/2*tan(x)","A"
490,1,57,46,0.086000," ","int(x*sin(x)^3/cos(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{i x^{2}}{2}+\frac{\left(2 x +i\right) {\mathrm e}^{2 i x}}{16}+\frac{\left(-i+2 x \right) {\mathrm e}^{-2 i x}}{16}-x \ln \left(1+{\mathrm e}^{2 i x}\right)+\frac{i \polylog \left(2, -{\mathrm e}^{2 i x}\right)}{2}$&$57$\\ \hline \end{longtable}"," ",0,"1/2*I*x^2+1/16*(2*x+I)*exp(2*I*x)+1/16*(-I+2*x)*exp(-2*I*x)-x*ln(1+exp(2*I*x))+1/2*I*polylog(2,-exp(2*I*x))","A"
491,1,59,43,0.069000," ","int(x*sin(x)^3/cos(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{i x^{2}}{2}+\frac{2 x \,{\mathrm e}^{2 i x}-i {\mathrm e}^{2 i x}-i}{\left(1+{\mathrm e}^{2 i x}\right)^{2}}+x \ln \left(1+{\mathrm e}^{2 i x}\right)-\frac{i \polylog \left(2, -{\mathrm e}^{2 i x}\right)}{2}$&$59$\\ \hline \end{longtable}"," ",0,"-1/2*I*x^2+(2*x*exp(2*I*x)-I*exp(2*I*x)-I)/(1+exp(2*I*x))^2+x*ln(1+exp(2*I*x))-1/2*I*polylog(2,-exp(2*I*x))","A"
492,1,44,12,0.832000," ","int((2*x+sin(2*x))/(cos(x)+x*sin(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 i}{x +i}-\frac{4 i x}{\left(x +i\right) \left(x \,{\mathrm e}^{2 i x}-x +i {\mathrm e}^{2 i x}+i\right)}$&$44$\\ \hline \end{longtable}"," ",0,"-2*I/(x+I)-4*I*x/(x+I)/(x*exp(2*I*x)-x+I*exp(2*I*x)+I)","C"
493,1,29,20,0.253000," ","int(x^2/(x*cos(x)-sin(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{2 i \left(x -i\right)}{i {\mathrm e}^{2 i x}+x \,{\mathrm e}^{2 i x}-i+x}$&$29$\\ norman&$\frac{-1+\tan^{2}\left(\frac{x}{2}\right)-2 x \tan \left(\frac{x}{2}\right)}{x \left(\tan^{2}\left(\frac{x}{2}\right)\right)-x +2 \tan \left(\frac{x}{2}\right)}$&$37$\\ \hline \end{longtable}"," ",0,"2*I*(x-I)/(I*exp(2*I*x)+x*exp(2*I*x)-I+x)","C"
494,1,23,22,0.065000," ","int(a^(m*x)*b^(n*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{a^{m x} b^{n x}}{m \ln \left(a \right)+n \ln \left(b \right)}$&$23$\\ risch&$\frac{a^{m x} b^{n x}}{m \ln \left(a \right)+n \ln \left(b \right)}$&$23$\\ norman&$\frac{{\mathrm e}^{m x \ln \left(a \right)} {\mathrm e}^{n x \ln \left(b \right)}}{m \ln \left(a \right)+n \ln \left(b \right)}$&$25$\\ meijerg&$-\frac{1-{\mathrm e}^{x n \ln \left(b \right) \left(1+\frac{m \ln \left(a \right)}{n \ln \left(b \right)}\right)}}{n \ln \left(b \right) \left(1+\frac{m \ln \left(a \right)}{n \ln \left(b \right)}\right)}$&$48$\\ \hline \end{longtable}"," ",0,"a^(m*x)*b^(n*x)/(m*ln(a)+n*ln(b))","A"
495,1,42,34,0.048000," ","int((a^x-b^x)^2/(a^x)/(b^x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-2 x +\frac{a^{x} b^{-x}}{\ln \left(a \right)-\ln \left(b \right)}-\frac{b^{x} a^{-x}}{\ln \left(a \right)-\ln \left(b \right)}$&$42$\\ norman&$\left(\frac{{\mathrm e}^{2 x \ln \left(a \right)}}{\ln \left(a \right)-\ln \left(b \right)}-\frac{{\mathrm e}^{2 x \ln \left(b \right)}}{\ln \left(a \right)-\ln \left(b \right)}-2 x \,{\mathrm e}^{x \ln \left(a \right)} {\mathrm e}^{x \ln \left(b \right)}\right) {\mathrm e}^{-x \ln \left(a \right)} {\mathrm e}^{-x \ln \left(b \right)}$&$65$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"-2*x+a^x/(b^x)/(ln(a)-ln(b))-b^x/(a^x)/(ln(a)-ln(b))","A"
496,1,8,7,0.028000," ","int(-1/exp(x)+exp(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&${\mathrm e}^{-x}+{\mathrm e}^{x}$&$8$\\ default&${\mathrm e}^{-x}+{\mathrm e}^{x}$&$8$\\ risch&${\mathrm e}^{-x}+{\mathrm e}^{x}$&$8$\\ meijerg&$-2+{\mathrm e}^{-x}+{\mathrm e}^{x}$&$9$\\ norman&$\left(1+{\mathrm e}^{2 x}\right) {\mathrm e}^{-x}$&$12$\\ \hline \end{longtable}"," ",0,"1/exp(x)+exp(x)","A"
497,1,17,18,0.032000," ","int((-1/exp(x)+exp(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-2 x +\frac{{\mathrm e}^{2 x}}{2}-\frac{{\mathrm e}^{-2 x}}{2}$&$17$\\ derivativedivides&$\frac{{\mathrm e}^{2 x}}{2}-2 \ln \left({\mathrm e}^{x}\right)-\frac{{\mathrm e}^{-2 x}}{2}$&$19$\\ default&$\frac{{\mathrm e}^{2 x}}{2}-2 \ln \left({\mathrm e}^{x}\right)-\frac{{\mathrm e}^{-2 x}}{2}$&$19$\\ norman&$\left(-\frac{1}{2}+\frac{{\mathrm e}^{4 x}}{2}-2 x \,{\mathrm e}^{2 x}\right) {\mathrm e}^{-2 x}$&$21$\\ \hline \end{longtable}"," ",0,"-2*x+1/2*exp(2*x)-1/2*exp(-2*x)","A"
498,1,24,25,0.038000," ","int((-1/exp(x)+exp(x))^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{{\mathrm e}^{3 x}}{3}-3 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-x}+\frac{{\mathrm e}^{-3 x}}{3}$&$24$\\ default&$\frac{{\mathrm e}^{3 x}}{3}-3 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-x}+\frac{{\mathrm e}^{-3 x}}{3}$&$24$\\ risch&$\frac{{\mathrm e}^{3 x}}{3}-3 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-x}+\frac{{\mathrm e}^{-3 x}}{3}$&$24$\\ meijerg&$\frac{16}{3}+\frac{{\mathrm e}^{-3 x}}{3}-3 \,{\mathrm e}^{-x}-3 \,{\mathrm e}^{x}+\frac{{\mathrm e}^{3 x}}{3}$&$25$\\ norman&$\left(\frac{1}{3}-3 \,{\mathrm e}^{2 x}-3 \,{\mathrm e}^{4 x}+\frac{{\mathrm e}^{6 x}}{3}\right) {\mathrm e}^{-3 x}$&$26$\\ \hline \end{longtable}"," ",0,"1/3*exp(x)^3-3*exp(x)-3/exp(x)+1/3/exp(x)^3","A"
499,1,29,32,0.038000," ","int((-1/exp(x)+exp(x))^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$6 x +\frac{{\mathrm e}^{4 x}}{4}-2 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{-2 x}-\frac{{\mathrm e}^{-4 x}}{4}$&$29$\\ derivativedivides&$\frac{{\mathrm e}^{4 x}}{4}-2 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{-2 x}-\frac{{\mathrm e}^{-4 x}}{4}+6 \ln \left({\mathrm e}^{x}\right)$&$31$\\ default&$\frac{{\mathrm e}^{4 x}}{4}-2 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{-2 x}-\frac{{\mathrm e}^{-4 x}}{4}+6 \ln \left({\mathrm e}^{x}\right)$&$31$\\ norman&$\left(-\frac{1}{4}+2 \,{\mathrm e}^{2 x}-2 \,{\mathrm e}^{6 x}+\frac{{\mathrm e}^{8 x}}{4}+6 x \,{\mathrm e}^{4 x}\right) {\mathrm e}^{-4 x}$&$33$\\ \hline \end{longtable}"," ",0,"6*x+1/4*exp(4*x)-2*exp(2*x)+2*exp(-2*x)-1/4*exp(-4*x)","A"
500,0,0,42,0.010000," ","int((-1/exp(x)+exp(x))^n,x)","\[\int \left(-{\mathrm e}^{-x}+{\mathrm e}^{x}\right)^{n}\, dx\]"," ",0,"int((-1/exp(x)+exp(x))^n,x)","F"
501,1,44,41,0.071000," ","int((1/(a^(4*x))-a^(2*x))^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$3 x -\frac{a^{6 x}}{6 \ln \left(a \right)}+\frac{a^{-6 x}}{2 \ln \left(a \right)}-\frac{a^{-12 x}}{12 \ln \left(a \right)}$&$44$\\ norman&$\left(-\frac{1}{12 \ln \left(a \right)}+3 x \,{\mathrm e}^{12 x \ln \left(a \right)}+\frac{{\mathrm e}^{6 x \ln \left(a \right)}}{2 \ln \left(a \right)}-\frac{{\mathrm e}^{18 x \ln \left(a \right)}}{6 \ln \left(a \right)}\right) {\mathrm e}^{-12 x \ln \left(a \right)}$&$56$\\ \hline \end{longtable}"," ",0,"3*x-1/6/ln(a)*(a^(2*x))^3+1/2/ln(a)/(a^(2*x))^3-1/12/ln(a)/(a^(2*x))^6","A"
502,1,28,27,0.043000," ","int(a^(k*x)+a^(l*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{a^{k x}}{k \ln \left(a \right)}+\frac{a^{l x}}{l \ln \left(a \right)}$&$28$\\ risch&$\frac{a^{k x}}{k \ln \left(a \right)}+\frac{a^{l x}}{l \ln \left(a \right)}$&$28$\\ norman&$\frac{{\mathrm e}^{k x \ln \left(a \right)}}{k \ln \left(a \right)}+\frac{{\mathrm e}^{l x \ln \left(a \right)}}{l \ln \left(a \right)}$&$30$\\ meijerg&$-\frac{1-{\mathrm e}^{k x \ln \left(a \right)}}{k \ln \left(a \right)}-\frac{1-{\mathrm e}^{l x \ln \left(a \right)}}{l \ln \left(a \right)}$&$40$\\ \hline \end{longtable}"," ",0,"a^(k*x)/k/ln(a)+a^(l*x)/l/ln(a)","A"
503,1,55,49,0.045000," ","int((a^(k*x)+a^(l*x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{a^{2 k x}}{2 k \ln \left(a \right)}+\frac{a^{2 l x}}{2 l \ln \left(a \right)}+\frac{2 a^{k x} a^{l x}}{\ln \left(a \right) \left(k +l \right)}$&$55$\\ norman&$\frac{{\mathrm e}^{2 k x \ln \left(a \right)}}{2 k \ln \left(a \right)}+\frac{{\mathrm e}^{2 l x \ln \left(a \right)}}{2 l \ln \left(a \right)}+\frac{2 \,{\mathrm e}^{k x \ln \left(a \right)} {\mathrm e}^{l x \ln \left(a \right)}}{\ln \left(a \right) \left(k +l \right)}$&$59$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/2/k/ln(a)*(a^(k*x))^2+1/2/l/ln(a)*(a^(l*x))^2+2/ln(a)/(k+l)*a^(k*x)*a^(l*x)","A"
504,1,84,75,0.072000," ","int((a^(k*x)+a^(l*x))^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{a^{3 k x}}{3 k \ln \left(a \right)}+\frac{a^{3 l x}}{3 l \ln \left(a \right)}+\frac{3 a^{k x} a^{2 l x}}{\ln \left(a \right) \left(k +2 l \right)}+\frac{3 a^{2 k x} a^{l x}}{\ln \left(a \right) \left(2 k +l \right)}$&$84$\\ norman&$\frac{{\mathrm e}^{3 k x \ln \left(a \right)}}{3 k \ln \left(a \right)}+\frac{{\mathrm e}^{3 l x \ln \left(a \right)}}{3 l \ln \left(a \right)}+\frac{3 \,{\mathrm e}^{k x \ln \left(a \right)} {\mathrm e}^{2 l x \ln \left(a \right)}}{\ln \left(a \right) \left(k +2 l \right)}+\frac{3 \,{\mathrm e}^{2 k x \ln \left(a \right)} {\mathrm e}^{l x \ln \left(a \right)}}{\ln \left(a \right) \left(2 k +l \right)}$&$90$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/3/k/ln(a)*(a^(k*x))^3+1/3/l/ln(a)*(a^(l*x))^3+3/ln(a)/(k+2*l)*a^(k*x)*(a^(l*x))^2+3/ln(a)/(2*k+l)*(a^(k*x))^2*a^(l*x)","A"
505,1,109,94,0.026000," ","int((a^(k*x)+a^(l*x))^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{a^{4 k x}}{4 k \ln \left(a \right)}+\frac{4 a^{3 k x} a^{l x}}{\ln \left(a \right) \left(3 k +l \right)}+\frac{3 a^{2 k x} a^{2 l x}}{\ln \left(a \right) \left(k +l \right)}+\frac{4 a^{k x} a^{3 l x}}{\ln \left(a \right) \left(k +3 l \right)}+\frac{a^{4 l x}}{4 l \ln \left(a \right)}$&$109$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/4/ln(a)/k*(a^(k*x))^4+4*(a^(k*x))^3/ln(a)/(3*k+l)*a^(l*x)+3*(a^(k*x))^2/ln(a)/(k+l)*(a^(l*x))^2+4*a^(k*x)/ln(a)/(k+3*l)*(a^(l*x))^3+1/4/ln(a)/l*(a^(l*x))^4","A"
506,0,0,74,0.050000," ","int((a^(k*x)+a^(l*x))^n,x)","\[\int \left(a^{k x}+a^{l x}\right)^{n}\, dx\]"," ",0,"int((a^(k*x)+a^(l*x))^n,x)","F"
507,1,29,28,0.033000," ","int(a^(k*x)-a^(l*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{a^{k x}}{k \ln \left(a \right)}-\frac{a^{l x}}{l \ln \left(a \right)}$&$29$\\ risch&$\frac{a^{k x}}{k \ln \left(a \right)}-\frac{a^{l x}}{l \ln \left(a \right)}$&$29$\\ norman&$\frac{{\mathrm e}^{k x \ln \left(a \right)}}{k \ln \left(a \right)}-\frac{{\mathrm e}^{l x \ln \left(a \right)}}{l \ln \left(a \right)}$&$31$\\ meijerg&$-\frac{1-{\mathrm e}^{k x \ln \left(a \right)}}{k \ln \left(a \right)}+\frac{1-{\mathrm e}^{l x \ln \left(a \right)}}{l \ln \left(a \right)}$&$39$\\ \hline \end{longtable}"," ",0,"a^(k*x)/k/ln(a)-a^(l*x)/l/ln(a)","A"
508,1,55,49,0.044000," ","int((a^(k*x)-a^(l*x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{a^{2 k x}}{2 k \ln \left(a \right)}+\frac{a^{2 l x}}{2 l \ln \left(a \right)}-\frac{2 a^{k x} a^{l x}}{\ln \left(a \right) \left(k +l \right)}$&$55$\\ norman&$\frac{{\mathrm e}^{2 k x \ln \left(a \right)}}{2 k \ln \left(a \right)}+\frac{{\mathrm e}^{2 l x \ln \left(a \right)}}{2 l \ln \left(a \right)}-\frac{2 \,{\mathrm e}^{k x \ln \left(a \right)} {\mathrm e}^{l x \ln \left(a \right)}}{\ln \left(a \right) \left(k +l \right)}$&$59$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/2/k/ln(a)*(a^(k*x))^2+1/2/l/ln(a)*(a^(l*x))^2-2/ln(a)/(k+l)*a^(k*x)*a^(l*x)","A"
509,1,84,75,0.072000," ","int((a^(k*x)-a^(l*x))^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{a^{3 k x}}{3 k \ln \left(a \right)}-\frac{a^{3 l x}}{3 l \ln \left(a \right)}+\frac{3 a^{k x} a^{2 l x}}{\ln \left(a \right) \left(k +2 l \right)}-\frac{3 a^{2 k x} a^{l x}}{\ln \left(a \right) \left(2 k +l \right)}$&$84$\\ norman&$\frac{{\mathrm e}^{3 k x \ln \left(a \right)}}{3 k \ln \left(a \right)}-\frac{{\mathrm e}^{3 l x \ln \left(a \right)}}{3 l \ln \left(a \right)}+\frac{3 \,{\mathrm e}^{k x \ln \left(a \right)} {\mathrm e}^{2 l x \ln \left(a \right)}}{\ln \left(a \right) \left(k +2 l \right)}-\frac{3 \,{\mathrm e}^{2 k x \ln \left(a \right)} {\mathrm e}^{l x \ln \left(a \right)}}{\ln \left(a \right) \left(2 k +l \right)}$&$90$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/3/k/ln(a)*(a^(k*x))^3-1/3/l/ln(a)*(a^(l*x))^3+3/ln(a)/(k+2*l)*a^(k*x)*(a^(l*x))^2-3/ln(a)/(2*k+l)*(a^(k*x))^2*a^(l*x)","A"
510,1,109,94,0.025000," ","int((a^(k*x)-a^(l*x))^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{a^{4 k x}}{4 k \ln \left(a \right)}-\frac{4 a^{3 k x} a^{l x}}{\ln \left(a \right) \left(3 k +l \right)}+\frac{3 a^{2 k x} a^{2 l x}}{\ln \left(a \right) \left(k +l \right)}-\frac{4 a^{k x} a^{3 l x}}{\ln \left(a \right) \left(k +3 l \right)}+\frac{a^{4 l x}}{4 l \ln \left(a \right)}$&$109$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/4/ln(a)/k*(a^(k*x))^4-4*(a^(k*x))^3/ln(a)/(3*k+l)*a^(l*x)+3*(a^(k*x))^2/ln(a)/(k+l)*(a^(l*x))^2-4*a^(k*x)/ln(a)/(k+3*l)*(a^(l*x))^3+1/4/ln(a)/l*(a^(l*x))^4","A"
511,0,0,76,0.052000," ","int((a^(k*x)-a^(l*x))^n,x)","\[\int \left(a^{k x}-a^{l x}\right)^{n}\, dx\]"," ",0,"int((a^(k*x)-a^(l*x))^n,x)","F"
512,1,16,15,0.039000," ","int(1+a^(m*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x +\frac{a^{m x}}{m \ln \left(a \right)}$&$16$\\ risch&$x +\frac{a^{m x}}{m \ln \left(a \right)}$&$16$\\ norman&$x +\frac{{\mathrm e}^{m x \ln \left(a \right)}}{m \ln \left(a \right)}$&$17$\\ derivativedivides&$\frac{a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$21$\\ \hline \end{longtable}"," ",0,"x+a^(m*x)/m/ln(a)","A"
513,1,32,31,0.039000," ","int((1+a^(m*x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{a^{2 m x}}{2}+2 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$32$\\ default&$\frac{\frac{a^{2 m x}}{2}+2 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$32$\\ risch&$x +\frac{2 a^{m x}}{m \ln \left(a \right)}+\frac{a^{2 m x}}{2 m \ln \left(a \right)}$&$33$\\ norman&$x +\frac{2 \,{\mathrm e}^{m x \ln \left(a \right)}}{m \ln \left(a \right)}+\frac{{\mathrm e}^{2 m x \ln \left(a \right)}}{2 m \ln \left(a \right)}$&$35$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/m/ln(a)*(1/2*(a^(m*x))^2+2*a^(m*x)+ln(a^(m*x)))","A"
514,1,41,46,0.036000," ","int((1+a^(m*x))^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{a^{3 m x}}{3}+\frac{3 a^{2 m x}}{2}+3 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$41$\\ default&$\frac{\frac{a^{3 m x}}{3}+\frac{3 a^{2 m x}}{2}+3 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$41$\\ risch&$x +\frac{3 a^{m x}}{m \ln \left(a \right)}+\frac{3 a^{2 m x}}{2 m \ln \left(a \right)}+\frac{a^{3 m x}}{3 m \ln \left(a \right)}$&$49$\\ norman&$x +\frac{3 \,{\mathrm e}^{m x \ln \left(a \right)}}{m \ln \left(a \right)}+\frac{3 \,{\mathrm e}^{2 m x \ln \left(a \right)}}{2 m \ln \left(a \right)}+\frac{{\mathrm e}^{3 m x \ln \left(a \right)}}{3 m \ln \left(a \right)}$&$52$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/m/ln(a)*(1/3*(a^(m*x))^3+3/2*(a^(m*x))^2+3*a^(m*x)+ln(a^(m*x)))","A"
515,1,50,61,0.039000," ","int((1+a^(m*x))^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{a^{4 m x}}{4}+\frac{4 a^{3 m x}}{3}+3 a^{2 m x}+4 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$50$\\ default&$\frac{\frac{a^{4 m x}}{4}+\frac{4 a^{3 m x}}{3}+3 a^{2 m x}+4 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$50$\\ risch&$x +\frac{4 a^{m x}}{m \ln \left(a \right)}+\frac{3 a^{2 m x}}{m \ln \left(a \right)}+\frac{4 a^{3 m x}}{3 m \ln \left(a \right)}+\frac{a^{4 m x}}{4 m \ln \left(a \right)}$&$65$\\ norman&$x +\frac{4 \,{\mathrm e}^{m x \ln \left(a \right)}}{m \ln \left(a \right)}+\frac{3 \,{\mathrm e}^{2 m x \ln \left(a \right)}}{m \ln \left(a \right)}+\frac{4 \,{\mathrm e}^{3 m x \ln \left(a \right)}}{3 m \ln \left(a \right)}+\frac{{\mathrm e}^{4 m x \ln \left(a \right)}}{4 m \ln \left(a \right)}$&$69$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/m/ln(a)*(1/4*(a^(m*x))^4+4/3*(a^(m*x))^3+3*(a^(m*x))^2+4*a^(m*x)+ln(a^(m*x)))","A"
516,0,0,42,0.017000," ","int((1+a^(m*x))^n,x)","\[\int \left(1+a^{m x}\right)^{n}\, dx\]"," ",0,"int((1+a^(m*x))^n,x)","F"
517,1,17,16,0.031000," ","int(1-a^(m*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x -\frac{a^{m x}}{m \ln \left(a \right)}$&$17$\\ risch&$x -\frac{a^{m x}}{m \ln \left(a \right)}$&$17$\\ norman&$x -\frac{{\mathrm e}^{m x \ln \left(a \right)}}{m \ln \left(a \right)}$&$18$\\ derivativedivides&$\frac{-a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$23$\\ \hline \end{longtable}"," ",0,"x-a^(m*x)/m/ln(a)","A"
518,1,32,31,0.030000," ","int((1-a^(m*x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{a^{2 m x}}{2}-2 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$32$\\ default&$\frac{\frac{a^{2 m x}}{2}-2 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$32$\\ risch&$x -\frac{2 a^{m x}}{m \ln \left(a \right)}+\frac{a^{2 m x}}{2 m \ln \left(a \right)}$&$33$\\ norman&$x -\frac{2 \,{\mathrm e}^{m x \ln \left(a \right)}}{m \ln \left(a \right)}+\frac{{\mathrm e}^{2 m x \ln \left(a \right)}}{2 m \ln \left(a \right)}$&$35$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/m/ln(a)*(1/2*(a^(m*x))^2-2*a^(m*x)+ln(a^(m*x)))","A"
519,1,41,46,0.036000," ","int((1-a^(m*x))^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{-\frac{a^{3 m x}}{3}+\frac{3 a^{2 m x}}{2}-3 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$41$\\ default&$\frac{-\frac{a^{3 m x}}{3}+\frac{3 a^{2 m x}}{2}-3 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$41$\\ risch&$x -\frac{3 a^{m x}}{m \ln \left(a \right)}+\frac{3 a^{2 m x}}{2 m \ln \left(a \right)}-\frac{a^{3 m x}}{3 m \ln \left(a \right)}$&$49$\\ norman&$x -\frac{3 \,{\mathrm e}^{m x \ln \left(a \right)}}{m \ln \left(a \right)}+\frac{3 \,{\mathrm e}^{2 m x \ln \left(a \right)}}{2 m \ln \left(a \right)}-\frac{{\mathrm e}^{3 m x \ln \left(a \right)}}{3 m \ln \left(a \right)}$&$52$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/m/ln(a)*(-1/3*(a^(m*x))^3+3/2*(a^(m*x))^2-3*a^(m*x)+ln(a^(m*x)))","A"
520,1,50,61,0.036000," ","int((1-a^(m*x))^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\frac{a^{4 m x}}{4}-\frac{4 a^{3 m x}}{3}+3 a^{2 m x}-4 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$50$\\ default&$\frac{\frac{a^{4 m x}}{4}-\frac{4 a^{3 m x}}{3}+3 a^{2 m x}-4 a^{m x}+\ln \left(a^{m x}\right)}{m \ln \left(a \right)}$&$50$\\ risch&$x -\frac{4 a^{m x}}{m \ln \left(a \right)}+\frac{3 a^{2 m x}}{m \ln \left(a \right)}-\frac{4 a^{3 m x}}{3 m \ln \left(a \right)}+\frac{a^{4 m x}}{4 m \ln \left(a \right)}$&$65$\\ norman&$x -\frac{4 \,{\mathrm e}^{m x \ln \left(a \right)}}{m \ln \left(a \right)}+\frac{3 \,{\mathrm e}^{2 m x \ln \left(a \right)}}{m \ln \left(a \right)}-\frac{4 \,{\mathrm e}^{3 m x \ln \left(a \right)}}{3 m \ln \left(a \right)}+\frac{{\mathrm e}^{4 m x \ln \left(a \right)}}{4 m \ln \left(a \right)}$&$69$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/m/ln(a)*(1/4*(a^(m*x))^4-4/3*(a^(m*x))^3+3*(a^(m*x))^2-4*a^(m*x)+ln(a^(m*x)))","A"
521,0,0,46,0.018000," ","int((1-a^(m*x))^n,x)","\[\int \left(1-a^{m x}\right)^{n}\, dx\]"," ",0,"int((1-a^(m*x))^n,x)","F"
522,1,24,23,0.028000," ","int(1/(b+a*exp(n*x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$\frac{x}{b}-\frac{\ln \left(b +a \,{\mathrm e}^{n x}\right)}{b n}$&$24$\\ risch&$\frac{x}{b}-\frac{\ln \left({\mathrm e}^{n x}+\frac{b}{a}\right)}{b n}$&$26$\\ derivativedivides&$\frac{-\frac{\ln \left(b +a \,{\mathrm e}^{n x}\right)}{b}+\frac{\ln \left({\mathrm e}^{n x}\right)}{b}}{n}$&$29$\\ default&$\frac{-\frac{\ln \left(b +a \,{\mathrm e}^{n x}\right)}{b}+\frac{\ln \left({\mathrm e}^{n x}\right)}{b}}{n}$&$29$\\ \hline \end{longtable}"," ",0,"x/b-ln(b+a*exp(n*x))/b/n","A"
523,1,26,68,0.058000," ","int(exp(x)/(b+a*exp(3*x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\munderset{\textit{\_R} =\RootOf \left(27 b^{2} a \,\textit{\_Z}^{3}-1\right)}{\sum}\textit{\_R} \ln \left(3 b \textit{\_R} +{\mathrm e}^{x}\right)$&$26$\\ default&$\frac{\ln \left({\mathrm e}^{x}+\left(\frac{b}{a}\right)^{\frac{1}{3}}\right)}{3 a \left(\frac{b}{a}\right)^{\frac{2}{3}}}-\frac{\ln \left({\mathrm e}^{2 x}-\left(\frac{b}{a}\right)^{\frac{1}{3}} {\mathrm e}^{x}+\left(\frac{b}{a}\right)^{\frac{2}{3}}\right)}{6 a \left(\frac{b}{a}\right)^{\frac{2}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,{\mathrm e}^{x}}{\left(\frac{b}{a}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 a \left(\frac{b}{a}\right)^{\frac{2}{3}}}$&$95$\\ \hline \end{longtable}"," ",0,"sum(_R*ln(3*b*_R+exp(x)),_R=RootOf(27*_Z^3*a*b^2-1))","C"
524,1,12,11,0.023000," ","int((-1+exp(x))/(1+exp(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$-x +2 \ln \left(1+{\mathrm e}^{x}\right)$&$12$\\ risch&$-x +2 \ln \left(1+{\mathrm e}^{x}\right)$&$12$\\ derivativedivides&$2 \ln \left(1+{\mathrm e}^{x}\right)-\ln \left({\mathrm e}^{x}\right)$&$14$\\ default&$2 \ln \left(1+{\mathrm e}^{x}\right)-\ln \left({\mathrm e}^{x}\right)$&$14$\\ \hline \end{longtable}"," ",0,"-x+2*ln(1+exp(x))","A"
525,1,38,37,0.052000," ","int(exp(4*x)/(1-2*exp(2*x)+3*exp(4*x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(1-2 \,{\mathrm e}^{2 x}+3 \,{\mathrm e}^{4 x}\right)}{12}+\frac{\sqrt{2}\, \arctan \left(\frac{\left(6 \,{\mathrm e}^{2 x}-2\right) \sqrt{2}}{4}\right)}{12}$&$38$\\ risch&$\frac{\ln \left({\mathrm e}^{2 x}-\frac{1}{3}+\frac{i \sqrt{2}}{3}\right)}{12}+\frac{i \ln \left({\mathrm e}^{2 x}-\frac{1}{3}+\frac{i \sqrt{2}}{3}\right) \sqrt{2}}{24}+\frac{\ln \left({\mathrm e}^{2 x}-\frac{1}{3}-\frac{i \sqrt{2}}{3}\right)}{12}-\frac{i \ln \left({\mathrm e}^{2 x}-\frac{1}{3}-\frac{i \sqrt{2}}{3}\right) \sqrt{2}}{24}$&$70$\\ \hline \end{longtable}"," ",0,"1/12*ln(1-2*exp(x)^2+3*exp(x)^4)+1/12*2^(1/2)*arctan(1/4*(6*exp(x)^2-2)*2^(1/2))","A"
526,1,29,30,0.089000," ","int((exp(x)+exp(5*x))/(-1+exp(x)-exp(2*x)+exp(3*x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\ln \left(1+{\mathrm e}^{2 x}\right)}{2}-\arctan \left({\mathrm e}^{x}\right)+\ln \left(-1+{\mathrm e}^{x}\right)+{\mathrm e}^{x}+\frac{{\mathrm e}^{2 x}}{2}$&$29$\\ risch&$\frac{{\mathrm e}^{2 x}}{2}+{\mathrm e}^{x}+\ln \left(-1+{\mathrm e}^{x}\right)-\frac{\ln \left({\mathrm e}^{x}-i\right)}{2}+\frac{i \ln \left({\mathrm e}^{x}-i\right)}{2}-\frac{\ln \left({\mathrm e}^{x}+i\right)}{2}-\frac{i \ln \left({\mathrm e}^{x}+i\right)}{2}$&$49$\\ meijerg&$\frac{\left(\moverset{\infty}{\munderset{\textit{\_k1} =0}{\sum}}\frac{1-{\mathrm e}^{-x \left(3+\textit{\_k1} \right) \left(1-\frac{1}{3+\textit{\_k1}}\right)}}{\left(3+\textit{\_k1} \right) \left(1-\frac{1}{3+\textit{\_k1}}\right)}\right)}{2}-\frac{\left(\moverset{\infty}{\munderset{\textit{\_k1} =0}{\sum}}\frac{1-{\mathrm e}^{x \left(2-\textit{\_k1} \right)}}{2-\textit{\_k1}}\right)}{2}$&$75$\\ \hline \end{longtable}"," ",0,"-1/2*ln(exp(x)^2+1)-arctan(exp(x))+ln(-1+exp(x))+exp(x)+1/2*exp(x)^2","A"
527,1,33,29,0.044000," ","int(exp(n*x)*(a+b*exp(n*x))^(r/s),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(a +b \,{\mathrm e}^{n x}\right)^{\frac{r}{s}+1}}{n b \left(\frac{r}{s}+1\right)}$&$33$\\ default&$\frac{\left(a +b \,{\mathrm e}^{n x}\right)^{\frac{r}{s}+1}}{n b \left(\frac{r}{s}+1\right)}$&$33$\\ risch&$\frac{s \left(a +b \,{\mathrm e}^{n x}\right) \left(a +b \,{\mathrm e}^{n x}\right)^{\frac{r}{s}}}{b n \left(r +s \right)}$&$36$\\ norman&$\frac{s \,{\mathrm e}^{n x} {\mathrm e}^{\frac{r \ln \left(a +b \,{\mathrm e}^{n x}\right)}{s}}}{n \left(r +s \right)}+\frac{a s \,{\mathrm e}^{\frac{r \ln \left(a +b \,{\mathrm e}^{n x}\right)}{s}}}{b n \left(r +s \right)}$&$60$\\ \hline \end{longtable}"," ",0,"1/n*(a+b*exp(n*x))^(r/s+1)/b/(r/s+1)","A"
528,1,57,39,0.077000," ","int((1-2*exp(1/3*x))^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$12 \left(1-2 \,{\mathrm e}^{\frac{x}{3}}\right)^{\frac{1}{4}}+3 \ln \left(\left(1-2 \,{\mathrm e}^{\frac{x}{3}}\right)^{\frac{1}{4}}-1\right)-3 \ln \left(\left(1-2 \,{\mathrm e}^{\frac{x}{3}}\right)^{\frac{1}{4}}+1\right)-6 \arctan \left(\left(1-2 \,{\mathrm e}^{\frac{x}{3}}\right)^{\frac{1}{4}}\right)$&$57$\\ default&$12 \left(1-2 \,{\mathrm e}^{\frac{x}{3}}\right)^{\frac{1}{4}}+3 \ln \left(\left(1-2 \,{\mathrm e}^{\frac{x}{3}}\right)^{\frac{1}{4}}-1\right)-3 \ln \left(\left(1-2 \,{\mathrm e}^{\frac{x}{3}}\right)^{\frac{1}{4}}+1\right)-6 \arctan \left(\left(1-2 \,{\mathrm e}^{\frac{x}{3}}\right)^{\frac{1}{4}}\right)$&$57$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"12*(1-2*exp(1/3*x))^(1/4)+3*ln((1-2*exp(1/3*x))^(1/4)-1)-3*ln((1-2*exp(1/3*x))^(1/4)+1)-6*arctan((1-2*exp(1/3*x))^(1/4))","A"
529,0,0,59,0.015000," ","int((a+b*exp(n*x))^(r/s),x)","\[\int \left(a +b \,{\mathrm e}^{n x}\right)^{\frac{r}{s}}\, dx\]"," ",0,"int((a+b*exp(n*x))^(r/s),x)","F"
530,1,15,14,0.038000," ","int(exp(x)/(a^2+exp(2*x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\ln \left({\mathrm e}^{x}+\sqrt{a^{2}+{\mathrm e}^{2 x}}\right)$&$15$\\ \hline \end{longtable}"," ",0,"ln(exp(x)+(a^2+exp(x)^2)^(1/2))","A"
531,1,17,16,0.040000," ","int(exp(x)/(-a^2+exp(2*x))^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\ln \left({\mathrm e}^{x}+\sqrt{-a^{2}+{\mathrm e}^{2 x}}\right)$&$17$\\ \hline \end{longtable}"," ",0,"ln(exp(x)+(-a^2+exp(x)^2)^(1/2))","A"
532,0,0,25,0.013000," ","int(exp(3/4*x)/(-2+exp(3/4*x))/(-2+exp(3/4*x)+exp(3/2*x))^(1/2),x)","\[\int \frac{{\mathrm e}^{\frac{3 x}{4}}}{\left(-2+{\mathrm e}^{\frac{3 x}{4}}\right) \sqrt{-2+{\mathrm e}^{\frac{3 x}{4}}+{\mathrm e}^{\frac{3 x}{2}}}}\, dx\]"," ",0,"int(exp(3/4*x)/(-2+exp(3/4*x))/(-2+exp(3/4*x)+exp(3/2*x))^(1/2),x)","F"
533,0,0,28,180.000000," ","int((-3+exp(7*x))^(2/3)/exp(2*x),x)","\[\int \left(-3+{\mathrm e}^{7 x}\right)^{\frac{2}{3}} {\mathrm e}^{-2 x}\, dx\]"," ",0,"int((-3+exp(7*x))^(2/3)/exp(2*x),x)","F"
534,1,37,49,0.034000," ","int(exp(2*x)/(3-exp(1/2*x))^(3/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{8 \left(5 \,{\mathrm e}^{\frac{3 x}{2}}+20 \,{\mathrm e}^{x}+96 \,{\mathrm e}^{\frac{x}{2}}+1152\right) \left(-3+{\mathrm e}^{\frac{x}{2}}\right)}{65 \left(3-{\mathrm e}^{\frac{x}{2}}\right)^{\frac{3}{4}}}$&$37$\\ \hline \end{longtable}"," ",0,"8/65/(3-exp(1/2*x))^(3/4)*(5*exp(3/2*x)+20*exp(x)+96*exp(1/2*x)+1152)*(-3+exp(1/2*x))","A"
535,1,21,40,0.042000," ","int(x^3/exp(1/2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\left(-2 x^{3}-12 x^{2}-48 x -96\right) {\mathrm e}^{-\frac{x}{2}}$&$21$\\ gosper&$-2 \left(x^{3}+6 x^{2}+24 x +48\right) {\mathrm e}^{-\frac{x}{2}}$&$22$\\ norman&$\left(-2 x^{3}-12 x^{2}-48 x -96\right) {\mathrm e}^{-\frac{x}{2}}$&$23$\\ meijerg&$96-4 \left(\frac{1}{2} x^{3}+3 x^{2}+12 x +24\right) {\mathrm e}^{-\frac{x}{2}}$&$24$\\ derivativedivides&$-96 \,{\mathrm e}^{-\frac{x}{2}}-48 x \,{\mathrm e}^{-\frac{x}{2}}-12 x^{2} {\mathrm e}^{-\frac{x}{2}}-2 x^{3} {\mathrm e}^{-\frac{x}{2}}$&$41$\\ default&$-96 \,{\mathrm e}^{-\frac{x}{2}}-48 x \,{\mathrm e}^{-\frac{x}{2}}-12 x^{2} {\mathrm e}^{-\frac{x}{2}}-2 x^{3} {\mathrm e}^{-\frac{x}{2}}$&$41$\\ \hline \end{longtable}"," ",0,"(-2*x^3-12*x^2-48*x-96)*exp(-1/2*x)","A"
536,1,27,29,0.069000," ","int(1/exp(1/2*x)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{{\mathrm e}^{-\frac{x}{2}}}{2 x^{2}}+\frac{{\mathrm e}^{-\frac{x}{2}}}{4 x}-\frac{\expIntegralEi \left(1, \frac{x}{2}\right)}{8}$&$27$\\ derivativedivides&$-\frac{{\mathrm e}^{-\frac{x}{2}}}{2 x^{2}}+\frac{{\mathrm e}^{-\frac{x}{2}}}{4 x}-\frac{\expIntegralEi \left(1, \frac{x}{2}\right)}{8}$&$31$\\ default&$-\frac{{\mathrm e}^{-\frac{x}{2}}}{2 x^{2}}+\frac{{\mathrm e}^{-\frac{x}{2}}}{4 x}-\frac{\expIntegralEi \left(1, \frac{x}{2}\right)}{8}$&$31$\\ meijerg&$\frac{\frac{9}{4} x^{2}-6 x +6}{12 x^{2}}-\frac{\left(-\frac{3 x}{2}+3\right) {\mathrm e}^{-\frac{x}{2}}}{6 x^{2}}-\frac{\ln \left(\frac{x}{2}\right)}{8}-\frac{\expIntegralEi \left(1, \frac{x}{2}\right)}{8}-\frac{3}{16}+\frac{\ln \left(x \right)}{8}-\frac{\ln \left(2\right)}{8}-\frac{1}{2 x^{2}}+\frac{1}{2 x}$&$63$\\ \hline \end{longtable}"," ",0,"-1/2*exp(-1/2*x)/x^2+1/4*exp(-1/2*x)/x-1/8*Ei(1,1/2*x)","A"
537,1,28,38,0.044000," ","int(a^(3*x)*x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{\left(9 x^{2} \ln \left(a \right)^{2}-6 x \ln \left(a \right)+2\right) a^{3 x}}{27 \ln \left(a \right)^{3}}$&$28$\\ risch&$\frac{\left(9 x^{2} \ln \left(a \right)^{2}-6 x \ln \left(a \right)+2\right) a^{3 x}}{27 \ln \left(a \right)^{3}}$&$28$\\ meijerg&$-\frac{2-\frac{\left(27 x^{2} \ln \left(a \right)^{2}-18 x \ln \left(a \right)+6\right) {\mathrm e}^{3 x \ln \left(a \right)}}{3}}{27 \ln \left(a \right)^{3}}$&$33$\\ norman&$\frac{2 \,{\mathrm e}^{3 x \ln \left(a \right)}}{27 \ln \left(a \right)^{3}}-\frac{2 x \,{\mathrm e}^{3 x \ln \left(a \right)}}{9 \ln \left(a \right)^{2}}+\frac{x^{2} {\mathrm e}^{3 x \ln \left(a \right)}}{3 \ln \left(a \right)}$&$42$\\ \hline \end{longtable}"," ",0,"1/27*(9*x^2*ln(a)^2-6*x*ln(a)+2)*a^(3*x)/ln(a)^3","A"
538,1,10,9,0.033000," ","int(exp(x^2)*x*(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$\frac{{\mathrm e}^{x^{2}} x^{2}}{2}$&$10$\\ derivativedivides&$\frac{{\mathrm e}^{x^{2}} x^{2}}{2}$&$10$\\ default&$\frac{{\mathrm e}^{x^{2}} x^{2}}{2}$&$10$\\ norman&$\frac{{\mathrm e}^{x^{2}} x^{2}}{2}$&$10$\\ risch&$\frac{{\mathrm e}^{x^{2}} x^{2}}{2}$&$10$\\ meijerg&$-\frac{\left(-2 x^{2}+2\right) {\mathrm e}^{x^{2}}}{4}+\frac{{\mathrm e}^{x^{2}}}{2}$&$21$\\ \hline \end{longtable}"," ",0,"1/2*exp(x^2)*x^2","A"
539,1,25,24,0.043000," ","int(x/(exp(-x)+exp(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x}{2}-\frac{x}{2 \left(1+{\mathrm e}^{2 x}\right)}-\frac{\ln \left(1+{\mathrm e}^{2 x}\right)}{4}$&$25$\\ default&$-\frac{\ln \left(1+{\mathrm e}^{2 x}\right)}{4}+\frac{x \,{\mathrm e}^{2 x}}{2+2 \,{\mathrm e}^{2 x}}$&$26$\\ norman&$-\frac{\ln \left(1+{\mathrm e}^{2 x}\right)}{4}+\frac{x \,{\mathrm e}^{2 x}}{2+2 \,{\mathrm e}^{2 x}}$&$26$\\ \hline \end{longtable}"," ",0,"1/2*x-1/2*x/(1+exp(2*x))-1/4*ln(1+exp(2*x))","A"
540,1,20,12,0.305000," ","int(exp(x)*(-x^2-x+1)/(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline gosper&$-\frac{{\mathrm e}^{x} \left(1+x \right) \left(-1+x \right)}{\sqrt{-x^{2}+1}}$&$20$\\ \hline \end{longtable}"," ",0,"-exp(x)*(1+x)*(-1+x)/(-x^2+1)^(1/2)","A"
541,1,22,25,0.054000," ","int(cos(2*x)/exp(3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{3 \,{\mathrm e}^{-3 x} \cos \left(2 x \right)}{13}+\frac{2 \,{\mathrm e}^{-3 x} \sin \left(2 x \right)}{13}$&$22$\\ norman&$\frac{\left(-\frac{3}{13}+\frac{3 \left(\tan^{2}\left(x \right)\right)}{13}+\frac{4 \tan \left(x \right)}{13}\right) {\mathrm e}^{-3 x}}{1+\tan^{2}\left(x \right)}$&$28$\\ risch&$-\frac{3 \,{\mathrm e}^{\left(-3+2 i\right) x}}{26}-\frac{i {\mathrm e}^{\left(-3+2 i\right) x}}{13}-\frac{3 \,{\mathrm e}^{\left(-3-2 i\right) x}}{26}+\frac{i {\mathrm e}^{\left(-3-2 i\right) x}}{13}$&$36$\\ \hline \end{longtable}"," ",0,"-3/13*exp(-3*x)*cos(2*x)+2/13*exp(-3*x)*sin(2*x)","A"
542,1,22,21,0.100000," ","int((cos(1/2*x)+sin(1/2*x))/exp(x)^(1/3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{30 \,{\mathrm e}^{-\frac{x}{3}} \cos \left(\frac{x}{2}\right)}{13}+\frac{6 \,{\mathrm e}^{-\frac{x}{3}} \sin \left(\frac{x}{2}\right)}{13}$&$22$\\ risch&$\frac{\left(-\frac{15}{169}-\frac{3 i}{169}\right) \left(\left(25-5 i\right) \cos \left(\frac{x}{2}\right)+\left(-5+i\right) \sin \left(\frac{x}{2}\right)\right)}{\left({\mathrm e}^{x}\right)^{\frac{1}{3}}}$&$26$\\ \hline \end{longtable}"," ",0,"-30/13*exp(-1/3*x)*cos(1/2*x)+6/13*exp(-1/3*x)*sin(1/2*x)","A"
543,1,37,45,0.087000," ","int(cos(3/2*x)/(3^(3*x))^(1/4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 \left(2 \cos \left(\frac{3 x}{2}\right) \ln \left(3\right)-4 \sin \left(\frac{3 x}{2}\right)\right)}{3 \left(2 i+\ln \left(3\right)\right) \left(-2 i+\ln \left(3\right)\right) \left(27^{x}\right)^{\frac{1}{4}}}$&$37$\\ \hline \end{longtable}"," ",0,"-2/3/(2*I+ln(3))/(-2*I+ln(3))/(27^x)^(1/4)*(2*cos(3/2*x)*ln(3)-4*sin(3/2*x))","C"
544,1,41,51,0.079000," ","int(exp(m*x)*cos(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{{\mathrm e}^{m x}}{2 m}+\frac{{\mathrm e}^{\left(2 i+m \right) x}}{8 i+4 m}+\frac{{\mathrm e}^{x \left(m -2 i\right)}}{4 m -8 i}$&$41$\\ norman&$\frac{\frac{\left(m^{2}+2\right) {\mathrm e}^{m x}}{m \left(m^{2}+4\right)}+\frac{\left(m^{2}+2\right) {\mathrm e}^{m x} \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{m \left(m^{2}+4\right)}+\frac{4 \,{\mathrm e}^{m x} \tan \left(\frac{x}{2}\right)}{m^{2}+4}-\frac{4 \,{\mathrm e}^{m x} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{m^{2}+4}-\frac{2 \left(m^{2}-2\right) {\mathrm e}^{m x} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{m \left(m^{2}+4\right)}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{2}}$&$122$\\ \hline \end{longtable}"," ",0,"1/2*exp(m*x)/m+1/4/(2*I+m)*exp((2*I+m)*x)+1/4/(m-2*I)*exp(x*(m-2*I))","C"
545,1,66,78,0.107000," ","int(exp(m*x)*sin(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{i {\mathrm e}^{\left(3 i+m \right) x}}{24 i+8 m}-\frac{3 i {\mathrm e}^{\left(i+m \right) x}}{8 \left(i+m \right)}+\frac{3 i {\mathrm e}^{x \left(m -i\right)}}{8 \left(m -i\right)}-\frac{i {\mathrm e}^{x \left(m -3 i\right)}}{8 \left(m -3 i\right)}$&$66$\\ norman&$\frac{-\frac{6 \,{\mathrm e}^{m x}}{m^{4}+10 m^{2}+9}+\frac{6 \,{\mathrm e}^{m x} \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{m^{4}+10 m^{2}+9}+\frac{12 m \,{\mathrm e}^{m x} \tan \left(\frac{x}{2}\right)}{m^{4}+10 m^{2}+9}+\frac{12 m \,{\mathrm e}^{m x} \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{m^{4}+10 m^{2}+9}-\frac{6 \left(2 m^{2}+3\right) {\mathrm e}^{m x} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{m^{4}+10 m^{2}+9}+\frac{6 \left(2 m^{2}+3\right) {\mathrm e}^{m x} \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{m^{4}+10 m^{2}+9}+\frac{8 m \left(m^{2}+4\right) {\mathrm e}^{m x} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{m^{4}+10 m^{2}+9}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{3}}$&$195$\\ \hline \end{longtable}"," ",0,"1/8*I/(3*I+m)*exp((3*I+m)*x)-3/8*I/(I+m)*exp((I+m)*x)+3/8*I/(m-I)*exp(x*(m-I))-1/8*I/(m-3*I)*exp(x*(m-3*I))","C"
546,1,48,49,0.100000," ","int(cos(1/3*x)^3/exp(x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{\left(-\frac{1}{1300}-\frac{i}{650}\right) \left(-52 i {\mathrm e}^{-i x}+65 \,{\mathrm e}^{i x}-39 \,{\mathrm e}^{-i x}+\left(270-540 i\right) \cos \left(\frac{x}{3}\right)+\left(-180+360 i\right) \sin \left(\frac{x}{3}\right)\right)}{\sqrt{{\mathrm e}^{x}}}$&$48$\\ \hline \end{longtable}"," ",0,"(-1/1300-1/650*I)/exp(x)^(1/2)*(-52*I*exp(-I*x)+65*exp(I*x)-39*exp(-I*x)+(270-540*I)*cos(1/3*x)+(-180+360*I)*sin(1/3*x))","C"
547,1,28,27,0.076000," ","int(exp(2*x)*cos(x)^2*sin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{{\mathrm e}^{2 x}}{16}-\frac{{\mathrm e}^{2 x} \cos \left(4 x \right)}{80}-\frac{{\mathrm e}^{2 x} \sin \left(4 x \right)}{40}$&$28$\\ risch&$\frac{{\mathrm e}^{2 x}}{16}-\frac{{\mathrm e}^{\left(2+4 i\right) x}}{160}+\frac{i {\mathrm e}^{\left(2+4 i\right) x}}{80}-\frac{{\mathrm e}^{\left(2-4 i\right) x}}{160}-\frac{i {\mathrm e}^{\left(2-4 i\right) x}}{80}$&$42$\\ norman&$\frac{-\frac{{\mathrm e}^{2 x} \tan \left(\frac{x}{2}\right)}{5}+\frac{3 \,{\mathrm e}^{2 x} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{5}+\frac{7 \,{\mathrm e}^{2 x} \left(\tan^{3}\left(\frac{x}{2}\right)\right)}{5}-\frac{{\mathrm e}^{2 x} \left(\tan^{4}\left(\frac{x}{2}\right)\right)}{2}-\frac{7 \,{\mathrm e}^{2 x} \left(\tan^{5}\left(\frac{x}{2}\right)\right)}{5}+\frac{3 \,{\mathrm e}^{2 x} \left(\tan^{6}\left(\frac{x}{2}\right)\right)}{5}+\frac{{\mathrm e}^{2 x} \left(\tan^{7}\left(\frac{x}{2}\right)\right)}{5}+\frac{{\mathrm e}^{2 x} \left(\tan^{8}\left(\frac{x}{2}\right)\right)}{20}+\frac{{\mathrm e}^{2 x}}{20}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right)^{4}}$&$113$\\ \hline \end{longtable}"," ",0,"-1/80*exp(2*x)*cos(4*x)-1/40*exp(2*x)*sin(4*x)+1/16*exp(x)^2","A"
548,1,42,27,0.080000," ","int(exp(3*x)*cos(3/2*x)^2*sin(3/2*x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{{\mathrm e}^{3 x}}{24}-\frac{{\mathrm e}^{\left(3+6 i\right) x}}{240}+\frac{i {\mathrm e}^{\left(3+6 i\right) x}}{120}-\frac{{\mathrm e}^{\left(3-6 i\right) x}}{240}-\frac{i {\mathrm e}^{\left(3-6 i\right) x}}{120}$&$42$\\ norman&$\frac{-\frac{2 \,{\mathrm e}^{3 x} \tan \left(\frac{3 x}{4}\right)}{15}+\frac{2 \,{\mathrm e}^{3 x} \left(\tan^{2}\left(\frac{3 x}{4}\right)\right)}{5}+\frac{14 \,{\mathrm e}^{3 x} \left(\tan^{3}\left(\frac{3 x}{4}\right)\right)}{15}-\frac{{\mathrm e}^{3 x} \left(\tan^{4}\left(\frac{3 x}{4}\right)\right)}{3}-\frac{14 \,{\mathrm e}^{3 x} \left(\tan^{5}\left(\frac{3 x}{4}\right)\right)}{15}+\frac{2 \,{\mathrm e}^{3 x} \left(\tan^{6}\left(\frac{3 x}{4}\right)\right)}{5}+\frac{2 \,{\mathrm e}^{3 x} \left(\tan^{7}\left(\frac{3 x}{4}\right)\right)}{15}+\frac{{\mathrm e}^{3 x} \left(\tan^{8}\left(\frac{3 x}{4}\right)\right)}{30}+\frac{{\mathrm e}^{3 x}}{30}}{\left(1+\tan^{2}\left(\frac{3 x}{4}\right)\right)^{4}}$&$113$\\ \hline \end{longtable}"," ",0,"1/24*exp(3*x)-1/240*exp((3+6*I)*x)+1/120*I*exp((3+6*I)*x)-1/240*exp((3-6*I)*x)-1/120*I*exp((3-6*I)*x)","C"
549,0,0,48,0.009000," ","int(exp(m*x)*tan(x)^2,x)","\[\int {\mathrm e}^{m x} \left(\tan^{2}\left(x \right)\right)\, dx\]"," ",0,"int(exp(m*x)*tan(x)^2,x)","F"
550,0,0,36,0.036000," ","int(exp(m*x)/sin(x)^2,x)","\[\int \frac{{\mathrm e}^{m x}}{\sin \left(x \right)^{2}}\, dx\]"," ",0,"int(exp(m*x)/sin(x)^2,x)","F"
551,0,0,38,0.087000," ","int(exp(m*x)/cos(x)^3,x)","\[\int \frac{{\mathrm e}^{m x}}{\cos \left(x \right)^{3}}\, dx\]"," ",0,"int(exp(m*x)/cos(x)^3,x)","F"
552,0,0,27,0.016000," ","int(exp(x)/(1+cos(x)),x)","\[\int \frac{{\mathrm e}^{x}}{1+\cos \left(x \right)}\, dx\]"," ",0,"int(exp(x)/(1+cos(x)),x)","F"
553,0,0,25,0.023000," ","int(exp(x)/(1-cos(x)),x)","\[\int \frac{{\mathrm e}^{x}}{1-\cos \left(x \right)}\, dx\]"," ",0,"int(exp(x)/(1-cos(x)),x)","F"
554,0,0,30,0.021000," ","int(exp(x)/(1+sin(x)),x)","\[\int \frac{{\mathrm e}^{x}}{1+\sin \left(x \right)}\, dx\]"," ",0,"int(exp(x)/(1+sin(x)),x)","F"
555,0,0,28,0.040000," ","int(exp(x)/(1-sin(x)),x)","\[\int \frac{{\mathrm e}^{x}}{1-\sin \left(x \right)}\, dx\]"," ",0,"int(exp(x)/(1-sin(x)),x)","F"
556,1,21,14,0.095000," ","int(exp(x)*(1-sin(x))/(1-cos(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-i {\mathrm e}^{x}-\frac{2 i {\mathrm e}^{x}}{{\mathrm e}^{i x}-1}$&$21$\\ norman&$\frac{-{\mathrm e}^{x} \left(\tan^{2}\left(\frac{x}{2}\right)\right)-{\mathrm e}^{x}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \tan \left(\frac{x}{2}\right)}$&$33$\\ \hline \end{longtable}"," ",0,"-I*exp(x)-2*I*exp(x)/(exp(I*x)-1)","C"
557,0,0,39,0.072000," ","int(exp(x)*(1+sin(x))/(1-cos(x)),x)","\[\int \frac{{\mathrm e}^{x} \left(1+\sin \left(x \right)\right)}{1-\cos \left(x \right)}\, dx\]"," ",0,"int(exp(x)*(1+sin(x))/(1-cos(x)),x)","F"
558,1,8,11,0.085000," ","int(exp(x)*(1+sin(x))/(1+cos(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&${\mathrm e}^{x} \tan \left(\frac{x}{2}\right)$&$8$\\ risch&$-i {\mathrm e}^{x}+\frac{2 i {\mathrm e}^{x}}{{\mathrm e}^{i x}+1}$&$21$\\ \hline \end{longtable}"," ",0,"exp(x)*tan(1/2*x)","A"
559,0,0,40,0.084000," ","int(exp(x)*(1-sin(x))/(1+cos(x)),x)","\[\int \frac{{\mathrm e}^{x} \left(1-\sin \left(x \right)\right)}{1+\cos \left(x \right)}\, dx\]"," ",0,"int(exp(x)*(1-sin(x))/(1+cos(x)),x)","F"
560,0,0,43,0.085000," ","int(exp(x)*(1-cos(x))/(1-sin(x)),x)","\[\int \frac{{\mathrm e}^{x} \left(1-\cos \left(x \right)\right)}{1-\sin \left(x \right)}\, dx\]"," ",0,"int(exp(x)*(1-cos(x))/(1-sin(x)),x)","F"
561,1,21,13,0.125000," ","int(exp(x)*(1+cos(x))/(1-sin(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-i {\mathrm e}^{x}+\frac{2 \,{\mathrm e}^{x}}{{\mathrm e}^{i x}-i}$&$21$\\ norman&$\frac{-{\mathrm e}^{x} \tan \left(\frac{x}{2}\right)-{\mathrm e}^{x} \left(\tan^{2}\left(\frac{x}{2}\right)\right)-{\mathrm e}^{x} \left(\tan^{3}\left(\frac{x}{2}\right)\right)-{\mathrm e}^{x}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \left(\tan \left(\frac{x}{2}\right)-1\right)}$&$53$\\ \hline \end{longtable}"," ",0,"-I*exp(x)+2*exp(x)/(exp(I*x)-I)","C"
562,0,0,40,0.067000," ","int(exp(x)*(1+cos(x))/(1+sin(x)),x)","\[\int \frac{{\mathrm e}^{x} \left(1+\cos \left(x \right)\right)}{1+\sin \left(x \right)}\, dx\]"," ",0,"int(exp(x)*(1+cos(x))/(1+sin(x)),x)","F"
563,1,21,12,0.109000," ","int(exp(x)*(1-cos(x))/(1+sin(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-i {\mathrm e}^{x}-\frac{2 \,{\mathrm e}^{x}}{{\mathrm e}^{i x}+i}$&$21$\\ norman&$\frac{{\mathrm e}^{x} \tan \left(\frac{x}{2}\right)+{\mathrm e}^{x} \left(\tan^{3}\left(\frac{x}{2}\right)\right)-{\mathrm e}^{x} \left(\tan^{2}\left(\frac{x}{2}\right)\right)-{\mathrm e}^{x}}{\left(1+\tan^{2}\left(\frac{x}{2}\right)\right) \left(\tan \left(\frac{x}{2}\right)+1\right)}$&$51$\\ \hline \end{longtable}"," ",0,"-I*exp(x)-2*exp(x)/(exp(I*x)+I)","C"
564,1,20,21,0.059000," ","int(exp(x)*x*cos(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{{\mathrm e}^{x} x \cos \left(x \right)}{2}-\left(-\frac{x}{2}+\frac{1}{2}\right) {\mathrm e}^{x} \sin \left(x \right)$&$20$\\ risch&$\left(\frac{1}{8}-\frac{i}{8}\right) \left(-1+i+2 x \right) {\mathrm e}^{\left(1+i\right) x}+\left(\frac{1}{8}+\frac{i}{8}\right) \left(-1-i+2 x \right) {\mathrm e}^{\left(1-i\right) x}$&$36$\\ norman&$\frac{{\mathrm e}^{x} x \tan \left(\frac{x}{2}\right)+\frac{{\mathrm e}^{x} x}{2}-{\mathrm e}^{x} \tan \left(\frac{x}{2}\right)-\frac{{\mathrm e}^{x} x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2}}{1+\tan^{2}\left(\frac{x}{2}\right)}$&$45$\\ \hline \end{longtable}"," ",0,"1/2*exp(x)*x*cos(x)-(-1/2*x+1/2)*exp(x)*sin(x)","A"
565,1,27,37,0.064000," ","int(exp(x)*x^2*sin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\left(-\frac{1}{2} x^{2}+x -\frac{1}{2}\right) {\mathrm e}^{x} \cos \left(x \right)+\left(\frac{x^{2}}{2}-\frac{1}{2}\right) {\mathrm e}^{x} \sin \left(x \right)$&$27$\\ risch&$\left(-\frac{1}{4}-\frac{i}{4}\right) \left(x^{2}+i x -x -i\right) {\mathrm e}^{\left(1+i\right) x}+\left(-\frac{1}{4}+\frac{i}{4}\right) \left(x^{2}-i x -x +i\right) {\mathrm e}^{\left(1-i\right) x}$&$48$\\ norman&$\frac{{\mathrm e}^{x} x +{\mathrm e}^{x} x^{2} \tan \left(\frac{x}{2}\right)-\frac{{\mathrm e}^{x} x^{2}}{2}-{\mathrm e}^{x} \tan \left(\frac{x}{2}\right)+\frac{{\mathrm e}^{x} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2}-{\mathrm e}^{x} x \left(\tan^{2}\left(\frac{x}{2}\right)\right)+\frac{{\mathrm e}^{x} x^{2} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{2}-\frac{{\mathrm e}^{x}}{2}}{1+\tan^{2}\left(\frac{x}{2}\right)}$&$80$\\ \hline \end{longtable}"," ",0,"(-1/2*x^2+x-1/2)*exp(x)*cos(x)+(1/2*x^2-1/2)*exp(x)*sin(x)","A"
566,1,36,69,0.083000," ","int(x^2*sin(x)/exp(3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\left(-\frac{1}{10} x^{2}-\frac{3}{25} x -\frac{13}{250}\right) {\mathrm e}^{-3 x} \cos \left(x \right)+\left(-\frac{3}{10} x^{2}-\frac{4}{25} x -\frac{9}{250}\right) {\mathrm e}^{-3 x} \sin \left(x \right)$&$36$\\ risch&$\left(-\frac{1}{500}+\frac{3 i}{500}\right) \left(25 x^{2}+5 i x +15 x +3 i+4\right) {\mathrm e}^{\left(-3+i\right) x}+\left(-\frac{1}{500}-\frac{3 i}{500}\right) \left(25 x^{2}-5 i x +15 x -3 i+4\right) {\mathrm e}^{\left(-3-i\right) x}$&$54$\\ norman&$\frac{\left(-\frac{13}{250}-\frac{3 x}{25}-\frac{x^{2}}{10}+\frac{13 \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{250}-\frac{8 x \tan \left(\frac{x}{2}\right)}{25}+\frac{3 x \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{25}-\frac{3 x^{2} \tan \left(\frac{x}{2}\right)}{5}+\frac{x^{2} \left(\tan^{2}\left(\frac{x}{2}\right)\right)}{10}-\frac{9 \tan \left(\frac{x}{2}\right)}{125}\right) {\mathrm e}^{-3 x}}{1+\tan^{2}\left(\frac{x}{2}\right)}$&$78$\\ \hline \end{longtable}"," ",0,"(-1/10*x^2-3/25*x-13/250)*exp(-3*x)*cos(x)+(-3/10*x^2-4/25*x-9/250)*exp(-3*x)*sin(x)","A"
567,1,106,127,0.106000," ","int(exp(1/2*x)*x^2*cos(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\left(\frac{1}{202612}-\frac{3 i}{101306}\right) \left(1369 x^{2}+888 i x -148 x -96 i-280\right) {\mathrm e}^{\left(\frac{1}{2}+3 i\right) x}+\left(\frac{3}{500}-\frac{3 i}{250}\right) \left(25 x^{2}+40 i x -20 x -32 i-24\right) {\mathrm e}^{\left(\frac{1}{2}+i\right) x}+\left(\frac{3}{500}+\frac{3 i}{250}\right) \left(25 x^{2}-40 i x -20 x +32 i-24\right) {\mathrm e}^{\left(\frac{1}{2}-i\right) x}+\left(\frac{1}{202612}+\frac{3 i}{101306}\right) \left(1369 x^{2}-888 i x -148 x +96 i-280\right) {\mathrm e}^{\left(\frac{1}{2}-3 i\right) x}$&$106$\\ \hline \end{longtable}"," ",0,"(1/202612-3/101306*I)*(888*I*x+1369*x^2-280-96*I-148*x)*exp((1/2+3*I)*x)+(3/500-3/250*I)*(40*I*x+25*x^2-24-32*I-20*x)*exp((1/2+I)*x)+(3/500+3/250*I)*(-40*I*x+25*x^2-24+32*I-20*x)*exp((1/2-I)*x)+(1/202612+3/101306*I)*(-888*I*x+1369*x^2-280+96*I-148*x)*exp((1/2-3*I)*x)","C"
568,1,40,69,0.072000," ","int(exp(2*x)*x^2*sin(4*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\left(-\frac{1}{5} x^{2}+\frac{2}{25} x +\frac{1}{250}\right) {\mathrm e}^{2 x} \cos \left(4 x \right)+\left(\frac{1}{10} x^{2}+\frac{3}{50} x -\frac{11}{500}\right) {\mathrm e}^{2 x} \sin \left(4 x \right)$&$40$\\ risch&$\left(-\frac{1}{500}-\frac{i}{1000}\right) \left(50 x^{2}+20 i x -10 x -4 i-3\right) {\mathrm e}^{\left(2+4 i\right) x}+\left(-\frac{1}{500}+\frac{i}{1000}\right) \left(50 x^{2}-20 i x -10 x +4 i-3\right) {\mathrm e}^{\left(2-4 i\right) x}$&$54$\\ norman&$\frac{\frac{2 x \,{\mathrm e}^{2 x}}{25}-\frac{{\mathrm e}^{2 x} x^{2}}{5}-\frac{11 \,{\mathrm e}^{2 x} \tan \left(2 x \right)}{250}-\frac{{\mathrm e}^{2 x} \left(\tan^{2}\left(2 x \right)\right)}{250}+\frac{3 x \,{\mathrm e}^{2 x} \tan \left(2 x \right)}{25}-\frac{2 x \,{\mathrm e}^{2 x} \left(\tan^{2}\left(2 x \right)\right)}{25}+\frac{{\mathrm e}^{2 x} x^{2} \tan \left(2 x \right)}{5}+\frac{{\mathrm e}^{2 x} x^{2} \left(\tan^{2}\left(2 x \right)\right)}{5}+\frac{{\mathrm e}^{2 x}}{250}}{1+\tan^{2}\left(2 x \right)}$&$109$\\ \hline \end{longtable}"," ",0,"(-1/5*x^2+2/25*x+1/250)*exp(2*x)*cos(4*x)+(1/10*x^2+3/50*x-11/500)*exp(2*x)*sin(4*x)","A"
569,1,106,125,0.091000," ","int(exp(1/2*x)*x^2*cos(x)*sin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\left(-\frac{1}{202612}+\frac{3 i}{101306}\right) \left(1369 x^{2}+888 i x -148 x -96 i-280\right) {\mathrm e}^{\left(\frac{1}{2}+3 i\right) x}+\left(\frac{1}{500}-\frac{i}{250}\right) \left(25 x^{2}+40 i x -20 x -32 i-24\right) {\mathrm e}^{\left(\frac{1}{2}+i\right) x}+\left(\frac{1}{500}+\frac{i}{250}\right) \left(25 x^{2}-40 i x -20 x +32 i-24\right) {\mathrm e}^{\left(\frac{1}{2}-i\right) x}+\left(-\frac{1}{202612}-\frac{3 i}{101306}\right) \left(1369 x^{2}-888 i x -148 x +96 i-280\right) {\mathrm e}^{\left(\frac{1}{2}-3 i\right) x}$&$106$\\ \hline \end{longtable}"," ",0,"(-1/202612+3/101306*I)*(888*I*x+1369*x^2-280-96*I-148*x)*exp((1/2+3*I)*x)+(1/500-1/250*I)*(40*I*x+25*x^2-24-32*I-20*x)*exp((1/2+I)*x)+(1/500+1/250*I)*(-40*I*x+25*x^2-24+32*I-20*x)*exp((1/2-I)*x)-(1/202612+3/101306*I)*(-888*I*x+1369*x^2-280+96*I-148*x)*exp((1/2-3*I)*x)","C"
570,1,3,2,0.052000," ","int(cosh(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline lookup&$\sinh \left(x \right)$&$3$\\ default&$\sinh \left(x \right)$&$3$\\ meijerg&$\sinh \left(x \right)$&$3$\\ risch&$-\frac{{\mathrm e}^{-x}}{2}+\frac{{\mathrm e}^{x}}{2}$&$12$\\ \hline \end{longtable}"," ",0,"sinh(x)","A"
571,1,3,2,0.030000," ","int(sinh(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline lookup&$\cosh \left(x \right)$&$3$\\ default&$\cosh \left(x \right)$&$3$\\ risch&$\frac{{\mathrm e}^{-x}}{2}+\frac{{\mathrm e}^{x}}{2}$&$12$\\ meijerg&$-\sqrt{\pi}\, \left(\frac{1}{\sqrt{\pi}}-\frac{\cosh \left(x \right)}{\sqrt{\pi}}\right)$&$17$\\ \hline \end{longtable}"," ",0,"cosh(x)","A"
572,1,4,3,0.020000," ","int(tanh(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline lookup&$\ln \left(\cosh \left(x \right)\right)$&$4$\\ default&$\ln \left(\cosh \left(x \right)\right)$&$4$\\ risch&$-x +\ln \left(1+{\mathrm e}^{2 x}\right)$&$12$\\ derivativedivides&$-\frac{\ln \left(\tanh \left(x \right)-1\right)}{2}-\frac{\ln \left(1+\tanh \left(x \right)\right)}{2}$&$16$\\ \hline \end{longtable}"," ",0,"ln(cosh(x))","A"
573,1,4,3,0.024000," ","int(coth(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline lookup&$\ln \left(\sinh \left(x \right)\right)$&$4$\\ default&$\ln \left(\sinh \left(x \right)\right)$&$4$\\ risch&$-x +\ln \left(-1+{\mathrm e}^{2 x}\right)$&$12$\\ derivativedivides&$-\frac{\ln \left(\coth \left(x \right)-1\right)}{2}-\frac{\ln \left(\coth \left(x \right)+1\right)}{2}$&$16$\\ \hline \end{longtable}"," ",0,"ln(sinh(x))","A"
574,1,4,3,0.027000," ","int(sech(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline lookup&$\arctan \left(\sinh \left(x \right)\right)$&$4$\\ default&$\arctan \left(\sinh \left(x \right)\right)$&$4$\\ risch&$i \ln \left({\mathrm e}^{x}+i\right)-i \ln \left({\mathrm e}^{x}-i\right)$&$20$\\ \hline \end{longtable}"," ",0,"arctan(sinh(x))","A"
575,1,6,5,0.016000," ","int(csch(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline lookup&$\ln \left(\tanh \left(\frac{x}{2}\right)\right)$&$6$\\ default&$\ln \left(\tanh \left(\frac{x}{2}\right)\right)$&$6$\\ risch&$\ln \left(-1+{\mathrm e}^{x}\right)-\ln \left(1+{\mathrm e}^{x}\right)$&$14$\\ \hline \end{longtable}"," ",0,"ln(tanh(1/2*x))","A"
576,1,11,10,0.030000," ","int(cosh(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{2}+\frac{\cosh \left(x \right) \sinh \left(x \right)}{2}$&$11$\\ risch&$\frac{x}{2}+\frac{{\mathrm e}^{2 x}}{8}-\frac{{\mathrm e}^{-2 x}}{8}$&$17$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"1/2*x+1/2*cosh(x)*sinh(x)","A"
577,1,18,15,0.340000," ","int(sinh(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\left(\frac{8}{15}+\frac{\left(\sinh^{4}\left(x \right)\right)}{5}-\frac{4 \left(\sinh^{2}\left(x \right)\right)}{15}\right) \cosh \left(x \right)$&$18$\\ risch&$\frac{{\mathrm e}^{5 x}}{160}-\frac{5 \,{\mathrm e}^{3 x}}{96}+\frac{5 \,{\mathrm e}^{x}}{16}+\frac{5 \,{\mathrm e}^{-x}}{16}-\frac{5 \,{\mathrm e}^{-3 x}}{96}+\frac{{\mathrm e}^{-5 x}}{160}$&$36$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"(8/15+1/5*sinh(x)^4-4/15*sinh(x)^2)*cosh(x)","A"
578,1,26,12,0.025000," ","int(tanh(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\left(\tanh^{3}\left(x \right)\right)}{3}-\tanh \left(x \right)-\frac{\ln \left(\tanh \left(x \right)-1\right)}{2}+\frac{\ln \left(1+\tanh \left(x \right)\right)}{2}$&$26$\\ default&$-\frac{\left(\tanh^{3}\left(x \right)\right)}{3}-\tanh \left(x \right)-\frac{\ln \left(\tanh \left(x \right)-1\right)}{2}+\frac{\ln \left(1+\tanh \left(x \right)\right)}{2}$&$26$\\ risch&$x +\frac{4 \,{\mathrm e}^{4 x}+4 \,{\mathrm e}^{2 x}+\frac{8}{3}}{\left(1+{\mathrm e}^{2 x}\right)^{3}}$&$27$\\ \hline \end{longtable}"," ",0,"-1/3*tanh(x)^3-tanh(x)-1/2*ln(tanh(x)-1)+1/2*ln(1+tanh(x))","B"
579,1,11,12,0.344000," ","int(csch(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\coth \left(x \right) \mathrm{csch}\left(x \right)}{2}+\arctanh \left({\mathrm e}^{x}\right)$&$11$\\ risch&$-\frac{{\mathrm e}^{x} \left(1+{\mathrm e}^{2 x}\right)}{\left(-1+{\mathrm e}^{2 x}\right)^{2}}+\frac{\ln \left(1+{\mathrm e}^{x}\right)}{2}-\frac{\ln \left(-1+{\mathrm e}^{x}\right)}{2}$&$34$\\ \hline \end{longtable}"," ",0,"-1/2*coth(x)*csch(x)+arctanh(exp(x))","A"
580,1,21,20,0.347000," ","int(1/cosh(x)^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\left(\frac{\mathrm{sech}\left(x \right)^{3}}{4}+\frac{3 \,\mathrm{sech}\left(x \right)}{8}\right) \tanh \left(x \right)+\frac{3 \arctan \left({\mathrm e}^{x}\right)}{4}$&$21$\\ risch&$\frac{{\mathrm e}^{x} \left(3 \,{\mathrm e}^{6 x}+11 \,{\mathrm e}^{4 x}-11 \,{\mathrm e}^{2 x}-3\right)}{4 \left(1+{\mathrm e}^{2 x}\right)^{4}}+\frac{3 i \ln \left({\mathrm e}^{x}+i\right)}{8}-\frac{3 i \ln \left({\mathrm e}^{x}-i\right)}{8}$&$52$\\ \hline \end{longtable}"," ",0,"(1/4*sech(x)^3+3/8*sech(x))*tanh(x)+3/4*arctan(exp(x))","A"
581,1,17,16,0.043000," ","int(tanh(x)^5/sech(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(\sinh^{4}\left(x \right)\right)}{4}-\frac{\left(\sinh^{2}\left(x \right)\right)}{2}+\ln \left(\cosh \left(x \right)\right)$&$17$\\ risch&$-x +\frac{{\mathrm e}^{4 x}}{64}-\frac{3 \,{\mathrm e}^{2 x}}{16}-\frac{3 \,{\mathrm e}^{-2 x}}{16}+\frac{{\mathrm e}^{-4 x}}{64}+\ln \left(1+{\mathrm e}^{2 x}\right)$&$36$\\ \hline \end{longtable}"," ",0,"1/4*sinh(x)^4-1/2*sinh(x)^2+ln(cosh(x))","A"
582,0,0,19,0.059000," ","int(sech(x)^(3/4)*tanh(x)^5,x)","\[\int \mathrm{sech}\left(x \right)^{\frac{3}{4}} \left(\tanh^{5}\left(x \right)\right)\, dx\]"," ",0,"int(sech(x)^(3/4)*tanh(x)^5,x)","F"
583,1,36,35,0.069000," ","int(1/(a+b*cosh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{2 \arctanh \left(\frac{\left(a -b \right) \tanh \left(\frac{x}{2}\right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}$&$36$\\ risch&$\frac{\ln \left({\mathrm e}^{x}+\frac{a \sqrt{a^{2}-b^{2}}-a^{2}+b^{2}}{b \sqrt{a^{2}-b^{2}}}\right)}{\sqrt{a^{2}-b^{2}}}-\frac{\ln \left({\mathrm e}^{x}+\frac{a \sqrt{a^{2}-b^{2}}+a^{2}-b^{2}}{b \sqrt{a^{2}-b^{2}}}\right)}{\sqrt{a^{2}-b^{2}}}$&$109$\\ \hline \end{longtable}"," ",0,"2/((a+b)*(a-b))^(1/2)*arctanh((a-b)*tanh(1/2*x)/((a+b)*(a-b))^(1/2))","A"
584,1,15,21,0.037000," ","int(1/(1+cosh(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 \left(1+3 \,{\mathrm e}^{x}\right)}{3 \left(1+{\mathrm e}^{x}\right)^{3}}$&$15$\\ default&$-\frac{\left(\tanh^{3}\left(\frac{x}{2}\right)\right)}{6}+\frac{\tanh \left(\frac{x}{2}\right)}{2}$&$16$\\ \hline \end{longtable}"," ",0,"-2/3*(1+3*exp(x))/(1+exp(x))^3","A"
585,1,55,39,0.057000," ","int(1/(a+b*tanh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(1+\tanh \left(x \right)\right)}{2 a -2 b}-\frac{b \ln \left(a +b \tanh \left(x \right)\right)}{\left(a +b \right) \left(a -b \right)}-\frac{\ln \left(\tanh \left(x \right)-1\right)}{2 a +2 b}$&$55$\\ default&$\frac{\ln \left(1+\tanh \left(x \right)\right)}{2 a -2 b}-\frac{b \ln \left(a +b \tanh \left(x \right)\right)}{\left(a +b \right) \left(a -b \right)}-\frac{\ln \left(\tanh \left(x \right)-1\right)}{2 a +2 b}$&$55$\\ risch&$\frac{x}{a +b}+\frac{2 b x}{a^{2}-b^{2}}-\frac{b \ln \left({\mathrm e}^{2 x}+\frac{a -b}{a +b}\right)}{a^{2}-b^{2}}$&$55$\\ \hline \end{longtable}"," ",0,"1/(2*a-2*b)*ln(1+tanh(x))-b/(a+b)/(a-b)*ln(a+b*tanh(x))-1/(2*a+2*b)*ln(tanh(x)-1)","A"
586,1,98,27,0.170000," ","int(1/(a^2+b^2*cosh(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\ln \left(\sqrt{a^{2}+b^{2}}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+2 a \tanh \left(\frac{x}{2}\right)+\sqrt{a^{2}+b^{2}}\right)}{2 a \sqrt{a^{2}+b^{2}}}-\frac{\ln \left(\sqrt{a^{2}+b^{2}}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)-2 a \tanh \left(\frac{x}{2}\right)+\sqrt{a^{2}+b^{2}}\right)}{2 a \sqrt{a^{2}+b^{2}}}$&$98$\\ risch&$\frac{\ln \left({\mathrm e}^{2 x}+\frac{2 a^{2} \sqrt{a^{2}+b^{2}}+b^{2} \sqrt{a^{2}+b^{2}}-2 a^{3}-2 b^{2} a}{b^{2} \sqrt{a^{2}+b^{2}}}\right)}{2 a \sqrt{a^{2}+b^{2}}}-\frac{\ln \left({\mathrm e}^{2 x}+\frac{2 a^{2} \sqrt{a^{2}+b^{2}}+b^{2} \sqrt{a^{2}+b^{2}}+2 a^{3}+2 b^{2} a}{b^{2} \sqrt{a^{2}+b^{2}}}\right)}{2 a \sqrt{a^{2}+b^{2}}}$&$146$\\ \hline \end{longtable}"," ",0,"1/2/a/(a^2+b^2)^(1/2)*ln((a^2+b^2)^(1/2)*tanh(1/2*x)^2+2*a*tanh(1/2*x)+(a^2+b^2)^(1/2))-1/2/a/(a^2+b^2)^(1/2)*ln((a^2+b^2)^(1/2)*tanh(1/2*x)^2-2*a*tanh(1/2*x)+(a^2+b^2)^(1/2))","B"
587,1,74,31,0.131000," ","int(1/(a^2-b^2*cosh(x)^2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctanh \left(\frac{\left(a -b \right) \tanh \left(\frac{x}{2}\right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{a \sqrt{\left(a +b \right) \left(a -b \right)}}+\frac{\arctanh \left(\frac{\left(a +b \right) \tanh \left(\frac{x}{2}\right)}{\sqrt{\left(a +b \right) \left(a -b \right)}}\right)}{a \sqrt{\left(a +b \right) \left(a -b \right)}}$&$74$\\ risch&$\frac{\ln \left({\mathrm e}^{2 x}-\frac{2 a^{2} \sqrt{a^{2}-b^{2}}-b^{2} \sqrt{a^{2}-b^{2}}-2 a^{3}+2 b^{2} a}{b^{2} \sqrt{a^{2}-b^{2}}}\right)}{2 \sqrt{a^{2}-b^{2}}\, a}-\frac{\ln \left({\mathrm e}^{2 x}-\frac{2 a^{2} \sqrt{a^{2}-b^{2}}-b^{2} \sqrt{a^{2}-b^{2}}+2 a^{3}-2 b^{2} a}{b^{2} \sqrt{a^{2}-b^{2}}}\right)}{2 \sqrt{a^{2}-b^{2}}\, a}$&$166$\\ \hline \end{longtable}"," ",0,"1/a/((a+b)*(a-b))^(1/2)*arctanh((a-b)*tanh(1/2*x)/((a+b)*(a-b))^(1/2))+1/a/((a+b)*(a-b))^(1/2)*arctanh((a+b)*tanh(1/2*x)/((a+b)*(a-b))^(1/2))","B"
588,1,46,17,0.083000," ","int(1/(1-sinh(x)^4),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{1}{1+{\mathrm e}^{2 x}}+\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 x}-3+2 \sqrt{2}\right)}{8}-\frac{\sqrt{2}\, \ln \left({\mathrm e}^{2 x}-3-2 \sqrt{2}\right)}{8}$&$46$\\ default&$\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 \tanh \left(\frac{x}{2}\right)+2\right) \sqrt{2}}{4}\right)}{4}+\frac{\tanh \left(\frac{x}{2}\right)}{\tanh^{2}\left(\frac{x}{2}\right)+1}+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 \tanh \left(\frac{x}{2}\right)-2\right) \sqrt{2}}{4}\right)}{4}$&$55$\\ \hline \end{longtable}"," ",0,"-1/(1+exp(2*x))+1/8*2^(1/2)*ln(exp(2*x)-3+2*2^(1/2))-1/8*2^(1/2)*ln(exp(2*x)-3-2*2^(1/2))","B"
589,1,44,26,0.207000," ","int((cosh(x)^3-sinh(x)^3)/(cosh(x)^3+sinh(x)^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{{\mathrm e}^{-2 x}}{6}+\frac{2 i \sqrt{3}\, \ln \left({\mathrm e}^{2 x}+i \sqrt{3}\right)}{9}-\frac{2 i \sqrt{3}\, \ln \left({\mathrm e}^{2 x}-i \sqrt{3}\right)}{9}$&$44$\\ default&$\frac{2 i \sqrt{3}\, \ln \left(\tanh^{2}\left(\frac{x}{2}\right)+\left(-1-i \sqrt{3}\right) \tanh \left(\frac{x}{2}\right)+1\right)}{9}-\frac{2 i \sqrt{3}\, \ln \left(\tanh^{2}\left(\frac{x}{2}\right)+\left(-1+i \sqrt{3}\right) \tanh \left(\frac{x}{2}\right)+1\right)}{9}-\frac{2}{3 \left(1+\tanh \left(\frac{x}{2}\right)\right)^{2}}+\frac{2}{3 \left(1+\tanh \left(\frac{x}{2}\right)\right)}$&$78$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"-1/6*exp(-2*x)+2/9*I*3^(1/2)*ln(exp(2*x)+I*3^(1/2))-2/9*I*3^(1/2)*ln(exp(2*x)-I*3^(1/2))","C"
590,1,23,22,0.128000," ","int(cosh(x)*cosh(2*x)*cosh(3*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{4}+\frac{\sinh \left(2 x \right)}{8}+\frac{\sinh \left(4 x \right)}{16}+\frac{\sinh \left(6 x \right)}{24}$&$23$\\ risch&$\frac{x}{4}+\frac{{\mathrm e}^{6 x}}{48}+\frac{{\mathrm e}^{4 x}}{32}+\frac{{\mathrm e}^{2 x}}{16}-\frac{{\mathrm e}^{-2 x}}{16}-\frac{{\mathrm e}^{-4 x}}{32}-\frac{{\mathrm e}^{-6 x}}{48}$&$41$\\ \hline \end{longtable}"," ",0,"1/4*x+1/8*sinh(2*x)+1/16*sinh(4*x)+1/24*sinh(6*x)","A"
591,1,23,22,0.197000," ","int(cosh(3/2*x)*sinh(x)*sinh(5/2*x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{x}{4}+\frac{\sinh \left(2 x \right)}{8}-\frac{\sinh \left(3 x \right)}{12}+\frac{\sinh \left(5 x \right)}{20}$&$23$\\ risch&$-\frac{x}{4}+\frac{{\mathrm e}^{5 x}}{40}-\frac{{\mathrm e}^{3 x}}{24}+\frac{{\mathrm e}^{2 x}}{16}-\frac{{\mathrm e}^{-2 x}}{16}+\frac{{\mathrm e}^{-3 x}}{24}-\frac{{\mathrm e}^{-5 x}}{40}$&$41$\\ \hline \end{longtable}"," ",0,"-1/4*x+1/8*sinh(2*x)-1/12*sinh(3*x)+1/20*sinh(5*x)","A"
592,1,987,53,0.484000," ","int(cosh(x)*(-cosh(2*x)+tanh(x))/(sinh(x)^2+sinh(2*x))/sinh(2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{\frac{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}{\left(\tanh^{2}\left(\frac{x}{2}\right)-1\right)^{2}}}\, \left(\tanh^{2}\left(\frac{x}{2}\right)-1\right) \left(\sqrt{3}\, \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}\, \sqrt{2}\, \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)-\sqrt{3}\, \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}\, \sqrt{2}\, \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}-i-\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)+i \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{2}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}+24 i \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{2}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}-8 i \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{2}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}+i \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{2}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}-i-\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}-18 i \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{2}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticF \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}-2 \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}\, \sqrt{2}\, \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}-i+\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)-24 \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{2}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}-\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}-8 \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{2}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}+\frac{i}{2}, \frac{\sqrt{2}}{2}\right) \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}-2 \sqrt{\left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right)}\, \sqrt{2}\, \sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{-i \left(-\tanh \left(\frac{x}{2}\right)+i\right)}\, \sqrt{i \tanh \left(\frac{x}{2}\right)}\, \EllipticPi \left(\sqrt{-i \left(\tanh \left(\frac{x}{2}\right)+i\right)}, \frac{1}{2}-i-\frac{i \sqrt{3}}{2}, \frac{\sqrt{2}}{2}\right)+12 \sqrt{\tanh^{3}\left(\frac{x}{2}\right)+\tanh \left(\frac{x}{2}\right)}\, \left(\tanh^{2}\left(\frac{x}{2}\right)\right)+12 \sqrt{\tanh^{3}\left(\frac{x}{2}\right)+\tanh \left(\frac{x}{2}\right)}\right)}{24 \left(\tanh^{2}\left(\frac{x}{2}\right)+1\right) \tanh \left(\frac{x}{2}\right) \sqrt{\tanh^{3}\left(\frac{x}{2}\right)+\tanh \left(\frac{x}{2}\right)}}$&$987$\\ \hline \end{longtable}"," ",0,"-1/24*((tanh(1/2*x)^2+1)*tanh(1/2*x)/(tanh(1/2*x)^2-1)^2)^(1/2)*(tanh(1/2*x)^2-1)*(3^(1/2)*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)*2^(1/2)*(-I*(tanh(1/2*x)+I))^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2-I+1/2*I*3^(1/2),1/2*2^(1/2))-3^(1/2)*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)*2^(1/2)*(-I*(tanh(1/2*x)+I))^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2-I-1/2*I*3^(1/2),1/2*2^(1/2))+I*(-I*(tanh(1/2*x)+I))^(1/2)*2^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2-I+1/2*I*3^(1/2),1/2*2^(1/2))*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)+24*I*(-I*(tanh(1/2*x)+I))^(1/2)*2^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)-8*I*(-I*(tanh(1/2*x)+I))^(1/2)*2^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)+I*(-I*(tanh(1/2*x)+I))^(1/2)*2^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2-I-1/2*I*3^(1/2),1/2*2^(1/2))*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)-18*I*(-I*(tanh(1/2*x)+I))^(1/2)*2^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticF((-I*(tanh(1/2*x)+I))^(1/2),1/2*2^(1/2))*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)-2*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)*2^(1/2)*(-I*(tanh(1/2*x)+I))^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2-I+1/2*I*3^(1/2),1/2*2^(1/2))-24*(-I*(tanh(1/2*x)+I))^(1/2)*2^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2-1/2*I,1/2*2^(1/2))*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)-8*(-I*(tanh(1/2*x)+I))^(1/2)*2^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2+1/2*I,1/2*2^(1/2))*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)-2*((tanh(1/2*x)^2+1)*tanh(1/2*x))^(1/2)*2^(1/2)*(-I*(tanh(1/2*x)+I))^(1/2)*(-I*(-tanh(1/2*x)+I))^(1/2)*(I*tanh(1/2*x))^(1/2)*EllipticPi((-I*(tanh(1/2*x)+I))^(1/2),1/2-I-1/2*I*3^(1/2),1/2*2^(1/2))+12*(tanh(1/2*x)^3+tanh(1/2*x))^(1/2)*tanh(1/2*x)^2+12*(tanh(1/2*x)^3+tanh(1/2*x))^(1/2))/(tanh(1/2*x)^2+1)/tanh(1/2*x)/(tanh(1/2*x)^3+tanh(1/2*x))^(1/2)","C"
593,1,30,29,0.054000," ","int(sinh(x)/(-9+4*cosh(x)^2)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\cosh \left(x \right)}{27 \left(-9+4 \left(\cosh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{2 \cosh \left(x \right)}{243 \sqrt{-9+4 \left(\cosh^{2}\left(x \right)\right)}}$&$30$\\ default&$-\frac{\cosh \left(x \right)}{27 \left(-9+4 \left(\cosh^{2}\left(x \right)\right)\right)^{\frac{3}{2}}}+\frac{2 \cosh \left(x \right)}{243 \sqrt{-9+4 \left(\cosh^{2}\left(x \right)\right)}}$&$30$\\ \hline \end{longtable}"," ",0,"-1/27*cosh(x)/(-9+4*cosh(x)^2)^(3/2)+2/243*cosh(x)/(-9+4*cosh(x)^2)^(1/2)","A"
594,1,28,25,0.130000," ","int(sinh(x)^2*sinh(2*x)/(1-sinh(x)^2)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\mathit{`\,int/indef0`\,}\left(-\frac{2 \left(\sinh^{3}\left(x \right)\right)}{\left(\sinh^{2}\left(x \right)-1\right) \sqrt{1-\left(\sinh^{2}\left(x \right)\right)}}, \sinh \left(x \right)\right)$&$28$\\ meijerg&\verb|error in int/gbinthm/express: improper op or subscript selector\|& N/A\\ \hline \end{longtable}"," ",0,"`int/indef0`(-2*sinh(x)^3/(sinh(x)^2-1)/(1-sinh(x)^2)^(1/2),sinh(x))","C"
595,1,63,12,0.175000," ","int(cosh(x)/cosh(2*x)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\left(2 \left(\cosh^{2}\left(x \right)\right)-1\right) \left(\sinh^{2}\left(x \right)\right)}\, \ln \left(\sqrt{2}\, \left(\sinh^{2}\left(x \right)\right)+\frac{\sqrt{2}}{4}+\sqrt{2 \left(\sinh^{4}\left(x \right)\right)+\sinh^{2}\left(x \right)}\right) \sqrt{2}}{4 \sinh \left(x \right) \sqrt{2 \left(\cosh^{2}\left(x \right)\right)-1}}$&$63$\\ \hline \end{longtable}"," ",0,"1/4*((2*cosh(x)^2-1)*sinh(x)^2)^(1/2)*ln(2^(1/2)*sinh(x)^2+1/4*2^(1/2)+(2*sinh(x)^4+sinh(x)^2)^(1/2))*2^(1/2)/sinh(x)/(2*cosh(x)^2-1)^(1/2)","B"
596,1,28,14,0.030000," ","int(x*tanh(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{2}}{2}-2 x +\frac{2 x}{1+{\mathrm e}^{2 x}}+\ln \left(1+{\mathrm e}^{2 x}\right)$&$28$\\ \hline \end{longtable}"," ",0,"1/2*x^2-2*x+2*x/(1+exp(2*x))+ln(1+exp(2*x))","A"
597,1,28,14,0.033000," ","int(x*coth(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x^{2}}{2}-2 x -\frac{2 x}{-1+{\mathrm e}^{2 x}}+\ln \left(-1+{\mathrm e}^{2 x}\right)$&$28$\\ \hline \end{longtable}"," ",0,"1/2*x^2-2*x-2*x/(-1+exp(2*x))+ln(-1+exp(2*x))","A"
598,1,14,15,0.091000," ","int((x+cosh(x)+sinh(x))/(cosh(x)-sinh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\left(-1+x \right) {\mathrm e}^{x}+\frac{{\mathrm e}^{2 x}}{2}$&$14$\\ \hline \end{longtable}"," ",0,"(-1+x)*exp(x)+1/2*exp(2*x)","A"
599,1,16,13,0.060000," ","int((x+cosh(x)+sinh(x))/(1+cosh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$2 x -\frac{2 \left(-1+x \right)}{1+{\mathrm e}^{x}}$&$16$\\ \hline \end{longtable}"," ",0,"2*x-2*(-1+x)/(1+exp(x))","A"
600,1,25,16,0.105000," ","int(exp(2*x)/sinh(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{8 \left(3 \,{\mathrm e}^{4 x}-3 \,{\mathrm e}^{2 x}+1\right)}{3 \left(-1+{\mathrm e}^{2 x}\right)^{3}}$&$25$\\ \hline \end{longtable}"," ",0,"-8/3*(3*exp(4*x)-3*exp(2*x)+1)/(-1+exp(2*x))^3","A"
601,1,11,10,0.350000," ","int(1/exp(2*x)/cosh(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{8}{3 \left(1+{\mathrm e}^{2 x}\right)^{3}}$&$11$\\ default&$2 \tanh \left(x \right)+\frac{1}{\cosh \left(x \right)^{2}}-\left(\frac{2}{3}+\frac{\mathrm{sech}\left(x \right)^{2}}{3}\right) \tanh \left(x \right)$&$22$\\ \hline \end{longtable}"," ",0,"-8/3/(1+exp(2*x))^3","A"
602,1,7,6,0.097000," ","int(exp(x)/(cosh(x)-sinh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{{\mathrm e}^{2 x}}{2}$&$7$\\ gosper&$\frac{{\mathrm e}^{x}}{2 \cosh \left(x \right)-2 \sinh \left(x \right)}$&$14$\\ default&$\frac{2}{\left(\tanh \left(\frac{x}{2}\right)-1\right)^{2}}+\frac{2}{\tanh \left(\frac{x}{2}\right)-1}$&$22$\\ \hline \end{longtable}"," ",0,"1/2*exp(2*x)","A"
603,1,13,12,0.142000," ","int(exp(m*x)/(cosh(x)+sinh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{{\mathrm e}^{\left(-1+m \right) x}}{-1+m}$&$13$\\ gosper&$\frac{{\mathrm e}^{m x}}{\left(-1+m \right) \left(\cosh \left(x \right)+\sinh \left(x \right)\right)}$&$18$\\ default&$\frac{\sinh \left(\left(-1+m \right) x \right)}{-1+m}+\frac{\cosh \left(\left(-1+m \right) x \right)}{-1+m}$&$26$\\ \hline \end{longtable}"," ",0,"exp((-1+m)*x)/(-1+m)","A"
604,1,2,1,0.059000," ","int(exp(x)/(cosh(x)+sinh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x$&$2$\\ \hline \end{longtable}"," ",0,"x","A"
605,1,17,20,0.048000," ","int(exp(x)/(1-cosh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{2}{-1+{\mathrm e}^{x}}-2 \ln \left(-1+{\mathrm e}^{x}\right)$&$17$\\ default&$2 \ln \left(\tanh \left(\frac{x}{2}\right)-1\right)+\frac{1}{\tanh \left(\frac{x}{2}\right)}-2 \ln \left(\tanh \left(\frac{x}{2}\right)\right)$&$24$\\ \hline \end{longtable}"," ",0,"2/(-1+exp(x))-2*ln(-1+exp(x))","A"
606,1,12,11,0.052000," ","int(exp(x)*(1+sinh(x))/(1+cosh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&${\mathrm e}^{x}+\frac{2}{1+{\mathrm e}^{x}}$&$12$\\ default&$-\tanh \left(\frac{x}{2}\right)-\frac{2}{\tanh \left(\frac{x}{2}\right)-1}$&$18$\\ \hline \end{longtable}"," ",0,"exp(x)+2/(1+exp(x))","A"
607,1,12,13,0.067000," ","int(exp(x)*(1-sinh(x))/(1-cosh(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&${\mathrm e}^{x}+\frac{2}{-1+{\mathrm e}^{x}}$&$12$\\ default&$\frac{1}{\tanh \left(\frac{x}{2}\right)}-\frac{2}{\tanh \left(\frac{x}{2}\right)-1}$&$18$\\ \hline \end{longtable}"," ",0,"exp(x)+2/(-1+exp(x))","A"
608,1,19,26,0.030000," ","int(x^m*ln(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x \left(m \ln \left(x \right)+\ln \left(x \right)-1\right) x^{m}}{\left(1+m \right)^{2}}$&$19$\\ norman&$\frac{x \ln \left(x \right) {\mathrm e}^{m \ln \left(x \right)}}{1+m}-\frac{x \,{\mathrm e}^{m \ln \left(x \right)}}{m^{2}+2 m +1}$&$34$\\ \hline \end{longtable}"," ",0,"x*(m*ln(x)+ln(x)-1)/(1+m)^2*x^m","A"
609,1,41,42,0.036000," ","int(x^m*ln(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{x \left(m^{2} \ln \left(x \right)^{2}+2 m \ln \left(x \right)^{2}-2 m \ln \left(x \right)+\ln \left(x \right)^{2}-2 \ln \left(x \right)+2\right) x^{m}}{\left(1+m \right)^{3}}$&$41$\\ norman&$\frac{x \ln \left(x \right)^{2} {\mathrm e}^{m \ln \left(x \right)}}{1+m}+\frac{2 x \,{\mathrm e}^{m \ln \left(x \right)}}{m^{3}+3 m^{2}+3 m +1}-\frac{2 x \ln \left(x \right) {\mathrm e}^{m \ln \left(x \right)}}{m^{2}+2 m +1}$&$61$\\ \hline \end{longtable}"," ",0,"x*(m^2*ln(x)^2+2*m*ln(x)^2-2*m*ln(x)+ln(x)^2-2*ln(x)+2)/(1+m)^3*x^m","A"
610,1,23,22,0.104000," ","int(ln(x)^2/x^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{16}{27 x^{\frac{3}{2}}}-\frac{8 \ln \left(x \right)}{9 x^{\frac{3}{2}}}-\frac{2 \ln \left(x \right)^{2}}{3 x^{\frac{3}{2}}}$&$23$\\ default&$-\frac{16}{27 x^{\frac{3}{2}}}-\frac{8 \ln \left(x \right)}{9 x^{\frac{3}{2}}}-\frac{2 \ln \left(x \right)^{2}}{3 x^{\frac{3}{2}}}$&$23$\\ risch&$-\frac{16}{27 x^{\frac{3}{2}}}-\frac{8 \ln \left(x \right)}{9 x^{\frac{3}{2}}}-\frac{2 \ln \left(x \right)^{2}}{3 x^{\frac{3}{2}}}$&$23$\\ \hline \end{longtable}"," ",0,"-16/27/x^(3/2)-8/9*ln(x)/x^(3/2)-2/3*ln(x)^2/x^(3/2)","A"
611,1,25,24,0.022000," ","int((b*x+a)*ln(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline norman&$-a x -\frac{b \,x^{2}}{4}+a x \ln \left(x \right)+\frac{b \,x^{2} \ln \left(x \right)}{2}$&$25$\\ risch&$\left(\frac{1}{2} b \,x^{2}+a x \right) \ln \left(x \right)-\frac{b \,x^{2}}{4}-a x$&$25$\\ default&$b \left(\frac{x^{2} \ln \left(x \right)}{2}-\frac{x^{2}}{4}\right)+a \left(x \ln \left(x \right)-x \right)$&$27$\\ \hline \end{longtable}"," ",0,"-a*x-1/4*b*x^2+a*x*ln(x)+1/2*b*x^2*ln(x)","A"
612,1,58,57,0.316000," ","int((b*x+a)^3*ln(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-a^{3} x -\frac{3 a^{2} b \,x^{2}}{4}-\frac{a \,b^{2} x^{3}}{3}-\frac{b^{3} x^{4}}{16}-\frac{a^{4} \ln \left(x \right)}{4 b}+\frac{\left(b x +a \right)^{4} \ln \left(x \right)}{4 b}$&$58$\\ default&$b^{3} \left(\frac{x^{4} \ln \left(x \right)}{4}-\frac{x^{4}}{16}\right)+3 b^{2} a \left(\frac{x^{3} \ln \left(x \right)}{3}-\frac{x^{3}}{9}\right)+3 a^{2} b \left(\frac{x^{2} \ln \left(x \right)}{2}-\frac{x^{2}}{4}\right)+a^{3} \left(x \ln \left(x \right)-x \right)$&$69$\\ norman&$a^{3} x \ln \left(x \right)+a \,b^{2} x^{3} \ln \left(x \right)-a^{3} x -\frac{b^{3} x^{4}}{16}-\frac{a \,b^{2} x^{3}}{3}-\frac{3 a^{2} b \,x^{2}}{4}+\frac{b^{3} x^{4} \ln \left(x \right)}{4}+\frac{3 a^{2} b \,x^{2} \ln \left(x \right)}{2}$&$72$\\ \hline \end{longtable}"," ",0,"-a^3*x-3/4*a^2*b*x^2-1/3*a*b^2*x^3-1/16*b^3*x^4-1/4*a^4*ln(x)/b+1/4*(b*x+a)^4*ln(x)/b","A"
613,1,24,23,0.023000," ","int(-1-8*ln(x)^2+3*ln(x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-35 x +34 x \ln \left(x \right)-17 x \ln \left(x \right)^{2}+3 x \ln \left(x \right)^{3}$&$24$\\ norman&$-35 x +34 x \ln \left(x \right)-17 x \ln \left(x \right)^{2}+3 x \ln \left(x \right)^{3}$&$24$\\ risch&$-35 x +34 x \ln \left(x \right)-17 x \ln \left(x \right)^{2}+3 x \ln \left(x \right)^{3}$&$24$\\ \hline \end{longtable}"," ",0,"-35*x+34*x*ln(x)-17*x*ln(x)^2+3*x*ln(x)^3","A"
614,1,48,52,0.025000," ","int((x^4+1)*(1-2*ln(x)+ln(x)^3),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\left(\frac{1}{5} x^{5}+x \right) \ln \left(x \right)^{3}+\left(-\frac{3}{25} x^{5}-3 x \right) \ln \left(x \right)^{2}+\left(-\frac{44}{125} x^{5}+4 x \right) \ln \left(x \right)+\frac{169 x^{5}}{625}-3 x$&$48$\\ default&$-3 x +\frac{169 x^{5}}{625}+4 x \ln \left(x \right)-\frac{44 x^{5} \ln \left(x \right)}{125}-3 x \ln \left(x \right)^{2}-\frac{3 x^{5} \ln \left(x \right)^{2}}{25}+x \ln \left(x \right)^{3}+\frac{x^{5} \ln \left(x \right)^{3}}{5}$&$53$\\ norman&$-3 x +\frac{169 x^{5}}{625}+4 x \ln \left(x \right)-\frac{44 x^{5} \ln \left(x \right)}{125}-3 x \ln \left(x \right)^{2}-\frac{3 x^{5} \ln \left(x \right)^{2}}{25}+x \ln \left(x \right)^{3}+\frac{x^{5} \ln \left(x \right)^{3}}{5}$&$53$\\ \hline \end{longtable}"," ",0,"(1/5*x^5+x)*ln(x)^3+(-3/25*x^5-3*x)*ln(x)^2+(-44/125*x^5+4*x)*ln(x)+169/625*x^5-3*x","A"
615,1,31,35,0.030000," ","int(1/x^3/ln(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 \ln \left(x \right)^{2}-\ln \left(x \right)+1}{3 x^{2} \ln \left(x \right)^{3}}+\frac{4 \expIntegralEi \left(1, 2 \ln \left(x \right)\right)}{3}$&$31$\\ default&$-\frac{1}{3 x^{2} \ln \left(x \right)^{3}}+\frac{1}{3 x^{2} \ln \left(x \right)^{2}}-\frac{2}{3 x^{2} \ln \left(x \right)}+\frac{4 \expIntegralEi \left(1, 2 \ln \left(x \right)\right)}{3}$&$37$\\ \hline \end{longtable}"," ",0,"-1/3*(2*ln(x)^2-ln(x)+1)/x^2/ln(x)^3+4/3*Ei(1,2*ln(x))","A"
616,1,32,29,0.313000," ","int(ln(x)/(b*x+a),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\dilog \left(\frac{b x +a}{a}\right)}{b}+\frac{\ln \left(x \right) \ln \left(\frac{b x +a}{a}\right)}{b}$&$32$\\ risch&$\frac{\dilog \left(\frac{b x +a}{a}\right)}{b}+\frac{\ln \left(x \right) \ln \left(\frac{b x +a}{a}\right)}{b}$&$32$\\ \hline \end{longtable}"," ",0,"dilog((b*x+a)/a)/b+ln(x)*ln((b*x+a)/a)/b","A"
617,1,30,29,0.309000," ","int(ln(x)/(b*x+a)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x \ln \left(x \right)}{a \left(b x +a \right)}-\frac{\ln \left(b x +a \right)}{a b}$&$30$\\ norman&$\frac{x \ln \left(x \right)}{a \left(b x +a \right)}-\frac{\ln \left(b x +a \right)}{a b}$&$30$\\ risch&$-\frac{\ln \left(x \right)}{b \left(b x +a \right)}+\frac{\ln \left(-x \right)}{a b}-\frac{\ln \left(b x +a \right)}{a b}$&$41$\\ \hline \end{longtable}"," ",0,"x*ln(x)/a/(b*x+a)-ln(b*x+a)/a/b","A"
618,1,13,12,0.029000," ","int(ln(x)^n/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(x \right)^{1+n}}{1+n}$&$13$\\ default&$\frac{\ln \left(x \right)^{1+n}}{1+n}$&$13$\\ risch&$\frac{\ln \left(x \right) \ln \left(x \right)^{n}}{1+n}$&$13$\\ norman&$\frac{\ln \left(x \right) {\mathrm e}^{n \ln \left(\ln \left(x \right)\right)}}{1+n}$&$15$\\ \hline \end{longtable}"," ",0,"ln(x)^(1+n)/(1+n)","A"
619,1,20,19,0.037000," ","int((a+b*ln(x))^n/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(a +b \ln \left(x \right)\right)^{1+n}}{b \left(1+n \right)}$&$20$\\ default&$\frac{\left(a +b \ln \left(x \right)\right)^{1+n}}{b \left(1+n \right)}$&$20$\\ risch&$\frac{\left(a +b \ln \left(x \right)\right) \left(a +b \ln \left(x \right)\right)^{n}}{b \left(1+n \right)}$&$24$\\ norman&$\frac{\ln \left(x \right) {\mathrm e}^{n \ln \left(a +b \ln \left(x \right)\right)}}{1+n}+\frac{a \,{\mathrm e}^{n \ln \left(a +b \ln \left(x \right)\right)}}{b \left(1+n \right)}$&$40$\\ \hline \end{longtable}"," ",0,"(a+b*ln(x))^(1+n)/b/(1+n)","A"
620,1,12,11,0.020000," ","int(1/x/(a+b*ln(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(a +b \ln \left(x \right)\right)}{b}$&$12$\\ default&$\frac{\ln \left(a +b \ln \left(x \right)\right)}{b}$&$12$\\ norman&$\frac{\ln \left(a +b \ln \left(x \right)\right)}{b}$&$12$\\ risch&$\frac{\ln \left(\ln \left(x \right)+\frac{a}{b}\right)}{b}$&$14$\\ \hline \end{longtable}"," ",0,"ln(a+b*ln(x))/b","A"
621,1,24,23,0.039000," ","int(1/x/((a+b*ln(x))^n),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\left(a +b \ln \left(x \right)\right)^{1-n}}{b \left(1-n \right)}$&$24$\\ default&$\frac{\left(a +b \ln \left(x \right)\right)^{1-n}}{b \left(1-n \right)}$&$24$\\ risch&$-\frac{\left(a +b \ln \left(x \right)\right) \left(a +b \ln \left(x \right)\right)^{-n}}{b \left(-1+n \right)}$&$27$\\ norman&$\left(-\frac{\ln \left(x \right)}{-1+n}-\frac{a}{b \left(-1+n \right)}\right) {\mathrm e}^{-n \ln \left(a +b \ln \left(x \right)\right)}$&$35$\\ \hline \end{longtable}"," ",0,"(a+b*ln(x))^(1-n)/b/(1-n)","A"
622,1,15,14,0.022000," ","int(1/x/(a^2+ln(x)^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\ln \left(\ln \left(x \right)+\sqrt{a^{2}+\ln \left(x \right)^{2}}\right)$&$15$\\ default&$\ln \left(\ln \left(x \right)+\sqrt{a^{2}+\ln \left(x \right)^{2}}\right)$&$15$\\ \hline \end{longtable}"," ",0,"ln(ln(x)+(a^2+ln(x)^2)^(1/2))","A"
623,1,17,16,0.022000," ","int(1/x/(-a^2+ln(x)^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\ln \left(\ln \left(x \right)+\sqrt{-a^{2}+\ln \left(x \right)^{2}}\right)$&$17$\\ default&$\ln \left(\ln \left(x \right)+\sqrt{-a^{2}+\ln \left(x \right)^{2}}\right)$&$17$\\ \hline \end{longtable}"," ",0,"ln(ln(x)+(-a^2+ln(x)^2)^(1/2))","A"
624,1,17,16,0.021000," ","int(1/x/(a^2-ln(x)^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\arctan \left(\frac{\ln \left(x \right)}{\sqrt{a^{2}-\ln \left(x \right)^{2}}}\right)$&$17$\\ default&$\arctan \left(\frac{\ln \left(x \right)}{\sqrt{a^{2}-\ln \left(x \right)^{2}}}\right)$&$17$\\ \hline \end{longtable}"," ",0,"arctan(ln(x)/(a^2-ln(x)^2)^(1/2))","A"
625,1,37,20,0.022000," ","int(1/x/ln(x)/(a^2+ln(x)^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(\frac{2 a^{2}+2 \sqrt{a^{2}}\, \sqrt{a^{2}+\ln \left(x \right)^{2}}}{\ln \left(x \right)}\right)}{\sqrt{a^{2}}}$&$37$\\ default&$-\frac{\ln \left(\frac{2 a^{2}+2 \sqrt{a^{2}}\, \sqrt{a^{2}+\ln \left(x \right)^{2}}}{\ln \left(x \right)}\right)}{\sqrt{a^{2}}}$&$37$\\ \hline \end{longtable}"," ",0,"-1/(a^2)^(1/2)*ln((2*a^2+2*(a^2)^(1/2)*(a^2+ln(x)^2)^(1/2))/ln(x))","A"
626,1,39,22,0.023000," ","int(1/x/ln(x)/(a^2-ln(x)^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(\frac{2 a^{2}+2 \sqrt{a^{2}}\, \sqrt{a^{2}-\ln \left(x \right)^{2}}}{\ln \left(x \right)}\right)}{\sqrt{a^{2}}}$&$39$\\ default&$-\frac{\ln \left(\frac{2 a^{2}+2 \sqrt{a^{2}}\, \sqrt{a^{2}-\ln \left(x \right)^{2}}}{\ln \left(x \right)}\right)}{\sqrt{a^{2}}}$&$39$\\ \hline \end{longtable}"," ",0,"-1/(a^2)^(1/2)*ln((2*a^2+2*(a^2)^(1/2)*(a^2-ln(x)^2)^(1/2))/ln(x))","A"
627,1,43,21,0.022000," ","int(1/x/ln(x)/(-a^2+ln(x)^2)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(\frac{-2 a^{2}+2 \sqrt{-a^{2}}\, \sqrt{-a^{2}+\ln \left(x \right)^{2}}}{\ln \left(x \right)}\right)}{\sqrt{-a^{2}}}$&$43$\\ default&$-\frac{\ln \left(\frac{-2 a^{2}+2 \sqrt{-a^{2}}\, \sqrt{-a^{2}+\ln \left(x \right)^{2}}}{\ln \left(x \right)}\right)}{\sqrt{-a^{2}}}$&$43$\\ \hline \end{longtable}"," ",0,"-1/(-a^2)^(1/2)*ln((-2*a^2+2*(-a^2)^(1/2)*(-a^2+ln(x)^2)^(1/2))/ln(x))","A"
628,1,12,11,0.020000," ","int(ln(ln(x))/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\ln \left(x \right)+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)$&$12$\\ default&$-\ln \left(x \right)+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)$&$12$\\ norman&$-\ln \left(x \right)+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)$&$12$\\ risch&$-\ln \left(x \right)+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)$&$12$\\ \hline \end{longtable}"," ",0,"-ln(x)+ln(x)*ln(ln(x))","A"
629,1,21,20,0.036000," ","int(ln(ln(x))^2/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$2 \ln \left(x \right)-2 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}$&$21$\\ default&$2 \ln \left(x \right)-2 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}$&$21$\\ norman&$2 \ln \left(x \right)-2 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}$&$21$\\ risch&$2 \ln \left(x \right)-2 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}$&$21$\\ \hline \end{longtable}"," ",0,"2*ln(x)-2*ln(x)*ln(ln(x))+ln(x)*ln(ln(x))^2","A"
630,1,30,29,0.039000," ","int(ln(ln(x))^3/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-6 \ln \left(x \right)+6 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)-3 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{3}$&$30$\\ default&$-6 \ln \left(x \right)+6 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)-3 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{3}$&$30$\\ norman&$-6 \ln \left(x \right)+6 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)-3 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{3}$&$30$\\ risch&$-6 \ln \left(x \right)+6 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)-3 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{3}$&$30$\\ \hline \end{longtable}"," ",0,"-6*ln(x)+6*ln(x)*ln(ln(x))-3*ln(x)*ln(ln(x))^2+ln(x)*ln(ln(x))^3","A"
631,1,39,38,0.039000," ","int(ln(ln(x))^4/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$24 \ln \left(x \right)-24 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)+12 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}-4 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{3}+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{4}$&$39$\\ default&$24 \ln \left(x \right)-24 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)+12 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}-4 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{3}+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{4}$&$39$\\ norman&$24 \ln \left(x \right)-24 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)+12 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}-4 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{3}+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{4}$&$39$\\ risch&$24 \ln \left(x \right)-24 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)+12 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{2}-4 \ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{3}+\ln \left(x \right) \ln \left(\ln \left(x \right)\right)^{4}$&$39$\\ \hline \end{longtable}"," ",0,"24*ln(x)-24*ln(x)*ln(ln(x))+12*ln(x)*ln(ln(x))^2-4*ln(x)*ln(ln(x))^3+ln(x)*ln(ln(x))^4","A"
632,0,0,24,0.007000," ","int(ln(ln(x))^n/x,x)","\[\int \frac{\ln \left(\ln \left(x \right)\right)^{n}}{x}\, dx\]"," ",0,"int(ln(ln(x))^n/x,x)","F"
633,1,5,4,0.175000," ","int(cot(x)/ln(sin(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\ln \left(\ln \left(\sin \left(x \right)\right)\right)$&$5$\\ default&$\ln \left(\ln \left(\sin \left(x \right)\right)\right)$&$5$\\ risch&$\ln \left(-\frac{i \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)}{2}-\frac{i \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2}}{2}-\frac{i \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\sin \left(x \right)\right)^{2}}{2}-\frac{i \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)}{2}-\frac{i \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{3}}{2}-\frac{i \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)}{2}+\frac{i \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2}}{2}+\frac{i \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{3}}{2}+\frac{i \pi}{2}+\ln \left(2\right)-\ln \left({\mathrm e}^{2 i x}-1\right)+\ln \left({\mathrm e}^{i x}\right)\right)$&$151$\\ \hline \end{longtable}"," ",0,"ln(ln(sin(x)))","A"
634,1,10,7,0.073000," ","int((1/cos(x)+cos(x))*tan(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\cos \left(x \right)+\frac{1}{\cos \left(x \right)}$&$10$\\ default&$-\cos \left(x \right)+\frac{1}{\cos \left(x \right)}$&$10$\\ risch&$-\frac{{\mathrm e}^{i x}}{2}-\frac{{\mathrm e}^{-i x}}{2}+\frac{2 \,{\mathrm e}^{i x}}{1+{\mathrm e}^{2 i x}}$&$32$\\ \hline \end{longtable}"," ",0,"-cos(x)+1/cos(x)","A"
635,1,12,11,0.158000," ","int(ln(cosh(x))*sinh(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\cosh \left(x \right)+\cosh \left(x \right) \ln \left(\cosh \left(x \right)\right)$&$12$\\ default&$-\cosh \left(x \right)+\cosh \left(x \right) \ln \left(\cosh \left(x \right)\right)$&$12$\\ risch&$-\frac{\left(1+{\mathrm e}^{2 x}\right) {\mathrm e}^{-x} \ln \left({\mathrm e}^{x}\right)}{2}-\frac{\left(-i \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{2}+i \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right) {\mathrm e}^{2 x}+i \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \pi -i \pi  \,\mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{2}+i \pi  \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{3}+i \pi  \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{3} {\mathrm e}^{2 x}-i \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{2} {\mathrm e}^{2 x}-i \pi  \,\mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{2} {\mathrm e}^{2 x}+2+2 \ln \left(2\right) {\mathrm e}^{2 x}-2 \,{\mathrm e}^{2 x} \ln \left(1+{\mathrm e}^{2 x}\right)+2 \,{\mathrm e}^{2 x}+2 \ln \left(2\right)-2 \ln \left(1+{\mathrm e}^{2 x}\right)\right) {\mathrm e}^{-x}}{4}$&$309$\\ \hline \end{longtable}"," ",0,"-cosh(x)+cosh(x)*ln(cosh(x))","A"
636,1,8,7,0.149000," ","int(ln(cosh(x))*tanh(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{\ln \left(\cosh \left(x \right)\right)^{2}}{2}$&$8$\\ default&$\frac{\ln \left(\cosh \left(x \right)\right)^{2}}{2}$&$8$\\ risch&$\left(x -\ln \left(1+{\mathrm e}^{2 x}\right)\right) \ln \left({\mathrm e}^{x}\right)+\frac{\ln \left(1+{\mathrm e}^{2 x}\right)^{2}}{2}-\frac{x^{2}}{2}+\frac{i \ln \left(1+{\mathrm e}^{2 x}\right) \pi  \,\mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{2}}{2}+\frac{i \ln \left(1+{\mathrm e}^{2 x}\right) \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{2}}{2}-\frac{i \ln \left(1+{\mathrm e}^{2 x}\right) \pi  \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{3}}{2}-\frac{i \pi  \,\mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{2} x}{2}+\frac{i \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right) x}{2}-\frac{i \ln \left(1+{\mathrm e}^{2 x}\right) \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left(1+{\mathrm e}^{2 x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)}{2}-\frac{i \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{2} x}{2}+\frac{i \pi  \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(1+{\mathrm e}^{2 x}\right)\right)^{3} x}{2}-\ln \left(1+{\mathrm e}^{2 x}\right) \ln \left(2\right)+\ln \left(2\right) x$&$308$\\ \hline \end{longtable}"," ",0,"1/2*ln(cosh(x))^2","A"
637,1,23,22,0.014000," ","int(ln(x-(x^2+1)^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x \ln \left(x -\sqrt{x^{2}+1}\right)+\sqrt{x^{2}+1}$&$23$\\ \hline \end{longtable}"," ",0,"x*ln(x-(x^2+1)^(1/2))+(x^2+1)^(1/2)","A"
638,1,26,27,0.043000," ","int(ln(-1+x)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{1}{2 x}-\frac{\ln \left(x \right)}{2}+\frac{\ln \left(-1+x \right) \left(-1+x \right) \left(1+x \right)}{2 x^{2}}$&$26$\\ default&$\frac{1}{2 x}-\frac{\ln \left(x \right)}{2}+\frac{\ln \left(-1+x \right) \left(-1+x \right) \left(1+x \right)}{2 x^{2}}$&$26$\\ norman&$\frac{\frac{x}{2}+\frac{x^{2} \ln \left(-1+x \right)}{2}-\frac{\ln \left(-1+x \right)}{2}}{x^{2}}-\frac{\ln \left(x \right)}{2}$&$29$\\ risch&$-\frac{\ln \left(-1+x \right)}{2 x^{2}}+\frac{\ln \left(-1+x \right) x -x \ln \left(x \right)+1}{2 x}$&$29$\\ \hline \end{longtable}"," ",0,"1/2/x-1/2*ln(x)+1/2*ln(-1+x)*(-1+x)*(1+x)/x^2","A"
639,1,24,27,0.029000," ","int((-1/exp(x)+exp(x))*ln(1+exp(2*x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\left(1+{\mathrm e}^{2 x}\right) {\mathrm e}^{-x} \ln \left(1+{\mathrm e}^{2 x}\right)-2 \,{\mathrm e}^{x}$&$24$\\ norman&$\left({\mathrm e}^{2 x} \ln \left(1+{\mathrm e}^{2 x}\right)-2 \,{\mathrm e}^{2 x}+\ln \left(1+{\mathrm e}^{2 x}\right)\right) {\mathrm e}^{-x}$&$32$\\ \hline \end{longtable}"," ",0,"(1+exp(2*x))*exp(-x)*ln(1+exp(2*x))-2*exp(x)","A"
640,1,43,31,0.032000," ","int(exp(3/2*x)*ln(-1+exp(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{2 \,{\mathrm e}^{\frac{3 x}{2}} \ln \left(-1+{\mathrm e}^{x}\right)}{3}-\frac{4 \,{\mathrm e}^{\frac{3 x}{2}}}{9}-\frac{4 \,{\mathrm e}^{\frac{x}{2}}}{3}-\frac{2 \ln \left(-1+{\mathrm e}^{\frac{x}{2}}\right)}{3}+\frac{2 \ln \left({\mathrm e}^{\frac{x}{2}}+1\right)}{3}$&$43$\\ \hline \end{longtable}"," ",0,"2/3*exp(3/2*x)*ln(-1+exp(x))-4/9*exp(3/2*x)-4/3*exp(1/2*x)-2/3*ln(-1+exp(1/2*x))+2/3*ln(exp(1/2*x)+1)","A"
641,1,197,26,0.375000," ","int(cos(x)^3*ln(sin(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{i \left(\frac{{\mathrm e}^{3 i x} \ln \left(i \left(-{\mathrm e}^{2 i x}+1\right) {\mathrm e}^{-i x}\right)}{3}-\frac{{\mathrm e}^{3 i x}}{9}-\frac{11 \,{\mathrm e}^{i x}}{3}+3 \,{\mathrm e}^{i x} \ln \left(i \left(-{\mathrm e}^{2 i x}+1\right) {\mathrm e}^{-i x}\right)-3 \,{\mathrm e}^{-i x} \ln \left(i \left(-{\mathrm e}^{2 i x}+1\right) {\mathrm e}^{-i x}\right)+\frac{11 \,{\mathrm e}^{-i x}}{3}-\frac{{\mathrm e}^{-3 i x} \ln \left(i \left(-{\mathrm e}^{2 i x}+1\right) {\mathrm e}^{-i x}\right)}{3}+\frac{{\mathrm e}^{-3 i x}}{9}-\frac{\ln \left(2\right) {\mathrm e}^{3 i x}}{3}-3 \ln \left(2\right) {\mathrm e}^{i x}+3 \,{\mathrm e}^{-i x} \ln \left(2\right)+\frac{\ln \left(2\right) {\mathrm e}^{-3 i x}}{3}\right)}{8}$&$197$\\ risch&$\frac{3 i {\mathrm e}^{-i x} \ln \left({\mathrm e}^{2 i x}-1\right)}{8}+2 i \left(\frac{i \ln \left(2\right)}{24}-\frac{i \ln \left({\mathrm e}^{2 i x}-1\right)}{24}-\frac{\pi}{48}+\frac{i}{72}+\frac{\mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{2 i x}-i\right) \pi}{48}+\frac{\mathrm{csgn}\left(\sin \left(x \right)\right)^{3} \pi}{48}+\frac{\pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)}{48}-\frac{\mathrm{csgn}\left(i \sin \left(x \right)\right)^{2} \mathrm{csgn}\left(\sin \left(x \right)\right) \pi}{48}+\frac{\mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \pi}{48}+\frac{\mathrm{csgn}\left(i \sin \left(x \right)\right)^{2} \pi}{48}-\frac{\mathrm{csgn}\left(i \sin \left(x \right)\right)^{3} \pi}{48}+\frac{\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i x}-i\right) \mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)}{48}\right) \sin \left(3 x \right)+\frac{3 \,{\mathrm e}^{i x} \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{3}}{16}-\frac{3 \,{\mathrm e}^{-i x} \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{3}}{16}+\frac{i \ln \left({\mathrm e}^{i x}\right) \left(18 i \sin \left(x \right)+2 i \sin \left(3 x \right)\right)}{24}+\frac{3 \,{\mathrm e}^{i x} \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2}}{16}+\frac{3 \,{\mathrm e}^{-i x} \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{3}}{16}-\frac{3 \,{\mathrm e}^{i x} \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{3}}{16}-\frac{3 \,{\mathrm e}^{-i x} \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2}}{16}-\frac{3 i {\mathrm e}^{-i x} \ln \left(2\right)}{8}-\frac{3 i {\mathrm e}^{i x} \ln \left({\mathrm e}^{2 i x}-1\right)}{8}+\frac{3 i {\mathrm e}^{i x} \ln \left(2\right)}{8}-\frac{11 i {\mathrm e}^{-i x}}{24}+\frac{3 \,{\mathrm e}^{-i x} \pi}{16}-\frac{3 \,{\mathrm e}^{i x} \pi}{16}+\frac{11 i {\mathrm e}^{i x}}{24}-\frac{3 \,{\mathrm e}^{-i x} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i x}-i\right) \mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)}{16}+\frac{3 \,{\mathrm e}^{i x} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i x}-i\right) \mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)}{16}+\frac{3 \,{\mathrm e}^{i x} \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)}{16}-\frac{3 \,{\mathrm e}^{-i x} \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)}{16}-\frac{3 \,{\mathrm e}^{-i x} \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)}{16}+\frac{3 \,{\mathrm e}^{-i x} \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2}}{16}+\frac{3 \,{\mathrm e}^{i x} \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)}{16}-\frac{3 \,{\mathrm e}^{i x} \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2}}{16}+\frac{3 \,{\mathrm e}^{i x} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i x}-i\right) \mathrm{csgn}\left(\sin \left(x \right)\right)^{2}}{16}-\frac{3 \,{\mathrm e}^{-i x} \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{2 i x}-i\right) \mathrm{csgn}\left(\sin \left(x \right)\right)^{2}}{16}$&$577$\\ \hline \end{longtable}"," ",0,"-1/8*I*(1/3*exp(3*I*x)*ln(I*(-exp(I*x)^2+1)/exp(I*x))-1/9*exp(I*x)^3-11/3*exp(I*x)+3*exp(I*x)*ln(I*(-exp(I*x)^2+1)/exp(I*x))-3*exp(-I*x)*ln(I*(-exp(I*x)^2+1)/exp(I*x))+11/3/exp(I*x)-1/3*exp(-3*I*x)*ln(I*(-exp(I*x)^2+1)/exp(I*x))+1/9/exp(I*x)^3-1/3*ln(2)*exp(I*x)^3-3*ln(2)*exp(I*x)+3*ln(2)/exp(I*x)+1/3*ln(2)/exp(I*x)^3)","C"
642,1,55,26,0.522000," ","int(ln(tan(x))/cos(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(6 \left(\cos^{2}\left(x \right)\right) \ln \left(2\right)+6 \left(\cos^{2}\left(x \right)\right) \ln \left(\frac{\sin \left(x \right)}{2 \cos \left(x \right)}\right)-8 \left(\cos^{2}\left(x \right)\right)+3 \ln \left(2\right)+3 \ln \left(\frac{\sin \left(x \right)}{2 \cos \left(x \right)}\right)-1\right) \sin \left(x \right)}{9 \cos \left(x \right)^{3}}$&$55$\\ risch&$-\frac{4 i \left(3 \,{\mathrm e}^{2 i x}+1\right) \ln \left(1+{\mathrm e}^{2 i x}\right)}{3 \left(1+{\mathrm e}^{2 i x}\right)^{3}}+\frac{\frac{2 \pi}{3}+\frac{2 \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right)^{3}}{3}-\frac{2 \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i x}-1}{1+{\mathrm e}^{2 i x}}\right)^{2} \pi}{3}+2 \pi  \,{\mathrm e}^{2 i x}+\frac{2 \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i x}-1}{1+{\mathrm e}^{2 i x}}\right)^{3}}{3}-\frac{2 \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \pi}{3}-2 \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i x}-1}{1+{\mathrm e}^{2 i x}}\right)^{2} {\mathrm e}^{2 i x}-\frac{2 \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right)^{2} \mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 i x}}\right) \pi}{3}+\frac{2 \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i x}-1}{1+{\mathrm e}^{2 i x}}\right)}{3}+\frac{2 i \ln \left(1+{\mathrm e}^{2 i x}\right) {\mathrm e}^{6 i x}}{3}+2 i \ln \left(1+{\mathrm e}^{2 i x}\right) {\mathrm e}^{4 i x}-\frac{2 i {\mathrm e}^{6 i x} \ln \left({\mathrm e}^{2 i x}-1\right)}{3}-2 i {\mathrm e}^{4 i x} \ln \left({\mathrm e}^{2 i x}-1\right)+2 i {\mathrm e}^{2 i x} \ln \left({\mathrm e}^{2 i x}-1\right)-\frac{2 \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i x}-1}{1+{\mathrm e}^{2 i x}}\right)^{2} \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right) \pi}{3}+2 \pi  \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right)^{3} {\mathrm e}^{2 i x}+2 \pi  \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i x}-1}{1+{\mathrm e}^{2 i x}}\right)^{3} {\mathrm e}^{2 i x}-\frac{16 i}{9}-4 i {\mathrm e}^{2 i x}+\frac{2 i \ln \left(1+{\mathrm e}^{2 i x}\right)}{3}-\frac{4 i {\mathrm e}^{4 i x}}{3}+2 i \ln \left(1+{\mathrm e}^{2 i x}\right) {\mathrm e}^{2 i x}+\frac{2 i \ln \left({\mathrm e}^{2 i x}-1\right)}{3}-2 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right)^{2} {\mathrm e}^{2 i x}-2 \pi  \,\mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 i x}}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right)^{2} {\mathrm e}^{2 i x}-2 \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i x}-1}{1+{\mathrm e}^{2 i x}}\right)^{2} {\mathrm e}^{2 i x}+\frac{2 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 i x}}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right)}{3}+2 \pi  \,\mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right) \mathrm{csgn}\left(\frac{{\mathrm e}^{2 i x}-1}{1+{\mathrm e}^{2 i x}}\right) {\mathrm e}^{2 i x}+2 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\frac{i}{1+{\mathrm e}^{2 i x}}\right) \mathrm{csgn}\left(\frac{i \left({\mathrm e}^{2 i x}-1\right)}{1+{\mathrm e}^{2 i x}}\right) {\mathrm e}^{2 i x}}{\left(1+{\mathrm e}^{2 i x}\right)^{3}}$&$782$\\ \hline \end{longtable}"," ",0,"1/9*(6*cos(x)^2*ln(2)+6*cos(x)^2*ln(1/2*sin(x)/cos(x))-8*cos(x)^2+3*ln(2)+3*ln(1/2*sin(x)/cos(x))-1)*sin(x)/cos(x)^3","B"
643,1,164,22,0.247000," ","int(ln(cos(1/2*x))/(1+cos(x)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$-\frac{2 i \ln \left({\mathrm e}^{\frac{i x}{2}}\right)}{{\mathrm e}^{i x}+1}+\frac{-i \ln \left({\mathrm e}^{i x}+1\right) {\mathrm e}^{i x}+\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{i x}+1\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-\frac{i x}{2}}\right) \mathrm{csgn}\left(i \cos \left(\frac{x}{2}\right)\right)-\pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{i x}+1\right)\right) \mathrm{csgn}\left(i \cos \left(\frac{x}{2}\right)\right)^{2}-\pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-\frac{i x}{2}}\right) \mathrm{csgn}\left(i \cos \left(\frac{x}{2}\right)\right)^{2}+\pi  \mathrm{csgn}\left(i \cos \left(\frac{x}{2}\right)\right)^{3}-x \,{\mathrm e}^{i x}+i \ln \left({\mathrm e}^{i x}+1\right)-2 i \ln \left(2\right)+2 i-x}{{\mathrm e}^{i x}+1}$&$164$\\ \hline \end{longtable}"," ",0,"-2*I/(exp(I*x)+1)*ln(exp(1/2*I*x))+(-I*ln(exp(I*x)+1)*exp(I*x)+Pi*csgn(I*(exp(I*x)+1))*csgn(I*exp(-1/2*I*x))*csgn(I*cos(1/2*x))-Pi*csgn(I*(exp(I*x)+1))*csgn(I*cos(1/2*x))^2-Pi*csgn(I*exp(-1/2*I*x))*csgn(I*cos(1/2*x))^2+Pi*csgn(I*cos(1/2*x))^3-x*exp(I*x)+I*ln(exp(I*x)+1)-2*I*ln(2)+2*I-x)/(exp(I*x)+1)","C"
644,1,106,50,0.439000," ","int(cos(x)*ln(sin(x))/(1+cos(x))^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{6 \left(\cos^{3}\left(x \right)\right) \ln \left(2\right)+6 \left(\cos^{3}\left(x \right)\right) \ln \left(\frac{\sin \left(x \right)}{2}\right)-12 \left(\cos^{2}\left(x \right)\right) \sin \left(x \right) \arctan \left(\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right)+8 \left(\cos^{3}\left(x \right)\right)-9 \left(\cos^{2}\left(x \right)\right) \ln \left(2\right)-9 \left(\cos^{2}\left(x \right)\right) \ln \left(\frac{\sin \left(x \right)}{2}\right)-9 \left(\cos^{2}\left(x \right)\right)+12 \arctan \left(\frac{-1+\cos \left(x \right)}{\sin \left(x \right)}\right) \sin \left(x \right)-6 \cos \left(x \right)+3 \ln \left(2\right)+3 \ln \left(\frac{\sin \left(x \right)}{2}\right)+7}{9 \sin \left(x \right)^{3}}$&$106$\\ risch&$-\frac{2 i \left(3 \,{\mathrm e}^{2 i x}+3 \,{\mathrm e}^{i x}+2\right) \ln \left({\mathrm e}^{i x}\right)}{3 \left({\mathrm e}^{i x}+1\right)^{3}}+\frac{6 \pi -12 x +9 \pi  \,{\mathrm e}^{2 i x}+16 i-9 \,{\mathrm e}^{i x} \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)+9 \,{\mathrm e}^{i x} \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2}-9 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} {\mathrm e}^{2 i x}-9 \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) {\mathrm e}^{2 i x}+9 \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2} {\mathrm e}^{2 i x}-6 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right)-9 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} {\mathrm e}^{i x}-9 \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right) {\mathrm e}^{2 i x}-36 x \,{\mathrm e}^{i x}-6 \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)+6 \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2} \mathrm{csgn}\left(\sin \left(x \right)\right) \pi -6 \,\mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \pi -9 \,{\mathrm e}^{i x} \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{3}+18 i {\mathrm e}^{2 i x}-9 \,{\mathrm e}^{i x} \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2}+9 \,{\mathrm e}^{i x} \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{3}-18 i {\mathrm e}^{i x} \ln \left(2\right)-36 x \,{\mathrm e}^{2 i x}-12 i \ln \left(2\right)-12 x \,{\mathrm e}^{3 i x}+9 \,{\mathrm e}^{i x} \pi +30 i {\mathrm e}^{i x}+6 i \ln \left({\mathrm e}^{2 i x}-1\right)-6 \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2} \pi +6 \mathrm{csgn}\left(i \sin \left(x \right)\right)^{3} \pi -6 \mathrm{csgn}\left(\sin \left(x \right)\right)^{3} \pi -9 \pi  \mathrm{csgn}\left(\sin \left(x \right)\right)^{3} {\mathrm e}^{2 i x}-6 i \ln \left({\mathrm e}^{2 i x}-1\right) {\mathrm e}^{3 i x}-9 \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{2} {\mathrm e}^{2 i x}-18 i \ln \left(2\right) {\mathrm e}^{2 i x}+9 \pi  \mathrm{csgn}\left(i \sin \left(x \right)\right)^{3} {\mathrm e}^{2 i x}-6 \mathrm{csgn}\left(\sin \left(x \right)\right)^{2} \mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \pi -9 \,{\mathrm e}^{i x} \pi  \,\mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i \sin \left(x \right)\right)-9 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) {\mathrm e}^{i x}-9 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 i x}-1\right)\right) \mathrm{csgn}\left(\sin \left(x \right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-i x}\right) {\mathrm e}^{2 i x}}{9 \left({\mathrm e}^{i x}+1\right)^{3}}$&$598$\\ \hline \end{longtable}"," ",0,"1/9*(6*cos(x)^3*ln(2)+6*cos(x)^3*ln(1/2*sin(x))-12*cos(x)^2*sin(x)*arctan((-1+cos(x))/sin(x))+8*cos(x)^3-9*cos(x)^2*ln(2)-9*cos(x)^2*ln(1/2*sin(x))-9*cos(x)^2+12*arctan((-1+cos(x))/sin(x))*sin(x)-6*cos(x)+3*ln(2)+3*ln(1/2*sin(x))+7)/sin(x)^3","B"
645,1,52,51,0.081000," ","int(arccos(x)^2/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{12 x^{2}}-\frac{\arccos \left(x \right)^{2}}{4 x^{4}}+\frac{\ln \left(x \right)}{3}+\frac{\arccos \left(x \right) \sqrt{-x^{2}+1}}{6 x^{3}}+\frac{\arccos \left(x \right) \sqrt{-x^{2}+1}}{3 x}$&$52$\\ \hline \end{longtable}"," ",0,"-1/12/x^2-1/4*arccos(x)^2/x^4+1/3*ln(x)+1/6*arccos(x)*(-x^2+1)^(1/2)/x^3+1/3*arccos(x)*(-x^2+1)^(1/2)/x","A"
646,1,37,47,0.360000," ","int(x^2*arcsin(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{3} \arcsin \left(x \right)^{2}}{3}+\frac{2 \arcsin \left(x \right) \left(x^{2}+2\right) \sqrt{-x^{2}+1}}{9}-\frac{2 x^{3}}{27}-\frac{4 x}{9}$&$37$\\ \hline \end{longtable}"," ",0,"1/3*x^3*arcsin(x)^2+2/9*arcsin(x)*(x^2+2)*(-x^2+1)^(1/2)-2/27*x^3-4/9*x","A"
647,1,42,41,0.096000," ","int(x^3*arctan(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{2}}{12}+\frac{x \arctan \left(x \right)}{2}-\frac{x^{3} \arctan \left(x \right)}{6}-\frac{\arctan \left(x \right)^{2}}{4}+\frac{x^{4} \arctan \left(x \right)^{2}}{4}-\frac{\ln \left(x^{2}+1\right)}{3}$&$42$\\ risch&$-\frac{\left(\frac{x^{4}}{4}-\frac{1}{4}\right) \ln \left(i x +1\right)^{2}}{4}-\frac{\left(-\frac{x^{4} \ln \left(-i x +1\right)}{2}-\frac{i x^{3}}{3}+i x +\frac{\ln \left(-i x +1\right)}{2}\right) \ln \left(i x +1\right)}{4}-\frac{x^{4} \ln \left(-i x +1\right)^{2}}{16}+\frac{\ln \left(-i x +1\right)^{2}}{16}-\frac{i x^{3} \ln \left(-i x +1\right)}{12}+\frac{i \ln \left(-i x +1\right) x}{4}+\frac{x^{2}}{12}-\frac{\ln \left(x^{2}+1\right)}{3}$&$123$\\ \hline \end{longtable}"," ",0,"1/12*x^2+1/2*x*arctan(x)-1/6*x^3*arctan(x)-1/4*arctan(x)^2+1/4*x^4*arctan(x)^2-1/3*ln(x^2+1)","A"
648,1,48,47,0.137000," ","int(arctan(x)^2/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{12 x^{2}}-\frac{\arctan \left(x \right)}{6 x^{3}}+\frac{\arctan \left(x \right)}{2 x}+\frac{\arctan \left(x \right)^{2}}{4}-\frac{\arctan \left(x \right)^{2}}{4 x^{4}}-\frac{2 \ln \left(x \right)}{3}+\frac{\ln \left(x^{2}+1\right)}{3}$&$48$\\ risch&$-\frac{\left(x^{4}-1\right) \ln \left(i x +1\right)^{2}}{16 x^{4}}+\frac{\left(3 x^{4} \ln \left(-i x +1\right)-6 i x^{3}+2 i x -3 \ln \left(-i x +1\right)\right) \ln \left(i x +1\right)}{24 x^{4}}-\frac{3 x^{4} \ln \left(-i x +1\right)^{2}+32 x^{4} \ln \left(x \right)-16 \ln \left(x^{2}+1\right) x^{4}-12 i x^{3} \ln \left(-i x +1\right)+4 i \ln \left(-i x +1\right) x +4 x^{2}-3 \ln \left(-i x +1\right)^{2}}{48 x^{4}}$&$143$\\ \hline \end{longtable}"," ",0,"-1/12/x^2-1/6*arctan(x)/x^3+1/2*arctan(x)/x+1/4*arctan(x)^2-1/4*arctan(x)^2/x^4-2/3*ln(x)+1/3*ln(x^2+1)","A"
649,1,56,49,0.079000," ","int(x^3*arccsc(x)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{4} \mathrm{arccsc}\left(x \right)^{2}}{4}+\frac{x^{3} \mathrm{arccsc}\left(x \right) \sqrt{\frac{x^{2}-1}{x^{2}}}}{6}+\frac{x^{2}}{12}+\frac{\mathrm{arccsc}\left(x \right) \sqrt{\frac{x^{2}-1}{x^{2}}}\, x}{3}-\frac{\ln \left(\frac{1}{x}\right)}{3}$&$56$\\ \hline \end{longtable}"," ",0,"1/4*x^4*arccsc(x)^2+1/6*x^3*arccsc(x)*((x^2-1)/x^2)^(1/2)+1/12*x^2+1/3*arccsc(x)*((x^2-1)/x^2)^(1/2)*x-1/3*ln(1/x)","A"
650,1,165,118,0.385000," ","int(arcsec(x)^4/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\mathrm{arcsec}\left(x \right)^{4}}{4 x^{4}}+\frac{\mathrm{arcsec}\left(x \right)^{3} \left(3 \,\mathrm{arcsec}\left(x \right) x^{3}+3 x^{2} \sqrt{\frac{x^{2}-1}{x^{2}}}+2 \sqrt{\frac{x^{2}-1}{x^{2}}}\right)}{8 x^{3}}+\frac{3 \mathrm{arcsec}\left(x \right)^{2}}{16 x^{4}}-\frac{3 \,\mathrm{arcsec}\left(x \right) \left(3 \,\mathrm{arcsec}\left(x \right) x^{3}+3 x^{2} \sqrt{\frac{x^{2}-1}{x^{2}}}+2 \sqrt{\frac{x^{2}-1}{x^{2}}}\right)}{64 x^{3}}+\frac{45 \mathrm{arcsec}\left(x \right)^{2}}{128}-\frac{3}{128 x^{4}}-\frac{45}{128 x^{2}}+\frac{9 \mathrm{arcsec}\left(x \right)^{2}}{16 x^{2}}-\frac{9 \,\mathrm{arcsec}\left(x \right) \left(\mathrm{arcsec}\left(x \right) x +\sqrt{\frac{x^{2}-1}{x^{2}}}\right)}{16 x}+\frac{9}{32}-\frac{9 \mathrm{arcsec}\left(x \right)^{4}}{32}$&$165$\\ \hline \end{longtable}"," ",0,"-1/4*arcsec(x)^4/x^4+1/8*arcsec(x)^3*(3*arcsec(x)*x^3+3*x^2*((x^2-1)/x^2)^(1/2)+2*((x^2-1)/x^2)^(1/2))/x^3+3/16*arcsec(x)^2/x^4-3/64*arcsec(x)*(3*arcsec(x)*x^3+3*x^2*((x^2-1)/x^2)^(1/2)+2*((x^2-1)/x^2)^(1/2))/x^3+45/128*arcsec(x)^2-3/128/x^4-45/128/x^2+9/16*arcsec(x)^2/x^2-9/16*arcsec(x)*(arcsec(x)*x+((x^2-1)/x^2)^(1/2))/x+9/32-9/32*arcsec(x)^4","A"
651,1,31,26,0.312000," ","int(arcsin(x)*(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arcsin \left(x \right) \left(\sqrt{-x^{2}+1}\, x +\arcsin \left(x \right)\right)}{2}-\frac{\arcsin \left(x \right)^{2}}{4}-\frac{x^{2}}{4}$&$31$\\ \hline \end{longtable}"," ",0,"1/2*arcsin(x)*((-x^2+1)^(1/2)*x+arcsin(x))-1/4*arcsin(x)^2-1/4*x^2","A"
652,1,33,26,0.315000," ","int(arccos(x)*(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arccos \left(x \right) \left(-\sqrt{-x^{2}+1}\, x +\arccos \left(x \right)\right)}{2}+\frac{\arccos \left(x \right)^{2}}{4}+\frac{x^{2}}{4}-\frac{1}{4}$&$33$\\ \hline \end{longtable}"," ",0,"-1/2*arccos(x)*(-(-x^2+1)^(1/2)*x+arccos(x))+1/4*arccos(x)^2+1/4*x^2-1/4","A"
653,1,134,22,0.322000," ","int(x*arccos(x)*(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(i+3 \arccos \left(x \right)\right) \left(4 i x^{3}-4 \sqrt{-x^{2}+1}\, x^{2}-3 i x +\sqrt{-x^{2}+1}\right)}{72}+\frac{\left(\arccos \left(x \right)+i\right) \left(i x -\sqrt{-x^{2}+1}\right)}{8}-\frac{\left(\arccos \left(x \right)-i\right) \left(i x +\sqrt{-x^{2}+1}\right)}{8}+\frac{\left(-i+3 \arccos \left(x \right)\right) \left(4 i x^{3}+4 \sqrt{-x^{2}+1}\, x^{2}-3 i x -\sqrt{-x^{2}+1}\right)}{72}$&$134$\\ \hline \end{longtable}"," ",0,"-1/72*(I+3*arccos(x))*(4*I*x^3-4*(-x^2+1)^(1/2)*x^2-3*I*x+(-x^2+1)^(1/2))+1/8*(arccos(x)+I)*(I*x-(-x^2+1)^(1/2))-1/8*(arccos(x)-I)*(I*x+(-x^2+1)^(1/2))+1/72*(-I+3*arccos(x))*(4*I*x^3+4*(-x^2+1)^(1/2)*x^2-3*I*x-(-x^2+1)^(1/2))","C"
654,1,58,45,0.372000," ","int((-x^2+1)^(3/2)*arcsin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arcsin \left(x \right) \left(-2 \sqrt{-x^{2}+1}\, x^{3}+5 \sqrt{-x^{2}+1}\, x +3 \arcsin \left(x \right)\right)}{8}-\frac{3 \arcsin \left(x \right)^{2}}{16}+\frac{\left(x^{2}-1\right)^{2}}{16}-\frac{3 x^{2}}{16}+\frac{3}{16}$&$58$\\ \hline \end{longtable}"," ",0,"1/8*arcsin(x)*(-2*(-x^2+1)^(1/2)*x^3+5*(-x^2+1)^(1/2)*x+3*arcsin(x))-3/16*arcsin(x)^2+1/16*(x^2-1)^2-3/16*x^2+3/16","A"
655,1,37,27,0.350000," ","int(x*(-x^2+1)^(3/2)*arcsin(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(x^{2}-1\right)^{2} \sqrt{-x^{2}+1}\, \arcsin \left(x \right)}{5}+\frac{\left(3 x^{4}-10 x^{2}+15\right) x}{75}$&$37$\\ \hline \end{longtable}"," ",0,"-1/5*(x^2-1)^2*(-x^2+1)^(1/2)*arcsin(x)+1/75*(3*x^4-10*x^2+15)*x","A"
656,1,286,45,0.487000," ","int(x^3*(-x^2+1)^(3/2)*arccos(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(i+7 \arccos \left(x \right)\right) \left(64 i x^{7}-64 \sqrt{-x^{2}+1}\, x^{6}-112 i x^{5}+80 \sqrt{-x^{2}+1}\, x^{4}+56 i x^{3}-24 \sqrt{-x^{2}+1}\, x^{2}-7 i x +\sqrt{-x^{2}+1}\right)}{6272}+\frac{3 \left(\arccos \left(x \right)+i\right) \left(i x -\sqrt{-x^{2}+1}\right)}{128}-\frac{3 \left(\arccos \left(x \right)-i\right) \left(i x +\sqrt{-x^{2}+1}\right)}{128}+\frac{\left(-i+3 \arccos \left(x \right)\right) \left(4 i x^{3}+4 \sqrt{-x^{2}+1}\, x^{2}-3 i x -\sqrt{-x^{2}+1}\right)}{384}-\frac{3 \cos \left(6 \arccos \left(x \right)\right) \left(2 i+35 \arccos \left(x \right)\right) \left(i x +\sqrt{-x^{2}+1}\right)}{39200}+\frac{\sin \left(6 \arccos \left(x \right)\right) \left(37 i+35 \arccos \left(x \right)\right) \left(-i \sqrt{-x^{2}+1}+x \right)}{78400}-\frac{\cos \left(4 \arccos \left(x \right)\right) \left(7 i+15 \arccos \left(x \right)\right) \left(i x +\sqrt{-x^{2}+1}\right)}{2400}+\frac{\sin \left(4 \arccos \left(x \right)\right) \left(11 i+45 \arccos \left(x \right)\right) \left(-i \sqrt{-x^{2}+1}+x \right)}{4800}$&$286$\\ \hline \end{longtable}"," ",0,"1/6272*(I+7*arccos(x))*(64*I*x^7-64*(-x^2+1)^(1/2)*x^6-112*I*x^5+80*(-x^2+1)^(1/2)*x^4+56*I*x^3-24*(-x^2+1)^(1/2)*x^2-7*I*x+(-x^2+1)^(1/2))+3/128*(arccos(x)+I)*(I*x-(-x^2+1)^(1/2))-3/128*(arccos(x)-I)*(I*x+(-x^2+1)^(1/2))+1/384*(-I+3*arccos(x))*(4*I*x^3+4*(-x^2+1)^(1/2)*x^2-3*I*x-(-x^2+1)^(1/2))-3/39200*cos(6*arccos(x))*(2*I+35*arccos(x))*(I*x+(-x^2+1)^(1/2))+1/78400*sin(6*arccos(x))*(37*I+35*arccos(x))*(-I*(-x^2+1)^(1/2)+x)-1/2400*cos(4*arccos(x))*(7*I+15*arccos(x))*(I*x+(-x^2+1)^(1/2))+1/4800*sin(4*arccos(x))*(11*I+45*arccos(x))*(-I*(-x^2+1)^(1/2)+x)","C"
657,1,230,98,0.441000," ","int((-x^2+1)^(3/2)*arccos(x)/x,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(i+3 \arccos \left(x \right)\right) \left(4 i x^{3}-4 \sqrt{-x^{2}+1}\, x^{2}-3 i x +\sqrt{-x^{2}+1}\right)}{72}-\frac{5 \left(\arccos \left(x \right)+i\right) \left(i x -\sqrt{-x^{2}+1}\right)}{8}+\frac{5 \left(\arccos \left(x \right)-i\right) \left(i x +\sqrt{-x^{2}+1}\right)}{8}-\frac{\left(-i+3 \arccos \left(x \right)\right) \left(4 i x^{3}+4 \sqrt{-x^{2}+1}\, x^{2}-3 i x -\sqrt{-x^{2}+1}\right)}{72}-i \left(i \arccos \left(x \right) \ln \left(1+i \left(x +i \sqrt{-x^{2}+1}\right)\right)-i \arccos \left(x \right) \ln \left(1-i \left(x +i \sqrt{-x^{2}+1}\right)\right)+\dilog \left(1+i \left(x +i \sqrt{-x^{2}+1}\right)\right)-\dilog \left(1-i \left(x +i \sqrt{-x^{2}+1}\right)\right)\right)$&$230$\\ \hline \end{longtable}"," ",0,"1/72*(I+3*arccos(x))*(4*I*x^3-4*(-x^2+1)^(1/2)*x^2-3*I*x+(-x^2+1)^(1/2))-5/8*(arccos(x)+I)*(I*x-(-x^2+1)^(1/2))+5/8*(arccos(x)-I)*(I*x+(-x^2+1)^(1/2))-1/72*(-I+3*arccos(x))*(4*I*x^3+4*(-x^2+1)^(1/2)*x^2-3*I*x-(-x^2+1)^(1/2))-I*(I*arccos(x)*ln(1+I*(x+I*(-x^2+1)^(1/2)))-I*arccos(x)*ln(1-I*(x+I*(-x^2+1)^(1/2)))+dilog(1+I*(x+I*(-x^2+1)^(1/2)))-dilog(1-I*(x+I*(-x^2+1)^(1/2))))","B"
658,1,201,31,0.997000," ","int((-x^2+1)^(3/2)*arcsin(x)/x^6,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{2 i \arcsin \left(x \right)}{5}+\frac{\left(-\sqrt{-x^{2}+1}\, x^{4}+i x^{5}+2 \sqrt{-x^{2}+1}\, x^{2}-\sqrt{-x^{2}+1}\right) \left(20 \arcsin \left(x \right) x^{8}-4 i x^{8}-4 \sqrt{-x^{2}+1}\, x^{7}-40 \arcsin \left(x \right) x^{6}+i x^{6}+9 \sqrt{-x^{2}+1}\, x^{5}+40 \arcsin \left(x \right) x^{4}-6 \sqrt{-x^{2}+1}\, x^{3}-20 \arcsin \left(x \right) x^{2}+\sqrt{-x^{2}+1}\, x +4 \arcsin \left(x \right)\right)}{20 \left(5 x^{8}-10 x^{6}+10 x^{4}-5 x^{2}+1\right) x^{5}}+\frac{\ln \left(\left(i x +\sqrt{-x^{2}+1}\right)^{2}-1\right)}{5}$&$201$\\ \hline \end{longtable}"," ",0,"-2/5*I*arcsin(x)+1/20*(-(-x^2+1)^(1/2)*x^4+I*x^5+2*(-x^2+1)^(1/2)*x^2-(-x^2+1)^(1/2))*(20*arcsin(x)*x^8-4*I*x^8-4*(-x^2+1)^(1/2)*x^7-40*arcsin(x)*x^6+I*x^6+9*(-x^2+1)^(1/2)*x^5+40*arcsin(x)*x^4-6*(-x^2+1)^(1/2)*x^3-20*arcsin(x)*x^2+(-x^2+1)^(1/2)*x+4*arcsin(x))/(5*x^8-10*x^6+10*x^4-5*x^2+1)/x^5+1/5*ln((I*x+(-x^2+1)^(1/2))^2-1)","C"
659,1,32,26,0.318000," ","int(x^2*arcsin(x)/(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arcsin \left(x \right) \left(-\sqrt{-x^{2}+1}\, x +\arcsin \left(x \right)\right)}{2}-\frac{\arcsin \left(x \right)^{2}}{4}+\frac{x^{2}}{4}$&$32$\\ \hline \end{longtable}"," ",0,"1/2*arcsin(x)*(-(-x^2+1)^(1/2)*x+arcsin(x))-1/4*arcsin(x)^2+1/4*x^2","A"
660,1,53,47,0.376000," ","int(x^4*arcsin(x)/(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arcsin \left(x \right) \left(-2 \sqrt{-x^{2}+1}\, x^{3}-3 \sqrt{-x^{2}+1}\, x +3 \arcsin \left(x \right)\right)}{8}-\frac{3 \arcsin \left(x \right)^{2}}{16}+\frac{x^{4}}{16}+\frac{3 x^{2}}{16}$&$53$\\ \hline \end{longtable}"," ",0,"1/8*arcsin(x)*(-2*(-x^2+1)^(1/2)*x^3-3*(-x^2+1)^(1/2)*x+3*arcsin(x))-3/16*arcsin(x)^2+1/16*x^4+3/16*x^2","A"
661,1,46,17,0.315000," ","int(x*arcsin(x)/(-x^2+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{-x^{2}+1}\, \arcsin \left(x \right)}{x^{2}-1}-\ln \left(\frac{1}{\sqrt{-x^{2}+1}}+\frac{x}{\sqrt{-x^{2}+1}}\right)$&$46$\\ \hline \end{longtable}"," ",0,"-(-x^2+1)^(1/2)/(x^2-1)*arcsin(x)-ln(1/(-x^2+1)^(1/2)+x/(-x^2+1)^(1/2))","B"
662,1,47,15,0.309000," ","int(x*arccos(x)/(-x^2+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{-x^{2}+1}\, \arccos \left(x \right)}{x^{2}-1}-\ln \left(\frac{1}{\sqrt{-x^{2}+1}}-\frac{x}{\sqrt{-x^{2}+1}}\right)$&$47$\\ \hline \end{longtable}"," ",0,"-(-x^2+1)^(1/2)/(x^2-1)*arccos(x)-ln(1/(-x^2+1)^(1/2)-x/(-x^2+1)^(1/2))","B"
663,1,63,50,0.316000," ","int(arcsin(x)/(-x^2+1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{1}{6 x^{2}-6}+\frac{x \arcsin \left(x \right) \sqrt{-x^{2}+1}}{3 \left(x^{2}-1\right)^{2}}+\frac{\ln \left(-x^{2}+1\right)}{3}-\frac{2 \sqrt{-x^{2}+1}\, \arcsin \left(x \right) x}{3 \left(x^{2}-1\right)}$&$63$\\ \hline \end{longtable}"," ",0,"1/6/(x^2-1)+1/3*x*arcsin(x)*(-x^2+1)^(1/2)/(x^2-1)^2+1/3*ln(-x^2+1)-2/3*(-x^2+1)^(1/2)/(x^2-1)*arcsin(x)*x","A"
664,1,61,32,0.529000," ","int(x^3*arcsin(x)/(-x^2+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-x +\arcsin \left(x \right) \sqrt{-x^{2}+1}-\frac{\sqrt{-x^{2}+1}\, \arcsin \left(x \right)}{x^{2}-1}-\ln \left(\frac{1}{\sqrt{-x^{2}+1}}+\frac{x}{\sqrt{-x^{2}+1}}\right)$&$61$\\ \hline \end{longtable}"," ",0,"-x+arcsin(x)*(-x^2+1)^(1/2)-(-x^2+1)^(1/2)/(x^2-1)*arcsin(x)-ln(1/(-x^2+1)^(1/2)+x/(-x^2+1)^(1/2))","A"
665,1,97,76,0.636000," ","int(arcsin(x)/x/(-x^2+1)^(3/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{-x^{2}+1}\, \arcsin \left(x \right)}{x^{2}-1}+2 i \arctan \left(i x +\sqrt{-x^{2}+1}\right)+i \dilog \left(i x +\sqrt{-x^{2}+1}+1\right)-\arcsin \left(x \right) \ln \left(i x +\sqrt{-x^{2}+1}+1\right)+i \dilog \left(i x +\sqrt{-x^{2}+1}\right)$&$97$\\ \hline \end{longtable}"," ",0,"-(-x^2+1)^(1/2)/(x^2-1)*arcsin(x)+2*I*arctan(I*x+(-x^2+1)^(1/2))+I*dilog(I*x+(-x^2+1)^(1/2)+1)-arcsin(x)*ln(I*x+(-x^2+1)^(1/2)+1)+I*dilog(I*x+(-x^2+1)^(1/2))","A"
666,1,43,42,0.312000," ","int(arccos(x)/x^4/(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{1}{6 x^{2}}-\frac{2 \ln \left(x \right)}{3}-\frac{\arccos \left(x \right) \sqrt{-x^{2}+1}}{3 x^{3}}-\frac{2 \arccos \left(x \right) \sqrt{-x^{2}+1}}{3 x}$&$43$\\ \hline \end{longtable}"," ",0,"1/6/x^2-2/3*ln(x)-1/3*arccos(x)*(-x^2+1)^(1/2)/x^3-2/3*arccos(x)*(-x^2+1)^(1/2)/x","A"
667,1,158,50,0.325000," ","int(x*arccos(x)^2*(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\left(6 i \arccos \left(x \right)+9 \arccos \left(x \right)^{2}-2\right) \left(4 i x^{3}-4 \sqrt{-x^{2}+1}\, x^{2}-3 i x +\sqrt{-x^{2}+1}\right)}{216}+\frac{\left(\arccos \left(x \right)^{2}-2+2 i \arccos \left(x \right)\right) \left(i x -\sqrt{-x^{2}+1}\right)}{8}-\frac{\left(\arccos \left(x \right)^{2}-2-2 i \arccos \left(x \right)\right) \left(i x +\sqrt{-x^{2}+1}\right)}{8}+\frac{\left(-6 i \arccos \left(x \right)+9 \arccos \left(x \right)^{2}-2\right) \left(4 i x^{3}+4 \sqrt{-x^{2}+1}\, x^{2}-3 i x -\sqrt{-x^{2}+1}\right)}{216}$&$158$\\ \hline \end{longtable}"," ",0,"-1/216*(6*I*arccos(x)+9*arccos(x)^2-2)*(4*I*x^3-4*(-x^2+1)^(1/2)*x^2-3*I*x+(-x^2+1)^(1/2))+1/8*(arccos(x)^2-2+2*I*arccos(x))*(I*x-(-x^2+1)^(1/2))-1/8*(arccos(x)^2-2-2*I*arccos(x))*(I*x+(-x^2+1)^(1/2))+1/216*(-6*I*arccos(x)+9*arccos(x)^2-2)*(4*I*x^3+4*(-x^2+1)^(1/2)*x^2-3*I*x-(-x^2+1)^(1/2))","C"
668,1,69,57,0.325000," ","int(x^2*arcsin(x)^3/(-x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arcsin \left(x \right)^{3} \left(-\sqrt{-x^{2}+1}\, x +\arcsin \left(x \right)\right)}{2}+\frac{3 \arcsin \left(x \right)^{2} \left(x^{2}-1\right)}{4}+\frac{3 \arcsin \left(x \right) \left(\sqrt{-x^{2}+1}\, x +\arcsin \left(x \right)\right)}{4}-\frac{3 \arcsin \left(x \right)^{2}}{8}-\frac{3 x^{2}}{8}-\frac{3 \arcsin \left(x \right)^{4}}{8}$&$69$\\ \hline \end{longtable}"," ",0,"1/2*arcsin(x)^3*(-(-x^2+1)^(1/2)*x+arcsin(x))+3/4*arcsin(x)^2*(x^2-1)+3/4*arcsin(x)*((-x^2+1)^(1/2)*x+arcsin(x))-3/8*arcsin(x)^2-3/8*x^2-3/8*arcsin(x)^4","A"
669,1,27,26,0.358000," ","int(x*arctan(x)/(x^2+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{4 x^{2}+4}+\frac{\arctan \left(x \right)}{4}-\frac{\arctan \left(x \right)}{2 \left(x^{2}+1\right)}$&$27$\\ risch&$\frac{i \ln \left(i x +1\right)}{4 x^{2}+4}-\frac{i \left(2 \ln \left(-i x +1\right)+\ln \left(x -i\right) x^{2}+\ln \left(x -i\right)-\ln \left(x +i\right) x^{2}-\ln \left(x +i\right)+2 i x \right)}{8 \left(x +i\right) \left(x -i\right)}$&$79$\\ \hline \end{longtable}"," ",0,"1/4*x/(x^2+1)+1/4*arctan(x)-1/2*arctan(x)/(x^2+1)","A"
670,1,37,36,0.363000," ","int(x*arctan(x)/(x^2+1)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x}{16 \left(x^{2}+1\right)^{2}}+\frac{3 x}{32 \left(x^{2}+1\right)}+\frac{3 \arctan \left(x \right)}{32}-\frac{\arctan \left(x \right)}{4 \left(x^{2}+1\right)^{2}}$&$37$\\ risch&$\frac{i \ln \left(i x +1\right)}{8 \left(x^{2}+1\right)^{2}}-\frac{i \left(8 \ln \left(-i x +1\right)+3 \ln \left(x -i\right) x^{4}+6 \ln \left(x -i\right) x^{2}+3 \ln \left(x -i\right)-3 \ln \left(x +i\right) x^{4}-6 \ln \left(x +i\right) x^{2}-3 \ln \left(x +i\right)+6 i x^{3}+10 i x \right)}{64 \left(x +i\right)^{2} \left(x -i\right)^{2}}$&$108$\\ \hline \end{longtable}"," ",0,"1/16*x/(x^2+1)^2+3/32*x/(x^2+1)+3/32*arctan(x)-1/4*arctan(x)/(x^2+1)^2","A"
671,1,20,19,0.293000," ","int(x^2*arctan(x)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x \arctan \left(x \right)-\frac{\arctan \left(x \right)^{2}}{2}-\frac{\ln \left(x^{2}+1\right)}{2}$&$20$\\ risch&$\frac{\ln \left(i x +1\right)^{2}}{8}+\frac{i \left(-x +\frac{i \ln \left(-i x +1\right)}{2}\right) \ln \left(i x +1\right)}{2}+\frac{\ln \left(-i x +1\right)^{2}}{8}+\frac{i \ln \left(-i x +1\right) x}{2}-\frac{\ln \left(x^{2}+1\right)}{2}$&$67$\\ \hline \end{longtable}"," ",0,"x*arctan(x)-1/2*arctan(x)^2-1/2*ln(x^2+1)","A"
672,1,113,53,0.329000," ","int(x^3*arctan(x)/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{i \ln \left(-i x +1\right) x^{2}}{4}+\frac{\arctan \left(x \right)}{2}-\frac{x}{2}-\frac{i \ln \left(\frac{1}{2}+\frac{i x}{2}\right) \ln \left(-i x +1\right)}{4}+\frac{i \dilog \left(\frac{1}{2}-\frac{i x}{2}\right)}{4}-\frac{i \ln \left(-i x +1\right)^{2}}{8}-\frac{i \ln \left(i x +1\right) x^{2}}{4}+\frac{i \ln \left(\frac{1}{2}-\frac{i x}{2}\right) \ln \left(i x +1\right)}{4}-\frac{i \dilog \left(\frac{1}{2}+\frac{i x}{2}\right)}{4}+\frac{i \ln \left(i x +1\right)^{2}}{8}$&$113$\\ default&$\frac{x^{2} \arctan \left(x \right)}{2}-\frac{\arctan \left(x \right) \ln \left(x^{2}+1\right)}{2}-\frac{x}{2}+\frac{\arctan \left(x \right)}{2}-\frac{i \ln \left(x -i\right) \ln \left(x^{2}+1\right)}{4}+\frac{i \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{4}+\frac{i \ln \left(x -i\right) \ln \left(-\frac{i \left(x +i\right)}{2}\right)}{4}+\frac{i \ln \left(x -i\right)^{2}}{8}+\frac{i \ln \left(x +i\right) \ln \left(x^{2}+1\right)}{4}-\frac{i \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{4}-\frac{i \ln \left(x +i\right) \ln \left(\frac{i \left(x -i\right)}{2}\right)}{4}-\frac{i \ln \left(x +i\right)^{2}}{8}$&$128$\\ \hline \end{longtable}"," ",0,"1/4*I*ln(1-I*x)*x^2+1/2*arctan(x)-1/2*x-1/4*I*ln(1/2+1/2*I*x)*ln(1-I*x)+1/4*I*dilog(1/2-1/2*I*x)-1/8*I*ln(1-I*x)^2-1/4*I*ln(1+I*x)*x^2+1/4*I*ln(1/2-1/2*I*x)*ln(1+I*x)-1/4*I*dilog(1/2+1/2*I*x)+1/8*I*ln(1+I*x)^2","B"
673,1,29,28,0.391000," ","int(x^2*arctan(x)/(x^2+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{4 \left(x^{2}+1\right)}-\frac{x \arctan \left(x \right)}{2 \left(x^{2}+1\right)}+\frac{\arctan \left(x \right)^{2}}{4}$&$29$\\ risch&$-\frac{\ln \left(i x +1\right)^{2}}{16}+\frac{\left(x^{2} \ln \left(-i x +1\right)+\ln \left(-i x +1\right)+2 i x \right) \ln \left(i x +1\right)}{8 x^{2}+8}-\frac{x^{2} \ln \left(-i x +1\right)^{2}+\ln \left(-i x +1\right)^{2}+4 i \ln \left(-i x +1\right) x +4}{16 \left(x +i\right) \left(x -i\right)}$&$101$\\ \hline \end{longtable}"," ",0,"-1/4/(x^2+1)-1/2*x*arctan(x)/(x^2+1)+1/4*arctan(x)^2","A"
674,1,139,65,0.349000," ","int(x^3*arctan(x)/(x^2+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(x \right) \ln \left(x^{2}+1\right)}{2}+\frac{\arctan \left(x \right)}{2 x^{2}+2}-\frac{x}{4 \left(x^{2}+1\right)}-\frac{\arctan \left(x \right)}{4}+\frac{i \ln \left(x -i\right) \ln \left(x^{2}+1\right)}{4}-\frac{i \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{4}-\frac{i \ln \left(x -i\right) \ln \left(-\frac{i \left(x +i\right)}{2}\right)}{4}-\frac{i \ln \left(x -i\right)^{2}}{8}-\frac{i \ln \left(x +i\right) \ln \left(x^{2}+1\right)}{4}+\frac{i \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{4}+\frac{i \ln \left(x +i\right) \ln \left(\frac{i \left(x -i\right)}{2}\right)}{4}+\frac{i \ln \left(x +i\right)^{2}}{8}$&$139$\\ risch&$\frac{i \ln \left(-i x +1\right)}{-8 i x +8}+\frac{i \ln \left(\frac{1}{2}+\frac{i x}{2}\right) \ln \left(-i x +1\right)}{4}-\frac{i}{8 \left(i x +1\right)}-\frac{i \ln \left(i x +1\right)^{2}}{8}-\frac{i \ln \left(i x +1\right)}{8 \left(i x +1\right)}-\frac{i \ln \left(\frac{1}{2}-\frac{i x}{2}\right) \ln \left(i x +1\right)}{4}-\frac{\ln \left(-i x +1\right) x}{16 \left(-i x -1\right)}+\frac{i \ln \left(i x +1\right)}{16 i x -16}-\frac{\arctan \left(x \right)}{8}-\frac{i \ln \left(-i x +1\right)}{16 \left(-i x -1\right)}+\frac{i \dilog \left(\frac{1}{2}+\frac{i x}{2}\right)}{4}+\frac{i}{-8 i x +8}+\frac{i \ln \left(-i x +1\right)^{2}}{8}-\frac{i \dilog \left(\frac{1}{2}-\frac{i x}{2}\right)}{4}-\frac{\ln \left(i x +1\right) x}{16 \left(i x -1\right)}$&$214$\\ \hline \end{longtable}"," ",0,"1/2*arctan(x)*ln(x^2+1)+1/2*arctan(x)/(x^2+1)-1/4*x/(x^2+1)-1/4*arctan(x)+1/4*I*ln(x-I)*ln(x^2+1)-1/4*I*dilog(-1/2*I*(x+I))-1/4*I*ln(x-I)*ln(-1/2*I*(x+I))-1/8*I*ln(x-I)^2-1/4*I*ln(x+I)*ln(x^2+1)+1/4*I*dilog(1/2*I*(x-I))+1/4*I*ln(x+I)*ln(1/2*I*(x-I))+1/8*I*ln(x+I)^2","B"
675,1,149,75,0.344000," ","int(x^5*arctan(x)/(x^2+1)^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{x^{2} \arctan \left(x \right)}{2}-\arctan \left(x \right) \ln \left(x^{2}+1\right)-\frac{\arctan \left(x \right)}{2 \left(x^{2}+1\right)}-\frac{x}{2}+\frac{x}{4 x^{2}+4}+\frac{3 \arctan \left(x \right)}{4}-\frac{i \ln \left(x -i\right) \ln \left(x^{2}+1\right)}{2}+\frac{i \dilog \left(-\frac{i \left(x +i\right)}{2}\right)}{2}+\frac{i \ln \left(x -i\right) \ln \left(-\frac{i \left(x +i\right)}{2}\right)}{2}+\frac{i \ln \left(x -i\right)^{2}}{4}+\frac{i \ln \left(x +i\right) \ln \left(x^{2}+1\right)}{2}-\frac{i \dilog \left(\frac{i \left(x -i\right)}{2}\right)}{2}-\frac{i \ln \left(x +i\right) \ln \left(\frac{i \left(x -i\right)}{2}\right)}{2}-\frac{i \ln \left(x +i\right)^{2}}{4}$&$149$\\ risch&$-\frac{x}{2}+\frac{5 \arctan \left(x \right)}{8}-\frac{i \dilog \left(\frac{1}{2}+\frac{i x}{2}\right)}{2}-\frac{i \ln \left(i x +1\right) x^{2}}{4}+\frac{i}{8 i x +8}-\frac{i \ln \left(-i x +1\right)}{8 \left(-i x +1\right)}+\frac{i \dilog \left(\frac{1}{2}-\frac{i x}{2}\right)}{2}+\frac{i \ln \left(-i x +1\right) x^{2}}{4}-\frac{i \ln \left(-i x +1\right)^{2}}{4}+\frac{i \ln \left(i x +1\right)^{2}}{4}+\frac{\ln \left(i x +1\right) x}{16 i x -16}+\frac{\ln \left(-i x +1\right) x}{-16 i x -16}-\frac{i \ln \left(\frac{1}{2}+\frac{i x}{2}\right) \ln \left(-i x +1\right)}{2}+\frac{i \ln \left(-i x +1\right)}{-16 i x -16}-\frac{i \ln \left(i x +1\right)}{16 \left(i x -1\right)}+\frac{i \ln \left(\frac{1}{2}-\frac{i x}{2}\right) \ln \left(i x +1\right)}{2}-\frac{i}{8 \left(-i x +1\right)}+\frac{i \ln \left(i x +1\right)}{8 i x +8}$&$243$\\ \hline \end{longtable}"," ",0,"1/2*x^2*arctan(x)-arctan(x)*ln(x^2+1)-1/2*arctan(x)/(x^2+1)-1/2*x+1/4*x/(x^2+1)+3/4*arctan(x)-1/2*I*ln(x-I)*ln(x^2+1)+1/2*I*dilog(-1/2*I*(x+I))+1/2*I*ln(x-I)*ln(-1/2*I*(x+I))+1/4*I*ln(x-I)^2+1/2*I*ln(x+I)*ln(x^2+1)-1/2*I*dilog(1/2*I*(x-I))-1/2*I*ln(x+I)*ln(1/2*I*(x-I))-1/4*I*ln(x+I)^2","A"
676,1,23,22,0.127000," ","int((x^2+1)*arctan(x)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(x \right)}{x}+x \arctan \left(x \right)+\ln \left(x \right)-\ln \left(x^{2}+1\right)$&$23$\\ meijerg&$-\frac{\arctan \left(\sqrt{x^{2}}\right)}{\sqrt{x^{2}}}-\ln \left(x^{2}+1\right)+\ln \left(x \right)+\frac{x^{2} \arctan \left(\sqrt{x^{2}}\right)}{\sqrt{x^{2}}}$&$40$\\ risch&$-\frac{i \left(x^{2}-1\right) \ln \left(i x +1\right)}{2 x}+\frac{i \left(-2 i \ln \left(x \right) x +2 i \ln \left(x^{2}+1\right) x +x^{2} \ln \left(-i x +1\right)-\ln \left(-i x +1\right)\right)}{2 x}$&$63$\\ \hline \end{longtable}"," ",0,"-arctan(x)/x+x*arctan(x)+ln(x)-ln(x^2+1)","A"
677,1,30,25,0.084000," ","int((x^2+1)*arctan(x)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(x \right)}{2 x^{2}}-\frac{\arctan \left(x \right)}{4 x^{4}}-\frac{1}{12 x^{3}}-\frac{1}{4 x}-\frac{\arctan \left(x \right)}{4}$&$30$\\ meijerg&$-\frac{1}{12 x^{3}}-\frac{1}{4 x}-\frac{2 \left(-\frac{3 x^{4}}{8}+\frac{3}{8}\right) \arctan \left(\sqrt{x^{2}}\right)}{3 x^{3} \sqrt{x^{2}}}-\frac{\left(x^{2}+1\right) \arctan \left(x \right)}{2 x^{2}}$&$47$\\ risch&$\frac{i \left(2 x^{2}+1\right) \ln \left(i x +1\right)}{8 x^{4}}+\frac{i \left(3 \ln \left(x -i\right) x^{4}-3 \ln \left(x +i\right) x^{4}+6 i x^{3}-6 x^{2} \ln \left(-i x +1\right)+2 i x -3 \ln \left(-i x +1\right)\right)}{24 x^{4}}$&$80$\\ \hline \end{longtable}"," ",0,"-1/2*arctan(x)/x^2-1/4*arctan(x)/x^4-1/12/x^3-1/4/x-1/4*arctan(x)","A"
678,1,79,47,0.357000," ","int((x^2+1)^2*arctan(x)/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\arctan \left(x \right) \ln \left(x \right)-\frac{\arctan \left(x \right)}{x^{2}}-\frac{\arctan \left(x \right)}{4 x^{4}}+\frac{i \ln \left(x \right) \ln \left(i x +1\right)}{2}-\frac{i \ln \left(x \right) \ln \left(-i x +1\right)}{2}+\frac{i \dilog \left(i x +1\right)}{2}-\frac{i \dilog \left(-i x +1\right)}{2}-\frac{3 \arctan \left(x \right)}{4}-\frac{1}{12 x^{3}}-\frac{3}{4 x}$&$79$\\ meijerg&$-\frac{1}{12 x^{3}}-\frac{3}{4 x}-\frac{2 \left(-\frac{3 x^{4}}{8}+\frac{3}{8}\right) \arctan \left(\sqrt{x^{2}}\right)}{3 x^{3} \sqrt{x^{2}}}-\frac{i x \polylog \left(2, i \sqrt{x^{2}}\right)}{2 \sqrt{x^{2}}}+\frac{i x \polylog \left(2, -i \sqrt{x^{2}}\right)}{2 \sqrt{x^{2}}}-\frac{\left(x^{2}+1\right) \arctan \left(x \right)}{x^{2}}$&$85$\\ risch&$\frac{3 i \ln \left(-i x \right)}{8}-\frac{3}{4 x}-\frac{3 \arctan \left(x \right)}{4}-\frac{i \ln \left(-i x +1\right)}{2 x^{2}}-\frac{i \dilog \left(-i x +1\right)}{2}-\frac{1}{12 x^{3}}-\frac{i \ln \left(-i x +1\right)}{8 x^{4}}-\frac{3 i \ln \left(i x \right)}{8}+\frac{i \ln \left(i x +1\right)}{2 x^{2}}+\frac{i \dilog \left(i x +1\right)}{2}+\frac{i \ln \left(i x +1\right)}{8 x^{4}}$&$104$\\ \hline \end{longtable}"," ",0,"arctan(x)*ln(x)-arctan(x)/x^2-1/4*arctan(x)/x^4+1/2*I*ln(x)*ln(1+I*x)-1/2*I*ln(x)*ln(1-I*x)+1/2*I*dilog(1+I*x)-1/2*I*dilog(1-I*x)-3/4*arctan(x)-1/12/x^3-3/4/x","A"
679,1,25,24,0.402000," ","int(arctan(x)/x^2/(x^2+1),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(x \right)}{x}-\frac{\arctan \left(x \right)^{2}}{2}+\ln \left(x \right)-\frac{\ln \left(x^{2}+1\right)}{2}$&$25$\\ risch&$\frac{\ln \left(i x +1\right)^{2}}{8}-\frac{\left(\ln \left(-i x +1\right) x -2 i\right) \ln \left(i x +1\right)}{4 x}-\frac{-x \ln \left(-i x +1\right)^{2}-8 x \ln \left(x \right)+4 \ln \left(x^{2}+1\right) x +4 i \ln \left(-i x +1\right)}{8 x}$&$79$\\ \hline \end{longtable}"," ",0,"-arctan(x)/x-1/2*arctan(x)^2+ln(x)-1/2*ln(x^2+1)","A"
680,1,34,33,0.108000," ","int(arctan(x)^2/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(x \right)}{x}-\frac{\arctan \left(x \right)^{2}}{2}-\frac{\arctan \left(x \right)^{2}}{2 x^{2}}+\ln \left(x \right)-\frac{\ln \left(x^{2}+1\right)}{2}$&$34$\\ risch&$\frac{\left(x^{2}+1\right) \ln \left(i x +1\right)^{2}}{8 x^{2}}-\frac{\left(x^{2} \ln \left(-i x +1\right)-2 i x +\ln \left(-i x +1\right)\right) \ln \left(i x +1\right)}{4 x^{2}}+\frac{x^{2} \ln \left(-i x +1\right)^{2}-4 i \ln \left(-i x +1\right) x +8 x^{2} \ln \left(x \right)-4 \ln \left(x^{2}+1\right) x^{2}+\ln \left(-i x +1\right)^{2}}{8 x^{2}}$&$113$\\ \hline \end{longtable}"," ",0,"-arctan(x)/x-1/2*arctan(x)^2-1/2*arctan(x)^2/x^2+ln(x)-1/2*ln(x^2+1)","A"
681,1,57,48,0.151000," ","int((x^2+1)*arctan(x)^2/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\arctan \left(x \right)^{2}}{2 x^{2}}-\frac{\arctan \left(x \right)^{2}}{4 x^{4}}-\frac{\arctan \left(x \right)}{6 x^{3}}-\frac{\arctan \left(x \right)}{2 x}-\frac{\arctan \left(x \right)^{2}}{4}-\frac{\ln \left(x^{2}+1\right)}{6}-\frac{1}{12 x^{2}}+\frac{\ln \left(x \right)}{3}$&$57$\\ risch&$\frac{\left(x^{4}+2 x^{2}+1\right) \ln \left(i x +1\right)^{2}}{16 x^{4}}-\frac{\left(3 x^{4} \ln \left(-i x +1\right)-6 i x^{3}+6 x^{2} \ln \left(-i x +1\right)-2 i x +3 \ln \left(-i x +1\right)\right) \ln \left(i x +1\right)}{24 x^{4}}+\frac{3 x^{4} \ln \left(-i x +1\right)^{2}+16 x^{4} \ln \left(x \right)-8 \ln \left(x^{2}+1\right) x^{4}-12 i x^{3} \ln \left(-i x +1\right)+6 x^{2} \ln \left(-i x +1\right)^{2}-4 i \ln \left(-i x +1\right) x -4 x^{2}+3 \ln \left(-i x +1\right)^{2}}{48 x^{4}}$&$174$\\ \hline \end{longtable}"," ",0,"-1/2*arctan(x)^2/x^2-1/4*arctan(x)^2/x^4-1/6*arctan(x)/x^3-1/2*arctan(x)/x-1/4*arctan(x)^2-1/6*ln(x^2+1)-1/12/x^2+1/3*ln(x)","A"
682,1,78,67,0.420000," ","int(x^3*arctan(x)^2/(x^2+1)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\arctan \left(x \right)^{2}}{4 \left(x^{2}+1\right)^{2}}-\frac{\arctan \left(x \right)^{2}}{2 \left(x^{2}+1\right)}+\frac{5 x^{3} \arctan \left(x \right)}{16 \left(x^{2}+1\right)^{2}}+\frac{3 x \arctan \left(x \right)}{16 \left(x^{2}+1\right)^{2}}+\frac{5 \arctan \left(x \right)^{2}}{32}-\frac{1}{32 \left(x^{2}+1\right)^{2}}+\frac{5}{32 \left(x^{2}+1\right)}$&$78$\\ risch&$-\frac{\left(5 x^{4}-6 x^{2}-3\right) \ln \left(i x +1\right)^{2}}{128 \left(x^{2}+1\right)^{2}}+\frac{\left(-6 x^{2} \ln \left(-i x +1\right)-3 \ln \left(-i x +1\right)+5 x^{4} \ln \left(-i x +1\right)-10 i x^{3}-6 i x \right) \ln \left(i x +1\right)}{64 \left(x +i\right)^{2} \left(x -i\right)^{2}}-\frac{5 x^{4} \ln \left(-i x +1\right)^{2}-6 x^{2} \ln \left(-i x +1\right)^{2}-3 \ln \left(-i x +1\right)^{2}-20 i x^{3} \ln \left(-i x +1\right)-12 i \ln \left(-i x +1\right) x -20 x^{2}-16}{128 \left(x +i\right)^{2} \left(x -i\right)^{2}}$&$181$\\ \hline \end{longtable}"," ",0,"1/4*arctan(x)^2/(x^2+1)^2-1/2*arctan(x)^2/(x^2+1)+5/16*x^3*arctan(x)/(x^2+1)^2+3/16*x*arctan(x)/(x^2+1)^2+5/32*arctan(x)^2-1/32/(x^2+1)^2+5/32/(x^2+1)","A"
683,1,708,119,0.739000," ","int(arcsec(x)*(x^2-1)^(1/2)/x^2,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{x^{2}-1}\, \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-3 i x^{2}-4 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +4 i\right)}{4 \left(-i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) x}-\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +2 x^{2}-2\right) \mathrm{arcsec}\left(x \right)}{4 \sqrt{x^{2}-1}\, x}-\frac{\sqrt{x^{2}-1}\, \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) x}{2 \left(-i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right)}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -2 x^{2}+2\right) \mathrm{arcsec}\left(x \right)}{4 \sqrt{x^{2}-1}\, x}+\frac{i \sqrt{x^{2}-1}\, x^{3}}{4 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-8 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +8 x^{2}-8}-\frac{\left(i x^{2}+\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \mathrm{arcsec}\left(x \right) \ln \left(1+i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)}{2 \sqrt{x^{2}-1}}+\frac{\left(i x^{2}+\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \mathrm{arcsec}\left(x \right) \ln \left(1-i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)}{2 \sqrt{x^{2}-1}}-\frac{\left(-i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \dilog \left(1+i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)}{2 \sqrt{x^{2}-1}}+\frac{\left(-i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \dilog \left(1-i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)}{2 \sqrt{x^{2}-1}}+\frac{\left(i x^{2}-\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \mathrm{arcsec}\left(x \right) \ln \left(1+i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)}{2 \sqrt{x^{2}-1}}-\frac{\left(i x^{2}-\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \mathrm{arcsec}\left(x \right) \ln \left(1-i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)}{2 \sqrt{x^{2}-1}}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \dilog \left(1+i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)}{2 \sqrt{x^{2}-1}}-\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \dilog \left(1-i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)}{2 \sqrt{x^{2}-1}}$&$708$\\ \hline \end{longtable}"," ",0,"1/4*(x^2-1)^(1/2)*(((x^2-1)/x^2)^(1/2)*x^3-3*I*x^2-4*((x^2-1)/x^2)^(1/2)*x+4*I)/(-I*((x^2-1)/x^2)^(1/2)*x+x^2-1)/x-1/4/(x^2-1)^(1/2)/x*(I*((x^2-1)/x^2)^(1/2)*x^3-2*I*((x^2-1)/x^2)^(1/2)*x+2*x^2-2)*arcsec(x)-1/2*(x^2-1)^(1/2)*(((x^2-1)/x^2)^(1/2)*x-I)*x/(-I*((x^2-1)/x^2)^(1/2)*x+x^2-1)+1/4/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x^3-2*I*((x^2-1)/x^2)^(1/2)*x-2*x^2+2)*arcsec(x)/x+I*(x^2-1)^(1/2)*x^3/(4*I*((x^2-1)/x^2)^(1/2)*x^3-8*I*((x^2-1)/x^2)^(1/2)*x+8*x^2-8)-1/2/(x^2-1)^(1/2)*(I*x^2+((x^2-1)/x^2)^(1/2)*x-I)*arcsec(x)*ln(1+I*(1/x+I*(1-1/x^2)^(1/2)))+1/2/(x^2-1)^(1/2)*(I*x^2+((x^2-1)/x^2)^(1/2)*x-I)*arcsec(x)*ln(1-I*(1/x+I*(1-1/x^2)^(1/2)))-1/2/(x^2-1)^(1/2)*(-I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*dilog(1+I*(1/x+I*(1-1/x^2)^(1/2)))+1/2/(x^2-1)^(1/2)*(-I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*dilog(1-I*(1/x+I*(1-1/x^2)^(1/2)))+1/2/(x^2-1)^(1/2)*(I*x^2-((x^2-1)/x^2)^(1/2)*x-I)*arcsec(x)*ln(1+I*(1/x+I*(1-1/x^2)^(1/2)))-1/2/(x^2-1)^(1/2)*(I*x^2-((x^2-1)/x^2)^(1/2)*x-I)*arcsec(x)*ln(1-I*(1/x+I*(1-1/x^2)^(1/2)))+1/2/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*dilog(1+I*(1/x+I*(1-1/x^2)^(1/2)))-1/2/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*dilog(1-I*(1/x+I*(1-1/x^2)^(1/2)))","B"
684,1,305,82,0.594000," ","int((x^2-1)^(5/2)*arccsc(x)/x^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{5 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \mathrm{arccsc}\left(x \right)^{2}}{4 \sqrt{x^{2}-1}}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -2 x^{2}+2\right) \left(2 \,\mathrm{arccsc}\left(x \right)+i\right)}{16 \sqrt{x^{2}-1}\, x^{2}}-\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +2 x^{2}-2\right) \left(-i+2 \,\mathrm{arccsc}\left(x \right)\right)}{16 \sqrt{x^{2}-1}\, x^{2}}-\frac{14 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \,\mathrm{arccsc}\left(x \right)}{3 \sqrt{x^{2}-1}}+\frac{\left(x^{4}+7 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -8 x^{2}+7\right) \left(2 \,\mathrm{arccsc}\left(x \right) x^{4}+\sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-30 \,\mathrm{arccsc}\left(x \right) x^{2}-7 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +126 \,\mathrm{arccsc}\left(x \right)-7 i\right)}{6 \sqrt{x^{2}-1}\, \left(x^{4}-15 x^{2}+63\right)}+\frac{7 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \ln \left(\left(\frac{i}{x}+\sqrt{1-\frac{1}{x^{2}}}\right)^{2}-1\right)}{3 \sqrt{x^{2}-1}}$&$305$\\ \hline \end{longtable}"," ",0,"-5/4/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*arccsc(x)^2+1/16/(x^2-1)^(1/2)/x^2*(I*((x^2-1)/x^2)^(1/2)*x^3-2*I*((x^2-1)/x^2)^(1/2)*x-2*x^2+2)*(2*arccsc(x)+I)-1/16/(x^2-1)^(1/2)/x^2*(I*((x^2-1)/x^2)^(1/2)*x^3-2*I*((x^2-1)/x^2)^(1/2)*x+2*x^2-2)*(-I+2*arccsc(x))-14/3*I/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*arccsc(x)+1/6/(x^2-1)^(1/2)*(x^4+7*I*((x^2-1)/x^2)^(1/2)*x-8*x^2+7)*(2*arccsc(x)*x^4+((x^2-1)/x^2)^(1/2)*x^3-30*arccsc(x)*x^2-7*((x^2-1)/x^2)^(1/2)*x+126*arccsc(x)-7*I)/(x^4-15*x^2+63)+7/3/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*ln((I/x+(1-1/x^2)^(1/2))^2-1)","C"
685,1,329,32,0.778000," ","int(arcsec(x)*(x^2-1)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{x^{2}-1}\, \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}-5 i x^{4}-12 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}+20 i x^{2}+16 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -16 i\right)}{144 \left(-i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) x^{3}}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}-8 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}+4 x^{4}+8 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -12 x^{2}+8\right) \mathrm{arcsec}\left(x \right)}{48 \sqrt{x^{2}-1}\, x^{3}}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \left(-13 i+3 \,\mathrm{arcsec}\left(x \right)\right)}{72 \sqrt{x^{2}-1}\, x}-\frac{\left(5 i+3 \,\mathrm{arcsec}\left(x \right)\right) \left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -1\right) \sqrt{x^{2}-1}}{72 x}-\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \left(7 i+9 \,\mathrm{arcsec}\left(x \right)\right) \cos \left(3 \,\mathrm{arcsec}\left(x \right)\right)}{144 \sqrt{x^{2}-1}}-\frac{\left(i x^{2}-\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \left(3 i+\mathrm{arcsec}\left(x \right)\right) \sin \left(3 \,\mathrm{arcsec}\left(x \right)\right)}{48 \sqrt{x^{2}-1}}$&$329$\\ \hline \end{longtable}"," ",0,"-1/144*(x^2-1)^(1/2)*(((x^2-1)/x^2)^(1/2)*x^5-5*I*x^4-12*((x^2-1)/x^2)^(1/2)*x^3+20*I*x^2+16*((x^2-1)/x^2)^(1/2)*x-16*I)/(-I*((x^2-1)/x^2)^(1/2)*x+x^2-1)/x^3+1/48/(x^2-1)^(1/2)/x^3*(I*((x^2-1)/x^2)^(1/2)*x^5-8*I*((x^2-1)/x^2)^(1/2)*x^3+4*x^4+8*I*((x^2-1)/x^2)^(1/2)*x-12*x^2+8)*arcsec(x)+1/72/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*(-13*I+3*arcsec(x))/x-1/72*(5*I+3*arcsec(x))*(I*((x^2-1)/x^2)^(1/2)*x-1)*(x^2-1)^(1/2)/x-1/144/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*(7*I+9*arcsec(x))*cos(3*arcsec(x))-1/48/(x^2-1)^(1/2)*(I*x^2-((x^2-1)/x^2)^(1/2)*x-I)*(3*I+arcsec(x))*sin(3*arcsec(x))","C"
686,1,128,49,0.574000," ","int(arcsec(x)/(x^2-1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{x^{2}-1}\, x \left(4 \,\mathrm{arcsec}\left(x \right) x^{2}-\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -6 \,\mathrm{arcsec}\left(x \right)\right)}{6 x^{4}-12 x^{2}+6}+\frac{5 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \ln \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}+1\right)}{6 \sqrt{x^{2}-1}}-\frac{5 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \ln \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}-1\right)}{6 \sqrt{x^{2}-1}}$&$128$\\ \hline \end{longtable}"," ",0,"1/6*(x^2-1)^(1/2)*x/(x^4-2*x^2+1)*(4*arcsec(x)*x^2-((x^2-1)/x^2)^(1/2)*x-6*arcsec(x))+5/6/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*ln(1/x+I*(1-1/x^2)^(1/2)+1)-5/6/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*ln(1/x+I*(1-1/x^2)^(1/2)-1)","C"
687,1,121,39,0.619000," ","int(x^2*arcsec(x)/(x^2-1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{x^{2}-1}\, x^{2} \left(2 x \,\mathrm{arcsec}\left(x \right)+\sqrt{\frac{x^{2}-1}{x^{2}}}\right)}{6 \left(x^{4}-2 x^{2}+1\right)}+\frac{\sqrt{\frac{x^{2}-1}{x^{2}}}\, x \ln \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}-1\right)}{6 \sqrt{x^{2}-1}}-\frac{\sqrt{\frac{x^{2}-1}{x^{2}}}\, x \ln \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}+1\right)}{6 \sqrt{x^{2}-1}}$&$121$\\ \hline \end{longtable}"," ",0,"-1/6*(x^2-1)^(1/2)*x^2/(x^4-2*x^2+1)*(2*x*arcsec(x)+((x^2-1)/x^2)^(1/2))+1/6/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*ln(1/x+I*(1-1/x^2)^(1/2)-1)-1/6/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*ln(1/x+I*(1-1/x^2)^(1/2)+1)","C"
688,1,197,64,0.839000," ","int(x^3*arcsec(x)/(x^2-1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{4 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \,\mathrm{arcsec}\left(x \right)}{3 \sqrt{x^{2}-1}}+\frac{\sqrt{x^{2}-1}\, \left(2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -3 x^{2}+2\right) \left(8 x^{4} \mathrm{arcsec}\left(x \right)+2 i x^{4}+3 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-6 \,\mathrm{arcsec}\left(x \right) x^{2}-4 i x^{2}-2 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +2 i\right)}{6 x^{2} \left(4 x^{6}-11 x^{4}+10 x^{2}-3\right)}+\frac{2 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \ln \left(\left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)^{2}-1\right)}{3 \sqrt{x^{2}-1}}$&$197$\\ \hline \end{longtable}"," ",0,"-4/3*I/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*arcsec(x)+1/6*(x^2-1)^(1/2)/x^2*(2*I*((x^2-1)/x^2)^(1/2)*x^3-2*I*((x^2-1)/x^2)^(1/2)*x-3*x^2+2)*(8*x^4*arcsec(x)+2*I*x^4+3*((x^2-1)/x^2)^(1/2)*x^3-6*arcsec(x)*x^2-4*I*x^2-2*((x^2-1)/x^2)^(1/2)*x+2*I)/(4*x^6-11*x^4+10*x^2-3)+2/3/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*ln((1/x+I*(1-1/x^2)^(1/2))^2-1)","C"
689,1,240,164,0.892000," ","int(x^6*arcsec(x)/(x^2-1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{x^{2}-1}\, x \left(3 x^{4} \mathrm{arcsec}\left(x \right)-3 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-20 \,\mathrm{arcsec}\left(x \right) x^{2}+2 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +15 \,\mathrm{arcsec}\left(x \right)\right)}{6 x^{4}-12 x^{2}+6}+\frac{i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \left(15 i \mathrm{arcsec}\left(x \right) \ln \left(1+i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)-15 i \mathrm{arcsec}\left(x \right) \ln \left(1-i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)+13 i \ln \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}+1\right)-13 i \ln \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}-1\right)+15 \dilog \left(1+i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)-15 \dilog \left(1-i \left(\frac{1}{x}+i \sqrt{1-\frac{1}{x^{2}}}\right)\right)\right)}{6 \sqrt{x^{2}-1}}$&$240$\\ \hline \end{longtable}"," ",0,"1/6*(x^2-1)^(1/2)*x/(x^4-2*x^2+1)*(3*x^4*arcsec(x)-3*((x^2-1)/x^2)^(1/2)*x^3-20*arcsec(x)*x^2+2*((x^2-1)/x^2)^(1/2)*x+15*arcsec(x))+1/6*I/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*(15*I*arcsec(x)*ln(1+I*(1/x+I*(1-1/x^2)^(1/2)))-15*I*arcsec(x)*ln(1-I*(1/x+I*(1-1/x^2)^(1/2)))+13*I*ln(1/x+I*(1-1/x^2)^(1/2)+1)-13*I*ln(1/x+I*(1-1/x^2)^(1/2)-1)+15*dilog(1+I*(1/x+I*(1-1/x^2)^(1/2)))-15*dilog(1-I*(1/x+I*(1-1/x^2)^(1/2))))","A"
690,1,178,19,0.509000," ","int(arcsec(x)/x^2/(x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{\sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-3 i x^{2}-4 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +4 i}{4 \sqrt{x^{2}-1}\, \left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +1\right) x}+\frac{\left(x^{2}-2-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right) \mathrm{arcsec}\left(x \right)}{4 \sqrt{x^{2}-1}\, x}-\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -1\right) \left(\mathrm{arcsec}\left(x \right)+i\right)}{4 \sqrt{x^{2}-1}\, x}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \left(3 \,\mathrm{arcsec}\left(x \right)-i\right)}{4 \sqrt{x^{2}-1}\, x}$&$178$\\ \hline \end{longtable}"," ",0,"-1/4*(((x^2-1)/x^2)^(1/2)*x^3-3*I*x^2-4*((x^2-1)/x^2)^(1/2)*x+4*I)/(x^2-1)^(1/2)/(I*((x^2-1)/x^2)^(1/2)*x+1)/x+1/4/(x^2-1)^(1/2)/x*(x^2-2-2*I*((x^2-1)/x^2)^(1/2)*x)*arcsec(x)-1/4/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x-1)*(arcsec(x)+I)/x+1/4/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*(3*arcsec(x)-I)/x","C"
691,1,702,56,0.834000," ","int(arccsc(x)/x^2/(x^2-1)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{3 i x^{2}-4 i-4 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +\sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}}{4 \left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -1\right) x \sqrt{x^{2}-1}}+\frac{\left(x^{2}-2+2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right) \mathrm{arccsc}\left(x \right)}{4 \sqrt{x^{2}-1}\, x}+\frac{x \,\mathrm{arccsc}\left(x \right)}{2 \sqrt{x^{2}-1}}+\frac{\left(x^{2}-2-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right) \mathrm{arccsc}\left(x \right)}{4 \sqrt{x^{2}-1}\, x}+\frac{x^{3}}{4 \sqrt{x^{2}-1}\, \left(i x^{2}-2 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -2 i\right)}-\frac{x^{5} \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x +i\right)}{24 \sqrt{x^{2}-1}\, \left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}-5 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-3 x^{4}+4 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +7 x^{2}-4\right)}+\frac{x \left(5 i x^{4}-20 i x^{2}-12 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}+\sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}+16 i+16 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right)}{24 \sqrt{x^{2}-1}\, \left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}-5 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-3 x^{4}+4 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +7 x^{2}-4\right)}+\frac{2 \sqrt{x^{2}-1}\, x^{3} \mathrm{arccsc}\left(x \right)}{3 \left(x^{4}-2 x^{2}+1\right)}+\frac{\sqrt{x^{2}-1}\, x \left(x^{2}-2-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right) \mathrm{arccsc}\left(x \right)}{2 x^{4}-4 x^{2}+2}+\frac{\sqrt{x^{2}-1}\, x \left(x^{2}-2+2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right) \mathrm{arccsc}\left(x \right)}{2 x^{4}-4 x^{2}+2}+\frac{11 \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x +i\right) \ln \left(\frac{i}{x}+\sqrt{1-\frac{1}{x^{2}}}-i\right)}{12 \sqrt{x^{2}-1}}+\frac{11 \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \ln \left(\frac{i}{x}+\sqrt{1-\frac{1}{x^{2}}}-i\right)}{12 \sqrt{x^{2}-1}}-\frac{11 \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x +i\right) \ln \left(\frac{i}{x}+\sqrt{1-\frac{1}{x^{2}}}+i\right)}{12 \sqrt{x^{2}-1}}-\frac{11 \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \ln \left(\frac{i}{x}+\sqrt{1-\frac{1}{x^{2}}}+i\right)}{12 \sqrt{x^{2}-1}}$&$702$\\ \hline \end{longtable}"," ",0,"-1/4/(I*((x^2-1)/x^2)^(1/2)*x-1)/x/(x^2-1)^(1/2)*(3*I*x^2-4*I-4*((x^2-1)/x^2)^(1/2)*x+((x^2-1)/x^2)^(1/2)*x^3)+1/4/(x^2-1)^(1/2)/x*(x^2-2+2*I*((x^2-1)/x^2)^(1/2)*x)*arccsc(x)+1/2*x*arccsc(x)/(x^2-1)^(1/2)+1/4/(x^2-1)^(1/2)*(x^2-2-2*I*((x^2-1)/x^2)^(1/2)*x)*arccsc(x)/x+1/4*x^3/(x^2-1)^(1/2)/(I*x^2-2*((x^2-1)/x^2)^(1/2)*x-2*I)-1/24*x^5*(((x^2-1)/x^2)^(1/2)*x+I)/(x^2-1)^(1/2)/(I*((x^2-1)/x^2)^(1/2)*x^5-5*I*((x^2-1)/x^2)^(1/2)*x^3-3*x^4+4*I*((x^2-1)/x^2)^(1/2)*x+7*x^2-4)+1/24*x*(5*I*x^4-20*I*x^2-12*((x^2-1)/x^2)^(1/2)*x^3+((x^2-1)/x^2)^(1/2)*x^5+16*I+16*((x^2-1)/x^2)^(1/2)*x)/(x^2-1)^(1/2)/(I*((x^2-1)/x^2)^(1/2)*x^5-5*I*((x^2-1)/x^2)^(1/2)*x^3-3*x^4+4*I*((x^2-1)/x^2)^(1/2)*x+7*x^2-4)+2/3*(x^2-1)^(1/2)*x^3/(x^4-2*x^2+1)*arccsc(x)+1/2*(x^2-1)^(1/2)*x*(x^2-2-2*I*((x^2-1)/x^2)^(1/2)*x)*arccsc(x)/(x^4-2*x^2+1)+1/2*(x^2-1)^(1/2)*x*(x^2-2+2*I*((x^2-1)/x^2)^(1/2)*x)*arccsc(x)/(x^4-2*x^2+1)+11/12/(x^2-1)^(1/2)*(((x^2-1)/x^2)^(1/2)*x+I)*ln(I/x+(1-1/x^2)^(1/2)-I)+11/12/(x^2-1)^(1/2)*(((x^2-1)/x^2)^(1/2)*x-I)*ln(I/x+(1-1/x^2)^(1/2)-I)-11/12/(x^2-1)^(1/2)*(((x^2-1)/x^2)^(1/2)*x+I)*ln(I/x+(1-1/x^2)^(1/2)+I)-11/12/(x^2-1)^(1/2)*(((x^2-1)/x^2)^(1/2)*x-I)*ln(I/x+(1-1/x^2)^(1/2)+I)","C"
692,1,330,64,0.665000," ","int(arccsc(x)^4/x^2/(x^2-1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(i x^{2}-2 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -2 i\right) \mathrm{arccsc}\left(x \right)^{3}}{\sqrt{x^{2}-1}\, x}+\frac{\left(x^{2}-2+2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right) \mathrm{arccsc}\left(x \right)^{4}}{4 \sqrt{x^{2}-1}\, x}-\frac{6 \left(i x^{2}-2 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -2 i\right) \mathrm{arccsc}\left(x \right)}{\sqrt{x^{2}-1}\, x}-\frac{3 \left(x^{2}-2+2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right) \mathrm{arccsc}\left(x \right)^{2}}{\sqrt{x^{2}-1}\, x}+\frac{6 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-24 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -18 x^{2}+24}{\sqrt{x^{2}-1}\, \left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -1\right) x}+\frac{\left(-i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \left(3 \mathrm{arccsc}\left(x \right)^{4}-4 i \mathrm{arccsc}\left(x \right)^{3}-36 \mathrm{arccsc}\left(x \right)^{2}+24 i \mathrm{arccsc}\left(x \right)+72\right)}{4 \sqrt{x^{2}-1}\, x}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +1\right) \left(\mathrm{arccsc}\left(x \right)^{4}+4 i \mathrm{arccsc}\left(x \right)^{3}-12 \mathrm{arccsc}\left(x \right)^{2}-24 i \mathrm{arccsc}\left(x \right)+24\right)}{4 \sqrt{x^{2}-1}\, x}$&$330$\\ \hline \end{longtable}"," ",0,"1/(x^2-1)^(1/2)/x*(I*x^2-2*((x^2-1)/x^2)^(1/2)*x-2*I)*arccsc(x)^3+1/4/(x^2-1)^(1/2)/x*(x^2-2+2*I*((x^2-1)/x^2)^(1/2)*x)*arccsc(x)^4-6/(x^2-1)^(1/2)/x*(I*x^2-2*((x^2-1)/x^2)^(1/2)*x-2*I)*arccsc(x)-3/(x^2-1)^(1/2)/x*(x^2-2+2*I*((x^2-1)/x^2)^(1/2)*x)*arccsc(x)^2+6*(I*((x^2-1)/x^2)^(1/2)*x^3-4*I*((x^2-1)/x^2)^(1/2)*x-3*x^2+4)/(x^2-1)^(1/2)/(I*((x^2-1)/x^2)^(1/2)*x-1)/x+1/4/(x^2-1)^(1/2)*(-I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*(3*arccsc(x)^4-4*I*arccsc(x)^3-36*arccsc(x)^2+24*I*arccsc(x)+72)/x+1/4/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+1)*(arccsc(x)^4+4*I*arccsc(x)^3-12*arccsc(x)^2-24*I*arccsc(x)+24)/x","C"
693,1,386,105,0.702000," ","int((x^2-1)^(3/2)*arcsec(x)^2/x^5,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\sqrt{\frac{x^{2}-1}{x^{2}}}\, x \mathrm{arcsec}\left(x \right)^{3}}{8 \sqrt{x^{2}-1}}+\frac{\left(-5 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}+x^{6}+20 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-13 x^{4}-16 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +28 x^{2}-16\right) \left(4 i \mathrm{arcsec}\left(x \right)+8 \mathrm{arcsec}\left(x \right)^{2}-1\right)}{1024 \sqrt{x^{2}-1}\, x^{4}}-\frac{\left(-i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \left(2 \mathrm{arcsec}\left(x \right)^{2}-1+2 i \mathrm{arcsec}\left(x \right)\right)}{32 \sqrt{x^{2}-1}}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}-2 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -2 x^{2}+2\right) \left(2 \mathrm{arcsec}\left(x \right)^{2}-1-2 i \mathrm{arcsec}\left(x \right)\right)}{16 \sqrt{x^{2}-1}\, x^{2}}-\frac{\left(-5 x^{2}+4+3 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}+x^{4}-4 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x \right) \left(-4 i \mathrm{arcsec}\left(x \right)+8 \mathrm{arcsec}\left(x \right)^{2}-1\right)}{1024 \sqrt{x^{2}-1}\, x^{2}}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \left(7 i \mathrm{arcsec}\left(x \right)+8 \mathrm{arcsec}\left(x \right)^{2}-4\right) \cos \left(4 \,\mathrm{arcsec}\left(x \right)\right)}{128 \sqrt{x^{2}-1}}+\frac{\left(i x^{2}-\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \left(32 i \mathrm{arcsec}\left(x \right)+24 \mathrm{arcsec}\left(x \right)^{2}-15\right) \sin \left(4 \,\mathrm{arcsec}\left(x \right)\right)}{512 \sqrt{x^{2}-1}}$&$386$\\ \hline \end{longtable}"," ",0,"1/8/(x^2-1)^(1/2)*((x^2-1)/x^2)^(1/2)*x*arcsec(x)^3+1/1024/(x^2-1)^(1/2)/x^4*(-5*I*((x^2-1)/x^2)^(1/2)*x^5+x^6+20*I*((x^2-1)/x^2)^(1/2)*x^3-13*x^4-16*I*((x^2-1)/x^2)^(1/2)*x+28*x^2-16)*(4*I*arcsec(x)+8*arcsec(x)^2-1)-1/32/(x^2-1)^(1/2)*(-I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*(2*arcsec(x)^2-1+2*I*arcsec(x))+1/16/(x^2-1)^(1/2)/x^2*(I*((x^2-1)/x^2)^(1/2)*x^3-2*I*((x^2-1)/x^2)^(1/2)*x-2*x^2+2)*(2*arcsec(x)^2-1-2*I*arcsec(x))-1/1024/(x^2-1)^(1/2)*(-5*x^2+4+3*I*((x^2-1)/x^2)^(1/2)*x^3+x^4-4*I*((x^2-1)/x^2)^(1/2)*x)*(-4*I*arcsec(x)+8*arcsec(x)^2-1)/x^2+1/128/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*(7*I*arcsec(x)+8*arcsec(x)^2-4)*cos(4*arcsec(x))+1/512/(x^2-1)^(1/2)*(I*x^2-((x^2-1)/x^2)^(1/2)*x-I)*(32*I*arcsec(x)+24*arcsec(x)^2-15)*sin(4*arcsec(x))","C"
694,1,536,92,0.844000," ","int(arcsec(x)^3*(x^2-1)^(1/2)/x^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}-8 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}+4 x^{4}+8 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -12 x^{2}+8\right) \mathrm{arcsec}\left(x \right)^{3}}{48 \sqrt{x^{2}-1}\, x^{3}}+\frac{\sqrt{x^{2}-1}\, \left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}-5 i x^{4}-12 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}+20 i x^{2}+16 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -16 i\right)}{216 \left(-i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) x^{3}}-\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}-8 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}+4 x^{4}+8 i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -12 x^{2}+8\right) \mathrm{arcsec}\left(x \right)}{72 \sqrt{x^{2}-1}\, x^{3}}-\frac{\left(\sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{5}-4 i x^{4}-8 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x^{3}+12 i x^{2}+8 \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -8 i\right) \mathrm{arcsec}\left(x \right)^{2}}{48 \sqrt{x^{2}-1}\, x^{3}}+\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \left(9 \mathrm{arcsec}\left(x \right)^{3}-117 i \mathrm{arcsec}\left(x \right)^{2}-78 \,\mathrm{arcsec}\left(x \right)+242 i\right)}{216 \sqrt{x^{2}-1}\, x}-\frac{\left(45 i \mathrm{arcsec}\left(x \right)^{2}+9 \mathrm{arcsec}\left(x \right)^{3}-82 i-78 \,\mathrm{arcsec}\left(x \right)\right) \left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x -1\right) \sqrt{x^{2}-1}}{216 x}-\frac{\left(i \sqrt{\frac{x^{2}-1}{x^{2}}}\, x +x^{2}-1\right) \left(63 i \mathrm{arcsec}\left(x \right)^{2}+27 \mathrm{arcsec}\left(x \right)^{3}-158 i-162 \,\mathrm{arcsec}\left(x \right)\right) \cos \left(3 \,\mathrm{arcsec}\left(x \right)\right)}{432 \sqrt{x^{2}-1}}-\frac{\left(i x^{2}-\sqrt{\frac{x^{2}-1}{x^{2}}}\, x -i\right) \left(27 i \mathrm{arcsec}\left(x \right)^{2}+3 \mathrm{arcsec}\left(x \right)^{3}-54 i-50 \,\mathrm{arcsec}\left(x \right)\right) \sin \left(3 \,\mathrm{arcsec}\left(x \right)\right)}{144 \sqrt{x^{2}-1}}$&$536$\\ \hline \end{longtable}"," ",0,"1/48/(x^2-1)^(1/2)/x^3*(I*((x^2-1)/x^2)^(1/2)*x^5-8*I*((x^2-1)/x^2)^(1/2)*x^3+4*x^4+8*I*((x^2-1)/x^2)^(1/2)*x-12*x^2+8)*arcsec(x)^3+1/216*(x^2-1)^(1/2)*(((x^2-1)/x^2)^(1/2)*x^5-5*I*x^4-12*((x^2-1)/x^2)^(1/2)*x^3+20*I*x^2+16*((x^2-1)/x^2)^(1/2)*x-16*I)/(-I*((x^2-1)/x^2)^(1/2)*x+x^2-1)/x^3-1/72/(x^2-1)^(1/2)/x^3*(I*((x^2-1)/x^2)^(1/2)*x^5-8*I*((x^2-1)/x^2)^(1/2)*x^3+4*x^4+8*I*((x^2-1)/x^2)^(1/2)*x-12*x^2+8)*arcsec(x)-1/48/(x^2-1)^(1/2)/x^3*(((x^2-1)/x^2)^(1/2)*x^5-4*I*x^4-8*((x^2-1)/x^2)^(1/2)*x^3+12*I*x^2+8*((x^2-1)/x^2)^(1/2)*x-8*I)*arcsec(x)^2+1/216/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*(9*arcsec(x)^3-117*I*arcsec(x)^2-78*arcsec(x)+242*I)/x-1/216*(45*I*arcsec(x)^2+9*arcsec(x)^3-82*I-78*arcsec(x))*(I*((x^2-1)/x^2)^(1/2)*x-1)*(x^2-1)^(1/2)/x-1/432/(x^2-1)^(1/2)*(I*((x^2-1)/x^2)^(1/2)*x+x^2-1)*(63*I*arcsec(x)^2+27*arcsec(x)^3-158*I-162*arcsec(x))*cos(3*arcsec(x))-1/144/(x^2-1)^(1/2)*(I*x^2-((x^2-1)/x^2)^(1/2)*x-I)*(27*I*arcsec(x)^2+3*arcsec(x)^3-54*I-50*arcsec(x))*sin(3*arcsec(x))","C"
695,1,87,47,0.057000," ","int(arcsin(((-a+x)/(a+x))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x \arcsin \left(\sqrt{\frac{-a +x}{a +x}}\right)-\frac{\sqrt{-a +x}\, \sqrt{2}\, \sqrt{\frac{a}{a +x}}\, \left(-\sqrt{a}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{-a +x}\, \sqrt{2}}{2 \sqrt{a}}\right)+2 \sqrt{-a +x}\right)}{2 \sqrt{-\frac{a -x}{a +x}}}$&$87$\\ \hline \end{longtable}"," ",0,"x*arcsin(((-a+x)/(a+x))^(1/2))-1/2/(-(a-x)/(a+x))^(1/2)*(-a+x)^(1/2)*2^(1/2)*(a/(a+x))^(1/2)*(-a^(1/2)*2^(1/2)*arctan(1/2*(-a+x)^(1/2)*2^(1/2)/a^(1/2))+2*(-a+x)^(1/2))","A"
696,1,66,34,0.056000," ","int(arctan(((-a+x)/(a+x))^(1/2)),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$x \arctan \left(\sqrt{\frac{-a +x}{a +x}}\right)+\frac{\left(a -x \right) a \ln \left(x +\sqrt{-a^{2}+x^{2}}\right)}{2 \sqrt{-\frac{a -x}{a +x}}\, \sqrt{-\left(a -x \right) \left(a +x \right)}}$&$66$\\ \hline \end{longtable}"," ",0,"x*arctan(((-a+x)/(a+x))^(1/2))+1/2*(a-x)*a*ln(x+(-a^2+x^2)^(1/2))/(-(a-x)/(a+x))^(1/2)/(-(a-x)*(a+x))^(1/2)","A"
697,1,32,31,0.358000," ","int(arctan(x)/(1+x)^3,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline default&$-\frac{1}{4 \left(1+x \right)}-\frac{\arctan \left(x \right)}{2 \left(1+x \right)^{2}}+\frac{\ln \left(1+x \right)}{4}-\frac{\ln \left(x^{2}+1\right)}{8}$&$32$\\ risch&$\frac{i \ln \left(i x +1\right)}{4 \left(1+x \right)^{2}}-\frac{i \left(2 i \ln \left(1+x \right) x^{2}-i \ln \left(x^{2}+1\right) x^{2}+4 i \ln \left(1+x \right) x -2 i \ln \left(x^{2}+1\right) x +2 i \ln \left(1+x \right)-i \ln \left(x^{2}+1\right)-2 i x -2 i+2 \ln \left(-i x +1\right)\right)}{8 \left(1+x \right)^{2}}$&$97$\\ \hline \end{longtable}"," ",0,"-1/4/(1+x)-1/2*arctan(x)/(1+x)^2+1/4*ln(1+x)-1/8*ln(x^2+1)","A"
698,1,102,110,0.374000," ","int(-arctan(a-x)/(a+x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\ln \left(a +x \right) \arctan \left(a -x \right)+\frac{i \ln \left(a +x \right) \ln \left(\frac{i+a -x}{2 a +i}\right)}{2}-\frac{i \ln \left(a +x \right) \ln \left(\frac{i-a +x}{i-2 a}\right)}{2}+\frac{i \dilog \left(\frac{i+a -x}{2 a +i}\right)}{2}-\frac{i \dilog \left(\frac{i-a +x}{i-2 a}\right)}{2}$&$102$\\ default&$-\ln \left(a +x \right) \arctan \left(a -x \right)+\frac{i \ln \left(a +x \right) \ln \left(\frac{i+a -x}{2 a +i}\right)}{2}-\frac{i \ln \left(a +x \right) \ln \left(\frac{i-a +x}{i-2 a}\right)}{2}+\frac{i \dilog \left(\frac{i+a -x}{2 a +i}\right)}{2}-\frac{i \dilog \left(\frac{i-a +x}{i-2 a}\right)}{2}$&$102$\\ risch&$-\frac{i \dilog \left(\frac{i a +i x}{2 i a -1}\right)}{2}-\frac{i \ln \left(-i a +i x +1\right) \ln \left(\frac{i a +i x}{2 i a -1}\right)}{2}+\frac{i \dilog \left(\frac{-i a -i x}{-2 i a -1}\right)}{2}+\frac{i \ln \left(i a -i x +1\right) \ln \left(\frac{-i a -i x}{-2 i a -1}\right)}{2}$&$112$\\ \hline \end{longtable}"," ",0,"-ln(a+x)*arctan(a-x)+1/2*I*ln(a+x)*ln((I+a-x)/(2*a+I))-1/2*I*ln(a+x)*ln((I-a+x)/(I-2*a))+1/2*I*dilog((I+a-x)/(2*a+I))-1/2*I*dilog((I-a+x)/(I-2*a))","A"
699,0,0,22,0.080000," ","int(arcsin((-x^2+1)^(1/2))/(-x^2+1)^(1/2),x)","\[\int \frac{\arcsin \left(\sqrt{-x^{2}+1}\right)}{\sqrt{-x^{2}+1}}\, dx\]"," ",0,"int(arcsin((-x^2+1)^(1/2))/(-x^2+1)^(1/2),x)","F"
700,1,26,25,0.310000," ","int(x*arctan((x^2+1)^(1/2))/(x^2+1)^(1/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$-\frac{\ln \left(x^{2}+2\right)}{2}+\arctan \left(\sqrt{x^{2}+1}\right) \sqrt{x^{2}+1}$&$26$\\ default&$-\frac{\ln \left(x^{2}+2\right)}{2}+\arctan \left(\sqrt{x^{2}+1}\right) \sqrt{x^{2}+1}$&$26$\\ \hline \end{longtable}"," ",0,"-1/2*ln(x^2+2)+arctan((x^2+1)^(1/2))*(x^2+1)^(1/2)","A"
701,1,70,42,0.319000," ","int(arcsin(x)/(1-x)^(5/2),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \arcsin \left(x \right)}{3 \left(1-x \right)^{\frac{3}{2}}}-\frac{\sqrt{1+x}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{\sqrt{1+x}}\right) \left(1-x \right)+2 \sqrt{1+x}\right)}{6 \sqrt{1-x}\, \sqrt{-\left(1-x \right)^{2}+2-2 x}}$&$70$\\ default&$\frac{2 \arcsin \left(x \right)}{3 \left(1-x \right)^{\frac{3}{2}}}-\frac{\sqrt{1+x}\, \left(\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}}{\sqrt{1+x}}\right) \left(1-x \right)+2 \sqrt{1+x}\right)}{6 \sqrt{1-x}\, \sqrt{-\left(1-x \right)^{2}+2-2 x}}$&$70$\\ \hline \end{longtable}"," ",0,"2/3*arcsin(x)/(1-x)^(3/2)-1/6/(1-x)^(1/2)*(1+x)^(1/2)*(2^(1/2)*arctanh(2^(1/2)/(1+x)^(1/2))*(1-x)+2*(1+x)^(1/2))/(-(1-x)^2+2-2*x)^(1/2)","A"
702,1,76,62,0.326000," ","int((-1+x)^(5/2)*arccsc(x),x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline derivativedivides&$\frac{2 \left(-1+x \right)^{\frac{7}{2}} \mathrm{arccsc}\left(x \right)}{7}+\frac{4 \sqrt{-1+x}\, \sqrt{1+x}\, \left(3 \left(-1+x \right)^{2} \sqrt{1+x}-13 \left(-1+x \right) \sqrt{1+x}+15 \arctanh \left(\sqrt{1+x}\right)+67 \sqrt{1+x}\right)}{105 \sqrt{\frac{\left(-1+x \right) \left(1+x \right)}{x^{2}}}\, x}$&$76$\\ default&$\frac{2 \left(-1+x \right)^{\frac{7}{2}} \mathrm{arccsc}\left(x \right)}{7}+\frac{4 \sqrt{-1+x}\, \sqrt{1+x}\, \left(3 \left(-1+x \right)^{2} \sqrt{1+x}-13 \left(-1+x \right) \sqrt{1+x}+15 \arctanh \left(\sqrt{1+x}\right)+67 \sqrt{1+x}\right)}{105 \sqrt{\frac{\left(-1+x \right) \left(1+x \right)}{x^{2}}}\, x}$&$76$\\ \hline \end{longtable}"," ",0,"2/7*(-1+x)^(7/2)*arccsc(x)+4/105*(-1+x)^(1/2)*(1+x)^(1/2)*(3*(-1+x)^2*(1+x)^(1/2)-13*(-1+x)*(1+x)^(1/2)+15*arctanh((1+x)^(1/2))+67*(1+x)^(1/2))/((-1+x)*(1+x)/x^2)^(1/2)/x","A"
703,0,0,40,0.048000," ","int(arcsin(sinh(x))*sech(x)^4,x)","\[\int \arcsin \left(\sinh \left(x \right)\right) \mathrm{sech}\left(x \right)^{4}\, dx\]"," ",0,"int(arcsin(sinh(x))*sech(x)^4,x)","F"
704,1,854,27,0.642000," ","int(arccot(cosh(x))*cosh(x)/sinh(x)^4,x,method=_RETURNVERBOSE)","\begin{longtable}{|l|l|l|}\hline method& result & size\\ \hline risch&$\frac{4 i {\mathrm e}^{3 x} \ln \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)}{3 \left(-1+{\mathrm e}^{2 x}\right)^{3}}-\frac{-8+16 \,{\mathrm e}^{2 x}-8 \,{\mathrm e}^{4 x}+16 \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right) {\mathrm e}^{3 x}-16 \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right) {\mathrm e}^{3 x}-\sqrt{2}\, \ln \left({\mathrm e}^{2 x}+\left(1+\sqrt{2}\right)^{2}\right)+\sqrt{2}\, \ln \left({\mathrm e}^{2 x}+\left(\sqrt{2}-1\right)^{2}\right)-3 \sqrt{2}\, \ln \left({\mathrm e}^{2 x}+\left(1+\sqrt{2}\right)^{2}\right) {\mathrm e}^{4 x}-3 \sqrt{2}\, \ln \left({\mathrm e}^{2 x}+\left(\sqrt{2}-1\right)^{2}\right) {\mathrm e}^{2 x}+3 \sqrt{2}\, \ln \left({\mathrm e}^{2 x}+\left(1+\sqrt{2}\right)^{2}\right) {\mathrm e}^{2 x}-\sqrt{2}\, \ln \left({\mathrm e}^{2 x}+\left(\sqrt{2}-1\right)^{2}\right) {\mathrm e}^{6 x}+\sqrt{2}\, \ln \left({\mathrm e}^{2 x}+\left(1+\sqrt{2}\right)^{2}\right) {\mathrm e}^{6 x}+3 \sqrt{2}\, \ln \left({\mathrm e}^{2 x}+\left(\sqrt{2}-1\right)^{2}\right) {\mathrm e}^{4 x}+16 \pi  \,\mathrm{csgn}\left(i \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right)^{2} {\mathrm e}^{3 x}+16 \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right)^{2} {\mathrm e}^{3 x}-16 \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right) {\mathrm e}^{3 x}+16 \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right) {\mathrm e}^{3 x}+16 \pi  \,\mathrm{csgn}\left(i \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right)^{2} {\mathrm e}^{3 x}+16 \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right) \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right)^{2} {\mathrm e}^{3 x}-16 \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right)^{2} {\mathrm e}^{3 x}+16 \pi  \,\mathrm{csgn}\left(i {\mathrm e}^{-x}\right) \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right)^{2} {\mathrm e}^{3 x}-16 \pi  \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right)^{3} {\mathrm e}^{3 x}+16 \pi  \mathrm{csgn}\left({\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right)^{3} {\mathrm e}^{3 x}+16 \pi  \mathrm{csgn}\left({\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right)^{2} {\mathrm e}^{3 x}-16 \pi  \mathrm{csgn}\left(i {\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right)^{3} {\mathrm e}^{3 x}-16 \pi  \mathrm{csgn}\left(i {\mathrm e}^{-x} \left(-{\mathrm e}^{2 x}-1+2 i {\mathrm e}^{x}\right)\right)^{3} {\mathrm e}^{3 x}+32 i {\mathrm e}^{3 x} \ln \left({\mathrm e}^{2 x}+1-2 i {\mathrm e}^{x}\right)+16 \pi  \mathrm{csgn}\left({\mathrm e}^{-x} \left({\mathrm e}^{2 x}+1+2 i {\mathrm e}^{x}\right)\right)^{2} {\mathrm e}^{3 x}}{24 \left(-1+{\mathrm e}^{2 x}\right)^{3}}$&$854$\\ \hline \end{longtable}"," ",0,"4/3*I*exp(3*x)/(-1+exp(2*x))^3*ln(exp(2*x)+1+2*I*exp(x))-1/24*(-8+16*exp(2*x)-8*exp(4*x)-16*Pi*csgn(exp(-x)*(exp(2*x)+1+2*I*exp(x)))^3*exp(3*x)+16*Pi*csgn(exp(-x)*(-exp(2*x)-1+2*I*exp(x)))^3*exp(3*x)+16*Pi*csgn(exp(-x)*(-exp(2*x)-1+2*I*exp(x)))^2*exp(3*x)+16*Pi*csgn(I*(exp(2*x)+1+2*I*exp(x)))*csgn(I*exp(-x)*(exp(2*x)+1+2*I*exp(x)))^2*exp(3*x)+16*Pi*csgn(I*exp(-x)*(-exp(2*x)-1+2*I*exp(x)))*csgn(exp(-x)*(-exp(2*x)-1+2*I*exp(x)))^2*exp(3*x)-16*Pi*csgn(I*exp(-x)*(exp(2*x)+1+2*I*exp(x)))*csgn(exp(-x)*(exp(2*x)+1+2*I*exp(x)))*exp(3*x)-16*Pi*csgn(I*exp(-x)*(exp(2*x)+1+2*I*exp(x)))^3*exp(3*x)+16*Pi*csgn(I*exp(-x)*(-exp(2*x)-1+2*I*exp(x)))*csgn(exp(-x)*(-exp(2*x)-1+2*I*exp(x)))*exp(3*x)-16*Pi*csgn(I*exp(-x)*(-exp(2*x)-1+2*I*exp(x)))^3*exp(3*x)+16*Pi*csgn(I*(-exp(2*x)-1+2*I*exp(x)))*csgn(I*exp(-x)*(-exp(2*x)-1+2*I*exp(x)))^2*exp(3*x)+16*Pi*csgn(I*exp(-x)*(exp(2*x)+1+2*I*exp(x)))*csgn(exp(-x)*(exp(2*x)+1+2*I*exp(x)))^2*exp(3*x)-2^(1/2)*ln(exp(2*x)+(1+2^(1/2))^2)+2^(1/2)*ln(exp(2*x)+(2^(1/2)-1)^2)-3*2^(1/2)*ln(exp(2*x)+(1+2^(1/2))^2)*exp(4*x)-3*2^(1/2)*ln(exp(2*x)+(2^(1/2)-1)^2)*exp(2*x)+3*2^(1/2)*ln(exp(2*x)+(1+2^(1/2))^2)*exp(2*x)+32*I*exp(3*x)*ln(exp(2*x)+1-2*I*exp(x))-2^(1/2)*ln(exp(2*x)+(2^(1/2)-1)^2)*exp(6*x)+2^(1/2)*ln(exp(2*x)+(1+2^(1/2))^2)*exp(6*x)+3*2^(1/2)*ln(exp(2*x)+(2^(1/2)-1)^2)*exp(4*x)+16*Pi*csgn(exp(-x)*(exp(2*x)+1+2*I*exp(x)))^2*exp(3*x)+16*Pi*csgn(I*exp(-x))*csgn(I*(-exp(2*x)-1+2*I*exp(x)))*csgn(I*exp(-x)*(-exp(2*x)-1+2*I*exp(x)))*exp(3*x)-16*Pi*csgn(I*exp(-x))*csgn(I*(exp(2*x)+1+2*I*exp(x)))*csgn(I*exp(-x)*(exp(2*x)+1+2*I*exp(x)))*exp(3*x)-16*Pi*csgn(I*exp(-x))*csgn(I*exp(-x)*(-exp(2*x)-1+2*I*exp(x)))^2*exp(3*x)+16*Pi*csgn(I*exp(-x))*csgn(I*exp(-x)*(exp(2*x)+1+2*I*exp(x)))^2*exp(3*x))/(-1+exp(2*x))^3","C"
705,0,0,24,0.037000," ","int(exp(x)*arcsin(tanh(x)),x)","\[\int {\mathrm e}^{x} \arcsin \left(\tanh \left(x \right)\right)\, dx\]"," ",0,"int(exp(x)*arcsin(tanh(x)),x)","F"