1,1,125,112,0.059000," ","int(x^2*(e*x+d)*(-e^2*x^2+d^2)^(1/2),x)","\frac{d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{2}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} x}{8 e^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} x^{2}}{5 e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d x}{4 e^{2}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2}}{15 e^{3}}"," ",0,"-1/5*x^2*(-e^2*x^2+d^2)^(3/2)/e-2/15*d^2*(-e^2*x^2+d^2)^(3/2)/e^3-1/4*d*x*(-e^2*x^2+d^2)^(3/2)/e^2+1/8*d^3*x*(-e^2*x^2+d^2)^(1/2)/e^2+1/8*d^5/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)*x/(-e^2*x^2+d^2)^(1/2))","A"
2,1,198,173,0.045000," ","int(x^4*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x)","\frac{3 d^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{128 \sqrt{e^{2}}\, e^{4}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7} x}{128 e^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x^{4}}{9 e}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5} x}{64 e^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d \,x^{3}}{8 e^{2}}-\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} x^{2}}{63 e^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3} x}{16 e^{4}}-\frac{8 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{4}}{315 e^{5}}"," ",0,"-1/9*x^4*(-e^2*x^2+d^2)^(5/2)/e-4/63*d^2*x^2*(-e^2*x^2+d^2)^(5/2)/e^3-8/315*d^4/e^5*(-e^2*x^2+d^2)^(5/2)-1/8*d*x^3*(-e^2*x^2+d^2)^(5/2)/e^2-1/16*d^3/e^4*x*(-e^2*x^2+d^2)^(5/2)+1/64*d^5*x*(-e^2*x^2+d^2)^(3/2)/e^4+3/128*d^7*x*(-e^2*x^2+d^2)^(1/2)/e^4+3/128*d^9/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
3,1,173,148,0.023000," ","int(x^3*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x)","\frac{3 d^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{128 \sqrt{e^{2}}\, e^{3}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6} x}{128 e^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4} x}{64 e^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x^{3}}{8 e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d \,x^{2}}{7 e^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} x}{16 e^{3}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3}}{35 e^{4}}"," ",0,"-1/8*x^3*(-e^2*x^2+d^2)^(5/2)/e-1/16*d^2/e^3*x*(-e^2*x^2+d^2)^(5/2)+1/64*d^4*x*(-e^2*x^2+d^2)^(3/2)/e^3+3/128*d^6*x*(-e^2*x^2+d^2)^(1/2)/e^3+3/128*d^8/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/7*d*x^2*(-e^2*x^2+d^2)^(5/2)/e^2-2/35*d^3/e^4*(-e^2*x^2+d^2)^(5/2)","A"
4,1,148,135,0.045000," ","int(x^2*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x)","\frac{d^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}\, e^{2}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} x}{16 e^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} x}{24 e^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x^{2}}{7 e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d x}{6 e^{2}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2}}{35 e^{3}}"," ",0,"-1/7*x^2*(-e^2*x^2+d^2)^(5/2)/e-2/35*d^2*(-e^2*x^2+d^2)^(5/2)/e^3-1/6*d*x*(-e^2*x^2+d^2)^(5/2)/e^2+1/24*d^3*x*(-e^2*x^2+d^2)^(3/2)/e^2+1/16*d^5*x*(-e^2*x^2+d^2)^(1/2)/e^2+1/16*d^7/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
5,1,123,100,0.015000," ","int(x*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x)","\frac{d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}\, e}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x}{16 e}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} x}{24 e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x}{6 e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d}{5 e^{2}}"," ",0,"-1/6*x*(-e^2*x^2+d^2)^(5/2)/e+1/24*d^2*x*(-e^2*x^2+d^2)^(3/2)/e+1/16*d^4*x*(-e^2*x^2+d^2)^(1/2)/e+1/16*d^6/e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/5*d/e^2*(-e^2*x^2+d^2)^(5/2)","A"
6,1,123,100,0.000000," ","int(x*(e*x+d)*(-e^2*x^2+d^2)^(3/2),x)","\frac{d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}\, e}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x}{16 e}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} x}{24 e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x}{6 e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d}{5 e^{2}}"," ",0,"1/16/(e^2)^(1/2)*d^6/e*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/16*(-e^2*x^2+d^2)^(1/2)*d^4/e*x+1/24*(-e^2*x^2+d^2)^(3/2)*d^2/e*x-1/6*(-e^2*x^2+d^2)^(5/2)/e*x-1/5*(-e^2*x^2+d^2)^(5/2)*d/e^2","A"
7,1,151,99,0.019000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x,x)","-\frac{d^{5} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{3 d^{4} e \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e x}{8}+\sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e x}{4}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d}{3}"," ",0,"1/4*e*x*(-e^2*x^2+d^2)^(3/2)+3/8*e*d^2*x*(-e^2*x^2+d^2)^(1/2)+3/8*e*d^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/3*d*(-e^2*x^2+d^2)^(3/2)+d^3*(-e^2*x^2+d^2)^(1/2)-d^5/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
8,1,182,103,0.033000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^2,x)","-\frac{d^{4} e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}-\frac{3 d^{3} e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{2} x}{2}+\sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e -\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2} x}{d}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{3}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{d x}"," ",0,"-1/d/x*(-e^2*x^2+d^2)^(5/2)-e^2/d*x*(-e^2*x^2+d^2)^(3/2)-3/2*d*e^2*x*(-e^2*x^2+d^2)^(1/2)-3/2*e^2*d^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/3*e*(-e^2*x^2+d^2)^(3/2)+e*d^2*(-e^2*x^2+d^2)^(1/2)-e*d^4/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
9,1,212,105,0.022000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^3,x)","\frac{3 d^{3} e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}-\frac{3 d^{2} e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3} x}{2}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{2}}{2}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3} x}{d^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}{2 d}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{d^{2} x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{2 d \,x^{2}}"," ",0,"-e/d^2/x*(-e^2*x^2+d^2)^(5/2)-e^3/d^2*x*(-e^2*x^2+d^2)^(3/2)-3/2*e^3*x*(-e^2*x^2+d^2)^(1/2)-3/2*e^3*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/2/d/x^2*(-e^2*x^2+d^2)^(5/2)-1/2*e^2/d*(-e^2*x^2+d^2)^(3/2)-3/2*d*e^2*(-e^2*x^2+d^2)^(1/2)+3/2*e^2*d^3/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","B"
10,1,235,106,0.022000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^4,x)","\frac{3 d^{2} e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}+\frac{d \,e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{4} x}{d}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}{2}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4} x}{3 d^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}{2 d^{2}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}{3 d^{3} x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{2 d^{2} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{3 d \,x^{3}}"," ",0,"-1/3/d/x^3*(-e^2*x^2+d^2)^(5/2)+2/3*e^2/d^3/x*(-e^2*x^2+d^2)^(5/2)+2/3*e^4/d^3*x*(-e^2*x^2+d^2)^(3/2)+e^4/d*x*(-e^2*x^2+d^2)^(1/2)+d*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/2*e/d^2/x^2*(-e^2*x^2+d^2)^(5/2)-1/2*e^3/d^2*(-e^2*x^2+d^2)^(3/2)-3/2*e^3*(-e^2*x^2+d^2)^(1/2)+3/2*e^3*d^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","B"
11,1,260,104,0.025000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^5,x)","-\frac{3 d \,e^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}}+\frac{e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{5} x}{d^{2}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}{8 d}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5} x}{3 d^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}{8 d^{3}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}{3 d^{4} x}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}{8 d^{3} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{3 d^{2} x^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{4 d \,x^{4}}"," ",0,"-1/4/d/x^4*(-e^2*x^2+d^2)^(5/2)+1/8*e^2/d^3/x^2*(-e^2*x^2+d^2)^(5/2)+1/8*e^4/d^3*(-e^2*x^2+d^2)^(3/2)+3/8*e^4/d*(-e^2*x^2+d^2)^(1/2)-3/8*d*e^4/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/3*e/d^2/x^3*(-e^2*x^2+d^2)^(5/2)+2/3*e^3/d^4/x*(-e^2*x^2+d^2)^(5/2)+2/3*e^5/d^4*x*(-e^2*x^2+d^2)^(3/2)+e^5/d^2*x*(-e^2*x^2+d^2)^(1/2)+e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","B"
12,1,158,92,0.033000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^6,x)","-\frac{3 e^{5} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}{8 d^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}{8 d^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}{8 d^{4} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{4 d^{2} x^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{5 d \,x^{5}}"," ",0,"-1/5*(-e^2*x^2+d^2)^(5/2)/d/x^5-1/4*e/d^2/x^4*(-e^2*x^2+d^2)^(5/2)+1/8*e^3/d^4/x^2*(-e^2*x^2+d^2)^(5/2)+1/8*e^5/d^4*(-e^2*x^2+d^2)^(3/2)+3/8*e^5/d^2*(-e^2*x^2+d^2)^(1/2)-3/8*e^5/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
13,1,186,123,0.031000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^7,x)","-\frac{e^{6} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{16 \sqrt{d^{2}}\, d}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{6}}{16 d^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6}}{48 d^{5}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}{48 d^{5} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}{24 d^{3} x^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{5 d^{2} x^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{6 d \,x^{6}}"," ",0,"-1/5*e*(-e^2*x^2+d^2)^(5/2)/d^2/x^5-1/6*(-e^2*x^2+d^2)^(5/2)/d/x^6-1/24*e^2/d^3/x^4*(-e^2*x^2+d^2)^(5/2)+1/48*e^4/d^5/x^2*(-e^2*x^2+d^2)^(5/2)+1/48*e^6/d^5*(-e^2*x^2+d^2)^(3/2)+1/16*e^6/d^3*(-e^2*x^2+d^2)^(1/2)-1/16*e^6/d/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
14,1,211,148,0.042000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^8,x)","-\frac{e^{7} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{16 \sqrt{d^{2}}\, d^{2}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{7}}{16 d^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7}}{48 d^{6}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}{48 d^{6} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}{24 d^{4} x^{4}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}{35 d^{3} x^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{6 d^{2} x^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{7 d \,x^{7}}"," ",0,"-1/7*(-e^2*x^2+d^2)^(5/2)/d/x^7-2/35*e^2*(-e^2*x^2+d^2)^(5/2)/d^3/x^5-1/6*e*(-e^2*x^2+d^2)^(5/2)/d^2/x^6-1/24*e^3/d^4/x^4*(-e^2*x^2+d^2)^(5/2)+1/48*e^5/d^6/x^2*(-e^2*x^2+d^2)^(5/2)+1/48*e^7/d^6*(-e^2*x^2+d^2)^(3/2)+1/16*e^7/d^4*(-e^2*x^2+d^2)^(1/2)-1/16*e^7/d^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
15,1,236,173,0.073000," ","int((e*x+d)*(-e^2*x^2+d^2)^(3/2)/x^9,x)","-\frac{3 e^{8} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{128 \sqrt{d^{2}}\, d^{3}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{8}}{128 d^{5}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{8}}{128 d^{7}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}{128 d^{7} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}{64 d^{5} x^{4}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}{35 d^{4} x^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}{16 d^{3} x^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{7 d^{2} x^{7}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{8 d \,x^{8}}"," ",0,"-1/8*(-e^2*x^2+d^2)^(5/2)/d/x^8-1/16*e^2*(-e^2*x^2+d^2)^(5/2)/d^3/x^6-1/64*e^4/d^5/x^4*(-e^2*x^2+d^2)^(5/2)+1/128*e^6/d^7/x^2*(-e^2*x^2+d^2)^(5/2)+1/128*e^8/d^7*(-e^2*x^2+d^2)^(3/2)+3/128*e^8/d^5*(-e^2*x^2+d^2)^(1/2)-3/128*e^8/d^3/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/7*e*(-e^2*x^2+d^2)^(5/2)/d^2/x^7-2/35*e^3*(-e^2*x^2+d^2)^(5/2)/d^4/x^5","A"
16,1,102,89,0.019000," ","int(x^2*(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","\frac{d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{2}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x^{2}}{3 e}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d x}{2 e^{2}}-\frac{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2}}{3 e^{3}}"," ",0,"-1/3*x^2/e*(-e^2*x^2+d^2)^(1/2)-2/3*d^2*(-e^2*x^2+d^2)^(1/2)/e^3-1/2*d*x*(-e^2*x^2+d^2)^(1/2)/e^2+1/2*d^3/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
17,1,99,67,0.019000," ","int(x^2*(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","-\frac{x^{2}}{\sqrt{-e^{2} x^{2}+d^{2}}\, e}+\frac{d x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{2}}-\frac{d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{2}}+\frac{2 d^{2}}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}"," ",0,"-x^2/e/(-e^2*x^2+d^2)^(1/2)+2*d^2/e^3/(-e^2*x^2+d^2)^(1/2)+d*x/e^2/(-e^2*x^2+d^2)^(1/2)-d/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
18,1,55,50,0.009000," ","int(x^2*(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{\left(-e x +d \right) \left(e x +d \right)^{2} \left(-e^{2} x^{2}-2 d e x +2 d^{2}\right)}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d \,e^{3}}"," ",0,"-1/3*(-e*x+d)*(e*x+d)^2*(-e^2*x^2-2*d*e*x+2*d^2)/d/e^3/(-e^2*x^2+d^2)^(5/2)","A"
19,1,227,141,0.074000," ","int(x^7*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","-\frac{x^{7}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}-\frac{d \,x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{7 d^{2} x^{5}}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}+\frac{6 d^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{8 d^{5} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}-\frac{7 d^{2} x^{3}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}+\frac{16 d^{7}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{8}}+\frac{7 d^{2} x}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{7}}-\frac{7 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{7}}"," ",0,"-1/2*x^7/e/(-e^2*x^2+d^2)^(5/2)+7/10*d^2/e^3*x^5/(-e^2*x^2+d^2)^(5/2)-7/6*d^2/e^5*x^3/(-e^2*x^2+d^2)^(3/2)+7/2*d^2/e^7*x/(-e^2*x^2+d^2)^(1/2)-7/2*d^2/e^7/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-d*x^6/e^2/(-e^2*x^2+d^2)^(5/2)+6*d^3/e^4*x^4/(-e^2*x^2+d^2)^(5/2)-8*d^5/e^6*x^2/(-e^2*x^2+d^2)^(5/2)+16/5*d^7/e^8/(-e^2*x^2+d^2)^(5/2)","A"
20,1,195,129,0.025000," ","int(x^6*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","-\frac{x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{d \,x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{6 d^{2} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{8 d^{4} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}-\frac{d \,x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}+\frac{16 d^{6}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{7}}+\frac{d x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{6}}-\frac{d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{6}}"," ",0,"-x^6/e/(-e^2*x^2+d^2)^(5/2)+6*d^2/e^3*x^4/(-e^2*x^2+d^2)^(5/2)-8*d^4/e^5*x^2/(-e^2*x^2+d^2)^(5/2)+16/5*d^6/e^7/(-e^2*x^2+d^2)^(5/2)+1/5*d*x^5/e^2/(-e^2*x^2+d^2)^(5/2)-1/3*d/e^4*x^3/(-e^2*x^2+d^2)^(3/2)+d/e^6*x/(-e^2*x^2+d^2)^(1/2)-d/e^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
21,1,166,108,0.021000," ","int(x^5*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","\frac{x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{d \,x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{4 d^{3} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}+\frac{8 d^{5}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}+\frac{x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}-\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{5}}"," ",0,"1/5*x^5/e/(-e^2*x^2+d^2)^(5/2)-1/3/e^3*x^3/(-e^2*x^2+d^2)^(3/2)+1/e^5*x/(-e^2*x^2+d^2)^(1/2)-1/e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+d*x^4/e^2/(-e^2*x^2+d^2)^(5/2)-4/3*d^3/e^4*x^2/(-e^2*x^2+d^2)^(5/2)+8/15*d^5/e^6/(-e^2*x^2+d^2)^(5/2)","A"
22,1,77,72,0.010000," ","int(x^4*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{2} \left(3 x^{4} e^{4}+12 x^{3} d \,e^{3}-12 d^{2} x^{2} e^{2}-8 d^{3} x e +8 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d \,e^{5}}"," ",0,"1/15*(-e*x+d)*(e*x+d)^2*(3*e^4*x^4+12*d*e^3*x^3-12*d^2*e^2*x^2-8*d^3*e*x+8*d^4)/d/e^5/(-e^2*x^2+d^2)^(7/2)","A"
23,1,77,78,0.010000," ","int(x^3*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(e x +d \right)^{2} \left(-3 x^{4} e^{4}+3 x^{3} d \,e^{3}-3 d^{2} x^{2} e^{2}-2 d^{3} x e +2 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} e^{4}}"," ",0,"-1/15*(-e*x+d)*(e*x+d)^2*(-3*e^4*x^4+3*d*e^3*x^3-3*d^2*e^2*x^2-2*d^3*e*x+2*d^4)/d^2/e^4/(-e^2*x^2+d^2)^(7/2)","A"
24,1,77,82,0.009000," ","int(x^2*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(e x +d \right)^{2} \left(2 x^{4} e^{4}-2 x^{3} d \,e^{3}-3 d^{2} x^{2} e^{2}-2 d^{3} x e +2 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} e^{3}}"," ",0,"-1/15*(-e*x+d)*(e*x+d)^2*(2*e^4*x^4-2*d*e^3*x^3-3*d^2*e^2*x^2-2*d^3*e*x+2*d^4)/d^3/e^3/(-e^2*x^2+d^2)^(7/2)","A"
25,1,77,71,0.009000," ","int(x*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{2} \left(-2 x^{4} e^{4}+2 x^{3} d \,e^{3}+3 d^{2} x^{2} e^{2}-3 d^{3} x e +3 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{4} e^{2}}"," ",0,"1/15*(-e*x+d)*(e*x+d)^2*(-2*e^4*x^4+2*d*e^3*x^3+3*d^2*e^2*x^2-3*d^3*e*x+3*d^4)/d^4/e^2/(-e^2*x^2+d^2)^(7/2)","A"
26,1,77,68,0.009000," ","int((e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{2} \left(8 x^{4} e^{4}-8 x^{3} d \,e^{3}-12 d^{2} x^{2} e^{2}+12 d^{3} x e +3 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{5} e}"," ",0,"1/15*(-e*x+d)*(e*x+d)^2*(8*e^4*x^4-8*d*e^3*x^3-12*d^2*e^2*x^2+12*d^3*e*x+3*d^4)/d^5/e/(-e^2*x^2+d^2)^(7/2)","A"
27,1,163,103,0.013000," ","int((e*x+d)/x/(-e^2*x^2+d^2)^(7/2),x)","\frac{e x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2}}+\frac{1}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d}+\frac{4 e x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4}}+\frac{1}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3}}-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{5}}+\frac{8 e x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}+\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}"," ",0,"1/5*e*x/d^2/(-e^2*x^2+d^2)^(5/2)+4/15*e/d^4*x/(-e^2*x^2+d^2)^(3/2)+8/15*e/d^6*x/(-e^2*x^2+d^2)^(1/2)+1/5/d/(-e^2*x^2+d^2)^(5/2)+1/3/d^3/(-e^2*x^2+d^2)^(3/2)+1/d^5/(-e^2*x^2+d^2)^(1/2)-1/d^5/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
28,1,195,135,0.016000," ","int((e*x+d)/x^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{6 e^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3}}+\frac{e}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2}}-\frac{1}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d x}+\frac{8 e^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5}}+\frac{e}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4}}-\frac{e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{6}}+\frac{16 e^{2} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7}}+\frac{e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}"," ",0,"1/5*e/d^2/(-e^2*x^2+d^2)^(5/2)+1/3*e/d^4/(-e^2*x^2+d^2)^(3/2)+e/d^6/(-e^2*x^2+d^2)^(1/2)-e/d^6/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/d/x/(-e^2*x^2+d^2)^(5/2)+6/5*e^2/d^3*x/(-e^2*x^2+d^2)^(5/2)+8/5*e^2/d^5*x/(-e^2*x^2+d^2)^(3/2)+16/5*e^2/d^7*x/(-e^2*x^2+d^2)^(1/2)","A"
29,1,227,160,0.016000," ","int((e*x+d)/x^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{6 e^{3} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{4}}+\frac{7 e^{2}}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3}}-\frac{e}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} x}+\frac{8 e^{3} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{6}}-\frac{1}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d \,x^{2}}+\frac{7 e^{2}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5}}-\frac{7 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{7}}+\frac{16 e^{3} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{8}}+\frac{7 e^{2}}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7}}"," ",0,"-1/2/d/x^2/(-e^2*x^2+d^2)^(5/2)+7/10*e^2/d^3/(-e^2*x^2+d^2)^(5/2)+7/6*e^2/d^5/(-e^2*x^2+d^2)^(3/2)+7/2*e^2/d^7/(-e^2*x^2+d^2)^(1/2)-7/2*e^2/d^7/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-e/d^2/x/(-e^2*x^2+d^2)^(5/2)+6/5*e^3/d^4*x/(-e^2*x^2+d^2)^(5/2)+8/5*e^3/d^6*x/(-e^2*x^2+d^2)^(3/2)+16/5*e^3/d^8*x/(-e^2*x^2+d^2)^(1/2)","A"
30,1,99,105,0.012000," ","int(x^2*(e*x+d)/(-e^2*x^2+d^2)^(9/2),x)","-\frac{\left(-e x +d \right) \left(e x +d \right)^{2} \left(-8 e^{6} x^{6}+8 e^{5} x^{5} d +20 e^{4} x^{4} d^{2}-20 x^{3} d^{3} e^{3}-15 x^{2} d^{4} e^{2}-6 x \,d^{5} e +6 d^{6}\right)}{105 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{9}{2}} d^{5} e^{3}}"," ",0,"-1/105*(-e*x+d)*(e*x+d)^2*(-8*e^6*x^6+8*d*e^5*x^5+20*d^2*e^4*x^4-20*d^3*e^3*x^3-15*d^4*e^2*x^2-6*d^5*e*x+6*d^6)/d^5/e^3/(-e^2*x^2+d^2)^(9/2)","A"
31,1,121,128,0.014000," ","int(x^2*(e*x+d)/(-e^2*x^2+d^2)^(11/2),x)","-\frac{\left(-e x +d \right) \left(e x +d \right)^{2} \left(16 e^{8} x^{8}-16 e^{7} x^{7} d -56 e^{6} x^{6} d^{2}+56 e^{5} x^{5} d^{3}+70 e^{4} x^{4} d^{4}-70 x^{3} d^{5} e^{3}-35 x^{2} d^{6} e^{2}-10 x \,d^{7} e +10 d^{8}\right)}{315 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{11}{2}} d^{7} e^{3}}"," ",0,"-1/315*(-e*x+d)*(e*x+d)^2*(16*e^8*x^8-16*d*e^7*x^7-56*d^2*e^6*x^6+56*d^3*e^5*x^5+70*d^4*e^4*x^4-70*d^5*e^3*x^3-35*d^6*e^2*x^2-10*d^7*e*x+10*d^8)/d^7/e^3/(-e^2*x^2+d^2)^(11/2)","A"
32,1,85,48,0.016000," ","int(x^2*(-a*x+1)/(-a^2*x^2+1)^(3/2),x)","\frac{x^{2}}{\sqrt{-a^{2} x^{2}+1}\, a}+\frac{x}{\sqrt{-a^{2} x^{2}+1}\, a^{2}}-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}\, a^{2}}-\frac{2}{\sqrt{-a^{2} x^{2}+1}\, a^{3}}"," ",0,"x^2/a/(-a^2*x^2+1)^(1/2)-2/a^3/(-a^2*x^2+1)^(1/2)+x/a^2/(-a^2*x^2+1)^(1/2)-1/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))","A"
33,1,174,149,0.028000," ","int(x^4*(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x^{5}}{6}-\frac{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,x^{4}}{5 e}+\frac{11 d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}\, e^{4}}-\frac{11 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} x^{3}}{24 e^{2}}-\frac{8 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} x^{2}}{15 e^{3}}-\frac{11 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x}{16 e^{4}}-\frac{16 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}{15 e^{5}}"," ",0,"-1/6*x^5*(-e^2*x^2+d^2)^(1/2)-11/24*d^2*x^3*(-e^2*x^2+d^2)^(1/2)/e^2-11/16*d^4*x*(-e^2*x^2+d^2)^(1/2)/e^4+11/16/e^4*d^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2/5*d*x^4*(-e^2*x^2+d^2)^(1/2)/e-8/15*d^3*x^2*(-e^2*x^2+d^2)^(1/2)/e^3-16/15*d^5*(-e^2*x^2+d^2)^(1/2)/e^5","A"
34,1,149,124,0.010000," ","int(x^3*(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x^{4}}{5}+\frac{3 d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{4 \sqrt{e^{2}}\, e^{3}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d \,x^{3}}{2 e}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} x^{2}}{5 e^{2}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} x}{4 e^{3}}-\frac{6 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4}}{5 e^{4}}"," ",0,"-1/5*x^4*(-e^2*x^2+d^2)^(1/2)-3/5*d^2*x^2*(-e^2*x^2+d^2)^(1/2)/e^2-6/5*d^4*(-e^2*x^2+d^2)^(1/2)/e^4-1/2*d*x^3*(-e^2*x^2+d^2)^(1/2)/e-3/4*d^3*x*(-e^2*x^2+d^2)^(1/2)/e^3+3/4*d^5/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
35,1,124,99,0.011000," ","int(x^2*(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x)","\frac{7 d^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{2}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x^{3}}{4}-\frac{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,x^{2}}{3 e}-\frac{7 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} x}{8 e^{2}}-\frac{4 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}}{3 e^{3}}"," ",0,"-1/4*x^3*(-e^2*x^2+d^2)^(1/2)-7/8/e^2*d^2*x*(-e^2*x^2+d^2)^(1/2)+7/8/e^2*d^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2/3*d*x^2*(-e^2*x^2+d^2)^(1/2)/e-4/3*d^3*(-e^2*x^2+d^2)^(1/2)/e^3","A"
36,1,98,73,0.009000," ","int(x*(e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x)","\frac{d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x^{2}}{3}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d x}{e}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2}}{3 e^{2}}"," ",0,"-1/3*x^2*(-e^2*x^2+d^2)^(1/2)-5/3*d^2/e^2*(-e^2*x^2+d^2)^(1/2)-d*x*(-e^2*x^2+d^2)^(1/2)/e+d^3/e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
37,1,71,71,0.008000," ","int((e*x+d)^2/(-e^2*x^2+d^2)^(1/2),x)","\frac{3 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x}{2}-\frac{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d}{e}"," ",0,"-1/2*x*(-e^2*x^2+d^2)^(1/2)+3/2*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2*d*(-e^2*x^2+d^2)^(1/2)/e","A"
38,1,91,60,0.010000," ","int((e*x+d)^2/x/(-e^2*x^2+d^2)^(1/2),x)","-\frac{d^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{2 d e \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}-\sqrt{-e^{2} x^{2}+d^{2}}"," ",0,"-(-e^2*x^2+d^2)^(1/2)+2*e*d/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-d^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
39,1,93,62,0.011000," ","int((e*x+d)^2/x^2/(-e^2*x^2+d^2)^(1/2),x)","-\frac{2 d e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{x}"," ",0,"e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-(-e^2*x^2+d^2)^(1/2)/x-2*d*e/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
40,1,86,70,0.012000," ","int((e*x+d)^2/x^3/(-e^2*x^2+d^2)^(1/2),x)","-\frac{3 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}-\frac{2 \sqrt{-e^{2} x^{2}+d^{2}}\, e}{d x}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{2 x^{2}}"," ",0,"-1/2*(-e^2*x^2+d^2)^(1/2)/x^2-3/2*e^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-2*e*(-e^2*x^2+d^2)^(1/2)/d/x","A"
41,1,114,95,0.013000," ","int((e*x+d)^2/x^4/(-e^2*x^2+d^2)^(1/2),x)","-\frac{e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{2}}{3 d^{2} x}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e}{d \,x^{2}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{3 x^{3}}"," ",0,"-e*(-e^2*x^2+d^2)^(1/2)/d/x^2-1/d*e^3/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-5/3*e^2*(-e^2*x^2+d^2)^(1/2)/d^2/x-1/3*(-e^2*x^2+d^2)^(1/2)/x^3","A"
42,1,139,120,0.015000," ","int((e*x+d)^2/x^5/(-e^2*x^2+d^2)^(1/2),x)","-\frac{7 e^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}\, d^{2}}-\frac{4 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}{3 d^{3} x}-\frac{7 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{2}}{8 d^{2} x^{2}}-\frac{2 \sqrt{-e^{2} x^{2}+d^{2}}\, e}{3 d \,x^{3}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{4 x^{4}}"," ",0,"-2/3*e*(-e^2*x^2+d^2)^(1/2)/d/x^3-4/3*e^3*(-e^2*x^2+d^2)^(1/2)/d^3/x-7/8*e^2*(-e^2*x^2+d^2)^(1/2)/d^2/x^2-7/8*e^4/d^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/4*(-e^2*x^2+d^2)^(1/2)/x^4","A"
43,1,164,145,0.016000," ","int((e*x+d)^2/x^6/(-e^2*x^2+d^2)^(1/2),x)","-\frac{3 e^{5} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{4 \sqrt{d^{2}}\, d^{3}}-\frac{6 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}{5 d^{4} x}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}{4 d^{3} x^{2}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{2}}{5 d^{2} x^{3}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e}{2 d \,x^{4}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{5 x^{5}}"," ",0,"-3/5*e^2*(-e^2*x^2+d^2)^(1/2)/d^2/x^3-6/5*e^4*(-e^2*x^2+d^2)^(1/2)/d^4/x-1/2*e*(-e^2*x^2+d^2)^(1/2)/d/x^4-3/4*e^3*(-e^2*x^2+d^2)^(1/2)/d^3/x^2-3/4/d^3*e^5/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5*(-e^2*x^2+d^2)^(1/2)/x^5","A"
44,1,193,127,0.010000," ","int(x^5*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","-\frac{x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{2 d \,x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{7 d^{2} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{28 d^{4} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{2 d \,x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}+\frac{56 d^{6}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}+\frac{2 d x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}-\frac{2 d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{5}}"," ",0,"-x^6/(-e^2*x^2+d^2)^(5/2)+7/e^2*d^2*x^4/(-e^2*x^2+d^2)^(5/2)-28/3/e^4*d^4*x^2/(-e^2*x^2+d^2)^(5/2)+56/15/e^6*d^6/(-e^2*x^2+d^2)^(5/2)+2/5/e*d*x^5/(-e^2*x^2+d^2)^(5/2)-2/3/e^3*d*x^3/(-e^2*x^2+d^2)^(3/2)+2/e^5*d*x/(-e^2*x^2+d^2)^(1/2)-2/e^5*d/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
45,1,236,107,0.018000," ","int(x^4*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{2 d \,x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{d^{2} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{8 d^{3} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{3 d^{4} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}+\frac{16 d^{5}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}+\frac{d^{2} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}+\frac{6 x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}-\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}"," ",0,"1/5*x^5/(-e^2*x^2+d^2)^(5/2)-1/3*x^3/e^2/(-e^2*x^2+d^2)^(3/2)+6/5/e^4*x/(-e^2*x^2+d^2)^(1/2)-1/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+2*d/e*x^4/(-e^2*x^2+d^2)^(5/2)-8/3*d^3/e^3*x^2/(-e^2*x^2+d^2)^(5/2)+16/15*d^5/e^5/(-e^2*x^2+d^2)^(5/2)+1/2*d^2*x^3/e^2/(-e^2*x^2+d^2)^(5/2)-3/10*d^4/e^4*x/(-e^2*x^2+d^2)^(5/2)+1/10*d^2/e^4*x/(-e^2*x^2+d^2)^(3/2)","B"
46,1,65,85,0.008000," ","int(x^3*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{3} \left(2 e^{3} x^{3}+d \,e^{2} x^{2}-4 d^{2} e x +2 d^{3}\right)}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d \,e^{4}}"," ",0,"1/5*(-e*x+d)*(e*x+d)^3*(2*e^3*x^3+d*e^2*x^2-4*d^2*e*x+2*d^3)/d/e^4/(-e^2*x^2+d^2)^(7/2)","A"
47,1,66,75,0.010000," ","int(x^2*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(e x +d \right)^{3} \left(-e^{3} x^{3}+2 d \,e^{2} x^{2}-8 d^{2} e x +4 d^{3}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} e^{3}}"," ",0,"-1/15*(-e*x+d)*(e*x+d)^3*(-e^3*x^3+2*d*e^2*x^2-8*d^2*e*x+4*d^3)/d^2/e^3/(-e^2*x^2+d^2)^(7/2)","A"
48,1,64,77,0.008000," ","int(x*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{3} \left(-4 e^{3} x^{3}+8 d \,e^{2} x^{2}-2 d^{2} e x +d^{3}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} e^{2}}"," ",0,"1/15*(-e*x+d)*(e*x+d)^3*(-4*e^3*x^3+8*d*e^2*x^2-2*d^2*e*x+d^3)/d^3/e^2/(-e^2*x^2+d^2)^(7/2)","A"
49,1,65,65,0.008000," ","int((e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{3} \left(2 e^{3} x^{3}-4 d \,e^{2} x^{2}+d^{2} e x +2 d^{3}\right)}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{4} e}"," ",0,"1/5*(-e*x+d)*(e*x+d)^3*(2*e^3*x^3-4*d*e^2*x^2+d^2*e*x+2*d^3)/d^4/e/(-e^2*x^2+d^2)^(7/2)","A"
50,1,160,103,0.010000," ","int((e*x+d)^2/x/(-e^2*x^2+d^2)^(7/2),x)","\frac{2 e x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d}+\frac{8 e x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3}}+\frac{1}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2}}-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{4}}+\frac{16 e x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}+\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{4}}+\frac{2}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}"," ",0,"2/5/(-e^2*x^2+d^2)^(5/2)+2/5/d*e*x/(-e^2*x^2+d^2)^(5/2)+8/15/d^3*e*x/(-e^2*x^2+d^2)^(3/2)+16/15/d^5*e*x/(-e^2*x^2+d^2)^(1/2)+1/3/d^2/(-e^2*x^2+d^2)^(3/2)+1/d^4/(-e^2*x^2+d^2)^(1/2)-1/d^4/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
51,1,193,129,0.011000," ","int((e*x+d)^2/x^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{7 e^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2}}+\frac{2 e}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d}+\frac{28 e^{2} x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4}}-\frac{1}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x}+\frac{2 e}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3}}-\frac{2 e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{5}}+\frac{56 e^{2} x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}+\frac{2 e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}"," ",0,"7/5*e^2*x/d^2/(-e^2*x^2+d^2)^(5/2)+28/15*e^2/d^4*x/(-e^2*x^2+d^2)^(3/2)+56/15*e^2/d^6*x/(-e^2*x^2+d^2)^(1/2)+2/5/d*e/(-e^2*x^2+d^2)^(5/2)+2/3/d^3*e/(-e^2*x^2+d^2)^(3/2)+2/d^5*e/(-e^2*x^2+d^2)^(1/2)-2/d^5*e/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/x/(-e^2*x^2+d^2)^(5/2)","A"
52,1,224,160,0.016000," ","int((e*x+d)^2/x^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{12 e^{3} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3}}+\frac{9 e^{2}}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2}}-\frac{2 e}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d x}+\frac{16 e^{3} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5}}+\frac{3 e^{2}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4}}-\frac{1}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x^{2}}-\frac{9 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{6}}+\frac{32 e^{3} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7}}+\frac{9 e^{2}}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}"," ",0,"9/10*e^2/d^2/(-e^2*x^2+d^2)^(5/2)+3/2*e^2/d^4/(-e^2*x^2+d^2)^(3/2)+9/2*e^2/d^6/(-e^2*x^2+d^2)^(1/2)-9/2*e^2/d^6/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-2/d*e/x/(-e^2*x^2+d^2)^(5/2)+12/5/d^3*e^3*x/(-e^2*x^2+d^2)^(5/2)+16/5/d^5*e^3*x/(-e^2*x^2+d^2)^(3/2)+32/5/d^7*e^3*x/(-e^2*x^2+d^2)^(1/2)-1/2/x^2/(-e^2*x^2+d^2)^(5/2)","A"
53,1,249,185,0.020000," ","int((e*x+d)^2/x^4/(-e^2*x^2+d^2)^(7/2),x)","\frac{22 e^{4} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{4}}+\frac{7 e^{3}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3}}-\frac{11 e^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} x}+\frac{88 e^{4} x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{6}}-\frac{e}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d \,x^{2}}+\frac{7 e^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5}}-\frac{7 e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{7}}+\frac{176 e^{4} x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{8}}-\frac{1}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x^{3}}+\frac{7 e^{3}}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{7}}"," ",0,"-1/d*e/x^2/(-e^2*x^2+d^2)^(5/2)+7/5/d^3*e^3/(-e^2*x^2+d^2)^(5/2)+7/3/d^5*e^3/(-e^2*x^2+d^2)^(3/2)+7/d^7*e^3/(-e^2*x^2+d^2)^(1/2)-7/d^7*e^3/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-11/3*e^2/d^2/x/(-e^2*x^2+d^2)^(5/2)+22/5*e^4/d^4*x/(-e^2*x^2+d^2)^(5/2)+88/15*e^4/d^6*x/(-e^2*x^2+d^2)^(3/2)+176/15*e^4/d^8*x/(-e^2*x^2+d^2)^(1/2)-1/3/x^3/(-e^2*x^2+d^2)^(5/2)","A"
54,1,71,63,0.012000," ","int(x^3*(1+x)^2/(-x^2+1)^(1/2),x)","-\frac{\sqrt{-x^{2}+1}\, x^{4}}{5}-\frac{\sqrt{-x^{2}+1}\, x^{3}}{2}-\frac{3 \sqrt{-x^{2}+1}\, x^{2}}{5}-\frac{3 \sqrt{-x^{2}+1}\, x}{4}+\frac{3 \arcsin \left(x \right)}{4}-\frac{6 \sqrt{-x^{2}+1}}{5}"," ",0,"-1/5*x^4*(-x^2+1)^(1/2)-3/5*x^2*(-x^2+1)^(1/2)-6/5*(-x^2+1)^(1/2)-1/2*x^3*(-x^2+1)^(1/2)-3/4*x*(-x^2+1)^(1/2)+3/4*arcsin(x)","A"
55,1,57,49,0.007000," ","int(x^2*(1+x)^2/(-x^2+1)^(1/2),x)","-\frac{\sqrt{-x^{2}+1}\, x^{3}}{4}-\frac{2 \sqrt{-x^{2}+1}\, x^{2}}{3}-\frac{7 \sqrt{-x^{2}+1}\, x}{8}+\frac{7 \arcsin \left(x \right)}{8}-\frac{4 \sqrt{-x^{2}+1}}{3}"," ",0,"-1/4*(-x^2+1)^(1/2)*x^3-7/8*(-x^2+1)^(1/2)*x+7/8*arcsin(x)-2/3*(-x^2+1)^(1/2)*x^2-4/3*(-x^2+1)^(1/2)","A"
56,1,41,33,0.005000," ","int(x*(1+x)^2/(-x^2+1)^(1/2),x)","-\frac{\sqrt{-x^{2}+1}\, x^{2}}{3}-\sqrt{-x^{2}+1}\, x +\arcsin \left(x \right)-\frac{5 \sqrt{-x^{2}+1}}{3}"," ",0,"-1/3*(-x^2+1)^(1/2)*x^2-5/3*(-x^2+1)^(1/2)-(-x^2+1)^(1/2)*x+arcsin(x)","A"
57,1,29,30,0.003000," ","int((1+x)^2/(-x^2+1)^(1/2),x)","-\frac{\sqrt{-x^{2}+1}\, x}{2}+\frac{3 \arcsin \left(x \right)}{2}-2 \sqrt{-x^{2}+1}"," ",0,"-1/2*(-x^2+1)^(1/2)*x+3/2*arcsin(x)-2*(-x^2+1)^(1/2)","A"
58,1,29,28,0.005000," ","int((1+x)^2/x/(-x^2+1)^(1/2),x)","-\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)+2 \arcsin \left(x \right)-\sqrt{-x^{2}+1}"," ",0,"-(-x^2+1)^(1/2)+2*arcsin(x)-arctanh(1/(-x^2+1)^(1/2))","A"
59,1,30,29,0.008000," ","int((1+x)^2/x^2/(-x^2+1)^(1/2),x)","-2 \arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)+\arcsin \left(x \right)-\frac{\sqrt{-x^{2}+1}}{x}"," ",0,"arcsin(x)-(-x^2+1)^(1/2)/x-2*arctanh(1/(-x^2+1)^(1/2))","A"
60,1,42,41,0.007000," ","int((1+x)^2/x^3/(-x^2+1)^(1/2),x)","-\frac{3 \arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)}{2}-\frac{2 \sqrt{-x^{2}+1}}{x}-\frac{\sqrt{-x^{2}+1}}{2 x^{2}}"," ",0,"-2*(-x^2+1)^(1/2)/x-3/2*arctanh(1/(-x^2+1)^(1/2))-1/2*(-x^2+1)^(1/2)/x^2","A"
61,1,56,55,0.008000," ","int((1+x)^2/x^4/(-x^2+1)^(1/2),x)","-\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)-\frac{5 \sqrt{-x^{2}+1}}{3 x}-\frac{\sqrt{-x^{2}+1}}{x^{2}}-\frac{\sqrt{-x^{2}+1}}{3 x^{3}}"," ",0,"-5/3*(-x^2+1)^(1/2)/x-1/3*(-x^2+1)^(1/2)/x^3-(-x^2+1)^(1/2)/x^2-arctanh(1/(-x^2+1)^(1/2))","A"
62,1,70,69,0.009000," ","int((1+x)^2/x^5/(-x^2+1)^(1/2),x)","-\frac{7 \arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)}{8}-\frac{4 \sqrt{-x^{2}+1}}{3 x}-\frac{7 \sqrt{-x^{2}+1}}{8 x^{2}}-\frac{2 \sqrt{-x^{2}+1}}{3 x^{3}}-\frac{\sqrt{-x^{2}+1}}{4 x^{4}}"," ",0,"-7/8*(-x^2+1)^(1/2)/x^2-7/8*arctanh(1/(-x^2+1)^(1/2))-2/3*(-x^2+1)^(1/2)/x^3-4/3*(-x^2+1)^(1/2)/x-1/4*(-x^2+1)^(1/2)/x^4","A"
63,1,84,83,0.008000," ","int((1+x)^2/x^6/(-x^2+1)^(1/2),x)","-\frac{3 \arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)}{4}-\frac{6 \sqrt{-x^{2}+1}}{5 x}-\frac{3 \sqrt{-x^{2}+1}}{4 x^{2}}-\frac{3 \sqrt{-x^{2}+1}}{5 x^{3}}-\frac{\sqrt{-x^{2}+1}}{2 x^{4}}-\frac{\sqrt{-x^{2}+1}}{5 x^{5}}"," ",0,"-1/5*(-x^2+1)^(1/2)/x^5-3/5*(-x^2+1)^(1/2)/x^3-6/5*(-x^2+1)^(1/2)/x-1/2*(-x^2+1)^(1/2)/x^4-3/4*(-x^2+1)^(1/2)/x^2-3/4*arctanh(1/(-x^2+1)^(1/2))","A"
64,1,212,118,0.022000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(1/2)/x^5,x)","\frac{13 d \,e^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}}-\frac{e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{5} x}{d^{2}}-\frac{13 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}{8 d}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}{d^{2} x}-\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}{8 d \,x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{x^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d}{4 x^{4}}"," ",0,"-1/4*d*(-e^2*x^2+d^2)^(3/2)/x^4-13/8/d*e^2/x^2*(-e^2*x^2+d^2)^(3/2)-13/8*(-e^2*x^2+d^2)^(1/2)/d*e^4+13/8/(d^2)^(1/2)*d*e^4*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-e^3/d^2/x*(-e^2*x^2+d^2)^(3/2)-(-e^2*x^2+d^2)^(1/2)/d^2*e^5*x-1/(e^2)^(1/2)*e^5*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-e*(-e^2*x^2+d^2)^(3/2)/x^3","A"
65,1,291,266,0.107000," ","int(x^5*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x)","\frac{35 d^{14} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2048 \sqrt{e^{2}}\, e^{5}}+\frac{35 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{12} x}{2048 e^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e \,x^{7}}{14}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d \,x^{6}}{13}+\frac{35 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{10} x}{3072 e^{5}}-\frac{7 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} x^{5}}{24 e}-\frac{31 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} x^{4}}{143 e^{2}}+\frac{7 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{8} x}{768 e^{5}}-\frac{7 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{4} x^{3}}{48 e^{3}}-\frac{124 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{5} x^{2}}{1287 e^{4}}-\frac{7 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{6} x}{128 e^{5}}-\frac{248 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{7}}{9009 e^{6}}"," ",0,"-1/14*e*x^7*(-e^2*x^2+d^2)^(7/2)-7/24*d^2*x^5*(-e^2*x^2+d^2)^(7/2)/e-7/48*d^4*x^3*(-e^2*x^2+d^2)^(7/2)/e^3-7/128/e^5*d^6*x*(-e^2*x^2+d^2)^(7/2)+7/768*d^8*x*(-e^2*x^2+d^2)^(5/2)/e^5+35/3072*d^10*x*(-e^2*x^2+d^2)^(3/2)/e^5+35/2048*d^12*x*(-e^2*x^2+d^2)^(1/2)/e^5+35/2048/e^5*d^14/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-3/13*d*x^6*(-e^2*x^2+d^2)^(7/2)-31/143*d^3*x^4*(-e^2*x^2+d^2)^(7/2)/e^2-124/1287*d^5*x^2*(-e^2*x^2+d^2)^(7/2)/e^4-248/9009/e^6*d^7*(-e^2*x^2+d^2)^(7/2)","A"
66,1,266,241,0.018000," ","int(x^4*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x)","\frac{27 d^{13} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{1024 \sqrt{e^{2}}\, e^{4}}+\frac{27 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{11} x}{1024 e^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e \,x^{6}}{13}+\frac{9 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{9} x}{512 e^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d \,x^{5}}{4}-\frac{45 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} x^{4}}{143 e}+\frac{9 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{7} x}{640 e^{4}}-\frac{9 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} x^{3}}{40 e^{2}}-\frac{20 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{4} x^{2}}{143 e^{3}}-\frac{27 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{5} x}{320 e^{4}}-\frac{40 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{6}}{1001 e^{5}}"," ",0,"-1/13*e*x^6*(-e^2*x^2+d^2)^(7/2)-45/143*d^2*x^4*(-e^2*x^2+d^2)^(7/2)/e-20/143*d^4*x^2*(-e^2*x^2+d^2)^(7/2)/e^3-40/1001/e^5*d^6*(-e^2*x^2+d^2)^(7/2)-1/4*d*x^5*(-e^2*x^2+d^2)^(7/2)-9/40*d^3*x^3*(-e^2*x^2+d^2)^(7/2)/e^2-27/320/e^4*d^5*x*(-e^2*x^2+d^2)^(7/2)+9/640*d^7*x*(-e^2*x^2+d^2)^(5/2)/e^4+9/512*d^9*x*(-e^2*x^2+d^2)^(3/2)/e^4+27/1024*d^11*x*(-e^2*x^2+d^2)^(1/2)/e^4+27/1024/e^4*d^13/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
67,1,241,216,0.015000," ","int(x^3*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x)","\frac{41 d^{12} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{1024 \sqrt{e^{2}}\, e^{3}}+\frac{41 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{10} x}{1024 e^{3}}+\frac{41 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{8} x}{1536 e^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e \,x^{5}}{12}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d \,x^{4}}{11}+\frac{41 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{6} x}{1920 e^{3}}-\frac{41 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} x^{3}}{120 e}-\frac{23 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} x^{2}}{99 e^{2}}-\frac{41 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{4} x}{320 e^{3}}-\frac{46 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{5}}{693 e^{4}}"," ",0,"-1/12*e*x^5*(-e^2*x^2+d^2)^(7/2)-41/120*d^2*x^3*(-e^2*x^2+d^2)^(7/2)/e-41/320/e^3*d^4*x*(-e^2*x^2+d^2)^(7/2)+41/1920*d^6*x*(-e^2*x^2+d^2)^(5/2)/e^3+41/1536*d^8*x*(-e^2*x^2+d^2)^(3/2)/e^3+41/1024*d^10*x*(-e^2*x^2+d^2)^(1/2)/e^3+41/1024/e^3*d^12/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-3/11*d*x^4*(-e^2*x^2+d^2)^(7/2)-23/99*d^3*x^2*(-e^2*x^2+d^2)^(7/2)/e^2-46/693/e^4*d^5*(-e^2*x^2+d^2)^(7/2)","A"
68,1,216,191,0.014000," ","int(x^2*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x)","\frac{19 d^{11} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{256 \sqrt{e^{2}}\, e^{2}}+\frac{19 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{9} x}{256 e^{2}}+\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{7} x}{384 e^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e \,x^{4}}{11}+\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{5} x}{480 e^{2}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d \,x^{3}}{10}-\frac{37 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} x^{2}}{99 e}-\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} x}{80 e^{2}}-\frac{74 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{4}}{693 e^{3}}"," ",0,"-1/11*e*x^4*(-e^2*x^2+d^2)^(7/2)-37/99*d^2*x^2*(-e^2*x^2+d^2)^(7/2)/e-74/693/e^3*d^4*(-e^2*x^2+d^2)^(7/2)-3/10*d*x^3*(-e^2*x^2+d^2)^(7/2)-19/80/e^2*d^3*x*(-e^2*x^2+d^2)^(7/2)+19/480*d^5*x*(-e^2*x^2+d^2)^(5/2)/e^2+19/384*d^7*x*(-e^2*x^2+d^2)^(3/2)/e^2+19/256*d^9*x*(-e^2*x^2+d^2)^(1/2)/e^2+19/256/e^2*d^11/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
69,1,191,198,0.010000," ","int(x*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x)","\frac{33 d^{10} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{256 \sqrt{e^{2}}\, e}+\frac{33 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{8} x}{256 e}+\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{6} x}{128 e}+\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{4} x}{160 e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e \,x^{3}}{10}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d \,x^{2}}{3}-\frac{33 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} x}{80 e}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3}}{21 e^{2}}"," ",0,"-1/10*e*x^3*(-e^2*x^2+d^2)^(7/2)-33/80/e*d^2*x*(-e^2*x^2+d^2)^(7/2)+11/160*d^4*x*(-e^2*x^2+d^2)^(5/2)/e+11/128*d^6*x*(-e^2*x^2+d^2)^(3/2)/e+33/256*d^8*x*(-e^2*x^2+d^2)^(1/2)/e+33/256/e*d^10/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/3*d*x^2*(-e^2*x^2+d^2)^(7/2)-5/21*d^3*(-e^2*x^2+d^2)^(7/2)/e^2","A"
70,1,154,160,0.010000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x)","\frac{55 d^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{128 \sqrt{e^{2}}}+\frac{55 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7} x}{128}+\frac{55 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5} x}{192}+\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3} x}{48}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e \,x^{2}}{9}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d x}{8}-\frac{29 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2}}{63 e}"," ",0,"-1/9*e*x^2*(-e^2*x^2+d^2)^(7/2)-29/63*d^2*(-e^2*x^2+d^2)^(7/2)/e-3/8*d*x*(-e^2*x^2+d^2)^(7/2)+11/48*d^3*x*(-e^2*x^2+d^2)^(5/2)+55/192*d^5*x*(-e^2*x^2+d^2)^(3/2)+55/128*d^7*x*(-e^2*x^2+d^2)^(1/2)+55/128*d^9/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","A"
71,1,231,164,0.011000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x,x)","-\frac{d^{9} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{125 d^{8} e \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{128 \sqrt{e^{2}}}+\frac{125 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6} e x}{128}+\sqrt{-e^{2} x^{2}+d^{2}}\, d^{7}+\frac{125 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4} e x}{192}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5}}{3}+\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} e x}{48}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3}}{5}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e x}{8}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{7}"," ",0,"-1/8*e*x*(-e^2*x^2+d^2)^(7/2)+25/48*d^2*e*x*(-e^2*x^2+d^2)^(5/2)+125/192*e*d^4*x*(-e^2*x^2+d^2)^(3/2)+125/128*e*d^6*x*(-e^2*x^2+d^2)^(1/2)+125/128*e*d^8/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-3/7*d*(-e^2*x^2+d^2)^(7/2)+1/5*d^3*(-e^2*x^2+d^2)^(5/2)+1/3*d^5*(-e^2*x^2+d^2)^(3/2)+d^7*(-e^2*x^2+d^2)^(1/2)-d^9/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
72,1,243,169,0.013000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^2,x)","-\frac{3 d^{8} e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}-\frac{15 d^{7} e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}}-\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} e^{2} x}{16}+3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6} e -\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} e^{2} x}{8}+\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4} e -\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d \,e^{2} x}{2}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} e}{5}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{7}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{x}"," ",0,"-1/7*e*(-e^2*x^2+d^2)^(7/2)-1/2*d*e^2*x*(-e^2*x^2+d^2)^(5/2)-5/8*d^3*e^2*x*(-e^2*x^2+d^2)^(3/2)-15/16*d^5*e^2*x*(-e^2*x^2+d^2)^(1/2)-15/16*d^7*e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-d*(-e^2*x^2+d^2)^(7/2)/x+3/5*d^2*e*(-e^2*x^2+d^2)^(5/2)+d^4*e*(-e^2*x^2+d^2)^(3/2)+3*d^6*e*(-e^2*x^2+d^2)^(1/2)-3*d^8*e/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
73,1,252,181,0.017000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^3,x)","-\frac{d^{7} e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}-\frac{85 d^{6} e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}}-\frac{85 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} e^{3} x}{16}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} e^{2}}{2}-\frac{85 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} e^{3} x}{24}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} e^{2}}{6}-\frac{17 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3} x}{6}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d \,e^{2}}{10}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{2 x^{2}}"," ",0,"-17/6*e^3*x*(-e^2*x^2+d^2)^(5/2)-85/24*e^3*d^2*x*(-e^2*x^2+d^2)^(3/2)-85/16*e^3*d^4*x*(-e^2*x^2+d^2)^(1/2)-85/16*e^3*d^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/2*d*(-e^2*x^2+d^2)^(7/2)/x^2+1/10*d*e^2*(-e^2*x^2+d^2)^(5/2)+1/6*d^3*e^2*(-e^2*x^2+d^2)^(3/2)+1/2*d^5*e^2*(-e^2*x^2+d^2)^(1/2)-1/2*d^7*e^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-3*e*(-e^2*x^2+d^2)^(7/2)/x","A"
74,1,277,182,0.017000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^4,x)","\frac{13 d^{6} e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}-\frac{25 d^{5} e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{25 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} e^{4} x}{8}-\frac{13 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} e^{3}}{2}-\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d \,e^{4} x}{12}-\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} e^{3}}{6}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4} x}{3 d}-\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}{10}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{3 d x}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{2 x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{3 x^{3}}"," ",0,"-1/3*d*(-e^2*x^2+d^2)^(7/2)/x^3-5/3/d*e^2/x*(-e^2*x^2+d^2)^(7/2)-5/3/d*e^4*x*(-e^2*x^2+d^2)^(5/2)-25/12*d*e^4*x*(-e^2*x^2+d^2)^(3/2)-25/8*d^3*e^4*x*(-e^2*x^2+d^2)^(1/2)-25/8*d^5*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-3/2*e*(-e^2*x^2+d^2)^(7/2)/x^2-13/10*e^3*(-e^2*x^2+d^2)^(5/2)-13/6*d^2*e^3*(-e^2*x^2+d^2)^(3/2)-13/2*d^4*e^3*(-e^2*x^2+d^2)^(1/2)+13/2*d^6*e^3/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
75,1,302,183,0.021000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^5,x)","\frac{45 d^{5} e^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}}+\frac{45 d^{4} e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{45 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e^{5} x}{8}-\frac{45 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} e^{4}}{8}+\frac{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5} x}{4}-\frac{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d \,e^{4}}{8}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5} x}{d^{2}}-\frac{9 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}{8 d}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{d^{2} x}-\frac{9 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{8 d \,x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{x^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{4 x^{4}}"," ",0,"-e*(-e^2*x^2+d^2)^(7/2)/x^3+3/d^2*e^3/x*(-e^2*x^2+d^2)^(7/2)+3/d^2*e^5*x*(-e^2*x^2+d^2)^(5/2)+15/4*e^5*x*(-e^2*x^2+d^2)^(3/2)+45/8*d^2*e^5*x*(-e^2*x^2+d^2)^(1/2)+45/8*d^4*e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-9/8/d*e^2/x^2*(-e^2*x^2+d^2)^(7/2)-9/8/d*e^4*(-e^2*x^2+d^2)^(5/2)-15/8*d*e^4*(-e^2*x^2+d^2)^(3/2)-45/8*d^3*e^4*(-e^2*x^2+d^2)^(1/2)+45/8*d^5*e^4/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/4*d*(-e^2*x^2+d^2)^(7/2)/x^4","A"
76,1,327,188,0.027000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^6,x)","-\frac{25 d^{4} e^{5} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}}+\frac{13 d^{3} e^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}+\frac{13 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{6} x}{2}+\frac{25 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e^{5}}{8}+\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6} x}{3 d}+\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}{24}+\frac{52 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6} x}{15 d^{3}}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}{8 d^{2}}+\frac{52 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{15 d^{3} x}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{8 d^{2} x^{2}}-\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{15 d \,x^{3}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{4 x^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{5 x^{5}}"," ",0,"-3/4*e*(-e^2*x^2+d^2)^(7/2)/x^4+5/8/d^2*e^3/x^2*(-e^2*x^2+d^2)^(7/2)+5/8/d^2*e^5*(-e^2*x^2+d^2)^(5/2)+25/24*e^5*(-e^2*x^2+d^2)^(3/2)+25/8*d^2*e^5*(-e^2*x^2+d^2)^(1/2)-25/8*d^4*e^5/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-13/15/d*e^2/x^3*(-e^2*x^2+d^2)^(7/2)+52/15/d^3*e^4/x*(-e^2*x^2+d^2)^(7/2)+52/15/d^3*e^6*x*(-e^2*x^2+d^2)^(5/2)+13/3/d*e^6*x*(-e^2*x^2+d^2)^(3/2)+13/2*d*e^6*x*(-e^2*x^2+d^2)^(1/2)+13/2*d^3*e^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/5*d*(-e^2*x^2+d^2)^(7/2)/x^5","A"
77,1,352,186,0.034000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^7,x)","-\frac{85 d^{3} e^{6} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{16 \sqrt{d^{2}}}-\frac{d^{2} e^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{7} x}{2}+\frac{85 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{6}}{16}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7} x}{3 d^{2}}+\frac{85 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6}}{48 d}-\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{7} x}{15 d^{4}}+\frac{17 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}{16 d^{3}}-\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{15 d^{4} x}+\frac{17 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{16 d^{3} x^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{15 d^{2} x^{3}}-\frac{17 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{24 d \,x^{4}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{5 x^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{6 x^{6}}"," ",0,"1/15*e^3/d^2/x^3*(-e^2*x^2+d^2)^(7/2)-4/15*e^5/d^4/x*(-e^2*x^2+d^2)^(7/2)-4/15*e^7/d^4*x*(-e^2*x^2+d^2)^(5/2)-1/3*e^7/d^2*x*(-e^2*x^2+d^2)^(3/2)-1/2*e^7*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-17/24/d*e^2/x^4*(-e^2*x^2+d^2)^(7/2)+17/16/d^3*e^4/x^2*(-e^2*x^2+d^2)^(7/2)-85/16*d^3*e^6/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-3/5*e*(-e^2*x^2+d^2)^(7/2)/x^5-1/6*d*(-e^2*x^2+d^2)^(7/2)/x^6-1/2*e^7*x*(-e^2*x^2+d^2)^(1/2)+17/16/d^3*e^6*(-e^2*x^2+d^2)^(5/2)+85/48/d*e^6*(-e^2*x^2+d^2)^(3/2)+85/16*d*e^6*(-e^2*x^2+d^2)^(1/2)","A"
78,1,377,180,0.046000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^8,x)","-\frac{15 d^{2} e^{7} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{16 \sqrt{d^{2}}}-\frac{3 d \,e^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{8} x}{d}+\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{7}}{16}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{8} x}{d^{3}}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7}}{16 d^{2}}-\frac{8 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{8} x}{5 d^{5}}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{7}}{16 d^{4}}-\frac{8 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{6}}{5 d^{5} x}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{16 d^{4} x^{2}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{5 d^{3} x^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{8 d^{2} x^{4}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{5 d \,x^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{2 x^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{7 x^{7}}"," ",0,"-3/5/d*e^2/x^5*(-e^2*x^2+d^2)^(7/2)+2/5/d^3*e^4/x^3*(-e^2*x^2+d^2)^(7/2)-8/5/d^5*e^6/x*(-e^2*x^2+d^2)^(7/2)-8/5/d^5*e^8*x*(-e^2*x^2+d^2)^(5/2)-2/d^3*e^8*x*(-e^2*x^2+d^2)^(3/2)-3/d*e^8*x*(-e^2*x^2+d^2)^(1/2)-3*d*e^8/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/2*e*(-e^2*x^2+d^2)^(7/2)/x^6-1/8/d^2*e^3/x^4*(-e^2*x^2+d^2)^(7/2)+3/16/d^4*e^5/x^2*(-e^2*x^2+d^2)^(7/2)+3/16/d^4*e^7*(-e^2*x^2+d^2)^(5/2)+5/16/d^2*e^7*(-e^2*x^2+d^2)^(3/2)+15/16*e^7*(-e^2*x^2+d^2)^(1/2)-15/16*d^2*e^7/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/7*d*(-e^2*x^2+d^2)^(7/2)/x^7","B"
79,1,402,178,0.065000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^9,x)","\frac{125 d \,e^{8} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{128 \sqrt{d^{2}}}-\frac{e^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{9} x}{d^{2}}-\frac{125 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{8}}{128 d}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{9} x}{3 d^{4}}-\frac{125 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{8}}{384 d^{3}}-\frac{8 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{9} x}{15 d^{6}}-\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{8}}{128 d^{5}}-\frac{8 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{7}}{15 d^{6} x}-\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{6}}{128 d^{5} x^{2}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{15 d^{4} x^{3}}+\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{192 d^{3} x^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{5 d^{2} x^{5}}-\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{48 d \,x^{6}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{7 x^{7}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{8 x^{8}}"," ",0,"-1/8*d*(-e^2*x^2+d^2)^(7/2)/x^8-25/48/d*e^2/x^6*(-e^2*x^2+d^2)^(7/2)+25/192/d^3*e^4/x^4*(-e^2*x^2+d^2)^(7/2)-25/128/d^5*e^6/x^2*(-e^2*x^2+d^2)^(7/2)-25/128/d^5*e^8*(-e^2*x^2+d^2)^(5/2)-125/384/d^3*e^8*(-e^2*x^2+d^2)^(3/2)-125/128/d*e^8*(-e^2*x^2+d^2)^(1/2)+125/128*d*e^8/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-3/7*e*(-e^2*x^2+d^2)^(7/2)/x^7-1/5*e^3/d^2/x^5*(-e^2*x^2+d^2)^(7/2)+2/15*e^5/d^4/x^3*(-e^2*x^2+d^2)^(7/2)-8/15*e^7/d^6/x*(-e^2*x^2+d^2)^(7/2)-8/15*e^9/d^6*x*(-e^2*x^2+d^2)^(5/2)-2/3*e^9/d^4*x*(-e^2*x^2+d^2)^(3/2)-e^9/d^2*x*(-e^2*x^2+d^2)^(1/2)-e^9/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","B"
80,1,250,159,0.098000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^10,x)","\frac{55 e^{9} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{128 \sqrt{d^{2}}}-\frac{55 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{9}}{128 d^{2}}-\frac{55 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{9}}{384 d^{4}}-\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{9}}{128 d^{6}}-\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{7}}{128 d^{6} x^{2}}+\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{192 d^{4} x^{4}}-\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{48 d^{2} x^{6}}-\frac{29 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{63 d \,x^{7}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{8 x^{8}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{9 x^{9}}"," ",0,"-29/63*e^2*(-e^2*x^2+d^2)^(7/2)/d/x^7-3/8*e*(-e^2*x^2+d^2)^(7/2)/x^8-11/48/d^2*e^3/x^6*(-e^2*x^2+d^2)^(7/2)+11/192/d^4*e^5/x^4*(-e^2*x^2+d^2)^(7/2)-11/128/d^6*e^7/x^2*(-e^2*x^2+d^2)^(7/2)-11/128/d^6*e^9*(-e^2*x^2+d^2)^(5/2)-55/384/d^4*e^9*(-e^2*x^2+d^2)^(3/2)-55/128/d^2*e^9*(-e^2*x^2+d^2)^(1/2)+55/128*e^9/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/9*d*(-e^2*x^2+d^2)^(7/2)/x^9","A"
81,1,278,193,0.152000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^11,x)","\frac{33 e^{10} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{256 \sqrt{d^{2}}\, d}-\frac{33 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{10}}{256 d^{3}}-\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{10}}{256 d^{5}}-\frac{33 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{10}}{1280 d^{7}}-\frac{33 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{8}}{1280 d^{7} x^{2}}+\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{6}}{640 d^{5} x^{4}}-\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{160 d^{3} x^{6}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{21 d^{2} x^{7}}-\frac{33 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{80 d \,x^{8}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{3 x^{9}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{10 x^{10}}"," ",0,"-1/3*e*(-e^2*x^2+d^2)^(7/2)/x^9-5/21*e^3*(-e^2*x^2+d^2)^(7/2)/d^2/x^7-33/80*e^2*(-e^2*x^2+d^2)^(7/2)/d/x^8-11/160/d^3*e^4/x^6*(-e^2*x^2+d^2)^(7/2)+11/640/d^5*e^6/x^4*(-e^2*x^2+d^2)^(7/2)-33/1280/d^7*e^8/x^2*(-e^2*x^2+d^2)^(7/2)-33/1280/d^7*e^10*(-e^2*x^2+d^2)^(5/2)-11/256/d^5*e^10*(-e^2*x^2+d^2)^(3/2)-33/256/d^3*e^10*(-e^2*x^2+d^2)^(1/2)+33/256/d*e^10/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/10*d*(-e^2*x^2+d^2)^(7/2)/x^10","A"
82,1,303,218,0.241000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^(5/2)/x^12,x)","\frac{19 e^{11} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{256 \sqrt{d^{2}}\, d^{2}}-\frac{19 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{11}}{256 d^{4}}-\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{11}}{768 d^{6}}-\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{11}}{1280 d^{8}}-\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{9}}{1280 d^{8} x^{2}}+\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{7}}{1920 d^{6} x^{4}}-\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{480 d^{4} x^{6}}-\frac{74 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{693 d^{3} x^{7}}-\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{80 d^{2} x^{8}}-\frac{37 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{99 d \,x^{9}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{10 x^{10}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{11 x^{11}}"," ",0,"-37/99*e^2*(-e^2*x^2+d^2)^(7/2)/d/x^9-74/693*e^4*(-e^2*x^2+d^2)^(7/2)/d^3/x^7-19/80*e^3*(-e^2*x^2+d^2)^(7/2)/d^2/x^8-19/480*e^5/d^4/x^6*(-e^2*x^2+d^2)^(7/2)+19/1920*e^7/d^6/x^4*(-e^2*x^2+d^2)^(7/2)-19/1280*e^9/d^8/x^2*(-e^2*x^2+d^2)^(7/2)-19/1280*e^11/d^8*(-e^2*x^2+d^2)^(5/2)-19/768*e^11/d^6*(-e^2*x^2+d^2)^(3/2)-19/256*e^11/d^4*(-e^2*x^2+d^2)^(1/2)+19/256*e^11/d^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/11*d*(-e^2*x^2+d^2)^(7/2)/x^11-3/10*e*(-e^2*x^2+d^2)^(7/2)/x^10","A"
83,1,222,152,0.013000," ","int(x^5*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","-\frac{e \,x^{7}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{3 d \,x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{13 d^{2} x^{5}}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{19 d^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{76 d^{5} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{13 d^{2} x^{3}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}+\frac{152 d^{7}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}+\frac{13 d^{2} x}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}-\frac{13 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{5}}"," ",0,"-1/2*e*x^7/(-e^2*x^2+d^2)^(5/2)+13/10/e*d^2*x^5/(-e^2*x^2+d^2)^(5/2)-13/6/e^3*d^2*x^3/(-e^2*x^2+d^2)^(3/2)+13/2/e^5*d^2*x/(-e^2*x^2+d^2)^(1/2)-13/2/e^5*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-3*d*x^6/(-e^2*x^2+d^2)^(5/2)+19/e^2*d^3*x^4/(-e^2*x^2+d^2)^(5/2)-76/3/e^4*d^5*x^2/(-e^2*x^2+d^2)^(5/2)+152/15/e^6*d^7/(-e^2*x^2+d^2)^(5/2)","A"
84,1,262,126,0.010000," ","int(x^4*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","-\frac{e \,x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{3 d \,x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{9 d^{2} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{d^{3} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{12 d^{4} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{3 d^{5} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{d \,x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}+\frac{24 d^{6}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}+\frac{d^{3} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}+\frac{16 d x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}-\frac{3 d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}"," ",0,"-e*x^6/(-e^2*x^2+d^2)^(5/2)+9/e*d^2*x^4/(-e^2*x^2+d^2)^(5/2)-12/e^3*d^4*x^2/(-e^2*x^2+d^2)^(5/2)+24/5/e^5*d^6/(-e^2*x^2+d^2)^(5/2)+3/5*d*x^5/(-e^2*x^2+d^2)^(5/2)-d/e^2*x^3/(-e^2*x^2+d^2)^(3/2)+16/5*d/e^4*x/(-e^2*x^2+d^2)^(1/2)-3*d/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/2*d^3*x^3/e^2/(-e^2*x^2+d^2)^(5/2)-3/10*d^5/e^4*x/(-e^2*x^2+d^2)^(5/2)+1/10*d^3/e^4*x/(-e^2*x^2+d^2)^(3/2)","B"
85,1,234,104,0.013000," ","int(x^3*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{e \,x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{3 d \,x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{3 d^{2} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}-\frac{11 d^{3} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{9 d^{4} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}+\frac{22 d^{5}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}+\frac{3 d^{2} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}+\frac{8 x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}-\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{3}}"," ",0,"1/5*e*x^5/(-e^2*x^2+d^2)^(5/2)-1/3/e*x^3/(-e^2*x^2+d^2)^(3/2)+8/5/e^3*x/(-e^2*x^2+d^2)^(1/2)-1/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+3*d*x^4/(-e^2*x^2+d^2)^(5/2)-11/3/e^2*d^3*x^2/(-e^2*x^2+d^2)^(5/2)+22/15/e^4*d^5/(-e^2*x^2+d^2)^(5/2)+3/2/e*d^2*x^3/(-e^2*x^2+d^2)^(5/2)-9/10/e^3*d^4*x/(-e^2*x^2+d^2)^(5/2)+3/10/e^3*d^2*x/(-e^2*x^2+d^2)^(3/2)","B"
86,1,55,81,0.006000," ","int(x^2*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{4} \left(7 e^{2} x^{2}-6 d e x +2 d^{2}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d \,e^{3}}"," ",0,"1/15*(-e*x+d)*(e*x+d)^4*(7*e^2*x^2-6*d*e*x+2*d^2)/d/e^3/(-e^2*x^2+d^2)^(7/2)","A"
87,1,52,74,0.009000," ","int(x*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(e x +d \right)^{4} \left(e^{2} x^{2}-3 d e x +d^{2}\right)}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2} e^{2}}"," ",0,"-1/5*(-e*x+d)*(e*x+d)^4*(e^2*x^2-3*d*e*x+d^2)/d^2/e^2/(-e^2*x^2+d^2)^(7/2)","A"
88,1,55,91,0.008000," ","int((e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{4} \left(2 e^{2} x^{2}-6 d e x +7 d^{2}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} e}"," ",0,"1/15*(-e*x+d)*(e*x+d)^4*(2*e^2*x^2-6*d*e*x+7*d^2)/d^3/e/(-e^2*x^2+d^2)^(7/2)","A"
89,1,158,100,0.014000," ","int((e*x+d)^3/x/(-e^2*x^2+d^2)^(7/2),x)","\frac{4 e x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{4 d}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{11 e x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2}}+\frac{1}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d}-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{3}}+\frac{22 e x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4}}+\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}}"," ",0,"4/5*e*x/(-e^2*x^2+d^2)^(5/2)+11/15*e/d^2*x/(-e^2*x^2+d^2)^(3/2)+22/15*e/d^4*x/(-e^2*x^2+d^2)^(1/2)+4/5*d/(-e^2*x^2+d^2)^(5/2)+1/3/d/(-e^2*x^2+d^2)^(3/2)+1/d^3/(-e^2*x^2+d^2)^(1/2)-1/d^3/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
90,1,190,129,0.012000," ","int((e*x+d)^3/x^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{9 e^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d}+\frac{4 e}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{d}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x}+\frac{12 e^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3}}+\frac{e}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2}}-\frac{3 e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{4}}+\frac{24 e^{2} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}+\frac{3 e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{4}}"," ",0,"4/5*e/(-e^2*x^2+d^2)^(5/2)+9/5*e^2/d*x/(-e^2*x^2+d^2)^(5/2)+12/5*e^2/d^3*x/(-e^2*x^2+d^2)^(3/2)+24/5*e^2/d^5*x/(-e^2*x^2+d^2)^(1/2)-d/x/(-e^2*x^2+d^2)^(5/2)+e/d^2/(-e^2*x^2+d^2)^(3/2)+3*e/d^4/(-e^2*x^2+d^2)^(1/2)-3*e/d^4/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
91,1,222,160,0.014000," ","int((e*x+d)^3/x^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{19 e^{3} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2}}+\frac{13 e^{2}}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d}+\frac{76 e^{3} x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4}}-\frac{3 e}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x}-\frac{d}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x^{2}}+\frac{13 e^{2}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3}}-\frac{13 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{5}}+\frac{152 e^{3} x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}+\frac{13 e^{2}}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}"," ",0,"19/5*e^3*x/d^2/(-e^2*x^2+d^2)^(5/2)+76/15*e^3/d^4*x/(-e^2*x^2+d^2)^(3/2)+152/15*e^3/d^6*x/(-e^2*x^2+d^2)^(1/2)-3*e/x/(-e^2*x^2+d^2)^(5/2)+13/10*e^2/d/(-e^2*x^2+d^2)^(5/2)+13/6*e^2/d^3/(-e^2*x^2+d^2)^(3/2)+13/2*e^2/d^5/(-e^2*x^2+d^2)^(1/2)-13/2*e^2/d^5/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/2*d/x^2/(-e^2*x^2+d^2)^(5/2)","A"
92,1,208,127,0.018000," ","int(x^4*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x)","\frac{d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}-\frac{5 d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{4}}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} x}{8 e^{4}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4}}{e^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} x^{2}}{5 e^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d x}{4 e^{4}}-\frac{7 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2}}{15 e^{5}}"," ",0,"-1/5/e^3*x^2*(-e^2*x^2+d^2)^(3/2)-7/15*d^2/e^5*(-e^2*x^2+d^2)^(3/2)+1/4*d/e^4*x*(-e^2*x^2+d^2)^(3/2)-5/8*d^3/e^4*x*(-e^2*x^2+d^2)^(1/2)-5/8*d^5/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+d^4/e^5*(-(x+d/e)^2*e^2+2*d*e*(x+d/e))^(1/2)+d^5/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)*x/(-(x+d/e)^2*e^2+2*d*e*(x+d/e))^(1/2))","A"
93,1,185,102,0.013000," ","int(x^3*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x)","-\frac{d^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e^{3}}+\frac{5 d^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{3}}+\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} x}{8 e^{3}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3}}{e^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} x}{4 e^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d}{3 e^{4}}"," ",0,"-1/4/e^3*x*(-e^2*x^2+d^2)^(3/2)+5/8*d^2/e^3*x*(-e^2*x^2+d^2)^(1/2)+5/8/e^3*d^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/3*d/e^4*(-e^2*x^2+d^2)^(3/2)-d^3/e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-d^4/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","A"
94,1,160,74,0.012000," ","int(x^2*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x)","\frac{d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e^{2}}-\frac{d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{2}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d x}{2 e^{2}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2}}{e^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{3 e^{3}}"," ",0,"-1/3*(-e^2*x^2+d^2)^(3/2)/e^3-1/2*(-e^2*x^2+d^2)^(1/2)*d/e^2*x-1/2/(e^2)^(1/2)*d^3/e^2*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+d^2/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+d^3/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
95,1,140,54,0.010000," ","int(x*(-e^2*x^2+d^2)^(1/2)/(e*x+d),x)","-\frac{d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e}+\frac{d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x}{2 e}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d}{e^{2}}"," ",0,"1/2/e*x*(-e^2*x^2+d^2)^(1/2)+1/2/e*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-d/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-d^2/e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
96,1,77,42,0.004000," ","int((-e^2*x^2+d^2)^(1/2)/(e*x+d),x)","\frac{d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{e}"," ",0,"1/e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+d/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","A"
97,1,137,42,0.013000," ","int((-e^2*x^2+d^2)^(1/2)/x/(e*x+d),x)","-\frac{d \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}-\frac{e \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{d}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{d}"," ",0,"(-e^2*x^2+d^2)^(1/2)/d-d/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
98,1,222,47,0.012000," ","int((-e^2*x^2+d^2)^(1/2)/x^2/(e*x+d),x)","\frac{e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, d}-\frac{e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, d}+\frac{e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{2} x}{d^{3}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e}{d^{2}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e}{d^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{d^{3} x}"," ",0,"-1/d^3/x*(-e^2*x^2+d^2)^(3/2)-1/d^3*e^2*x*(-e^2*x^2+d^2)^(1/2)-1/d*e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-e/d^2*(-e^2*x^2+d^2)^(1/2)+e/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+e/d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+e^2/d/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
99,1,254,72,0.011000," ","int((-e^2*x^2+d^2)^(1/2)/x^3/(e*x+d),x)","-\frac{e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d}-\frac{e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, d^{2}}+\frac{e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, d^{2}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{3} x}{d^{4}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{2}}{2 d^{3}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{2}}{d^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{d^{4} x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{2 d^{3} x^{2}}"," ",0,"e/d^4/x*(-e^2*x^2+d^2)^(3/2)+e^3/d^4*x*(-e^2*x^2+d^2)^(1/2)+e^3/d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/2/d^3/x^2*(-e^2*x^2+d^2)^(3/2)+1/2/d^3*e^2*(-e^2*x^2+d^2)^(1/2)-1/2/d*e^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/d^3*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-1/d^2*e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
100,1,280,98,0.012000," ","int((-e^2*x^2+d^2)^(1/2)/x^4/(e*x+d),x)","\frac{e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{2}}+\frac{e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, d^{3}}-\frac{e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, d^{3}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{4} x}{d^{5}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}{2 d^{4}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{3}}{d^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}{d^{5} x}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{2 d^{4} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{3 d^{3} x^{3}}"," ",0,"-1/d^5*e^2/x*(-e^2*x^2+d^2)^(3/2)-1/d^5*e^4*x*(-e^2*x^2+d^2)^(1/2)-1/d^3*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/2*e/d^4/x^2*(-e^2*x^2+d^2)^(3/2)-1/2*e^3/d^4*(-e^2*x^2+d^2)^(1/2)+1/2*e^3/d^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/3/d^3/x^3*(-e^2*x^2+d^2)^(3/2)+1/d^4*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+1/d^3*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
101,1,304,123,0.013000," ","int((-e^2*x^2+d^2)^(1/2)/x^5/(e*x+d),x)","-\frac{3 e^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}\, d^{3}}-\frac{e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, d^{4}}+\frac{e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, d^{4}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{5} x}{d^{6}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}{8 d^{5}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{4}}{d^{5}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}{d^{6} x}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}{8 d^{5} x^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{3 d^{4} x^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{4 d^{3} x^{4}}"," ",0,"-1/4/d^3/x^4*(-e^2*x^2+d^2)^(3/2)-5/8/d^5*e^2/x^2*(-e^2*x^2+d^2)^(3/2)+3/8/d^5*e^4*(-e^2*x^2+d^2)^(1/2)-3/8/d^3*e^4/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/d^6*e^3/x*(-e^2*x^2+d^2)^(3/2)+1/d^6*e^5*x*(-e^2*x^2+d^2)^(1/2)+1/d^4*e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/3*e/d^4/x^3*(-e^2*x^2+d^2)^(3/2)-1/d^5*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-1/d^4*e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
102,1,222,97,0.015000," ","int(x^2*(-e^2*x^2+d^2)^(3/2)/(e*x+d),x)","\frac{d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{2}}-\frac{3 d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{2}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} x}{8 e^{2}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3} x}{2 e^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d x}{4 e^{2}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2}}{3 e^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{5 e^{3}}"," ",0,"-1/5*(-e^2*x^2+d^2)^(5/2)/e^3-1/4*(-e^2*x^2+d^2)^(3/2)*d/e^2*x-3/8*(-e^2*x^2+d^2)^(1/2)*d^3/e^2*x-3/8/(e^2)^(1/2)*d^5/e^2*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/3*d^2/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+1/2*d^3/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+1/2*d^5/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
103,1,330,173,0.016000," ","int(x^4*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x)","\frac{3 d^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{4}}-\frac{45 d^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{128 \sqrt{e^{2}}\, e^{4}}-\frac{45 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7} x}{128 e^{4}}+\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{7} x}{8 e^{4}}-\frac{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5} x}{64 e^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{5} x}{4 e^{4}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3} x}{16 e^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{4}}{5 e^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} x^{2}}{9 e^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d x}{8 e^{4}}-\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2}}{63 e^{5}}"," ",0,"-1/9/e^3*x^2*(-e^2*x^2+d^2)^(7/2)-11/63*d^2/e^5*(-e^2*x^2+d^2)^(7/2)+1/8*d/e^4*x*(-e^2*x^2+d^2)^(7/2)-3/16*(-e^2*x^2+d^2)^(5/2)*d^3/e^4*x-15/64*(-e^2*x^2+d^2)^(3/2)*d^5/e^4*x-45/128*(-e^2*x^2+d^2)^(1/2)*d^7/e^4*x-45/128/(e^2)^(1/2)*d^9/e^4*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/5*d^4/e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/4*d^5/e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+3/8*d^7/e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+3/8*d^9/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","A"
104,1,305,148,0.012000," ","int(x^3*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x)","-\frac{3 d^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{3}}+\frac{45 d^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{128 \sqrt{e^{2}}\, e^{3}}+\frac{45 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6} x}{128 e^{3}}-\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{6} x}{8 e^{3}}+\frac{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4} x}{64 e^{3}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{4} x}{4 e^{3}}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} x}{16 e^{3}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{3}}{5 e^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} x}{8 e^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{7 e^{4}}"," ",0,"-1/8/e^3*x*(-e^2*x^2+d^2)^(7/2)+3/16*(-e^2*x^2+d^2)^(5/2)*d^2/e^3*x+15/64*(-e^2*x^2+d^2)^(3/2)*d^4/e^3*x+45/128*(-e^2*x^2+d^2)^(1/2)*d^6/e^3*x+45/128/(e^2)^(1/2)*d^8/e^3*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/7*d/e^4*(-e^2*x^2+d^2)^(7/2)-1/5*d^3/e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/4*d^4/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-3/8*d^6/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-3/8*d^8/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
105,1,282,120,0.014000," ","int(x^2*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x)","\frac{3 d^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{2}}-\frac{5 d^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}\, e^{2}}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} x}{16 e^{2}}+\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{5} x}{8 e^{2}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} x}{24 e^{2}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{3} x}{4 e^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d x}{6 e^{2}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{2}}{5 e^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{7 e^{3}}"," ",0,"-1/7*(-e^2*x^2+d^2)^(7/2)/e^3-1/6*(-e^2*x^2+d^2)^(5/2)*d/e^2*x-5/24*(-e^2*x^2+d^2)^(3/2)*d^3/e^2*x-5/16*(-e^2*x^2+d^2)^(1/2)*d^5/e^2*x-5/16/(e^2)^(1/2)*d^7/e^2*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/5*d^2/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/4*d^3/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+3/8*d^5/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+3/8*d^7/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
106,1,260,100,0.010000," ","int(x*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x)","-\frac{3 d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, e}+\frac{5 d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}\, e}+\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x}{16 e}-\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4} x}{8 e}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} x}{24 e}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2} x}{4 e}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x}{6 e}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d}{5 e^{2}}"," ",0,"1/6*(-e^2*x^2+d^2)^(5/2)/e*x+5/24*(-e^2*x^2+d^2)^(3/2)*d^2/e*x+5/16*(-e^2*x^2+d^2)^(1/2)*d^4/e*x+5/16/(e^2)^(1/2)*d^6/e*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/5*d/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/4*d^2/e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-3/8*d^4/e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-3/8*d^6/e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
107,1,147,84,0.006000," ","int((-e^2*x^2+d^2)^(5/2)/(e*x+d),x)","\frac{3 d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3} x}{8}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d x}{4}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{5 e}"," ",0,"1/5/e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/4*d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+3/8*d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+3/8*d^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","A"
108,1,245,99,0.011000," ","int((-e^2*x^2+d^2)^(5/2)/x/(e*x+d),x)","-\frac{d^{5} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}-\frac{3 d^{4} e \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2} e x}{8}+\sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e x}{4}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d}{3}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{5 d}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{5 d}"," ",0,"1/5/d*(-e^2*x^2+d^2)^(5/2)+1/3*(-e^2*x^2+d^2)^(3/2)*d+(-e^2*x^2+d^2)^(1/2)*d^3-1/(d^2)^(1/2)*d^5*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/4*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-3/8*d^2*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-3/8*d^4*e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
109,1,380,101,0.011000," ","int((-e^2*x^2+d^2)^(5/2)/x^2/(e*x+d),x)","\frac{d^{4} e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{3 d^{3} e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{15 d^{3} e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{2} x}{8}+\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d \,e^{2} x}{8}-\sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e -\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2} x}{4 d}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{2} x}{4 d}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{3}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2} x}{d^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{5 d^{2}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e}{5 d^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{d^{3} x}"," ",0,"-1/d^3/x*(-e^2*x^2+d^2)^(7/2)-1/d^3*e^2*x*(-e^2*x^2+d^2)^(5/2)-5/4*(-e^2*x^2+d^2)^(3/2)/d*e^2*x-15/8*(-e^2*x^2+d^2)^(1/2)*d*e^2*x-15/8/(e^2)^(1/2)*d^3*e^2*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/5*e/d^2*(-e^2*x^2+d^2)^(5/2)-1/3*(-e^2*x^2+d^2)^(3/2)*e-(-e^2*x^2+d^2)^(1/2)*d^2*e+1/(d^2)^(1/2)*d^4*e*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/5*e/d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/4*e^2/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+3/8*e^2*d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+3/8*e^2*d^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
110,1,411,105,0.012000," ","int((-e^2*x^2+d^2)^(5/2)/x^3/(e*x+d),x)","\frac{3 d^{3} e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}-\frac{3 d^{2} e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{15 d^{2} e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3} x}{8}-\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{3} x}{8}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{2}}{2}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3} x}{4 d^{2}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{3} x}{4 d^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}{2 d}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3} x}{d^{4}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}{10 d^{3}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{2}}{5 d^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{d^{4} x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{2 d^{3} x^{2}}"," ",0,"e/d^4/x*(-e^2*x^2+d^2)^(7/2)+e^3/d^4*x*(-e^2*x^2+d^2)^(5/2)+5/4*(-e^2*x^2+d^2)^(3/2)/d^2*e^3*x+15/8*(-e^2*x^2+d^2)^(1/2)*e^3*x+15/8/(e^2)^(1/2)*d^2*e^3*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/2/d^3/x^2*(-e^2*x^2+d^2)^(7/2)-3/10/d^3*e^2*(-e^2*x^2+d^2)^(5/2)-1/2*(-e^2*x^2+d^2)^(3/2)/d*e^2-3/2*(-e^2*x^2+d^2)^(1/2)*d*e^2+3/2/(d^2)^(1/2)*d^3*e^2*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5/d^3*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/4/d^2*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-3/8*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-3/8*d^2*e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
111,1,439,106,0.013000," ","int((-e^2*x^2+d^2)^(5/2)/x^4/(e*x+d),x)","-\frac{3 d^{2} e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}+\frac{3 d \,e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{5 d \,e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4} x}{8 d}+\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{4} x}{8 d}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}{2}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4} x}{12 d^{3}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{4} x}{4 d^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}{2 d^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4} x}{3 d^{5}}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}{10 d^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{3}}{5 d^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{3 d^{5} x}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{2 d^{4} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{3 d^{3} x^{3}}"," ",0,"1/3/d^5*e^2/x*(-e^2*x^2+d^2)^(7/2)+1/3/d^5*e^4*x*(-e^2*x^2+d^2)^(5/2)+5/12*(-e^2*x^2+d^2)^(3/2)/d^3*e^4*x+5/8*(-e^2*x^2+d^2)^(1/2)/d*e^4*x+5/8/(e^2)^(1/2)*d*e^4*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/2*e/d^4/x^2*(-e^2*x^2+d^2)^(7/2)+3/10*e^3/d^4*(-e^2*x^2+d^2)^(5/2)+1/2*(-e^2*x^2+d^2)^(3/2)/d^2*e^3+3/2*(-e^2*x^2+d^2)^(1/2)*e^3-3/2/(d^2)^(1/2)*d^2*e^3*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/3/d^3/x^3*(-e^2*x^2+d^2)^(7/2)+1/5/d^4*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/4/d^3*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+3/8/d*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+3/8*d*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
112,1,463,105,0.014000," ","int((-e^2*x^2+d^2)^(5/2)/x^5/(e*x+d),x)","-\frac{3 d \,e^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}}-\frac{3 e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{5 e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{5} x}{8 d^{2}}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5} x}{8 d^{2}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}{8 d}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{5} x}{4 d^{4}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5} x}{12 d^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}{8 d^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5} x}{3 d^{6}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{4}}{5 d^{5}}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}{40 d^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{3 d^{6} x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{8 d^{5} x^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{3 d^{4} x^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{4 d^{3} x^{4}}"," ",0,"-5/8/(e^2)^(1/2)*e^5*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/8*(-e^2*x^2+d^2)^(3/2)/d^3*e^4+3/8*(-e^2*x^2+d^2)^(1/2)/d*e^4-1/4/d^4*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-3/8/d^2*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+1/3*e/d^4/x^3*(-e^2*x^2+d^2)^(7/2)-1/3/d^6*e^3/x*(-e^2*x^2+d^2)^(7/2)-1/3/d^6*e^5*x*(-e^2*x^2+d^2)^(5/2)-1/8/d^5*e^2/x^2*(-e^2*x^2+d^2)^(7/2)-5/12*(-e^2*x^2+d^2)^(3/2)/d^4*e^5*x-5/8*(-e^2*x^2+d^2)^(1/2)/d^2*e^5*x-3/8/(d^2)^(1/2)*d*e^4*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5/d^5*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-3/8*e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/4/d^3/x^4*(-e^2*x^2+d^2)^(7/2)+3/40/d^5*e^4*(-e^2*x^2+d^2)^(5/2)","B"
113,1,493,92,0.016000," ","int((-e^2*x^2+d^2)^(5/2)/x^6/(e*x+d),x)","\frac{3 e^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, d}-\frac{3 e^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, d}+\frac{3 e^{5} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}}+\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{6} x}{8 d^{3}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{6} x}{8 d^{3}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}{8 d^{2}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{6} x}{4 d^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6} x}{4 d^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}{8 d^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6} x}{5 d^{7}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{5}}{5 d^{6}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}{40 d^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{5 d^{7} x}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{8 d^{6} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{5 d^{5} x^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{4 d^{4} x^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{5 d^{3} x^{5}}"," ",0,"-1/8*(-e^2*x^2+d^2)^(3/2)/d^4*e^5-3/8*(-e^2*x^2+d^2)^(1/2)/d^2*e^5+3/8/(d^2)^(1/2)*e^5*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/4/d^5*e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+3/8/d^3*e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+3/8/d*e^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/5/d^5*e^2/x^3*(-e^2*x^2+d^2)^(7/2)-1/5/d^7*e^4/x*(-e^2*x^2+d^2)^(7/2)-1/5/d^7*e^6*x*(-e^2*x^2+d^2)^(5/2)-1/4/d^5*e^6*x*(-e^2*x^2+d^2)^(3/2)-3/8/d^3*e^6*x*(-e^2*x^2+d^2)^(1/2)-3/8/d*e^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/4*e/d^4/x^4*(-e^2*x^2+d^2)^(7/2)+1/8*e^3/d^6/x^2*(-e^2*x^2+d^2)^(7/2)+1/5/d^6*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/5/d^3/x^5*(-e^2*x^2+d^2)^(7/2)-3/40*e^5/d^6*(-e^2*x^2+d^2)^(5/2)","B"
114,1,521,123,0.014000," ","int((-e^2*x^2+d^2)^(5/2)/x^7/(e*x+d),x)","-\frac{e^{6} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{16 \sqrt{d^{2}}\, d}-\frac{3 e^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{2}}+\frac{3 e^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{2}}-\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{7} x}{8 d^{4}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{7} x}{8 d^{4}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{6}}{16 d^{3}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{7} x}{4 d^{6}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7} x}{4 d^{6}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6}}{48 d^{5}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{7} x}{5 d^{8}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{6}}{5 d^{7}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}{80 d^{7}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{5 d^{8} x}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{16 d^{7} x^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{5 d^{6} x^{3}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{24 d^{5} x^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{5 d^{4} x^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{6 d^{3} x^{6}}"," ",0,"1/48*(-e^2*x^2+d^2)^(3/2)/d^5*e^6+1/16*(-e^2*x^2+d^2)^(1/2)/d^3*e^6+1/5*e/d^4/x^5*(-e^2*x^2+d^2)^(7/2)-1/4/d^6*e^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-3/8/d^4*e^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-3/8/d^2*e^7/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+1/5/d^6*e^3/x^3*(-e^2*x^2+d^2)^(7/2)+1/5/d^8*e^5/x*(-e^2*x^2+d^2)^(7/2)+1/5/d^8*e^7*x*(-e^2*x^2+d^2)^(5/2)+1/4/d^6*e^7*x*(-e^2*x^2+d^2)^(3/2)+3/8/d^4*e^7*x*(-e^2*x^2+d^2)^(1/2)+3/8/d^2*e^7/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-5/24/d^5*e^2/x^4*(-e^2*x^2+d^2)^(7/2)-3/16/d^7*e^4/x^2*(-e^2*x^2+d^2)^(7/2)-1/16/(d^2)^(1/2)/d*e^6*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5/d^7*e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/6/d^3/x^6*(-e^2*x^2+d^2)^(7/2)+1/80/d^7*e^6*(-e^2*x^2+d^2)^(5/2)","B"
115,1,546,148,0.015000," ","int((-e^2*x^2+d^2)^(5/2)/x^8/(e*x+d),x)","\frac{e^{7} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{16 \sqrt{d^{2}}\, d^{2}}+\frac{3 e^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{3}}-\frac{3 e^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{3}}+\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{8} x}{8 d^{5}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{8} x}{8 d^{5}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{7}}{16 d^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{8} x}{4 d^{7}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{8} x}{4 d^{7}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7}}{48 d^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{8} x}{5 d^{9}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{7}}{5 d^{8}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{7}}{80 d^{8}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{6}}{5 d^{9} x}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{16 d^{8} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{5 d^{7} x^{3}}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{24 d^{6} x^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{5 d^{5} x^{5}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{6 d^{4} x^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{7 d^{3} x^{7}}"," ",0,"1/4/d^7*e^8*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+3/8/d^5*e^8*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+3/8/d^3*e^8/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/5/d^5*e^2/x^5*(-e^2*x^2+d^2)^(7/2)+1/6*e/d^4/x^6*(-e^2*x^2+d^2)^(7/2)-1/5/d^7*e^4/x^3*(-e^2*x^2+d^2)^(7/2)-1/5/d^9*e^6/x*(-e^2*x^2+d^2)^(7/2)-1/5/d^9*e^8*x*(-e^2*x^2+d^2)^(5/2)-1/4/d^7*e^8*x*(-e^2*x^2+d^2)^(3/2)-3/8/d^5*e^8*x*(-e^2*x^2+d^2)^(1/2)-3/8/d^3*e^8/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+5/24/d^6*e^3/x^4*(-e^2*x^2+d^2)^(7/2)+3/16/d^8*e^5/x^2*(-e^2*x^2+d^2)^(7/2)+1/16/(d^2)^(1/2)/d^2*e^7*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/5/d^8*e^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/80/d^8*e^7*(-e^2*x^2+d^2)^(5/2)-1/7/d^3/x^7*(-e^2*x^2+d^2)^(7/2)-1/48*(-e^2*x^2+d^2)^(3/2)/d^6*e^7-1/16*(-e^2*x^2+d^2)^(1/2)/d^4*e^7","B"
116,1,571,173,0.017000," ","int((-e^2*x^2+d^2)^(5/2)/x^9/(e*x+d),x)","-\frac{3 e^{8} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{128 \sqrt{d^{2}}\, d^{3}}-\frac{3 e^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{4}}+\frac{3 e^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{4}}-\frac{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{9} x}{8 d^{6}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{9} x}{8 d^{6}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{8}}{128 d^{5}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{9} x}{4 d^{8}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{9} x}{4 d^{8}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{8}}{128 d^{7}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{9} x}{5 d^{10}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{8}}{5 d^{9}}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{8}}{640 d^{9}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{7}}{5 d^{10} x}-\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{6}}{128 d^{9} x^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{5 d^{8} x^{3}}-\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{64 d^{7} x^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{5 d^{6} x^{5}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{16 d^{5} x^{6}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{7 d^{4} x^{7}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{8 d^{3} x^{8}}"," ",0,"-1/4/d^8*e^9*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-3/8/d^6*e^9*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-3/8/d^4*e^9/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+1/5/d^6*e^3/x^5*(-e^2*x^2+d^2)^(7/2)-3/16/d^5*e^2/x^6*(-e^2*x^2+d^2)^(7/2)+1/5/d^8*e^5/x^3*(-e^2*x^2+d^2)^(7/2)+1/5/d^10*e^7/x*(-e^2*x^2+d^2)^(7/2)+1/5/d^10*e^9*x*(-e^2*x^2+d^2)^(5/2)+1/4/d^8*e^9*x*(-e^2*x^2+d^2)^(3/2)+3/8/d^6*e^9*x*(-e^2*x^2+d^2)^(1/2)+3/8/d^4*e^9/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-13/64/d^7*e^4/x^4*(-e^2*x^2+d^2)^(7/2)-25/128/d^9*e^6/x^2*(-e^2*x^2+d^2)^(7/2)+1/7*e/d^4/x^7*(-e^2*x^2+d^2)^(7/2)-3/128/(d^2)^(1/2)/d^3*e^8*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5/d^9*e^8*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/8/d^3/x^8*(-e^2*x^2+d^2)^(7/2)+3/640/d^9*e^8*(-e^2*x^2+d^2)^(5/2)+1/128*(-e^2*x^2+d^2)^(3/2)/d^7*e^8+3/128*(-e^2*x^2+d^2)^(1/2)/d^5*e^8","B"
117,1,34,21,0.007000," ","int(x*(-x^2+1)^(1/2)/(1+x),x)","\frac{\sqrt{-x^{2}+1}\, x}{2}-\frac{\arcsin \left(x \right)}{2}-\sqrt{2 x -\left(x +1\right)^{2}+2}"," ",0,"1/2*(-x^2+1)^(1/2)*x-1/2*arcsin(x)-(-(1+x)^2+2+2*x)^(1/2)","A"
118,1,238,47,0.018000," ","int((-a^2*x^2+1)^(3/2)/x^2/(-a*x+1),x)","\frac{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}\, a^{2} x}{2}-\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a^{2} x -\frac{3 \sqrt{-a^{2} x^{2}+1}\, a^{2} x}{2}+\frac{a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}}\right)}{2 \sqrt{a^{2}}}-\frac{3 a^{2} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}}-a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\left(-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a \right)^{\frac{3}{2}} a}{3}+\frac{\left(-a^{2} x^{2}+1\right)^{\frac{3}{2}} a}{3}+\sqrt{-a^{2} x^{2}+1}\, a -\frac{\left(-a^{2} x^{2}+1\right)^{\frac{5}{2}}}{x}"," ",0,"-1/3*a*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(3/2)+1/2*a^2*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)*x+1/2*a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2))-1/x*(-a^2*x^2+1)^(5/2)-a^2*x*(-a^2*x^2+1)^(3/2)-3/2*a^2*x*(-a^2*x^2+1)^(1/2)-3/2*a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)/(-a^2*x^2+1)^(1/2)*x)+1/3*a*(-a^2*x^2+1)^(3/2)+a*(-a^2*x^2+1)^(1/2)-a*arctanh(1/(-a^2*x^2+1)^(1/2))","B"
119,1,147,104,0.014000," ","int(x^4/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","-\frac{3 d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{4}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x^{2}}{3 e^{3}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d x}{2 e^{4}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3}}{\left(x +\frac{d}{e}\right) e^{6}}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2}}{3 e^{5}}"," ",0,"-1/3*x^2*(-e^2*x^2+d^2)^(1/2)/e^3-5/3/e^5*d^2*(-e^2*x^2+d^2)^(1/2)+1/2*d/e^4*x*(-e^2*x^2+d^2)^(1/2)-3/2*d^3/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-d^3/e^6/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
120,1,120,81,0.011000," ","int(x^3/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","\frac{3 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{3}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x}{2 e^{3}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2}}{\left(x +\frac{d}{e}\right) e^{5}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, d}{e^{4}}"," ",0,"-1/2/e^3*x*(-e^2*x^2+d^2)^(1/2)+3/2*d^2/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+d/e^4*(-e^2*x^2+d^2)^(1/2)+d^2/e^5/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
121,1,97,71,0.010000," ","int(x^2/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","-\frac{d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{2}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d}{\left(x +\frac{d}{e}\right) e^{4}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{e^{3}}"," ",0,"-(-e^2*x^2+d^2)^(1/2)/e^3-1/(e^2)^(1/2)*d/e^2*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-d/e^4/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
122,1,74,48,0.010000," ","int(x/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{\left(x +\frac{d}{e}\right) e^{3}}"," ",0,"1/e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/e^3/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
123,1,29,29,0.006000," ","int(1/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","-\frac{-e x +d}{\sqrt{-e^{2} x^{2}+d^{2}}\, d e}"," ",0,"-(-e*x+d)/d/e/(-e^2*x^2+d^2)^(1/2)","A"
124,1,88,50,0.012000," ","int(1/x/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{\left(x +\frac{d}{e}\right) d^{2} e}"," ",0,"-1/d/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/d^2/e/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
125,1,108,75,0.012000," ","int(1/x^2/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","\frac{e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{2}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{\left(x +\frac{d}{e}\right) d^{3}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{d^{3} x}"," ",0,"-(-e^2*x^2+d^2)^(1/2)/d^3/x+e/d^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/d^3/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
126,1,133,101,0.014000," ","int(1/x^3/(e*x+d)/(-e^2*x^2+d^2)^(1/2),x)","-\frac{3 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{3}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e}{\left(x +\frac{d}{e}\right) d^{4}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e}{d^{4} x}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{2 d^{3} x^{2}}"," ",0,"e*(-e^2*x^2+d^2)^(1/2)/d^4/x-1/2*(-e^2*x^2+d^2)^(1/2)/d^3/x^2-3/2/d^3*e^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/d^4*e/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
127,1,208,112,0.021000," ","int(x^5/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","-\frac{x^{3}}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}+\frac{d \,x^{2}}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}+\frac{7 d^{2} x}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}-\frac{2 d^{2} x}{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{5}}-\frac{5 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{5}}+\frac{d^{4}}{3 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{7}}-\frac{3 d^{3}}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{6}}"," ",0,"-1/2/e^3*x^3/(-e^2*x^2+d^2)^(1/2)+7/2/(-e^2*x^2+d^2)^(1/2)*d^2/e^5*x-5/2/(e^2)^(1/2)*d^2/e^5*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+d/e^4*x^2/(-e^2*x^2+d^2)^(1/2)-3*d^3/e^6/(-e^2*x^2+d^2)^(1/2)+1/3*d^4/e^7/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-2/3*d^2/e^5/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
128,1,179,99,0.010000," ","int(x^4/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","-\frac{x^{2}}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}-\frac{2 d x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}+\frac{2 d x}{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{4}}+\frac{d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}-\frac{d^{3}}{3 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{6}}+\frac{3 d^{2}}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}"," ",0,"-1/e^3*x^2/(-e^2*x^2+d^2)^(1/2)+3*d^2/e^5/(-e^2*x^2+d^2)^(1/2)-2/(-e^2*x^2+d^2)^(1/2)*d/e^4*x+1/(e^2)^(1/2)*d/e^4*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/3*d^3/e^6/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+2/3*d/e^4/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
129,1,153,79,0.011000," ","int(x^3/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","\frac{2 x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}-\frac{2 x}{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{3}}-\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{3}}+\frac{d^{2}}{3 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{5}}-\frac{d}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}"," ",0,"2/(-e^2*x^2+d^2)^(1/2)/e^3*x-1/(e^2)^(1/2)/e^3*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-d/e^4/(-e^2*x^2+d^2)^(1/2)+1/3*d^2/e^5/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-2/3/e^3/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
130,1,48,52,0.008000," ","int(x^2/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","\frac{\left(-e x +d \right) \left(-e^{2} x^{2}+2 d e x +2 d^{2}\right)}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d \,e^{3}}"," ",0,"1/3*(-e*x+d)*(-e^2*x^2+2*d*e*x+2*d^2)/d/e^3/(-e^2*x^2+d^2)^(3/2)","A"
131,1,44,50,0.008000," ","int(x/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","\frac{\left(-e x +d \right) \left(e^{2} x^{2}+d e x +d^{2}\right)}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} e^{2}}"," ",0,"1/3*(-e*x+d)*(e^2*x^2+d*e*x+d^2)/d^2/e^2/(-e^2*x^2+d^2)^(3/2)","A"
132,1,46,50,0.007000," ","int(1/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","-\frac{\left(-e x +d \right) \left(-2 e^{2} x^{2}-2 d e x +d^{2}\right)}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} e}"," ",0,"-1/3*(-e*x+d)*(-2*e^2*x^2-2*d*e*x+d^2)/d^3/e/(-e^2*x^2+d^2)^(3/2)","A"
133,1,142,78,0.012000," ","int(1/x/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{3}}-\frac{2 e x}{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4}}+\frac{1}{3 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2} e}+\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}}"," ",0,"1/(-e^2*x^2+d^2)^(1/2)/d^3-1/(d^2)^(1/2)/d^3*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/3/d^2/e/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-2/3/d^4*e/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
134,1,188,106,0.017000," ","int(1/x^2/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","\frac{e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{4}}+\frac{2 e^{2} x}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}+\frac{2 e^{2} x}{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{5}}-\frac{1}{3 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3}}-\frac{e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{4}}-\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} x}"," ",0,"-1/d^3/x/(-e^2*x^2+d^2)^(1/2)+2/(-e^2*x^2+d^2)^(1/2)/d^5*e^2*x-1/(-e^2*x^2+d^2)^(1/2)/d^4*e+1/(d^2)^(1/2)/d^4*e*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/3/d^3/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+2/3*e^2/d^5/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
135,1,216,132,0.016000," ","int(1/x^3/(e*x+d)/(-e^2*x^2+d^2)^(3/2),x)","-\frac{5 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{5}}-\frac{2 e^{3} x}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}-\frac{2 e^{3} x}{3 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{6}}+\frac{e}{3 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4}}+\frac{5 e^{2}}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}+\frac{e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x}-\frac{1}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} x^{2}}"," ",0,"e/d^4/x/(-e^2*x^2+d^2)^(1/2)-2/(-e^2*x^2+d^2)^(1/2)/d^6*e^3*x-1/2/d^3/x^2/(-e^2*x^2+d^2)^(1/2)+5/2/(-e^2*x^2+d^2)^(1/2)/d^5*e^2-5/2/(d^2)^(1/2)/d^5*e^2*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/3/d^4*e/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-2/3/d^6*e^3/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
136,1,318,142,0.049000," ","int(x^7/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{x^{5}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}+\frac{d \,x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}+\frac{7 d^{2} x^{3}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}-\frac{5 d^{3} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6}}+\frac{2 d^{4} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7}}-\frac{4 d^{4} x}{15 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{7}}+\frac{d^{6}}{5 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{9}}+\frac{3 d^{5}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{8}}-\frac{19 d^{2} x}{6 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{7}}-\frac{8 d^{2} x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{7}}+\frac{7 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{7}}"," ",0,"-1/2/e^3*x^5/(-e^2*x^2+d^2)^(3/2)+7/6/(-e^2*x^2+d^2)^(3/2)*d^2/e^5*x^3-19/6/(-e^2*x^2+d^2)^(1/2)*d^2/e^7*x+7/2/(e^2)^(1/2)*d^2/e^7*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+d/e^4*x^4/(-e^2*x^2+d^2)^(3/2)-5*d^3/e^6*x^2/(-e^2*x^2+d^2)^(3/2)+3*d^5/e^8/(-e^2*x^2+d^2)^(3/2)+2/3*d^4/e^7*x/(-e^2*x^2+d^2)^(3/2)+1/5*d^6/e^9/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-4/15*d^4/e^7/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-8/15*d^2/e^7/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","B"
137,1,288,130,0.011000," ","int(x^6/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}-\frac{d \,x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}+\frac{5 d^{2} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}-\frac{2 d^{3} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6}}+\frac{4 d^{3} x}{15 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{6}}-\frac{d^{5}}{5 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{8}}-\frac{3 d^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7}}+\frac{2 d x}{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{6}}+\frac{8 d x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{6}}-\frac{d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{6}}"," ",0,"-1/e^3*x^4/(-e^2*x^2+d^2)^(3/2)+5/e^5*d^2*x^2/(-e^2*x^2+d^2)^(3/2)-3*d^4/e^7/(-e^2*x^2+d^2)^(3/2)-1/3/(-e^2*x^2+d^2)^(3/2)*d/e^4*x^3+2/3/(-e^2*x^2+d^2)^(1/2)*d/e^6*x-1/(e^2)^(1/2)*d/e^6*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2/3*d^3/e^6*x/(-e^2*x^2+d^2)^(3/2)-1/5*d^5/e^8/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+4/15*d^3/e^6/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+8/15*d/e^6/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","B"
138,1,259,108,0.010000," ","int(x^5/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","\frac{x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}-\frac{d \,x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}+\frac{2 d^{2} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}-\frac{4 d^{2} x}{15 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{5}}+\frac{d^{4}}{5 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{7}}+\frac{d^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6}}-\frac{2 x}{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}-\frac{8 x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{5}}+\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{5}}"," ",0,"1/3/(-e^2*x^2+d^2)^(3/2)/e^3*x^3-2/3/(-e^2*x^2+d^2)^(1/2)/e^5*x+1/(e^2)^(1/2)/e^5*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-d/e^4*x^2/(-e^2*x^2+d^2)^(3/2)+1/3*d^3/e^6/(-e^2*x^2+d^2)^(3/2)+2/3*d^2/e^5*x/(-e^2*x^2+d^2)^(3/2)+1/5*d^4/e^7/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-4/15*d^2/e^5/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-8/15/e^5/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","B"
139,1,70,73,0.008000," ","int(x^4/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{\left(-e x +d \right) \left(3 x^{4} e^{4}-12 x^{3} d \,e^{3}-12 d^{2} x^{2} e^{2}+8 d^{3} x e +8 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d \,e^{5}}"," ",0,"-1/15*(-e*x+d)*(3*e^4*x^4-12*d*e^3*x^3-12*d^2*e^2*x^2+8*d^3*e*x+8*d^4)/d/e^5/(-e^2*x^2+d^2)^(5/2)","A"
140,1,70,79,0.008000," ","int(x^3/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{\left(-e x +d \right) \left(-3 x^{4} e^{4}-3 x^{3} d \,e^{3}-3 d^{2} x^{2} e^{2}+2 d^{3} x e +2 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} e^{4}}"," ",0,"-1/15*(-e*x+d)*(-3*e^4*x^4-3*d*e^3*x^3-3*d^2*e^2*x^2+2*d^3*e*x+2*d^4)/d^2/e^4/(-e^2*x^2+d^2)^(5/2)","A"
141,1,70,83,0.009000," ","int(x^2/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","\frac{\left(-e x +d \right) \left(2 x^{4} e^{4}+2 x^{3} d \,e^{3}-3 d^{2} x^{2} e^{2}+2 d^{3} x e +2 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3} e^{3}}"," ",0,"1/15*(-e*x+d)*(2*e^4*x^4+2*d*e^3*x^3-3*d^2*e^2*x^2+2*d^3*e*x+2*d^4)/d^3/e^3/(-e^2*x^2+d^2)^(5/2)","A"
142,1,70,73,0.008000," ","int(x/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","\frac{\left(-e x +d \right) \left(-2 x^{4} e^{4}-2 x^{3} d \,e^{3}+3 d^{2} x^{2} e^{2}+3 d^{3} x e +3 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{4} e^{2}}"," ",0,"1/15*(-e*x+d)*(-2*e^4*x^4-2*d*e^3*x^3+3*d^2*e^2*x^2+3*d^3*e*x+3*d^4)/d^4/e^2/(-e^2*x^2+d^2)^(5/2)","A"
143,1,70,70,0.008000," ","int(1/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{\left(-e x +d \right) \left(8 x^{4} e^{4}+8 x^{3} d \,e^{3}-12 d^{2} x^{2} e^{2}-12 d^{3} x e +3 d^{4}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{5} e}"," ",0,"-1/15*(-e*x+d)*(8*e^4*x^4+8*d*e^3*x^3-12*d^2*e^2*x^2-12*d^3*e*x+3*d^4)/d^5/e/(-e^2*x^2+d^2)^(5/2)","A"
144,1,196,105,0.015000," ","int(1/x/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{4 e x}{15 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{4}}+\frac{1}{5 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2} e}+\frac{1}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3}}-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{5}}-\frac{8 e x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{6}}+\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}"," ",0,"1/3/(-e^2*x^2+d^2)^(3/2)/d^3+1/(-e^2*x^2+d^2)^(1/2)/d^5-1/(d^2)^(1/2)/d^5*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/5/d^2/e/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-4/15/d^4*e/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-8/15/d^6*e/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
145,1,268,136,0.016000," ","int(1/x^2/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","\frac{4 e^{2} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5}}+\frac{4 e^{2} x}{15 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{5}}-\frac{1}{5 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{3}}-\frac{e}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4}}-\frac{1}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} x}+\frac{e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{6}}+\frac{8 e^{2} x}{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7}}+\frac{8 e^{2} x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{7}}-\frac{e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}"," ",0,"-1/d^3/x/(-e^2*x^2+d^2)^(3/2)+4/3/(-e^2*x^2+d^2)^(3/2)/d^5*e^2*x+8/3/(-e^2*x^2+d^2)^(1/2)/d^7*e^2*x-1/3/(-e^2*x^2+d^2)^(3/2)/d^4*e-1/(-e^2*x^2+d^2)^(1/2)/d^6*e+1/(d^2)^(1/2)/d^6*e*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5/d^3/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+4/15*e^2/d^5/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+8/15*e^2/d^7/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
146,1,298,162,0.017000," ","int(1/x^3/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","-\frac{4 e^{3} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{6}}-\frac{4 e^{3} x}{15 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{6}}+\frac{e}{5 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{4}}+\frac{7 e^{2}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5}}+\frac{e}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4} x}-\frac{7 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{7}}-\frac{8 e^{3} x}{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{8}}-\frac{8 e^{3} x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{8}}-\frac{1}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} x^{2}}+\frac{7 e^{2}}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7}}"," ",0,"e/d^4/x/(-e^2*x^2+d^2)^(3/2)-4/3/(-e^2*x^2+d^2)^(3/2)/d^6*e^3*x-8/3/(-e^2*x^2+d^2)^(1/2)/d^8*e^3*x-1/2/d^3/x^2/(-e^2*x^2+d^2)^(3/2)+7/6/(-e^2*x^2+d^2)^(3/2)/d^5*e^2+7/2/(-e^2*x^2+d^2)^(1/2)/d^7*e^2-7/2/(d^2)^(1/2)/d^7*e^2*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/5/d^4*e/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-4/15/d^6*e^3/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-8/15/d^8*e^3/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
147,1,326,187,0.021000," ","int(1/x^4/(e*x+d)/(-e^2*x^2+d^2)^(5/2),x)","\frac{4 e^{4} x}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{7}}+\frac{4 e^{4} x}{15 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{7}}-\frac{e^{2}}{5 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{5}}-\frac{7 e^{3}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{6}}-\frac{3 e^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5} x}+\frac{7 e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{8}}+\frac{8 e^{4} x}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{9}}+\frac{8 e^{4} x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{9}}+\frac{e}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4} x^{2}}-\frac{7 e^{3}}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{8}}-\frac{1}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} x^{3}}"," ",0,"-3/d^5*e^2/x/(-e^2*x^2+d^2)^(3/2)+4/d^7*e^4*x/(-e^2*x^2+d^2)^(3/2)+8/d^9*e^4*x/(-e^2*x^2+d^2)^(1/2)+1/2*e/d^4/x^2/(-e^2*x^2+d^2)^(3/2)-7/6*e^3/d^6/(-e^2*x^2+d^2)^(3/2)-7/2*e^3/d^8/(-e^2*x^2+d^2)^(1/2)+7/2*e^3/d^8/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/3/d^3/x^3/(-e^2*x^2+d^2)^(3/2)-1/5/d^5*e^2/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+4/15/d^7*e^4/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+8/15/d^9*e^4/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x","A"
148,1,92,102,0.010000," ","int(x^3/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(2 e^{6} x^{6}+2 e^{5} x^{5} d -5 e^{4} x^{4} d^{2}-5 x^{3} d^{3} e^{3}-5 x^{2} d^{4} e^{2}+2 d^{5} x e +2 d^{6}\right)}{35 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{4} e^{4}}"," ",0,"-1/35*(-e*x+d)*(2*e^6*x^6+2*d*e^5*x^5-5*d^2*e^4*x^4-5*d^3*e^3*x^3-5*d^4*e^2*x^2+2*d^5*e*x+2*d^6)/d^4/e^4/(-e^2*x^2+d^2)^(7/2)","A"
149,1,92,107,0.010000," ","int(x^2/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(-8 e^{6} x^{6}-8 e^{5} x^{5} d +20 e^{4} x^{4} d^{2}+20 x^{3} d^{3} e^{3}-15 x^{2} d^{4} e^{2}+6 d^{5} x e +6 d^{6}\right)}{105 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{5} e^{3}}"," ",0,"1/105*(-e*x+d)*(-8*e^6*x^6-8*d*e^5*x^5+20*d^2*e^4*x^4+20*d^3*e^3*x^3-15*d^4*e^2*x^2+6*d^5*e*x+6*d^6)/d^5/e^3/(-e^2*x^2+d^2)^(7/2)","A"
150,1,100,58,0.014000," ","int(x^3/(a*x+1)/(-a^2*x^2+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, x}{2 a^{3}}+\frac{3 \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{2 \sqrt{a^{2}}\, a^{3}}+\frac{\sqrt{-a^{2} x^{2}+1}}{a^{4}}+\frac{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2}+2 \left(x +\frac{1}{a}\right) a}}{\left(x +\frac{1}{a}\right) a^{5}}"," ",0,"-1/2/a^3*x*(-a^2*x^2+1)^(1/2)+3/2/a^3/(a^2)^(1/2)*arctan((a^2)^(1/2)/(-a^2*x^2+1)^(1/2)*x)+1/a^4*(-a^2*x^2+1)^(1/2)+1/a^5/(x+1/a)*(-(x+1/a)^2*a^2+2*(x+1/a)*a)^(1/2)","A"
151,1,84,51,0.008000," ","int(x^2/(a*x+1)/(-a^2*x^2+1)^(1/2),x)","-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}\, a^{2}}-\frac{\sqrt{-a^{2} x^{2}+1}}{a^{3}}-\frac{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2}+2 \left(x +\frac{1}{a}\right) a}}{\left(x +\frac{1}{a}\right) a^{4}}"," ",0,"-(-a^2*x^2+1)^(1/2)/a^3-1/(a^2)^(1/2)/a^2*arctan((a^2)^(1/2)/(-a^2*x^2+1)^(1/2)*x)-1/a^4/(x+1/a)*(-(x+1/a)^2*a^2+2*(x+1/a)*a)^(1/2)","A"
152,1,65,32,0.009000," ","int(x/(a*x+1)/(-a^2*x^2+1)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}\, a}+\frac{\sqrt{-\left(x +\frac{1}{a}\right)^{2} a^{2}+2 \left(x +\frac{1}{a}\right) a}}{\left(x +\frac{1}{a}\right) a^{3}}"," ",0,"1/a/(a^2)^(1/2)*arctan((a^2)^(1/2)/(-a^2*x^2+1)^(1/2)*x)+1/a^3/(x+1/a)*(-(x+1/a)^2*a^2+2*(x+1/a)*a)^(1/2)","A"
153,1,22,24,0.006000," ","int(1/(a*x+1)/(-a^2*x^2+1)^(1/2),x)","\frac{a x -1}{\sqrt{-a^{2} x^{2}+1}\, a}"," ",0,"(a*x-1)/a/(-a^2*x^2+1)^(1/2)","A"
154,1,58,37,0.014000," ","int(1/x/(-a*x+1)/(-a^2*x^2+1)^(1/2),x)","-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}}{\left(x -\frac{1}{a}\right) a}"," ",0,"-1/a/(x-1/a)*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)-arctanh(1/(-a^2*x^2+1)^(1/2))","A"
155,1,73,58,0.013000," ","int(1/x^2/(-a*x+1)/(-a^2*x^2+1)^(1/2),x)","-a \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)-\frac{\sqrt{-a^{2} x^{2}+1}}{x}-\frac{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}}{x -\frac{1}{a}}"," ",0,"-1/(x-1/a)*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)-(-a^2*x^2+1)^(1/2)/x-a*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
156,1,94,78,0.013000," ","int(1/x^3/(-a*x+1)/(-a^2*x^2+1)^(1/2),x)","-\frac{3 a^{2} \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)}{2}-\frac{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}\, a}{x -\frac{1}{a}}-\frac{\sqrt{-a^{2} x^{2}+1}\, a}{x}-\frac{\sqrt{-a^{2} x^{2}+1}}{2 x^{2}}"," ",0,"-a/(x-1/a)*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)-a*(-a^2*x^2+1)^(1/2)/x-1/2*(-a^2*x^2+1)^(1/2)/x^2-3/2*a^2*arctanh(1/(-a^2*x^2+1)^(1/2))","A"
157,1,375,197,0.020000," ","int(x^5*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x)","\frac{5 d^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{4 \sqrt{e^{2}}\, e^{5}}-\frac{85 d^{9} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{64 \sqrt{e^{2}}\, e^{5}}-\frac{85 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{7} x}{64 e^{5}}+\frac{5 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{7} x}{4 e^{5}}-\frac{85 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{5} x}{96 e^{5}}+\frac{5 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{5} x}{6 e^{5}}-\frac{17 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{3} x}{24 e^{5}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{4}}{3 e^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} x^{2}}{9 e^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d x}{4 e^{5}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{4}}{3 \left(x +\frac{d}{e}\right)^{2} e^{8}}-\frac{29 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{2}}{63 e^{6}}"," ",0,"-1/9/e^4*x^2*(-e^2*x^2+d^2)^(7/2)-29/63*d^2/e^6*(-e^2*x^2+d^2)^(7/2)+1/4/e^5*d*x*(-e^2*x^2+d^2)^(7/2)-17/24/e^5*d^3*x*(-e^2*x^2+d^2)^(5/2)-85/96/e^5*d^5*x*(-e^2*x^2+d^2)^(3/2)-85/64*d^7*x*(-e^2*x^2+d^2)^(1/2)/e^5-85/64/e^5*d^9/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+2/3/e^6*d^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+5/6/e^5*d^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+5/4/e^5*d^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+5/4/e^5*d^9/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/3*d^4/e^8/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","A"
158,1,350,172,0.015000," ","int(x^4*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x)","-\frac{7 d^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{4}}+\frac{125 d^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{128 \sqrt{e^{2}}\, e^{4}}+\frac{125 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6} x}{128 e^{4}}-\frac{7 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{6} x}{8 e^{4}}+\frac{125 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4} x}{192 e^{4}}-\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{4} x}{12 e^{4}}+\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{2} x}{48 e^{4}}-\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{3}}{15 e^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} x}{8 e^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{3}}{3 \left(x +\frac{d}{e}\right)^{2} e^{7}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d}{7 e^{5}}"," ",0,"-1/8/e^4*x*(-e^2*x^2+d^2)^(7/2)+25/48*d^2/e^4*x*(-e^2*x^2+d^2)^(5/2)+125/192/e^4*d^4*x*(-e^2*x^2+d^2)^(3/2)+125/128*d^6*x*(-e^2*x^2+d^2)^(1/2)/e^4+125/128/e^4*d^8/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+2/7*d/e^5*(-e^2*x^2+d^2)^(7/2)-7/15/e^5*d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-7/12/e^4*d^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-7/8/e^4*d^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-7/8/e^4*d^8/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+1/3*d^3/e^7/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","B"
159,1,327,147,0.016000," ","int(x^3*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x)","\frac{d^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{3}}-\frac{5 d^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{3}}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} x}{8 e^{3}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{5} x}{2 e^{3}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} x}{12 e^{3}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{3} x}{3 e^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d x}{3 e^{3}}+\frac{4 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{2}}{15 e^{4}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{2}}{3 \left(x +\frac{d}{e}\right)^{2} e^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{7 e^{4}}"," ",0,"-1/7/e^4*(-e^2*x^2+d^2)^(7/2)-1/3*d/e^3*x*(-e^2*x^2+d^2)^(5/2)-5/12/e^3*d^3*x*(-e^2*x^2+d^2)^(3/2)-5/8*d^5*x*(-e^2*x^2+d^2)^(1/2)/e^3-5/8/e^3*d^7/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+4/15/e^4*d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/3/e^3*d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+1/2/e^3*d^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+1/2/e^3*d^7/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/3*d^2/e^6/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","B"
160,1,303,122,0.014000," ","int(x^2*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x)","-\frac{d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{2}}+\frac{5 d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}\, e^{2}}+\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x}{16 e^{2}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4} x}{8 e^{2}}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} x}{24 e^{2}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2} x}{12 e^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x}{6 e^{2}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d}{15 e^{3}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d}{3 \left(x +\frac{d}{e}\right)^{2} e^{5}}"," ",0,"1/6*x*(-e^2*x^2+d^2)^(5/2)/e^2+5/24/e^2*d^2*x*(-e^2*x^2+d^2)^(3/2)+5/16*d^4*x*(-e^2*x^2+d^2)^(1/2)/e^2+5/16/e^2*d^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/15*d/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/12*d^2/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-1/8*d^4/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-1/8*d^6/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+1/3*d/e^5/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","B"
161,1,198,116,0.013000," ","int(x*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x)","-\frac{d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{4 \sqrt{e^{2}}\, e}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3} x}{4 e}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d x}{6 e}-\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{15 e^{2}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} e^{4}}"," ",0,"-2/15/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/6/e*d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-1/4/e*d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-1/4/e*d^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/3/e^4/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","A"
162,1,194,92,0.006000," ","int((-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x)","\frac{5 d^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{5 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2} x}{8}+\frac{5 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{12}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{3 d e}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} d \,e^{3}}"," ",0,"1/3/e^3/d/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+1/3/e/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+5/12*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+5/8*d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+5/8*d^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
163,1,290,86,0.012000," ","int((-e^2*x^2+d^2)^(5/2)/x/(e*x+d)^2,x)","-\frac{d^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}-\frac{d^{3} e \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}}-\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d e x +\sqrt{-e^{2} x^{2}+d^{2}}\, d^{2}-\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e x}{3 d}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{5 d^{2}}-\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{15 d^{2}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} d^{2} e^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{3}"," ",0,"1/5/d^2*(-e^2*x^2+d^2)^(5/2)+1/3*(-e^2*x^2+d^2)^(3/2)+d^2*(-e^2*x^2+d^2)^(1/2)-d^4/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-8/15/d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-2/3/d*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-d*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-d^3*e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/3/d^2/e^2/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","B"
164,1,425,93,0.013000," ","int((-e^2*x^2+d^2)^(5/2)/x^2/(e*x+d)^2,x)","\frac{2 d^{3} e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{11 d^{2} e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{15 d^{2} e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{2} x}{8}+\frac{11 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{2} x}{8}-2 \sqrt{-e^{2} x^{2}+d^{2}}\, d e -\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2} x}{4 d^{2}}+\frac{11 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{2} x}{12 d^{2}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{3 d}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2} x}{d^{4}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{5 d^{3}}+\frac{11 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e}{15 d^{3}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} d^{3} e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{d^{4} x}"," ",0,"-1/d^4/x*(-e^2*x^2+d^2)^(7/2)-1/d^4*e^2*x*(-e^2*x^2+d^2)^(5/2)-5/4/d^2*e^2*x*(-e^2*x^2+d^2)^(3/2)-15/8*e^2*x*(-e^2*x^2+d^2)^(1/2)-15/8*d^2*e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2/5/d^3*e*(-e^2*x^2+d^2)^(5/2)-2/3/d*e*(-e^2*x^2+d^2)^(3/2)-2*d*e*(-e^2*x^2+d^2)^(1/2)+2*d^3*e/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+11/15/d^3*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+11/12/d^2*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+11/8*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+11/8*d^2*e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+1/3/d^3/e/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","B"
165,1,456,96,0.014000," ","int((-e^2*x^2+d^2)^(5/2)/x^3/(e*x+d)^2,x)","-\frac{d^{2} e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}-\frac{7 d \,e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{4 \sqrt{e^{2}}}+\frac{15 d \,e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{4 \sqrt{e^{2}}}+\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3} x}{4 d}-\frac{7 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{3} x}{4 d}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{2}}{2}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3} x}{2 d^{3}}-\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{3} x}{6 d^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}{6 d^{2}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3} x}{d^{5}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}{10 d^{4}}-\frac{14 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{2}}{15 d^{4}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} d^{4}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{d^{5} x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{2 d^{4} x^{2}}"," ",0,"2/d^5*e/x*(-e^2*x^2+d^2)^(7/2)+2/d^5*e^3*x*(-e^2*x^2+d^2)^(5/2)+5/2/d^3*e^3*x*(-e^2*x^2+d^2)^(3/2)+15/4/d*e^3*x*(-e^2*x^2+d^2)^(1/2)+15/4*d*e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/2/d^4/x^2*(-e^2*x^2+d^2)^(7/2)+1/10/d^4*e^2*(-e^2*x^2+d^2)^(5/2)+1/6/d^2*e^2*(-e^2*x^2+d^2)^(3/2)+1/2*e^2*(-e^2*x^2+d^2)^(1/2)-1/2*d^2*e^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-14/15/d^4*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-7/6/d^3*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-7/4/d*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-7/4*d*e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/3/d^4/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","B"
166,1,479,92,0.016000," ","int((-e^2*x^2+d^2)^(5/2)/x^4/(e*x+d)^2,x)","-\frac{d \,e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{17 e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{25 e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}+\frac{17 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{4} x}{8 d^{2}}-\frac{25 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4} x}{8 d^{2}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}{d}+\frac{17 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{4} x}{12 d^{4}}-\frac{25 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4} x}{12 d^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}{3 d^{3}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4} x}{3 d^{6}}+\frac{17 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{3}}{15 d^{5}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}{5 d^{5}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e}{3 \left(x +\frac{d}{e}\right)^{2} d^{5}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{3 d^{6} x}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{d^{5} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{3 d^{4} x^{3}}"," ",0,"17/12/d^4*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+17/8/d^2*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+1/3/d^5*e/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+1/d^5*e/x^2*(-e^2*x^2+d^2)^(7/2)-d*e^3/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-5/3/d^6*e^2/x*(-e^2*x^2+d^2)^(7/2)-5/3/d^6*e^4*x*(-e^2*x^2+d^2)^(5/2)-25/12/d^4*e^4*x*(-e^2*x^2+d^2)^(3/2)-25/8/d^2*e^4*x*(-e^2*x^2+d^2)^(1/2)+17/15/d^5*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+17/8*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/3/d^4/x^3*(-e^2*x^2+d^2)^(7/2)+1/5/d^5*e^3*(-e^2*x^2+d^2)^(5/2)+1/3/d^3*e^3*(-e^2*x^2+d^2)^(3/2)+1/d*e^3*(-e^2*x^2+d^2)^(1/2)-25/8*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)","B"
167,1,513,92,0.016000," ","int((-e^2*x^2+d^2)^(5/2)/x^5/(e*x+d)^2,x)","-\frac{5 e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}\, d}+\frac{5 e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, d}+\frac{5 e^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}}-\frac{5 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{5} x}{2 d^{3}}+\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5} x}{2 d^{3}}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}{8 d^{2}}-\frac{5 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{5} x}{3 d^{5}}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5} x}{3 d^{5}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}{24 d^{4}}+\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5} x}{3 d^{7}}-\frac{4 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{4}}{3 d^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}{8 d^{6}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e^{2}}{3 \left(x +\frac{d}{e}\right)^{2} d^{6}}+\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{3 d^{7} x}-\frac{9 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{8 d^{6} x^{2}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{3 d^{5} x^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{4 d^{4} x^{4}}"," ",0,"-1/3/d^6*e^2/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-5/3/d^5*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-5/2/d^3*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-5/2/d*e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+2/3/d^5*e/x^3*(-e^2*x^2+d^2)^(7/2)+4/3/d^7*e^5*x*(-e^2*x^2+d^2)^(5/2)+5/3/d^5*e^5*x*(-e^2*x^2+d^2)^(3/2)+5/2/d^3*e^5*x*(-e^2*x^2+d^2)^(1/2)+5/2/d*e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+4/3/d^7*e^3/x*(-e^2*x^2+d^2)^(7/2)-9/8/d^6*e^2/x^2*(-e^2*x^2+d^2)^(7/2)-4/3/d^6*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-5/8/d^2*e^4*(-e^2*x^2+d^2)^(1/2)+5/8*e^4/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/4/d^4/x^4*(-e^2*x^2+d^2)^(7/2)-1/8/d^6*e^4*(-e^2*x^2+d^2)^(5/2)-5/24/d^4*e^4*(-e^2*x^2+d^2)^(3/2)","B"
168,1,541,120,0.016000," ","int((-e^2*x^2+d^2)^(5/2)/x^6/(e*x+d)^2,x)","-\frac{e^{5} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{4 \sqrt{d^{2}}\, d}+\frac{23 e^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{2}}-\frac{23 e^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{2}}+\frac{23 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{6} x}{8 d^{4}}-\frac{23 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{6} x}{8 d^{4}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}{4 d^{3}}+\frac{23 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{6} x}{12 d^{6}}-\frac{23 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6} x}{12 d^{6}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}{12 d^{5}}-\frac{23 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6} x}{15 d^{8}}+\frac{23 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{5}}{15 d^{7}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}{20 d^{7}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e^{3}}{3 \left(x +\frac{d}{e}\right)^{2} d^{7}}-\frac{23 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{15 d^{8} x}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{4 d^{7} x^{2}}-\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{15 d^{6} x^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{2 d^{5} x^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{5 d^{4} x^{5}}"," ",0,"1/3/d^7*e^3/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+23/12/d^6*e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+23/8/d^4*e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+23/8/d^2*e^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-13/15/d^6*e^2/x^3*(-e^2*x^2+d^2)^(7/2)-23/15/d^8*e^4/x*(-e^2*x^2+d^2)^(7/2)-23/15/d^8*e^6*x*(-e^2*x^2+d^2)^(5/2)-23/12/d^6*e^6*x*(-e^2*x^2+d^2)^(3/2)-23/8/d^4*e^6*x*(-e^2*x^2+d^2)^(1/2)-23/8/d^2*e^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/2/d^5*e/x^4*(-e^2*x^2+d^2)^(7/2)+5/4/d^7*e^3/x^2*(-e^2*x^2+d^2)^(7/2)-1/4/d*e^5/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+23/15/d^7*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/5/d^4/x^5*(-e^2*x^2+d^2)^(7/2)+1/20/d^7*e^5*(-e^2*x^2+d^2)^(5/2)+1/12/d^5*e^5*(-e^2*x^2+d^2)^(3/2)+1/4/d^3*e^5*(-e^2*x^2+d^2)^(1/2)","B"
169,1,566,145,0.017000," ","int((-e^2*x^2+d^2)^(5/2)/x^7/(e*x+d)^2,x)","\frac{3 e^{6} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{16 \sqrt{d^{2}}\, d^{2}}-\frac{13 e^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{4 \sqrt{e^{2}}\, d^{3}}+\frac{13 e^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{4 \sqrt{e^{2}}\, d^{3}}-\frac{13 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{7} x}{4 d^{5}}+\frac{13 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{7} x}{4 d^{5}}-\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{6}}{16 d^{4}}-\frac{13 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{7} x}{6 d^{7}}+\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7} x}{6 d^{7}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6}}{16 d^{6}}+\frac{26 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{7} x}{15 d^{9}}-\frac{26 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{6}}{15 d^{8}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}{80 d^{8}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e^{4}}{3 \left(x +\frac{d}{e}\right)^{2} d^{8}}+\frac{26 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{15 d^{9} x}-\frac{23 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{16 d^{8} x^{2}}+\frac{16 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{15 d^{7} x^{3}}-\frac{17 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{24 d^{6} x^{4}}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{5 d^{5} x^{5}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{6 d^{4} x^{6}}"," ",0,"-13/6/d^7*e^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-13/4/d^5*e^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-13/4/d^3*e^7/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/3/d^8*e^4/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+2/5/d^5*e/x^5*(-e^2*x^2+d^2)^(7/2)+16/15/d^7*e^3/x^3*(-e^2*x^2+d^2)^(7/2)+13/4/d^5*e^7*x*(-e^2*x^2+d^2)^(1/2)+13/4/d^3*e^7/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+26/15/d^9*e^5/x*(-e^2*x^2+d^2)^(7/2)+26/15/d^9*e^7*x*(-e^2*x^2+d^2)^(5/2)+13/6/d^7*e^7*x*(-e^2*x^2+d^2)^(3/2)-17/24/d^6*e^2/x^4*(-e^2*x^2+d^2)^(7/2)-23/16/d^8*e^4/x^2*(-e^2*x^2+d^2)^(7/2)+3/16/d^2*e^6/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-26/15/d^8*e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-1/6/d^4/x^6*(-e^2*x^2+d^2)^(7/2)-3/80/d^8*e^6*(-e^2*x^2+d^2)^(5/2)-1/16/d^6*e^6*(-e^2*x^2+d^2)^(3/2)-3/16/d^4*e^6*(-e^2*x^2+d^2)^(1/2)","B"
170,1,591,170,0.018000," ","int((-e^2*x^2+d^2)^(5/2)/x^8/(e*x+d)^2,x)","-\frac{e^{7} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}\, d^{3}}+\frac{29 e^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{4}}-\frac{29 e^{8} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{4}}+\frac{29 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{8} x}{8 d^{6}}-\frac{29 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{8} x}{8 d^{6}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{7}}{8 d^{5}}+\frac{29 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{8} x}{12 d^{8}}-\frac{29 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{8} x}{12 d^{8}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{7}}{24 d^{7}}-\frac{29 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{8} x}{15 d^{10}}+\frac{29 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{7}}{15 d^{9}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{7}}{40 d^{9}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e^{5}}{3 \left(x +\frac{d}{e}\right)^{2} d^{9}}-\frac{29 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{6}}{15 d^{10} x}+\frac{13 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{5}}{8 d^{9} x^{2}}-\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{15 d^{8} x^{3}}+\frac{11 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{12 d^{7} x^{4}}-\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{5 d^{6} x^{5}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{3 d^{5} x^{6}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{7 d^{4} x^{7}}"," ",0,"1/3/d^9*e^5/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+29/12/d^8*e^8*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+29/8/d^6*e^8*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+29/8/d^4*e^8/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-3/5/d^6*e^2/x^5*(-e^2*x^2+d^2)^(7/2)+1/3/d^5*e/x^6*(-e^2*x^2+d^2)^(7/2)-19/15/d^8*e^4/x^3*(-e^2*x^2+d^2)^(7/2)-29/15/d^10*e^6/x*(-e^2*x^2+d^2)^(7/2)-29/15/d^10*e^8*x*(-e^2*x^2+d^2)^(5/2)-29/12/d^8*e^8*x*(-e^2*x^2+d^2)^(3/2)-29/8/d^6*e^8*x*(-e^2*x^2+d^2)^(1/2)-29/8/d^4*e^8/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+11/12/d^7*e^3/x^4*(-e^2*x^2+d^2)^(7/2)+13/8/d^9*e^5/x^2*(-e^2*x^2+d^2)^(7/2)-1/8/d^3*e^7/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+29/15/d^9*e^7*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/40/d^9*e^7*(-e^2*x^2+d^2)^(5/2)+1/24/d^7*e^7*(-e^2*x^2+d^2)^(3/2)+1/8/d^5*e^7*(-e^2*x^2+d^2)^(1/2)-1/7/d^4/x^7*(-e^2*x^2+d^2)^(7/2)","B"
171,1,198,109,0.017000," ","int(x^4/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x)","\frac{4 x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}-\frac{34 x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{4}}-\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}-\frac{d^{3}}{5 \left(x +\frac{d}{e}\right)^{2} \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{7}}+\frac{17 d^{2}}{15 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{6}}-\frac{2 d}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}"," ",0,"4/(-e^2*x^2+d^2)^(1/2)/e^4*x-1/(e^2)^(1/2)/e^4*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2*d/e^5/(-e^2*x^2+d^2)^(1/2)+17/15/e^6*d^2/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-34/15/e^4/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-1/5*d^3/e^7/(x+d/e)^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
172,1,65,87,0.007000," ","int(x^3/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x)","\frac{\left(-e x +d \right) \left(-2 e^{3} x^{3}+d \,e^{2} x^{2}+4 d^{2} e x +2 d^{3}\right)}{5 \left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d \,e^{4}}"," ",0,"1/5*(-e*x+d)*(-2*e^3*x^3+d*e^2*x^2+4*d^2*e*x+2*d^3)/(e*x+d)/d/e^4/(-e^2*x^2+d^2)^(3/2)","A"
173,1,65,77,0.009000," ","int(x^2/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x)","\frac{\left(-e x +d \right) \left(e^{3} x^{3}+2 d \,e^{2} x^{2}+8 d^{2} e x +4 d^{3}\right)}{15 \left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} e^{3}}"," ",0,"1/15*(-e*x+d)*(e^3*x^3+2*d*e^2*x^2+8*d^2*e*x+4*d^3)/(e*x+d)/d^2/e^3/(-e^2*x^2+d^2)^(3/2)","A"
174,1,64,79,0.010000," ","int(x/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x)","\frac{\left(-e x +d \right) \left(4 e^{3} x^{3}+8 d \,e^{2} x^{2}+2 d^{2} e x +d^{3}\right)}{15 \left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} e^{2}}"," ",0,"1/15*(-e*x+d)*(4*e^3*x^3+8*d*e^2*x^2+2*d^2*e*x+d^3)/(e*x+d)/d^3/e^2/(-e^2*x^2+d^2)^(3/2)","A"
175,1,66,79,0.008000," ","int(1/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x)","-\frac{\left(-e x +d \right) \left(-2 e^{3} x^{3}-4 d \,e^{2} x^{2}-d^{2} e x +2 d^{3}\right)}{5 \left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{4} e}"," ",0,"-1/5*(-e*x+d)*(-2*e^3*x^3-4*d*e^2*x^2-d^2*e*x+2*d^3)/(e*x+d)/d^4/e/(-e^2*x^2+d^2)^(3/2)","A"
176,1,187,104,0.012000," ","int(1/x/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x)","-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{4}}-\frac{16 e x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{5}}+\frac{1}{5 \left(x +\frac{d}{e}\right)^{2} \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2} e^{2}}+\frac{8}{15 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3} e}+\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{4}}"," ",0,"1/(-e^2*x^2+d^2)^(1/2)/d^4-1/(d^2)^(1/2)/d^4*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+8/15/d^3/e/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-16/15/d^5*e/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+1/5/d^2/e^2/(x+d/e)^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
177,1,234,130,0.012000," ","int(1/x^2/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x)","\frac{2 e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{5}}+\frac{2 e^{2} x}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}+\frac{26 e^{2} x}{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{6}}-\frac{1}{5 \left(x +\frac{d}{e}\right)^{2} \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3} e}-\frac{13}{15 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4}}-\frac{2 e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{5}}-\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x}"," ",0,"-1/d^4/x/(-e^2*x^2+d^2)^(1/2)+2/(-e^2*x^2+d^2)^(1/2)/d^6*e^2*x-2/(-e^2*x^2+d^2)^(1/2)/d^5*e+2/(d^2)^(1/2)/d^5*e*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-13/15/d^4/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+26/15/d^6*e^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-1/5/d^3/e/(x+d/e)^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
178,1,259,161,0.017000," ","int(1/x^3/(e*x+d)^2/(-e^2*x^2+d^2)^(3/2),x)","-\frac{9 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{6}}-\frac{4 e^{3} x}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{7}}-\frac{12 e^{3} x}{5 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{7}}+\frac{1}{5 \left(x +\frac{d}{e}\right)^{2} \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4}}+\frac{6 e}{5 \left(x +\frac{d}{e}\right) \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{5}}+\frac{9 e^{2}}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{6}}+\frac{2 e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} x}-\frac{1}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x^{2}}"," ",0,"2/d^5*e/x/(-e^2*x^2+d^2)^(1/2)-4/(-e^2*x^2+d^2)^(1/2)/d^7*e^3*x-1/2/d^4/x^2/(-e^2*x^2+d^2)^(1/2)+9/2/(-e^2*x^2+d^2)^(1/2)/d^6*e^2-9/2/(d^2)^(1/2)/d^6*e^2*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+6/5/d^5*e/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-12/5/d^7*e^3/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+1/5/d^4/(x+d/e)^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
179,1,212,155,0.019000," ","int(x^5/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","\frac{13 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{5}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x}{2 e^{5}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4}}{5 \left(x +\frac{d}{e}\right)^{3} e^{9}}-\frac{23 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3}}{15 \left(x +\frac{d}{e}\right)^{2} e^{8}}+\frac{127 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2}}{15 \left(x +\frac{d}{e}\right) e^{7}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d}{e^{6}}"," ",0,"-1/2*x*(-e^2*x^2+d^2)^(1/2)/e^5+13/2/(e^2)^(1/2)*d^2/e^5*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+3*d*(-e^2*x^2+d^2)^(1/2)/e^6+1/5*d^4/e^9/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-23/15*d^3/e^8/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+127/15/e^7*d^2/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
180,1,187,130,0.016000," ","int(x^4/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","-\frac{3 d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3}}{5 \left(x +\frac{d}{e}\right)^{3} e^{8}}+\frac{6 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2}}{5 \left(x +\frac{d}{e}\right)^{2} e^{7}}-\frac{24 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d}{5 \left(x +\frac{d}{e}\right) e^{6}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{e^{5}}"," ",0,"-(-e^2*x^2+d^2)^(1/2)/e^5-3/(e^2)^(1/2)*d/e^4*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/5*d^3/e^8/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+6/5*d^2/e^7/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-24/5/e^6*d/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
181,1,163,106,0.013000," ","int(x^3/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{3}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2}}{5 \left(x +\frac{d}{e}\right)^{3} e^{7}}-\frac{13 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d}{15 \left(x +\frac{d}{e}\right)^{2} e^{6}}+\frac{32 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{15 \left(x +\frac{d}{e}\right) e^{5}}"," ",0,"1/(e^2)^(1/2)/e^3*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/5*d^2/e^7/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-13/15*d/e^6/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+32/15/e^5/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
182,1,55,83,0.008000," ","int(x^2/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\left(-e x +d \right) \left(7 e^{2} x^{2}+6 d e x +2 d^{2}\right)}{15 \left(e x +d \right)^{2} \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{3}}"," ",0,"-1/15*(-e*x+d)*(7*e^2*x^2+6*d*e*x+2*d^2)/(e*x+d)^2/d/e^3/(-e^2*x^2+d^2)^(1/2)","A"
183,1,52,85,0.008000," ","int(x/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\left(-e x +d \right) \left(e^{2} x^{2}+3 d e x +d^{2}\right)}{5 \left(e x +d \right)^{2} \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e^{2}}"," ",0,"-1/5*(-e*x+d)*(e^2*x^2+3*d*e*x+d^2)/(e*x+d)^2/d^2/e^2/(-e^2*x^2+d^2)^(1/2)","A"
184,1,55,88,0.007000," ","int(1/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\left(-e x +d \right) \left(2 e^{2} x^{2}+6 d e x +7 d^{2}\right)}{15 \left(e x +d \right)^{2} \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3} e}"," ",0,"-1/15*(-e*x+d)*(2*e^2*x^2+6*d*e*x+7*d^2)/(e*x+d)^2/d^3/e/(-e^2*x^2+d^2)^(1/2)","A"
185,1,179,101,0.012000," ","int(1/x/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{3}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{5 \left(x +\frac{d}{e}\right)^{3} d^{2} e^{3}}+\frac{7 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{15 \left(x +\frac{d}{e}\right)^{2} d^{3} e^{2}}+\frac{22 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{15 \left(x +\frac{d}{e}\right) d^{4} e}"," ",0,"-1/(d^2)^(1/2)/d^3*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/5/d^2/e^3/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+7/15/d^3/e^2/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+22/15/d^4/e/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
186,1,199,130,0.013000," ","int(1/x^2/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","\frac{3 e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{4}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{5 \left(x +\frac{d}{e}\right)^{3} d^{3} e^{2}}-\frac{4 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{5 \left(x +\frac{d}{e}\right)^{2} d^{4} e}-\frac{19 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{5 \left(x +\frac{d}{e}\right) d^{5}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{d^{5} x}"," ",0,"-(-e^2*x^2+d^2)^(1/2)/d^5/x+3/(d^2)^(1/2)/d^4*e*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5/d^3/e^2/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-4/5/d^4/e/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-19/5/d^5/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
187,1,222,161,0.014000," ","int(1/x^3/(e*x+d)^3/(-e^2*x^2+d^2)^(1/2),x)","-\frac{13 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{5}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{5 \left(x +\frac{d}{e}\right)^{3} d^{4} e}+\frac{17 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{15 \left(x +\frac{d}{e}\right)^{2} d^{5}}+\frac{107 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e}{15 \left(x +\frac{d}{e}\right) d^{6}}+\frac{3 \sqrt{-e^{2} x^{2}+d^{2}}\, e}{d^{6} x}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{2 d^{5} x^{2}}"," ",0,"3*e*(-e^2*x^2+d^2)^(1/2)/d^6/x-1/2*(-e^2*x^2+d^2)^(1/2)/d^5/x^2-13/2/(d^2)^(1/2)/d^5*e^2*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/5/d^4/e/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+17/15/d^5/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+107/15/d^6*e/(x+d/e)*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)","A"
188,1,297,182,0.025000," ","int(x^5*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x)","\frac{20 d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e^{5}}-\frac{2 d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{5}}-\frac{2 \sqrt{-e^{2} x^{2}+d^{2}}\, d x}{e^{5}}+\frac{20 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2}}{e^{6}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{4}}{5 \left(x +\frac{d}{e}\right)^{4} e^{10}}-\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{3}}{5 \left(x +\frac{d}{e}\right)^{3} e^{9}}+\frac{10 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2}}{\left(x +\frac{d}{e}\right)^{2} e^{8}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{3 e^{6}}"," ",0,"-1/3/e^6*(-e^2*x^2+d^2)^(3/2)-2*d*x*(-e^2*x^2+d^2)^(1/2)/e^5-2/e^5*d^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/5*d^4/e^10/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-8/5/e^9*d^3/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+20/e^6*d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+20/e^5*d^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+10/e^8*d^2/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)","A"
189,1,273,142,0.014000," ","int(x^4*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x)","-\frac{10 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}+\frac{d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{4}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, x}{2 e^{4}}-\frac{10 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d}{e^{5}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{3}}{5 \left(x +\frac{d}{e}\right)^{4} e^{9}}+\frac{19 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2}}{15 \left(x +\frac{d}{e}\right)^{3} e^{8}}-\frac{6 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d}{\left(x +\frac{d}{e}\right)^{2} e^{7}}"," ",0,"1/2/e^4*x*(-e^2*x^2+d^2)^(1/2)+1/2/e^4*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/5*d^3/e^9/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+19/15/e^8*d^2/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-10/e^5*d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-10/e^4*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-6/e^7*d/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)","A"
190,1,212,134,0.011000," ","int(x^3*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x)","\frac{4 d \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e^{3}}+\frac{4 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{e^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2}}{5 \left(x +\frac{d}{e}\right)^{4} e^{8}}-\frac{14 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d}{15 \left(x +\frac{d}{e}\right)^{3} e^{7}}+\frac{3 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{\left(x +\frac{d}{e}\right)^{2} e^{6}}"," ",0,"1/5*d^2/e^8/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-14/15*d/e^7/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+4/e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+4/e^3*d/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+3/e^6/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)","A"
191,1,214,103,0.011000," ","int(x^2*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x)","-\frac{\arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e^{2}}-\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}{d \,e^{3}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d}{5 \left(x +\frac{d}{e}\right)^{4} e^{7}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{\left(x +\frac{d}{e}\right)^{2} d \,e^{5}}+\frac{3 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{5 \left(x +\frac{d}{e}\right)^{3} e^{6}}"," ",0,"-1/5*d/e^7/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+3/5/e^6/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-1/e^5/d/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-1/e^3/d*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-1/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
192,1,42,56,0.007000," ","int(x*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x)","-\frac{\left(-e x +d \right) \left(4 e x +d \right) \sqrt{-e^{2} x^{2}+d^{2}}}{15 \left(e x +d \right)^{3} d \,e^{2}}"," ",0,"-1/15*(-e*x+d)*(4*e*x+d)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^3/e^2/d","A"
193,1,43,59,0.006000," ","int((-e^2*x^2+d^2)^(1/2)/(e*x+d)^4,x)","-\frac{\left(-e x +d \right) \left(e x +4 d \right) \sqrt{-e^{2} x^{2}+d^{2}}}{15 \left(e x +d \right)^{3} d^{2} e}"," ",0,"-1/15*(-e*x+d)*(e*x+4*d)*(-e^2*x^2+d^2)^(1/2)/(e*x+d)^3/d^2/e","A"
194,1,196,96,0.013000," ","int((-e^2*x^2+d^2)^(1/2)/x/(e*x+d)^4,x)","-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{2}}+\frac{\sqrt{-e^{2} x^{2}+d^{2}}}{d^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{5 \left(x +\frac{d}{e}\right)^{4} d^{2} e^{4}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{5 \left(x +\frac{d}{e}\right)^{3} d^{3} e^{3}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{\left(x +\frac{d}{e}\right)^{2} d^{4} e^{2}}"," ",0,"1/5/d^2/e^4/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+2/5/e^3/d^3/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+1/d^4*(-e^2*x^2+d^2)^(1/2)-1/d^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/d^4/e^2/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)","B"
195,1,361,127,0.012000," ","int((-e^2*x^2+d^2)^(1/2)/x^2/(e*x+d)^4,x)","\frac{4 e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{3}}+\frac{e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, d^{4}}-\frac{e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, d^{4}}-\frac{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{2} x}{d^{6}}-\frac{4 \sqrt{-e^{2} x^{2}+d^{2}}\, e}{d^{5}}+\frac{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e}{d^{5}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{5 \left(x +\frac{d}{e}\right)^{4} d^{3} e^{3}}-\frac{11 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{15 \left(x +\frac{d}{e}\right)^{3} d^{4} e^{2}}-\frac{3 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{\left(x +\frac{d}{e}\right)^{2} d^{5} e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{d^{6} x}"," ",0,"-1/5/d^3/e^3/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-11/15/d^4/e^2/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-1/d^6/x*(-e^2*x^2+d^2)^(3/2)-1/d^6*e^2*x*(-e^2*x^2+d^2)^(1/2)-1/d^4*e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-4/d^5*e*(-e^2*x^2+d^2)^(1/2)+4/d^3*e/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/d^5*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+1/d^4*e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-3/d^5/e/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)","B"
196,1,389,161,0.013000," ","int((-e^2*x^2+d^2)^(1/2)/x^3/(e*x+d)^4,x)","-\frac{19 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{4}}-\frac{4 e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, d^{5}}+\frac{4 e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, d^{5}}+\frac{4 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3} x}{d^{7}}+\frac{19 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{2}}{2 d^{6}}-\frac{4 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{2}}{d^{6}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{5 \left(x +\frac{d}{e}\right)^{4} d^{4} e^{2}}+\frac{16 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{15 \left(x +\frac{d}{e}\right)^{3} d^{5} e}+\frac{6 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{\left(x +\frac{d}{e}\right)^{2} d^{6}}+\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{d^{7} x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{2 d^{6} x^{2}}"," ",0,"1/5/d^4/e^2/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+16/15/d^5/e/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)+4/d^7*e/x*(-e^2*x^2+d^2)^(3/2)+4/d^7*e^3*x*(-e^2*x^2+d^2)^(1/2)+4/d^5*e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/2/d^6/x^2*(-e^2*x^2+d^2)^(3/2)+19/2/d^6*e^2*(-e^2*x^2+d^2)^(1/2)-19/2/d^4*e^2/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-4/d^6*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)-4/d^5*e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+6/d^6/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)","B"
197,1,412,186,0.019000," ","int((-e^2*x^2+d^2)^(1/2)/x^4/(e*x+d)^4,x)","\frac{18 e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{5}}+\frac{10 e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, d^{6}}-\frac{10 e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, d^{6}}-\frac{10 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4} x}{d^{8}}-\frac{18 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}{d^{7}}+\frac{10 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{3}}{d^{7}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{5 \left(x +\frac{d}{e}\right)^{4} d^{5} e}-\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}}}{5 \left(x +\frac{d}{e}\right)^{3} d^{6}}-\frac{10 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e}{\left(x +\frac{d}{e}\right)^{2} d^{7}}-\frac{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}{d^{8} x}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{d^{7} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{3 d^{6} x^{3}}"," ",0,"-1/5/d^5/e/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-7/5/d^6/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)-10/d^8*e^2/x*(-e^2*x^2+d^2)^(3/2)-10/d^8*e^4*x*(-e^2*x^2+d^2)^(1/2)-10/d^6*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+2/d^7*e/x^2*(-e^2*x^2+d^2)^(3/2)-18/d^7*e^3*(-e^2*x^2+d^2)^(1/2)+18/d^5*e^3/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/3/d^6/x^3*(-e^2*x^2+d^2)^(3/2)+10/d^7*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)+10/d^6*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-10/d^7*e/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)","B"
198,1,416,218,0.026000," ","int(x^5*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x)","\frac{35 d^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{5}}-\frac{5 d^{7} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{4 \sqrt{e^{2}}\, e^{5}}+\frac{35 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{5} x}{2 e^{5}}-\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{5} x}{4 e^{5}}+\frac{35 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{3} x}{3 e^{5}}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{3} x}{6 e^{5}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d x}{3 e^{5}}+\frac{28 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{2}}{3 e^{6}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{4}}{\left(x +\frac{d}{e}\right)^{4} e^{10}}+\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{3}}{\left(x +\frac{d}{e}\right)^{3} e^{9}}+\frac{22 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{2}}{3 \left(x +\frac{d}{e}\right)^{2} e^{8}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{7 e^{6}}"," ",0,"d^4/e^10/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+8*d^3/e^9/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+22/3*d^2/e^8/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+35/3*d^3/e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+35/2*d^5/e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+35/2*d^7/e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-2/3/e^5*d*x*(-e^2*x^2+d^2)^(5/2)-5/6/e^5*d^3*x*(-e^2*x^2+d^2)^(3/2)-5/4*d^5*x*(-e^2*x^2+d^2)^(1/2)/e^5-5/4/e^5*d^7/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/7/e^6*(-e^2*x^2+d^2)^(7/2)+28/3*d^2/e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)","A"
199,1,393,194,0.015000," ","int(x^4*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x)","-\frac{61 d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{4 \sqrt{e^{2}}\, e^{4}}+\frac{5 d^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{16 \sqrt{e^{2}}\, e^{4}}-\frac{61 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{4} x}{4 e^{4}}+\frac{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{4} x}{16 e^{4}}-\frac{61 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{2} x}{6 e^{4}}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{2} x}{24 e^{4}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} x}{6 e^{4}}-\frac{122 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d}{15 e^{5}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{3}}{\left(x +\frac{d}{e}\right)^{4} e^{9}}-\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{2}}{\left(x +\frac{d}{e}\right)^{3} e^{8}}-\frac{22 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d}{3 \left(x +\frac{d}{e}\right)^{2} e^{7}}"," ",0,"-d^3/e^9/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-7*d^2/e^8/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-22/3*d/e^7/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-61/6*d^2/e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-61/4*d^4/e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-61/4*d^6/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+5/24/e^4*d^2*x*(-e^2*x^2+d^2)^(3/2)+5/16/(e^2)^(1/2)*d^6/e^4*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+5/16*(-e^2*x^2+d^2)^(1/2)*d^4/e^4*x-122/15*d/e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/6/e^4*x*(-e^2*x^2+d^2)^(5/2)","B"
200,1,285,168,0.017000," ","int(x^3*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x)","\frac{27 d^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{3}}+\frac{27 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{3} x}{2 e^{3}}+\frac{9 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d x}{e^{3}}+\frac{36 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{5 e^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d^{2}}{\left(x +\frac{d}{e}\right)^{4} e^{8}}+\frac{6 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d}{\left(x +\frac{d}{e}\right)^{3} e^{7}}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{2} e^{6}}"," ",0,"d^2/e^8/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+6*d/e^7/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+7/e^6/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+36/5/e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+9*d/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+27/2*d^3/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+27/2*d^5/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","A"
201,1,288,160,0.012000," ","int(x^2*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x)","-\frac{95 d^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, e^{2}}-\frac{95 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{2} x}{8 e^{2}}-\frac{95 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{12 e^{2}}-\frac{19 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{3 d \,e^{3}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} d}{\left(x +\frac{d}{e}\right)^{4} e^{7}}-\frac{19 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} d \,e^{5}}-\frac{5 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{3} e^{6}}"," ",0,"-d/e^7/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-5/e^6/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-19/3/d/e^5/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-19/3/d/e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-95/12/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-95/8*d^2/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-95/8*d^4/e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","A"
202,1,290,118,0.011000," ","int(x*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x)","\frac{10 d^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}\, e}+\frac{10 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d x}{e}+\frac{20 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{3 d e}+\frac{16 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{3 d^{2} e^{2}}+\frac{4 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{3} d \,e^{5}}+\frac{16 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} d^{2} e^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{4} e^{6}}"," ",0,"1/e^6/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+4/d/e^5/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+16/3/d^2/e^4/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+16/3/d^2/e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+20/3/d/e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+10*d/e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+10*d^3/e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
203,1,284,99,0.007000," ","int((-e^2*x^2+d^2)^(5/2)/(e*x+d)^4,x)","-\frac{15 d^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}}-\frac{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, x}{2}-\frac{5 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} x}{d^{2}}-\frac{4 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{d^{3} e}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{4} d \,e^{5}}-\frac{3 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{3} d^{2} e^{4}}-\frac{4 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{2} d^{3} e^{3}}"," ",0,"-1/e^5/d/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-3/e^4/d^2/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-4/e^3/d^3/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-4/e/d^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-5/d^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-15/2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-15/2*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
204,1,378,81,0.012000," ","int((-e^2*x^2+d^2)^(5/2)/x/(e*x+d)^4,x)","-\frac{d^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{4 d e \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{\sqrt{e^{2}}}+\frac{4 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e x}{d}+\frac{8 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e x}{3 d^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}}}{3 d^{2}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}{5 d^{4}}+\frac{32 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}}}{15 d^{4}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{4} d^{2} e^{4}}+\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{3} d^{3} e^{3}}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} d^{4} e^{2}}+\sqrt{-e^{2} x^{2}+d^{2}}"," ",0,"-1/(d^2)^(1/2)*d^2*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+1/d^2/e^4/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+2/d^3/e^3/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+7/3/d^4/e^2/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+8/3/d^3*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+4/d*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+(-e^2*x^2+d^2)^(1/2)+4*d*e/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)+1/5/d^4*(-e^2*x^2+d^2)^(5/2)+1/3/d^2*(-e^2*x^2+d^2)^(3/2)+32/15/d^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)","B"
205,1,515,86,0.013000," ","int((-e^2*x^2+d^2)^(5/2)/x^2/(e*x+d)^4,x)","\frac{4 d e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}}+\frac{7 e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{15 e^{2} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}}-\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{2} x}{8 d^{2}}+\frac{7 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{2} x}{8 d^{2}}-\frac{4 \sqrt{-e^{2} x^{2}+d^{2}}\, e}{d}-\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2} x}{4 d^{4}}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{2} x}{12 d^{4}}-\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}{3 d^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2} x}{d^{6}}-\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}{5 d^{5}}+\frac{7 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e}{15 d^{5}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{4} d^{3} e^{3}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{3} d^{4} e^{2}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{3 \left(x +\frac{d}{e}\right)^{2} d^{5} e}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{d^{6} x}"," ",0,"-15/8/(e^2)^(1/2)*e^2*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-1/d^6*e^2*x*(-e^2*x^2+d^2)^(5/2)-5/4/d^4*e^2*x*(-e^2*x^2+d^2)^(3/2)-15/8/d^2*e^2*x*(-e^2*x^2+d^2)^(1/2)-1/d^3/e^3/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-1/d^4/e^2/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-1/3/d^5/e/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+7/12/d^4*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+7/8/d^2*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+4/(d^2)^(1/2)*d*e*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-4/d*e*(-e^2*x^2+d^2)^(1/2)-4/5/d^5*e*(-e^2*x^2+d^2)^(5/2)-4/3/d^3*e*(-e^2*x^2+d^2)^(3/2)-1/d^6/x*(-e^2*x^2+d^2)^(7/2)+7/15/d^5*e*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+7/8*e^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)","B"
206,1,504,98,0.013000," ","int((-e^2*x^2+d^2)^(5/2)/x^3/(e*x+d)^4,x)","-\frac{15 e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}\, d}+\frac{15 e^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, d}-\frac{15 e^{2} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}}+\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3} x}{2 d^{3}}-\frac{15 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{3} x}{2 d^{3}}+\frac{15 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{2}}{2 d^{2}}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3} x}{d^{5}}-\frac{5 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{3} x}{d^{5}}+\frac{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}{2 d^{4}}+\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3} x}{d^{7}}+\frac{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}{2 d^{6}}-\frac{4 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{2}}{d^{6}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{4} d^{4} e^{2}}-\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{2} d^{6}}+\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{d^{7} x}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{2 d^{6} x^{2}}"," ",0,"-15/2/(d^2)^(1/2)*e^2*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+4/d^7*e/x*(-e^2*x^2+d^2)^(7/2)+4/d^7*e^3*x*(-e^2*x^2+d^2)^(5/2)+5/d^5*e^3*x*(-e^2*x^2+d^2)^(3/2)+15/2/d^3*e^3*x*(-e^2*x^2+d^2)^(1/2)+15/2/d*e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/d^4/e^2/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-5/d^5*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-15/2/d^3*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-15/2/d*e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/2/d^6/x^2*(-e^2*x^2+d^2)^(7/2)+3/2/d^6*e^2*(-e^2*x^2+d^2)^(5/2)+5/2/d^4*e^2*(-e^2*x^2+d^2)^(3/2)+15/2/d^2*e^2*(-e^2*x^2+d^2)^(1/2)-2/d^6/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-4/d^6*e^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)","B"
207,1,575,123,0.018000," ","int((-e^2*x^2+d^2)^(5/2)/x^4/(e*x+d)^4,x)","\frac{10 e^{3} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d}+\frac{65 e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{4 \sqrt{e^{2}}\, d^{2}}-\frac{65 e^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{4 \sqrt{e^{2}}\, d^{2}}-\frac{65 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4} x}{4 d^{4}}+\frac{65 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{4} x}{4 d^{4}}-\frac{10 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}{d^{3}}-\frac{65 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4} x}{6 d^{6}}+\frac{65 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{4} x}{6 d^{6}}-\frac{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}{3 d^{5}}-\frac{26 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4} x}{3 d^{8}}-\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}{d^{7}}+\frac{26 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{3}}{3 d^{7}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{4} d^{5} e}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{3} d^{6}}+\frac{14 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e}{3 \left(x +\frac{d}{e}\right)^{2} d^{7}}-\frac{26 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{3 d^{8} x}+\frac{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{d^{7} x^{2}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{3 d^{6} x^{3}}"," ",0,"-26/3/d^8*e^4*x*(-e^2*x^2+d^2)^(5/2)-65/6/d^6*e^4*x*(-e^2*x^2+d^2)^(3/2)-65/4/d^4*e^4*x*(-e^2*x^2+d^2)^(1/2)-65/4/d^2*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+2/d^7*e/x^2*(-e^2*x^2+d^2)^(7/2)-1/d^5/e/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+14/3/d^7*e/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+65/6/d^6*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+65/4/d^4*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+65/4/d^2*e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-26/3/d^8*e^2/x*(-e^2*x^2+d^2)^(7/2)+10/(d^2)^(1/2)/d*e^3*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/3/d^6/x^3*(-e^2*x^2+d^2)^(7/2)-2/d^7*e^3*(-e^2*x^2+d^2)^(5/2)-10/3/d^5*e^3*(-e^2*x^2+d^2)^(3/2)-10/d^3*e^3*(-e^2*x^2+d^2)^(1/2)+26/3/d^7*e^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+1/d^6/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)","B"
208,1,600,148,0.017000," ","int((-e^2*x^2+d^2)^(5/2)/x^5/(e*x+d)^4,x)","-\frac{95 e^{4} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{8 \sqrt{d^{2}}\, d^{2}}-\frac{55 e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{2 \sqrt{e^{2}}\, d^{3}}+\frac{55 e^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, d^{3}}+\frac{55 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5} x}{2 d^{5}}-\frac{55 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{5} x}{2 d^{5}}+\frac{95 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}{8 d^{4}}+\frac{55 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5} x}{3 d^{7}}-\frac{55 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{5} x}{3 d^{7}}+\frac{95 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}{24 d^{6}}+\frac{44 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5} x}{3 d^{9}}+\frac{19 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}{8 d^{8}}-\frac{44 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{4}}{3 d^{8}}+\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}}}{\left(x +\frac{d}{e}\right)^{4} d^{6}}-\frac{2 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e}{\left(x +\frac{d}{e}\right)^{3} d^{7}}-\frac{23 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e^{2}}{3 \left(x +\frac{d}{e}\right)^{2} d^{8}}+\frac{44 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{3 d^{9} x}-\frac{37 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{8 d^{8} x^{2}}+\frac{4 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{3 d^{7} x^{3}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{4 d^{6} x^{4}}"," ",0,"4/3/d^7*e/x^3*(-e^2*x^2+d^2)^(7/2)-37/8/d^8*e^2/x^2*(-e^2*x^2+d^2)^(7/2)+44/3/d^9*e^3/x*(-e^2*x^2+d^2)^(7/2)+44/3/d^9*e^5*x*(-e^2*x^2+d^2)^(5/2)+55/3/d^7*e^5*x*(-e^2*x^2+d^2)^(3/2)+55/2/d^5*e^5*x*(-e^2*x^2+d^2)^(1/2)+55/2/d^3*e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)-2/d^7*e/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-23/3/d^8*e^2/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-55/3/d^7*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-55/2/d^5*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-55/2/d^3*e^5/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-95/8/(d^2)^(1/2)/d^2*e^4*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/4/d^6/x^4*(-e^2*x^2+d^2)^(7/2)+19/8/d^8*e^4*(-e^2*x^2+d^2)^(5/2)+95/24/d^6*e^4*(-e^2*x^2+d^2)^(3/2)+95/8/d^4*e^4*(-e^2*x^2+d^2)^(1/2)+1/d^6/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)-44/3/d^8*e^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)","B"
209,1,628,172,0.018000," ","int((-e^2*x^2+d^2)^(5/2)/x^6/(e*x+d)^4,x)","\frac{27 e^{5} \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{2 \sqrt{d^{2}}\, d^{3}}+\frac{333 e^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{4}}-\frac{333 e^{6} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{8 \sqrt{e^{2}}\, d^{4}}-\frac{333 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{6} x}{8 d^{6}}+\frac{333 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, e^{6} x}{8 d^{6}}-\frac{27 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}{2 d^{5}}-\frac{111 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{6} x}{4 d^{8}}+\frac{111 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} e^{6} x}{4 d^{8}}-\frac{9 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{5}}{2 d^{7}}-\frac{111 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6} x}{5 d^{10}}-\frac{27 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}{10 d^{9}}+\frac{111 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} e^{5}}{5 d^{9}}-\frac{\left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e}{\left(x +\frac{d}{e}\right)^{4} d^{7}}+\frac{3 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e^{2}}{\left(x +\frac{d}{e}\right)^{3} d^{8}}+\frac{11 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{7}{2}} e^{3}}{\left(x +\frac{d}{e}\right)^{2} d^{9}}-\frac{111 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{4}}{5 d^{10} x}+\frac{17 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{3}}{2 d^{9} x^{2}}-\frac{16 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e^{2}}{5 d^{8} x^{3}}+\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} e}{d^{7} x^{4}}-\frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}{5 d^{6} x^{5}}"," ",0,"1/d^7*e/x^4*(-e^2*x^2+d^2)^(7/2)-16/5/d^8*e^2/x^3*(-e^2*x^2+d^2)^(7/2)-111/5/d^10*e^4/x*(-e^2*x^2+d^2)^(7/2)-111/5/d^10*e^6*x*(-e^2*x^2+d^2)^(5/2)-111/4/d^8*e^6*x*(-e^2*x^2+d^2)^(3/2)-333/8/d^6*e^6*x*(-e^2*x^2+d^2)^(1/2)-333/8/d^4*e^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+17/2/d^9*e^3/x^2*(-e^2*x^2+d^2)^(7/2)+333/8/d^4*e^6/(e^2)^(1/2)*arctan((e^2)^(1/2)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x)-1/d^7*e/(x+d/e)^4*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+3/d^8*e^2/(x+d/e)^3*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+11/d^9*e^3/(x+d/e)^2*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(7/2)+111/4/d^8*e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+333/8/d^6*e^6*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+27/2/(d^2)^(1/2)/d^3*e^5*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)-1/5/d^6/x^5*(-e^2*x^2+d^2)^(7/2)-27/10/d^9*e^5*(-e^2*x^2+d^2)^(5/2)-9/2/d^7*e^5*(-e^2*x^2+d^2)^(3/2)-27/2/d^5*e^5*(-e^2*x^2+d^2)^(1/2)+111/5/d^9*e^5*(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)","B"
210,1,200,85,0.018000," ","int(x^2*(-a^2*x^2+1)^(1/2)/(-a*x+1)^4,x)","-\frac{\arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}}\right)}{\sqrt{a^{2}}\, a^{2}}+\frac{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}}{a^{3}}+\frac{\left(-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a \right)^{\frac{3}{2}}}{\left(x -\frac{1}{a}\right)^{2} a^{5}}+\frac{3 \left(-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a \right)^{\frac{3}{2}}}{5 \left(x -\frac{1}{a}\right)^{3} a^{6}}+\frac{\left(-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a \right)^{\frac{3}{2}}}{5 \left(x -\frac{1}{a}\right)^{4} a^{7}}"," ",0,"1/a^5/(x-1/a)^2*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(3/2)+1/a^3*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)-1/a^2/(a^2)^(1/2)*arctan((a^2)^(1/2)/(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)*x)+1/5/a^7/(x-1/a)^4*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(3/2)+3/5/a^6/(x-1/a)^3*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(3/2)","B"
211,1,44,76,0.007000," ","int(x^2*(-a^2*x^2+1)^(1/2)/(-a*x+1)^5,x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \left(23 a^{2} x^{2}-10 a x +2\right) \left(a x +1\right)}{105 \left(a x -1\right)^{4} a^{3}}"," ",0,"1/105*(-a^2*x^2+1)^(1/2)*(23*a^2*x^2-10*a*x+2)*(a*x+1)/(a*x-1)^4/a^3","A"
212,1,132,181,0.011000," ","int(x^3/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(-64 e^{9} x^{9}-256 e^{8} x^{8} d -224 e^{7} x^{7} d^{2}+384 e^{6} x^{6} d^{3}+776 e^{5} x^{5} d^{4}+160 x^{4} d^{5} e^{4}-540 x^{3} d^{6} e^{3}+315 x^{2} d^{7} e^{2}+360 d^{8} x e +90 d^{9}\right)}{5005 \left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{7} e^{4}}"," ",0,"1/5005*(-e*x+d)*(-64*e^9*x^9-256*d*e^8*x^8-224*d^2*e^7*x^7+384*d^3*e^6*x^6+776*d^4*e^5*x^5+160*d^5*e^4*x^4-540*d^6*e^3*x^3+315*d^7*e^2*x^2+360*d^8*e*x+90*d^9)/(e*x+d)^3/d^7/e^4/(-e^2*x^2+d^2)^(7/2)","A"
213,1,132,181,0.013000," ","int(x^2/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(112 e^{9} x^{9}+448 e^{8} x^{8} d +392 e^{7} x^{7} d^{2}-672 e^{6} x^{6} d^{3}-1358 e^{5} x^{5} d^{4}-280 x^{4} d^{5} e^{4}+945 x^{3} d^{6} e^{3}+700 x^{2} d^{7} e^{2}+800 d^{8} x e +200 d^{9}\right)}{6435 \left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{8} e^{3}}"," ",0,"1/6435*(-e*x+d)*(112*e^9*x^9+448*d*e^8*x^8+392*d^2*e^7*x^7-672*d^3*e^6*x^6-1358*d^4*e^5*x^5-280*d^5*e^4*x^4+945*d^6*e^3*x^3+700*d^7*e^2*x^2+800*d^8*e*x+200*d^9)/(e*x+d)^3/d^8/e^3/(-e^2*x^2+d^2)^(7/2)","A"
214,1,132,183,0.011000," ","int(x/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(-512 e^{9} x^{9}-2048 e^{8} x^{8} d -1792 e^{7} x^{7} d^{2}+3072 e^{6} x^{6} d^{3}+6208 e^{5} x^{5} d^{4}+1280 x^{4} d^{5} e^{4}-4320 x^{3} d^{6} e^{3}-3200 x^{2} d^{7} e^{2}+20 d^{8} x e +5 d^{9}\right)}{6435 \left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{9} e^{2}}"," ",0,"-1/6435*(-e*x+d)*(-512*e^9*x^9-2048*d*e^8*x^8-1792*d^2*e^7*x^7+3072*d^3*e^6*x^6+6208*d^4*e^5*x^5+1280*d^5*e^4*x^4-4320*d^6*e^3*x^3-3200*d^7*e^2*x^2+20*d^8*e*x+5*d^9)/(e*x+d)^3/d^9/e^2/(-e^2*x^2+d^2)^(7/2)","A"
215,1,132,177,0.010000," ","int(1/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(-128 e^{9} x^{9}-512 e^{8} x^{8} d -448 e^{7} x^{7} d^{2}+768 e^{6} x^{6} d^{3}+1552 e^{5} x^{5} d^{4}+320 x^{4} d^{5} e^{4}-1080 x^{3} d^{6} e^{3}-800 x^{2} d^{7} e^{2}+5 d^{8} x e +180 d^{9}\right)}{715 \left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{10} e}"," ",0,"-1/715*(-e*x+d)*(-128*e^9*x^9-512*d*e^8*x^8-448*d^2*e^7*x^7+768*d^3*e^6*x^6+1552*d^4*e^5*x^5+320*d^5*e^4*x^4-1080*d^6*e^3*x^3-800*d^7*e^2*x^2+5*d^8*e*x+180*d^9)/(e*x+d)^3/d^10/e/(-e^2*x^2+d^2)^(7/2)","A"
216,1,385,204,0.028000," ","int(1/x/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x)","-\frac{128 e x}{273 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{7}}+\frac{1}{13 \left(x +\frac{d}{e}\right)^{4} \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{2} e^{4}}+\frac{2}{13 \left(x +\frac{d}{e}\right)^{3} \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{3} e^{3}}+\frac{29}{117 \left(x +\frac{d}{e}\right)^{2} \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{4} e^{2}}+\frac{320}{819 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{5} e}+\frac{1}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{6}}-\frac{512 e x}{819 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{9}}+\frac{1}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{8}}-\frac{\ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{10}}-\frac{1024 e x}{819 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{11}}+\frac{1}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{10}}"," ",0,"1/13/d^2/e^4/(x+d/e)^4/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+2/13/d^3/e^3/(x+d/e)^3/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+29/117/d^4/e^2/(x+d/e)^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+320/819/d^5/e/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-128/273/d^7*e/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x-512/819/d^9*e/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x-1024/819/d^11*e/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x+1/5/d^6/(-e^2*x^2+d^2)^(5/2)+1/3/d^8/(-e^2*x^2+d^2)^(3/2)+1/d^10/(-e^2*x^2+d^2)^(1/2)-1/d^10/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)","A"
217,1,484,239,0.018000," ","int(1/x^2/(e*x+d)^4/(-e^2*x^2+d^2)^(7/2),x)","\frac{6 e^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{8}}+\frac{20222 e^{2} x}{15015 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{8}}-\frac{1}{13 \left(x +\frac{d}{e}\right)^{4} \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{3} e^{3}}-\frac{35}{143 \left(x +\frac{d}{e}\right)^{3} \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{4} e^{2}}-\frac{709}{1287 \left(x +\frac{d}{e}\right)^{2} \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{5} e}-\frac{10111}{9009 \left(x +\frac{d}{e}\right) \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{5}{2}} d^{6}}-\frac{4 e}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{7}}-\frac{1}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} d^{6} x}+\frac{8 e^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{10}}+\frac{80888 e^{2} x}{45045 \left(2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}\right)^{\frac{3}{2}} d^{10}}-\frac{4 e}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d^{9}}+\frac{4 e \ln \left(\frac{2 d^{2}+2 \sqrt{d^{2}}\, \sqrt{-e^{2} x^{2}+d^{2}}}{x}\right)}{\sqrt{d^{2}}\, d^{11}}+\frac{16 e^{2} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{12}}+\frac{161776 e^{2} x}{45045 \sqrt{2 \left(x +\frac{d}{e}\right) d e -\left(x +\frac{d}{e}\right)^{2} e^{2}}\, d^{12}}-\frac{4 e}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{11}}"," ",0,"4/d^11*e/(d^2)^(1/2)*ln((2*d^2+2*(d^2)^(1/2)*(-e^2*x^2+d^2)^(1/2))/x)+6/5/d^8*e^2*x/(-e^2*x^2+d^2)^(5/2)+8/5/d^10*e^2*x/(-e^2*x^2+d^2)^(3/2)+16/5/d^12*e^2*x/(-e^2*x^2+d^2)^(1/2)-35/143/d^4/e^2/(x+d/e)^3/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-709/1287/d^5/e/(x+d/e)^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)+20222/15015/d^8*e^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)*x+80888/45045/d^10*e^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(3/2)*x+161776/45045/d^12*e^2/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(1/2)*x-1/13/d^3/e^3/(x+d/e)^4/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)-4/5/d^7*e/(-e^2*x^2+d^2)^(5/2)-4/3/d^9*e/(-e^2*x^2+d^2)^(3/2)-4/d^11*e/(-e^2*x^2+d^2)^(1/2)-1/d^6/x/(-e^2*x^2+d^2)^(5/2)-10111/9009/d^6/(x+d/e)/(2*(x+d/e)*d*e-(x+d/e)^2*e^2)^(5/2)","B"
218,1,95,86,0.049000," ","int((-a*c*x+c)^(1/2)*(-a^2*x^2+1)^(1/2)/x^2,x)","\frac{\left(-a c x \arctanh \left(\frac{\sqrt{\left(a x +1\right) c}}{\sqrt{c}}\right)+2 \sqrt{\left(a x +1\right) c}\, a \sqrt{c}\, x +\sqrt{\left(a x +1\right) c}\, \sqrt{c}\right) \sqrt{-\left(a x -1\right) c}\, \sqrt{-a^{2} x^{2}+1}}{\left(a x -1\right) \sqrt{\left(a x +1\right) c}\, \sqrt{c}\, x}"," ",0,"(-arctanh((c*(a*x+1))^(1/2)/c^(1/2))*x*a*c+2*x*a*(c*(a*x+1))^(1/2)*c^(1/2)+(c*(a*x+1))^(1/2)*c^(1/2))*(-c*(a*x-1))^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/(c*(a*x+1))^(1/2)/x/c^(1/2)","A"
219,1,58,31,0.018000," ","int((-a*c*x+c)^(1/2)/x/(-a^2*x^2+1)^(1/2),x)","\frac{2 \sqrt{-\left(a x -1\right) c}\, \sqrt{-a^{2} x^{2}+1}\, \sqrt{c}\, \arctanh \left(\frac{\sqrt{\left(a x +1\right) c}}{\sqrt{c}}\right)}{\left(a x -1\right) \sqrt{\left(a x +1\right) c}}"," ",0,"2*(-(a*x-1)*c)^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x-1)/((a*x+1)*c)^(1/2)*c^(1/2)*arctanh(((a*x+1)*c)^(1/2)/c^(1/2))","A"
220,1,62,25,0.008000," ","int((-a*x+1)^(1/2)/x^(1/2),x)","\sqrt{-a x +1}\, \sqrt{x}+\frac{\sqrt{\left(-a x +1\right) x}\, \arctan \left(\frac{\left(x -\frac{1}{2 a}\right) \sqrt{a}}{\sqrt{-a \,x^{2}+x}}\right)}{2 \sqrt{-a x +1}\, \sqrt{a}\, \sqrt{x}}"," ",0,"x^(1/2)*(-a*x+1)^(1/2)+1/2*((-a*x+1)*x)^(1/2)/(-a*x+1)^(1/2)/x^(1/2)/a^(1/2)*arctan(a^(1/2)*(x-1/2/a)/(-a*x^2+x)^(1/2))","B"
221,1,76,25,0.016000," ","int((-a^2*x^2+1)^(1/2)/x^(1/2)/(a*x+1)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \left(\arctan \left(\frac{2 a x -1}{2 \sqrt{-\left(a x -1\right) x}\, \sqrt{a}}\right)+2 \sqrt{-\left(a x -1\right) x}\, \sqrt{a}\right) \sqrt{x}}{2 \sqrt{a x +1}\, \sqrt{-\left(a x -1\right) x}\, \sqrt{a}}"," ",0,"1/2*(-a^2*x^2+1)^(1/2)*x^(1/2)/(a*x+1)^(1/2)*(2*a^(1/2)*(-x*(a*x-1))^(1/2)+arctan(1/2/a^(1/2)*(2*a*x-1)/(-x*(a*x-1))^(1/2)))/(-x*(a*x-1))^(1/2)/a^(1/2)","B"
222,1,57,24,0.006000," ","int((a*x+1)^(1/2)/x^(1/2),x)","\sqrt{a x +1}\, \sqrt{x}+\frac{\sqrt{\left(a x +1\right) x}\, \ln \left(\frac{a x +\frac{1}{2}}{\sqrt{a}}+\sqrt{a \,x^{2}+x}\right)}{2 \sqrt{a x +1}\, \sqrt{a}\, \sqrt{x}}"," ",0,"x^(1/2)*(a*x+1)^(1/2)+1/2*((a*x+1)*x)^(1/2)/(a*x+1)^(1/2)/x^(1/2)*ln((1/2+a*x)/a^(1/2)+(a*x^2+x)^(1/2))/a^(1/2)","B"
223,1,86,24,0.014000," ","int((-a^2*x^2+1)^(1/2)/x^(1/2)/(-a*x+1)^(1/2),x)","-\frac{\sqrt{-a^{2} x^{2}+1}\, \sqrt{-a x +1}\, \left(\ln \left(\frac{2 a x +2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}+1}{2 \sqrt{a}}\right)+2 \sqrt{\left(a x +1\right) x}\, \sqrt{a}\right) \sqrt{x}}{2 \left(a x -1\right) \sqrt{\left(a x +1\right) x}\, \sqrt{a}}"," ",0,"-1/2*(-a^2*x^2+1)^(1/2)*x^(1/2)*(-a*x+1)^(1/2)*(2*((a*x+1)*x)^(1/2)*a^(1/2)+ln(1/2*(2*((a*x+1)*x)^(1/2)*a^(1/2)+2*a*x+1)/a^(1/2)))/(a*x-1)/((a*x+1)*x)^(1/2)/a^(1/2)","B"
224,1,79,43,0.005000," ","int((-a*x+1)^(1/2)*x^(1/2),x)","\frac{\sqrt{-a x +1}\, x^{\frac{3}{2}}}{2}-\frac{\sqrt{-a x +1}\, \sqrt{x}}{4 a}+\frac{\sqrt{\left(-a x +1\right) x}\, \arctan \left(\frac{\left(x -\frac{1}{2 a}\right) \sqrt{a}}{\sqrt{-a \,x^{2}+x}}\right)}{8 \sqrt{-a x +1}\, a^{\frac{3}{2}} \sqrt{x}}"," ",0,"1/2*x^(3/2)*(-a*x+1)^(1/2)-1/4*x^(1/2)*(-a*x+1)^(1/2)/a+1/8/a^(3/2)*((-a*x+1)*x)^(1/2)/(-a*x+1)^(1/2)/x^(1/2)*arctan((x-1/2/a)/(-a*x^2+x)^(1/2)*a^(1/2))","A"
225,1,92,43,0.014000," ","int(x^(1/2)*(-a^2*x^2+1)^(1/2)/(a*x+1)^(1/2),x)","\frac{\sqrt{-a^{2} x^{2}+1}\, \left(4 \sqrt{-\left(a x -1\right) x}\, a^{\frac{3}{2}} x +\arctan \left(\frac{2 a x -1}{2 \sqrt{-\left(a x -1\right) x}\, \sqrt{a}}\right)-2 \sqrt{-\left(a x -1\right) x}\, \sqrt{a}\right) \sqrt{x}}{8 \sqrt{a x +1}\, \sqrt{-\left(a x -1\right) x}\, a^{\frac{3}{2}}}"," ",0,"1/8*x^(1/2)*(-a^2*x^2+1)^(1/2)/a^(3/2)*(4*x*a^(3/2)*(-(a*x-1)*x)^(1/2)-2*(-(a*x-1)*x)^(1/2)*a^(1/2)+arctan(1/2*(2*a*x-1)/(-(a*x-1)*x)^(1/2)/a^(1/2)))/(a*x+1)^(1/2)/(-(a*x-1)*x)^(1/2)","B"
226,0,0,230,0.061000," ","int((g*x)^m*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x)","\int \left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} \left(g x \right)^{m}\, dx"," ",0,"int((g*x)^m*(e*x+d)^3*(-e^2*x^2+d^2)^(5/2),x)","F"
227,0,0,188,0.025000," ","int((g*x)^m*(e*x+d)^2*(-e^2*x^2+d^2)^(5/2),x)","\int \left(e x +d \right)^{2} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} \left(g x \right)^{m}\, dx"," ",0,"int((g*x)^m*(e*x+d)^2*(-e^2*x^2+d^2)^(5/2),x)","F"
228,0,0,146,0.018000," ","int((g*x)^m*(e*x+d)*(-e^2*x^2+d^2)^(5/2),x)","\int \left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} \left(g x \right)^{m}\, dx"," ",0,"int((g*x)^m*(e*x+d)*(-e^2*x^2+d^2)^(5/2),x)","F"
229,0,0,72,0.017000," ","int((g*x)^m*(-e^2*x^2+d^2)^(5/2),x)","\int \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} \left(g x \right)^{m}\, dx"," ",0,"int((g*x)^m*(-e^2*x^2+d^2)^(5/2),x)","F"
230,0,0,147,0.032000," ","int((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} \left(g x \right)^{m}}{e x +d}\, dx"," ",0,"int((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d),x)","F"
231,0,0,186,0.025000," ","int((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} \left(g x \right)^{m}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^2,x)","F"
232,0,0,230,0.025000," ","int((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^3,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} \left(g x \right)^{m}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((g*x)^m*(-e^2*x^2+d^2)^(5/2)/(e*x+d)^3,x)","F"
233,0,0,189,0.024000," ","int((g*x)^m*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","\int \frac{\left(e x +d \right)^{3} \left(g x \right)^{m}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"int((g*x)^m*(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","F"
234,0,0,192,0.025000," ","int((g*x)^m*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","\int \frac{\left(e x +d \right)^{2} \left(g x \right)^{m}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"int((g*x)^m*(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","F"
235,0,0,116,0.019000," ","int((g*x)^m*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","\int \frac{\left(e x +d \right) \left(g x \right)^{m}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"int((g*x)^m*(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","F"
236,0,0,72,0.018000," ","int((g*x)^m/(-e^2*x^2+d^2)^(7/2),x)","\int \frac{\left(g x \right)^{m}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"int((g*x)^m/(-e^2*x^2+d^2)^(7/2),x)","F"
237,0,0,147,0.025000," ","int((g*x)^m/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","\int \frac{\left(g x \right)^{m}}{\left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"int((g*x)^m/(e*x+d)/(-e^2*x^2+d^2)^(7/2),x)","F"
238,0,0,193,0.025000," ","int((g*x)^m/(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","\int \frac{\left(g x \right)^{m}}{\left(e x +d \right)^{2} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"int((g*x)^m/(e*x+d)^2/(-e^2*x^2+d^2)^(7/2),x)","F"
239,0,0,190,0.026000," ","int((g*x)^m/(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","\int \frac{\left(g x \right)^{m}}{\left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"int((g*x)^m/(e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","F"
240,0,0,140,0.077000," ","int(x^5*(e*x+d)*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right) x^{5} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^5*(e*x+d)*(-e^2*x^2+d^2)^p,x)","F"
241,0,0,139,0.055000," ","int(x^4*(e*x+d)*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right) x^{4} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^4*(e*x+d)*(-e^2*x^2+d^2)^p,x)","F"
242,0,0,112,0.050000," ","int(x^3*(e*x+d)*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right) x^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^3*(e*x+d)*(-e^2*x^2+d^2)^p,x)","F"
243,0,0,111,0.042000," ","int(x^2*(e*x+d)*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right) x^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^2*(e*x+d)*(-e^2*x^2+d^2)^p,x)","F"
244,0,0,83,0.037000," ","int(x*(e*x+d)*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right) x \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x*(e*x+d)*(-e^2*x^2+d^2)^p,x)","F"
245,0,0,79,0.036000," ","int((e*x+d)*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int((e*x+d)*(-e^2*x^2+d^2)^p,x)","F"
246,0,0,102,0.027000," ","int((e*x+d)*(-e^2*x^2+d^2)^p/x,x)","\int \frac{\left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x}\, dx"," ",0,"int((e*x+d)*(-e^2*x^2+d^2)^p/x,x)","F"
247,0,0,106,0.033000," ","int((e*x+d)*(-e^2*x^2+d^2)^p/x^2,x)","\int \frac{\left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"int((e*x+d)*(-e^2*x^2+d^2)^p/x^2,x)","F"
248,0,0,108,0.041000," ","int((e*x+d)*(-e^2*x^2+d^2)^p/x^3,x)","\int \frac{\left(e x +d \right) \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x^{3}}\, dx"," ",0,"int((e*x+d)*(-e^2*x^2+d^2)^p/x^3,x)","F"
249,0,0,170,0.071000," ","int(x^5*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{2} x^{5} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^5*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","F"
250,0,0,181,0.065000," ","int(x^4*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{2} x^{4} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^4*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","F"
251,0,0,141,0.058000," ","int(x^3*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{2} x^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^3*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","F"
252,0,0,151,0.052000," ","int(x^2*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{2} x^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^2*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","F"
253,0,0,112,0.043000," ","int(x*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{2} x \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","F"
254,0,0,71,0.038000," ","int((e*x+d)^2*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int((e*x+d)^2*(-e^2*x^2+d^2)^p,x)","F"
255,0,0,124,0.029000," ","int((e*x+d)^2*(-e^2*x^2+d^2)^p/x,x)","\int \frac{\left(e x +d \right)^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x}\, dx"," ",0,"int((e*x+d)^2*(-e^2*x^2+d^2)^p/x,x)","F"
256,0,0,128,0.033000," ","int((e*x+d)^2*(-e^2*x^2+d^2)^p/x^2,x)","\int \frac{\left(e x +d \right)^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"int((e*x+d)^2*(-e^2*x^2+d^2)^p/x^2,x)","F"
257,0,0,135,0.043000," ","int((e*x+d)^2*(-e^2*x^2+d^2)^p/x^3,x)","\int \frac{\left(e x +d \right)^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x^{3}}\, dx"," ",0,"int((e*x+d)^2*(-e^2*x^2+d^2)^p/x^3,x)","F"
258,0,0,214,0.062000," ","int(x^5*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{3} x^{5} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^5*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","F"
259,0,0,210,0.079000," ","int(x^4*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{3} x^{4} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^4*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","F"
260,0,0,185,0.071000," ","int(x^3*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{3} x^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^3*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","F"
261,0,0,181,0.063000," ","int(x^2*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{3} x^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x^2*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","F"
262,0,0,116,0.070000," ","int(x*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{3} x \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int(x*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","F"
263,0,0,73,0.044000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int((e*x+d)^3*(-e^2*x^2+d^2)^p,x)","F"
264,0,0,167,0.029000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^p/x,x)","\int \frac{\left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x}\, dx"," ",0,"int((e*x+d)^3*(-e^2*x^2+d^2)^p/x,x)","F"
265,0,0,155,0.036000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^p/x^2,x)","\int \frac{\left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"int((e*x+d)^3*(-e^2*x^2+d^2)^p/x^2,x)","F"
266,0,0,162,0.044000," ","int((e*x+d)^3*(-e^2*x^2+d^2)^p/x^3,x)","\int \frac{\left(e x +d \right)^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{x^{3}}\, dx"," ",0,"int((e*x+d)^3*(-e^2*x^2+d^2)^p/x^3,x)","F"
267,0,0,140,0.062000," ","int(x^4*(-e^2*x^2+d^2)^p/(e*x+d),x)","\int \frac{x^{4} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{e x +d}\, dx"," ",0,"int(x^4*(-e^2*x^2+d^2)^p/(e*x+d),x)","F"
268,0,0,113,0.057000," ","int(x^3*(-e^2*x^2+d^2)^p/(e*x+d),x)","\int \frac{x^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{e x +d}\, dx"," ",0,"int(x^3*(-e^2*x^2+d^2)^p/(e*x+d),x)","F"
269,0,0,111,0.050000," ","int(x^2*(-e^2*x^2+d^2)^p/(e*x+d),x)","\int \frac{x^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{e x +d}\, dx"," ",0,"int(x^2*(-e^2*x^2+d^2)^p/(e*x+d),x)","F"
270,0,0,84,0.041000," ","int(x*(-e^2*x^2+d^2)^p/(e*x+d),x)","\int \frac{x \left(-e^{2} x^{2}+d^{2}\right)^{p}}{e x +d}\, dx"," ",0,"int(x*(-e^2*x^2+d^2)^p/(e*x+d),x)","F"
271,0,0,73,0.048000," ","int((-e^2*x^2+d^2)^p/(e*x+d),x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{e x +d}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/(e*x+d),x)","F"
272,0,0,102,0.034000," ","int((-e^2*x^2+d^2)^p/x/(e*x+d),x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right) x}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x/(e*x+d),x)","F"
273,0,0,104,0.044000," ","int((-e^2*x^2+d^2)^p/x^2/(e*x+d),x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right) x^{2}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^2/(e*x+d),x)","F"
274,0,0,106,0.056000," ","int((-e^2*x^2+d^2)^p/x^3/(e*x+d),x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right) x^{3}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^3/(e*x+d),x)","F"
275,0,0,171,0.080000," ","int(x^5*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","\int \frac{x^{5} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x^5*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","F"
276,0,0,180,0.073000," ","int(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","\int \frac{x^{4} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","F"
277,0,0,142,0.063000," ","int(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","\int \frac{x^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","F"
278,0,0,152,0.054000," ","int(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","\int \frac{x^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","F"
279,0,0,113,0.054000," ","int(x*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","\int \frac{x \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","F"
280,0,0,73,0.053000," ","int((-e^2*x^2+d^2)^p/(e*x+d)^2,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/(e*x+d)^2,x)","F"
281,0,0,126,0.035000," ","int((-e^2*x^2+d^2)^p/x/(e*x+d)^2,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2} x}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x/(e*x+d)^2,x)","F"
282,0,0,137,0.048000," ","int((-e^2*x^2+d^2)^p/x^2/(e*x+d)^2,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2} x^{2}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^2/(e*x+d)^2,x)","F"
283,0,0,139,0.061000," ","int((-e^2*x^2+d^2)^p/x^3/(e*x+d)^2,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2} x^{3}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^3/(e*x+d)^2,x)","F"
284,0,0,141,0.072000," ","int((-e^2*x^2+d^2)^p/x^4/(e*x+d)^2,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2} x^{4}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^4/(e*x+d)^2,x)","F"
285,0,0,139,0.089000," ","int((-e^2*x^2+d^2)^p/x^5/(e*x+d)^2,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2} x^{5}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^5/(e*x+d)^2,x)","F"
286,0,0,212,0.092000," ","int(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","\int \frac{x^{4} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","F"
287,0,0,186,0.082000," ","int(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","\int \frac{x^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","F"
288,0,0,151,0.080000," ","int(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","\int \frac{x^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","F"
289,0,0,114,0.077000," ","int(x*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","\int \frac{x \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int(x*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","F"
290,0,0,73,0.077000," ","int((-e^2*x^2+d^2)^p/(e*x+d)^3,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/(e*x+d)^3,x)","F"
291,0,0,173,0.039000," ","int((-e^2*x^2+d^2)^p/x/(e*x+d)^3,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3} x}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x/(e*x+d)^3,x)","F"
292,0,0,164,0.068000," ","int((-e^2*x^2+d^2)^p/x^2/(e*x+d)^3,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3} x^{2}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^2/(e*x+d)^3,x)","F"
293,0,0,169,0.082000," ","int((-e^2*x^2+d^2)^p/x^3/(e*x+d)^3,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3} x^{3}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^3/(e*x+d)^3,x)","F"
294,0,0,171,0.125000," ","int((-e^2*x^2+d^2)^p/x^4/(e*x+d)^3,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3} x^{4}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^4/(e*x+d)^3,x)","F"
295,0,0,170,0.063000," ","int((-e^2*x^2+d^2)^p/x^5/(e*x+d)^3,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3} x^{5}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^5/(e*x+d)^3,x)","F"
296,0,0,261,0.113000," ","int(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^4,x)","\int \frac{x^{4} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4}}\, dx"," ",0,"int(x^4*(-e^2*x^2+d^2)^p/(e*x+d)^4,x)","F"
297,0,0,205,0.107000," ","int(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^4,x)","\int \frac{x^{3} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4}}\, dx"," ",0,"int(x^3*(-e^2*x^2+d^2)^p/(e*x+d)^4,x)","F"
298,0,0,159,0.109000," ","int(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^4,x)","\int \frac{x^{2} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4}}\, dx"," ",0,"int(x^2*(-e^2*x^2+d^2)^p/(e*x+d)^4,x)","F"
299,0,0,116,0.109000," ","int(x*(-e^2*x^2+d^2)^p/(e*x+d)^4,x)","\int \frac{x \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4}}\, dx"," ",0,"int(x*(-e^2*x^2+d^2)^p/(e*x+d)^4,x)","F"
300,0,0,73,0.107000," ","int((-e^2*x^2+d^2)^p/(e*x+d)^4,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/(e*x+d)^4,x)","F"
301,0,0,200,0.041000," ","int((-e^2*x^2+d^2)^p/x/(e*x+d)^4,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4} x}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x/(e*x+d)^4,x)","F"
302,0,0,207,0.084000," ","int((-e^2*x^2+d^2)^p/x^2/(e*x+d)^4,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4} x^{2}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^2/(e*x+d)^4,x)","F"
303,0,0,205,0.107000," ","int((-e^2*x^2+d^2)^p/x^3/(e*x+d)^4,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4} x^{3}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^3/(e*x+d)^4,x)","F"
304,0,0,204,0.063000," ","int((-e^2*x^2+d^2)^p/x^4/(e*x+d)^4,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4} x^{4}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^4/(e*x+d)^4,x)","F"
305,0,0,206,0.076000," ","int((-e^2*x^2+d^2)^p/x^5/(e*x+d)^4,x)","\int \frac{\left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{4} x^{5}}\, dx"," ",0,"int((-e^2*x^2+d^2)^p/x^5/(e*x+d)^4,x)","F"
306,0,0,260,0.140000," ","int((g*x)^m*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{3} \left(g x \right)^{m} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int((g*x)^m*(e*x+d)^3*(-e^2*x^2+d^2)^p,x)","F"
307,0,0,202,0.075000," ","int((g*x)^m*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right)^{2} \left(g x \right)^{m} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int((g*x)^m*(e*x+d)^2*(-e^2*x^2+d^2)^p,x)","F"
308,0,0,149,0.069000," ","int((g*x)^m*(e*x+d)*(-e^2*x^2+d^2)^p,x)","\int \left(e x +d \right) \left(g x \right)^{m} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int((g*x)^m*(e*x+d)*(-e^2*x^2+d^2)^p,x)","F"
309,0,0,73,0.081000," ","int((g*x)^m*(-e^2*x^2+d^2)^p,x)","\int \left(g x \right)^{m} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int((g*x)^m*(-e^2*x^2+d^2)^p,x)","F"
310,0,0,159,0.072000," ","int((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d),x)","\int \frac{\left(g x \right)^{m} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{e x +d}\, dx"," ",0,"int((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d),x)","F"
311,0,0,210,0.081000," ","int((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","\int \frac{\left(g x \right)^{m} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d)^2,x)","F"
312,0,0,271,0.100000," ","int((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","\int \frac{\left(g x \right)^{m} \left(-e^{2} x^{2}+d^{2}\right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((g*x)^m*(-e^2*x^2+d^2)^p/(e*x+d)^3,x)","F"
313,0,0,85,0.123000," ","int((g*x)^m*(-a^2*x^2+1)^p/(a*x+1),x)","\int \frac{\left(g x \right)^{m} \left(-a^{2} x^{2}+1\right)^{p}}{a x +1}\, dx"," ",0,"int((g*x)^m*(-a^2*x^2+1)^p/(a*x+1),x)","F"
314,0,0,96,0.135000," ","int((g*x)^m*(e*x+d)^n*(-e^2*x^2+d^2)^p,x)","\int \left(g x \right)^{m} \left(e x +d \right)^{n} \left(-e^{2} x^{2}+d^{2}\right)^{p}\, dx"," ",0,"int((g*x)^m*(e*x+d)^n*(-e^2*x^2+d^2)^p,x)","F"
315,1,240,152,0.117000," ","int(x*(x+1)^(1/2)/(x^2+1),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{\arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}-\frac{\sqrt{2}\, \arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2+2 \sqrt{2}}\, \ln \left(x +1+\sqrt{2}-\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{4}-\frac{\sqrt{2+2 \sqrt{2}}\, \ln \left(x +1+\sqrt{2}+\sqrt{x +1}\, \sqrt{2+2 \sqrt{2}}\right)}{4}+2 \sqrt{x +1}"," ",0,"2*(x+1)^(1/2)+1/4*ln(1+x+2^(1/2)-(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))*(2+2*2^(1/2))^(1/2)-1/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)+1/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/4*ln(1+x+2^(1/2)+(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))*(2+2*2^(1/2))^(1/2)+1/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/(-2+2*2^(1/2))^(1/2)*arctan((2*(x+1)^(1/2)+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))*2^(1/2)","A"
316,1,560,225,0.021000," ","int(x^4*(c*x^2+a)^(1/2)/(e*x+d),x)","-\frac{a \,d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{c \,d^{6} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{7}}+\frac{a^{2} d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 c^{\frac{3}{2}} e^{2}}-\frac{a \,d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 \sqrt{c}\, e^{4}}-\frac{\sqrt{c}\, d^{5} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e^{6}}+\frac{\sqrt{c \,x^{2}+a}\, a d x}{8 c \,e^{2}}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} x^{2}}{5 c e}-\frac{\sqrt{c \,x^{2}+a}\, d^{3} x}{2 e^{4}}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} d x}{4 c \,e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{4}}{e^{5}}-\frac{2 \left(c \,x^{2}+a \right)^{\frac{3}{2}} a}{15 c^{2} e}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} d^{2}}{3 c \,e^{3}}"," ",0,"1/5/e*x^2*(c*x^2+a)^(3/2)/c-2/15/e*a/c^2*(c*x^2+a)^(3/2)-1/4*d/e^2*x*(c*x^2+a)^(3/2)/c+1/8*d/e^2*a/c*x*(c*x^2+a)^(1/2)+1/8*d/e^2*a^2/c^(3/2)*ln(x*c^(1/2)+(c*x^2+a)^(1/2))+1/3*d^2/e^3*(c*x^2+a)^(3/2)/c-1/2*d^3/e^4*x*(c*x^2+a)^(1/2)-1/2*d^3/e^4*a/c^(1/2)*ln(x*c^(1/2)+(c*x^2+a)^(1/2))+d^4/e^5*((x+d/e)^2*c-2*c*d/e*(x+d/e)+(a*e^2+c*d^2)/e^2)^(1/2)-d^5/e^6*c^(1/2)*ln((-c*d/e+c*(x+d/e))/c^(1/2)+((x+d/e)^2*c-2*c*d/e*(x+d/e)+(a*e^2+c*d^2)/e^2)^(1/2))-d^4/e^5/((a*e^2+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2+c*d^2)/e^2-2*c*d/e*(x+d/e)+2*((a*e^2+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c-2*c*d/e*(x+d/e)+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-d^6/e^7/((a*e^2+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2+c*d^2)/e^2-2*c*d/e*(x+d/e)+2*((a*e^2+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c-2*c*d/e*(x+d/e)+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c","B"
317,1,515,185,0.011000," ","int(x^3*(c*x^2+a)^(1/2)/(e*x+d),x)","\frac{a \,d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{4}}+\frac{c \,d^{5} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{6}}-\frac{a^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{8 c^{\frac{3}{2}} e}+\frac{a \,d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 \sqrt{c}\, e^{3}}+\frac{\sqrt{c}\, d^{4} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e^{5}}-\frac{\sqrt{c \,x^{2}+a}\, a x}{8 c e}+\frac{\sqrt{c \,x^{2}+a}\, d^{2} x}{2 e^{3}}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} x}{4 c e}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{3}}{e^{4}}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} d}{3 c \,e^{2}}"," ",0,"1/4/e*x*(c*x^2+a)^(3/2)/c-1/8/e*a/c*x*(c*x^2+a)^(1/2)-1/8/e*a^2/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-1/3*d*(c*x^2+a)^(3/2)/c/e^2+1/2*d^2/e^3*x*(c*x^2+a)^(1/2)+1/2*d^2/e^3*a/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-d^3/e^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d^4/e^5*c^(1/2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+d^3/e^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+d^5/e^6/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c","B"
318,1,448,131,0.013000," ","int(x^2*(c*x^2+a)^(1/2)/(e*x+d),x)","-\frac{a \,d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{c \,d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{a d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 \sqrt{c}\, e^{2}}-\frac{\sqrt{c}\, d^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e^{4}}-\frac{\sqrt{c \,x^{2}+a}\, d x}{2 e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}{e^{3}}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}}}{3 c e}"," ",0,"1/3*(c*x^2+a)^(3/2)/c/e-1/2*d/e^2*x*(c*x^2+a)^(1/2)-1/2/e^2*d*a/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+d^2/e^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-d^3/e^4*c^(1/2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-d^2/e^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-d^4/e^5/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c","B"
319,1,423,109,0.008000," ","int(x*(c*x^2+a)^(1/2)/(e*x+d),x)","\frac{a d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{c \,d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{4}}+\frac{a \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 \sqrt{c}\, e}+\frac{\sqrt{c}\, d^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e^{3}}+\frac{\sqrt{c \,x^{2}+a}\, x}{2 e}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d}{e^{2}}"," ",0,"1/2/e*x*(c*x^2+a)^(1/2)+1/2/e*a/c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-d/e^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d^2/e^3*c^(1/2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+d/e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+d^3/e^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c","B"
320,1,381,89,0.006000," ","int((c*x^2+a)^(1/2)/(e*x+d),x)","-\frac{a \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{c \,d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{\sqrt{c}\, d \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{e}"," ",0,"1/e*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/e^2*c^(1/2)*d*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/e^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2","B"
321,1,420,98,0.010000," ","int((c*x^2+a)^(1/2)/x/(e*x+d),x)","\frac{a \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d}+\frac{c d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{\sqrt{a}\, \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{d}+\frac{\sqrt{c}\, \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{e}+\frac{\sqrt{c \,x^{2}+a}}{d}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{d}"," ",0,"-1/d*a^(1/2)*ln((2*a+2*a^(1/2)*(c*x^2+a)^(1/2))/x)+1/d*(c*x^2+a)^(1/2)-1/d*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+c^(1/2)/e*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/d/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+d/e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c","B"
322,1,486,91,0.012000," ","int((c*x^2+a)^(1/2)/x^2/(e*x+d),x)","-\frac{a e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}-\frac{c \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{\sqrt{a}\, e \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{d^{2}}+\frac{\sqrt{c}\, \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{d}-\frac{\sqrt{c}\, \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{d}+\frac{\sqrt{c \,x^{2}+a}\, c x}{a d}-\frac{\sqrt{c \,x^{2}+a}\, e}{d^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}{d^{2}}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}}}{a d x}"," ",0,"-1/d/a/x*(c*x^2+a)^(3/2)+1/d*c/a*x*(c*x^2+a)^(1/2)+1/d*c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+e/d^2*a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-e/d^2*(c*x^2+a)^(1/2)+e/d^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/d*c^(1/2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-e/d^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c","B"
323,1,567,134,0.013000," ","int((c*x^2+a)^(1/2)/x^3/(e*x+d),x)","\frac{a \,e^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{3}}+\frac{c \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d}-\frac{\sqrt{a}\, e^{2} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{d^{3}}-\frac{c \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 \sqrt{a}\, d}-\frac{\sqrt{c}\, e \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{d^{2}}+\frac{\sqrt{c}\, e \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{d^{2}}-\frac{\sqrt{c \,x^{2}+a}\, c e x}{a \,d^{2}}+\frac{\sqrt{c \,x^{2}+a}\, c}{2 a d}+\frac{\sqrt{c \,x^{2}+a}\, e^{2}}{d^{3}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}{d^{3}}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e}{a \,d^{2} x}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}}}{2 a d \,x^{2}}"," ",0,"e/d^2/a/x*(c*x^2+a)^(3/2)-e/d^2*c/a*x*(c*x^2+a)^(1/2)-e/d^2*c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-1/2/d/a/x^2*(c*x^2+a)^(3/2)-1/2/d*c/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+1/2/d*c/a*(c*x^2+a)^(1/2)-1/d^3*e^2*a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+1/d^3*e^2*(c*x^2+a)^(1/2)-1/d^3*e^2*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/d^2*e*c^(1/2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/d^3*e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/d/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c","B"
324,1,600,161,0.015000," ","int((c*x^2+a)^(1/2)/x^4/(e*x+d),x)","-\frac{a \,e^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{4}}-\frac{c e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}+\frac{\sqrt{a}\, e^{3} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{d^{4}}+\frac{c e \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 \sqrt{a}\, d^{2}}+\frac{\sqrt{c}\, e^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{d^{3}}-\frac{\sqrt{c}\, e^{2} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{d^{3}}+\frac{\sqrt{c \,x^{2}+a}\, c \,e^{2} x}{a \,d^{3}}-\frac{\sqrt{c \,x^{2}+a}\, c e}{2 a \,d^{2}}-\frac{\sqrt{c \,x^{2}+a}\, e^{3}}{d^{4}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}{d^{4}}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e^{2}}{a \,d^{3} x}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e}{2 a \,d^{2} x^{2}}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}}}{3 a d \,x^{3}}"," ",0,"-1/d^3*e^2/a/x*(c*x^2+a)^(3/2)+1/d^3*e^2*c/a*x*(c*x^2+a)^(1/2)+1/d^3*e^2*c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+1/2*e/d^2/a/x^2*(c*x^2+a)^(3/2)+1/2*e/d^2*c/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-1/2*e/d^2*c/a*(c*x^2+a)^(1/2)-1/3*(c*x^2+a)^(3/2)/a/d/x^3+1/d^4*e^3*a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-1/d^4*e^3*(c*x^2+a)^(1/2)+1/d^4*e^3*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/d^3*e^2*c^(1/2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))-1/d^4*e^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/d^2*e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c","B"
325,1,703,228,0.016000," ","int((c*x^2+a)^(1/2)/x^5/(e*x+d),x)","\frac{a \,e^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{5}}+\frac{c \,e^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{3}}-\frac{\sqrt{a}\, e^{4} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{d^{5}}-\frac{c \,e^{2} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 \sqrt{a}\, d^{3}}+\frac{c^{2} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{8 a^{\frac{3}{2}} d}-\frac{\sqrt{c}\, e^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{d^{4}}+\frac{\sqrt{c}\, e^{3} \ln \left(\frac{-\frac{c d}{e}+\left(x +\frac{d}{e}\right) c}{\sqrt{c}}+\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\right)}{d^{4}}-\frac{\sqrt{c \,x^{2}+a}\, c \,e^{3} x}{a \,d^{4}}+\frac{\sqrt{c \,x^{2}+a}\, c \,e^{2}}{2 a \,d^{3}}-\frac{\sqrt{c \,x^{2}+a}\, c^{2}}{8 a^{2} d}+\frac{\sqrt{c \,x^{2}+a}\, e^{4}}{d^{5}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{4}}{d^{5}}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e^{3}}{a \,d^{4} x}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e^{2}}{2 a \,d^{3} x^{2}}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} c}{8 a^{2} d \,x^{2}}+\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}} e}{3 a \,d^{2} x^{3}}-\frac{\left(c \,x^{2}+a \right)^{\frac{3}{2}}}{4 a d \,x^{4}}"," ",0,"1/d^4*e^3/a/x*(c*x^2+a)^(3/2)-1/d^4*e^3*c/a*x*(c*x^2+a)^(1/2)-1/d^4*e^3*c^(1/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-1/2/d^3*e^2/a/x^2*(c*x^2+a)^(3/2)-1/2/d^3*e^2*c/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+1/2/d^3*e^2*c/a*(c*x^2+a)^(1/2)+1/3*e*(c*x^2+a)^(3/2)/a/d^2/x^3-1/d^5*e^4*a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+1/d^5*e^4*(c*x^2+a)^(1/2)-1/d^5*e^4*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/d^4*e^3*c^(1/2)*ln((-c*d/e+(x+d/e)*c)/c^(1/2)+(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))+1/d^5*e^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/d^3*e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))*c-1/4/d/a/x^4*(c*x^2+a)^(3/2)+1/8/d*c/a^2/x^2*(c*x^2+a)^(3/2)+1/8/d*c^2/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-1/8/d*c^2/a^2*(c*x^2+a)^(1/2)","B"
326,1,260,169,0.016000," ","int(x^4/(e*x+d)/(c*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+a}\, x^{2}}{3 c e}-\frac{d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}+\frac{a d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 c^{\frac{3}{2}} e^{2}}-\frac{d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, e^{4}}-\frac{\sqrt{c \,x^{2}+a}\, d x}{2 c \,e^{2}}-\frac{2 \sqrt{c \,x^{2}+a}\, a}{3 c^{2} e}+\frac{\sqrt{c \,x^{2}+a}\, d^{2}}{c \,e^{3}}"," ",0,"1/3/e*x^2/c*(c*x^2+a)^(1/2)-2/3/e*a/c^2*(c*x^2+a)^(1/2)-1/2*d/e^2*x/c*(c*x^2+a)^(1/2)+1/2*d/e^2*a/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+d^2/e^3/c*(c*x^2+a)^(1/2)-d^3/e^4*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)-d^4/e^5/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","A"
327,1,217,130,0.010000," ","int(x^3/(e*x+d)/(c*x^2+a)^(1/2),x)","\frac{d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{a \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 c^{\frac{3}{2}} e}+\frac{d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, e^{3}}+\frac{\sqrt{c \,x^{2}+a}\, x}{2 c e}-\frac{\sqrt{c \,x^{2}+a}\, d}{c \,e^{2}}"," ",0,"1/2/e*x/c*(c*x^2+a)^(1/2)-1/2/e*a/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-d*(c*x^2+a)^(1/2)/c/e^2+d^2/e^3*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)+d^3/e^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","A"
328,1,172,95,0.009000," ","int(x^2/(e*x+d)/(c*x^2+a)^(1/2),x)","-\frac{d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, e^{2}}+\frac{\sqrt{c \,x^{2}+a}}{c e}"," ",0,"(c*x^2+a)^(1/2)/c/e-1/e^2*d*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)-d^2/e^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","A"
329,1,151,74,0.010000," ","int(x/(e*x+d)/(c*x^2+a)^(1/2),x)","\frac{d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{\ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, e}"," ",0,"1/e*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)+d/e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
330,1,127,48,0.005000," ","int(1/(e*x+d)/(c*x^2+a)^(1/2),x)","-\frac{\ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}"," ",0,"-1/e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
331,1,158,74,0.012000," ","int(1/x/(e*x+d)/(c*x^2+a)^(1/2),x)","\frac{\ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d}-\frac{\ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}\, d}"," ",0,"-1/d/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+1/d/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
332,1,180,97,0.012000," ","int(1/x^2/(e*x+d)/(c*x^2+a)^(1/2),x)","-\frac{e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}+\frac{e \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}\, d^{2}}-\frac{\sqrt{c \,x^{2}+a}}{a d x}"," ",0,"-(c*x^2+a)^(1/2)/a/d/x+e/d^2/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-1/d^2*e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","A"
333,1,236,142,0.014000," ","int(1/x^3/(e*x+d)/(c*x^2+a)^(1/2),x)","\frac{e^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{3}}-\frac{e^{2} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}\, d^{3}}+\frac{c \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{3}{2}} d}+\frac{\sqrt{c \,x^{2}+a}\, e}{a \,d^{2} x}-\frac{\sqrt{c \,x^{2}+a}}{2 a d \,x^{2}}"," ",0,"e*(c*x^2+a)^(1/2)/a/d^2/x-1/2*(c*x^2+a)^(1/2)/a/d/x^2+1/2/d*c/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-1/d^3*e^2/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+1/d^3*e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","A"
334,1,396,130,0.020000," ","int(x^4/(e*x+d)/(c*x^2+a)^(3/2),x)","\frac{c \,d^{5} x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,e^{4}}-\frac{d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{d^{4}}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{x^{2}}{\sqrt{c \,x^{2}+a}\, c e}-\frac{d^{3} x}{\sqrt{c \,x^{2}+a}\, a \,e^{4}}+\frac{d x}{\sqrt{c \,x^{2}+a}\, c \,e^{2}}-\frac{d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{3}{2}} e^{2}}+\frac{2 a}{\sqrt{c \,x^{2}+a}\, c^{2} e}-\frac{d^{2}}{\sqrt{c \,x^{2}+a}\, c \,e^{3}}"," ",0,"1/e*x^2/c/(c*x^2+a)^(1/2)+2/e*a/c^2/(c*x^2+a)^(1/2)+d/e^2*x/c/(c*x^2+a)^(1/2)-d/e^2/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-d^2/e^3/c/(c*x^2+a)^(1/2)-d^3/e^4*x/a/(c*x^2+a)^(1/2)+d^4/e^3/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d^5/e^4/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x-d^4/e^3/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
335,1,354,109,0.010000," ","int(x^3/(e*x+d)/(c*x^2+a)^(3/2),x)","-\frac{c \,d^{4} x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,e^{3}}+\frac{d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{d^{3}}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{d^{2} x}{\sqrt{c \,x^{2}+a}\, a \,e^{3}}-\frac{x}{\sqrt{c \,x^{2}+a}\, c e}+\frac{\ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{3}{2}} e}+\frac{d}{\sqrt{c \,x^{2}+a}\, c \,e^{2}}"," ",0,"-1/e*x/c/(c*x^2+a)^(1/2)+1/e/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+d/e^2/c/(c*x^2+a)^(1/2)+d^2/e^3*x/a/(c*x^2+a)^(1/2)-d^3/e^2/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-d^4/e^3/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x+d^3/e^2/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
336,1,311,88,0.012000," ","int(x^2/(e*x+d)/(c*x^2+a)^(3/2),x)","\frac{c \,d^{3} x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,e^{2}}-\frac{d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}+\frac{d^{2}}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{d x}{\sqrt{c \,x^{2}+a}\, a \,e^{2}}-\frac{1}{\sqrt{c \,x^{2}+a}\, c e}"," ",0,"-1/e/c/(c*x^2+a)^(1/2)-1/e^2*d*x/a/(c*x^2+a)^(1/2)+d^2/e/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d^3/e^2/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x-d^2/e/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
337,1,283,80,0.007000," ","int(x/(e*x+d)/(c*x^2+a)^(3/2),x)","-\frac{c \,d^{2} x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a e}+\frac{d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}-\frac{d}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{x}{\sqrt{c \,x^{2}+a}\, a e}"," ",0,"1/e*x/a/(c*x^2+a)^(1/2)-d/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-d^2/e/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x+d/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
338,1,260,86,0.006000," ","int(1/(e*x+d)/(c*x^2+a)^(3/2),x)","\frac{c d x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}-\frac{e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{e}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}"," ",0,"e/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x-e/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
339,1,318,131,0.013000," ","int(1/x/(e*x+d)/(c*x^2+a)^(3/2),x)","-\frac{c e x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a}+\frac{e^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d}-\frac{e^{2}}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d}-\frac{\ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{a^{\frac{3}{2}} d}+\frac{1}{\sqrt{c \,x^{2}+a}\, a d}"," ",0,"1/a/d/(c*x^2+a)^(1/2)-1/d/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-1/d/(a*e^2+c*d^2)*e^2/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-e/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x+1/d/(a*e^2+c*d^2)*e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
340,1,363,174,0.012000," ","int(1/x^2/(e*x+d)/(c*x^2+a)^(3/2),x)","\frac{c \,e^{2} x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a d}-\frac{e^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}+\frac{e^{3}}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}-\frac{2 c x}{\sqrt{c \,x^{2}+a}\, a^{2} d}+\frac{e \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{a^{\frac{3}{2}} d^{2}}-\frac{e}{\sqrt{c \,x^{2}+a}\, a \,d^{2}}-\frac{1}{\sqrt{c \,x^{2}+a}\, a d x}"," ",0,"-1/a/d/x/(c*x^2+a)^(1/2)-2*c*x/a^2/d/(c*x^2+a)^(1/2)-e/a/d^2/(c*x^2+a)^(1/2)+e/d^2/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+e^3/d^2/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+e^2/d/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x-e^3/d^2/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
341,1,439,240,0.014000," ","int(1/x^3/(e*x+d)/(c*x^2+a)^(3/2),x)","-\frac{c \,e^{3} x}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, a \,d^{2}}+\frac{e^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{3}}-\frac{e^{4}}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{3}}+\frac{2 c e x}{\sqrt{c \,x^{2}+a}\, a^{2} d^{2}}-\frac{e^{2} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{a^{\frac{3}{2}} d^{3}}+\frac{3 c \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{5}{2}} d}+\frac{e^{2}}{\sqrt{c \,x^{2}+a}\, a \,d^{3}}-\frac{3 c}{2 \sqrt{c \,x^{2}+a}\, a^{2} d}+\frac{e}{\sqrt{c \,x^{2}+a}\, a \,d^{2} x}-\frac{1}{2 \sqrt{c \,x^{2}+a}\, a d \,x^{2}}"," ",0,"e/a/d^2/x/(c*x^2+a)^(1/2)+2*c*e*x/a^2/d^2/(c*x^2+a)^(1/2)-1/2/a/d/x^2/(c*x^2+a)^(1/2)-3/2*c/a^2/d/(c*x^2+a)^(1/2)+3/2/d*c/a^(5/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+e^2/a/d^3/(c*x^2+a)^(1/2)-1/d^3*e^2/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-1/d^3*e^4/(a*e^2+c*d^2)/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/d^2*e^3/(a*e^2+c*d^2)/a/(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)*c*x+1/d^3*e^4/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","A"
342,1,474,218,0.019000," ","int(x^5/(e*x+d)^2/(c*x^2+a)^(1/2),x)","\frac{c \,d^{6} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{6}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{5}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) e^{5}}+\frac{\sqrt{c \,x^{2}+a}\, x^{2}}{3 c \,e^{2}}-\frac{5 d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{6}}+\frac{a d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{c^{\frac{3}{2}} e^{3}}-\frac{4 d^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, e^{5}}-\frac{\sqrt{c \,x^{2}+a}\, d x}{c \,e^{3}}-\frac{2 \sqrt{c \,x^{2}+a}\, a}{3 c^{2} e^{2}}+\frac{3 \sqrt{c \,x^{2}+a}\, d^{2}}{c \,e^{4}}"," ",0,"1/3/e^2*x^2/c*(c*x^2+a)^(1/2)-2/3/e^2*a/c^2*(c*x^2+a)^(1/2)-d/e^3*x/c*(c*x^2+a)^(1/2)+d/e^3*a/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))+3*d^2/e^4/c*(c*x^2+a)^(1/2)-4*d^3/e^5*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)-5/e^6*d^4/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+d^5/e^5/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d^6/e^6*c/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
343,1,435,180,0.013000," ","int(x^4/(e*x+d)^2/(c*x^2+a)^(1/2),x)","-\frac{c \,d^{5} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{4}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) e^{4}}+\frac{4 d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{a \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{2 c^{\frac{3}{2}} e^{2}}+\frac{3 d^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, e^{4}}+\frac{\sqrt{c \,x^{2}+a}\, x}{2 c \,e^{2}}-\frac{2 \sqrt{c \,x^{2}+a}\, d}{c \,e^{3}}"," ",0,"1/2/e^2*x/c*(c*x^2+a)^(1/2)-1/2/e^2*a/c^(3/2)*ln(c^(1/2)*x+(c*x^2+a)^(1/2))-2*d*(c*x^2+a)^(1/2)/c/e^3+3*d^2/e^4*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)+4/e^5*d^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-d^4/e^4/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-d^5/e^5*c/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
344,1,386,144,0.013000," ","int(x^3/(e*x+d)^2/(c*x^2+a)^(1/2),x)","\frac{c \,d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{4}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{3}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) e^{3}}-\frac{3 d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{2 d \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, e^{3}}+\frac{\sqrt{c \,x^{2}+a}}{c \,e^{2}}"," ",0,"(c*x^2+a)^(1/2)/c/e^2-2/e^3*d*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)-3/e^4*d^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+d^3/e^3/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d^4/e^4*c/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
345,1,368,123,0.011000," ","int(x^2/(e*x+d)^2/(c*x^2+a)^(1/2),x)","-\frac{c \,d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) e^{2}}+\frac{2 d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{\ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+a}\right)}{\sqrt{c}\, e^{2}}"," ",0,"1/e^2*ln(c^(1/2)*x+(c*x^2+a)^(1/2))/c^(1/2)+2*d/e^3/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-d^2/e^2/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-d^3/e^3*c/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
346,1,340,82,0.009000," ","int(x/(e*x+d)^2/(c*x^2+a)^(1/2),x)","\frac{c \,d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) e}-\frac{\ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}"," ",0,"-1/e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+d/e/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+d^2/e^2*c/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
347,1,210,83,0.006000," ","int(1/(e*x+d)^2/(c*x^2+a)^(1/2),x)","-\frac{c d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right)}"," ",0,"-1/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/e*c*d/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
348,1,364,159,0.011000," ","int(1/x/(e*x+d)^2/(c*x^2+a)^(1/2),x)","\frac{c \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) d}+\frac{\ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}-\frac{\ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}\, d^{2}}"," ",0,"-1/d^2/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+1/d^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/d*e/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+c/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
349,1,395,190,0.012000," ","int(1/x^2/(e*x+d)^2/(c*x^2+a)^(1/2),x)","-\frac{c e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{2}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) d^{2}}-\frac{2 e \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{3}}+\frac{2 e \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}\, d^{3}}-\frac{\sqrt{c \,x^{2}+a}}{a \,d^{2} x}"," ",0,"-(c*x^2+a)^(1/2)/a/d^2/x+2/d^3*e/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-2/d^3*e/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))-1/d^2/(a*e^2+c*d^2)*e^2/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)-1/d*c*e/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
350,1,452,234,0.012000," ","int(1/x^3/(e*x+d)^2/(c*x^2+a)^(1/2),x)","\frac{c \,e^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{2}}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, e^{3}}{\left(a \,e^{2}+c \,d^{2}\right) \left(x +\frac{d}{e}\right) d^{3}}+\frac{3 e^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\frac{2 a \,e^{2}+2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) c d}{e}+\left(x +\frac{d}{e}\right)^{2} c +\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}+c \,d^{2}}{e^{2}}}\, d^{4}}-\frac{3 e^{2} \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}\, d^{4}}+\frac{c \ln \left(\frac{2 a +2 \sqrt{c \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{3}{2}} d^{2}}+\frac{2 \sqrt{c \,x^{2}+a}\, e}{a \,d^{3} x}-\frac{\sqrt{c \,x^{2}+a}}{2 a \,d^{2} x^{2}}"," ",0,"2*e*(c*x^2+a)^(1/2)/a/d^3/x-1/2*(c*x^2+a)^(1/2)/a/d^2/x^2+1/2/d^2*c/a^(3/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)-3/d^4*e^2/a^(1/2)*ln((2*a+2*(c*x^2+a)^(1/2)*a^(1/2))/x)+3/d^4*e^2/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))+1/d^3*e^3/(a*e^2+c*d^2)/(x+d/e)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2)+1/d^2*e^2*c/(a*e^2+c*d^2)/((a*e^2+c*d^2)/e^2)^(1/2)*ln((-2*(x+d/e)*c*d/e+2*(a*e^2+c*d^2)/e^2+2*((a*e^2+c*d^2)/e^2)^(1/2)*(-2*(x+d/e)*c*d/e+(x+d/e)^2*c+(a*e^2+c*d^2)/e^2)^(1/2))/(x+d/e))","A"
351,1,328,135,0.007000," ","int(x^2*(b*x+a)^n*(d*x^2+c),x)","\frac{\left(b^{4} d \,n^{4} x^{4}+10 b^{4} d \,n^{3} x^{4}-4 a \,b^{3} d \,n^{3} x^{3}+b^{4} c \,n^{4} x^{2}+35 b^{4} d \,n^{2} x^{4}-24 a \,b^{3} d \,n^{2} x^{3}+12 b^{4} c \,n^{3} x^{2}+50 b^{4} d n \,x^{4}+12 a^{2} b^{2} d \,n^{2} x^{2}-2 a \,b^{3} c \,n^{3} x -44 a \,b^{3} d n \,x^{3}+49 b^{4} c \,n^{2} x^{2}+24 d \,x^{4} b^{4}+36 a^{2} b^{2} d n \,x^{2}-20 a \,b^{3} c \,n^{2} x -24 d a \,x^{3} b^{3}+78 b^{4} c n \,x^{2}-24 a^{3} b d n x +2 a^{2} b^{2} c \,n^{2}+24 a^{2} b^{2} d \,x^{2}-58 a \,b^{3} c n x +40 b^{4} c \,x^{2}-24 a^{3} b d x +18 a^{2} b^{2} c n -40 a \,b^{3} c x +24 a^{4} d +40 a^{2} b^{2} c \right) \left(b x +a \right)^{n +1}}{\left(n^{5}+15 n^{4}+85 n^{3}+225 n^{2}+274 n +120\right) b^{5}}"," ",0,"(b*x+a)^(1+n)*(b^4*d*n^4*x^4+10*b^4*d*n^3*x^4-4*a*b^3*d*n^3*x^3+b^4*c*n^4*x^2+35*b^4*d*n^2*x^4-24*a*b^3*d*n^2*x^3+12*b^4*c*n^3*x^2+50*b^4*d*n*x^4+12*a^2*b^2*d*n^2*x^2-2*a*b^3*c*n^3*x-44*a*b^3*d*n*x^3+49*b^4*c*n^2*x^2+24*b^4*d*x^4+36*a^2*b^2*d*n*x^2-20*a*b^3*c*n^2*x-24*a*b^3*d*x^3+78*b^4*c*n*x^2-24*a^3*b*d*n*x+2*a^2*b^2*c*n^2+24*a^2*b^2*d*x^2-58*a*b^3*c*n*x+40*b^4*c*x^2-24*a^3*b*d*x+18*a^2*b^2*c*n-40*a*b^3*c*x+24*a^4*d+40*a^2*b^2*c)/b^5/(n^5+15*n^4+85*n^3+225*n^2+274*n+120)","B"
352,1,195,102,0.005000," ","int(x*(b*x+a)^n*(d*x^2+c),x)","-\frac{\left(-b^{3} d \,n^{3} x^{3}-6 b^{3} d \,n^{2} x^{3}+3 a \,b^{2} d \,n^{2} x^{2}-b^{3} c \,n^{3} x -11 b^{3} d n \,x^{3}+9 a \,b^{2} d n \,x^{2}-8 b^{3} c \,n^{2} x -6 d \,x^{3} b^{3}-6 a^{2} b d n x +a \,b^{2} c \,n^{2}+6 a d \,x^{2} b^{2}-19 b^{3} c n x -6 a^{2} b d x +7 a \,b^{2} c n -12 b^{3} c x +6 a^{3} d +12 a \,b^{2} c \right) \left(b x +a \right)^{n +1}}{\left(n^{4}+10 n^{3}+35 n^{2}+50 n +24\right) b^{4}}"," ",0,"-(b*x+a)^(n+1)*(-b^3*d*n^3*x^3-6*b^3*d*n^2*x^3+3*a*b^2*d*n^2*x^2-b^3*c*n^3*x-11*b^3*d*n*x^3+9*a*b^2*d*n*x^2-8*b^3*c*n^2*x-6*b^3*d*x^3-6*a^2*b*d*n*x+a*b^2*c*n^2+6*a*b^2*d*x^2-19*b^3*c*n*x-6*a^2*b*d*x+7*a*b^2*c*n-12*b^3*c*x+6*a^3*d+12*a*b^2*c)/b^4/(n^4+10*n^3+35*n^2+50*n+24)","A"
353,1,100,70,0.004000," ","int((b*x+a)^n*(d*x^2+c),x)","\frac{\left(b^{2} d \,n^{2} x^{2}+3 b^{2} d n \,x^{2}-2 a b d n x +b^{2} c \,n^{2}+2 d \,x^{2} b^{2}-2 a d x b +5 b^{2} c n +2 a^{2} d +6 b^{2} c \right) \left(b x +a \right)^{n +1}}{\left(n^{3}+6 n^{2}+11 n +6\right) b^{3}}"," ",0,"(b*x+a)^(n+1)*(b^2*d*n^2*x^2+3*b^2*d*n*x^2-2*a*b*d*n*x+b^2*c*n^2+2*b^2*d*x^2-2*a*b*d*x+5*b^2*c*n+2*a^2*d+6*b^2*c)/b^3/(n^3+6*n^2+11*n+6)","A"
354,0,0,79,0.031000," ","int((b*x+a)^n*(d*x^2+c)/x,x)","\int \frac{\left(d \,x^{2}+c \right) \left(b x +a \right)^{n}}{x}\, dx"," ",0,"int((b*x+a)^n*(d*x^2+c)/x,x)","F"
355,1,1000,232,0.016000," ","int(x^2*(b*x+a)^n*(d*x^2+c)^2,x)","\frac{\left(b^{6} d^{2} n^{6} x^{6}+21 b^{6} d^{2} n^{5} x^{6}-6 a \,b^{5} d^{2} n^{5} x^{5}+2 b^{6} c d \,n^{6} x^{4}+175 b^{6} d^{2} n^{4} x^{6}-90 a \,b^{5} d^{2} n^{4} x^{5}+46 b^{6} c d \,n^{5} x^{4}+735 b^{6} d^{2} n^{3} x^{6}+30 a^{2} b^{4} d^{2} n^{4} x^{4}-8 a \,b^{5} c d \,n^{5} x^{3}-510 a \,b^{5} d^{2} n^{3} x^{5}+b^{6} c^{2} n^{6} x^{2}+414 b^{6} c d \,n^{4} x^{4}+1624 b^{6} d^{2} n^{2} x^{6}+300 a^{2} b^{4} d^{2} n^{3} x^{4}-152 a \,b^{5} c d \,n^{4} x^{3}-1350 a \,b^{5} d^{2} n^{2} x^{5}+25 b^{6} c^{2} n^{5} x^{2}+1850 b^{6} c d \,n^{3} x^{4}+1764 b^{6} d^{2} n \,x^{6}-120 a^{3} b^{3} d^{2} n^{3} x^{3}+24 a^{2} b^{4} c d \,n^{4} x^{2}+1050 a^{2} b^{4} d^{2} n^{2} x^{4}-2 a \,b^{5} c^{2} n^{5} x -1048 a \,b^{5} c d \,n^{3} x^{3}-1644 a \,b^{5} d^{2} n \,x^{5}+247 b^{6} c^{2} n^{4} x^{2}+4288 b^{6} c d \,n^{2} x^{4}+720 d^{2} x^{6} b^{6}-720 a^{3} b^{3} d^{2} n^{2} x^{3}+384 a^{2} b^{4} c d \,n^{3} x^{2}+1500 a^{2} b^{4} d^{2} n \,x^{4}-46 a \,b^{5} c^{2} n^{4} x -3208 a \,b^{5} c d \,n^{2} x^{3}-720 a \,d^{2} x^{5} b^{5}+1219 b^{6} c^{2} n^{3} x^{2}+4824 b^{6} c d n \,x^{4}+360 a^{4} b^{2} d^{2} n^{2} x^{2}-48 a^{3} b^{3} c d \,n^{3} x -1320 a^{3} b^{3} d^{2} n \,x^{3}+2 a^{2} b^{4} c^{2} n^{4}+1992 a^{2} b^{4} c d \,n^{2} x^{2}+720 a^{2} b^{4} d^{2} x^{4}-402 a \,b^{5} c^{2} n^{3} x -4320 a \,b^{5} c d n \,x^{3}+3112 b^{6} c^{2} n^{2} x^{2}+2016 b^{6} c d \,x^{4}+1080 a^{4} b^{2} d^{2} n \,x^{2}-672 a^{3} b^{3} c d \,n^{2} x -720 a^{3} b^{3} d^{2} x^{3}+44 a^{2} b^{4} c^{2} n^{3}+3648 a^{2} b^{4} c d n \,x^{2}-1634 a \,b^{5} c^{2} n^{2} x -2016 a \,b^{5} c d \,x^{3}+3796 b^{6} c^{2} n \,x^{2}-720 a^{5} b \,d^{2} n x +48 a^{4} b^{2} c d \,n^{2}+720 a^{4} b^{2} d^{2} x^{2}-2640 a^{3} b^{3} c d n x +358 a^{2} b^{4} c^{2} n^{2}+2016 a^{2} b^{4} c d \,x^{2}-2956 a \,b^{5} c^{2} n x +1680 b^{6} c^{2} x^{2}-720 a^{5} b \,d^{2} x +624 a^{4} b^{2} c d n -2016 a^{3} b^{3} c d x +1276 a^{2} b^{4} c^{2} n -1680 a \,b^{5} c^{2} x +720 a^{6} d^{2}+2016 a^{4} b^{2} c d +1680 a^{2} b^{4} c^{2}\right) \left(b x +a \right)^{n +1}}{\left(n^{7}+28 n^{6}+322 n^{5}+1960 n^{4}+6769 n^{3}+13132 n^{2}+13068 n +5040\right) b^{7}}"," ",0,"(b*x+a)^(n+1)*(b^6*d^2*n^6*x^6+21*b^6*d^2*n^5*x^6-6*a*b^5*d^2*n^5*x^5+2*b^6*c*d*n^6*x^4+175*b^6*d^2*n^4*x^6-90*a*b^5*d^2*n^4*x^5+46*b^6*c*d*n^5*x^4+735*b^6*d^2*n^3*x^6+30*a^2*b^4*d^2*n^4*x^4-8*a*b^5*c*d*n^5*x^3-510*a*b^5*d^2*n^3*x^5+b^6*c^2*n^6*x^2+414*b^6*c*d*n^4*x^4+1624*b^6*d^2*n^2*x^6+300*a^2*b^4*d^2*n^3*x^4-152*a*b^5*c*d*n^4*x^3-1350*a*b^5*d^2*n^2*x^5+25*b^6*c^2*n^5*x^2+1850*b^6*c*d*n^3*x^4+1764*b^6*d^2*n*x^6-120*a^3*b^3*d^2*n^3*x^3+24*a^2*b^4*c*d*n^4*x^2+1050*a^2*b^4*d^2*n^2*x^4-2*a*b^5*c^2*n^5*x-1048*a*b^5*c*d*n^3*x^3-1644*a*b^5*d^2*n*x^5+247*b^6*c^2*n^4*x^2+4288*b^6*c*d*n^2*x^4+720*b^6*d^2*x^6-720*a^3*b^3*d^2*n^2*x^3+384*a^2*b^4*c*d*n^3*x^2+1500*a^2*b^4*d^2*n*x^4-46*a*b^5*c^2*n^4*x-3208*a*b^5*c*d*n^2*x^3-720*a*b^5*d^2*x^5+1219*b^6*c^2*n^3*x^2+4824*b^6*c*d*n*x^4+360*a^4*b^2*d^2*n^2*x^2-48*a^3*b^3*c*d*n^3*x-1320*a^3*b^3*d^2*n*x^3+2*a^2*b^4*c^2*n^4+1992*a^2*b^4*c*d*n^2*x^2+720*a^2*b^4*d^2*x^4-402*a*b^5*c^2*n^3*x-4320*a*b^5*c*d*n*x^3+3112*b^6*c^2*n^2*x^2+2016*b^6*c*d*x^4+1080*a^4*b^2*d^2*n*x^2-672*a^3*b^3*c*d*n^2*x-720*a^3*b^3*d^2*x^3+44*a^2*b^4*c^2*n^3+3648*a^2*b^4*c*d*n*x^2-1634*a*b^5*c^2*n^2*x-2016*a*b^5*c*d*x^3+3796*b^6*c^2*n*x^2-720*a^5*b*d^2*n*x+48*a^4*b^2*c*d*n^2+720*a^4*b^2*d^2*x^2-2640*a^3*b^3*c*d*n*x+358*a^2*b^4*c^2*n^2+2016*a^2*b^4*c*d*x^2-2956*a*b^5*c^2*n*x+1680*b^6*c^2*x^2-720*a^5*b*d^2*x+624*a^4*b^2*c*d*n-2016*a^3*b^3*c*d*x+1276*a^2*b^4*c^2*n-1680*a*b^5*c^2*x+720*a^6*d^2+2016*a^4*b^2*c*d+1680*a^2*b^4*c^2)/b^7/(n^7+28*n^6+322*n^5+1960*n^4+6769*n^3+13132*n^2+13068*n+5040)","B"
356,1,677,185,0.012000," ","int(x*(b*x+a)^n*(d*x^2+c)^2,x)","-\frac{\left(-b^{5} d^{2} n^{5} x^{5}-15 b^{5} d^{2} n^{4} x^{5}+5 a \,b^{4} d^{2} n^{4} x^{4}-2 b^{5} c d \,n^{5} x^{3}-85 b^{5} d^{2} n^{3} x^{5}+50 a \,b^{4} d^{2} n^{3} x^{4}-34 b^{5} c d \,n^{4} x^{3}-225 b^{5} d^{2} n^{2} x^{5}-20 a^{2} b^{3} d^{2} n^{3} x^{3}+6 a \,b^{4} c d \,n^{4} x^{2}+175 a \,b^{4} d^{2} n^{2} x^{4}-b^{5} c^{2} n^{5} x -214 b^{5} c d \,n^{3} x^{3}-274 b^{5} d^{2} n \,x^{5}-120 a^{2} b^{3} d^{2} n^{2} x^{3}+84 a \,b^{4} c d \,n^{3} x^{2}+250 a \,b^{4} d^{2} n \,x^{4}-19 b^{5} c^{2} n^{4} x -614 b^{5} c d \,n^{2} x^{3}-120 d^{2} x^{5} b^{5}+60 a^{3} b^{2} d^{2} n^{2} x^{2}-12 a^{2} b^{3} c d \,n^{3} x -220 a^{2} b^{3} d^{2} n \,x^{3}+a \,b^{4} c^{2} n^{4}+390 a \,b^{4} c d \,n^{2} x^{2}+120 a \,d^{2} x^{4} b^{4}-137 b^{5} c^{2} n^{3} x -792 b^{5} c d n \,x^{3}+180 a^{3} b^{2} d^{2} n \,x^{2}-144 a^{2} b^{3} c d \,n^{2} x -120 a^{2} b^{3} d^{2} x^{3}+18 a \,b^{4} c^{2} n^{3}+672 a \,b^{4} c d n \,x^{2}-461 b^{5} c^{2} n^{2} x -360 b^{5} c d \,x^{3}-120 a^{4} b \,d^{2} n x +12 a^{3} b^{2} c d \,n^{2}+120 a^{3} b^{2} d^{2} x^{2}-492 a^{2} b^{3} c d n x +119 a \,b^{4} c^{2} n^{2}+360 a \,b^{4} c d \,x^{2}-702 b^{5} c^{2} n x -120 a^{4} b \,d^{2} x +132 a^{3} b^{2} c d n -360 a^{2} b^{3} c d x +342 a \,b^{4} c^{2} n -360 b^{5} c^{2} x +120 a^{5} d^{2}+360 a^{3} b^{2} c d +360 a \,b^{4} c^{2}\right) \left(b x +a \right)^{n +1}}{\left(n^{6}+21 n^{5}+175 n^{4}+735 n^{3}+1624 n^{2}+1764 n +720\right) b^{6}}"," ",0,"-(b*x+a)^(n+1)*(-b^5*d^2*n^5*x^5-15*b^5*d^2*n^4*x^5+5*a*b^4*d^2*n^4*x^4-2*b^5*c*d*n^5*x^3-85*b^5*d^2*n^3*x^5+50*a*b^4*d^2*n^3*x^4-34*b^5*c*d*n^4*x^3-225*b^5*d^2*n^2*x^5-20*a^2*b^3*d^2*n^3*x^3+6*a*b^4*c*d*n^4*x^2+175*a*b^4*d^2*n^2*x^4-b^5*c^2*n^5*x-214*b^5*c*d*n^3*x^3-274*b^5*d^2*n*x^5-120*a^2*b^3*d^2*n^2*x^3+84*a*b^4*c*d*n^3*x^2+250*a*b^4*d^2*n*x^4-19*b^5*c^2*n^4*x-614*b^5*c*d*n^2*x^3-120*b^5*d^2*x^5+60*a^3*b^2*d^2*n^2*x^2-12*a^2*b^3*c*d*n^3*x-220*a^2*b^3*d^2*n*x^3+a*b^4*c^2*n^4+390*a*b^4*c*d*n^2*x^2+120*a*b^4*d^2*x^4-137*b^5*c^2*n^3*x-792*b^5*c*d*n*x^3+180*a^3*b^2*d^2*n*x^2-144*a^2*b^3*c*d*n^2*x-120*a^2*b^3*d^2*x^3+18*a*b^4*c^2*n^3+672*a*b^4*c*d*n*x^2-461*b^5*c^2*n^2*x-360*b^5*c*d*x^3-120*a^4*b*d^2*n*x+12*a^3*b^2*c*d*n^2+120*a^3*b^2*d^2*x^2-492*a^2*b^3*c*d*n*x+119*a*b^4*c^2*n^2+360*a*b^4*c*d*x^2-702*b^5*c^2*n*x-120*a^4*b*d^2*x+132*a^3*b^2*c*d*n-360*a^2*b^3*c*d*x+342*a*b^4*c^2*n-360*b^5*c^2*x+120*a^5*d^2+360*a^3*b^2*c*d+360*a*b^4*c^2)/b^6/(n^6+21*n^5+175*n^4+735*n^3+1624*n^2+1764*n+720)","B"
357,1,420,140,0.010000," ","int((b*x+a)^n*(d*x^2+c)^2,x)","\frac{\left(b^{4} d^{2} n^{4} x^{4}+10 b^{4} d^{2} n^{3} x^{4}-4 a \,b^{3} d^{2} n^{3} x^{3}+2 b^{4} c d \,n^{4} x^{2}+35 b^{4} d^{2} n^{2} x^{4}-24 a \,b^{3} d^{2} n^{2} x^{3}+24 b^{4} c d \,n^{3} x^{2}+50 b^{4} d^{2} n \,x^{4}+12 a^{2} b^{2} d^{2} n^{2} x^{2}-4 a \,b^{3} c d \,n^{3} x -44 a \,b^{3} d^{2} n \,x^{3}+b^{4} c^{2} n^{4}+98 b^{4} c d \,n^{2} x^{2}+24 d^{2} x^{4} b^{4}+36 a^{2} b^{2} d^{2} n \,x^{2}-40 a \,b^{3} c d \,n^{2} x -24 a \,d^{2} x^{3} b^{3}+14 b^{4} c^{2} n^{3}+156 b^{4} c d n \,x^{2}-24 a^{3} b \,d^{2} n x +4 a^{2} b^{2} c d \,n^{2}+24 a^{2} b^{2} d^{2} x^{2}-116 a \,b^{3} c d n x +71 b^{4} c^{2} n^{2}+80 b^{4} c d \,x^{2}-24 a^{3} b \,d^{2} x +36 a^{2} b^{2} c d n -80 a \,b^{3} c d x +154 b^{4} c^{2} n +24 a^{4} d^{2}+80 a^{2} b^{2} c d +120 b^{4} c^{2}\right) \left(b x +a \right)^{n +1}}{\left(n^{5}+15 n^{4}+85 n^{3}+225 n^{2}+274 n +120\right) b^{5}}"," ",0,"(b*x+a)^(n+1)*(b^4*d^2*n^4*x^4+10*b^4*d^2*n^3*x^4-4*a*b^3*d^2*n^3*x^3+2*b^4*c*d*n^4*x^2+35*b^4*d^2*n^2*x^4-24*a*b^3*d^2*n^2*x^3+24*b^4*c*d*n^3*x^2+50*b^4*d^2*n*x^4+12*a^2*b^2*d^2*n^2*x^2-4*a*b^3*c*d*n^3*x-44*a*b^3*d^2*n*x^3+b^4*c^2*n^4+98*b^4*c*d*n^2*x^2+24*b^4*d^2*x^4+36*a^2*b^2*d^2*n*x^2-40*a*b^3*c*d*n^2*x-24*a*b^3*d^2*x^3+14*b^4*c^2*n^3+156*b^4*c*d*n*x^2-24*a^3*b*d^2*n*x+4*a^2*b^2*c*d*n^2+24*a^2*b^2*d^2*x^2-116*a*b^3*c*d*n*x+71*b^4*c^2*n^2+80*b^4*c*d*x^2-24*a^3*b*d^2*x+36*a^2*b^2*c*d*n-80*a*b^3*c*d*x+154*b^4*c^2*n+24*a^4*d^2+80*a^2*b^2*c*d+120*b^4*c^2)/b^5/(n^5+15*n^4+85*n^3+225*n^2+274*n+120)","B"
358,0,0,150,0.030000," ","int((b*x+a)^n*(d*x^2+c)^2/x,x)","\int \frac{\left(d \,x^{2}+c \right)^{2} \left(b x +a \right)^{n}}{x}\, dx"," ",0,"int((b*x+a)^n*(d*x^2+c)^2/x,x)","F"
359,1,2232,343,0.024000," ","int(x^2*(b*x+a)^n*(d*x^2+c)^3,x)","\frac{\left(b^{8} d^{3} n^{8} x^{8}+36 b^{8} d^{3} n^{7} x^{8}-8 a \,b^{7} d^{3} n^{7} x^{7}+3 b^{8} c \,d^{2} n^{8} x^{6}+546 b^{8} d^{3} n^{6} x^{8}-224 a \,b^{7} d^{3} n^{6} x^{7}+114 b^{8} c \,d^{2} n^{7} x^{6}+4536 b^{8} d^{3} n^{5} x^{8}+56 a^{2} b^{6} d^{3} n^{6} x^{6}-18 a \,b^{7} c \,d^{2} n^{7} x^{5}-2576 a \,b^{7} d^{3} n^{5} x^{7}+3 b^{8} c^{2} d \,n^{8} x^{4}+1812 b^{8} c \,d^{2} n^{6} x^{6}+22449 b^{8} d^{3} n^{4} x^{8}+1176 a^{2} b^{6} d^{3} n^{5} x^{6}-576 a \,b^{7} c \,d^{2} n^{6} x^{5}-15680 a \,b^{7} d^{3} n^{4} x^{7}+120 b^{8} c^{2} d \,n^{7} x^{4}+15666 b^{8} c \,d^{2} n^{5} x^{6}+67284 b^{8} d^{3} n^{3} x^{8}-336 a^{3} b^{5} d^{3} n^{5} x^{5}+90 a^{2} b^{6} c \,d^{2} n^{6} x^{4}+9800 a^{2} b^{6} d^{3} n^{4} x^{6}-12 a \,b^{7} c^{2} d \,n^{7} x^{3}-7416 a \,b^{7} c \,d^{2} n^{5} x^{5}-54152 a \,b^{7} d^{3} n^{3} x^{7}+b^{8} c^{3} n^{8} x^{2}+2010 b^{8} c^{2} d \,n^{6} x^{4}+80157 b^{8} c \,d^{2} n^{4} x^{6}+118124 b^{8} d^{3} n^{2} x^{8}-5040 a^{3} b^{5} d^{3} n^{4} x^{5}+2430 a^{2} b^{6} c \,d^{2} n^{5} x^{4}+41160 a^{2} b^{6} d^{3} n^{3} x^{6}-432 a \,b^{7} c^{2} d \,n^{6} x^{3}-49500 a \,b^{7} c \,d^{2} n^{4} x^{5}-105056 a \,b^{7} d^{3} n^{2} x^{7}+42 b^{8} c^{3} n^{7} x^{2}+18300 b^{8} c^{2} d \,n^{5} x^{4}+246876 b^{8} c \,d^{2} n^{3} x^{6}+109584 b^{8} d^{3} n \,x^{8}+1680 a^{4} b^{4} d^{3} n^{4} x^{4}-360 a^{3} b^{5} c \,d^{2} n^{5} x^{3}-28560 a^{3} b^{5} d^{3} n^{3} x^{5}+36 a^{2} b^{6} c^{2} d \,n^{6} x^{2}+24930 a^{2} b^{6} c \,d^{2} n^{4} x^{4}+90944 a^{2} b^{6} d^{3} n^{2} x^{6}-2 a \,b^{7} c^{3} n^{7} x -6312 a \,b^{7} c^{2} d \,n^{5} x^{3}-183942 a \,b^{7} c \,d^{2} n^{3} x^{5}-104544 a \,b^{7} d^{3} n \,x^{7}+744 b^{8} c^{3} n^{6} x^{2}+98319 b^{8} c^{2} d \,n^{4} x^{4}+442908 b^{8} c \,d^{2} n^{2} x^{6}+40320 d^{3} x^{8} b^{8}+16800 a^{4} b^{4} d^{3} n^{3} x^{4}-8280 a^{3} b^{5} c \,d^{2} n^{4} x^{3}-75600 a^{3} b^{5} d^{3} n^{2} x^{5}+1188 a^{2} b^{6} c^{2} d \,n^{5} x^{2}+122850 a^{2} b^{6} c \,d^{2} n^{3} x^{4}+98784 a^{2} b^{6} d^{3} n \,x^{6}-80 a \,b^{7} c^{3} n^{6} x -47952 a \,b^{7} c^{2} d \,n^{4} x^{3}-377604 a \,b^{7} c \,d^{2} n^{2} x^{5}-40320 a \,d^{3} x^{7} b^{7}+7218 b^{8} c^{3} n^{5} x^{2}+316380 b^{8} c^{2} d \,n^{3} x^{4}+417744 b^{8} c \,d^{2} n \,x^{6}-6720 a^{5} b^{3} d^{3} n^{3} x^{3}+1080 a^{4} b^{4} c \,d^{2} n^{4} x^{2}+58800 a^{4} b^{4} d^{3} n^{2} x^{4}-72 a^{3} b^{5} c^{2} d \,n^{5} x -66600 a^{3} b^{5} c \,d^{2} n^{3} x^{3}-92064 a^{3} b^{5} d^{3} n \,x^{5}+2 a^{2} b^{6} c^{3} n^{6}+15372 a^{2} b^{6} c^{2} d \,n^{4} x^{2}+305460 a^{2} b^{6} c \,d^{2} n^{2} x^{4}+40320 a^{2} b^{6} d^{3} x^{6}-1328 a \,b^{7} c^{3} n^{5} x -201468 a \,b^{7} c^{2} d \,n^{3} x^{3}-391824 a \,b^{7} c \,d^{2} n \,x^{5}+41619 b^{8} c^{3} n^{4} x^{2}+589140 b^{8} c^{2} d \,n^{2} x^{4}+155520 b^{8} c \,d^{2} x^{6}-40320 a^{5} b^{3} d^{3} n^{2} x^{3}+21600 a^{4} b^{4} c \,d^{2} n^{3} x^{2}+84000 a^{4} b^{4} d^{3} n \,x^{4}-2232 a^{3} b^{5} c^{2} d \,n^{4} x -225000 a^{3} b^{5} c \,d^{2} n^{2} x^{3}-40320 a^{3} b^{5} d^{3} x^{5}+78 a^{2} b^{6} c^{3} n^{5}+97740 a^{2} b^{6} c^{2} d \,n^{3} x^{2}+360720 a^{2} b^{6} c \,d^{2} n \,x^{4}-11780 a \,b^{7} c^{3} n^{4} x -459648 a \,b^{7} c^{2} d \,n^{2} x^{3}-155520 a \,b^{7} c \,d^{2} x^{5}+144468 b^{8} c^{3} n^{3} x^{2}+572400 b^{8} c^{2} d n \,x^{4}+20160 a^{6} b^{2} d^{3} n^{2} x^{2}-2160 a^{5} b^{3} c \,d^{2} n^{3} x -73920 a^{5} b^{3} d^{3} n \,x^{3}+72 a^{4} b^{4} c^{2} d \,n^{4}+135000 a^{4} b^{4} c \,d^{2} n^{2} x^{2}+40320 a^{4} b^{4} d^{3} x^{4}-26280 a^{3} b^{5} c^{2} d \,n^{3} x -321840 a^{3} b^{5} c \,d^{2} n \,x^{3}+1250 a^{2} b^{6} c^{3} n^{4}+311184 a^{2} b^{6} c^{2} d \,n^{2} x^{2}+155520 a^{2} b^{6} c \,d^{2} x^{4}-59678 a \,b^{7} c^{3} n^{3} x -517968 a \,b^{7} c^{2} d n \,x^{3}+290276 b^{8} c^{3} n^{2} x^{2}+217728 b^{8} c^{2} d \,x^{4}+60480 a^{6} b^{2} d^{3} n \,x^{2}-38880 a^{5} b^{3} c \,d^{2} n^{2} x -40320 a^{5} b^{3} d^{3} x^{3}+2160 a^{4} b^{4} c^{2} d \,n^{3}+270000 a^{4} b^{4} c \,d^{2} n \,x^{2}-142920 a^{3} b^{5} c^{2} d \,n^{2} x -155520 a^{3} b^{5} c \,d^{2} x^{3}+10530 a^{2} b^{6} c^{3} n^{3}+445392 a^{2} b^{6} c^{2} d n \,x^{2}-169580 a \,b^{7} c^{3} n^{2} x -217728 a \,b^{7} c^{2} d \,x^{3}+301872 b^{8} c^{3} n \,x^{2}-40320 a^{7} b \,d^{3} n x +2160 a^{6} b^{2} c \,d^{2} n^{2}+40320 a^{6} b^{2} d^{3} x^{2}-192240 a^{5} b^{3} c \,d^{2} n x +24120 a^{4} b^{4} c^{2} d \,n^{2}+155520 a^{4} b^{4} c \,d^{2} x^{2}-336528 a^{3} b^{5} c^{2} d n x +49148 a^{2} b^{6} c^{3} n^{2}+217728 a^{2} b^{6} c^{2} d \,x^{2}-241392 a \,b^{7} c^{3} n x +120960 b^{8} c^{3} x^{2}-40320 a^{7} b \,d^{3} x +36720 a^{6} b^{2} c \,d^{2} n -155520 a^{5} b^{3} c \,d^{2} x +118800 a^{4} b^{4} c^{2} d n -217728 a^{3} b^{5} c^{2} d x +120432 a^{2} b^{6} c^{3} n -120960 a \,b^{7} c^{3} x +40320 a^{8} d^{3}+155520 a^{6} b^{2} c \,d^{2}+217728 a^{4} b^{4} c^{2} d +120960 a^{2} b^{6} c^{3}\right) \left(b x +a \right)^{n +1}}{\left(n^{9}+45 n^{8}+870 n^{7}+9450 n^{6}+63273 n^{5}+269325 n^{4}+723680 n^{3}+1172700 n^{2}+1026576 n +362880\right) b^{9}}"," ",0,"(b*x+a)^(n+1)*(b^8*d^3*n^8*x^8+36*b^8*d^3*n^7*x^8-8*a*b^7*d^3*n^7*x^7+3*b^8*c*d^2*n^8*x^6+546*b^8*d^3*n^6*x^8-224*a*b^7*d^3*n^6*x^7+114*b^8*c*d^2*n^7*x^6+4536*b^8*d^3*n^5*x^8+56*a^2*b^6*d^3*n^6*x^6-18*a*b^7*c*d^2*n^7*x^5-2576*a*b^7*d^3*n^5*x^7+3*b^8*c^2*d*n^8*x^4+1812*b^8*c*d^2*n^6*x^6+22449*b^8*d^3*n^4*x^8+1176*a^2*b^6*d^3*n^5*x^6-576*a*b^7*c*d^2*n^6*x^5-15680*a*b^7*d^3*n^4*x^7+120*b^8*c^2*d*n^7*x^4+15666*b^8*c*d^2*n^5*x^6+67284*b^8*d^3*n^3*x^8-336*a^3*b^5*d^3*n^5*x^5+90*a^2*b^6*c*d^2*n^6*x^4+9800*a^2*b^6*d^3*n^4*x^6-12*a*b^7*c^2*d*n^7*x^3-7416*a*b^7*c*d^2*n^5*x^5-54152*a*b^7*d^3*n^3*x^7+b^8*c^3*n^8*x^2+2010*b^8*c^2*d*n^6*x^4+80157*b^8*c*d^2*n^4*x^6+118124*b^8*d^3*n^2*x^8-5040*a^3*b^5*d^3*n^4*x^5+2430*a^2*b^6*c*d^2*n^5*x^4+41160*a^2*b^6*d^3*n^3*x^6-432*a*b^7*c^2*d*n^6*x^3-49500*a*b^7*c*d^2*n^4*x^5-105056*a*b^7*d^3*n^2*x^7+42*b^8*c^3*n^7*x^2+18300*b^8*c^2*d*n^5*x^4+246876*b^8*c*d^2*n^3*x^6+109584*b^8*d^3*n*x^8+1680*a^4*b^4*d^3*n^4*x^4-360*a^3*b^5*c*d^2*n^5*x^3-28560*a^3*b^5*d^3*n^3*x^5+36*a^2*b^6*c^2*d*n^6*x^2+24930*a^2*b^6*c*d^2*n^4*x^4+90944*a^2*b^6*d^3*n^2*x^6-2*a*b^7*c^3*n^7*x-6312*a*b^7*c^2*d*n^5*x^3-183942*a*b^7*c*d^2*n^3*x^5-104544*a*b^7*d^3*n*x^7+744*b^8*c^3*n^6*x^2+98319*b^8*c^2*d*n^4*x^4+442908*b^8*c*d^2*n^2*x^6+40320*b^8*d^3*x^8+16800*a^4*b^4*d^3*n^3*x^4-8280*a^3*b^5*c*d^2*n^4*x^3-75600*a^3*b^5*d^3*n^2*x^5+1188*a^2*b^6*c^2*d*n^5*x^2+122850*a^2*b^6*c*d^2*n^3*x^4+98784*a^2*b^6*d^3*n*x^6-80*a*b^7*c^3*n^6*x-47952*a*b^7*c^2*d*n^4*x^3-377604*a*b^7*c*d^2*n^2*x^5-40320*a*b^7*d^3*x^7+7218*b^8*c^3*n^5*x^2+316380*b^8*c^2*d*n^3*x^4+417744*b^8*c*d^2*n*x^6-6720*a^5*b^3*d^3*n^3*x^3+1080*a^4*b^4*c*d^2*n^4*x^2+58800*a^4*b^4*d^3*n^2*x^4-72*a^3*b^5*c^2*d*n^5*x-66600*a^3*b^5*c*d^2*n^3*x^3-92064*a^3*b^5*d^3*n*x^5+2*a^2*b^6*c^3*n^6+15372*a^2*b^6*c^2*d*n^4*x^2+305460*a^2*b^6*c*d^2*n^2*x^4+40320*a^2*b^6*d^3*x^6-1328*a*b^7*c^3*n^5*x-201468*a*b^7*c^2*d*n^3*x^3-391824*a*b^7*c*d^2*n*x^5+41619*b^8*c^3*n^4*x^2+589140*b^8*c^2*d*n^2*x^4+155520*b^8*c*d^2*x^6-40320*a^5*b^3*d^3*n^2*x^3+21600*a^4*b^4*c*d^2*n^3*x^2+84000*a^4*b^4*d^3*n*x^4-2232*a^3*b^5*c^2*d*n^4*x-225000*a^3*b^5*c*d^2*n^2*x^3-40320*a^3*b^5*d^3*x^5+78*a^2*b^6*c^3*n^5+97740*a^2*b^6*c^2*d*n^3*x^2+360720*a^2*b^6*c*d^2*n*x^4-11780*a*b^7*c^3*n^4*x-459648*a*b^7*c^2*d*n^2*x^3-155520*a*b^7*c*d^2*x^5+144468*b^8*c^3*n^3*x^2+572400*b^8*c^2*d*n*x^4+20160*a^6*b^2*d^3*n^2*x^2-2160*a^5*b^3*c*d^2*n^3*x-73920*a^5*b^3*d^3*n*x^3+72*a^4*b^4*c^2*d*n^4+135000*a^4*b^4*c*d^2*n^2*x^2+40320*a^4*b^4*d^3*x^4-26280*a^3*b^5*c^2*d*n^3*x-321840*a^3*b^5*c*d^2*n*x^3+1250*a^2*b^6*c^3*n^4+311184*a^2*b^6*c^2*d*n^2*x^2+155520*a^2*b^6*c*d^2*x^4-59678*a*b^7*c^3*n^3*x-517968*a*b^7*c^2*d*n*x^3+290276*b^8*c^3*n^2*x^2+217728*b^8*c^2*d*x^4+60480*a^6*b^2*d^3*n*x^2-38880*a^5*b^3*c*d^2*n^2*x-40320*a^5*b^3*d^3*x^3+2160*a^4*b^4*c^2*d*n^3+270000*a^4*b^4*c*d^2*n*x^2-142920*a^3*b^5*c^2*d*n^2*x-155520*a^3*b^5*c*d^2*x^3+10530*a^2*b^6*c^3*n^3+445392*a^2*b^6*c^2*d*n*x^2-169580*a*b^7*c^3*n^2*x-217728*a*b^7*c^2*d*x^3+301872*b^8*c^3*n*x^2-40320*a^7*b*d^3*n*x+2160*a^6*b^2*c*d^2*n^2+40320*a^6*b^2*d^3*x^2-192240*a^5*b^3*c*d^2*n*x+24120*a^4*b^4*c^2*d*n^2+155520*a^4*b^4*c*d^2*x^2-336528*a^3*b^5*c^2*d*n*x+49148*a^2*b^6*c^3*n^2+217728*a^2*b^6*c^2*d*x^2-241392*a*b^7*c^3*n*x+120960*b^8*c^3*x^2-40320*a^7*b*d^3*x+36720*a^6*b^2*c*d^2*n-155520*a^5*b^3*c*d^2*x+118800*a^4*b^4*c^2*d*n-217728*a^3*b^5*c^2*d*x+120432*a^2*b^6*c^3*n-120960*a*b^7*c^3*x+40320*a^8*d^3+155520*a^6*b^2*c*d^2+217728*a^4*b^4*c^2*d+120960*a^2*b^6*c^3)/b^9/(n^9+45*n^8+870*n^7+9450*n^6+63273*n^5+269325*n^4+723680*n^3+1172700*n^2+1026576*n+362880)","B"
360,1,1639,282,0.018000," ","int(x*(b*x+a)^n*(d*x^2+c)^3,x)","-\frac{\left(-b^{7} d^{3} n^{7} x^{7}-28 b^{7} d^{3} n^{6} x^{7}+7 a \,b^{6} d^{3} n^{6} x^{6}-3 b^{7} c \,d^{2} n^{7} x^{5}-322 b^{7} d^{3} n^{5} x^{7}+147 a \,b^{6} d^{3} n^{5} x^{6}-90 b^{7} c \,d^{2} n^{6} x^{5}-1960 b^{7} d^{3} n^{4} x^{7}-42 a^{2} b^{5} d^{3} n^{5} x^{5}+15 a \,b^{6} c \,d^{2} n^{6} x^{4}+1225 a \,b^{6} d^{3} n^{4} x^{6}-3 b^{7} c^{2} d \,n^{7} x^{3}-1098 b^{7} c \,d^{2} n^{5} x^{5}-6769 b^{7} d^{3} n^{3} x^{7}-630 a^{2} b^{5} d^{3} n^{4} x^{5}+375 a \,b^{6} c \,d^{2} n^{5} x^{4}+5145 a \,b^{6} d^{3} n^{3} x^{6}-96 b^{7} c^{2} d \,n^{6} x^{3}-7020 b^{7} c \,d^{2} n^{4} x^{5}-13132 b^{7} d^{3} n^{2} x^{7}+210 a^{3} b^{4} d^{3} n^{4} x^{4}-60 a^{2} b^{5} c \,d^{2} n^{5} x^{3}-3570 a^{2} b^{5} d^{3} n^{3} x^{5}+9 a \,b^{6} c^{2} d \,n^{6} x^{2}+3615 a \,b^{6} c \,d^{2} n^{4} x^{4}+11368 a \,b^{6} d^{3} n^{2} x^{6}-b^{7} c^{3} n^{7} x -1254 b^{7} c^{2} d \,n^{5} x^{3}-25227 b^{7} c \,d^{2} n^{3} x^{5}-13068 b^{7} d^{3} n \,x^{7}+2100 a^{3} b^{4} d^{3} n^{3} x^{4}-1260 a^{2} b^{5} c \,d^{2} n^{4} x^{3}-9450 a^{2} b^{5} d^{3} n^{2} x^{5}+261 a \,b^{6} c^{2} d \,n^{5} x^{2}+17025 a \,b^{6} c \,d^{2} n^{3} x^{4}+12348 a \,b^{6} d^{3} n \,x^{6}-34 b^{7} c^{3} n^{6} x -8592 b^{7} c^{2} d \,n^{4} x^{3}-50490 b^{7} c \,d^{2} n^{2} x^{5}-5040 d^{3} x^{7} b^{7}-840 a^{4} b^{3} d^{3} n^{3} x^{3}+180 a^{3} b^{4} c \,d^{2} n^{4} x^{2}+7350 a^{3} b^{4} d^{3} n^{2} x^{4}-18 a^{2} b^{5} c^{2} d \,n^{5} x -9420 a^{2} b^{5} c \,d^{2} n^{3} x^{3}-11508 a^{2} b^{5} d^{3} n \,x^{5}+a \,b^{6} c^{3} n^{6}+2979 a \,b^{6} c^{2} d \,n^{4} x^{2}+41010 a \,b^{6} c \,d^{2} n^{2} x^{4}+5040 a \,d^{3} x^{6} b^{6}-478 b^{7} c^{3} n^{5} x -32979 b^{7} c^{2} d \,n^{3} x^{3}-51432 b^{7} c \,d^{2} n \,x^{5}-5040 a^{4} b^{3} d^{3} n^{2} x^{3}+3240 a^{3} b^{4} c \,d^{2} n^{3} x^{2}+10500 a^{3} b^{4} d^{3} n \,x^{4}-486 a^{2} b^{5} c^{2} d \,n^{4} x -30420 a^{2} b^{5} c \,d^{2} n^{2} x^{3}-5040 a^{2} b^{5} d^{3} x^{5}+33 a \,b^{6} c^{3} n^{5}+16839 a \,b^{6} c^{2} d \,n^{3} x^{2}+47400 a \,b^{6} c \,d^{2} n \,x^{4}-3580 b^{7} c^{3} n^{4} x -69936 b^{7} c^{2} d \,n^{2} x^{3}-20160 b^{7} c \,d^{2} x^{5}+2520 a^{5} b^{2} d^{3} n^{2} x^{2}-360 a^{4} b^{3} c \,d^{2} n^{3} x -9240 a^{4} b^{3} d^{3} n \,x^{3}+18 a^{3} b^{4} c^{2} d \,n^{4}+18540 a^{3} b^{4} c \,d^{2} n^{2} x^{2}+5040 a^{3} b^{4} d^{3} x^{4}-4986 a^{2} b^{5} c^{2} d \,n^{3} x -42360 a^{2} b^{5} c \,d^{2} n \,x^{3}+445 a \,b^{6} c^{3} n^{4}+48420 a \,b^{6} c^{2} d \,n^{2} x^{2}+20160 a \,b^{6} c \,d^{2} x^{4}-15289 b^{7} c^{3} n^{3} x -74628 b^{7} c^{2} d n \,x^{3}+7560 a^{5} b^{2} d^{3} n \,x^{2}-5760 a^{4} b^{3} c \,d^{2} n^{2} x -5040 a^{4} b^{3} d^{3} x^{3}+468 a^{3} b^{4} c^{2} d \,n^{3}+35640 a^{3} b^{4} c \,d^{2} n \,x^{2}-23706 a^{2} b^{5} c^{2} d \,n^{2} x -20160 a^{2} b^{5} c \,d^{2} x^{3}+3135 a \,b^{6} c^{3} n^{3}+64548 a \,b^{6} c^{2} d n \,x^{2}-36706 b^{7} c^{3} n^{2} x -30240 b^{7} c^{2} d \,x^{3}-5040 a^{6} b \,d^{3} n x +360 a^{5} b^{2} c \,d^{2} n^{2}+5040 a^{5} b^{2} d^{3} x^{2}-25560 a^{4} b^{3} c \,d^{2} n x +4518 a^{3} b^{4} c^{2} d \,n^{2}+20160 a^{3} b^{4} c \,d^{2} x^{2}-49428 a^{2} b^{5} c^{2} d n x +12154 a \,b^{6} c^{3} n^{2}+30240 a \,b^{6} c^{2} d \,x^{2}-44712 b^{7} c^{3} n x -5040 a^{6} b \,d^{3} x +5400 a^{5} b^{2} c \,d^{2} n -20160 a^{4} b^{3} c \,d^{2} x +19188 a^{3} b^{4} c^{2} d n -30240 a^{2} b^{5} c^{2} d x +24552 a \,b^{6} c^{3} n -20160 b^{7} c^{3} x +5040 a^{7} d^{3}+20160 a^{5} b^{2} c \,d^{2}+30240 a^{3} b^{4} c^{2} d +20160 a \,b^{6} c^{3}\right) \left(b x +a \right)^{n +1}}{\left(n^{8}+36 n^{7}+546 n^{6}+4536 n^{5}+22449 n^{4}+67284 n^{3}+118124 n^{2}+109584 n +40320\right) b^{8}}"," ",0,"-(b*x+a)^(n+1)*(-b^7*d^3*n^7*x^7-28*b^7*d^3*n^6*x^7+7*a*b^6*d^3*n^6*x^6-3*b^7*c*d^2*n^7*x^5-322*b^7*d^3*n^5*x^7+147*a*b^6*d^3*n^5*x^6-90*b^7*c*d^2*n^6*x^5-1960*b^7*d^3*n^4*x^7-42*a^2*b^5*d^3*n^5*x^5+15*a*b^6*c*d^2*n^6*x^4+1225*a*b^6*d^3*n^4*x^6-3*b^7*c^2*d*n^7*x^3-1098*b^7*c*d^2*n^5*x^5-6769*b^7*d^3*n^3*x^7-630*a^2*b^5*d^3*n^4*x^5+375*a*b^6*c*d^2*n^5*x^4+5145*a*b^6*d^3*n^3*x^6-96*b^7*c^2*d*n^6*x^3-7020*b^7*c*d^2*n^4*x^5-13132*b^7*d^3*n^2*x^7+210*a^3*b^4*d^3*n^4*x^4-60*a^2*b^5*c*d^2*n^5*x^3-3570*a^2*b^5*d^3*n^3*x^5+9*a*b^6*c^2*d*n^6*x^2+3615*a*b^6*c*d^2*n^4*x^4+11368*a*b^6*d^3*n^2*x^6-b^7*c^3*n^7*x-1254*b^7*c^2*d*n^5*x^3-25227*b^7*c*d^2*n^3*x^5-13068*b^7*d^3*n*x^7+2100*a^3*b^4*d^3*n^3*x^4-1260*a^2*b^5*c*d^2*n^4*x^3-9450*a^2*b^5*d^3*n^2*x^5+261*a*b^6*c^2*d*n^5*x^2+17025*a*b^6*c*d^2*n^3*x^4+12348*a*b^6*d^3*n*x^6-34*b^7*c^3*n^6*x-8592*b^7*c^2*d*n^4*x^3-50490*b^7*c*d^2*n^2*x^5-5040*b^7*d^3*x^7-840*a^4*b^3*d^3*n^3*x^3+180*a^3*b^4*c*d^2*n^4*x^2+7350*a^3*b^4*d^3*n^2*x^4-18*a^2*b^5*c^2*d*n^5*x-9420*a^2*b^5*c*d^2*n^3*x^3-11508*a^2*b^5*d^3*n*x^5+a*b^6*c^3*n^6+2979*a*b^6*c^2*d*n^4*x^2+41010*a*b^6*c*d^2*n^2*x^4+5040*a*b^6*d^3*x^6-478*b^7*c^3*n^5*x-32979*b^7*c^2*d*n^3*x^3-51432*b^7*c*d^2*n*x^5-5040*a^4*b^3*d^3*n^2*x^3+3240*a^3*b^4*c*d^2*n^3*x^2+10500*a^3*b^4*d^3*n*x^4-486*a^2*b^5*c^2*d*n^4*x-30420*a^2*b^5*c*d^2*n^2*x^3-5040*a^2*b^5*d^3*x^5+33*a*b^6*c^3*n^5+16839*a*b^6*c^2*d*n^3*x^2+47400*a*b^6*c*d^2*n*x^4-3580*b^7*c^3*n^4*x-69936*b^7*c^2*d*n^2*x^3-20160*b^7*c*d^2*x^5+2520*a^5*b^2*d^3*n^2*x^2-360*a^4*b^3*c*d^2*n^3*x-9240*a^4*b^3*d^3*n*x^3+18*a^3*b^4*c^2*d*n^4+18540*a^3*b^4*c*d^2*n^2*x^2+5040*a^3*b^4*d^3*x^4-4986*a^2*b^5*c^2*d*n^3*x-42360*a^2*b^5*c*d^2*n*x^3+445*a*b^6*c^3*n^4+48420*a*b^6*c^2*d*n^2*x^2+20160*a*b^6*c*d^2*x^4-15289*b^7*c^3*n^3*x-74628*b^7*c^2*d*n*x^3+7560*a^5*b^2*d^3*n*x^2-5760*a^4*b^3*c*d^2*n^2*x-5040*a^4*b^3*d^3*x^3+468*a^3*b^4*c^2*d*n^3+35640*a^3*b^4*c*d^2*n*x^2-23706*a^2*b^5*c^2*d*n^2*x-20160*a^2*b^5*c*d^2*x^3+3135*a*b^6*c^3*n^3+64548*a*b^6*c^2*d*n*x^2-36706*b^7*c^3*n^2*x-30240*b^7*c^2*d*x^3-5040*a^6*b*d^3*n*x+360*a^5*b^2*c*d^2*n^2+5040*a^5*b^2*d^3*x^2-25560*a^4*b^3*c*d^2*n*x+4518*a^3*b^4*c^2*d*n^2+20160*a^3*b^4*c*d^2*x^2-49428*a^2*b^5*c^2*d*n*x+12154*a*b^6*c^3*n^2+30240*a*b^6*c^2*d*x^2-44712*b^7*c^3*n*x-5040*a^6*b*d^3*x+5400*a^5*b^2*c*d^2*n-20160*a^4*b^3*c*d^2*x+19188*a^3*b^4*c^2*d*n-30240*a^2*b^5*c^2*d*x+24552*a*b^6*c^3*n-20160*b^7*c^3*x+5040*a^7*d^3+20160*a^5*b^2*c*d^2+30240*a^3*b^4*c^2*d+20160*a*b^6*c^3)/b^8/(n^8+36*n^7+546*n^6+4536*n^5+22449*n^4+67284*n^3+118124*n^2+109584*n+40320)","B"
361,1,1140,223,0.014000," ","int((b*x+a)^n*(d*x^2+c)^3,x)","\frac{\left(b^{6} d^{3} n^{6} x^{6}+21 b^{6} d^{3} n^{5} x^{6}-6 a \,b^{5} d^{3} n^{5} x^{5}+3 b^{6} c \,d^{2} n^{6} x^{4}+175 b^{6} d^{3} n^{4} x^{6}-90 a \,b^{5} d^{3} n^{4} x^{5}+69 b^{6} c \,d^{2} n^{5} x^{4}+735 b^{6} d^{3} n^{3} x^{6}+30 a^{2} b^{4} d^{3} n^{4} x^{4}-12 a \,b^{5} c \,d^{2} n^{5} x^{3}-510 a \,b^{5} d^{3} n^{3} x^{5}+3 b^{6} c^{2} d \,n^{6} x^{2}+621 b^{6} c \,d^{2} n^{4} x^{4}+1624 b^{6} d^{3} n^{2} x^{6}+300 a^{2} b^{4} d^{3} n^{3} x^{4}-228 a \,b^{5} c \,d^{2} n^{4} x^{3}-1350 a \,b^{5} d^{3} n^{2} x^{5}+75 b^{6} c^{2} d \,n^{5} x^{2}+2775 b^{6} c \,d^{2} n^{3} x^{4}+1764 b^{6} d^{3} n \,x^{6}-120 a^{3} b^{3} d^{3} n^{3} x^{3}+36 a^{2} b^{4} c \,d^{2} n^{4} x^{2}+1050 a^{2} b^{4} d^{3} n^{2} x^{4}-6 a \,b^{5} c^{2} d \,n^{5} x -1572 a \,b^{5} c \,d^{2} n^{3} x^{3}-1644 a \,b^{5} d^{3} n \,x^{5}+b^{6} c^{3} n^{6}+741 b^{6} c^{2} d \,n^{4} x^{2}+6432 b^{6} c \,d^{2} n^{2} x^{4}+720 d^{3} x^{6} b^{6}-720 a^{3} b^{3} d^{3} n^{2} x^{3}+576 a^{2} b^{4} c \,d^{2} n^{3} x^{2}+1500 a^{2} b^{4} d^{3} n \,x^{4}-138 a \,b^{5} c^{2} d \,n^{4} x -4812 a \,b^{5} c \,d^{2} n^{2} x^{3}-720 a \,d^{3} x^{5} b^{5}+27 b^{6} c^{3} n^{5}+3657 b^{6} c^{2} d \,n^{3} x^{2}+7236 b^{6} c \,d^{2} n \,x^{4}+360 a^{4} b^{2} d^{3} n^{2} x^{2}-72 a^{3} b^{3} c \,d^{2} n^{3} x -1320 a^{3} b^{3} d^{3} n \,x^{3}+6 a^{2} b^{4} c^{2} d \,n^{4}+2988 a^{2} b^{4} c \,d^{2} n^{2} x^{2}+720 a^{2} b^{4} d^{3} x^{4}-1206 a \,b^{5} c^{2} d \,n^{3} x -6480 a \,b^{5} c \,d^{2} n \,x^{3}+295 b^{6} c^{3} n^{4}+9336 b^{6} c^{2} d \,n^{2} x^{2}+3024 b^{6} c \,d^{2} x^{4}+1080 a^{4} b^{2} d^{3} n \,x^{2}-1008 a^{3} b^{3} c \,d^{2} n^{2} x -720 a^{3} b^{3} d^{3} x^{3}+132 a^{2} b^{4} c^{2} d \,n^{3}+5472 a^{2} b^{4} c \,d^{2} n \,x^{2}-4902 a \,b^{5} c^{2} d \,n^{2} x -3024 a \,b^{5} c \,d^{2} x^{3}+1665 b^{6} c^{3} n^{3}+11388 b^{6} c^{2} d n \,x^{2}-720 a^{5} b \,d^{3} n x +72 a^{4} b^{2} c \,d^{2} n^{2}+720 a^{4} b^{2} d^{3} x^{2}-3960 a^{3} b^{3} c \,d^{2} n x +1074 a^{2} b^{4} c^{2} d \,n^{2}+3024 a^{2} b^{4} c \,d^{2} x^{2}-8868 a \,b^{5} c^{2} d n x +5104 b^{6} c^{3} n^{2}+5040 b^{6} c^{2} d \,x^{2}-720 a^{5} b \,d^{3} x +936 a^{4} b^{2} c \,d^{2} n -3024 a^{3} b^{3} c \,d^{2} x +3828 a^{2} b^{4} c^{2} d n -5040 a \,b^{5} c^{2} d x +8028 b^{6} c^{3} n +720 a^{6} d^{3}+3024 a^{4} b^{2} c \,d^{2}+5040 a^{2} b^{4} c^{2} d +5040 b^{6} c^{3}\right) \left(b x +a \right)^{n +1}}{\left(n^{7}+28 n^{6}+322 n^{5}+1960 n^{4}+6769 n^{3}+13132 n^{2}+13068 n +5040\right) b^{7}}"," ",0,"(b*x+a)^(n+1)*(b^6*d^3*n^6*x^6+21*b^6*d^3*n^5*x^6-6*a*b^5*d^3*n^5*x^5+3*b^6*c*d^2*n^6*x^4+175*b^6*d^3*n^4*x^6-90*a*b^5*d^3*n^4*x^5+69*b^6*c*d^2*n^5*x^4+735*b^6*d^3*n^3*x^6+30*a^2*b^4*d^3*n^4*x^4-12*a*b^5*c*d^2*n^5*x^3-510*a*b^5*d^3*n^3*x^5+3*b^6*c^2*d*n^6*x^2+621*b^6*c*d^2*n^4*x^4+1624*b^6*d^3*n^2*x^6+300*a^2*b^4*d^3*n^3*x^4-228*a*b^5*c*d^2*n^4*x^3-1350*a*b^5*d^3*n^2*x^5+75*b^6*c^2*d*n^5*x^2+2775*b^6*c*d^2*n^3*x^4+1764*b^6*d^3*n*x^6-120*a^3*b^3*d^3*n^3*x^3+36*a^2*b^4*c*d^2*n^4*x^2+1050*a^2*b^4*d^3*n^2*x^4-6*a*b^5*c^2*d*n^5*x-1572*a*b^5*c*d^2*n^3*x^3-1644*a*b^5*d^3*n*x^5+b^6*c^3*n^6+741*b^6*c^2*d*n^4*x^2+6432*b^6*c*d^2*n^2*x^4+720*b^6*d^3*x^6-720*a^3*b^3*d^3*n^2*x^3+576*a^2*b^4*c*d^2*n^3*x^2+1500*a^2*b^4*d^3*n*x^4-138*a*b^5*c^2*d*n^4*x-4812*a*b^5*c*d^2*n^2*x^3-720*a*b^5*d^3*x^5+27*b^6*c^3*n^5+3657*b^6*c^2*d*n^3*x^2+7236*b^6*c*d^2*n*x^4+360*a^4*b^2*d^3*n^2*x^2-72*a^3*b^3*c*d^2*n^3*x-1320*a^3*b^3*d^3*n*x^3+6*a^2*b^4*c^2*d*n^4+2988*a^2*b^4*c*d^2*n^2*x^2+720*a^2*b^4*d^3*x^4-1206*a*b^5*c^2*d*n^3*x-6480*a*b^5*c*d^2*n*x^3+295*b^6*c^3*n^4+9336*b^6*c^2*d*n^2*x^2+3024*b^6*c*d^2*x^4+1080*a^4*b^2*d^3*n*x^2-1008*a^3*b^3*c*d^2*n^2*x-720*a^3*b^3*d^3*x^3+132*a^2*b^4*c^2*d*n^3+5472*a^2*b^4*c*d^2*n*x^2-4902*a*b^5*c^2*d*n^2*x-3024*a*b^5*c*d^2*x^3+1665*b^6*c^3*n^3+11388*b^6*c^2*d*n*x^2-720*a^5*b*d^3*n*x+72*a^4*b^2*c*d^2*n^2+720*a^4*b^2*d^3*x^2-3960*a^3*b^3*c*d^2*n*x+1074*a^2*b^4*c^2*d*n^2+3024*a^2*b^4*c*d^2*x^2-8868*a*b^5*c^2*d*n*x+5104*b^6*c^3*n^2+5040*b^6*c^2*d*x^2-720*a^5*b*d^3*x+936*a^4*b^2*c*d^2*n-3024*a^3*b^3*c*d^2*x+3828*a^2*b^4*c^2*d*n-5040*a*b^5*c^2*d*x+8028*b^6*c^3*n+720*a^6*d^3+3024*a^4*b^2*c*d^2+5040*a^2*b^4*c^2*d+5040*b^6*c^3)/b^7/(n^7+28*n^6+322*n^5+1960*n^4+6769*n^3+13132*n^2+13068*n+5040)","B"
362,0,0,248,0.033000," ","int((b*x+a)^n*(d*x^2+c)^3/x,x)","\int \frac{\left(d \,x^{2}+c \right)^{3} \left(b x +a \right)^{n}}{x}\, dx"," ",0,"int((b*x+a)^n*(d*x^2+c)^3/x,x)","F"
363,0,0,226,0.063000," ","int(x^4*(e*x+d)^n/(c*x^2+a),x)","\int \frac{x^{4} \left(e x +d \right)^{n}}{c \,x^{2}+a}\, dx"," ",0,"int(x^4*(e*x+d)^n/(c*x^2+a),x)","F"
364,0,0,185,0.047000," ","int(x^3*(e*x+d)^n/(c*x^2+a),x)","\int \frac{x^{3} \left(e x +d \right)^{n}}{c \,x^{2}+a}\, dx"," ",0,"int(x^3*(e*x+d)^n/(c*x^2+a),x)","F"
365,0,0,170,0.043000," ","int(x^2*(e*x+d)^n/(c*x^2+a),x)","\int \frac{x^{2} \left(e x +d \right)^{n}}{c \,x^{2}+a}\, dx"," ",0,"int(x^2*(e*x+d)^n/(c*x^2+a),x)","F"
366,0,0,139,0.041000," ","int(x*(e*x+d)^n/(c*x^2+a),x)","\int \frac{x \left(e x +d \right)^{n}}{c \,x^{2}+a}\, dx"," ",0,"int(x*(e*x+d)^n/(c*x^2+a),x)","F"
367,0,0,143,0.041000," ","int((e*x+d)^n/(c*x^2+a),x)","\int \frac{\left(e x +d \right)^{n}}{c \,x^{2}+a}\, dx"," ",0,"int((e*x+d)^n/(c*x^2+a),x)","F"
368,0,0,185,0.036000," ","int((e*x+d)^n/x/(c*x^2+a),x)","\int \frac{\left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right) x}\, dx"," ",0,"int((e*x+d)^n/x/(c*x^2+a),x)","F"
369,0,0,185,0.054000," ","int((e*x+d)^n/x^2/(c*x^2+a),x)","\int \frac{\left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right) x^{2}}\, dx"," ",0,"int((e*x+d)^n/x^2/(c*x^2+a),x)","F"
370,0,0,298,0.094000," ","int(x^4*(e*x+d)^n/(c*x^2+a)^2,x)","\int \frac{x^{4} \left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right)^{2}}\, dx"," ",0,"int(x^4*(e*x+d)^n/(c*x^2+a)^2,x)","F"
371,0,0,265,0.092000," ","int(x^3*(e*x+d)^n/(c*x^2+a)^2,x)","\int \frac{x^{3} \left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right)^{2}}\, dx"," ",0,"int(x^3*(e*x+d)^n/(c*x^2+a)^2,x)","F"
372,0,0,272,0.061000," ","int(x^2*(e*x+d)^n/(c*x^2+a)^2,x)","\int \frac{x^{2} \left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right)^{2}}\, dx"," ",0,"int(x^2*(e*x+d)^n/(c*x^2+a)^2,x)","F"
373,0,0,243,0.060000," ","int(x*(e*x+d)^n/(c*x^2+a)^2,x)","\int \frac{x \left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right)^{2}}\, dx"," ",0,"int(x*(e*x+d)^n/(c*x^2+a)^2,x)","F"
374,0,0,270,0.055000," ","int((e*x+d)^n/(c*x^2+a)^2,x)","\int \frac{\left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right)^{2}}\, dx"," ",0,"int((e*x+d)^n/(c*x^2+a)^2,x)","F"
375,0,0,431,0.044000," ","int((e*x+d)^n/x/(c*x^2+a)^2,x)","\int \frac{\left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right)^{2} x}\, dx"," ",0,"int((e*x+d)^n/x/(c*x^2+a)^2,x)","F"
376,0,0,457,0.077000," ","int((e*x+d)^n/x^2/(c*x^2+a)^2,x)","\int \frac{\left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right)^{2} x^{2}}\, dx"," ",0,"int((e*x+d)^n/x^2/(c*x^2+a)^2,x)","F"
377,0,0,401,0.073000," ","int((g*x)^m*(e*x+d)^n*(c*x^2+a)^2,x)","\int \left(c \,x^{2}+a \right)^{2} \left(g x \right)^{m} \left(e x +d \right)^{n}\, dx"," ",0,"int((g*x)^m*(e*x+d)^n*(c*x^2+a)^2,x)","F"
378,0,0,166,0.053000," ","int((g*x)^m*(e*x+d)^n*(c*x^2+a),x)","\int \left(c \,x^{2}+a \right) \left(g x \right)^{m} \left(e x +d \right)^{n}\, dx"," ",0,"int((g*x)^m*(e*x+d)^n*(c*x^2+a),x)","F"
379,0,0,136,0.053000," ","int((g*x)^m*(e*x+d)^n/(c*x^2+a),x)","\int \frac{\left(g x \right)^{m} \left(e x +d \right)^{n}}{c \,x^{2}+a}\, dx"," ",0,"int((g*x)^m*(e*x+d)^n/(c*x^2+a),x)","F"
380,0,0,271,0.060000," ","int((g*x)^m*(e*x+d)^n/(c*x^2+a)^2,x)","\int \frac{\left(g x \right)^{m} \left(e x +d \right)^{n}}{\left(c \,x^{2}+a \right)^{2}}\, dx"," ",0,"int((g*x)^m*(e*x+d)^n/(c*x^2+a)^2,x)","F"
381,0,0,117,0.060000," ","int(x^5*(e*x+d)*(b*x^2+a)^p,x)","\int \left(e x +d \right) x^{5} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^5*(e*x+d)*(b*x^2+a)^p,x)","F"
382,0,0,117,0.050000," ","int(x^4*(e*x+d)*(b*x^2+a)^p,x)","\int \left(e x +d \right) x^{4} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^4*(e*x+d)*(b*x^2+a)^p,x)","F"
383,0,0,92,0.050000," ","int(x^3*(e*x+d)*(b*x^2+a)^p,x)","\int \left(e x +d \right) x^{3} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^3*(e*x+d)*(b*x^2+a)^p,x)","F"
384,0,0,92,0.036000," ","int(x^2*(e*x+d)*(b*x^2+a)^p,x)","\int \left(e x +d \right) x^{2} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^2*(e*x+d)*(b*x^2+a)^p,x)","F"
385,0,0,69,0.033000," ","int(x*(e*x+d)*(b*x^2+a)^p,x)","\int \left(e x +d \right) x \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x*(e*x+d)*(b*x^2+a)^p,x)","F"
386,0,0,66,0.027000," ","int((e*x+d)*(b*x^2+a)^p,x)","\int \left(e x +d \right) \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x+d)*(b*x^2+a)^p,x)","F"
387,0,0,86,0.023000," ","int((e*x+d)*(b*x^2+a)^p/x,x)","\int \frac{\left(e x +d \right) \left(b \,x^{2}+a \right)^{p}}{x}\, dx"," ",0,"int((e*x+d)*(b*x^2+a)^p/x,x)","F"
388,0,0,89,0.028000," ","int((e*x+d)*(b*x^2+a)^p/x^2,x)","\int \frac{\left(e x +d \right) \left(b \,x^{2}+a \right)^{p}}{x^{2}}\, dx"," ",0,"int((e*x+d)*(b*x^2+a)^p/x^2,x)","F"
389,0,0,90,0.037000," ","int((e*x+d)*(b*x^2+a)^p/x^3,x)","\int \frac{\left(e x +d \right) \left(b \,x^{2}+a \right)^{p}}{x^{3}}\, dx"," ",0,"int((e*x+d)*(b*x^2+a)^p/x^3,x)","F"
390,0,0,176,0.074000," ","int(x^5*(e*x+d)^2*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{2} x^{5} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^5*(e*x+d)^2*(b*x^2+a)^p,x)","F"
391,0,0,173,0.069000," ","int(x^4*(e*x+d)^2*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{2} x^{4} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^4*(e*x+d)^2*(b*x^2+a)^p,x)","F"
392,0,0,139,0.058000," ","int(x^3*(e*x+d)^2*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{2} x^{3} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^3*(e*x+d)^2*(b*x^2+a)^p,x)","F"
393,0,0,148,0.053000," ","int(x^2*(e*x+d)^2*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{2} x^{2} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^2*(e*x+d)^2*(b*x^2+a)^p,x)","F"
394,0,0,105,0.045000," ","int(x*(e*x+d)^2*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{2} x \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x*(e*x+d)^2*(b*x^2+a)^p,x)","F"
395,0,0,131,0.040000," ","int((e*x+d)^2*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{2} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x+d)^2*(b*x^2+a)^p,x)","F"
396,0,0,114,0.034000," ","int((e*x+d)^2*(b*x^2+a)^p/x,x)","\int \frac{\left(e x +d \right)^{2} \left(b \,x^{2}+a \right)^{p}}{x}\, dx"," ",0,"int((e*x+d)^2*(b*x^2+a)^p/x,x)","F"
397,0,0,127,0.033000," ","int((e*x+d)^2*(b*x^2+a)^p/x^2,x)","\int \frac{\left(e x +d \right)^{2} \left(b \,x^{2}+a \right)^{p}}{x^{2}}\, dx"," ",0,"int((e*x+d)^2*(b*x^2+a)^p/x^2,x)","F"
398,0,0,123,0.046000," ","int((e*x+d)^2*(b*x^2+a)^p/x^3,x)","\int \frac{\left(e x +d \right)^{2} \left(b \,x^{2}+a \right)^{p}}{x^{3}}\, dx"," ",0,"int((e*x+d)^2*(b*x^2+a)^p/x^3,x)","F"
399,0,0,235,0.073000," ","int(x^5*(e*x+d)^3*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{3} x^{5} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^5*(e*x+d)^3*(b*x^2+a)^p,x)","F"
400,0,0,237,0.085000," ","int(x^4*(e*x+d)^3*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{3} x^{4} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^4*(e*x+d)^3*(b*x^2+a)^p,x)","F"
401,0,0,197,0.070000," ","int(x^3*(e*x+d)^3*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{3} x^{3} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^3*(e*x+d)^3*(b*x^2+a)^p,x)","F"
402,0,0,200,0.064000," ","int(x^2*(e*x+d)^3*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{3} x^{2} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^2*(e*x+d)^3*(b*x^2+a)^p,x)","F"
403,0,0,161,0.053000," ","int(x*(e*x+d)^3*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{3} x \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x*(e*x+d)^3*(b*x^2+a)^p,x)","F"
404,0,0,170,0.046000," ","int((e*x+d)^3*(b*x^2+a)^p,x)","\int \left(e x +d \right)^{3} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((e*x+d)^3*(b*x^2+a)^p,x)","F"
405,0,0,167,0.031000," ","int((e*x+d)^3*(b*x^2+a)^p/x,x)","\int \frac{\left(e x +d \right)^{3} \left(b \,x^{2}+a \right)^{p}}{x}\, dx"," ",0,"int((e*x+d)^3*(b*x^2+a)^p/x,x)","F"
406,0,0,155,0.037000," ","int((e*x+d)^3*(b*x^2+a)^p/x^2,x)","\int \frac{\left(e x +d \right)^{3} \left(b \,x^{2}+a \right)^{p}}{x^{2}}\, dx"," ",0,"int((e*x+d)^3*(b*x^2+a)^p/x^2,x)","F"
407,0,0,164,0.048000," ","int((e*x+d)^3*(b*x^2+a)^p/x^3,x)","\int \frac{\left(e x +d \right)^{3} \left(b \,x^{2}+a \right)^{p}}{x^{3}}\, dx"," ",0,"int((e*x+d)^3*(b*x^2+a)^p/x^3,x)","F"
408,0,0,189,0.053000," ","int(x^4*(b*x^2+a)^p/(e*x+d),x)","\int \frac{x^{4} \left(b \,x^{2}+a \right)^{p}}{e x +d}\, dx"," ",0,"int(x^4*(b*x^2+a)^p/(e*x+d),x)","F"
409,0,0,155,0.047000," ","int(x^3*(b*x^2+a)^p/(e*x+d),x)","\int \frac{x^{3} \left(b \,x^{2}+a \right)^{p}}{e x +d}\, dx"," ",0,"int(x^3*(b*x^2+a)^p/(e*x+d),x)","F"
410,0,0,153,0.044000," ","int(x^2*(b*x^2+a)^p/(e*x+d),x)","\int \frac{x^{2} \left(b \,x^{2}+a \right)^{p}}{e x +d}\, dx"," ",0,"int(x^2*(b*x^2+a)^p/(e*x+d),x)","F"
411,0,0,167,0.037000," ","int(x*(b*x^2+a)^p/(e*x+d),x)","\int \frac{x \left(b \,x^{2}+a \right)^{p}}{e x +d}\, dx"," ",0,"int(x*(b*x^2+a)^p/(e*x+d),x)","F"
412,0,0,121,0.046000," ","int((b*x^2+a)^p/(e*x+d),x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{e x +d}\, dx"," ",0,"int((b*x^2+a)^p/(e*x+d),x)","F"
413,0,0,172,0.061000," ","int((b*x^2+a)^p/x/(e*x+d),x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right) x}\, dx"," ",0,"int((b*x^2+a)^p/x/(e*x+d),x)","F"
414,0,0,174,0.048000," ","int((b*x^2+a)^p/x^2/(e*x+d),x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right) x^{2}}\, dx"," ",0,"int((b*x^2+a)^p/x^2/(e*x+d),x)","F"
415,0,0,207,0.066000," ","int((b*x^2+a)^p/x^3/(e*x+d),x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right) x^{3}}\, dx"," ",0,"int((b*x^2+a)^p/x^3/(e*x+d),x)","F"
416,0,0,388,0.064000," ","int(x^4*(b*x^2+a)^p/(e*x+d)^2,x)","\int \frac{x^{4} \left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x^4*(b*x^2+a)^p/(e*x+d)^2,x)","F"
417,0,0,313,0.056000," ","int(x^3*(b*x^2+a)^p/(e*x+d)^2,x)","\int \frac{x^{3} \left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x^3*(b*x^2+a)^p/(e*x+d)^2,x)","F"
418,0,0,277,0.053000," ","int(x^2*(b*x^2+a)^p/(e*x+d)^2,x)","\int \frac{x^{2} \left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x^2*(b*x^2+a)^p/(e*x+d)^2,x)","F"
419,0,0,267,0.048000," ","int(x*(b*x^2+a)^p/(e*x+d)^2,x)","\int \frac{x \left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int(x*(b*x^2+a)^p/(e*x+d)^2,x)","F"
420,0,0,240,0.049000," ","int((b*x^2+a)^p/(e*x+d)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((b*x^2+a)^p/(e*x+d)^2,x)","F"
421,0,0,356,0.041000," ","int((b*x^2+a)^p/x/(e*x+d)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2} x}\, dx"," ",0,"int((b*x^2+a)^p/x/(e*x+d)^2,x)","F"
422,0,0,411,0.061000," ","int((b*x^2+a)^p/x^2/(e*x+d)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2} x^{2}}\, dx"," ",0,"int((b*x^2+a)^p/x^2/(e*x+d)^2,x)","F"
423,0,0,439,0.088000," ","int(x^4*(b*x^2+a)^p/(e*x+d)^3,x)","\int \frac{x^{4} \left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int(x^4*(b*x^2+a)^p/(e*x+d)^3,x)","F"
424,0,0,408,0.081000," ","int(x^3*(b*x^2+a)^p/(e*x+d)^3,x)","\int \frac{x^{3} \left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int(x^3*(b*x^2+a)^p/(e*x+d)^3,x)","F"
425,0,0,388,0.075000," ","int(x^2*(b*x^2+a)^p/(e*x+d)^3,x)","\int \frac{x^{2} \left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int(x^2*(b*x^2+a)^p/(e*x+d)^3,x)","F"
426,0,0,328,0.070000," ","int(x*(b*x^2+a)^p/(e*x+d)^3,x)","\int \frac{x \left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int(x*(b*x^2+a)^p/(e*x+d)^3,x)","F"
427,0,0,312,0.063000," ","int((b*x^2+a)^p/(e*x+d)^3,x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((b*x^2+a)^p/(e*x+d)^3,x)","F"
428,0,0,678,0.054000," ","int((b*x^2+a)^p/x/(e*x+d)^3,x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3} x}\, dx"," ",0,"int((b*x^2+a)^p/x/(e*x+d)^3,x)","F"
429,0,0,730,0.097000," ","int((b*x^2+a)^p/x^2/(e*x+d)^3,x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3} x^{2}}\, dx"," ",0,"int((b*x^2+a)^p/x^2/(e*x+d)^3,x)","F"
430,0,0,272,0.063000," ","int((g*x)^m*(e*x+d)^3*(c*x^2+a)^p,x)","\int \left(e x +d \right)^{3} \left(g x \right)^{m} \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((g*x)^m*(e*x+d)^3*(c*x^2+a)^p,x)","F"
431,0,0,201,0.056000," ","int((g*x)^m*(e*x+d)^2*(c*x^2+a)^p,x)","\int \left(e x +d \right)^{2} \left(g x \right)^{m} \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((g*x)^m*(e*x+d)^2*(c*x^2+a)^p,x)","F"
432,0,0,131,0.050000," ","int((g*x)^m*(e*x+d)*(c*x^2+a)^p,x)","\int \left(e x +d \right) \left(g x \right)^{m} \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((g*x)^m*(e*x+d)*(c*x^2+a)^p,x)","F"
433,0,0,64,0.064000," ","int((g*x)^m*(c*x^2+a)^p,x)","\int \left(g x \right)^{m} \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((g*x)^m*(c*x^2+a)^p,x)","F"
434,0,0,149,0.053000," ","int((g*x)^m*(c*x^2+a)^p/(e*x+d),x)","\int \frac{\left(g x \right)^{m} \left(c \,x^{2}+a \right)^{p}}{e x +d}\, dx"," ",0,"int((g*x)^m*(c*x^2+a)^p/(e*x+d),x)","F"
435,0,0,226,0.058000," ","int((g*x)^m*(c*x^2+a)^p/(e*x+d)^2,x)","\int \frac{\left(g x \right)^{m} \left(c \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((g*x)^m*(c*x^2+a)^p/(e*x+d)^2,x)","F"
436,0,0,305,0.069000," ","int((g*x)^m*(c*x^2+a)^p/(e*x+d)^3,x)","\int \frac{\left(g x \right)^{m} \left(c \,x^{2}+a \right)^{p}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((g*x)^m*(c*x^2+a)^p/(e*x+d)^3,x)","F"
437,1,946,315,0.028000," ","int(x^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)/(e*x+d),x)","-\frac{5 a^{4} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, c^{3} d^{3}}-\frac{a^{3} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32 \sqrt{c d e}\, c^{2} d}-\frac{3 a^{2} d \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{64 \sqrt{c d e}\, c}-\frac{a \,d^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, e^{2}}+\frac{11 a \,d^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32 \sqrt{c d e}\, e^{2}}+\frac{c \,d^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, e^{4}}-\frac{29 c \,d^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, e^{4}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e x}{32 c^{2} d^{2}}+\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a x}{16 c e}+\frac{29 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{2} x}{32 e^{3}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{2}}{64 c^{3} d^{3}}+\frac{19 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2}}{64 c^{2} d}+\frac{43 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a d}{64 c \,e^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{3}}{e^{4}}+\frac{29 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{3}}{64 e^{4}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} x}{4 c d \,e^{2}}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a}{24 c^{2} d^{2} e}-\frac{13 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{24 c \,e^{3}}"," ",0,"19/64/c^2/d*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*a^2+29/32/e^3*d^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*x-1/32*e^2/c^2*a^3/d*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(c*d*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(c*d*e)^(1/2)+5/32*e/c^2/d^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*x*a^2-5/128*e^4/c^3/d^3*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(c*d*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(c*d*e)^(1/2)*a^4+1/4/e^2*x*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)/c/d-5/24/e/c^2/d^2*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)*a+7/16/e/c*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*x*a+5/64*e^2/c^3/d^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*a^3+43/64/e^2/c*d*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)*a-3/64/c*d*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(c*d*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(c*d*e)^(1/2)*a^2-29/128/e^4*c*d^5*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(c*d*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(c*d*e)^(1/2)+11/32/e^2*a*d^3*ln((1/2*a*e^2+1/2*c*d^2+c*d*e*x)/(c*d*e)^(1/2)+(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2))/(c*d*e)^(1/2)-d^3/e^4*(c*d*e*(x+d/e)^2+(a*e^2-c*d^2)*(x+d/e))^(1/2)-13/24/e^3/c*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(3/2)+29/64/e^4*d^3*(a*d*e+(a*e^2+c*d^2)*x+c*d*e*x^2)^(1/2)-1/2*d^3/e^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+(c*d*e*(x+d/e)^2+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a+1/2*d^5/e^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+(c*d*e*(x+d/e)^2+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c","B"
438,1,713,225,0.014000," ","int(x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d),x)","\frac{a^{3} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c^{2} d^{2}}+\frac{a^{2} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c}+\frac{a \,d^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, e}-\frac{5 a \,d^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, e}-\frac{c \,d^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, e^{3}}+\frac{3 c \,d^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, e^{3}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a x}{4 c d}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d x}{4 e^{2}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e}{8 c^{2} d^{2}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a}{2 c e}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{2}}{8 e^{3}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{2}}{e^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{3 c d \,e^{2}}"," ",0,"1/3/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/c/d-1/4/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-3/4/e^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/8*e/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-1/2/e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-3/8/e^3*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/16*e^3/c^2/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+1/16*e/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-5/16/e*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+3/16/e^3*c*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+d^2/e^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/2*d^2/e*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a-1/2*d^4/e^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c","B"
439,1,516,181,0.010000," ","int(x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d),x)","-\frac{a^{2} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, c d}-\frac{a d \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}}+\frac{a d \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4 \sqrt{c d e}}+\frac{c \,d^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, e^{2}}-\frac{c \,d^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, e^{2}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, x}{2 e}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a}{4 c d}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d}{4 e^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d}{e^{2}}"," ",0,"1/2/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/4/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+1/4/e^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/8*e^2/c/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+1/4*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-1/8/e^2*c*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-d/e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/2*d*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a+1/2*d^3/e^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c","B"
440,1,205,111,0.006000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d),x)","\frac{a e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}}-\frac{c \,d^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}{e}"," ",0,"1/e*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/2*e*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a-1/2/e*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c*d^2","A"
441,1,439,136,0.015000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/x/(e*x+d),x)","-\frac{a \,e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, d}+\frac{a \,e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, d}-\frac{a e \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{\sqrt{a d e}}+\frac{c d \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}}+\frac{c d \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}{d}"," ",0,"1/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a*e^2+1/2*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c-a*e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-1/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/2/d*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a*e^2+1/2*d*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c","B"
442,1,594,117,0.015000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/x^2/(e*x+d),x)","\frac{a \,e^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}\, d}+\frac{a \,e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, d^{2}}-\frac{a \,e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, d^{2}}-\frac{c d \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}}-\frac{c e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}}+\frac{c e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c x}{a d}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}{a e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e}{d^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{a \,d^{2} e x}"," ",0,"-1/d^2/a/e/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/a/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+1/2*e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c+1/2/d*a*e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-1/2*d/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c+1/d*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/2*e^3/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+e/d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/2*e^3/d^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a-1/2*e*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c","B"
443,1,882,176,0.017000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/x^3/(e*x+d),x)","-\frac{3 a \,e^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}\, d^{2}}-\frac{a \,e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, d^{3}}+\frac{a \,e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, d^{3}}+\frac{c^{2} d^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}\, a e}+\frac{c \,e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, d}-\frac{c \,e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, d}+\frac{c e \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{4 \sqrt{a d e}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c e x}{4 a \,d^{2}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} x}{4 a^{2} e}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}{a d}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}{4 a^{2} e^{2}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{2}}{4 d^{3}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{2}}{d^{3}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{4 a \,d^{3} x}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}{4 a^{2} d \,e^{2} x}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{2 a \,d^{2} e \,x^{2}}"," ",0,"5/4/d^3/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-1/4*e^2/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/d/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-1/2*e^2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c-3/8*e^3/d^2*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+1/4*e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-5/4*e/d^2*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/2/d^2/a/e/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/4/d/a^2/e^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c-1/4*d/a^2/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+1/8*d^2/a/e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-1/4/a^2/e*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/2/d^3*e^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-1/d^3*e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/2/d^3*e^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a+1/2/d*e^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c","B"
444,1,1165,256,0.019000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/x^4/(e*x+d),x)","\frac{5 a \,e^{4} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, d^{3}}+\frac{a \,e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, d^{4}}-\frac{a \,e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, d^{4}}-\frac{c^{2} d \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, a}-\frac{c^{3} d^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, a^{2} e^{2}}-\frac{3 c \,e^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, d}-\frac{c \,e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, d^{2}}+\frac{c \,e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, d^{2}}+\frac{11 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{2} x}{8 a \,d^{3}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} x}{2 a^{2} d}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d x}{8 a^{3} e^{2}}+\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c e}{8 a \,d^{2}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}{8 a^{2} e}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2}}{8 a^{3} e^{3}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{3}}{d^{4}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{3}}{8 d^{4}}-\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e}{8 a \,d^{4} x}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}{2 a^{2} d^{2} e x}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2}}{8 a^{3} e^{3} x}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{4 a \,d^{3} x^{2}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}{4 a^{2} d \,e^{2} x^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{3 a \,d^{2} e \,x^{3}}"," ",0,"3/4/d^3/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+3/8/e/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+1/4/d/a^2/e^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c-1/16*d^3/a^2/e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3+1/8*d/a^3/e^2*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/2/e/d^2/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c+11/8/d^3*e^2*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/d^4*e^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/8/d^4*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/16*d/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2+1/2/d/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/3/d^2/a/e/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-1/8/a^3/e^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2+1/8*d^2/a^3/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-1/2/d^4*e^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+1/2/d^4*e^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a-1/2/d^2*e^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c-11/8/d^4*e/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+9/8/d^2*e/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+1/2/d^2*e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c+5/16/d^3*e^4*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-3/16/d*e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c","B"
445,1,1494,355,0.023000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/x^5/(e*x+d),x)","-\frac{35 a \,e^{5} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{128 \sqrt{a d e}\, d^{4}}-\frac{a \,e^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, d^{5}}+\frac{a \,e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, d^{5}}+\frac{3 c^{2} e \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{64 \sqrt{a d e}\, a}+\frac{c^{3} d^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{32 \sqrt{a d e}\, a^{2} e}+\frac{5 c^{4} d^{4} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{128 \sqrt{a d e}\, a^{3} e^{3}}+\frac{5 c \,e^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{32 \sqrt{a d e}\, d^{2}}+\frac{c \,e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{2 \sqrt{c d e}\, d^{3}}-\frac{c \,e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, d^{3}}-\frac{93 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{3} x}{64 a \,d^{4}}-\frac{43 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} e x}{64 a^{2} d^{2}}-\frac{19 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} x}{64 a^{3} e}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{2} x}{64 a^{4} e^{3}}-\frac{39 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{2}}{32 a \,d^{3}}-\frac{17 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}{32 a^{2} d}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d}{32 a^{3} e^{2}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{3}}{64 a^{4} e^{4}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{4}}{d^{5}}-\frac{29 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{4}}{64 d^{5}}+\frac{93 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e^{2}}{64 a \,d^{5} x}+\frac{43 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}{64 a^{2} d^{3} x}+\frac{19 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2}}{64 a^{3} d \,e^{2} x}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} d}{64 a^{4} e^{4} x}-\frac{29 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e}{32 a \,d^{4} x^{2}}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}{16 a^{2} d^{2} e \,x^{2}}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2}}{32 a^{3} e^{3} x^{2}}+\frac{13 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{24 a \,d^{3} x^{3}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}{24 a^{2} d \,e^{2} x^{3}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{4 a \,d^{2} e \,x^{4}}"," ",0,"19/64/e^2/d/a^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2+1/32/e*d^2/a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3-43/64/d^2*e/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-93/64/d^4*e^3*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+13/24/d^3/a/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-17/32/d/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+5/128*d^4/a^3/e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^4-5/64*d^2/a^4/e^3*c^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+5/64*d/a^4/e^4/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^3+5/24/d/a^2/e^2/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c-7/16/e/d^2/a^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c-1/d^5*e^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-29/64/d^5*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/4/d^2/a/e/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/2/d^5*e^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-1/2/d^5*e^6*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*a+1/2/d^3*e^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)*c+93/64/d^5*e^2/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-39/32/d^3*e^2/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-1/2/d^3*e^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c-35/128/d^4*e^5*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+5/32/d^2*e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-29/32/d^4*e/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+43/64/d^3/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c+3/64*e/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-7/32/e^2*d/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-19/64/e/a^3*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-5/32/a^3/e^3/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2-5/64*d^3/a^4/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4","B"
446,1,1883,415,0.026000," ","int(x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d),x)","\frac{7 a^{6} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c^{4} d^{4}}-\frac{3 a^{5} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}\, c^{3} d^{2}}-\frac{3 a^{4} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c^{2}}+\frac{a^{3} d^{2} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c}-\frac{17 a^{3} d^{2} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c}-\frac{3 a^{2} d^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e}+\frac{177 a^{2} d^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, e}+\frac{3 a c \,d^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e^{3}}-\frac{75 a c \,d^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}\, e^{3}}-\frac{c^{2} d^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e^{5}}+\frac{43 c^{2} d^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, e^{5}}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{4} x}{256 c^{3} d^{3}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{2} x}{32 c^{2} d}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d x}{128 c}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{3} x}{4 e^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,d^{3} x}{4 e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{5} x}{4 e^{4}}-\frac{43 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{5} x}{256 e^{4}}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{5}}{512 c^{4} d^{4}}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{3}}{512 c^{3} d^{2}}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e}{256 c^{2}}+\frac{29 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{2}}{256 c e}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} d^{2}}{8 c e}+\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{4}}{512 e^{3}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{6}}{8 e^{5}}-\frac{43 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{6}}{512 e^{5}}+\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e x}{96 c^{2} d^{2}}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a x}{48 c e}+\frac{43 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{2} x}{96 e^{3}}+\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{2}}{192 c^{3} d^{3}}+\frac{29 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2}}{192 c^{2} d}+\frac{65 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a d}{192 c \,e^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} d^{3}}{3 e^{4}}+\frac{43 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{3}}{192 e^{4}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} x}{6 c d \,e^{2}}-\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a}{60 c^{2} d^{2} e}-\frac{19 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{60 c \,e^{3}}"," ",0,"1/8*d^6/e^5*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-43/512/e^5*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+43/96/e^3*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+21/512/e^3*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-7/256*e/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+29/192/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-75/512/e^3*c*d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+1/16*d^2*e*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/16*d^6/e^3*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/32*e^2/c^2*a^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+7/96*e/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2-7/256*e^4/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4+7/1024*e^7/c^4/d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6-3/512*e^5/c^3/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-17/256*e/c*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-3/16*d^4/e*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/4*d^5/e^4*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/16*d^8/e^5*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/128/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+1/4/e^2*a*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+11/48/e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a-3/1024*e^3/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+177/1024/e*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+65/192/e^2/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+7/192*e^2/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3-43/256/e^4*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-7/512*e^5/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5-15/512*e^3/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4+29/256/e/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+43/1024/e^5*c^2*d^8*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-7/60/e/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a+1/6/e^2*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/c/d-1/3*d^3/e^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-19/60/e^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+43/192/e^4*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-1/4*d^3/e^2*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8*d^2/e*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","B"
447,1,1560,322,0.016000," ","int(x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d),x)","-\frac{3 a^{5} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{3} d^{3}}+\frac{3 a^{4} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{2} d}-\frac{a^{3} d \,e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c}+\frac{9 a^{3} d \,e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, c}+\frac{3 a^{2} d^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}-\frac{21 a^{2} d^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}}-\frac{3 a c \,d^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e^{2}}+\frac{33 a c \,d^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, e^{2}}+\frac{c^{2} d^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e^{4}}-\frac{9 c^{2} d^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, e^{4}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{3} x}{64 c^{2} d^{2}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e x}{64 c}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,d^{2} x}{4 e}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2} x}{64 e}+\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{4} x}{64 e^{3}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{4} x}{4 e^{3}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{4}}{128 c^{3} d^{3}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{2}}{64 c^{2} d}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d}{32 c}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} d}{8 c}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{3}}{64 e^{2}}+\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{5}}{128 e^{4}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{5}}{8 e^{4}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a x}{8 c d}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d x}{8 e^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e}{16 c^{2} d^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a}{4 c e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} d^{2}}{3 e^{3}}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d^{2}}{16 e^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{5 c d \,e^{2}}"," ",0,"-21/128*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-3/32/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+9/128/e^4*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/4/e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-3/64/e^2*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+1/5/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/c/d-3/8/e^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/8*d*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/16*d^3*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/8*d^5/e^4*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/16*d*e^2*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/16*d^5/e^2*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64*e^3/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-3/256*e^6/c^3/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5+3/256*e^4/c^2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+9/128*e^2/c*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+33/256/e^2*c*d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+1/16*d^7/e^4*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/16*e/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2+9/64/e^3*c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+3/128*e^4/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-1/8/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a+3/64*e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+1/3*d^2/e^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-3/16/e^3*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/4*d^2/e*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/4*d^4/e^3*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/64*e^2/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-15/64/e*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-9/256/e^4*c^2*d^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","B"
448,1,1279,265,0.012000," ","int(x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d),x)","\frac{3 a^{4} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, c^{2} d^{2}}+\frac{a^{3} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c}-\frac{3 a^{3} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32 \sqrt{c d e}\, c}-\frac{3 a^{2} d^{2} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{9 a^{2} d^{2} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{64 \sqrt{c d e}}+\frac{3 a c \,d^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e}-\frac{3 a c \,d^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{32 \sqrt{c d e}\, e}-\frac{c^{2} d^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e^{3}}+\frac{3 c^{2} d^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, e^{3}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{2} x}{32 c d}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a d x}{16}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a d x}{4}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{3} x}{32 e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{3} x}{4 e^{2}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{3}}{64 c^{2} d^{2}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e}{64 c}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e}{8 c}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2}}{64 e}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{4}}{64 e^{3}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{4}}{8 e^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} x}{4 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a}{8 c d}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} d}{8 e^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} d}{3 e^{2}}"," ",0,"1/4/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/8/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+1/8/e^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-3/32*e^2/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+3/16*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-3/32/e^2*c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-3/64*e^3/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+3/64*e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+3/64/e*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-3/64/e^3*c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/128*e^5/c^2/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-3/32*e^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+9/64*e*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-3/32/e*c*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+3/128/e^3*c^2*d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-1/3*d/e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-1/4*d*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8*e*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/16*e^3*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/16*d^2*e*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/16*d^4/e*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/4*d^3/e^2*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/8*d^4/e^3*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/16*d^6/e^3*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
449,1,566,175,0.010000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d),x)","-\frac{a^{3} e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c d}+\frac{3 a^{2} d \,e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}-\frac{3 a c \,d^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{c^{2} d^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a e x}{4}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{2} x}{4 e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{2}}{8 c d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{3}}{8 e^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}}}{3 e}"," ",0,"1/3/e*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+1/4*e*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/8*e^2*a^2/c/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/16*e^4*a^3/c/d*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/16*e^2*a^2*d*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/16*a*c*d^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/4/e*c*d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8/e^2*c*d^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/16/e^2*c^2*d^5*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
450,1,1130,213,0.015000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/x/(e*x+d),x)","\frac{a^{3} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c \,d^{2}}-\frac{a^{3} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c \,d^{2}}-\frac{a^{2} d \,e^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{\sqrt{a d e}}-\frac{3 a^{2} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{9 a^{2} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}+\frac{3 a c \,d^{2} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{9 a c \,d^{2} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}-\frac{c^{2} d^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, e}-\frac{c^{2} d^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, e}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{2} x}{4 d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,e^{2} x}{4 d}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d x}{4}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c d x}{4}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{3}}{8 c \,d^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{3}}{8 c \,d^{2}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a e}{4}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,d^{2}}{8 e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,d^{2}}{8 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}{3 d}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}}}{3 d}"," ",0,"1/3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/4/d*a*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/8/d^2*a^2*e^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+5/4*a*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/16/d^2*a^3*e^5/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+9/16*a^2*e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+9/16*d^2*a*e*c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+1/4*d*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/8*d^2*c/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/16*d^4*c^2/e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-d*a^2*e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-1/3/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-1/4/d*a*e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8/d^2*a^2*e^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/16/d^2*a^3*e^5/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/16*a^2*e^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/16*d^2*a*e*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/4*d*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/8*d^2*c/e*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/16*d^4*c^2/e*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
451,1,1310,202,0.017000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/x^2/(e*x+d),x)","-\frac{a^{3} e^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c \,d^{3}}+\frac{a^{3} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c \,d^{3}}+\frac{3 a^{2} e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, d}-\frac{3 a^{2} e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, d}-\frac{a^{2} e^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}}-\frac{3 a c \,d^{2} e \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}}-\frac{3 a c d \,e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{27 a c d \,e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}+\frac{c^{2} d^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{7 c^{2} d^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{3} x}{4 d^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,e^{3} x}{4 d^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c e x}{4}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c e x}{4}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{4}}{8 c \,d^{3}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{4}}{8 c \,d^{3}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{2}}{d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c d}{8}+\frac{17 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d}{8}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c x}{a d}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c}{a e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} e}{3 d^{2}}+\frac{2 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e}{3 d^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{a \,d^{2} e x}"," ",0,"-1/4*e*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/16*d^3*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/d*a*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/a/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c+5/4*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c-1/2*a^2*e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+7/16*d^3*c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-1/16*e^6/d^3*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/16*e^2*d*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/16*e^6/d^3*a^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+27/16*d*a*e^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c-3/2*d^2*a*e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c+1/3*e/d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-1/8*d*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+2/3/d^2*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+17/8*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-1/4*e^3/d^2*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-3/16/d*a^2*e^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+1/d*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-1/d^2/a/e/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/8*e^4/d^3*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/4*e^3/d^2*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/8*e^4/d^3*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/16*e^4/d*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
452,1,1604,218,0.019000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/x^3/(e*x+d),x)","\frac{a^{3} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c \,d^{4}}-\frac{a^{3} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c \,d^{4}}+\frac{a^{2} e^{4} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}\, d}-\frac{3 a^{2} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, d^{2}}+\frac{3 a^{2} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, d^{2}}-\frac{3 a c d \,e^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{4 \sqrt{a d e}}+\frac{3 a c \,e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}-\frac{3 a c \,e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}-\frac{3 c^{2} d^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}}-\frac{c^{2} d^{2} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{17 c^{2} d^{2} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,e^{4} x}{4 d^{3}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{4} x}{4 d^{3}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d x}{4 a}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,e^{2} x}{4 d}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{2} x}{2 d}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{5}}{8 c \,d^{4}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{5}}{8 c \,d^{4}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{3}}{4 d^{2}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}{4 a e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c e}{8}+\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c e}{8}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c e x}{4 a \,d^{2}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} x}{4 a^{2} e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} d}{4 a^{2} e^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} e^{2}}{3 d^{3}}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e^{2}}{12 d^{3}}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{4 a \,d^{3} x}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c}{4 a^{2} d \,e^{2} x}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{2 a \,d^{2} e \,x^{2}}"," ",0,"1/16/d^4*e^7*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/16/d^4*e^7*a^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-1/4/d/a^2/e^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-3/4*e/d^2*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-3/4*e^2*d*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-3/8*d^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2+3/4/d^3/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/4*e^3/d^2*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/4/a^2/e*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+3/4*d^2/a/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-1/3/d^3*e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+1/8*e*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+7/8*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-5/12*e^2/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/4*d/a^2/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2+3/4*d/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2-1/2/d^2/a/e/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/4/d^3*e^4*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8/d^4*e^5*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/16/d^2*e^5*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/16*e^3*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/4/d*e^2*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/16*d^2*e*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/4/d^3*e^4*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/8/d^4*e^5*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/16*e^5/d^2*a^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+17/16*e*d^2*c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-3/16*e^3*a*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c-1/2*e^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c+1/8*e^4/d*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)","B"
453,1,1945,185,0.022000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/x^4/(e*x+d),x)","-\frac{a^{3} e^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c \,d^{5}}+\frac{a^{3} e^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c \,d^{5}}-\frac{a^{2} e^{5} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, d^{2}}+\frac{3 a^{2} e^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, d^{3}}-\frac{3 a^{2} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, d^{3}}-\frac{3 a c \,e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, d}+\frac{3 a c \,e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, d}+\frac{3 a c \,e^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}}+\frac{c^{3} d^{4} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, a e}-\frac{3 c^{2} d^{2} e \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}}+\frac{c^{2} d \,e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}-\frac{c^{2} d \,e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{5} x}{4 d^{4}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,e^{5} x}{4 d^{4}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2} x}{8 a^{2} e}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{3} x}{8 d^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,e^{3} x}{4 d^{2}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{6}}{8 c \,d^{5}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{6}}{8 c \,d^{5}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{4}}{8 d^{3}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}{8 a}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}{8 a^{2} e^{2}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,e^{2}}{8 d}+\frac{17 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,e^{2} x}{24 a \,d^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} x}{3 a^{2} d}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} d x}{24 a^{3} e^{2}}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c e}{24 a \,d^{2}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2}}{24 a^{2} e}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} d^{2}}{24 a^{3} e^{3}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} e^{3}}{3 d^{4}}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e^{3}}{8 d^{4}}-\frac{17 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e}{24 a \,d^{4} x}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c}{3 a^{2} d^{2} e x}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c^{2}}{24 a^{3} e^{3} x}+\frac{7 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{12 a \,d^{3} x^{2}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c}{12 a^{2} d \,e^{2} x^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{3 a \,d^{2} e \,x^{3}}"," ",0,"-3/16/d*e^4*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/24*d/a^3/e^2*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/12/d/a^2/e^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+1/16*d^4/a/e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3-1/8*d^2/a^2/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3-1/3/e/d^2/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+17/24/d^3*e^2*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+3/16/d*e^4*a*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c+1/16/d^5*e^8*a^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-1/16/d^5*e^8*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/8/d*e^2*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+7/12/d^3/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+1/8*d/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+5/24/e/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2+1/8/d^3*e^4*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/3/d^4*e^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+3/8/d^4*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/24/a^3/e^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2-1/8*d^3/a^2/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-1/24*d^2/a^3/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^3-1/3/d^2/a/e/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/4/d^4*e^5*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/8/d^5*e^6*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/16*e^3*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-17/24/d^4*e/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+11/24/d^2*e/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c+3/8/d^2*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c-1/16/d^2*e^5*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-3/16*e*d^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2+1/3/d/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/4/d^4*e^5*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/8/d^5*e^6*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/16/d^3*e^6*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/4/d^2*e^3*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/16*d*e^2*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/16/d^3*e^6*a^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-1/16*d*e^2*c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)","B"
454,1,2427,265,0.027000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/x^5/(e*x+d),x)","\frac{a^{3} e^{9} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, c \,d^{6}}-\frac{a^{3} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, c \,d^{6}}+\frac{5 a^{2} e^{6} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{128 \sqrt{a d e}\, d^{3}}-\frac{3 a^{2} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, d^{4}}+\frac{3 a^{2} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, d^{4}}-\frac{3 a c \,e^{4} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{32 \sqrt{a d e}\, d}+\frac{3 a c \,e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}\, d^{2}}-\frac{3 a c \,e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}\, d^{2}}+\frac{c^{3} d^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{32 \sqrt{a d e}\, a}-\frac{3 c^{4} d^{5} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{128 \sqrt{a d e}\, a^{2} e^{2}}+\frac{3 c^{2} d \,e^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{64 \sqrt{a d e}}-\frac{c^{2} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{16 \sqrt{c d e}}+\frac{c^{2} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{16 \sqrt{c d e}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{6} x}{4 d^{5}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a \,e^{6} x}{4 d^{5}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} e^{2} x}{64 a d}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d x}{64 a^{2}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{3} x}{64 a^{3} e^{2}}-\frac{21 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{4} x}{64 d^{3}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,e^{4} x}{4 d^{3}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{7}}{8 c \,d^{6}}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{7}}{8 c \,d^{6}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,e^{5}}{64 d^{4}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} e}{32 a}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2}}{32 a^{2} e}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{4}}{64 a^{3} e^{3}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c \,e^{3}}{8 d^{2}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{3}}{32 d^{2}}-\frac{133 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,e^{3} x}{192 a \,d^{4}}-\frac{91 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} e x}{192 a^{2} d^{2}}-\frac{19 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} x}{192 a^{3} e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{4} d^{2} x}{64 a^{4} e^{3}}-\frac{53 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,e^{2}}{96 a \,d^{3}}-\frac{29 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2}}{96 a^{2} d}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{3} d}{96 a^{3} e^{2}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{4} d^{3}}{64 a^{4} e^{4}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} e^{4}}{3 d^{5}}-\frac{23 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} e^{4}}{64 d^{5}}+\frac{133 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e^{2}}{192 a \,d^{5} x}+\frac{91 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c}{192 a^{2} d^{3} x}+\frac{19 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c^{2}}{192 a^{3} d \,e^{2} x}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c^{3} d}{64 a^{4} e^{4} x}-\frac{59 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e}{96 a \,d^{4} x^{2}}-\frac{13 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c}{48 a^{2} d^{2} e \,x^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c^{2}}{32 a^{3} e^{3} x^{2}}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{24 a \,d^{3} x^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c}{8 a^{2} d \,e^{2} x^{3}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{4 a \,d^{2} e \,x^{4}}"," ",0,"-3/64/d*e^2/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2-3/32/d*e^4*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-133/192/d^4*e^3*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-3/16/d^2*e^5*a*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c+3/64*d^3/a^3/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^4+1/8/d/a^2/e^2/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+1/64*d^2/a^4/e^3*c^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-1/64*d/a^4/e^4/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3-3/128*d^5/a^2/e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^4+1/16/d^6*e^9*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/16/d^2*e^5*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/16/d^6*e^9*a^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-13/48/e/d^2/a^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+19/192/e^2/d/a^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2-91/192/d^2*e/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/8/d^2*e^3*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/16*e^3*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+11/24/d^3/a/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/32*e/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-29/96/d/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2+1/16*e^3*c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-5/64/d^4*e^5*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/32/d^2*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-1/3/d^5*e^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-23/64/d^5*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+3/16/d^4*e^7*a^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+133/192/d^5*e^2/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+3/64*d*e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-1/32/a^3/e^3/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+3/64*d^4/a^3/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4+1/64*d^3/a^4/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^4-1/4/d^2/a/e/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-53/96/d^3*e^2/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c-21/64/d^3*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c+5/128/d^3*e^6*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-59/96/d^4*e/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+91/192/d^3/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+1/4/d^5*e^6*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/8/d^6*e^7*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/4/d^5*e^6*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8/d^6*e^7*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/16/d^4*e^7*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/4/d^3*e^4*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/32/e*d^2/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-5/96/e^2*d/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^3-19/192/e/a^3*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/32*d^3/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3+5/64*d/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3","B"
455,1,2888,361,0.033000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/x^6/(e*x+d),x)","\text{output too large to display}"," ",0,"7/128/d^5*e^6*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/32*d/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-3/128*e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-1/8/d^3*e^4*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/8/d^3/a/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+7/48/e/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^3+15/128/d^3*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+1/3/d^6*e^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+45/128/d^6*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+121/192/d^5*e^2/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+19/48/d^2*e/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2+1/32/d*e^2/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+1/4/d^6*e^7*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/8/d^7*e^8*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/16/d^5*e^8*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/4/d^4*e^5*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+1/16/d*e^4*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/16/a^3/e^3/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2-3/64/a^4/e^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3-1/5/d^2/a/e/x^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-3/128*d^3/a^3/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4+3/128*d^2/a^4/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^4-1/128*d^4/a^5/e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^5-3/128*d^5/a^4/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^5-3/16/d^5*e^8*a^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-1/16/d*e^4*c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-263/384/d^6*e^3/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+227/384/d^4*e^3/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c+39/128/d^4*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c-7/256/d^4*e^7*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-1/32*e/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3+23/96/d/a^3*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+73/192/d^3/a^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-25/48/d^4*e/a/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/4/d^6*e^7*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/8/d^7*e^8*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/8/d/a^2/e^2/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-1/4/d^2/a^2/e/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-1/128*d^2*e/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3-23/96/d^2/e/a^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+1/16/d^7*e^10*a^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+103/192/d^3*e^2/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-103/192/d^4*e/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+3/64/d^2*e^3/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2+263/384/d^5*e^4*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+3/16/d^3*e^6*a*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c+15/256/d^2*e^5*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-3/64/e*d^2/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^4-1/16/d^7*e^10*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/16/d^3*e^6*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/256*d^4/a^2/e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^4+3/256*d^6/a^3/e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^5-3/128*d^4/a^4/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^5+3/64*d/a^4/e^2*c^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-1/128*d^3/a^5/e^4*c^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+9/64/d/a^3/e^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+1/64*d/a^4/e^4/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3+1/128*d^2/a^5/e^5/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^4","B"
456,1,3387,460,0.045000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/x^7/(e*x+d),x)","\text{output too large to display}"," ",0,"1/8/d^4*e^5*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+19/60/d^3/a/x^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+1/64*e/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-23/96/d/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^3-21/512/d^6*e^7*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-1/8/d^4*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-15/512/d^2*e^3/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-703/1536/d^3*e^2/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2-491/768/d^6*e^3/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+257/768/d^3/a^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+107/192/d^5*e^2/a/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/3/d^7*e^6*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-533/1536/d^7*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/4/d^7*e^8*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/8/d^8*e^9*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/16/d^6*e^9*a^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/4/d^5*e^6*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/16/d^2*e^5*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+7/1536*d^5/a^6/e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^6+7/512*d^6/a^5/e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^6+7/256*d/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^4-1/6/d^2/a/e/x^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-7/96/a^3/e^3/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2-1/4/d^7*e^8*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8/d^8*e^9*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/12/e^3/a^4/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3-109/768/e/a^4*c^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+3/1024*d^3/a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^4+65/192/d^3/a^2/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-5/384/e^4*d^3/a^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^5-43/96*e/d^4/a/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+13/512/e*d^2/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4+1/64/e^3*d^4/a^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^5-131/1536/e^2*d/a^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^4+3/16/d^6*e^9*a^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+1/16/d^2*e^5*c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+1045/1536/d^7*e^4/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-235/384/d^5*e^4/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c-149/512/d^5*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c-91/384/e/d^2/a^3/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+29/192/e^2/d/a^3/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+109/768/e^2/d/a^4/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3+41/1536/e^4*d/a^5/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^4+3/512/e^2*d^5/a^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^5-41/1536/e^3*d^2/a^5*c^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+15/512/e^2*d^3/a^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^5-11/48/e/d^2/a^2/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-1/16/d^8*e^11*a^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-43/96/d^4*e/a^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+1/256*d*e^2/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3+3/256/d*e^2/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3-257/768/d^2*e/a^3*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-877/1536/d^4*e^3/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+877/1536/d^5*e^2/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-21/512/d^3*e^4/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2-1045/1536/d^6*e^5*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-21/512/d^3*e^6*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-3/16/d^4*e^7*a*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*c+7/192*d/a^4/e^4/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3-7/1536*d^3/a^6/e^6/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^5-7/768*d^2/a^5/e^5/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^4-7/1024*d^7/a^4/e^4/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^6+7/1536*d^4/a^6/e^5*c^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+7/60/d/a^2/e^2/x^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+7/512*d^5/a^5/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^6+1/16/d^8*e^11*a^3/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/16/d^4*e^7*a*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+21/1024/d^5*e^8*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+15/1024/d*e^4/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2","B"
457,1,3178,536,0.028000," ","int(x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d),x)","\text{output too large to display}"," ",0,"-975/16384*e^2/c*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+195/4096/e^4*c^2*d^9*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+3/64*e/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a^2+9/64*d^6/e^3*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/256*d*e^4*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/128*d^7/e^2*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/256*d^9/e^4*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64*d^2*e*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+15/256*d^3*e^2*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-5/256*e^2/c^2*a^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-15/1024*e^4/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^4+45/8192*e^7/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^6-855/8192/e^2*c*d^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-495/4096/e^3*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-15/4096*e^5/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5-105/2048*e/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-45/32768*e^10/c^5/d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^8+15/4096*e^8/c^4/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^7-15/8192*e^6/c^3/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6+45/4096*e^4/c^2*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-3/64*d^3*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/16*d^6/e^5*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-3/128*d^9/e^6*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/128*d^5*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-95/2048/e^5*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+285/16384/e^6*c^2*d^9*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+45/2048/e^3*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+165/16384/e^2*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+19/64/e^3*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-15/1024*e/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3+465/4096*d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+735/16384/c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+13/128/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^2-1/5*d^3/e^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+19/128/e^4*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-25/112/e^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+65/1024/e/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2+285/8192/e^5*c^2*d^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/8*d^3/e^2*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+1/8*d^5/e^4*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-1/16*d^2/e*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-9/64*d^4/e*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/128*d*e^2*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/64*d^7/e^4*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/64*d^8/e^5*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256*d^11/e^6*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+45/16384*e^8/c^5/d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^7+15/16384*e^6/c^4/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6-75/16384*e^4/c^3/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5-465/16384*e^2/c^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-285/32768/e^6*c^3*d^11*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+3/128*e^2/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^3+29/128/e^2/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a-5/512/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2+35/256/e^2*a*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+5/32/e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a-45/8192*e^3/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4+1155/8192/e*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+1/8/e^2*x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)/c/d-705/16384/e^4*c*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-9/112/e/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*a-95/1024/e^4*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-15/2048*e^5/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^5-35/2048*e^3/c^3/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4","B"
458,1,2731,418,0.018000," ","int(x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d),x)","\frac{5 a^{7} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{4} d^{4}}-\frac{15 a^{6} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{3} d^{2}}+\frac{3 a^{5} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c^{2}}-\frac{15 a^{5} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c^{2}}-\frac{15 a^{4} d^{2} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c}+\frac{125 a^{4} d^{2} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, c}+\frac{15 a^{3} d^{4} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}-\frac{225 a^{3} d^{4} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}}-\frac{15 a^{2} c \,d^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}\, e}+\frac{195 a^{2} c \,d^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, e}+\frac{15 a \,c^{2} d^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e^{3}}-\frac{85 a \,c^{2} d^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, e^{3}}-\frac{3 c^{3} d^{10} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e^{5}}+\frac{15 c^{3} d^{10} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2048 \sqrt{c d e}\, e^{5}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{6} x}{512 c^{3} d^{3}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{4} x}{512 c^{2} d}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} d \,e^{2} x}{64 c}+\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d \,e^{2} x}{256 c}+\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} d^{3} x}{64}-\frac{35 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{3} x}{256}-\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{5} x}{64 e^{2}}+\frac{55 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{5} x}{512 e^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{7} x}{64 e^{4}}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{7} x}{512 e^{4}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{6} e^{7}}{1024 c^{4} d^{4}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{3}}{128 c^{2}}+\frac{35 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{3}}{1024 c^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} d^{2} e}{64 c}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d^{2} e}{128 c}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{4}}{1024 e}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{6}}{64 e^{3}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{6}}{128 e^{3}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{8}}{128 e^{5}}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{8}}{1024 e^{5}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{3} x}{192 c^{2} d^{2}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e x}{192 c}-\frac{25 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{2} x}{192 e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a \,d^{2} x}{8 e}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{4} x}{8 e^{3}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{4} x}{64 e^{3}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{4} e^{4}}{384 c^{3} d^{3}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{2}}{192 c^{2} d}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} d}{16 c}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} d}{96 c}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{3}}{192 e^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{5}}{16 e^{4}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{5}}{128 e^{4}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a x}{12 c d}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d x}{4 e^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a^{2} e}{24 c^{2} d^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a}{6 c e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} d^{2}}{5 e^{3}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d^{2}}{8 e^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}}}{7 c d \,e^{2}}"," ",0,"195/2048/e*c*d^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-5/512*e^6/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^5-3/64*d*e^2*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-9/64*d^5/e^2*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-15/128*d^6/e*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256*d^8/e^3*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/256*d^2*e^3*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+5/512*e^4/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4+15/256*e^2/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-85/2048/e^3*c^2*d^8*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+5/192*e^3/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^3+5/2048*e^9/c^4/d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^7-15/2048*e^7/c^3/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6+55/512/e^2*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+125/2048*e^3/c*d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-1/16*d^5/e^4*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+3/128*d^8/e^5*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+9/64*d^3*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/128*e^3*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/16*d*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-1/6/e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a-15/1024/e*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-5/192/e^2*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a-15/1024/e^5*c^2*d^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+5/128/e^4*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/7/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)/c/d+35/1024*e^3/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-5/96/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2-35/256*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-1/4/e^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+1/5*d^2/e^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-1/8/e^3*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/12/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x*a-25/192/e*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a+15/2048/e^5*c^3*d^10*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+5/384*e^4/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^4+3/256*e^5*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/8*d^2/e*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+3/64*d^2*e*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/8*d^4/e^3*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-3/64*d^6/e^3*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+15/128*d^4*e*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64*d^7/e^4*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/256*d^10/e^5*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/512/e^4*c^2*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-5/1024*e^7/c^4/d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^6+5/128/e^3*c*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-5/128*e/c*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+5/64/e^3*c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-1/24*e/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a^2+5/192*e^2/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3-15/2048*e^5/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5-225/2048*e*d^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+5/192*e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2","B"
459,1,2411,347,0.013000," ","int(x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d),x)","-\frac{5 a^{6} e^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c^{3} d^{3}}-\frac{3 a^{5} e^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c^{2} d}+\frac{15 a^{5} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}\, c^{2} d}+\frac{15 a^{4} d \,e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c}-\frac{75 a^{4} d \,e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, c}-\frac{15 a^{3} d^{3} e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}+\frac{25 a^{3} d^{3} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}}+\frac{15 a^{2} c \,d^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}-\frac{75 a^{2} c \,d^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}}-\frac{15 a \,c^{2} d^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e^{2}}+\frac{15 a \,c^{2} d^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{512 \sqrt{c d e}\, e^{2}}+\frac{3 c^{3} d^{9} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e^{4}}-\frac{5 c^{3} d^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{1024 \sqrt{c d e}\, e^{4}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{5} x}{256 c^{2} d^{2}}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{3} x}{64 c}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{3} x}{64 c}+\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{2} e x}{128}-\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} d^{2} e x}{64}+\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{4} x}{64 e}-\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{4} x}{64 e}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{6} x}{256 e^{3}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{6} x}{64 e^{3}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{5} e^{6}}{512 c^{3} d^{3}}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{4}}{512 c^{2} d}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{4}}{128 c^{2} d}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d \,e^{2}}{256 c}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} d \,e^{2}}{64 c}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{3}}{256}-\frac{15 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{5}}{512 e^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{5}}{64 e^{2}}+\frac{5 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{7}}{512 e^{4}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{7}}{128 e^{4}}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{2} x}{96 c d}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a d x}{48}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a d x}{8}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{3} x}{96 e^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{3} x}{8 e^{2}}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{3} e^{3}}{192 c^{2} d^{2}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e}{192 c}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} e}{16 c}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,d^{2}}{192 e}-\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{4}}{192 e^{3}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{4}}{16 e^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} x}{6 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} a}{12 c d}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} d}{12 e^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} d}{5 e^{2}}"," ",0,"9/64*d^4/e*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/256/d*e^6*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/256*d^7/e^2*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256*d*e^4*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-75/1024*e^4/c*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-5/1024*e^8/c^3/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^6+5/256*e^5/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4-5/64/e*c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-5/96*e^2/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a^2+15/512/e^2*c^2*d^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+15/512*e^6/c^2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^5+5/512/e^4*c^2*d^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+5/192*e/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^2+5/192/e*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a+1/12/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*a+5/48*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*a-1/16*e*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-5/192/e^3*c*d^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/16*d^4/e^3*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-3/128*d^7/e^4*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/8*d*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-5/192*e^3/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*a^3-75/1024*c*d^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+1/12/e^2*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+1/6/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+5/256*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-1/5*d/e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-15/512/e^2*c*d^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-5/96/e^2*c*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+5/256*e^2/c*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-5/1024/e^4*c^3*d^9*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-5/64*e^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+15/128*e*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+25/256*e^2*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+5/512*e^6/c^3/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5-15/512*e^4/c^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4+5/256/e^3*c^2*d^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+3/64*e^3*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+15/128*d^5*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64*d*e^2*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/8*d^3/e^2*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-9/64*d^2*e*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/128/d*e^4*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/64*d^5/e^2*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/128*d^3*e^2*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64*d^6/e^3*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256*d^9/e^4*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)","B"
460,1,1123,244,0.010000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d),x)","\frac{3 a^{5} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c^{2} d^{2}}-\frac{15 a^{4} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c}+\frac{15 a^{3} d^{2} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}-\frac{15 a^{2} c \,d^{4} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}+\frac{15 a \,c^{2} d^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e}-\frac{3 c^{3} d^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e^{3}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{4} x}{64 c d}+\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} d \,e^{2} x}{64}-\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{3} x}{64}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{5} x}{64 e^{2}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{5}}{128 c^{2} d^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{3}}{64 c}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{4}}{64 e}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{6}}{128 e^{3}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a e x}{8}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{2} x}{8 e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} e^{2}}{16 c d}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{3}}{16 e^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}}}{5 e}"," ",0,"1/5/e*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+15/256/e*a*c^2*d^6*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64*e^4*a^3/c/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-9/64*a*c*d^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256*e^7*a^5/c^2/d^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/128*e*a^2*c*d^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/8*e*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+3/64*e^3*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/8/e*c*d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-1/16/e^2*c*d^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+3/128/e^3*c^2*d^6*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/256/e^3*c^3*d^8*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64/e*a*c*d^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/256*e^5*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/128*e^3*a^3*d^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64/e^2*c^2*d^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+9/64*e^2*a^2*d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/128*e^5*a^4/c^2/d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/16*e^2*a^2/c/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)","B"
461,1,2180,352,0.017000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x/(e*x+d),x)","-\frac{3 a^{5} e^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c^{2} d^{3}}+\frac{3 a^{5} e^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{2} d^{3}}+\frac{15 a^{4} e^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c d}-\frac{25 a^{4} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c d}-\frac{a^{3} d^{2} e^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{\sqrt{a d e}}-\frac{15 a^{3} d \,e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}+\frac{75 a^{3} d \,e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}}+\frac{15 a^{2} c \,d^{3} e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}+\frac{75 a^{2} c \,d^{3} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}}-\frac{15 a \,c^{2} d^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}}-\frac{25 a \,c^{2} d^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}}+\frac{3 c^{3} d^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e^{2}}+\frac{3 c^{3} d^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, e^{2}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{5} x}{64 c \,d^{2}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{5} x}{64 c \,d^{2}}-\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{3} x}{64}+\frac{19 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{3} x}{64}+\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{2} e x}{64}+\frac{19 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{2} e x}{64}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{4} x}{64 e}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{4} x}{64 e}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{6}}{128 c^{2} d^{3}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{6}}{128 c^{2} d^{3}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{4}}{64 c d}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{4}}{8 c d}+\frac{83 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d \,e^{2}}{64}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{3}}{64}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{3}}{8}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{5}}{128 e^{2}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{5}}{128 e^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a \,e^{2} x}{8 d}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{2} x}{8 d}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c d x}{8}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c d x}{8}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{3}}{16 c \,d^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} e^{3}}{16 c \,d^{2}}+\frac{11 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a e}{24}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,d^{2}}{16 e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,d^{2}}{16 e}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}}}{5 d}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}{5 d}"," ",0,"3/64/d^2*a^3*e^5/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+9/64*d^2*a*e*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/256/d^3*a^5*e^8/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/128*d^3*a^2*e^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256/d*a^4*e^6/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+75/128*d^3*a^2*e^2*c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-25/256/d*a^4*e^6/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+19/64*d^2*a*e*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+3/256/d^3*a^5*e^8/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-3/64/d^2*a^3*e^5/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/8*d*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+1/16*d^2*c/e*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-3/128*d^5*c^2/e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-9/64*a^2*e^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/64*d^3*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/8*d^3*a*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/128*d^5*c^2/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+83/64*d*a^2*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/8*d*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/16*d^2*c/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+19/64*a^2*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/5/d*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+1/5/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-15/128*d*a^3*e^4*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64*d^4*c^2/e*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256*d^7*c^3/e^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/16/d^2*a^2*e^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-3/128/d^3*a^4*e^6/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+75/128*d*a^3*e^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-3/64*d^4*c^2/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+3/256*d^7*c^3/e^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-1/8/d*a*e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-3/64/d*a^3*e^4/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/256*d^5*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/8/d*a^3*e^4/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/8/d*a*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-d^2*a^3*e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-25/256*d^5*a*c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+11/24*a*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-1/16/d^2*a^2*e^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+3/128/d^3*a^4*e^6/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","B"
462,1,2364,308,0.018000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x^2/(e*x+d),x)","\frac{3 a^{5} e^{9} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c^{2} d^{4}}-\frac{3 a^{5} e^{9} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{2} d^{4}}-\frac{15 a^{4} e^{7} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c \,d^{2}}+\frac{15 a^{4} e^{7} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c \,d^{2}}-\frac{3 a^{3} d \,e^{4} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}}+\frac{15 a^{3} e^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}+\frac{25 a^{3} e^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}}-\frac{5 a^{2} c \,d^{3} e^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}}-\frac{15 a^{2} c \,d^{2} e^{3} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}+\frac{375 a^{2} c \,d^{2} e^{3} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}}+\frac{15 a \,c^{2} d^{4} e \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}}+\frac{225 a \,c^{2} d^{4} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}}-\frac{3 c^{3} d^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, e}-\frac{13 c^{3} d^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, e}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{6} x}{64 c \,d^{3}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{6} x}{64 c \,d^{3}}+\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{4} x}{64 d}-\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{4} x}{64 d}-\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c d \,e^{2} x}{64}+\frac{121 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c d \,e^{2} x}{64}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{3} x}{64}+\frac{13 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{3} x}{64}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{7}}{128 c^{2} d^{4}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{7}}{128 c^{2} d^{4}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{5}}{64 c \,d^{2}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{5}}{64 c \,d^{2}}+\frac{19 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{3}}{8}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,d^{2} e}{64}+\frac{227 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,d^{2} e}{64}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{4}}{128 e}+\frac{13 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{4}}{128 e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a \,e^{3} x}{8 d^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{3} x}{8 d^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c e x}{8}+\frac{9 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c e x}{8}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} e^{4}}{16 c \,d^{3}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{4}}{16 c \,d^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{2}}{d}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c d}{16}+\frac{67 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c d}{48}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c x}{a d}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c}{a e}+\frac{4 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e}{5 d^{2}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} e}{5 d^{2}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}}}{a \,d^{2} e x}"," ",0,"-3/64*e^6/d^3*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-9/64*e^2*d*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256*e^9/d^4*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/128*e^3*d^2*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256*e*d^4*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/256*e^7/d^2*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64*e^6/d^3*a^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-3/256*e^9/d^4*a^5/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+121/64*d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a*c*e^2+15/256/d^2/c*e^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+375/128*d^2*c*e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+225/256*d^4*e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a*c^2-5/2*d^3*a^2*e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c+15/128*e^5*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64*d^3*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8*e*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+3/128/e*d^4*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+13/64*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2+13/128*d^4/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+1/d*a*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+9/8*e*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+25/128*e^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+1/a/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+4/5/d^2*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+1/5*e/d^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-1/16*d*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+67/48*d*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+19/8*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-13/256*d^6*c^3/e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+1/8*e^3/d^2*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+3/64*e^5/d^2*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/16*e^4/d^3*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+9/64*e^4/d*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/128*e^7/d^4*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/64*e*d^2*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/256/e*d^6*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-1/d^2/a/e/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)-3/2*d*a^3*e^4/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+1/d*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-9/64/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2*e^4-1/8*e^3/d^2*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-1/16*e^4/d^3*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+3/128*e^7/d^4*a^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/64/d^2/c*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+227/64*d^2*c*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a","B"
463,1,2688,295,0.021000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x^3/(e*x+d),x)","-\frac{3 a^{5} e^{10} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c^{2} d^{5}}+\frac{3 a^{5} e^{10} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c^{2} d^{5}}+\frac{15 a^{4} e^{8} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}\, c \,d^{3}}-\frac{15 a^{4} e^{8} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}\, c \,d^{3}}-\frac{15 a^{3} e^{6} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}\, d}+\frac{15 a^{3} e^{6} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}\, d}-\frac{3 a^{3} e^{5} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}}-\frac{15 a^{2} c \,d^{2} e^{3} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{4 \sqrt{a d e}}+\frac{15 a^{2} c d \,e^{4} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{128 \sqrt{c d e}}+\frac{225 a^{2} c d \,e^{4} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{128 \sqrt{c d e}}-\frac{15 a \,c^{2} d^{4} e \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}}-\frac{15 a \,c^{2} d^{3} e^{2} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}}+\frac{975 a \,c^{2} d^{3} e^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}}+\frac{3 c^{3} d^{5} \ln \left(\frac{\frac{a \,e^{2}}{2}-\frac{c \,d^{2}}{2}+\left(x +\frac{d}{e}\right) c d e}{\sqrt{c d e}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\right)}{256 \sqrt{c d e}}+\frac{93 c^{3} d^{5} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{256 \sqrt{c d e}}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{7} x}{64 c \,d^{4}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{7} x}{64 c \,d^{4}}-\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{2} e^{5} x}{64 d^{2}}+\frac{9 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{5} x}{64 d^{2}}+\frac{39 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c \,e^{3} x}{64}+\frac{9 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c \,e^{3} x}{64}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{2} e x}{64}+\frac{147 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2} e x}{64}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{4} e^{8}}{128 c^{2} d^{5}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{8}}{128 c^{2} d^{5}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{6}}{64 c \,d^{3}}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a^{3} e^{6}}{64 c \,d^{3}}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{4}}{4 d}+\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, a c d \,e^{2}}{64}+\frac{333 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a c d \,e^{2}}{64}-\frac{3 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, c^{2} d^{3}}{128}+\frac{387 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{3}}{128}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{4} x}{8 d^{3}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a \,e^{4} x}{8 d^{3}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} d x}{4 a}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c \,e^{2} x}{8 d}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c \,e^{2} x}{8 d}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} a^{2} e^{5}}{16 c \,d^{4}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a^{2} e^{5}}{16 c \,d^{4}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} a \,e^{3}}{4 d^{2}}+\frac{5 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c^{2} d^{2}}{4 a e}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{3}{2}} c e}{16}+\frac{31 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} c e}{16}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c e x}{4 a \,d^{2}}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c^{2} x}{4 a^{2} e}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c}{a d}+\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} c^{2} d}{4 a^{2} e^{2}}-\frac{\left(\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)\right)^{\frac{5}{2}} e^{2}}{5 d^{3}}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} e^{2}}{20 d^{3}}+\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}}}{4 a \,d^{3} x}-\frac{3 \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}} c}{4 a^{2} d \,e^{2} x}-\frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{7}{2}}}{2 a \,d^{2} e \,x^{2}}"," ",0,"-3/256/d^5*e^10*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/128*d*e^4*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256/d^3*e^8*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/256*d^3*e^2*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64/d^4*e^7*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/64/d^4*e^7*a^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+3/256/d^5*e^10*a^5/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-3/4/d/a^2/e^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-15/8*d^4*a*e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-1/4*e/d^2*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+975/256*e^2*d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a*c^2-15/256*e^8/d^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+225/128*e^4*d*c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-15/4*e^3*d^2*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c+3/256*d^5*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/4*e^3/d^2*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/d/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-3/8*e^5*a^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+93/256*d^5*c^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+3/4*e^4/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+1/4/d^3/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+39/64*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a*c-1/16/d^4*e^5*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-9/64/d^2*e^5*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/128/d^5*e^8*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/64*d*e^2*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/128/d*e^6*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64*d^2*e*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/4/a^2/e*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+5/4*d/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^2-1/2/d^2/a/e/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+3/4*d/a^2/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+5/4*d^2/a/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2+1/8/d^3*e^4*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/16/d^4*e^5*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-3/128/d^5*e^8*a^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/8*e^2/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c+15/128*e^6/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+3/64*e^6/d^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+333/64*e^2*d*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+9/64*e^3*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/8/d^3*e^4*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-3/64/d^3*e^6*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+1/8/d*e^2*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-1/5/d^3*e^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+1/16*e*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-3/128*d^3*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+31/16*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c+387/128*d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-1/20*e^2/d^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+9/64*e^5/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+147/64*e*d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2","B"
464,1,3144,327,0.027000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x^4/(e*x+d),x)","\text{output too large to display}"," ",0,"-1/16/d*e^2*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+3/128*d^2*e*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/64*e^3*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-5/16*d^5/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3+35/24*d/a*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+25/24/e/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+5/12/d^3/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+493/128*d^2*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-1/8/d^2*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+37/48/d*e^2*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-1/24/d^3*e^4*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+107/64*e^3*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+1/5/d^4*e^3*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+7/40/d^4*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/8/d^2*e^3*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+1/16/d^5*e^6*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+9/64/d^3*e^6*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/128/d^6*e^9*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+15/128/d^2*e^7*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64*d*e^2*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/256*d^4*e*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/128*e^5*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+5/8*d^4/a/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-1/3/d^2/a/e/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+5/24*d^3/a^2/e^2*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/8*d^2/a^3/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3+5/8*d^3/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3-1/8/a^3/e^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2-9/64/d^3*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+93/64*d*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2+15/128*e^5*c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-3/8/d^4*e/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+1/16/d*e^6*a^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-3/64/d^4*e^7/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+1/12/d^2*e^3*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-15/128/d^2*e^7*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3+387/256*d^4*e*c^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+19/24/d^2*e/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+5/6*e/a*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+5/6/d/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-1/8/d^4*e^5*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-1/16/d^5*e^6*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+3/128/d^6*e^9*a^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/8/d^3*e^2*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-15/16*d*e^4*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c+1/64/d*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a*c+15/256/d^4*e^9/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+625/256*d^2*e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a*c^2+5/24*d^2/a^2/e*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/8*d/a^3/e^2*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-1/12/d/a^2/e^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c+3/64/d^5*e^8*a^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-3/256/d^6*e^11*a^5/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-15/256/d^4*e^9*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64/d^5*e^8*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-9/64/d*e^4*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256/d^6*e^11*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256*d^2*e^3*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/8/d^4*e^5*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+3/64/d^4*e^7*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-5/6/e/d^2/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-45/16*e^2*d^3*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2","B"
465,1,3646,362,0.033000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x^5/(e*x+d),x)","\text{output too large to display}"," ",0,"1/16/d^2*e^3*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-3/128*d*e^2*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/64*e^3*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+25/32*d^3/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3+3/8/d^3/a/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+1/96/d/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+35/96*e/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2-1/8*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2+127/128*d*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+3/64/d^3*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+1/64/d^4*e^5*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-19/96/d^2*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c-1/5/d^5*e^4*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)-61/320/d^5*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)+15/256/d^5*e^10*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64/d^6*e^9*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+9/64/d^2*e^5*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/256/d^7*e^12*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/128/d*e^6*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/256*d*e^4*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-45/64*d^2*e^3*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-31/64/d^2*e/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-35/192/d*e^2/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^2-3/32/d^2*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a*c-15/256/d^5*e^10/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4-15/128/d*e^6*c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+15/256*d*e^4*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a*c^2-25/64/d^4*e^3*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-5/64*d^4/a^2/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^4+5/128*d^6/a/e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^4-5/192*d^3/a^3/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^4-1/64*d^2/a^4/e^3*c^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+1/64*d/a^4/e^4/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^3+1/24/d/a^2/e^2/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-3/64/d^6*e^9*a^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+3/256/d^7*e^12*a^5/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+45/64*e*d^2/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3-13/48/e/d^2/a^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-43/192/e^2/d/a^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2-5/192*d^4/a^3/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^4-1/64*d^3/a^4/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^4-5/64*d^5/a^2/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4+1/96/a^3/e^3/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2+5/32*e^5*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c+9/64/d^4*e^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+25/64/d^5*e^2/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)-7/64/d^3*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c+15/128/d^3*e^8*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-3/128/d^2*e^7*a^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-15/32/d^3*e^2/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-17/64/d*e^4*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+253/256*d^3*e^2*c^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+3/64/d^5*e^8/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+1/8/d^5*e^6*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/16/d^6*e^7*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-3/128/d^7*e^10*a^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/8/d^3*e^4*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-1/16/d^6*e^7*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-9/64/d^4*e^7*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/128/d^7*e^10*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/64/d*e^4*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/128/d^3*e^8*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/256*d^3*e^2*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+31/64/d^3/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-13/32/d^4*e/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)-15/32*e*d^4/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3+35/96/e*d^2/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^3+19/96/e^2*d/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3+85/192*d/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^3+43/192/e/a^3*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-1/4/d^2/a/e/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)-1/8/d^5*e^6*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-3/64/d^5*e^8*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","B"
466,1,3991,259,0.045000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x^6/(e*x+d),x)","\text{output too large to display}"," ",0,"-1/16/d^3*e^4*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+13/40/d^3/a/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+17/160/e/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3-3/128/d^4*e^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+15/128/d^3*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c-1/128/d^5*e^6*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+1/5/d^6*e^5*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+3/128*e^3*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/128*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+25/128/d^6*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-31/80/d^4*e/a/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+3/32*d^2*e/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-15/128*d^3*e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3+1/5/d/a^3*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+109/320/d^3/a^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c+1/8/d^6*e^7*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+3/64/d^6*e^9*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/8/d^4*e^5*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x+1/16/d^7*e^8*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)+9/64/d^5*e^8*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/128/d^8*e^11*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-3/64/d^2*e^5*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+15/128/d^4*e^9*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+3/64/d*e^4*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/256*d^2*e^3*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256*e^5*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+11/320/a^4/e^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^3-1/80/a^3/e^3/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2-9/128*d^4/a^2/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4+3/128*d^6/a^3/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^5+1/128*d^5/a^4/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^5+3/640*d^4/a^5/e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^5-7/128*d^3/a^3/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^4-17/640*d^2/a^4/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^4+15/256*d^5/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^4-3/64*d^3/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^4-1/5/d^2/a/e/x^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)-1/8/d^6*e^7*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x-15/256*e^5*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a*c^2-9/64/d^5*e^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-253/640/d^6*e^3/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+15/128/d^4*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c-15/128/d^4*e^9*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-3/64/d^6*e^9/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+15/128/d^2*e^5*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+3/256*d^2*e^3*c^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+3/256/d^3*e^8*a^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+273/640/d^4*e^3/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c+129/320/d^5*e^2/a/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+47/160/d^2*e/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+139/320/d^3*e^2/a^2*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+15/128*d*e^4*a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-139/320/d^4*e/a^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-15/256/d*e^6*a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c+15/128/d^2*e^7*c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+15/128/d^3*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a*c+15/256/d^6*e^11/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+253/640/d^5*e^4*c/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-5/64*d^2/a^3/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^4-1/5/d^2/a^2/e/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-11/320*d/a^4/e^2*c^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+3/640*d^3/a^5/e^4*c^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-3/640*d^2/a^5/e^5/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^4+19/320/d/a^3/e^2/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2-1/320*d/a^4/e^4/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^3+1/128*d^4/a^4/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^5+3/128*d^5/a^3/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^5-3/256*d^7/a^2/e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^5+3/40/d/a^2/e^2/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-3/64/d^7*e^10*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-9/64/d^3*e^6*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256/d^8*e^13*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/128/d^2*e^7*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/256/d^6*e^11*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/256/d^8*e^13*a^5/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+3/64/d^7*e^10*a^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-1/5/d^2/e/a^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2+5/64/d^2*e^3/a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^2-1/16/d^7*e^8*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+3/128/d^8*e^11*a^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)","B"
467,1,4735,352,0.064000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x^7/(e*x+d),x)","\text{output too large to display}"," ",0,"1/16/d^4*e^5*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-3/128/d*e^4*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+7/1536/d^6*a*e^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)+7/512/d^5*a^2*e^8*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-35/384/d^4*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c+17/60/d^3/a/x^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+1/512*d^3/a^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4-59/320/d/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^3+25/512/d*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+9/64/d^6*e^9*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+15/128/d^5*e^10*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^3-101/512/d^7*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)-1/5/d^7*e^6*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(5/2)+3/64/d^7*e^10/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-3/256*d*e^4*c^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+1017/2560/d^7/a*e^4/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)-1/512*d^5/a^6/e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^6-5/512*d^7/a^4/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^6-397/960/d^5/a*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c-35/1536/d^2/a*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^2+49/1536*d^2/a^3/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^4-5/64/d^3*a*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-2681/7680/d^3/a^2*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^2+1/64*d^5/a^3/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^5-221/7680*d/a^4/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^4-57/160/d^4/a*e/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+7/384*d^4/a^4/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^5-1/64*d/a*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-5/256/a*e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3-11/480/a^4/e^3/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^3-45/1024*a*e^5/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-1/32/a^3/e^3/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2-81/1280/a^4/e*c^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-1/6/d^2/a/e/x^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+35/768*d/a^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^4+5/256*d^2*e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3-185/1536/d^5*e^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c+381/1280/d^3/a^3/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2+15/512/d^2*e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2+89/320/d^3/a^2/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-7/1024/d^4*a^3*e^9/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+1/120*d^3/a^5/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*c^5-1543/3840/d^6/a*e^3/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)-5/1536*d^6/a^5/e^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*c^6+377/960/d^5/a*e^2/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)+1/8/d^5*e^6*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-1/8/d^7*e^8*a*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)*x-3/64/d^7*e^10*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-1/16/d^8*e^9*a^2/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(3/2)-9/64/d^6*e^9*a^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/128/d^9*e^12*a^4/c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+3/64/d^3*e^6*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-15/128/d^5*e^10*a^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-3/64/d^2*e^5*c^2*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+3/256*d*e^4*c^3*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+1/8/d^7*e^8*a*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x+1/16/d^8*e^9*a^2/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)-3/128/d^9*e^12*a^4/c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/64/d^8*e^11*a^3/c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+9/64/d^4*e^7*a*c*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-3/256/d^9*e^14*a^5/c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/128/d^3*e^8*a^2*c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/256/d*e^6*a*c^2*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)+15/256/d^7*e^12*a^4/c*ln((1/2*a*e^2-1/2*c*d^2+(x+d/e)*c*d*e)/(c*d*e)^(1/2)+((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2))/(c*d*e)^(1/2)-15/128/d^3*e^8*c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-3/64/d^8*e^11*a^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+3/256/d^9*e^14*a^5/c^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+15/256/d*e^6*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a*c^2-15/256/d^7*e^12/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^4+15/512/d^2*a^2*e^7/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c+3/512*d^4/a^3/e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^5-5/512*d^6/a^4/e^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^6-25/768/d/a^2*e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^3+89/7680*d^2/a^5/e^3*c^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-1/512*d^4/a^6/e^5*c^6*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x+1/768*d^2/a^5/e^5/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^4+43/1536*d^3/a^4/e^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^5-5/1536*d^5/a^5/e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^6+29/320/d/a^3/e^2/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2+1/192*d/a^4/e^4/x^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^3-9/512*d^6/a^2/e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^5+5/1024*d^8/a^3/e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^6+81/1280/d/a^4/e^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^3-89/7680*d/a^5/e^4/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^4+1/512*d^3/a^6/e^6/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^5-11/30/d^4/a^2*e/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c+3211/7680/d^5/a^2*e^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-1017/2560/d^6/a*e^5*c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-3211/7680/d^4/a^2*e^3*c^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-381/1280/d^2/a^3*e*c^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)*x-65/512/d^4*a*e^7*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c+7/256*d^2/a^2*e*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^4+1/12/d/a^2/e^2/x^5*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c+15/1024*d^4/a*e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^4-65/1536/d^3/a*e^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)*x*c^2-43/240/d^2/a^2/e/x^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c-113/640/d^2/a^3/e/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2)*c^2","B"
468,1,5353,462,0.086000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x^8/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
469,1,6030,586,0.128000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/x^9/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
470,1,391,243,0.021000," ","int(x^3/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{3 a^{2} e \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, c^{2} d^{2}}+\frac{3 a \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4 \sqrt{c d e}\, c e}+\frac{15 d^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, e^{3}}+\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{3}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) e^{4}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, x}{2 c d \,e^{2}}-\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a}{4 c^{2} d^{2} e}-\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{4 c \,e^{3}}"," ",0,"1/2/e^2*x/c/d*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/4/e/c^2/d^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-7/4/e^3/c*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/8*e/c^2/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2+3/4/e/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+15/8*d^2/e^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+2*d^3/e^4/(a*e^2-c*d^2)/(x+d/e)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","A"
471,1,241,173,0.013000," ","int(x^2/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{a \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, c d}-\frac{3 d \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, e^{2}}-\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{2}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) e^{3}}+\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{c d \,e^{2}}"," ",0,"(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/c/d/e^2-1/2/c/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-3/2/e^2*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)-2*d^2/e^3/(a*e^2-c*d^2)/(x+d/e)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","A"
472,1,131,121,0.010000," ","int(x/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{\sqrt{c d e}\, e}+\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) e^{2}}"," ",0,"1/e*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+2*d/e^2/(a*e^2-c*d^2)/(x+d/e)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","A"
473,1,51,50,0.008000," ","int(1/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right)}{\left(a \,e^{2}-c \,d^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2*(c*d*x+a*e)/(a*e^2-c*d^2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
474,1,136,125,0.016000," ","int(1/x/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{\ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{\sqrt{a d e}\, d}+\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) d}"," ",0,"-1/d/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+2/d/(a*e^2-c*d^2)/(x+d/e)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","A"
475,1,253,207,0.016000," ","int(1/x^2/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{c \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}\, a e}+\frac{3 e \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}\, d^{2}}-\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) d^{2}}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{a \,d^{2} e x}"," ",0,"-1/d^2/a/e/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/2*e/d^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+1/2/a/e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-2/d^2*e/(a*e^2-c*d^2)/(x+d/e)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","A"
476,1,414,301,0.017000," ","int(1/x^3/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{3 c \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{4 \sqrt{a d e}\, a d}-\frac{3 c^{2} d \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}\, a^{2} e^{2}}-\frac{15 e^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}\, d^{3}}+\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{2}}{\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) d^{3}}+\frac{7 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{4 a \,d^{3} x}+\frac{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}{4 a^{2} d \,e^{2} x}-\frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{2 a \,d^{2} e \,x^{2}}"," ",0,"7/4/d^3/a/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-15/8/d^3*e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)-3/4/d/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-1/2/d^2/a/e/x^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+3/4/d/a^2/e^2/x*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-3/8*d/a^2/e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2+2/d^3*e^2/(a*e^2-c*d^2)/(x+d/e)*((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","A"
477,1,1680,485,0.030000," ","int(x^5/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{16 c^{2} d^{7} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{4}}-\frac{8 a c \,d^{6}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{3}}-\frac{8 c^{2} d^{8}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{5}}+\frac{15 a^{4} e^{4} x}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}+\frac{5 a^{3} e^{2} x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}-\frac{a^{2} d x}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{11 a \,d^{3} x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{2}}+\frac{51 c \,d^{5} x}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{4}}+\frac{15 a^{5} e^{5}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{4}}+\frac{35 a^{4} e^{3}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2}}+\frac{9 a^{3} e}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2}}+\frac{21 a^{2} d^{2}}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c e}+\frac{95 a \,d^{4}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{3}}+\frac{51 c \,d^{6}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{5}}+\frac{x^{3}}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d \,e^{2}}+\frac{2 d^{5}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{6}}+\frac{2 \left(2 c d e x +a \,e^{2}+c \,d^{2}\right) d^{4}}{\left(4 a c \,d^{2} e^{2}-\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{5}}-\frac{5 a \,x^{2}}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2} e}-\frac{9 x^{2}}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{3}}-\frac{15 a^{2} x}{8 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}+\frac{15 a^{2} \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, c^{3} d^{3}}-\frac{15 a x}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d \,e^{2}}+\frac{15 a \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{4 \sqrt{c d e}\, c^{2} d \,e^{2}}-\frac{35 d x}{8 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{4}}+\frac{35 d \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{8 \sqrt{c d e}\, c \,e^{4}}+\frac{15 a^{3} e}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{4} d^{4}}+\frac{5 a^{2}}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{2} e}-\frac{7 a}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} e^{3}}+\frac{51 d^{2}}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{5}}"," ",0,"15/8*e^4/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^4+5/2*e^2/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3-7/16/e^3/c^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+51/16/e^5/c*d^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-9/4/e^3/c*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+51/8/e^4*c*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+15/16*e^5/c^4/d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^5+35/16*e^3/c^3/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-15/4/e^2/c^2/d*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+15/4/e^2/c^2/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a-8/3*d^6/e^3*c/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*a-16/3*d^7/e^4*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-1/4/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-5/4/e/c^2/d^2*x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+21/8/e/c*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+11/2/e^2*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+9/8*e/c^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+95/16/e^3*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+2*d^4/e^5*(2*c*d*e*x+a*e^2+c*d^2)/(4*a*c*d^2*e^2-(a*e^2+c*d^2)^2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+15/8/c^3/d^3*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a^2-15/8/c^3/d^3*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-35/8/e^4/c*d*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+15/16*e/c^4/d^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+51/16/e^5*c*d^6/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+35/8/e^4/c*d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+2/3*d^5/e^6/(a*e^2-c*d^2)/(x+d/e)/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-8/3*d^8/e^5*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+5/16/e/c^3/d^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+1/2/e^2*x^3/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)","B"
478,1,1266,408,0.013000," ","int(x^4/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{16 c^{2} d^{6} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{3}}+\frac{8 a c \,d^{5}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{2}}+\frac{8 c^{2} d^{7}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{4}}-\frac{3 a^{3} e^{3} x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}-\frac{3 a^{2} e x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{9 a \,d^{2} x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e}-\frac{9 c \,d^{4} x}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{3}}-\frac{3 a^{4} e^{4}}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}-\frac{3 a^{3} e^{2}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d}-\frac{3 a^{2} d}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}-\frac{9 a \,d^{3}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{2}}-\frac{9 c \,d^{5}}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{4}}-\frac{2 d^{4}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{5}}-\frac{2 \left(2 c d e x +a \,e^{2}+c \,d^{2}\right) d^{3}}{\left(4 a c \,d^{2} e^{2}-\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{4}}+\frac{x^{2}}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d \,e^{2}}+\frac{3 a x}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2} e}-\frac{3 a \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, c^{2} d^{2} e}+\frac{5 x}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{3}}-\frac{5 \ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{2 \sqrt{c d e}\, c \,e^{3}}-\frac{3 a^{2}}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{3} d^{3}}-\frac{9 d}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{4}}"," ",0,"-3/2*e^3/c^2/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^3+5/2/e^3/c*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/4/c^3/d^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-9/4/e^4/c*d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-5/2/e^3/c*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+16/3*d^6/e^3*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+8/3*d^5/e^2*c/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*a-9/2/e*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a-9/2/e^3*c*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x-3/4*e^4/c^3/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^4-3/2*e^2/c^2/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3-3/2/e/c^2/d^2*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)*a+3/2/e/c^2/d^2*x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-3/2*e/c/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2-2/3*d^4/e^5/(a*e^2-c*d^2)/(x+d/e)/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+8/3*d^7/e^4*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-2*d^3/e^4*(2*c*d*e*x+a*e^2+c*d^2)/(4*a*c*d^2*e^2-(a*e^2+c*d^2)^2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/e^2*x^2/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/c*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2-9/2/e^2*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a-9/4/e^4*c*d^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)","B"
479,1,977,273,0.014000," ","int(x^3/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{16 c^{2} d^{5} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{2}}-\frac{8 a c \,d^{4}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e}-\frac{8 c^{2} d^{6}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{3}}+\frac{a^{2} e^{2} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d}+\frac{4 a d x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{3 c \,d^{3} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{2}}+\frac{a^{3} e^{3}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2}}+\frac{5 a^{2} e}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c}+\frac{7 a \,d^{2}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e}+\frac{3 c \,d^{4}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{3}}+\frac{2 d^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, e^{4}}+\frac{2 \left(2 c d e x +a \,e^{2}+c \,d^{2}\right) d^{2}}{\left(4 a c \,d^{2} e^{2}-\left(a \,e^{2}+c \,d^{2}\right)^{2}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, e^{3}}-\frac{x}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c d \,e^{2}}+\frac{\ln \left(\frac{c d e x +\frac{1}{2} a \,e^{2}+\frac{1}{2} c \,d^{2}}{\sqrt{c d e}}+\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\right)}{\sqrt{c d e}\, c d \,e^{2}}+\frac{a}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c^{2} d^{2} e}+\frac{3}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, c \,e^{3}}"," ",0,"-1/e^2*x/c/d/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/2/e/c^2/d^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+3/2/e^3/c/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+e^2/c/d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a^2+4*d/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*a+3/e^2*c*d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x+1/2*e^3/c^2/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^3+5/2*e/c/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a^2+7/2/e*d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*a+3/2/e^3*c*d^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+1/e^2/c/d*ln((c*d*e*x+1/2*a*e^2+1/2*c*d^2)/(c*d*e)^(1/2)+(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/(c*d*e)^(1/2)+2*d^2/e^3*(2*c*d*e*x+a*e^2+c*d^2)/(4*a*c*d^2*e^2-(a*e^2+c*d^2)^2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+2/3*d^3/e^4/(a*e^2-c*d^2)/(x+d/e)/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-16/3*d^5/e^2*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-8/3*d^4/e*c/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*a-8/3*d^6/e^3*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","B"
480,1,145,118,0.011000," ","int(x^2/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(3 a^{2} e^{4} x^{2}+6 a c \,d^{2} e^{2} x^{2}-c^{2} d^{4} x^{2}+12 a^{2} d \,e^{3} x +4 a c \,d^{3} e x +8 a^{2} d^{2} e^{2}\right)}{3 \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"2/3*(c*d*x+a*e)*(3*a^2*e^4*x^2+6*a*c*d^2*e^2*x^2-c^2*d^4*x^2+12*a^2*d*e^3*x+4*a*c*d^3*e*x+8*a^2*d^2*e^2)/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
481,1,149,130,0.010000," ","int(x/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(6 a c d \,e^{3} x^{2}+2 c^{2} d^{3} e \,x^{2}+3 a^{2} e^{4} x +10 a c \,d^{2} e^{2} x +3 c^{2} d^{4} x +2 a^{2} d \,e^{3}+6 a c \,d^{3} e \right)}{3 \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2/3*(c*d*x+a*e)*(6*a*c*d*e^3*x^2+2*c^2*d^3*e*x^2+3*a^2*e^4*x+10*a*c*d^2*e^2*x+3*c^2*d^4*x+2*a^2*d*e^3+6*a*c*d^3*e)/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
482,1,138,113,0.010000," ","int(1/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-8 c^{2} d^{2} e^{2} x^{2}-4 a c d \,e^{3} x -12 c^{2} d^{3} e x +a^{2} e^{4}-6 a c \,d^{2} e^{2}-3 c^{2} d^{4}\right)}{3 \left(a^{3} e^{6}-3 a^{2} c \,d^{2} e^{4}+3 a \,c^{2} d^{4} e^{2}-c^{3} d^{6}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2/3*(c*d*x+a*e)*(-8*c^2*d^2*e^2*x^2-4*a*c*d*e^3*x-12*c^2*d^3*e*x+a^2*e^4-6*a*c*d^2*e^2-3*c^2*d^4)/(a^3*e^6-3*a^2*c*d^2*e^4+3*a*c^2*d^4*e^2-c^3*d^6)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
483,1,682,247,0.016000," ","int(1/x/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{16 c^{2} d \,e^{2} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}-\frac{8 a c \,e^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}-\frac{8 c^{2} d^{2} e}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}-\frac{2 c^{2} d x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a}-\frac{2 c \,e^{2} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d}-\frac{a \,e^{3}}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{2}}-\frac{c^{2} d^{2}}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a e}-\frac{2 c e}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}+\frac{2}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d}-\frac{\ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{\sqrt{a d e}\, a \,d^{2} e}+\frac{1}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2} e}"," ",0,"1/d^2/a/e/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-2/d*e^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c-2*d/a/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2-1/d^2*a*e^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-2*e/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-d^2/a/e/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-1/d^2/a/e/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+2/3/d/(a*e^2-c*d^2)/(x+d/e)/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)-16/3*d*c^2*e^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-8/3*c*e^3/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*a-8/3*d^2*c^2*e/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","B"
484,1,912,364,0.016000," ","int(1/x^2/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{16 c^{2} e^{3} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}+\frac{8 a c \,e^{4}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d}+\frac{8 c^{2} d \,e^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}+\frac{3 c^{3} d^{2} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e}+\frac{5 c \,e^{3} x}{\left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{2}}+\frac{5 a \,e^{4}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{3}}+\frac{3 c^{2} d}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a}+\frac{3 c^{3} d^{3}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e^{2}}+\frac{5 c \,e^{2}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d}-\frac{2 e}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{2}}+\frac{5 \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}\, a \,d^{3}}+\frac{3 c \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{2 \sqrt{a d e}\, a^{2} d \,e^{2}}-\frac{5}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{3}}-\frac{3 c}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d \,e^{2}}-\frac{1}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2} e x}"," ",0,"-1/d^2/a/e/x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-5/2/d^3/a/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-3/2/d/a^2/e^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+5/d^2*e^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c+3*d^2/a^2/e/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3+5/2/d^3*a*e^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+5/2/d*e^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+3/2*d/a/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+3/2*d^3/a^2/e^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3+5/2/d^3/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+3/2/d/a^2/e^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-2/3*e/d^2/(a*e^2-c*d^2)/(x+d/e)/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+16/3*e^3*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+8/3*e^4/d*c/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*a+8/3*e^2*d*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","B"
485,1,1319,488,0.020000," ","int(1/x^3/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{16 c^{2} e^{4} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d}-\frac{8 a c \,e^{5}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{2}}-\frac{8 c^{2} e^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}}+\frac{7 c^{2} e^{2} x}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a d}-\frac{5 c^{3} d x}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2}}-\frac{15 c^{4} d^{3} x}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{2}}-\frac{35 c \,e^{4} x}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{3}}-\frac{35 a \,e^{5}}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{4}}+\frac{c^{2} e}{4 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a}-\frac{5 c^{3} d^{2}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} e}-\frac{15 c^{4} d^{4}}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{3}}-\frac{7 c \,e^{3}}{2 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{2}}+\frac{2 e^{2}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{3}}-\frac{35 e \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}\, a \,d^{4}}-\frac{15 c \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{4 \sqrt{a d e}\, a^{2} d^{2} e}-\frac{15 c^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{8 \sqrt{a d e}\, a^{3} e^{3}}+\frac{35 e}{8 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{4}}+\frac{15 c}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{2} e}+\frac{15 c^{2}}{8 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{3}}+\frac{9}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{3} x}+\frac{5 c}{4 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d \,e^{2} x}-\frac{1}{2 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2} e \,x^{2}}"," ",0,"-15/4*d^3/a^3/e^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^4+7/4*e^2/d/a/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2-8/3*e^3*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+15/8/a^3/e^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+9/4/d^3/a/x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+35/8*e/d^4/a/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-16/3/d*e^4*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x-8/3/d^2*e^5*c/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*a-15/8*d^4/a^3/e^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4+5/4/d/a^2/e^2/x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-35/4*e^4/d^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c-5/4*d/a^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3-5/2/e*d^2/a^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-15/4/e/d^2/a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-15/8/a^3/e^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-1/2/d^2/a/e/x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+2/3/d^3*e^2/(a*e^2-c*d^2)/(x+d/e)/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+15/4/e/d^2/a^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-35/8*e^5/d^4*a/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-7/2*e^3/d^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+1/4*e/a/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-35/8*e/d^4/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)","B"
486,1,1705,626,0.021000," ","int(1/x^4/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{16 c^{2} e^{5} x}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{2}}+\frac{8 a c \,e^{6}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{3}}+\frac{8 c^{2} e^{4}}{3 \left(a \,e^{2}-c \,d^{2}\right)^{3} \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d}-\frac{41 c^{2} e^{3} x}{12 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2}}-\frac{c^{3} e x}{6 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2}}+\frac{25 c^{4} d^{2} x}{12 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e}+\frac{35 c^{5} d^{4} x}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{3}}+\frac{105 c \,e^{5} x}{8 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{4}}+\frac{105 a \,e^{6}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{5}}-\frac{43 c^{2} e^{2}}{24 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a d}+\frac{23 c^{3} d}{24 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2}}+\frac{155 c^{4} d^{3}}{48 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{2}}+\frac{35 c^{5} d^{5}}{16 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{4}}+\frac{233 c \,e^{4}}{48 \left(-a^{2} e^{4}+2 a c \,d^{2} e^{2}-c^{2} d^{4}\right) \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, d^{3}}-\frac{2 e^{3}}{3 \left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c d e +\left(a \,e^{2}-c \,d^{2}\right) \left(x +\frac{d}{e}\right)}\, d^{4}}+\frac{105 e^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, a \,d^{5}}+\frac{105 c \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, a^{2} d^{3}}+\frac{75 c^{2} \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, a^{3} d \,e^{2}}+\frac{35 c^{3} d \ln \left(\frac{2 a d e +\left(a \,e^{2}+c \,d^{2}\right) x +2 \sqrt{a d e}\, \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}{x}\right)}{16 \sqrt{a d e}\, a^{4} e^{4}}-\frac{105 e^{2}}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{5}}-\frac{105 c}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{3}}-\frac{75 c^{2}}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} d \,e^{2}}-\frac{35 c^{3} d}{16 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{4} e^{4}}-\frac{89 e}{24 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{4} x}-\frac{17 c}{6 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d^{2} e x}-\frac{35 c^{2}}{24 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{3} e^{3} x}+\frac{13}{12 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{3} x^{2}}+\frac{7 c}{12 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a^{2} d \,e^{2} x^{2}}-\frac{1}{3 \sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, a \,d^{2} e \,x^{3}}"," ",0,"35/8*d^4/a^4/e^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^5+25/12/e*d^2/a^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^4-41/12/d^2*e^3/a/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^2+75/16/e^2/d/a^3/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^2-1/6*e/a^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c^3-43/24/d*e^2/a/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2+105/8/d^4*e^5/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*x*c+35/16*d^5/a^4/e^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^5+35/16*d/a^4/e^4/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c^3+16/3/d^2*e^5*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*x+8/3/d^3*e^6*c/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)*a-17/6/e/d^2/a^2/x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+155/48/e^2*d^3/a^3/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^4+7/12/d/a^2/e^2/x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+13/12/d^3/a/x^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-105/16/d^5*e^2/a/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-105/16/d^3/a^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c-89/24/d^4*e/a/x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+105/16/d^5*e^6*a/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)+233/48/d^3*e^4/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c+23/24*d/a^2/(-a^2*e^4+2*a*c*d^2*e^2-c^2*d^4)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3+105/16/d^5*e^2/a/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)+105/16/d^3/a^2/(a*d*e)^(1/2)*ln((2*a*d*e+(a*e^2+c*d^2)*x+2*(a*d*e)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2))/x)*c-75/16/e^2/d/a^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-35/24/a^3/e^3/x/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^2-1/3/d^2/a/e/x^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)-35/16*d/a^4/e^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)*c^3-2/3/d^4*e^3/(a*e^2-c*d^2)/(x+d/e)/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)+8/3/d*e^4*c^2/(a*e^2-c*d^2)^3/((x+d/e)^2*c*d*e+(a*e^2-c*d^2)*(x+d/e))^(1/2)","B"
487,1,366,247,0.014000," ","int(x^2/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(40 a^{2} c^{2} d^{2} e^{6} x^{4}+80 a \,c^{3} d^{4} e^{4} x^{4}+8 c^{4} d^{6} e^{2} x^{4}+60 a^{3} c d \,e^{7} x^{3}+220 a^{2} c^{2} d^{3} e^{5} x^{3}+212 a \,c^{3} d^{5} e^{3} x^{3}+20 c^{4} d^{7} e \,x^{3}+15 a^{4} e^{8} x^{2}+180 a^{3} c \,d^{2} e^{6} x^{2}+378 a^{2} c^{2} d^{4} e^{4} x^{2}+180 a \,c^{3} d^{6} e^{2} x^{2}+15 c^{4} d^{8} x^{2}+20 a^{4} d \,e^{7} x +212 a^{3} c \,d^{3} e^{5} x +220 a^{2} c^{2} d^{5} e^{3} x +60 a \,c^{3} d^{7} e x +8 a^{4} d^{2} e^{6}+80 a^{3} c \,d^{4} e^{4}+40 a^{2} c^{2} d^{6} e^{2}\right)}{15 \left(a^{5} e^{10}-5 a^{4} c \,d^{2} e^{8}+10 a^{3} c^{2} d^{4} e^{6}-10 a^{2} c^{3} d^{6} e^{4}+5 a \,c^{4} d^{8} e^{2}-c^{5} d^{10}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"-2/15*(c*d*x+a*e)*(40*a^2*c^2*d^2*e^6*x^4+80*a*c^3*d^4*e^4*x^4+8*c^4*d^6*e^2*x^4+60*a^3*c*d*e^7*x^3+220*a^2*c^2*d^3*e^5*x^3+212*a*c^3*d^5*e^3*x^3+20*c^4*d^7*e*x^3+15*a^4*e^8*x^2+180*a^3*c*d^2*e^6*x^2+378*a^2*c^2*d^4*e^4*x^2+180*a*c^3*d^6*e^2*x^2+15*c^4*d^8*x^2+20*a^4*d*e^7*x+212*a^3*c*d^3*e^5*x+220*a^2*c^2*d^5*e^3*x+60*a*c^3*d^7*e*x+8*a^4*d^2*e^6+80*a^3*c*d^4*e^4+40*a^2*c^2*d^6*e^2)/(a^5*e^10-5*a^4*c*d^2*e^8+10*a^3*c^2*d^4*e^6-10*a^2*c^3*d^6*e^4+5*a*c^4*d^8*e^2-c^5*d^10)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
488,1,663,325,0.020000," ","int(x^2/(e*x+d)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(7/2),x)","-\frac{2 \left(c d x +a e \right) \left(-896 a^{2} c^{4} d^{4} e^{8} x^{6}-1792 a \,c^{5} d^{6} e^{6} x^{6}-384 c^{6} d^{8} e^{4} x^{6}-2240 a^{3} c^{3} d^{3} e^{9} x^{5}-7616 a^{2} c^{4} d^{5} e^{7} x^{5}-7232 a \,c^{5} d^{7} e^{5} x^{5}-1344 c^{6} d^{9} e^{3} x^{5}-1680 a^{4} c^{2} d^{2} e^{10} x^{4}-11200 a^{3} c^{3} d^{4} e^{8} x^{4}-20320 a^{2} c^{4} d^{6} e^{6} x^{4}-11200 a \,c^{5} d^{8} e^{4} x^{4}-1680 c^{6} d^{10} e^{2} x^{4}-280 a^{5} c d \,e^{11} x^{3}-6440 a^{4} c^{2} d^{3} e^{9} x^{3}-21680 a^{3} c^{3} d^{5} e^{7} x^{3}-24080 a^{2} c^{4} d^{7} e^{5} x^{3}-8120 a \,c^{5} d^{9} e^{3} x^{3}-840 c^{6} d^{11} e \,x^{3}+35 a^{6} e^{12} x^{2}-910 a^{5} c \,d^{2} e^{10} x^{2}-9295 a^{4} c^{2} d^{4} e^{8} x^{2}-20020 a^{3} c^{3} d^{6} e^{6} x^{2}-13195 a^{2} c^{4} d^{8} e^{4} x^{2}-2590 a \,c^{5} d^{10} e^{2} x^{2}-105 c^{6} d^{12} x^{2}+28 a^{6} d \,e^{11} x -764 a^{5} c \,d^{3} e^{9} x -6440 a^{4} c^{2} d^{5} e^{7} x -8120 a^{3} c^{3} d^{7} e^{5} x -2996 a^{2} c^{4} d^{9} e^{3} x -140 a \,c^{5} d^{11} e x +8 a^{6} d^{2} e^{10}-224 a^{5} c \,d^{4} e^{8}-1680 a^{4} c^{2} d^{6} e^{6}-1120 a^{3} c^{3} d^{8} e^{4}-56 a^{2} c^{4} d^{10} e^{2}\right)}{105 \left(a^{7} e^{14}-7 a^{6} c \,d^{2} e^{12}+21 a^{5} c^{2} d^{4} e^{10}-35 a^{4} c^{3} d^{6} e^{8}+35 a^{3} c^{4} d^{8} e^{6}-21 a^{2} c^{5} d^{10} e^{4}+7 a \,c^{6} d^{12} e^{2}-c^{7} d^{14}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{7}{2}}}"," ",0,"-2/105*(c*d*x+a*e)*(-896*a^2*c^4*d^4*e^8*x^6-1792*a*c^5*d^6*e^6*x^6-384*c^6*d^8*e^4*x^6-2240*a^3*c^3*d^3*e^9*x^5-7616*a^2*c^4*d^5*e^7*x^5-7232*a*c^5*d^7*e^5*x^5-1344*c^6*d^9*e^3*x^5-1680*a^4*c^2*d^2*e^10*x^4-11200*a^3*c^3*d^4*e^8*x^4-20320*a^2*c^4*d^6*e^6*x^4-11200*a*c^5*d^8*e^4*x^4-1680*c^6*d^10*e^2*x^4-280*a^5*c*d*e^11*x^3-6440*a^4*c^2*d^3*e^9*x^3-21680*a^3*c^3*d^5*e^7*x^3-24080*a^2*c^4*d^7*e^5*x^3-8120*a*c^5*d^9*e^3*x^3-840*c^6*d^11*e*x^3+35*a^6*e^12*x^2-910*a^5*c*d^2*e^10*x^2-9295*a^4*c^2*d^4*e^8*x^2-20020*a^3*c^3*d^6*e^6*x^2-13195*a^2*c^4*d^8*e^4*x^2-2590*a*c^5*d^10*e^2*x^2-105*c^6*d^12*x^2+28*a^6*d*e^11*x-764*a^5*c*d^3*e^9*x-6440*a^4*c^2*d^5*e^7*x-8120*a^3*c^3*d^7*e^5*x-2996*a^2*c^4*d^9*e^3*x-140*a*c^5*d^11*e*x+8*a^6*d^2*e^10-224*a^5*c*d^4*e^8-1680*a^4*c^2*d^6*e^6-1120*a^3*c^3*d^8*e^4-56*a^2*c^4*d^10*e^2)/(a^7*e^14-7*a^6*c*d^2*e^12+21*a^5*c^2*d^4*e^10-35*a^4*c^3*d^6*e^8+35*a^3*c^4*d^8*e^6-21*a^2*c^5*d^10*e^4+7*a*c^6*d^12*e^2-c^7*d^14)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(7/2)","B"
489,1,257,137,0.140000," ","int(x^3*(x+1)^(1/2)*(x^2-x+1)^(1/2),x)","\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(5 x^{7}+8 x^{4}+3 x +3 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-9 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{55 \left(x^{3}+1\right)}"," ",0,"2/55*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(5*x^7+3*I*3^(1/2)*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((I*3^(1/2)-2*x+1)/(I*3^(1/2)+3))^(1/2)*((I*3^(1/2)+2*x-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-9*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((I*3^(1/2)-2*x+1)/(I*3^(1/2)+3))^(1/2)*((I*3^(1/2)+2*x-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))+8*x^4+3*x)/(x^3+1)","A"
490,1,18,17,0.003000," ","int(x^2*(x+1)^(1/2)*(x^2-x+1)^(1/2),x)","\frac{2 \left(x +1\right)^{\frac{3}{2}} \left(x^{2}-x +1\right)^{\frac{3}{2}}}{9}"," ",0,"2/9*(x+1)^(3/2)*(x^2-x+1)^(3/2)","A"
491,1,361,234,0.034000," ","int(x*(x+1)^(1/2)*(x^2-x+1)^(1/2),x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(2 x^{5}+2 x^{2}-18 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+3 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+9 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{7 x^{3}+7}"," ",0,"1/7*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(3*I*3^(1/2)*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))+2*x^5+9*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-18*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))+2*x^2)/(x^3+1)","A"
492,1,252,117,0.029000," ","int((x+1)^(1/2)*(x^2-x+1)^(1/2),x)","-\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-2 x^{4}-2 x +3 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-9 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{5 \left(x^{3}+1\right)}"," ",0,"-1/5*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(3*I*3^(1/2)*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-9*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-2*x^4-2*x)/(x^3+1)","B"
493,1,43,50,0.026000," ","int((x+1)^(1/2)*(x^2-x+1)^(1/2)/x,x)","-\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(\arctanh \left(\sqrt{x^{3}+1}\right)-\sqrt{x^{3}+1}\right)}{3 \sqrt{x^{3}+1}}"," ",0,"-2/3*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(-(x^3+1)^(1/2)+arctanh((x^3+1)^(1/2)))/(x^3+1)^(1/2)","A"
494,1,363,233,0.030000," ","int((x+1)^(1/2)*(x^2-x+1)^(1/2)/x^2,x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-2 x^{3}-18 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+3 i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+9 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-2\right)}{2 \left(x^{3}+1\right) x}"," ",0,"1/2*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(3*I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)*x+9*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-18*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-2*x^3-2)/x/(x^3+1)","A"
495,1,259,119,0.032000," ","int((x+1)^(1/2)*(x^2-x+1)^(1/2)/x^3,x)","-\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(2 x^{3}+3 i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-9 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+2\right)}{4 \left(x^{3}+1\right) x^{2}}"," ",0,"-1/4*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(3*I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)*x^2-9*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^2+2*x^3+2)/(x^3+1)/x^2","B"
496,1,262,162,0.030000," ","int(x^3*(x+1)^(3/2)*(x^2-x+1)^(3/2),x)","\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(55 x^{10}+155 x^{7}+127 x^{4}+27 x +27 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-81 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{935 \left(x^{3}+1\right)}"," ",0,"2/935*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(55*x^10+155*x^7+27*I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)-81*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))+127*x^4+27*x)/(x^3+1)","A"
497,1,18,17,0.005000," ","int(x^2*(x+1)^(3/2)*(x^2-x+1)^(3/2),x)","\frac{2 \left(x +1\right)^{\frac{5}{2}} \left(x^{2}-x +1\right)^{\frac{5}{2}}}{15}"," ",0,"2/15*(x+1)^(5/2)*(x^2-x+1)^(5/2)","A"
498,1,366,259,0.031000," ","int(x*(x+1)^(3/2)*(x^2-x+1)^(3/2),x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(14 x^{8}+46 x^{5}+32 x^{2}-162 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+27 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+81 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{91 x^{3}+91}"," ",0,"1/91*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(14*x^8+27*I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)+46*x^5+81*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-162*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))+32*x^2)/(x^3+1)","A"
499,1,257,140,0.016000," ","int((x+1)^(3/2)*(x^2-x+1)^(3/2),x)","-\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-10 x^{7}-38 x^{4}-28 x +27 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-81 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{55 \left(x^{3}+1\right)}"," ",0,"-1/55*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(-10*x^7+27*I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)-81*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-38*x^4-28*x)/(x^3+1)","A"
500,1,57,72,0.011000," ","int((x+1)^(3/2)*(x^2-x+1)^(3/2)/x,x)","-\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-\sqrt{x^{3}+1}\, x^{3}+3 \arctanh \left(\sqrt{x^{3}+1}\right)-4 \sqrt{x^{3}+1}\right)}{9 \sqrt{x^{3}+1}}"," ",0,"-2/9*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(-x^3*(x^3+1)^(1/2)+3*arctanh((x^3+1)^(1/2))-4*(x^3+1)^(1/2))/(x^3+1)^(1/2)","A"
501,1,368,259,0.020000," ","int((x+1)^(3/2)*(x^2-x+1)^(3/2)/x^2,x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(4 x^{6}-10 x^{3}-162 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+27 i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+81 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-14\right)}{14 \left(x^{3}+1\right) x}"," ",0,"1/14*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(27*I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)*x+4*x^6+81*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-162*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-10*x^3-14)/x/(x^3+1)","A"
502,1,264,142,0.019000," ","int((x+1)^(3/2)*(x^2-x+1)^(3/2)/x^3,x)","-\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-8 x^{6}+2 x^{3}+27 i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-81 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+10\right)}{20 \left(x^{3}+1\right) x^{2}}"," ",0,"-1/20*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(27*I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)*x^2-81*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^2-8*x^6+2*x^3+10)/(x^3+1)/x^2","A"
503,1,248,115,0.043000," ","int(x^3/(x+1)^(1/2)/(x^2-x+1)^(1/2),x)","\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(x^{4}+x +i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{5 \left(x^{3}+1\right)}"," ",0,"2/5*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)-3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))+x^4+x)/(x^3+1)","B"
504,1,18,17,0.005000," ","int(x^2/(x+1)^(1/2)/(x^2-x+1)^(1/2),x)","\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}}{3}"," ",0,"2/3*(x+1)^(1/2)*(x^2-x+1)^(1/2)","A"
505,1,275,205,0.035000," ","int(x/(x+1)^(1/2)/(x^2-x+1)^(1/2),x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-3+i \sqrt{3}\right) \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \left(i \sqrt{3}\, \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+3 \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-i \sqrt{3}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-\EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{2 x^{3}+2}"," ",0,"1/2*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(-3+I*3^(1/2))*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*(I*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)-I*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)+3*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2)))/(x^3+1)","A"
506,1,137,91,0.019000," ","int(1/(x+1)^(1/2)/(x^2-x+1)^(1/2),x)","\frac{\left(3-i \sqrt{3}\right) \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)}{x^{3}+1}"," ",0,"(3-I*3^(1/2))*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))/(x^3+1)","A"
507,1,33,32,0.028000," ","int(1/x/(x+1)^(1/2)/(x^2-x+1)^(1/2),x)","-\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \arctanh \left(\sqrt{x^{3}+1}\right)}{3 \sqrt{x^{3}+1}}"," ",0,"-2/3*arctanh((x^3+1)^(1/2))*(x+1)^(1/2)*(x^2-x+1)^(1/2)/(x^3+1)^(1/2)","A"
508,1,363,230,0.024000," ","int(1/x^2/(x+1)^(1/2)/(x^2-x+1)^(1/2),x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-2 x^{3}-6 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-2\right)}{2 \left(x^{3}+1\right) x}"," ",0,"1/2*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)*x+3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-6*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-2*x^3-2)/x/(x^3+1)","A"
509,1,259,119,0.022000," ","int(1/x^3/(x+1)^(1/2)/(x^2-x+1)^(1/2),x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-2 x^{3}+i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-2\right)}{4 \left(x^{3}+1\right) x^{2}}"," ",0,"1/4*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)*x^2-3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^2-2*x^3-2)/(x^3+1)/x^2","B"
510,1,245,110,0.066000," ","int(x^3/(x+1)^(3/2)/(x^2-x+1)^(3/2),x)","-\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(x +i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{3 \left(x^{3}+1\right)}"," ",0,"-2/3*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)-3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))+x)/(x^3+1)","B"
511,1,18,17,0.006000," ","int(x^2/(x+1)^(3/2)/(x^2-x+1)^(3/2),x)","-\frac{2}{3 \sqrt{x +1}\, \sqrt{x^{2}-x +1}}"," ",0,"-2/3/(x+1)^(1/2)/(x^2-x+1)^(1/2)","A"
512,1,356,225,0.051000," ","int(x/(x+1)^(3/2)/(x^2-x+1)^(3/2),x)","-\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-2 x^{2}-6 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{3 \left(x^{3}+1\right)}"," ",0,"-1/3*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)+3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-6*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-2*x^2)/(x^3+1)","A"
513,1,247,110,0.036000," ","int(1/(x+1)^(3/2)/(x^2-x+1)^(3/2),x)","-\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-2 x +i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{3 \left(x^{3}+1\right)}"," ",0,"-1/3*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)-3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-2*x)/(x^3+1)","B"
514,1,43,50,0.041000," ","int(1/x/(x+1)^(3/2)/(x^2-x+1)^(3/2),x)","-\frac{2 \sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(\sqrt{x^{3}+1}\, \arctanh \left(\sqrt{x^{3}+1}\right)-1\right)}{3 \left(x^{3}+1\right)}"," ",0,"-2/3*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(arctanh((x^3+1)^(1/2))*(x^3+1)^(1/2)-1)/(x^3+1)","A"
515,1,363,250,0.040000," ","int(1/x^2/(x+1)^(3/2)/(x^2-x+1)^(3/2),x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-10 x^{3}-30 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+5 i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+15 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-6\right)}{6 \left(x^{3}+1\right) x}"," ",0,"1/6*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(5*I*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)*x*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)+15*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-30*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-10*x^3-6)/(x^3+1)/x","A"
516,1,259,137,0.039000," ","int(1/x^3/(x+1)^(3/2)/(x^2-x+1)^(3/2),x)","\frac{\sqrt{x +1}\, \sqrt{x^{2}-x +1}\, \left(-14 x^{3}+7 i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-21 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-6\right)}{12 \left(x^{3}+1\right) x^{2}}"," ",0,"1/12*(x+1)^(1/2)*(x^2-x+1)^(1/2)*(7*I*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)*x^2*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-21*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^2-14*x^3-6)/(x^3+1)/x^2","A"
517,1,467,135,0.072000," ","int(x^3/(x+1)^(5/2)/(x^2-x+1)^(5/2),x)","-\frac{2 \left(-2 x^{4}+i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{3} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{3} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+x +i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)\right)}{27 \left(x^{2}-x +1\right)^{\frac{3}{2}} \left(x +1\right)^{\frac{3}{2}}}"," ",0,"-2/27*(I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-3*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)+I*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*3^(1/2)-3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-2*x^4+x)/(x^2-x+1)^(3/2)/(x+1)^(3/2)","B"
518,1,18,17,0.005000," ","int(x^2/(x+1)^(5/2)/(x^2-x+1)^(5/2),x)","-\frac{2}{9 \left(x +1\right)^{\frac{3}{2}} \left(x^{2}-x +1\right)^{\frac{3}{2}}}"," ",0,"-2/9/(x+1)^(3/2)/(x^2-x+1)^(3/2)","A"
519,1,688,252,0.056000," ","int(x/(x+1)^(5/2)/(x^2-x+1)^(5/2),x)","-\frac{-10 x^{5}-30 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{3} \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+5 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{3} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+15 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{3} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-16 x^{2}-30 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+5 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+15 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)}{27 \left(x^{2}-x +1\right)^{\frac{3}{2}} \left(x +1\right)^{\frac{3}{2}}}"," ",0,"-1/27*(5*I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)+15*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-30*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)+5*I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-10*x^5+15*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-30*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-16*x^2)/(x^2-x+1)^(3/2)/(x+1)^(3/2)","B"
520,1,469,135,0.053000," ","int(1/(x+1)^(5/2)/(x^2-x+1)^(5/2),x)","-\frac{-14 x^{4}+7 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{3} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-21 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{3} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-20 x +7 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-21 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)}{27 \left(x^{2}-x +1\right)^{\frac{3}{2}} \left(x +1\right)^{\frac{3}{2}}}"," ",0,"-1/27*(7*I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-21*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)+7*I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-21*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))-14*x^4-20*x)/(x^2-x+1)^(3/2)/(x+1)^(3/2)","B"
521,1,69,74,0.063000," ","int(1/x/(x+1)^(5/2)/(x^2-x+1)^(5/2),x)","-\frac{2 \left(3 \sqrt{x^{3}+1}\, x^{3} \arctanh \left(\sqrt{x^{3}+1}\right)-3 x^{3}+3 \sqrt{x^{3}+1}\, \arctanh \left(\sqrt{x^{3}+1}\right)-4\right)}{9 \left(x^{3}+1\right) \sqrt{x^{2}-x +1}\, \sqrt{x +1}}"," ",0,"-2/9*(3*(x^3+1)^(1/2)*arctanh((x^3+1)^(1/2))*x^3-3*x^3+3*arctanh((x^3+1)^(1/2))*(x^3+1)^(1/2)-4)/(x^3+1)/(x^2-x+1)^(1/2)/(x+1)^(1/2)","A"
522,1,695,277,0.061000," ","int(1/x^2/(x+1)^(5/2)/(x^2-x+1)^(5/2),x)","\frac{-110 x^{6}-330 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{4} \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+55 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{4} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+165 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{4} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-176 x^{3}-330 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+55 i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)+165 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-54}{54 \left(x^{2}-x +1\right)^{\frac{3}{2}} \left(x +1\right)^{\frac{3}{2}} x}"," ",0,"1/54*(55*I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^4*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)+165*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^4*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-330*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^4*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)+55*I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-110*x^6+165*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-330*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x-176*x^3-54)/x/(x^2-x+1)^(3/2)/(x+1)^(3/2)","B"
523,1,481,164,0.063000," ","int(1/x^3/(x+1)^(5/2)/(x^2-x+1)^(5/2),x)","\frac{-182 x^{6}+91 i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{5} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-273 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{5} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-260 x^{3}+91 i \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, \sqrt{3}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-273 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{i \sqrt{3}+3}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{-3+i \sqrt{3}}}\, x^{2} \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{i \sqrt{3}+3}}\right)-54}{108 \left(x^{2}-x +1\right)^{\frac{3}{2}} \left(x +1\right)^{\frac{3}{2}} x^{2}}"," ",0,"1/108*(91*I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^5*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-273*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^5*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)+91*I*3^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^2*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)-273*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(I*3^(1/2)+3))^(1/2)*((2*x+I*3^(1/2)-1)/(-3+I*3^(1/2)))^(1/2)*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(I*3^(1/2)+3))^(1/2))*x^2-182*x^6-260*x^3-54)/x^2/(x^2-x+1)^(3/2)/(x+1)^(3/2)","B"
524,1,68,82,0.013000," ","int(x/(-1+x)^3/(4*x^2+5*x+3)^2,x)","\frac{6023 \sqrt{23}\, \arctan \left(\frac{\left(8 x +5\right) \sqrt{23}}{23}\right)}{1218816}+\frac{11 \ln \left(x -1\right)}{2304}-\frac{11 \ln \left(4 x^{2}+5 x +3\right)}{4608}-\frac{-\frac{2204 x}{23}-\frac{975}{23}}{6912 \left(x^{2}+\frac{5}{4} x +\frac{3}{4}\right)}-\frac{1}{288 \left(x -1\right)^{2}}+\frac{7}{864 \left(x -1\right)}"," ",0,"-1/6912*(-2204/23*x-975/23)/(x^2+5/4*x+3/4)-11/4608*ln(4*x^2+5*x+3)+6023/1218816*arctan(1/23*(5+8*x)*23^(1/2))*23^(1/2)-1/288/(-1+x)^2+7/864/(-1+x)+11/2304*ln(-1+x)","A"
525,1,2218,435,0.110000," ","int(x^4*(e*x+d)^(1/2)/(c*x^2+b*x+a),x)","\frac{5 \sqrt{2}\, a^{2} b \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{5 \sqrt{2}\, a^{2} b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{2 \sqrt{2}\, a^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, a^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{5 \sqrt{2}\, a \,b^{3} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{5 \sqrt{2}\, a \,b^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}+\frac{4 \sqrt{2}\, a \,b^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{4 \sqrt{2}\, a \,b^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{5} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{4}}+\frac{\sqrt{2}\, b^{5} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{4}}-\frac{\sqrt{2}\, b^{4} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{4} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, a^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, a^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, a \,b^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{3 \sqrt{2}\, a \,b^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{2 \sqrt{2}\, a b d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, a b d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{4} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{4}}+\frac{\sqrt{2}\, b^{4} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{4}}+\frac{\sqrt{2}\, b^{3} d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{3} d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}+\frac{4 \sqrt{e x +d}\, a b}{c^{3}}-\frac{2 \sqrt{e x +d}\, b^{3}}{c^{4}}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} a}{3 c^{2} e}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} b^{2}}{3 c^{3} e}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} b d}{3 c^{2} e^{2}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}} d^{2}}{3 c \,e^{3}}-\frac{2 \left(e x +d \right)^{\frac{5}{2}} b}{5 c^{2} e^{2}}-\frac{4 \left(e x +d \right)^{\frac{5}{2}} d}{5 c \,e^{3}}+\frac{2 \left(e x +d \right)^{\frac{7}{2}}}{7 c \,e^{3}}"," ",0,"2/7*(e*x+d)^(7/2)/c/e^3-2/5/e^2/c^2*(e*x+d)^(5/2)*b-2/3/e/c^2*(e*x+d)^(3/2)*a+2/3/e/c^3*(e*x+d)^(3/2)*b^2-4/5/e^3/c*(e*x+d)^(5/2)*d+2/3/e^3/c*(e*x+d)^(3/2)*d^2+4/c^3*a*b*(e*x+d)^(1/2)+4*e/c^2/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b^2*d+4*e/c^2/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b^2*d+5*e^2/c^2/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a^2*b-2*e/c/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a^2*d-e/c^3/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^4*d-2/c^4*b^3*(e*x+d)^(1/2)+2/c^2*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b*d-2/c^2*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b*d+e^2/c^4/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^5+3*e/c^3*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b^2+e^2/c^4/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^5-3*e/c^3*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b^2-5*e^2/c^3/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b^3+e/c^4*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^4+1/c^3*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^3*d-1/c^3*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^3*d-e/c^2*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a^2-e/c^4*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^4+e/c^2*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a^2+5*e^2/c^2/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctanh(c*(e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a^2*b-2*e/c/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a^2*d-5*e^2/c^3/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*a*b^3-e/c^3/(-e^2*(4*a*c-b^2))^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2)*arctan(c*(e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-e^2*(4*a*c-b^2))^(1/2))*c)^(1/2))*b^4*d+2/3/e^2/c^2*(e*x+d)^(3/2)*b*d","B"
526,1,1764,273,0.058000," ","int(x^3*(e*x+d)^(1/2)/(c*x^2+b*x+a),x)","-\frac{2 \sqrt{2}\, a^{2} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, a^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{4 \sqrt{2}\, a \,b^{2} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{4 \sqrt{2}\, a \,b^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{3 \sqrt{2}\, a b d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a b d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{4} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{4} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}+\frac{\sqrt{2}\, b^{3} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{3} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{2 \sqrt{2}\, a b e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, a b e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, a d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{3} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{3} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{2} d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{2 \sqrt{e x +d}\, a}{c^{2}}+\frac{2 \sqrt{e x +d}\, b^{2}}{c^{3}}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} b}{3 c^{2} e}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} d}{3 c \,e^{2}}+\frac{2 \left(e x +d \right)^{\frac{5}{2}}}{5 c \,e^{2}}"," ",0,"2/5*(e*x+d)^(5/2)/c/e^2-2/3/e/c^2*(e*x+d)^(3/2)*b-2/3/e^2/c*(e*x+d)^(3/2)*d-2/c^2*a*(e*x+d)^(1/2)+2/c^3*b^2*(e*x+d)^(1/2)-2*e^2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2+4*e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2-3*e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d-e^2/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4+e/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d-2*e/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b+1/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d+e/c^3*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3-1/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-2*e^2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2+4*e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2-3*e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d-e^2/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4+e/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d+2*e/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b-1/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d-e/c^3*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3+1/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d","B"
527,1,1329,269,0.045000," ","int(x^2*(e*x+d)^(1/2)/(c*x^2+b*x+a),x)","-\frac{3 \sqrt{2}\, a b \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, a d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, a d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b^{3} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{\sqrt{2}\, a e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{e x +d}\, b}{c^{2}}+\frac{2 \left(e x +d \right)^{\frac{3}{2}}}{3 c e}"," ",0,"2/3*(e*x+d)^(3/2)/c/e-2*b*(e*x+d)^(1/2)/c^2-3*e^2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b+2*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d+e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3-e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+e/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a-e/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2+1/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-3*e^2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b+2*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d+e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3-e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-e/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a+e/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2-1/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d","B"
528,1,926,241,0.038000," ","int(x*(e*x+d)^(1/2)/(c*x^2+b*x+a),x)","\frac{2 \sqrt{2}\, a \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, a \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{e x +d}}{c}"," ",0,"2*(e*x+d)^(1/2)/c+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^2-1/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^2+1/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e+1/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e-2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^2-1/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^2+1/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e-1/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e+2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d","B"
529,1,545,158,0.027000," ","int((e*x+d)^(1/2)/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, b \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}"," ",0,"e^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-2*c*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-e*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+e^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-2*c*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+e*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)","B"
530,1,581,225,0.058000," ","int((e*x+d)^(1/2)/x/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, b c d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{2 \sqrt{2}\, c \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, c d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{2 \sqrt{d}\, \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a}"," ",0,"-2*arctanh((e*x+d)^(1/2)/d^(1/2))*d^(1/2)/a-2*e^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+e/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+1/a*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-2*e^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+e/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d-1/a*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d","B"
531,1,999,298,0.050000," ","int((e*x+d)^(1/2)/x^2/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, b c \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{2 \sqrt{2}\, c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{2 \sqrt{2}\, c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} c d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, c e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b c d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a \sqrt{d}}+\frac{2 b \sqrt{d}\, \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a^{2}}-\frac{\sqrt{e x +d}}{a x}"," ",0,"-(e*x+d)^(1/2)/a/x-e*arctanh((e*x+d)^(1/2)/d^(1/2))/a/d^(1/2)+2/a^2*d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*b+e^2/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+2*e/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-e/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+e/a*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-1/a^2*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+e^2/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+2*e/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-e/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-e/a*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+1/a^2*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d","B"
532,1,1486,449,0.051000," ","int((e*x+d)^(1/2)/x^3/(c*x^2+b*x+a),x)","\frac{2 \sqrt{2}\, c^{2} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{2 \sqrt{2}\, c^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} c \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b \,c^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b \,c^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b^{3} c d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{3}}+\frac{\sqrt{2}\, b^{3} c d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{3}}-\frac{\sqrt{2}\, b c e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b c e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, c^{2} d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b^{2} c d \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{3}}-\frac{\sqrt{2}\, b^{2} c d \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{3}}+\frac{e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 a \,d^{\frac{3}{2}}}+\frac{b e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a^{2} \sqrt{d}}+\frac{2 c \sqrt{d}\, \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a^{2}}-\frac{2 b^{2} \sqrt{d}\, \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a^{3}}-\frac{\sqrt{e x +d}}{4 a \,x^{2}}-\frac{\sqrt{e x +d}\, b d}{a^{2} e \,x^{2}}-\frac{\left(e x +d \right)^{\frac{3}{2}}}{4 a d \,x^{2}}+\frac{\left(e x +d \right)^{\frac{3}{2}} b}{a^{2} e \,x^{2}}"," ",0,"-1/4/a/x^2/d*(e*x+d)^(3/2)+1/e/a^2/x^2*(e*x+d)^(3/2)*b-1/e/a^2/x^2*(e*x+d)^(1/2)*b*d-1/4*(e*x+d)^(1/2)/a/x^2+1/4*e^2*arctanh((e*x+d)^(1/2)/d^(1/2))/a/d^(3/2)+e/a^2/d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*b+2/a^2*d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-2/a^3*d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*b^2+2*e^2/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-e^2/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2-3*e/a^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+e/a^3*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d-e/a^2*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-1/a^2*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+1/a^3*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+2*e^2/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-e^2/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2-3*e/a^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+e/a^3*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d+e/a^2*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+1/a^2*c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-1/a^3*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d","B"
533,1,3685,590,0.081000," ","int(x^4*(e*x+d)^(3/2)/(c*x^2+b*x+a),x)","\text{output too large to display}"," ",0,"2/9*(e*x+d)^(9/2)/c/e^3+2*e/c^3*a^2*(e*x+d)^(1/2)+2*e/c^5*b^4*(e*x+d)^(1/2)-4/7/e^3/c*(e*x+d)^(7/2)*d+2/5/e^3/c*(e*x+d)^(5/2)*d^2+4/3/c^3*(e*x+d)^(3/2)*a*b-2/c^4*b^3*d*(e*x+d)^(1/2)-2/7/e^2/c^2*(e*x+d)^(7/2)*b-2/5/e/c^2*(e*x+d)^(5/2)*a+2/5/e/c^3*(e*x+d)^(5/2)*b^2-10*e^2/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^3*d+4*e/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2*d^2+10*e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*b*d-10*e^2/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^3*d+4*e/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2*d^2+10*e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*b*d+4/c^3*a*b*d*(e*x+d)^(1/2)+2*e^3/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^3-e^3/c^5/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^6+2*e^3/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^3-e^3/c^5/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^6-3*e^2/c^3*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*b+2*e/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*d+4*e^2/c^4*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^3+2*e/c^4*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4*d+3*e^2/c^3*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*b-2*e/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*d-4*e^2/c^4*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^3-2*e/c^4*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4*d+2/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d^2-2/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d^2+2/5/e^2/c^2*(e*x+d)^(5/2)*b*d-6*e/c^4*a*b^2*(e*x+d)^(1/2)+1/c^3*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d^2-1/c^3*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d^2+e^2/c^5*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^5-e^2/c^5*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^5-2/3/c^4*(e*x+d)^(3/2)*b^3+6*e/c^3*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2*d-6*e/c^3*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2*d-2*e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*d^2-9*e^3/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*b^2-2*e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*d^2+6*e^3/c^4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^4+2*e^2/c^4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^5*d-e/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4*d^2+6*e^3/c^4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^4+2*e^2/c^4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^5*d-e/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4*d^2-9*e^3/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*b^2","B"
534,1,2988,525,0.063000," ","int(x^3*(e*x+d)^(3/2)/(c*x^2+b*x+a),x)","\text{output too large to display}"," ",0,"2/7*(e*x+d)^(7/2)/c/e^2-2/5/e^2/c*(e*x+d)^(5/2)*d-2/c^2*a*d*(e*x+d)^(1/2)+2/c^3*b^2*d*(e*x+d)^(1/2)-2/5/e/c^2*(e*x+d)^(5/2)*b-2*e/c^4*b^3*(e*x+d)^(1/2)+8*e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2*d-3*e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d^2+8*e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2*d-3*e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d^2+e^3/c^4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^5+3*e^2/c^3*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2+2*e/c^3*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d-3*e^2/c^3*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2-2*e/c^3*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d+e^3/c^4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^5+4*e/c^3*a*b*(e*x+d)^(1/2)+5*e^3/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*b-4*e^2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*d-5*e^3/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^3-2*e^2/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4*d+e/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d^2+5*e^3/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*b-4*e/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d+4*e/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d-4*e^2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2*d-5*e^3/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^3-2*e^2/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4*d+e/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d^2-2/3/c^2*(e*x+d)^(3/2)*a+2/3/c^3*(e*x+d)^(3/2)*b^2+1/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2+1/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d^2-1/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2-e^2/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2-e^2/c^4*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4+e^2/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2+e^2/c^4*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4-1/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d^2","B"
535,1,2358,388,0.059000," ","int(x^2*(e*x+d)^(3/2)/(c*x^2+b*x+a),x)","-\frac{2 \sqrt{2}\, a^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, a^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{4 \sqrt{2}\, a \,b^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{4 \sqrt{2}\, a \,b^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{6 \sqrt{2}\, a b d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{6 \sqrt{2}\, a b d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, a \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, a \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{4} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{4} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}+\frac{2 \sqrt{2}\, b^{3} d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, b^{3} d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{\sqrt{2}\, b^{2} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, a b \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, a b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, a d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, a d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{3} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{\sqrt{2}\, b^{3} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{3}}-\frac{2 \sqrt{2}\, b^{2} d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, b^{2} d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b \,d^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{e x +d}\, a e}{c^{2}}+\frac{2 \sqrt{e x +d}\, b^{2} e}{c^{3}}-\frac{2 \sqrt{e x +d}\, b d}{c^{2}}-\frac{2 \left(e x +d \right)^{\frac{3}{2}} b}{3 c^{2}}+\frac{2 \left(e x +d \right)^{\frac{5}{2}}}{5 c e}"," ",0,"-e^2/c^3*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3-1/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+1/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+e^2/c^3*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3-2/3*b*(e*x+d)^(3/2)/c^2+2/5*(e*x+d)^(5/2)/c/e-2*e/c^2*a*(e*x+d)^(1/2)+2*e/c^3*b^2*(e*x+d)^(1/2)-2/c^2*b*d*(e*x+d)^(1/2)-6*e^2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d-6*e^2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*d-e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2+4*e^3/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2+2*e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d-e/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2+4*e^3/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b^2-2*e^3/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2-e^3/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4-2*e^2/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b+2*e/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d-2*e/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-2*e^3/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a^2-e^3/c^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^4+2*e^2/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b-2*e/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d+2*e/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d+2*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d^2+2*e/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d^2+2*e^2/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d","B"
536,1,1714,391,0.052000," ","int(x*(e*x+d)^(3/2)/(c*x^2+b*x+a),x)","-\frac{3 \sqrt{2}\, a b \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a b \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{4 \sqrt{2}\, a d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{4 \sqrt{2}\, a d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b^{3} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{3} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}-\frac{2 \sqrt{2}\, b^{2} d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, b^{2} d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, a \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c^{2}}+\frac{2 \sqrt{2}\, b d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, b d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, d^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{e x +d}\, b e}{c^{2}}+\frac{2 \sqrt{e x +d}\, d}{c}+\frac{2 \left(e x +d \right)^{\frac{3}{2}}}{3 c}"," ",0,"2/3*(e*x+d)^(3/2)/c-2/c^2*b*e*(e*x+d)^(1/2)+2/c*d*(e*x+d)^(1/2)-3/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*e^3+4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d*e^2+1/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*e^3-2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d*e^2+1/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2*e+1/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^2-1/c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^2+2/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e-2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-3/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*b*e^3+4/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*d*e^2+1/c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*e^3-2/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d*e^2+1/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2*e-1/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^2+1/c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^2-2/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e+2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2","B"
537,1,1138,272,0.038000," ","int((e*x+d)^(3/2)/(c*x^2+b*x+a),x)","\frac{2 \sqrt{2}\, a \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, a \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}+\frac{2 \sqrt{2}\, b d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, b d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, c}-\frac{2 \sqrt{2}\, d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{e x +d}\, e}{c}"," ",0,"2*e*(e*x+d)^(1/2)/c+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^3-1/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^3+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e^2-2*e*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+1/c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e^2-2*e*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*a*e^3-1/c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*e^3+2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d*e^2-2*e*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-1/c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*e^2+2*e*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d","B"
538,1,944,286,0.043000," ","int((e*x+d)^(3/2)/x/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, b c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, b \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{4 \sqrt{2}\, c d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{4 \sqrt{2}\, c d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, c \,d^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{\sqrt{2}\, e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 d^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a}"," ",0,"-2*d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))/a+e^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-4*e^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+e/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2-e^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+1/a*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+e^3/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b-4*e^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+e/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+e^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-1/a*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2","B"
539,1,1215,341,0.048000," ","int((e*x+d)^(3/2)/x^2/(c*x^2+b*x+a),x)","\frac{2 \sqrt{2}\, b c d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{2 \sqrt{2}\, b c d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{2 \sqrt{2}\, c^{2} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{2 \sqrt{2}\, c^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{2 \sqrt{2}\, c \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}-\frac{2 \sqrt{2}\, c \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}+\frac{2 \sqrt{2}\, c d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{2 \sqrt{2}\, c d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c \,d^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b c \,d^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{d}\, e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a}+\frac{2 b \,d^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a^{2}}-\frac{\sqrt{e x +d}\, d}{a x}"," ",0,"-d*(e*x+d)^(1/2)/a/x-3*e*arctanh((e*x+d)^(1/2)/d^(1/2))*d^(1/2)/a+2*d^(3/2)/a^2*arctanh((e*x+d)^(1/2)/d^(1/2))*b-2*e^3*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+2*e^2/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+2*e/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-e/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2+2*e/a*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-1/a^2*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2-2*e^3*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)+2*e^2/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+2*e/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2-e/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2-2*e/a*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+1/a^2*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2","B"
540,1,1880,521,0.056000," ","int((e*x+d)^(3/2)/x^3/(c*x^2+b*x+a),x)","\frac{\sqrt{2}\, b c \,e^{3} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c \,e^{3} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, c^{2} d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, c^{2} d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{2 \sqrt{2}\, b^{2} c d \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{2 \sqrt{2}\, b^{2} c d \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b \,c^{2} d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b \,c^{2} d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b^{3} c \,d^{2} e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{3}}+\frac{\sqrt{2}\, b^{3} c \,d^{2} e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\, \sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{3}}+\frac{\sqrt{2}\, c \,e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c \,e^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a}-\frac{2 \sqrt{2}\, b c d e \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{2 \sqrt{2}\, b c d e \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, c^{2} d^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, c^{2} d^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b^{2} c \,d^{2} \arctanh \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(-b e +2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{3}}-\frac{\sqrt{2}\, b^{2} c \,d^{2} \arctan \left(\frac{\sqrt{e x +d}\, \sqrt{2}\, c}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}}\right)}{\sqrt{\left(b e -2 c d +\sqrt{-\left(4 a c -b^{2}\right) e^{2}}\right) c}\, a^{3}}-\frac{3 e^{2} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{4 a \sqrt{d}}+\frac{3 b \sqrt{d}\, e \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a^{2}}+\frac{2 c \,d^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a^{2}}-\frac{2 b^{2} d^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{e x +d}}{\sqrt{d}}\right)}{a^{3}}+\frac{3 \sqrt{e x +d}\, d}{4 a \,x^{2}}-\frac{\sqrt{e x +d}\, b \,d^{2}}{a^{2} e \,x^{2}}-\frac{5 \left(e x +d \right)^{\frac{3}{2}}}{4 a \,x^{2}}+\frac{\left(e x +d \right)^{\frac{3}{2}} b d}{a^{2} e \,x^{2}}"," ",0,"-1/a^2*c^2*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+1/a^2*c^2*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d^2+e^2/a*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-e^2/a*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)-1/e/a^2/x^2*(e*x+d)^(1/2)*b*d^2+1/e/a^2/x^2*(e*x+d)^(3/2)*b*d-2/a^3*d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*b^2+2/a^2*d^(3/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*c-3*e/a^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+e/a^3*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d^2-2*e^2/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-3*e/a^2*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d^2+e/a^3*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^3*d^2-2*e^2/a^2*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d-3/4*e^2*arctanh((e*x+d)^(1/2)/d^(1/2))/a/d^(1/2)+3/4*d*(e*x+d)^(1/2)/a/x^2-5/4/a/x^2*(e*x+d)^(3/2)+3*e/a^2*d^(1/2)*arctanh((e*x+d)^(1/2)/d^(1/2))*b+2*e/a^2*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+e^3/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+4*e^2/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d-2*e/a^2*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b*d+e^3/a*c/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b+4*e^2/a*c^2/(-(4*a*c-b^2)*e^2)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*d+1/a^3*c*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctanh((e*x+d)^(1/2)*2^(1/2)/((-b*e+2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2-1/a^3*c*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*arctan((e*x+d)^(1/2)*2^(1/2)/((b*e-2*c*d+(-(4*a*c-b^2)*e^2)^(1/2))*c)^(1/2)*c)*b^2*d^2","B"
541,0,0,189,0.208000," ","int(x^m*(f*x+e)^n/(c*x^2+b*x+a),x)","\int \frac{x^{m} \left(f x +e \right)^{n}}{c \,x^{2}+b x +a}\, dx"," ",0,"int(x^m*(f*x+e)^n/(c*x^2+b*x+a),x)","F"
542,0,0,282,0.125000," ","int(x^3*(f*x+e)^n/(c*x^2+b*x+a),x)","\int \frac{x^{3} \left(f x +e \right)^{n}}{c \,x^{2}+b x +a}\, dx"," ",0,"int(x^3*(f*x+e)^n/(c*x^2+b*x+a),x)","F"
543,0,0,230,0.115000," ","int(x^2*(f*x+e)^n/(c*x^2+b*x+a),x)","\int \frac{x^{2} \left(f x +e \right)^{n}}{c \,x^{2}+b x +a}\, dx"," ",0,"int(x^2*(f*x+e)^n/(c*x^2+b*x+a),x)","F"
544,0,0,190,0.111000," ","int(x*(f*x+e)^n/(c*x^2+b*x+a),x)","\int \frac{x \left(f x +e \right)^{n}}{c \,x^{2}+b x +a}\, dx"," ",0,"int(x*(f*x+e)^n/(c*x^2+b*x+a),x)","F"
545,0,0,183,0.111000," ","int((f*x+e)^n/(c*x^2+b*x+a),x)","\int \frac{\left(f x +e \right)^{n}}{c \,x^{2}+b x +a}\, dx"," ",0,"int((f*x+e)^n/(c*x^2+b*x+a),x)","F"
546,0,0,236,0.101000," ","int((f*x+e)^n/x/(c*x^2+b*x+a),x)","\int \frac{\left(f x +e \right)^{n}}{\left(c \,x^{2}+b x +a \right) x}\, dx"," ",0,"int((f*x+e)^n/x/(c*x^2+b*x+a),x)","F"
547,0,0,293,0.129000," ","int((f*x+e)^n/x^2/(c*x^2+b*x+a),x)","\int \frac{\left(f x +e \right)^{n}}{\left(c \,x^{2}+b x +a \right) x^{2}}\, dx"," ",0,"int((f*x+e)^n/x^2/(c*x^2+b*x+a),x)","F"
548,1,186,135,0.006000," ","int((e*x+d)^4*(g*x+f)^2/(-e^2*x^2+d^2),x)","-\frac{e^{2} g^{2} x^{5}}{5}-d e \,g^{2} x^{4}-\frac{e^{2} f g \,x^{4}}{2}-\frac{7 d^{2} g^{2} x^{3}}{3}-\frac{8 d e f g \,x^{3}}{3}-\frac{e^{2} f^{2} x^{3}}{3}-\frac{4 d^{3} g^{2} x^{2}}{e}-7 d^{2} f g \,x^{2}-2 d e \,f^{2} x^{2}-\frac{8 d^{5} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{16 d^{4} f g \ln \left(e x -d \right)}{e^{2}}-\frac{8 d^{4} g^{2} x}{e^{2}}-\frac{8 d^{3} f^{2} \ln \left(e x -d \right)}{e}-\frac{16 d^{3} f g x}{e}-7 d^{2} f^{2} x"," ",0,"-1/5*e^2*g^2*x^5-e*x^4*d*g^2-1/2*e^2*x^4*f*g-7/3*x^3*d^2*g^2-8/3*e*x^3*d*f*g-1/3*e^2*x^3*f^2-4/e*x^2*d^3*g^2-7*x^2*d^2*f*g-2*e*x^2*d*f^2-8/e^2*x*d^4*g^2-16/e*x*d^3*f*g-7*x*d^2*f^2-8*d^5/e^3*ln(e*x-d)*g^2-16*d^4/e^2*ln(e*x-d)*f*g-8*d^3/e*ln(e*x-d)*f^2","A"
549,1,145,103,0.005000," ","int((e*x+d)^3*(g*x+f)^2/(-e^2*x^2+d^2),x)","-\frac{e \,g^{2} x^{4}}{4}-d \,g^{2} x^{3}-\frac{2 e f g \,x^{3}}{3}-\frac{2 d^{2} g^{2} x^{2}}{e}-3 d f g \,x^{2}-\frac{e \,f^{2} x^{2}}{2}-\frac{4 d^{4} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{8 d^{3} f g \ln \left(e x -d \right)}{e^{2}}-\frac{4 d^{3} g^{2} x}{e^{2}}-\frac{4 d^{2} f^{2} \ln \left(e x -d \right)}{e}-\frac{8 d^{2} f g x}{e}-3 d \,f^{2} x"," ",0,"-1/4*e*g^2*x^4-x^3*d*g^2-2/3*e*x^3*f*g-2/e*x^2*d^2*g^2-3*x^2*d*f*g-1/2*e*x^2*f^2-4/e^2*x*d^3*g^2-8/e*x*d^2*f*g-3*x*d*f^2-4*d^4/e^3*ln(e*x-d)*g^2-8*d^3/e^2*ln(e*x-d)*f*g-4*d^2/e*ln(e*x-d)*f^2","A"
550,1,110,63,0.003000," ","int((e*x+d)^2*(g*x+f)^2/(-e^2*x^2+d^2),x)","-\frac{g^{2} x^{3}}{3}-\frac{d \,g^{2} x^{2}}{e}-f g \,x^{2}-\frac{2 d^{3} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{4 d^{2} f g \ln \left(e x -d \right)}{e^{2}}-\frac{2 d^{2} g^{2} x}{e^{2}}-\frac{2 d \,f^{2} \ln \left(e x -d \right)}{e}-\frac{4 d f g x}{e}-f^{2} x"," ",0,"-1/3*g^2*x^3-1/e*x^2*d*g^2-x^2*f*g-2/e^2*x*d^2*g^2-4/e*x*d*f*g-x*f^2-2*d^3/e^3*ln(e*x-d)*g^2-4*d^2/e^2*ln(e*x-d)*f*g-2*d/e*ln(e*x-d)*f^2","A"
551,1,82,48,0.003000," ","int((e*x+d)*(g*x+f)^2/(-e^2*x^2+d^2),x)","-\frac{g^{2} x^{2}}{2 e}-\frac{d^{2} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{2 d f g \ln \left(e x -d \right)}{e^{2}}-\frac{d \,g^{2} x}{e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{e}-\frac{2 f g x}{e}"," ",0,"-1/2*g^2*x^2/e-g^2/e^2*d*x-2*g/e*f*x-1/e^3*ln(e*x-d)*d^2*g^2-2/e^2*ln(e*x-d)*d*f*g-1/e*ln(e*x-d)*f^2","A"
552,1,107,58,0.008000," ","int((g*x+f)^2/(-e^2*x^2+d^2),x)","-\frac{d \,g^{2} \ln \left(e x -d \right)}{2 e^{3}}+\frac{d \,g^{2} \ln \left(e x +d \right)}{2 e^{3}}-\frac{f^{2} \ln \left(e x -d \right)}{2 d e}+\frac{f^{2} \ln \left(e x +d \right)}{2 d e}-\frac{f g \ln \left(e x -d \right)}{e^{2}}-\frac{f g \ln \left(e x +d \right)}{e^{2}}-\frac{g^{2} x}{e^{2}}"," ",0,"-g^2*x/e^2-1/2/e^3*d*ln(e*x-d)*g^2-1/e^2*ln(e*x-d)*f*g-1/2/e/d*ln(e*x-d)*f^2+1/2/e^3*d*ln(e*x+d)*g^2-1/e^2*ln(e*x+d)*f*g+1/2/e/d*ln(e*x+d)*f^2","A"
553,1,149,80,0.010000," ","int((g*x+f)^2/(e*x+d)/(-e^2*x^2+d^2),x)","-\frac{d \,g^{2}}{2 \left(e x +d \right) e^{3}}-\frac{f^{2}}{2 \left(e x +d \right) d e}-\frac{f g \ln \left(e x -d \right)}{2 d \,e^{2}}+\frac{f g \ln \left(e x +d \right)}{2 d \,e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{4 d^{2} e}+\frac{f^{2} \ln \left(e x +d \right)}{4 d^{2} e}+\frac{f g}{\left(e x +d \right) e^{2}}-\frac{g^{2} \ln \left(e x -d \right)}{4 e^{3}}-\frac{3 g^{2} \ln \left(e x +d \right)}{4 e^{3}}"," ",0,"-1/4/e^3*ln(e*x-d)*g^2-1/2/e^2/d*ln(e*x-d)*f*g-1/4/e/d^2*ln(e*x-d)*f^2-3/4/e^3*ln(e*x+d)*g^2+1/2/e^2/d*ln(e*x+d)*f*g+1/4/e/d^2*ln(e*x+d)*f^2-1/2/e^3*d/(e*x+d)*g^2+1/e^2/(e*x+d)*f*g-1/2/e/d/(e*x+d)*f^2","A"
554,1,206,81,0.011000," ","int((g*x+f)^2/(e*x+d)^2/(-e^2*x^2+d^2),x)","-\frac{d \,g^{2}}{4 \left(e x +d \right)^{2} e^{3}}-\frac{f^{2}}{4 \left(e x +d \right)^{2} d e}+\frac{f g}{2 \left(e x +d \right)^{2} e^{2}}-\frac{f g}{2 \left(e x +d \right) d \,e^{2}}-\frac{g^{2} \ln \left(e x -d \right)}{8 d \,e^{3}}+\frac{g^{2} \ln \left(e x +d \right)}{8 d \,e^{3}}-\frac{f^{2}}{4 \left(e x +d \right) d^{2} e}-\frac{f g \ln \left(e x -d \right)}{4 d^{2} e^{2}}+\frac{f g \ln \left(e x +d \right)}{4 d^{2} e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{8 d^{3} e}+\frac{f^{2} \ln \left(e x +d \right)}{8 d^{3} e}+\frac{3 g^{2}}{4 \left(e x +d \right) e^{3}}"," ",0,"-1/8/e^3/d*ln(e*x-d)*g^2-1/4/e^2/d^2*ln(e*x-d)*f*g-1/8/e/d^3*ln(e*x-d)*f^2+3/4/e^3/(e*x+d)*g^2-1/2/d/e^2/(e*x+d)*f*g-1/4/d^2/e/(e*x+d)*f^2-1/4/e^3*d/(e*x+d)^2*g^2+1/2/e^2/(e*x+d)^2*f*g-1/4/e/d/(e*x+d)^2*f^2+1/8/e^3/d*ln(e*x+d)*g^2+1/4/e^2/d^2*ln(e*x+d)*f*g+1/8/e/d^3*ln(e*x+d)*f^2","B"
555,1,259,105,0.010000," ","int((g*x+f)^2/(e*x+d)^3/(-e^2*x^2+d^2),x)","-\frac{d \,g^{2}}{6 \left(e x +d \right)^{3} e^{3}}-\frac{f^{2}}{6 \left(e x +d \right)^{3} d e}+\frac{f g}{3 \left(e x +d \right)^{3} e^{2}}-\frac{f g}{4 \left(e x +d \right)^{2} d \,e^{2}}-\frac{f^{2}}{8 \left(e x +d \right)^{2} d^{2} e}+\frac{3 g^{2}}{8 \left(e x +d \right)^{2} e^{3}}-\frac{g^{2}}{8 \left(e x +d \right) d \,e^{3}}-\frac{f g}{4 \left(e x +d \right) d^{2} e^{2}}-\frac{g^{2} \ln \left(e x -d \right)}{16 d^{2} e^{3}}+\frac{g^{2} \ln \left(e x +d \right)}{16 d^{2} e^{3}}-\frac{f^{2}}{8 \left(e x +d \right) d^{3} e}-\frac{f g \ln \left(e x -d \right)}{8 d^{3} e^{2}}+\frac{f g \ln \left(e x +d \right)}{8 d^{3} e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{16 d^{4} e}+\frac{f^{2} \ln \left(e x +d \right)}{16 d^{4} e}"," ",0,"-1/16/e^3/d^2*ln(e*x-d)*g^2-1/8/e^2/d^3*ln(e*x-d)*f*g-1/16/e/d^4*ln(e*x-d)*f^2+3/8/e^3/(e*x+d)^2*g^2-1/4/d/e^2/(e*x+d)^2*f*g-1/8/d^2/e/(e*x+d)^2*f^2-1/6/e^3*d/(e*x+d)^3*g^2+1/3/e^2/(e*x+d)^3*f*g-1/6/e/d/(e*x+d)^3*f^2+1/16/e^3/d^2*ln(e*x+d)*g^2+1/8/e^2/d^3*ln(e*x+d)*f*g+1/16/e/d^4*ln(e*x+d)*f^2-1/8/d/e^3/(e*x+d)*g^2-1/4/d^2/e^2/(e*x+d)*f*g-1/8/d^3/e/(e*x+d)*f^2","B"
556,1,312,129,0.012000," ","int((g*x+f)^2/(e*x+d)^4/(-e^2*x^2+d^2),x)","-\frac{d \,g^{2}}{8 \left(e x +d \right)^{4} e^{3}}-\frac{f^{2}}{8 \left(e x +d \right)^{4} d e}+\frac{f g}{4 \left(e x +d \right)^{4} e^{2}}-\frac{f g}{6 \left(e x +d \right)^{3} d \,e^{2}}-\frac{f^{2}}{12 \left(e x +d \right)^{3} d^{2} e}+\frac{g^{2}}{4 \left(e x +d \right)^{3} e^{3}}-\frac{g^{2}}{16 \left(e x +d \right)^{2} d \,e^{3}}-\frac{f g}{8 \left(e x +d \right)^{2} d^{2} e^{2}}-\frac{f^{2}}{16 \left(e x +d \right)^{2} d^{3} e}-\frac{g^{2}}{16 \left(e x +d \right) d^{2} e^{3}}-\frac{f g}{8 \left(e x +d \right) d^{3} e^{2}}-\frac{g^{2} \ln \left(e x -d \right)}{32 d^{3} e^{3}}+\frac{g^{2} \ln \left(e x +d \right)}{32 d^{3} e^{3}}-\frac{f^{2}}{16 \left(e x +d \right) d^{4} e}-\frac{f g \ln \left(e x -d \right)}{16 d^{4} e^{2}}+\frac{f g \ln \left(e x +d \right)}{16 d^{4} e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{32 d^{5} e}+\frac{f^{2} \ln \left(e x +d \right)}{32 d^{5} e}"," ",0,"-1/32/e^3/d^3*ln(e*x-d)*g^2-1/16/e^2/d^4*ln(e*x-d)*f*g-1/32/e/d^5*ln(e*x-d)*f^2+1/4/e^3/(e*x+d)^3*g^2-1/6/d/e^2/(e*x+d)^3*f*g-1/12/d^2/e/(e*x+d)^3*f^2-1/8/e^3*d/(e*x+d)^4*g^2+1/4/e^2/(e*x+d)^4*f*g-1/8/e/d/(e*x+d)^4*f^2+1/32/e^3/d^3*ln(e*x+d)*g^2+1/16/e^2/d^4*ln(e*x+d)*f*g+1/32/e/d^5*ln(e*x+d)*f^2-1/16/d^2/e^3/(e*x+d)*g^2-1/8/d^3/e^2/(e*x+d)*f*g-1/16/d^4/e/(e*x+d)*f^2-1/16/d/e^3/(e*x+d)^2*g^2-1/8/d^2/e^2/(e*x+d)^2*f*g-1/16/d^3/e/(e*x+d)^2*f^2","B"
557,1,286,208,0.012000," ","int((e*x+d)^7*(g*x+f)^2/(-e^2*x^2+d^2)^2,x)","\frac{e^{3} g^{2} x^{6}}{6}+\frac{7 d \,e^{2} g^{2} x^{5}}{5}+\frac{2 e^{3} f g \,x^{5}}{5}+\frac{23 d^{2} e \,g^{2} x^{4}}{4}+\frac{7 d \,e^{2} f g \,x^{4}}{2}+\frac{e^{3} f^{2} x^{4}}{4}+\frac{49 d^{3} g^{2} x^{3}}{3}+\frac{46 d^{2} e f g \,x^{3}}{3}+\frac{7 d \,e^{2} f^{2} x^{3}}{3}+\frac{40 d^{4} g^{2} x^{2}}{e}+49 d^{3} f g \,x^{2}+\frac{23 d^{2} e \,f^{2} x^{2}}{2}-\frac{32 d^{7} g^{2}}{\left(e x -d \right) e^{3}}-\frac{64 d^{6} f g}{\left(e x -d \right) e^{2}}+\frac{144 d^{6} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{32 d^{5} f^{2}}{\left(e x -d \right) e}+\frac{224 d^{5} f g \ln \left(e x -d \right)}{e^{2}}+\frac{112 d^{5} g^{2} x}{e^{2}}+\frac{80 d^{4} f^{2} \ln \left(e x -d \right)}{e}+\frac{160 d^{4} f g x}{e}+49 d^{3} f^{2} x"," ",0,"1/6*e^3*g^2*x^6+7/5*e^2*x^5*d*g^2+2/5*e^3*x^5*f*g+23/4*e*x^4*d^2*g^2+7/2*e^2*x^4*d*f*g+1/4*e^3*x^4*f^2+49/3*x^3*d^3*g^2+46/3*e*x^3*d^2*f*g+7/3*e^2*x^3*d*f^2+40/e*x^2*d^4*g^2+49*x^2*d^3*f*g+23/2*e*x^2*d^2*f^2+112/e^2*d^5*g^2*x+160/e*d^4*f*g*x+49*d^3*f^2*x+144*d^6/e^3*ln(e*x-d)*g^2+224*d^5/e^2*ln(e*x-d)*f*g+80*d^4/e*ln(e*x-d)*f^2-32*d^7/e^3/(e*x-d)*g^2-64*d^6/e^2/(e*x-d)*f*g-32*d^5/e/(e*x-d)*f^2","A"
558,1,245,171,0.010000," ","int((e*x+d)^6*(g*x+f)^2/(-e^2*x^2+d^2)^2,x)","\frac{e^{2} g^{2} x^{5}}{5}+\frac{3 d e \,g^{2} x^{4}}{2}+\frac{e^{2} f g \,x^{4}}{2}+\frac{17 d^{2} g^{2} x^{3}}{3}+4 d e f g \,x^{3}+\frac{e^{2} f^{2} x^{3}}{3}+\frac{16 d^{3} g^{2} x^{2}}{e}+17 d^{2} f g \,x^{2}+3 d e \,f^{2} x^{2}-\frac{16 d^{6} g^{2}}{\left(e x -d \right) e^{3}}-\frac{32 d^{5} f g}{\left(e x -d \right) e^{2}}+\frac{64 d^{5} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{16 d^{4} f^{2}}{\left(e x -d \right) e}+\frac{96 d^{4} f g \ln \left(e x -d \right)}{e^{2}}+\frac{48 d^{4} g^{2} x}{e^{2}}+\frac{32 d^{3} f^{2} \ln \left(e x -d \right)}{e}+\frac{64 d^{3} f g x}{e}+17 d^{2} f^{2} x"," ",0,"1/5*e^2*g^2*x^5+3/2*d*e*g^2*x^4+1/2*e^2*f*g*x^4+17/3*d^2*g^2*x^3+4*d*e*f*g*x^3+1/3*e^2*f^2*x^3+16*d^3/e*g^2*x^2+17*d^2*f*g*x^2+3*d*e*f^2*x^2+48*d^4/e^2*g^2*x+64*d^3/e*f*g*x+17*d^2*f^2*x+64*d^5/e^3*g^2*ln(e*x-d)+96*d^4/e^2*f*g*ln(e*x-d)+32*d^3/e*f^2*ln(e*x-d)-16*d^6/e^3/(e*x-d)*g^2-32*d^5/e^2/(e*x-d)*f*g-16*d^4/e/(e*x-d)*f^2","A"
559,1,204,140,0.010000," ","int((e*x+d)^5*(g*x+f)^2/(-e^2*x^2+d^2)^2,x)","\frac{e \,g^{2} x^{4}}{4}+\frac{5 d \,g^{2} x^{3}}{3}+\frac{2 e f g \,x^{3}}{3}+\frac{6 d^{2} g^{2} x^{2}}{e}+5 d f g \,x^{2}+\frac{e \,f^{2} x^{2}}{2}-\frac{8 d^{5} g^{2}}{\left(e x -d \right) e^{3}}-\frac{16 d^{4} f g}{\left(e x -d \right) e^{2}}+\frac{28 d^{4} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{8 d^{3} f^{2}}{\left(e x -d \right) e}+\frac{40 d^{3} f g \ln \left(e x -d \right)}{e^{2}}+\frac{20 d^{3} g^{2} x}{e^{2}}+\frac{12 d^{2} f^{2} \ln \left(e x -d \right)}{e}+\frac{24 d^{2} f g x}{e}+5 d \,f^{2} x"," ",0,"1/4*e*g^2*x^4+5/3*d*g^2*x^3+2/3*e*f*g*x^3+6*d^2/e*g^2*x^2+5*d*f*g*x^2+1/2*e*f^2*x^2+20*d^3/e^2*g^2*x+24*d^2/e*f*g*x+5*d*f^2*x+28*d^4/e^3*g^2*ln(e*x-d)+40*d^3/e^2*f*g*ln(e*x-d)+12*d^2/e*f^2*ln(e*x-d)-8*d^5/e^3/(e*x-d)*g^2-16*d^4/e^2/(e*x-d)*f*g-8*d^3/e/(e*x-d)*f^2","A"
560,1,167,105,0.010000," ","int((e*x+d)^4*(g*x+f)^2/(-e^2*x^2+d^2)^2,x)","\frac{g^{2} x^{3}}{3}+\frac{2 d \,g^{2} x^{2}}{e}+f g \,x^{2}-\frac{4 d^{4} g^{2}}{\left(e x -d \right) e^{3}}-\frac{8 d^{3} f g}{\left(e x -d \right) e^{2}}+\frac{12 d^{3} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{4 d^{2} f^{2}}{\left(e x -d \right) e}+\frac{16 d^{2} f g \ln \left(e x -d \right)}{e^{2}}+\frac{8 d^{2} g^{2} x}{e^{2}}+\frac{4 d \,f^{2} \ln \left(e x -d \right)}{e}+\frac{8 d f g x}{e}+f^{2} x"," ",0,"1/3*g^2*x^3+2*d/e*g^2*x^2+f*g*x^2+8*d^2/e^2*g^2*x+8*d/e*f*g*x+f^2*x+12*d^3/e^3*g^2*ln(e*x-d)+16*d^2/e^2*f*g*ln(e*x-d)+4*d/e*f^2*ln(e*x-d)-4*d^4/e^3/(e*x-d)*g^2-8*d^3/e^2/(e*x-d)*f*g-4*d^2/e/(e*x-d)*f^2","A"
561,1,138,76,0.007000," ","int((e*x+d)^3*(g*x+f)^2/(-e^2*x^2+d^2)^2,x)","\frac{g^{2} x^{2}}{2 e}-\frac{2 d^{3} g^{2}}{\left(e x -d \right) e^{3}}-\frac{4 d^{2} f g}{\left(e x -d \right) e^{2}}+\frac{5 d^{2} g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{2 d \,f^{2}}{\left(e x -d \right) e}+\frac{6 d f g \ln \left(e x -d \right)}{e^{2}}+\frac{3 d \,g^{2} x}{e^{2}}+\frac{f^{2} \ln \left(e x -d \right)}{e}+\frac{2 f g x}{e}"," ",0,"1/2/e*g^2*x^2+3*d/e^2*g^2*x+2/e*f*g*x+5*d^2/e^3*g^2*ln(e*x-d)+6*d/e^2*f*g*ln(e*x-d)+1/e*f^2*ln(e*x-d)-2*d^3/e^3/(e*x-d)*g^2-4*d^2/e^2/(e*x-d)*f*g-2*d/e/(e*x-d)*f^2","A"
562,1,96,50,0.007000," ","int((e*x+d)^2*(g*x+f)^2/(-e^2*x^2+d^2)^2,x)","-\frac{d^{2} g^{2}}{\left(e x -d \right) e^{3}}-\frac{2 d f g}{\left(e x -d \right) e^{2}}+\frac{2 d \,g^{2} \ln \left(e x -d \right)}{e^{3}}-\frac{f^{2}}{\left(e x -d \right) e}+\frac{2 f g \ln \left(e x -d \right)}{e^{2}}+\frac{g^{2} x}{e^{2}}"," ",0,"1/e^2*g^2*x+2*d/e^3*g^2*ln(e*x-d)+2/e^2*f*g*ln(e*x-d)-1/e^3/(e*x-d)*d^2*g^2-2/e^2/(e*x-d)*d*f*g-1/e/(e*x-d)*f^2","A"
563,1,156,80,0.009000," ","int((e*x+d)*(g*x+f)^2/(-e^2*x^2+d^2)^2,x)","-\frac{d \,g^{2}}{2 \left(e x -d \right) e^{3}}-\frac{f^{2}}{2 \left(e x -d \right) d e}+\frac{f g \ln \left(e x -d \right)}{2 d \,e^{2}}-\frac{f g \ln \left(e x +d \right)}{2 d \,e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{4 d^{2} e}+\frac{f^{2} \ln \left(e x +d \right)}{4 d^{2} e}-\frac{f g}{\left(e x -d \right) e^{2}}+\frac{3 g^{2} \ln \left(e x -d \right)}{4 e^{3}}+\frac{g^{2} \ln \left(e x +d \right)}{4 e^{3}}"," ",0,"-1/2/e^3*d/(e*x-d)*g^2-1/e^2/(e*x-d)*f*g-1/2/e/d/(e*x-d)*f^2+3/4/e^3*g^2*ln(e*x-d)+1/2/d/e^2*f*g*ln(e*x-d)-1/4/d^2/e*f^2*ln(e*x-d)+1/4/e^3*g^2*ln(e*x+d)-1/2/d/e^2*f*g*ln(e*x+d)+1/4/d^2/e*f^2*ln(e*x+d)","A"
564,1,180,70,0.012000," ","int((g*x+f)^2/(-e^2*x^2+d^2)^2,x)","-\frac{f g}{2 \left(e x -d \right) d \,e^{2}}+\frac{f g}{2 \left(e x +d \right) d \,e^{2}}+\frac{g^{2} \ln \left(e x -d \right)}{4 d \,e^{3}}-\frac{g^{2} \ln \left(e x +d \right)}{4 d \,e^{3}}-\frac{f^{2}}{4 \left(e x -d \right) d^{2} e}-\frac{f^{2}}{4 \left(e x +d \right) d^{2} e}-\frac{f^{2} \ln \left(e x -d \right)}{4 d^{3} e}+\frac{f^{2} \ln \left(e x +d \right)}{4 d^{3} e}-\frac{g^{2}}{4 \left(e x -d \right) e^{3}}-\frac{g^{2}}{4 \left(e x +d \right) e^{3}}"," ",0,"1/4/d/e^3*g^2*ln(e*x-d)-1/4/d^3/e*f^2*ln(e*x-d)-1/4/e^3/(e*x-d)*g^2-1/2/e^2/d/(e*x-d)*f*g-1/4/e/d^2/(e*x-d)*f^2-1/4/d/e^3*g^2*ln(e*x+d)+1/4/d^3/e*f^2*ln(e*x+d)-1/4/(e*x+d)/e^3*g^2+1/2/(e*x+d)/d/e^2*f*g-1/4/(e*x+d)/d^2/e*f^2","B"
565,1,253,113,0.013000," ","int((g*x+f)^2/(e*x+d)/(-e^2*x^2+d^2)^2,x)","\frac{f g}{4 \left(e x +d \right)^{2} d \,e^{2}}-\frac{f^{2}}{8 \left(e x +d \right)^{2} d^{2} e}-\frac{g^{2}}{8 \left(e x +d \right)^{2} e^{3}}-\frac{g^{2}}{8 \left(e x -d \right) d \,e^{3}}+\frac{g^{2}}{4 \left(e x +d \right) d \,e^{3}}-\frac{f g}{4 \left(e x -d \right) d^{2} e^{2}}+\frac{g^{2} \ln \left(e x -d \right)}{16 d^{2} e^{3}}-\frac{g^{2} \ln \left(e x +d \right)}{16 d^{2} e^{3}}-\frac{f^{2}}{8 \left(e x -d \right) d^{3} e}-\frac{f^{2}}{4 \left(e x +d \right) d^{3} e}-\frac{f g \ln \left(e x -d \right)}{8 d^{3} e^{2}}+\frac{f g \ln \left(e x +d \right)}{8 d^{3} e^{2}}-\frac{3 f^{2} \ln \left(e x -d \right)}{16 d^{4} e}+\frac{3 f^{2} \ln \left(e x +d \right)}{16 d^{4} e}"," ",0,"1/16/d^2/e^3*g^2*ln(e*x-d)-1/8/d^3/e^2*f*g*ln(e*x-d)-3/16/d^4/e*f^2*ln(e*x-d)-1/8/e^3/d/(e*x-d)*g^2-1/4/e^2/d^2/(e*x-d)*f*g-1/8/e/d^3/(e*x-d)*f^2+1/4/(e*x+d)/d/e^3*g^2-1/4/(e*x+d)/d^3/e*f^2-1/16/d^2/e^3*g^2*ln(e*x+d)+1/8/d^3/e^2*f*g*ln(e*x+d)+3/16/d^4/e*f^2*ln(e*x+d)-1/8/(e*x+d)^2/e^3*g^2+1/4/(e*x+d)^2/d/e^2*f*g-1/8/(e*x+d)^2/d^2/e*f^2","B"
566,1,270,136,0.015000," ","int((g*x+f)^2/(e*x+d)^2/(-e^2*x^2+d^2)^2,x)","\frac{f g}{6 \left(e x +d \right)^{3} d \,e^{2}}-\frac{f^{2}}{12 \left(e x +d \right)^{3} d^{2} e}-\frac{g^{2}}{12 \left(e x +d \right)^{3} e^{3}}+\frac{g^{2}}{8 \left(e x +d \right)^{2} d \,e^{3}}-\frac{f^{2}}{8 \left(e x +d \right)^{2} d^{3} e}-\frac{g^{2}}{16 \left(e x -d \right) d^{2} e^{3}}+\frac{g^{2}}{16 \left(e x +d \right) d^{2} e^{3}}-\frac{f g}{8 \left(e x -d \right) d^{3} e^{2}}-\frac{f g}{8 \left(e x +d \right) d^{3} e^{2}}-\frac{f^{2}}{16 \left(e x -d \right) d^{4} e}-\frac{3 f^{2}}{16 \left(e x +d \right) d^{4} e}-\frac{f g \ln \left(e x -d \right)}{8 d^{4} e^{2}}+\frac{f g \ln \left(e x +d \right)}{8 d^{4} e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{8 d^{5} e}+\frac{f^{2} \ln \left(e x +d \right)}{8 d^{5} e}"," ",0,"-1/16/e^3/d^2/(e*x-d)*g^2-1/8/e^2/d^3/(e*x-d)*f*g-1/16/e/d^4/(e*x-d)*f^2-1/8/d^4/e^2*f*g*ln(e*x-d)-1/8/d^5/e*f^2*ln(e*x-d)+1/8/(e*x+d)^2/d/e^3*g^2-1/8/(e*x+d)^2/d^3/e*f^2+1/16/(e*x+d)/d^2/e^3*g^2-1/8/(e*x+d)/d^3/e^2*f*g-3/16/(e*x+d)/d^4/e*f^2-1/12/(e*x+d)^3/e^3*g^2+1/6/(e*x+d)^3/d/e^2*f*g-1/12/(e*x+d)^3/d^2/e*f^2+1/8/d^4/e^2*f*g*ln(e*x+d)+1/8/d^5/e*f^2*ln(e*x+d)","A"
567,1,341,166,0.016000," ","int((g*x+f)^2/(e*x+d)^3/(-e^2*x^2+d^2)^2,x)","\frac{f g}{8 \left(e x +d \right)^{4} d \,e^{2}}-\frac{f^{2}}{16 \left(e x +d \right)^{4} d^{2} e}-\frac{g^{2}}{16 \left(e x +d \right)^{4} e^{3}}+\frac{g^{2}}{12 \left(e x +d \right)^{3} d \,e^{3}}-\frac{f^{2}}{12 \left(e x +d \right)^{3} d^{3} e}+\frac{g^{2}}{32 \left(e x +d \right)^{2} d^{2} e^{3}}-\frac{f g}{16 \left(e x +d \right)^{2} d^{3} e^{2}}-\frac{3 f^{2}}{32 \left(e x +d \right)^{2} d^{4} e}-\frac{g^{2}}{32 \left(e x -d \right) d^{3} e^{3}}-\frac{f g}{16 \left(e x -d \right) d^{4} e^{2}}-\frac{f g}{8 \left(e x +d \right) d^{4} e^{2}}-\frac{g^{2} \ln \left(e x -d \right)}{64 d^{4} e^{3}}+\frac{g^{2} \ln \left(e x +d \right)}{64 d^{4} e^{3}}-\frac{f^{2}}{32 \left(e x -d \right) d^{5} e}-\frac{f^{2}}{8 \left(e x +d \right) d^{5} e}-\frac{3 f g \ln \left(e x -d \right)}{32 d^{5} e^{2}}+\frac{3 f g \ln \left(e x +d \right)}{32 d^{5} e^{2}}-\frac{5 f^{2} \ln \left(e x -d \right)}{64 d^{6} e}+\frac{5 f^{2} \ln \left(e x +d \right)}{64 d^{6} e}"," ",0,"-1/64/e^3/d^4*ln(e*x-d)*g^2-3/32/e^2/d^5*ln(e*x-d)*f*g-5/64/e/d^6*ln(e*x-d)*f^2-1/32/e^3/d^3/(e*x-d)*g^2-1/16/e^2/d^4/(e*x-d)*f*g-1/32/e/d^5/(e*x-d)*f^2+1/64/e^3/d^4*ln(e*x+d)*g^2+3/32/e^2/d^5*ln(e*x+d)*f*g+5/64/e/d^6*ln(e*x+d)*f^2+1/12/e^3/d/(e*x+d)^3*g^2-1/12/e/d^3/(e*x+d)^3*f^2+1/32/e^3/d^2/(e*x+d)^2*g^2-1/16/e^2/d^3/(e*x+d)^2*f*g-3/32/e/d^4/(e*x+d)^2*f^2-1/16/e^3/(e*x+d)^4*g^2+1/8/e^2/d/(e*x+d)^4*f*g-1/16/e/d^2/(e*x+d)^4*f^2-1/8/e^2*f/d^4/(e*x+d)*g-1/8/e*f^2/d^5/(e*x+d)","B"
568,1,394,196,0.018000," ","int((g*x+f)^2/(e*x+d)^4/(-e^2*x^2+d^2)^2,x)","\frac{f g}{10 \left(e x +d \right)^{5} d \,e^{2}}-\frac{f^{2}}{20 \left(e x +d \right)^{5} d^{2} e}-\frac{g^{2}}{20 \left(e x +d \right)^{5} e^{3}}+\frac{g^{2}}{16 \left(e x +d \right)^{4} d \,e^{3}}-\frac{f^{2}}{16 \left(e x +d \right)^{4} d^{3} e}+\frac{g^{2}}{48 \left(e x +d \right)^{3} d^{2} e^{3}}-\frac{f g}{24 \left(e x +d \right)^{3} d^{3} e^{2}}-\frac{f^{2}}{16 \left(e x +d \right)^{3} d^{4} e}-\frac{f g}{16 \left(e x +d \right)^{2} d^{4} e^{2}}-\frac{f^{2}}{16 \left(e x +d \right)^{2} d^{5} e}-\frac{g^{2}}{64 \left(e x -d \right) d^{4} e^{3}}-\frac{g^{2}}{64 \left(e x +d \right) d^{4} e^{3}}-\frac{f g}{32 \left(e x -d \right) d^{5} e^{2}}-\frac{3 f g}{32 \left(e x +d \right) d^{5} e^{2}}-\frac{g^{2} \ln \left(e x -d \right)}{64 d^{5} e^{3}}+\frac{g^{2} \ln \left(e x +d \right)}{64 d^{5} e^{3}}-\frac{f^{2}}{64 \left(e x -d \right) d^{6} e}-\frac{5 f^{2}}{64 \left(e x +d \right) d^{6} e}-\frac{f g \ln \left(e x -d \right)}{16 d^{6} e^{2}}+\frac{f g \ln \left(e x +d \right)}{16 d^{6} e^{2}}-\frac{3 f^{2} \ln \left(e x -d \right)}{64 d^{7} e}+\frac{3 f^{2} \ln \left(e x +d \right)}{64 d^{7} e}"," ",0,"-1/64/e^3/d^5*ln(e*x-d)*g^2-1/16/e^2/d^6*ln(e*x-d)*f*g-3/64/e/d^7*ln(e*x-d)*f^2-1/64/e^3/d^4/(e*x-d)*g^2-1/32/e^2/d^5/(e*x-d)*f*g-1/64/e/d^6/(e*x-d)*f^2+1/64/e^3/d^5*ln(e*x+d)*g^2+1/16/e^2/d^6*ln(e*x+d)*f*g+3/64/e/d^7*ln(e*x+d)*f^2-1/64/e^3/d^4/(e*x+d)*g^2-3/32/e^2/d^5/(e*x+d)*f*g-5/64/e/d^6/(e*x+d)*f^2+1/16/e^3/d/(e*x+d)^4*g^2-1/16/e/d^3/(e*x+d)^4*f^2+1/48/e^3/d^2/(e*x+d)^3*g^2-1/24/e^2/d^3/(e*x+d)^3*f*g-1/16/e/d^4/(e*x+d)^3*f^2-1/20/e^3/(e*x+d)^5*g^2+1/10/e^2/d/(e*x+d)^5*f*g-1/20/e/d^2/(e*x+d)^5*f^2-1/16/e^2*f/d^4/(e*x+d)^2*g-1/16/e*f^2/d^5/(e*x+d)^2","B"
569,1,263,173,0.010000," ","int((e*x+d)^7*(g*x+f)^2/(-e^2*x^2+d^2)^3,x)","-\frac{e \,g^{2} x^{4}}{4}-\frac{7 d \,g^{2} x^{3}}{3}-\frac{2 e f g \,x^{3}}{3}+\frac{8 d^{6} g^{2}}{\left(e x -d \right)^{2} e^{3}}+\frac{16 d^{5} f g}{\left(e x -d \right)^{2} e^{2}}+\frac{8 d^{4} f^{2}}{\left(e x -d \right)^{2} e}-\frac{12 d^{2} g^{2} x^{2}}{e}-7 d f g \,x^{2}-\frac{e \,f^{2} x^{2}}{2}+\frac{64 d^{5} g^{2}}{\left(e x -d \right) e^{3}}+\frac{96 d^{4} f g}{\left(e x -d \right) e^{2}}-\frac{104 d^{4} g^{2} \ln \left(e x -d \right)}{e^{3}}+\frac{32 d^{3} f^{2}}{\left(e x -d \right) e}-\frac{112 d^{3} f g \ln \left(e x -d \right)}{e^{2}}-\frac{56 d^{3} g^{2} x}{e^{2}}-\frac{24 d^{2} f^{2} \ln \left(e x -d \right)}{e}-\frac{48 d^{2} f g x}{e}-7 d \,f^{2} x"," ",0,"-1/4*e*g^2*x^4-7/3*d*g^2*x^3-2/3*e*f*g*x^3-12*d^2/e*g^2*x^2-7*d*f*g*x^2-1/2*e*f^2*x^2-56*d^3/e^2*g^2*x-48*d^2/e*f*g*x-7*d*f^2*x-104*d^4/e^3*g^2*ln(e*x-d)-112*d^3/e^2*f*g*ln(e*x-d)-24*d^2/e*f^2*ln(e*x-d)+8*d^6/e^3/(e*x-d)^2*g^2+16*d^5/e^2/(e*x-d)^2*f*g+8*d^4/e/(e*x-d)^2*f^2+64/(e*x-d)*d^5/e^3*g^2+96/(e*x-d)*d^4/e^2*f*g+32/(e*x-d)*d^3/e*f^2","A"
570,1,228,147,0.009000," ","int((e*x+d)^6*(g*x+f)^2/(-e^2*x^2+d^2)^3,x)","-\frac{g^{2} x^{3}}{3}+\frac{4 d^{5} g^{2}}{\left(e x -d \right)^{2} e^{3}}+\frac{8 d^{4} f g}{\left(e x -d \right)^{2} e^{2}}+\frac{4 d^{3} f^{2}}{\left(e x -d \right)^{2} e}-\frac{3 d \,g^{2} x^{2}}{e}-f g \,x^{2}+\frac{28 d^{4} g^{2}}{\left(e x -d \right) e^{3}}+\frac{40 d^{3} f g}{\left(e x -d \right) e^{2}}-\frac{38 d^{3} g^{2} \ln \left(e x -d \right)}{e^{3}}+\frac{12 d^{2} f^{2}}{\left(e x -d \right) e}-\frac{36 d^{2} f g \ln \left(e x -d \right)}{e^{2}}-\frac{18 d^{2} g^{2} x}{e^{2}}-\frac{6 d \,f^{2} \ln \left(e x -d \right)}{e}-\frac{12 d f g x}{e}-f^{2} x"," ",0,"-1/3*g^2*x^3-3*d/e*g^2*x^2-f*g*x^2-18*d^2/e^2*g^2*x-12*d/e*f*g*x-f^2*x-38*d^3/e^3*g^2*ln(e*x-d)-36*d^2/e^2*f*g*ln(e*x-d)-6*d/e*f^2*ln(e*x-d)+4*d^5/e^3/(e*x-d)^2*g^2+8*d^4/e^2/(e*x-d)^2*f*g+4*d^3/e/(e*x-d)^2*f^2+28/(e*x-d)*d^4/e^3*g^2+40/(e*x-d)*d^3/e^2*f*g+12/(e*x-d)*d^2/e*f^2","A"
571,1,198,116,0.009000," ","int((e*x+d)^5*(g*x+f)^2/(-e^2*x^2+d^2)^3,x)","\frac{2 d^{4} g^{2}}{\left(e x -d \right)^{2} e^{3}}+\frac{4 d^{3} f g}{\left(e x -d \right)^{2} e^{2}}+\frac{2 d^{2} f^{2}}{\left(e x -d \right)^{2} e}-\frac{g^{2} x^{2}}{2 e}+\frac{12 d^{3} g^{2}}{\left(e x -d \right) e^{3}}+\frac{16 d^{2} f g}{\left(e x -d \right) e^{2}}-\frac{13 d^{2} g^{2} \ln \left(e x -d \right)}{e^{3}}+\frac{4 d \,f^{2}}{\left(e x -d \right) e}-\frac{10 d f g \ln \left(e x -d \right)}{e^{2}}-\frac{5 d \,g^{2} x}{e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{e}-\frac{2 f g x}{e}"," ",0,"-1/2/e*g^2*x^2-5*d/e^2*g^2*x-2/e*f*g*x-13*d^2/e^3*g^2*ln(e*x-d)-10*d/e^2*f*g*ln(e*x-d)-1/e*f^2*ln(e*x-d)+2*d^4/e^3/(e*x-d)^2*g^2+4*d^3/e^2/(e*x-d)^2*f*g+2*d^2/e/(e*x-d)^2*f^2+12/(e*x-d)*d^3/e^3*g^2+16/(e*x-d)*d^2/e^2*f*g+4/(e*x-d)*d/e*f^2","A"
572,1,151,81,0.009000," ","int((e*x+d)^4*(g*x+f)^2/(-e^2*x^2+d^2)^3,x)","\frac{d^{3} g^{2}}{\left(e x -d \right)^{2} e^{3}}+\frac{2 d^{2} f g}{\left(e x -d \right)^{2} e^{2}}+\frac{d \,f^{2}}{\left(e x -d \right)^{2} e}+\frac{5 d^{2} g^{2}}{\left(e x -d \right) e^{3}}+\frac{6 d f g}{\left(e x -d \right) e^{2}}-\frac{4 d \,g^{2} \ln \left(e x -d \right)}{e^{3}}+\frac{f^{2}}{\left(e x -d \right) e}-\frac{2 f g \ln \left(e x -d \right)}{e^{2}}-\frac{g^{2} x}{e^{2}}"," ",0,"-1/e^2*g^2*x-4*d/e^3*g^2*ln(e*x-d)-2/e^2*f*g*ln(e*x-d)+d^3/e^3/(e*x-d)^2*g^2+2*d^2/e^2/(e*x-d)^2*f*g+d/e/(e*x-d)^2*f^2+5/(e*x-d)*d^2/e^3*g^2+6/(e*x-d)*d/e^2*f*g+1/(e*x-d)/e*f^2","A"
573,1,105,59,0.007000," ","int((e*x+d)^3*(g*x+f)^2/(-e^2*x^2+d^2)^3,x)","\frac{d^{2} g^{2}}{2 \left(e x -d \right)^{2} e^{3}}+\frac{d f g}{\left(e x -d \right)^{2} e^{2}}+\frac{f^{2}}{2 \left(e x -d \right)^{2} e}+\frac{2 d \,g^{2}}{\left(e x -d \right) e^{3}}+\frac{2 f g}{\left(e x -d \right) e^{2}}-\frac{g^{2} \ln \left(e x -d \right)}{e^{3}}"," ",0,"-1/e^3*g^2*ln(e*x-d)+1/2/e^3/(e*x-d)^2*d^2*g^2+1/e^2/(e*x-d)^2*d*f*g+1/2/e/(e*x-d)^2*f^2+2/(e*x-d)*d/e^3*g^2+2/(e*x-d)/e^2*f*g","A"
574,1,218,82,0.011000," ","int((e*x+d)^2*(g*x+f)^2/(-e^2*x^2+d^2)^3,x)","\frac{d \,g^{2}}{4 \left(e x -d \right)^{2} e^{3}}+\frac{f^{2}}{4 \left(e x -d \right)^{2} d e}+\frac{f g}{2 \left(e x -d \right)^{2} e^{2}}+\frac{f g}{2 \left(e x -d \right) d \,e^{2}}-\frac{g^{2} \ln \left(e x -d \right)}{8 d \,e^{3}}+\frac{g^{2} \ln \left(e x +d \right)}{8 d \,e^{3}}-\frac{f^{2}}{4 \left(e x -d \right) d^{2} e}+\frac{f g \ln \left(e x -d \right)}{4 d^{2} e^{2}}-\frac{f g \ln \left(e x +d \right)}{4 d^{2} e^{2}}-\frac{f^{2} \ln \left(e x -d \right)}{8 d^{3} e}+\frac{f^{2} \ln \left(e x +d \right)}{8 d^{3} e}+\frac{3 g^{2}}{4 \left(e x -d \right) e^{3}}"," ",0,"3/4/(e*x-d)/e^3*g^2+1/2/(e*x-d)/d/e^2*f*g-1/4/(e*x-d)/d^2/e*f^2+1/4/e^3*d/(e*x-d)^2*g^2+1/2/e^2/(e*x-d)^2*f*g+1/4/e/d/(e*x-d)^2*f^2-1/8/d/e^3*g^2*ln(e*x-d)+1/4/d^2/e^2*f*g*ln(e*x-d)-1/8/d^3/e*f^2*ln(e*x-d)+1/8/d/e^3*g^2*ln(e*x+d)-1/4/d^2/e^2*f*g*ln(e*x+d)+1/8/d^3/e*f^2*ln(e*x+d)","B"
575,1,257,114,0.030000," ","int((e*x+d)*(g*x+f)^2/(-e^2*x^2+d^2)^3,x)","\frac{f g}{4 \left(e x -d \right)^{2} d \,e^{2}}+\frac{f^{2}}{8 \left(e x -d \right)^{2} d^{2} e}+\frac{g^{2}}{8 \left(e x -d \right)^{2} e^{3}}+\frac{g^{2}}{4 \left(e x -d \right) d \,e^{3}}-\frac{g^{2}}{8 \left(e x +d \right) d \,e^{3}}+\frac{f g}{4 \left(e x +d \right) d^{2} e^{2}}+\frac{g^{2} \ln \left(e x -d \right)}{16 d^{2} e^{3}}-\frac{g^{2} \ln \left(e x +d \right)}{16 d^{2} e^{3}}-\frac{f^{2}}{4 \left(e x -d \right) d^{3} e}-\frac{f^{2}}{8 \left(e x +d \right) d^{3} e}+\frac{f g \ln \left(e x -d \right)}{8 d^{3} e^{2}}-\frac{f g \ln \left(e x +d \right)}{8 d^{3} e^{2}}-\frac{3 f^{2} \ln \left(e x -d \right)}{16 d^{4} e}+\frac{3 f^{2} \ln \left(e x +d \right)}{16 d^{4} e}"," ",0,"1/4/(e*x-d)/d/e^3*g^2-1/4/(e*x-d)/d^3/e*f^2+1/8/e^3/(e*x-d)^2*g^2+1/4/e^2/d/(e*x-d)^2*f*g+1/8/e/d^2/(e*x-d)^2*f^2+1/16/d^2/e^3*g^2*ln(e*x-d)+1/8/d^3/e^2*f*g*ln(e*x-d)-3/16/d^4/e*f^2*ln(e*x-d)-1/16/d^2/e^3*g^2*ln(e*x+d)-1/8/d^3/e^2*f*g*ln(e*x+d)+3/16/d^4/e*f^2*ln(e*x+d)-1/8/(e*x+d)/d/e^3*g^2+1/4/(e*x+d)/d^2/e^2*f*g-1/8/(e*x+d)/d^3/e*f^2","B"
576,1,298,121,0.015000," ","int((g*x+f)^2/(-e^2*x^2+d^2)^3,x)","\frac{g^{2}}{16 \left(e x -d \right)^{2} d \,e^{3}}-\frac{g^{2}}{16 \left(e x +d \right)^{2} d \,e^{3}}+\frac{f g}{8 \left(e x -d \right)^{2} d^{2} e^{2}}+\frac{f g}{8 \left(e x +d \right)^{2} d^{2} e^{2}}+\frac{f^{2}}{16 \left(e x -d \right)^{2} d^{3} e}-\frac{f^{2}}{16 \left(e x +d \right)^{2} d^{3} e}+\frac{g^{2}}{16 \left(e x -d \right) d^{2} e^{3}}+\frac{g^{2}}{16 \left(e x +d \right) d^{2} e^{3}}-\frac{f g}{8 \left(e x -d \right) d^{3} e^{2}}+\frac{f g}{8 \left(e x +d \right) d^{3} e^{2}}+\frac{g^{2} \ln \left(e x -d \right)}{16 d^{3} e^{3}}-\frac{g^{2} \ln \left(e x +d \right)}{16 d^{3} e^{3}}-\frac{3 f^{2}}{16 \left(e x -d \right) d^{4} e}-\frac{3 f^{2}}{16 \left(e x +d \right) d^{4} e}-\frac{3 f^{2} \ln \left(e x -d \right)}{16 d^{5} e}+\frac{3 f^{2} \ln \left(e x +d \right)}{16 d^{5} e}"," ",0,"1/16/d^3/e^3*g^2*ln(e*x-d)-3/16/d^5/e*f^2*ln(e*x-d)+1/16/e^3/d/(e*x-d)^2*g^2+1/8/e^2/d^2/(e*x-d)^2*f*g+1/16/e/d^3/(e*x-d)^2*f^2+1/16/(e*x-d)/d^2/e^3*g^2-1/8/(e*x-d)/d^3/e^2*f*g-3/16/(e*x-d)/d^4/e*f^2-1/16/d^3/e^3*g^2*ln(e*x+d)+3/16/d^5/e*f^2*ln(e*x+d)+1/16/(e*x+d)/d^2/e^3*g^2+1/8/(e*x+d)/d^3/e^2*f*g-3/16/(e*x+d)/d^4/e*f^2-1/16/(e*x+d)^2/d/e^3*g^2+1/8/(e*x+d)^2/d^2/e^2*f*g-1/16/(e*x+d)^2/d^3/e*f^2","B"
577,1,348,175,0.015000," ","int((g*x+f)^2/(e*x+d)/(-e^2*x^2+d^2)^3,x)","-\frac{g^{2}}{24 \left(e x +d \right)^{3} d \,e^{3}}+\frac{f g}{12 \left(e x +d \right)^{3} d^{2} e^{2}}-\frac{f^{2}}{24 \left(e x +d \right)^{3} d^{3} e}+\frac{g^{2}}{32 \left(e x -d \right)^{2} d^{2} e^{3}}+\frac{g^{2}}{32 \left(e x +d \right)^{2} d^{2} e^{3}}+\frac{f g}{16 \left(e x -d \right)^{2} d^{3} e^{2}}+\frac{f g}{16 \left(e x +d \right)^{2} d^{3} e^{2}}+\frac{f^{2}}{32 \left(e x -d \right)^{2} d^{4} e}-\frac{3 f^{2}}{32 \left(e x +d \right)^{2} d^{4} e}+\frac{g^{2}}{16 \left(e x +d \right) d^{3} e^{3}}-\frac{f g}{8 \left(e x -d \right) d^{4} e^{2}}+\frac{g^{2} \ln \left(e x -d \right)}{32 d^{4} e^{3}}-\frac{g^{2} \ln \left(e x +d \right)}{32 d^{4} e^{3}}-\frac{f^{2}}{8 \left(e x -d \right) d^{5} e}-\frac{3 f^{2}}{16 \left(e x +d \right) d^{5} e}-\frac{f g \ln \left(e x -d \right)}{16 d^{5} e^{2}}+\frac{f g \ln \left(e x +d \right)}{16 d^{5} e^{2}}-\frac{5 f^{2} \ln \left(e x -d \right)}{32 d^{6} e}+\frac{5 f^{2} \ln \left(e x +d \right)}{32 d^{6} e}"," ",0,"1/32/e^3/d^2/(e*x-d)^2*g^2+1/16/e^2/d^3/(e*x-d)^2*f*g+1/32/e/d^4/(e*x-d)^2*f^2+1/32/d^4/e^3*g^2*ln(e*x-d)-1/16/d^5/e^2*f*g*ln(e*x-d)-5/32/d^6/e*f^2*ln(e*x-d)-1/8/(e*x-d)/d^4/e^2*f*g-1/8/(e*x-d)/d^5/e*f^2+1/16/e^3/d^3/(e*x+d)*g^2-3/16/(e*x+d)/d^5/e*f^2+1/32/(e*x+d)^2/d^2/e^3*g^2+1/16/(e*x+d)^2/d^3/e^2*f*g-3/32/(e*x+d)^2/d^4/e*f^2-1/32/d^4/e^3*g^2*ln(e*x+d)+1/16/d^5/e^2*f*g*ln(e*x+d)+5/32/d^6/e*f^2*ln(e*x+d)-1/24/(e*x+d)^3/d/e^3*g^2+1/12/e^2/d^2/(e*x+d)^3*f*g-1/24/(e*x+d)^3/d^3/e*f^2","A"
578,1,421,219,0.017000," ","int((g*x+f)^2/(e*x+d)^2/(-e^2*x^2+d^2)^3,x)","-\frac{g^{2}}{32 \left(e x +d \right)^{4} d \,e^{3}}+\frac{f g}{16 \left(e x +d \right)^{4} d^{2} e^{2}}-\frac{f^{2}}{32 \left(e x +d \right)^{4} d^{3} e}+\frac{g^{2}}{48 \left(e x +d \right)^{3} d^{2} e^{3}}+\frac{f g}{24 \left(e x +d \right)^{3} d^{3} e^{2}}-\frac{f^{2}}{16 \left(e x +d \right)^{3} d^{4} e}+\frac{g^{2}}{64 \left(e x -d \right)^{2} d^{3} e^{3}}+\frac{g^{2}}{32 \left(e x +d \right)^{2} d^{3} e^{3}}+\frac{f g}{32 \left(e x -d \right)^{2} d^{4} e^{2}}+\frac{f^{2}}{64 \left(e x -d \right)^{2} d^{5} e}-\frac{3 f^{2}}{32 \left(e x +d \right)^{2} d^{5} e}-\frac{g^{2}}{64 \left(e x -d \right) d^{4} e^{3}}+\frac{g^{2}}{32 \left(e x +d \right) d^{4} e^{3}}-\frac{3 f g}{32 \left(e x -d \right) d^{5} e^{2}}-\frac{f g}{16 \left(e x +d \right) d^{5} e^{2}}+\frac{g^{2} \ln \left(e x -d \right)}{128 d^{5} e^{3}}-\frac{g^{2} \ln \left(e x +d \right)}{128 d^{5} e^{3}}-\frac{5 f^{2}}{64 \left(e x -d \right) d^{6} e}-\frac{5 f^{2}}{32 \left(e x +d \right) d^{6} e}-\frac{5 f g \ln \left(e x -d \right)}{64 d^{6} e^{2}}+\frac{5 f g \ln \left(e x +d \right)}{64 d^{6} e^{2}}-\frac{15 f^{2} \ln \left(e x -d \right)}{128 d^{7} e}+\frac{15 f^{2} \ln \left(e x +d \right)}{128 d^{7} e}"," ",0,"-1/64/(e*x-d)/d^4/e^3*g^2-3/32/(e*x-d)/d^5/e^2*f*g-5/64/(e*x-d)/d^6/e*f^2+1/64/e^3/d^3/(e*x-d)^2*g^2+1/32/e^2/d^4/(e*x-d)^2*f*g+1/64/e/d^5/(e*x-d)^2*f^2+1/128/d^5/e^3*g^2*ln(e*x-d)-5/64/d^6/e^2*f*g*ln(e*x-d)-15/128/d^7/e*f^2*ln(e*x-d)+1/32/e^3/d^3/(e*x+d)^2*g^2-3/32/(e*x+d)^2/d^5/e*f^2+1/48/(e*x+d)^3/d^2/e^3*g^2+1/24/(e*x+d)^3/d^3/e^2*f*g-1/16/(e*x+d)^3/d^4/e*f^2+1/32/(e*x+d)/d^4/e^3*g^2-1/16/(e*x+d)/d^5/e^2*f*g-5/32/(e*x+d)/d^6/e*f^2-1/128/d^5/e^3*g^2*ln(e*x+d)+5/64/d^6/e^2*f*g*ln(e*x+d)+15/128/d^7/e*f^2*ln(e*x+d)-1/32/(e*x+d)^4/d/e^3*g^2+1/16/e^2/d^2/(e*x+d)^4*f*g-1/32/(e*x+d)^4/d^3/e*f^2","A"
579,1,1308,247,0.059000," ","int((e*x+d)^3*(g*x+f)^5/(-e^2*x^2+d^2)^(7/2),x)","-\frac{e \,g^{5} x^{7}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{3 d \,g^{5} x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{5 e f \,g^{4} x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{13 d^{2} g^{5} x^{5}}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{3 d f \,g^{4} x^{5}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{2 e \,f^{2} g^{3} x^{5}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{19 d^{3} g^{5} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{45 d^{2} f \,g^{4} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{30 d \,f^{2} g^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{10 e \,f^{3} g^{2} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{5 d^{3} f \,g^{4} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{15 d^{2} f^{2} g^{3} x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{15 d \,f^{3} g^{2} x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{5 e \,f^{4} g \,x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{76 d^{5} g^{5} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{60 d^{4} f \,g^{4} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{110 d^{3} f^{2} g^{3} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{10 d^{2} f^{3} g^{2} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{5 d \,f^{4} g \,x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{e \,f^{5} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{3 d^{5} f \,g^{4} x}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{9 d^{4} f^{2} g^{3} x}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{7 d^{3} f^{3} g^{2} x}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{3 d^{2} f^{4} g x}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}-\frac{13 d^{2} g^{5} x^{3}}{6 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}-\frac{5 d f \,g^{4} x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}+\frac{4 d \,f^{5} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{10 f^{2} g^{3} x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}+\frac{152 d^{7} g^{5}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{6}}+\frac{24 d^{6} f \,g^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}+\frac{44 d^{5} f^{2} g^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}+\frac{4 d^{4} f^{3} g^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{d^{3} f^{4} g}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{7 d^{2} f^{5}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{d^{3} f \,g^{4} x}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}+\frac{3 d^{2} f^{2} g^{3} x}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}+\frac{7 d \,f^{3} g^{2} x}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}+\frac{f^{5} x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d}-\frac{f^{4} g x}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}+\frac{13 d^{2} g^{5} x}{2 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{5}}-\frac{13 d^{2} g^{5} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{2 \sqrt{e^{2}}\, e^{5}}+\frac{16 d f \,g^{4} x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}-\frac{15 d f \,g^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}+\frac{14 f^{3} g^{2} x}{3 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{2}}-\frac{f^{4} g x}{\sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e}+\frac{2 f^{5} x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}}+\frac{16 f^{2} g^{3} x}{\sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}-\frac{10 f^{2} g^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{3}}"," ",0,"3/2*d^2/e*x/(-e^2*x^2+d^2)^(5/2)*f^4*g+1/2/e^4*x/(-e^2*x^2+d^2)^(3/2)*d^3*f*g^4+3/e^3*x/(-e^2*x^2+d^2)^(3/2)*d^2*f^2*g^3+7/3/e^2*x/(-e^2*x^2+d^2)^(3/2)*d*f^3*g^2-5/e^2*x^3/(-e^2*x^2+d^2)^(3/2)*d*f*g^4+16/e^4*x/(-e^2*x^2+d^2)^(1/2)*d*f*g^4-15/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)*d*f*g^4-110/3*d^3/e^2*x^2/(-e^2*x^2+d^2)^(5/2)*f^2*g^3-10/3*d^2/e*x^2/(-e^2*x^2+d^2)^(5/2)*f^3*g^2+5/2*x^3/e^2/(-e^2*x^2+d^2)^(5/2)*d^3*f*g^4+15*x^3/e/(-e^2*x^2+d^2)^(5/2)*d^2*f^2*g^3-3/2*d^5/e^4*x/(-e^2*x^2+d^2)^(5/2)*f*g^4+45*d^2/e*x^4/(-e^2*x^2+d^2)^(5/2)*f*g^4-60*d^4/e^3*x^2/(-e^2*x^2+d^2)^(5/2)*f*g^4+14/3/d/e^2*x/(-e^2*x^2+d^2)^(1/2)*f^3*g^2-1/d^2/e*x/(-e^2*x^2+d^2)^(1/2)*f^4*g-9*d^4/e^3*x/(-e^2*x^2+d^2)^(5/2)*f^2*g^3-7*d^3/e^2*x/(-e^2*x^2+d^2)^(5/2)*f^3*g^2-1/2*e*g^5*x^7/(-e^2*x^2+d^2)^(5/2)+7/15*d^2/e/(-e^2*x^2+d^2)^(5/2)*f^5+4/5*x/(-e^2*x^2+d^2)^(5/2)*d*f^5+1/15/d*x/(-e^2*x^2+d^2)^(3/2)*f^5+2/15/d^3*x/(-e^2*x^2+d^2)^(1/2)*f^5+1/3*x^2*e/(-e^2*x^2+d^2)^(5/2)*f^5-3*x^6/(-e^2*x^2+d^2)^(5/2)*d*g^5+152/15*d^7/e^6/(-e^2*x^2+d^2)^(5/2)*g^5+5/2*x^3*e/(-e^2*x^2+d^2)^(5/2)*f^4*g-1/2/e*x/(-e^2*x^2+d^2)^(3/2)*f^4*g+5*x^2/(-e^2*x^2+d^2)^(5/2)*d*f^4*g-d^3/e^2/(-e^2*x^2+d^2)^(5/2)*f^4*g-5*x^6*e/(-e^2*x^2+d^2)^(5/2)*f*g^4+19*d^3/e^2*x^4/(-e^2*x^2+d^2)^(5/2)*g^5-76/3*d^5/e^4*x^2/(-e^2*x^2+d^2)^(5/2)*g^5+24*d^6/e^5/(-e^2*x^2+d^2)^(5/2)*f*g^4+3*x^5/(-e^2*x^2+d^2)^(5/2)*d*f*g^4+2*x^5*e/(-e^2*x^2+d^2)^(5/2)*f^2*g^3-10/3/e*x^3/(-e^2*x^2+d^2)^(3/2)*f^2*g^3+16/e^3*x/(-e^2*x^2+d^2)^(1/2)*f^2*g^3-10/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)*f^2*g^3+30*x^4/(-e^2*x^2+d^2)^(5/2)*d*f^2*g^3+10*x^4*e/(-e^2*x^2+d^2)^(5/2)*f^3*g^2+13/10/e*g^5*d^2*x^5/(-e^2*x^2+d^2)^(5/2)-13/6/e^3*g^5*d^2*x^3/(-e^2*x^2+d^2)^(3/2)+13/2/e^5*g^5*d^2*x/(-e^2*x^2+d^2)^(1/2)-13/2/e^5*g^5*d^2/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+44/3*d^5/e^4/(-e^2*x^2+d^2)^(5/2)*f^2*g^3+4/3*d^4/e^3/(-e^2*x^2+d^2)^(5/2)*f^3*g^2+15*x^3/(-e^2*x^2+d^2)^(5/2)*d*f^3*g^2","B"
580,1,1030,199,0.014000," ","int((e*x+d)^3*(g*x+f)^4/(-e^2*x^2+d^2)^(7/2),x)","-\frac{e \,g^{4} x^{6}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{3 d \,g^{4} x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{4 e f \,g^{3} x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{9 d^{2} g^{4} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{12 d f \,g^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{6 e \,f^{2} g^{2} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{d^{3} g^{4} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{6 d^{2} f \,g^{3} x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{9 d \,f^{2} g^{2} x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{2 e \,f^{3} g \,x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{12 d^{4} g^{4} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{44 d^{3} f \,g^{3} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{2 d^{2} f^{2} g^{2} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{4 d \,f^{3} g \,x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{e \,f^{4} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{3 d^{5} g^{4} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}-\frac{18 d^{4} f \,g^{3} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{21 d^{3} f^{2} g^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{6 d^{2} f^{3} g x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}-\frac{d \,g^{4} x^{3}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}+\frac{4 d \,f^{4} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{4 f \,g^{3} x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}+\frac{24 d^{6} g^{4}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{5}}+\frac{88 d^{5} f \,g^{3}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}+\frac{4 d^{4} f^{2} g^{2}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{4 d^{3} f^{3} g}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{7 d^{2} f^{4}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{d^{3} g^{4} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{4}}+\frac{6 d^{2} f \,g^{3} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}+\frac{7 d \,f^{2} g^{2} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}+\frac{f^{4} x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d}-\frac{2 f^{3} g x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}+\frac{16 d \,g^{4} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{4}}-\frac{3 d \,g^{4} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{4}}+\frac{14 f^{2} g^{2} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{2}}-\frac{4 f^{3} g x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e}+\frac{2 f^{4} x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}}+\frac{32 f \,g^{3} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}-\frac{4 f \,g^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{3}}"," ",0,"4/5*x/(-e^2*x^2+d^2)^(5/2)*d*f^4+1/15/d*x/(-e^2*x^2+d^2)^(3/2)*f^4+2/15/d^3*x/(-e^2*x^2+d^2)^(1/2)*f^4+1/3*x^2*e/(-e^2*x^2+d^2)^(5/2)*f^4+7/15*d^2/e/(-e^2*x^2+d^2)^(5/2)*f^4+3/5*x^5/(-e^2*x^2+d^2)^(5/2)*d*g^4+24/5/e^5*g^4*d^6/(-e^2*x^2+d^2)^(5/2)-e*g^4*x^6/(-e^2*x^2+d^2)^(5/2)+6*x^3/e/(-e^2*x^2+d^2)^(5/2)*d^2*f*g^3-18/5*d^4/e^3*x/(-e^2*x^2+d^2)^(5/2)*f*g^3-44/3*d^3/e^2*x^2/(-e^2*x^2+d^2)^(5/2)*f*g^3-2*d^2/e*x^2/(-e^2*x^2+d^2)^(5/2)*f^2*g^2+14/5/d/e^2*x/(-e^2*x^2+d^2)^(1/2)*f^2*g^2-4/5/d^2/e*x/(-e^2*x^2+d^2)^(1/2)*f^3*g-21/5*d^3/e^2*x/(-e^2*x^2+d^2)^(5/2)*f^2*g^2+6/5*d^2/e*x/(-e^2*x^2+d^2)^(5/2)*f^3*g+6/5/e^3*x/(-e^2*x^2+d^2)^(3/2)*d^2*f*g^3+7/5/e^2*x/(-e^2*x^2+d^2)^(3/2)*d*f^2*g^2+6*x^4*e/(-e^2*x^2+d^2)^(5/2)*f^2*g^2+88/15*d^5/e^4/(-e^2*x^2+d^2)^(5/2)*f*g^3+4/5*d^4/e^3/(-e^2*x^2+d^2)^(5/2)*f^2*g^2-1/e^2*x^3/(-e^2*x^2+d^2)^(3/2)*d*g^4-4/3/e*x^3/(-e^2*x^2+d^2)^(3/2)*f*g^3+16/5/e^4*x/(-e^2*x^2+d^2)^(1/2)*d*g^4+32/5/e^3*x/(-e^2*x^2+d^2)^(1/2)*f*g^3-3/e^4/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)*d*g^4-4/e^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)*f*g^3+4/5*x^5*e/(-e^2*x^2+d^2)^(5/2)*f*g^3+2*x^3*e/(-e^2*x^2+d^2)^(5/2)*f^3*g-3/10*d^5/e^4*x/(-e^2*x^2+d^2)^(5/2)*g^4+12*x^4/(-e^2*x^2+d^2)^(5/2)*d*f*g^3+9*x^3/(-e^2*x^2+d^2)^(5/2)*d*f^2*g^2+1/2*x^3/e^2/(-e^2*x^2+d^2)^(5/2)*d^3*g^4-12/e^3*g^4*d^4*x^2/(-e^2*x^2+d^2)^(5/2)+9/e*g^4*d^2*x^4/(-e^2*x^2+d^2)^(5/2)+1/10/e^4*x/(-e^2*x^2+d^2)^(3/2)*d^3*g^4-2/5/e*x/(-e^2*x^2+d^2)^(3/2)*f^3*g+4*x^2/(-e^2*x^2+d^2)^(5/2)*d*f^3*g-4/5*d^3/e^2/(-e^2*x^2+d^2)^(5/2)*f^3*g","B"
581,1,713,169,0.013000," ","int((e*x+d)^3*(g*x+f)^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{e \,g^{3} x^{5}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{3 d \,g^{3} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{3 e f \,g^{2} x^{4}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{3 d^{2} g^{3} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{9 d f \,g^{2} x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{3 e \,f^{2} g \,x^{3}}{2 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{11 d^{3} g^{3} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}-\frac{d^{2} f \,g^{2} x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{3 d \,f^{2} g \,x^{2}}{\left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}+\frac{e \,f^{3} x^{2}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{9 d^{4} g^{3} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{21 d^{3} f \,g^{2} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{9 d^{2} f^{2} g x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{4 d \,f^{3} x}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}}}-\frac{g^{3} x^{3}}{3 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}+\frac{22 d^{5} g^{3}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{4}}+\frac{2 d^{4} f \,g^{2}}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{3}}-\frac{3 d^{3} f^{2} g}{5 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e^{2}}+\frac{7 d^{2} f^{3}}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{5}{2}} e}+\frac{3 d^{2} g^{3} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{3}}+\frac{7 d f \,g^{2} x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e^{2}}+\frac{f^{3} x}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} d}-\frac{3 f^{2} g x}{10 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{3}{2}} e}+\frac{7 f \,g^{2} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d \,e^{2}}-\frac{3 f^{2} g x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{2} e}+\frac{2 f^{3} x}{15 \sqrt{-e^{2} x^{2}+d^{2}}\, d^{3}}+\frac{8 g^{3} x}{5 \sqrt{-e^{2} x^{2}+d^{2}}\, e^{3}}-\frac{g^{3} \arctan \left(\frac{\sqrt{e^{2}}\, x}{\sqrt{-e^{2} x^{2}+d^{2}}}\right)}{\sqrt{e^{2}}\, e^{3}}"," ",0,"4/5*x/(-e^2*x^2+d^2)^(5/2)*d*f^3+1/15/d*x/(-e^2*x^2+d^2)^(3/2)*f^3+2/15/d^3*x/(-e^2*x^2+d^2)^(1/2)*f^3+7/15*d^2/e/(-e^2*x^2+d^2)^(5/2)*f^3+1/3*x^2*e/(-e^2*x^2+d^2)^(5/2)*f^3+3*x^4/(-e^2*x^2+d^2)^(5/2)*d*g^3+22/15*d^5/e^4/(-e^2*x^2+d^2)^(5/2)*g^3+8/5/e^3*g^3*x/(-e^2*x^2+d^2)^(1/2)-1/e^3*g^3/(e^2)^(1/2)*arctan((e^2)^(1/2)/(-e^2*x^2+d^2)^(1/2)*x)+1/5*e*g^3*x^5/(-e^2*x^2+d^2)^(5/2)-1/3/e*g^3*x^3/(-e^2*x^2+d^2)^(3/2)-21/10*d^3/e^2*x/(-e^2*x^2+d^2)^(5/2)*f*g^2-d^2/e*x^2/(-e^2*x^2+d^2)^(5/2)*f*g^2+9/10*d^2/e*x/(-e^2*x^2+d^2)^(5/2)*f^2*g+7/10/e^2*x/(-e^2*x^2+d^2)^(3/2)*d*f*g^2+7/5/d/e^2*x/(-e^2*x^2+d^2)^(1/2)*f*g^2-3/5/d^2/e*x/(-e^2*x^2+d^2)^(1/2)*f^2*g-9/10*d^4/e^3*x/(-e^2*x^2+d^2)^(5/2)*g^3+3/10/e^3*x/(-e^2*x^2+d^2)^(3/2)*d^2*g^3-3/10/e*x/(-e^2*x^2+d^2)^(3/2)*f^2*g+3/2*x^3*e/(-e^2*x^2+d^2)^(5/2)*f^2*g+3*x^2/(-e^2*x^2+d^2)^(5/2)*d*f^2*g-3/5*d^3/e^2/(-e^2*x^2+d^2)^(5/2)*f^2*g-11/3*d^3/e^2*x^2/(-e^2*x^2+d^2)^(5/2)*g^3+2/5*d^4/e^3/(-e^2*x^2+d^2)^(5/2)*f*g^2+3/2*x^3/e/(-e^2*x^2+d^2)^(5/2)*d^2*g^3+9/2*x^3/(-e^2*x^2+d^2)^(5/2)*d*f*g^2+3*x^4*e/(-e^2*x^2+d^2)^(5/2)*f*g^2","B"
582,1,131,133,0.011000," ","int((e*x+d)^3*(g*x+f)^2/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{4} \left(7 d^{2} e^{2} g^{2} x^{2}-6 d \,e^{3} f g \,x^{2}+2 e^{4} f^{2} x^{2}-6 d^{3} e \,g^{2} x +18 d^{2} e^{2} f g x -6 d \,e^{3} f^{2} x +2 d^{4} g^{2}-6 d^{3} e f g +7 d^{2} e^{2} f^{2}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} e^{3}}"," ",0,"1/15*(-e*x+d)*(e*x+d)^4*(7*d^2*e^2*g^2*x^2-6*d*e^3*f*g*x^2+2*e^4*f^2*x^2-6*d^3*e*g^2*x+18*d^2*e^2*f*g*x-6*d*e^3*f^2*x+2*d^4*g^2-6*d^3*e*f*g+7*d^2*e^2*f^2)/d^3/e^3/(-e^2*x^2+d^2)^(7/2)","A"
583,1,85,105,0.009000," ","int((e*x+d)^3*(g*x+f)/(-e^2*x^2+d^2)^(7/2),x)","-\frac{\left(-e x +d \right) \left(e x +d \right)^{4} \left(3 d \,e^{2} g \,x^{2}-2 e^{3} f \,x^{2}-9 d^{2} e g x +6 d \,e^{2} f x +3 d^{3} g -7 d^{2} e f \right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} e^{2}}"," ",0,"-1/15*(-e*x+d)*(e*x+d)^4*(3*d*e^2*g*x^2-2*e^3*f*x^2-9*d^2*e*g*x+6*d*e^2*f*x+3*d^3*g-7*d^2*e*f)/d^3/e^2/(-e^2*x^2+d^2)^(7/2)","A"
584,1,55,91,0.008000," ","int((e*x+d)^3/(-e^2*x^2+d^2)^(7/2),x)","\frac{\left(-e x +d \right) \left(e x +d \right)^{4} \left(2 e^{2} x^{2}-6 d e x +7 d^{2}\right)}{15 \left(-e^{2} x^{2}+d^{2}\right)^{\frac{7}{2}} d^{3} e}"," ",0,"1/15*(-e*x+d)*(e*x+d)^4*(2*e^2*x^2-6*d*e*x+7*d^2)/d^3/e/(-e^2*x^2+d^2)^(7/2)","A"
585,1,3961,223,0.050000," ","int((e*x+d)^3/(g*x+f)/(-e^2*x^2+d^2)^(7/2),x)","\text{output too large to display}"," ",0,"g/(d^2*g^2-e^2*f^2)^3*f^4/d^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*e^5*x+3*g^4/(d^2*g^2-e^2*f^2)^3/((d^2*g^2-e^2*f^2)/g^2)^(1/2)*ln((2*(d^2*g^2-e^2*f^2)/g^2+2*e^2*f/g*(x+f/g)+2*((d^2*g^2-e^2*f^2)/g^2)^(1/2)*(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2))/(x+f/g))*d^2*e*f+1/3/g/(d^2*g^2-e^2*f^2)^2*e^5*f^4/d^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*x+2/3/g/(d^2*g^2-e^2*f^2)^2*e^5*f^4/d^4/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*x-g^4/(d^2*g^2-e^2*f^2)^3*f*d/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*e^2*x-3*g^2/(d^2*g^2-e^2*f^2)^3*f^3/d/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*e^4*x-4/5*e^2/g^2/d^3*f*x/(-e^2*x^2+d^2)^(3/2)+3/5/g*e^3*f^2/(d^2*g^2-e^2*f^2)/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(5/2)*x+8/15*e^3/g^3*f^2/d^6*x/(-e^2*x^2+d^2)^(1/2)-3/5*e^2/g^2/d*f*x/(-e^2*x^2+d^2)^(5/2)-8/5*e^2/g^2/d^5*f*x/(-e^2*x^2+d^2)^(1/2)+1/5*e^3/g^3*f^2*x/d^2/(-e^2*x^2+d^2)^(5/2)+4/15*e^3/g^3*f^2/d^4*x/(-e^2*x^2+d^2)^(3/2)+3/5/g/(d^2*g^2-e^2*f^2)/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(5/2)*d*e^2*f^2-g^2/(d^2*g^2-e^2*f^2)^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*d^2*e*f-1/5*e^2*f/(d^2*g^2-e^2*f^2)*d/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(5/2)*x-8/15*e^2*f/(d^2*g^2-e^2*f^2)/d^3/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*x-1/(d^2*g^2-e^2*f^2)^2*e^4*f^3/d/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*x-2/(d^2*g^2-e^2*f^2)^2*e^4*f^3/d^3/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*x-4/15*e^2*f/(d^2*g^2-e^2*f^2)/d/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*x+g/(d^2*g^2-e^2*f^2)^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*d*e^2*f^2-3*g^4/(d^2*g^2-e^2*f^2)^3/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*d^2*e*f+3*g^3/(d^2*g^2-e^2*f^2)^3/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*d*e^2*f^2+g^2/(d^2*g^2-e^2*f^2)^3/((d^2*g^2-e^2*f^2)/g^2)^(1/2)*ln((2*(d^2*g^2-e^2*f^2)/g^2+2*e^2*f/g*(x+f/g)+2*((d^2*g^2-e^2*f^2)/g^2)^(1/2)*(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2))/(x+f/g))*e^3*f^3+3*g^3/(d^2*g^2-e^2*f^2)^3*f^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*e^3*x+g/(d^2*g^2-e^2*f^2)^2*e^3*f^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*x+1/5*g/(d^2*g^2-e^2*f^2)/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(5/2)*d^3+1/3*g^3/(d^2*g^2-e^2*f^2)^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*d^3+g^5/(d^2*g^2-e^2*f^2)^3/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*d^3-1/3/(d^2*g^2-e^2*f^2)^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*e^3*f^3+4/5*e/g*x/(-e^2*x^2+d^2)^(5/2)-1/5*e/g^2/(-e^2*x^2+d^2)^(5/2)*f+3/5/g/(-e^2*x^2+d^2)^(5/2)*d+8/15/g^3*e^5*f^4/(d^2*g^2-e^2*f^2)/d^6/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*x-1/3*g^2/(d^2*g^2-e^2*f^2)^2*e^2*f*d/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*x+11/15*e/g/d^2*x/(-e^2*x^2+d^2)^(3/2)+22/15*e/g/d^4*x/(-e^2*x^2+d^2)^(1/2)-3/5/(d^2*g^2-e^2*f^2)/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(5/2)*d^2*e*f-1/5/g^2/(d^2*g^2-e^2*f^2)/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(5/2)*e^3*f^3-g^2/(d^2*g^2-e^2*f^2)^3/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*e^3*f^3-g^5/(d^2*g^2-e^2*f^2)^3/((d^2*g^2-e^2*f^2)/g^2)^(1/2)*ln((2*(d^2*g^2-e^2*f^2)/g^2+2*e^2*f/g*(x+f/g)+2*((d^2*g^2-e^2*f^2)/g^2)^(1/2)*(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2))/(x+f/g))*d^3-3*g^3/(d^2*g^2-e^2*f^2)^3/((d^2*g^2-e^2*f^2)/g^2)^(1/2)*ln((2*(d^2*g^2-e^2*f^2)/g^2+2*e^2*f/g*(x+f/g)+2*((d^2*g^2-e^2*f^2)/g^2)^(1/2)*(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2))/(x+f/g))*d*e^2*f^2-3/5/g^2*e^4*f^3/(d^2*g^2-e^2*f^2)/d/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(5/2)*x+1/5/g^3*e^5*f^4/(d^2*g^2-e^2*f^2)/d^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(5/2)*x+4/5/g*e^3*f^2/(d^2*g^2-e^2*f^2)/d^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*x-2/3*g^2/(d^2*g^2-e^2*f^2)^2*e^2*f/d/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*x+2*g/(d^2*g^2-e^2*f^2)^2*e^3*f^2/d^2/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*x-4/5/g^2*e^4*f^3/(d^2*g^2-e^2*f^2)/d^3/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*x+4/15/g^3*e^5*f^4/(d^2*g^2-e^2*f^2)/d^4/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(3/2)*x+8/5/g*e^3*f^2/(d^2*g^2-e^2*f^2)/d^4/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*x-8/5/g^2*e^4*f^3/(d^2*g^2-e^2*f^2)/d^5/(-(x+f/g)^2*e^2+2*e^2*f/g*(x+f/g)+(d^2*g^2-e^2*f^2)/g^2)^(1/2)*x","B"
586,1,6760,291,0.029000," ","int((e*x+d)^3/(g*x+f)^2/(-e^2*x^2+d^2)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
587,1,9593,370,0.032000," ","int((e*x+d)^3/(g*x+f)^3/(-e^2*x^2+d^2)^(7/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
588,1,114,98,0.019000," ","int((c*x^2+a)/(e*x+d)^(3/2)/(g*x+f),x)","\frac{-\frac{2 \left(a \,g^{2}+c \,f^{2}\right) e^{2} \arctanh \left(\frac{\sqrt{e x +d}\, g}{\sqrt{\left(d g -e f \right) g}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) g}\, g}+\frac{2 \sqrt{e x +d}\, c}{g}-\frac{2 \left(-a \,e^{2}-c \,d^{2}\right)}{\left(d g -e f \right) \sqrt{e x +d}}}{e^{2}}"," ",0,"2/e^2*(c/g*(e*x+d)^(1/2)-e^2*(a*g^2+c*f^2)/(d*g-e*f)/g/((d*g-e*f)*g)^(1/2)*arctanh(g*(e*x+d)^(1/2)/((d*g-e*f)*g)^(1/2))-(-a*e^2-c*d^2)/(d*g-e*f)/(e*x+d)^(1/2))","A"
589,1,365,218,0.007000," ","int((e*x+d)^3*(c*x^2+a)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(315 e^{3} c \,x^{5} g^{5}+1155 c d \,e^{2} g^{5} x^{4}-350 c \,e^{3} f \,g^{4} x^{4}+495 a \,e^{3} g^{5} x^{3}+1485 c \,d^{2} e \,g^{5} x^{3}-1320 c d \,e^{2} f \,g^{4} x^{3}+400 c \,e^{3} f^{2} g^{3} x^{3}+2079 a d \,e^{2} g^{5} x^{2}-594 a \,e^{3} f \,g^{4} x^{2}+693 c \,d^{3} g^{5} x^{2}-1782 c \,d^{2} e f \,g^{4} x^{2}+1584 c d \,e^{2} f^{2} g^{3} x^{2}-480 c \,e^{3} f^{3} g^{2} x^{2}+3465 a \,d^{2} e \,g^{5} x -2772 a d \,e^{2} f \,g^{4} x +792 a \,e^{3} f^{2} g^{3} x -924 c \,d^{3} f \,g^{4} x +2376 c \,d^{2} e \,f^{2} g^{3} x -2112 c d \,e^{2} f^{3} g^{2} x +640 c \,e^{3} f^{4} g x +3465 d^{3} a \,g^{5}-6930 a \,d^{2} e f \,g^{4}+5544 a d \,e^{2} f^{2} g^{3}-1584 a \,e^{3} f^{3} g^{2}+1848 c \,d^{3} f^{2} g^{3}-4752 c \,d^{2} e \,f^{3} g^{2}+4224 c d \,e^{2} f^{4} g -1280 c \,e^{3} f^{5}\right)}{3465 g^{6}}"," ",0,"2/3465*(g*x+f)^(1/2)*(315*c*e^3*g^5*x^5+1155*c*d*e^2*g^5*x^4-350*c*e^3*f*g^4*x^4+495*a*e^3*g^5*x^3+1485*c*d^2*e*g^5*x^3-1320*c*d*e^2*f*g^4*x^3+400*c*e^3*f^2*g^3*x^3+2079*a*d*e^2*g^5*x^2-594*a*e^3*f*g^4*x^2+693*c*d^3*g^5*x^2-1782*c*d^2*e*f*g^4*x^2+1584*c*d*e^2*f^2*g^3*x^2-480*c*e^3*f^3*g^2*x^2+3465*a*d^2*e*g^5*x-2772*a*d*e^2*f*g^4*x+792*a*e^3*f^2*g^3*x-924*c*d^3*f*g^4*x+2376*c*d^2*e*f^2*g^3*x-2112*c*d*e^2*f^3*g^2*x+640*c*e^3*f^4*g*x+3465*a*d^3*g^5-6930*a*d^2*e*f*g^4+5544*a*d*e^2*f^2*g^3-1584*a*e^3*f^3*g^2+1848*c*d^3*f^2*g^3-4752*c*d^2*e*f^3*g^2+4224*c*d*e^2*f^4*g-1280*c*e^3*f^5)/g^6","A"
590,1,215,157,0.007000," ","int((e*x+d)^2*(c*x^2+a)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(35 e^{2} c \,x^{4} g^{4}+90 c d e \,g^{4} x^{3}-40 c \,e^{2} f \,g^{3} x^{3}+63 a \,e^{2} g^{4} x^{2}+63 c \,d^{2} g^{4} x^{2}-108 c d e f \,g^{3} x^{2}+48 c \,e^{2} f^{2} g^{2} x^{2}+210 a d e \,g^{4} x -84 a \,e^{2} f \,g^{3} x -84 c \,d^{2} f \,g^{3} x +144 c d e \,f^{2} g^{2} x -64 c \,e^{2} f^{3} g x +315 d^{2} a \,g^{4}-420 a d e f \,g^{3}+168 a \,e^{2} f^{2} g^{2}+168 c \,d^{2} f^{2} g^{2}-288 c d e \,f^{3} g +128 c \,e^{2} f^{4}\right)}{315 g^{5}}"," ",0,"2/315*(g*x+f)^(1/2)*(35*c*e^2*g^4*x^4+90*c*d*e*g^4*x^3-40*c*e^2*f*g^3*x^3+63*a*e^2*g^4*x^2+63*c*d^2*g^4*x^2-108*c*d*e*f*g^3*x^2+48*c*e^2*f^2*g^2*x^2+210*a*d*e*g^4*x-84*a*e^2*f*g^3*x-84*c*d^2*f*g^3*x+144*c*d*e*f^2*g^2*x-64*c*e^2*f^3*g*x+315*a*d^2*g^4-420*a*d*e*f*g^3+168*a*e^2*f^2*g^2+168*c*d^2*f^2*g^2-288*c*d*e*f^3*g+128*c*e^2*f^4)/g^5","A"
591,1,101,99,0.005000," ","int((e*x+d)*(c*x^2+a)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(15 c e \,x^{3} g^{3}+21 c d \,g^{3} x^{2}-18 c e f \,g^{2} x^{2}+35 a e \,g^{3} x -28 c d f \,g^{2} x +24 c e \,f^{2} g x +105 a d \,g^{3}-70 a e f \,g^{2}+56 c d \,f^{2} g -48 c e \,f^{3}\right)}{105 g^{4}}"," ",0,"2/105*(g*x+f)^(1/2)*(15*c*e*g^3*x^3+21*c*d*g^3*x^2-18*c*e*f*g^2*x^2+35*a*e*g^3*x-28*c*d*f*g^2*x+24*c*e*f^2*g*x+105*a*d*g^3-70*a*e*f*g^2+56*c*d*f^2*g-48*c*e*f^3)/g^4","A"
592,1,41,51,0.004000," ","int((c*x^2+a)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(3 c \,x^{2} g^{2}-4 c f x g +15 a \,g^{2}+8 c \,f^{2}\right)}{15 g^{3}}"," ",0,"2/15*(g*x+f)^(1/2)*(3*c*g^2*x^2-4*c*f*g*x+15*a*g^2+8*c*f^2)/g^3","A"
593,1,132,88,0.015000," ","int((c*x^2+a)/(e*x+d)/(g*x+f)^(1/2),x)","\frac{2 a \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\sqrt{\left(d g -e f \right) e}}+\frac{2 c \,d^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\sqrt{\left(d g -e f \right) e}\, e^{2}}-\frac{2 \sqrt{g x +f}\, c d}{e^{2} g}-\frac{2 \sqrt{g x +f}\, c f}{e \,g^{2}}+\frac{2 \left(g x +f \right)^{\frac{3}{2}} c}{3 e \,g^{2}}"," ",0,"2/3*c*(g*x+f)^(3/2)/e/g^2-2/g*c/e^2*d*(g*x+f)^(1/2)-2/g^2*c/e*f*(g*x+f)^(1/2)+2/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)*e/((d*g-e*f)*e)^(1/2))*a+2/e^2/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)*e/((d*g-e*f)*e)^(1/2))*c*d^2","A"
594,1,237,108,0.017000," ","int((c*x^2+a)/(e*x+d)^2/(g*x+f)^(1/2),x)","\frac{a g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}}-\frac{3 c \,d^{2} g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}\, e^{2}}+\frac{4 c d f \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}\, e}+\frac{\sqrt{g x +f}\, a g}{\left(d g -e f \right) \left(e g x +d g \right)}+\frac{\sqrt{g x +f}\, c \,d^{2} g}{\left(d g -e f \right) \left(e g x +d g \right) e^{2}}+\frac{2 \sqrt{g x +f}\, c}{e^{2} g}"," ",0,"2*c*(g*x+f)^(1/2)/e^2/g+g/(d*g-e*f)*(g*x+f)^(1/2)/(e*g*x+d*g)*a+g/e^2/(d*g-e*f)*(g*x+f)^(1/2)/(e*g*x+d*g)*c*d^2+g/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*a-3*g/e^2/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d^2+4/e/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d*f","B"
595,1,384,158,0.021000," ","int((c*x^2+a)/(e*x+d)^3/(g*x+f)^(1/2),x)","\frac{3 a \,g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}}+\frac{3 c \,d^{2} g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}\, e^{2}}-\frac{2 c d f g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}\, e}+\frac{2 c \,f^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}}+\frac{\frac{\left(3 a \,e^{2} g -5 c \,d^{2} g +8 c d e f \right) \left(g x +f \right)^{\frac{3}{2}} g}{4 \left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) e}+\frac{\left(5 a \,e^{2} g -3 c \,d^{2} g +8 c d e f \right) \sqrt{g x +f}\, g}{4 \left(d g -e f \right) e^{2}}}{\left(d g -e f +\left(g x +f \right) e \right)^{2}}"," ",0,"2*(1/8*g*(3*a*e^2*g-5*c*d^2*g+8*c*d*e*f)/e/(d^2*g^2-2*d*e*f*g+e^2*f^2)*(g*x+f)^(3/2)+1/8*(5*a*e^2*g-3*c*d^2*g+8*c*d*e*f)/e^2*g/(d*g-e*f)*(g*x+f)^(1/2))/(e*(g*x+f)+d*g-e*f)^2+3/4/(d^2*g^2-2*d*e*f*g+e^2*f^2)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*a*g^2+3/4/(d^2*g^2-2*d*e*f*g+e^2*f^2)/e^2/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d^2*g^2-2/(d^2*g^2-2*d*e*f*g+e^2*f^2)/e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d*f*g+2/(d^2*g^2-2*d*e*f*g+e^2*f^2)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*f^2","B"
596,1,365,218,0.008000," ","int((e*x+d)^3*(c*x^2+a)/(g*x+f)^(3/2),x)","-\frac{2 \left(-35 e^{3} c \,x^{5} g^{5}-135 c d \,e^{2} g^{5} x^{4}+50 c \,e^{3} f \,g^{4} x^{4}-63 a \,e^{3} g^{5} x^{3}-189 c \,d^{2} e \,g^{5} x^{3}+216 c d \,e^{2} f \,g^{4} x^{3}-80 c \,e^{3} f^{2} g^{3} x^{3}-315 a d \,e^{2} g^{5} x^{2}+126 a \,e^{3} f \,g^{4} x^{2}-105 c \,d^{3} g^{5} x^{2}+378 c \,d^{2} e f \,g^{4} x^{2}-432 c d \,e^{2} f^{2} g^{3} x^{2}+160 c \,e^{3} f^{3} g^{2} x^{2}-945 a \,d^{2} e \,g^{5} x +1260 a d \,e^{2} f \,g^{4} x -504 a \,e^{3} f^{2} g^{3} x +420 c \,d^{3} f \,g^{4} x -1512 c \,d^{2} e \,f^{2} g^{3} x +1728 c d \,e^{2} f^{3} g^{2} x -640 c \,e^{3} f^{4} g x +315 d^{3} a \,g^{5}-1890 a \,d^{2} e f \,g^{4}+2520 a d \,e^{2} f^{2} g^{3}-1008 a \,e^{3} f^{3} g^{2}+840 c \,d^{3} f^{2} g^{3}-3024 c \,d^{2} e \,f^{3} g^{2}+3456 c d \,e^{2} f^{4} g -1280 c \,e^{3} f^{5}\right)}{315 \sqrt{g x +f}\, g^{6}}"," ",0,"-2/315/(g*x+f)^(1/2)*(-35*c*e^3*g^5*x^5-135*c*d*e^2*g^5*x^4+50*c*e^3*f*g^4*x^4-63*a*e^3*g^5*x^3-189*c*d^2*e*g^5*x^3+216*c*d*e^2*f*g^4*x^3-80*c*e^3*f^2*g^3*x^3-315*a*d*e^2*g^5*x^2+126*a*e^3*f*g^4*x^2-105*c*d^3*g^5*x^2+378*c*d^2*e*f*g^4*x^2-432*c*d*e^2*f^2*g^3*x^2+160*c*e^3*f^3*g^2*x^2-945*a*d^2*e*g^5*x+1260*a*d*e^2*f*g^4*x-504*a*e^3*f^2*g^3*x+420*c*d^3*f*g^4*x-1512*c*d^2*e*f^2*g^3*x+1728*c*d*e^2*f^3*g^2*x-640*c*e^3*f^4*g*x+315*a*d^3*g^5-1890*a*d^2*e*f*g^4+2520*a*d*e^2*f^2*g^3-1008*a*e^3*f^3*g^2+840*c*d^3*f^2*g^3-3024*c*d^2*e*f^3*g^2+3456*c*d*e^2*f^4*g-1280*c*e^3*f^5)/g^6","A"
597,1,215,157,0.006000," ","int((e*x+d)^2*(c*x^2+a)/(g*x+f)^(3/2),x)","-\frac{2 \left(-15 e^{2} c \,x^{4} g^{4}-42 c d e \,g^{4} x^{3}+24 c \,e^{2} f \,g^{3} x^{3}-35 a \,e^{2} g^{4} x^{2}-35 c \,d^{2} g^{4} x^{2}+84 c d e f \,g^{3} x^{2}-48 c \,e^{2} f^{2} g^{2} x^{2}-210 a d e \,g^{4} x +140 a \,e^{2} f \,g^{3} x +140 c \,d^{2} f \,g^{3} x -336 c d e \,f^{2} g^{2} x +192 c \,e^{2} f^{3} g x +105 d^{2} a \,g^{4}-420 a d e f \,g^{3}+280 a \,e^{2} f^{2} g^{2}+280 c \,d^{2} f^{2} g^{2}-672 c d e \,f^{3} g +384 c \,e^{2} f^{4}\right)}{105 \sqrt{g x +f}\, g^{5}}"," ",0,"-2/105/(g*x+f)^(1/2)*(-15*c*e^2*g^4*x^4-42*c*d*e*g^4*x^3+24*c*e^2*f*g^3*x^3-35*a*e^2*g^4*x^2-35*c*d^2*g^4*x^2+84*c*d*e*f*g^3*x^2-48*c*e^2*f^2*g^2*x^2-210*a*d*e*g^4*x+140*a*e^2*f*g^3*x+140*c*d^2*f*g^3*x-336*c*d*e*f^2*g^2*x+192*c*e^2*f^3*g*x+105*a*d^2*g^4-420*a*d*e*f*g^3+280*a*e^2*f^2*g^2+280*c*d^2*f^2*g^2-672*c*d*e*f^3*g+384*c*e^2*f^4)/g^5","A"
598,1,101,99,0.004000," ","int((e*x+d)*(c*x^2+a)/(g*x+f)^(3/2),x)","-\frac{2 \left(-3 c e \,x^{3} g^{3}-5 c d \,g^{3} x^{2}+6 c e f \,g^{2} x^{2}-15 a e \,g^{3} x +20 c d f \,g^{2} x -24 c e \,f^{2} g x +15 a d \,g^{3}-30 a e f \,g^{2}+40 c d \,f^{2} g -48 c e \,f^{3}\right)}{15 \sqrt{g x +f}\, g^{4}}"," ",0,"-2/15/(g*x+f)^(1/2)*(-3*c*e*g^3*x^3-5*c*d*g^3*x^2+6*c*e*f*g^2*x^2-15*a*e*g^3*x+20*c*d*f*g^2*x-24*c*e*f^2*g*x+15*a*d*g^3-30*a*e*f*g^2+40*c*d*f^2*g-48*c*e*f^3)/g^4","A"
599,1,41,51,0.004000," ","int((c*x^2+a)/(g*x+f)^(3/2),x)","-\frac{2 \left(-c \,x^{2} g^{2}+4 c f x g +3 a \,g^{2}+8 c \,f^{2}\right)}{3 \sqrt{g x +f}\, g^{3}}"," ",0,"-2/3/(g*x+f)^(1/2)*(-c*g^2*x^2+4*c*f*g*x+3*a*g^2+8*c*f^2)/g^3","A"
600,1,165,98,0.014000," ","int((c*x^2+a)/(e*x+d)/(g*x+f)^(3/2),x)","-\frac{2 a e \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}}-\frac{2 c \,d^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}\, e}-\frac{2 a}{\left(d g -e f \right) \sqrt{g x +f}}-\frac{2 c \,f^{2}}{\left(d g -e f \right) \sqrt{g x +f}\, g^{2}}+\frac{2 \sqrt{g x +f}\, c}{e \,g^{2}}"," ",0,"2*c*(g*x+f)^(1/2)/e/g^2-2/(d*g-e*f)*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*a-2/(d*g-e*f)/e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d^2-2/(d*g-e*f)/(g*x+f)^(1/2)*a-2/g^2/(d*g-e*f)/(g*x+f)^(1/2)*c*f^2","A"
601,1,269,130,0.021000," ","int((c*x^2+a)/(e*x+d)^2/(g*x+f)^(3/2),x)","-\frac{3 a e g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\left(d g -e f \right) e}}+\frac{c \,d^{2} g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\left(d g -e f \right) e}\, e}-\frac{4 c d f \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\left(d g -e f \right) e}}-\frac{\sqrt{g x +f}\, a e g}{\left(d g -e f \right)^{2} \left(e g x +d g \right)}-\frac{\sqrt{g x +f}\, c \,d^{2} g}{\left(d g -e f \right)^{2} \left(e g x +d g \right) e}-\frac{2 a g}{\left(d g -e f \right)^{2} \sqrt{g x +f}}-\frac{2 c \,f^{2}}{\left(d g -e f \right)^{2} \sqrt{g x +f}\, g}"," ",0,"-g/(d*g-e*f)^2*e*(g*x+f)^(1/2)/(e*g*x+d*g)*a-g/(d*g-e*f)^2/e*(g*x+f)^(1/2)/(e*g*x+d*g)*c*d^2-3*g/(d*g-e*f)^2*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*a+g/(d*g-e*f)^2/e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d^2-4/(d*g-e*f)^2/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d*f-2*g/(d*g-e*f)^2/(g*x+f)^(1/2)*a-2/g/(d*g-e*f)^2/(g*x+f)^(1/2)*c*f^2","B"
602,1,546,192,0.025000," ","int((c*x^2+a)/(e*x+d)^3/(g*x+f)^(3/2),x)","-\frac{9 \sqrt{g x +f}\, a d e \,g^{3}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}+\frac{9 \sqrt{g x +f}\, a \,e^{2} f \,g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{\sqrt{g x +f}\, c \,d^{3} g^{3}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2} e}-\frac{7 \sqrt{g x +f}\, c \,d^{2} f \,g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}+\frac{2 \sqrt{g x +f}\, c d e \,f^{2} g}{\left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{7 \left(g x +f \right)^{\frac{3}{2}} a \,e^{2} g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{15 a e \,g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}}+\frac{c \,d^{2} g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}\, e}+\frac{\left(g x +f \right)^{\frac{3}{2}} c \,d^{2} g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{2 \left(g x +f \right)^{\frac{3}{2}} c d e f g}{\left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{2 c d f g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}}-\frac{2 c e \,f^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}}-\frac{2 a \,g^{2}}{\left(d g -e f \right)^{3} \sqrt{g x +f}}-\frac{2 c \,f^{2}}{\left(d g -e f \right)^{3} \sqrt{g x +f}}"," ",0,"-7/4/(d*g-e*f)^3/(e*g*x+d*g)^2*(g*x+f)^(3/2)*a*e^2*g^2+1/4/(d*g-e*f)^3/(e*g*x+d*g)^2*(g*x+f)^(3/2)*c*d^2*g^2-2/(d*g-e*f)^3/(e*g*x+d*g)^2*(g*x+f)^(3/2)*c*d*e*f*g-9/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^3*e*(g*x+f)^(1/2)*a*d+9/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^2*e^2*(g*x+f)^(1/2)*a*f-1/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^3/e*(g*x+f)^(1/2)*c*d^3-7/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^2*(g*x+f)^(1/2)*f*c*d^2+2/(d*g-e*f)^3/(e*g*x+d*g)^2*g*e*(g*x+f)^(1/2)*c*d*f^2-15/4/(d*g-e*f)^3*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*a*g^2+1/4/(d*g-e*f)^3/e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d^2*g^2-2/(d*g-e*f)^3/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d*f*g-2/(d*g-e*f)^3*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*f^2-2/(d*g-e*f)^3/(g*x+f)^(1/2)*a*g^2-2/(d*g-e*f)^3/(g*x+f)^(1/2)*c*f^2","B"
603,1,306,121,0.038000," ","int((c*x^2+a)/(e*x+d)^(1/2)/(g*x+f)^(1/2),x)","\frac{\left(8 a \,e^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,d^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+2 c d e f g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,e^{2} f^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+4 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c e g x -6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c d g -6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c e f \right) \sqrt{e x +d}\, \sqrt{g x +f}}{8 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, e^{2} g^{2}}"," ",0,"1/8*(8*ln(1/2*(2*e*g*x+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+d*g+e*f)/(e*g)^(1/2))*a*e^2*g^2+3*ln(1/2*(2*e*g*x+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+d*g+e*f)/(e*g)^(1/2))*c*d^2*g^2+3*ln(1/2*(2*e*g*x+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+d*g+e*f)/(e*g)^(1/2))*c*e^2*f^2+2*ln(1/2*(2*e*g*x+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+d*g+e*f)/(e*g)^(1/2))*c*d*e*f*g+4*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*c*e*g-6*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)*c*d*g-6*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)*c*e*f)*(e*x+d)^(1/2)*(g*x+f)^(1/2)/(e*g)^(1/2)/g^2/e^2/((e*x+d)*(g*x+f))^(1/2)","B"
604,1,13,12,0.005000," ","int((2*x^2-1)/(x-1)^(1/2)/(x+1)^(1/2),x)","\sqrt{x -1}\, \sqrt{x +1}\, x"," ",0,"x*(x-1)^(1/2)*(x+1)^(1/2)","A"
605,1,2497,331,0.111000," ","int((e*x+d)^(3/2)*(g*x+f)^(1/2)/(c*x^2+a),x)","\frac{\sqrt{e x +d}\, \sqrt{g x +f}\, \left(-2 \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, a c d e g \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+2 \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, a c d e g \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, a c \,e^{2} f \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, a c \,e^{2} f \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, c^{2} d^{2} f \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, c^{2} d^{2} f \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+\sqrt{-a c}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, a \,e^{2} g \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, a \,e^{2} g \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{-a c}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, c \,d^{2} g \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, c \,d^{2} g \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-2 \sqrt{-a c}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, c d e f \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-2 \sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, c d e f \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+3 \sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c d e g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+\sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c \,e^{2} f \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+2 \sqrt{-a c}\, \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{e g}\, c e \right)}{2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-a c}\, \sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2}}"," ",0,"1/2*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(3*(-a*c)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*ln(1/2*(2*e*g*x+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(e*g)^(1/2)+d*g+e*f)/(e*g)^(1/2))*c*d*e*g+(-a*c)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*ln(1/2*(2*e*g*x+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(e*g)^(1/2)+d*g+e*f)/(e*g)^(1/2))*c*e^2*f+(-a*c)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((2*(-a*c)^(1/2)*x*e*g+x*c*d*g+x*c*e*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*a*e^2*g-(-a*c)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((2*(-a*c)^(1/2)*x*e*g+x*c*d*g+x*c*e*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*c*d^2*g-2*(-a*c)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((2*(-a*c)^(1/2)*x*e*g+x*c*d*g+x*c*e*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*c*d*e*f+(-a*c)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((x*c*d*g+x*c*e*f-2*(-a*c)^(1/2)*x*e*g+2*c*d*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*a*e^2*g-(-a*c)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((x*c*d*g+x*c*e*f-2*(-a*c)^(1/2)*x*e*g+2*c*d*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*c*d^2*g-2*(-a*c)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((x*c*d*g+x*c*e*f-2*(-a*c)^(1/2)*x*e*g+2*c*d*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*c*d*e*f+2*a*c*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((2*(-a*c)^(1/2)*x*e*g+x*c*d*g+x*c*e*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*d*e*g+a*c*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((2*(-a*c)^(1/2)*x*e*g+x*c*d*g+x*c*e*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*e^2*f-(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((2*(-a*c)^(1/2)*x*e*g+x*c*d*g+x*c*e*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*c^2*d^2*f-2*a*c*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((x*c*d*g+x*c*e*f-2*(-a*c)^(1/2)*x*e*g+2*c*d*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*d*e*g-a*c*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((x*c*d*g+x*c*e*f-2*(-a*c)^(1/2)*x*e*g+2*c*d*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*e^2*f+(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*(e*g)^(1/2)*ln((x*c*d*g+x*c*e*f-2*(-a*c)^(1/2)*x*e*g+2*c*d*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*c^2*d^2*f+2*(-a*c)^(1/2)*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)*(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)*(e*g)^(1/2)*c*e)/(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)/(-a*c)^(1/2)/c^2/(e*g)^(1/2)/(-((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+a*e*g-c*d*f)/c)^(1/2)/(((-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f-a*e*g+c*d*f)/c)^(1/2)","B"
606,1,1569,262,0.028000," ","int((e*x+d)^(1/2)*(g*x+f)^(1/2)/(c*x^2+a),x)","\frac{\sqrt{e x +d}\, \sqrt{g x +f}\, \left(-\sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a e g \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a e g \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+\sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c d f \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c d f \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, d g \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, d g \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, e f \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, e f \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+2 \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, e g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{e g}}{2 \sqrt{e g}}\right)\right)}{2 \sqrt{e g \,x^{2}+d g x +e f x +d f}\, \sqrt{-a c}\, \sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}"," ",0,"1/2*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(2*ln(1/2*(2*e*g*x+d*g+e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2)*e*g-(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*(-a*c)^(1/2)*d*g-(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*(-a*c)^(1/2)*e*f+(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a*e*g-(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*c*d*f-(e*g)^(1/2)*ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2)*d*g-(e*g)^(1/2)*ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2)*e*f-(e*g)^(1/2)*ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*a*e*g+(e*g)^(1/2)*ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c*d*f)/(e*g*x^2+d*g*x+e*f*x+d*f)^(1/2)/(-a*c)^(1/2)/c/(e*g)^(1/2)/(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)/((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)","B"
607,1,1383,176,0.038000," ","int((g*x+f)^(1/2)/(e*x+d)^(1/2)/(c*x^2+a),x)","-\frac{\sqrt{g x +f}\, \sqrt{e x +d}\, \left(-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,e^{2} f \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,e^{2} f \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2} d^{2} f \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2} d^{2} f \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, a \,e^{2} g \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a \,e^{2} g \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, c \,d^{2} g \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c \,d^{2} g \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)\right)}{2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \left(c d -\sqrt{-a c}\, e \right) \sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \left(c d +\sqrt{-a c}\, e \right) \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}}"," ",0,"-1/2*(g*x+f)^(1/2)*(e*x+d)^(1/2)*(ln((2*(-a*c)^(1/2)*e*g*x+c*d*g*x+c*e*f*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*a*c*e^2*f*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((2*(-a*c)^(1/2)*e*g*x+c*d*g*x+c*e*f*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*a*e^2*g*(-a*c)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((2*(-a*c)^(1/2)*e*g*x+c*d*g*x+c*e*f*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*c^2*d^2*f*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((2*(-a*c)^(1/2)*e*g*x+c*d*g*x+c*e*f*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c+2*c*d*f)/(c*x-(-a*c)^(1/2)))*c*d^2*g*(-a*c)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x-2*(-a*c)^(1/2)*e*g*x+2*c*d*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*a*c*e^2*f*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x-2*(-a*c)^(1/2)*e*g*x+2*c*d*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*a*e^2*g*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2)-ln((c*d*g*x+c*e*f*x-2*(-a*c)^(1/2)*e*g*x+2*c*d*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*c^2*d^2*f*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x-2*(-a*c)^(1/2)*e*g*x+2*c*d*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f)/(c*x+(-a*c)^(1/2)))*c*d^2*g*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2))/((e*x+d)*(g*x+f))^(1/2)/(c*d-(-a*c)^(1/2)*e)/(-a*c)^(1/2)/(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)/((-a*c)^(1/2)*e+c*d)/((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)","B"
608,1,5383,279,0.062000," ","int((g*x+f)^(1/2)/(e*x+d)^(3/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
609,1,14861,501,0.087000," ","int((g*x+f)^(1/2)/(e*x+d)^(5/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
610,1,2336,257,0.037000," ","int((e*x+d)^(3/2)/(c*x^2+a)/(g*x+f)^(1/2),x)","\frac{\sqrt{e x +d}\, \sqrt{g x +f}\, \left(-\sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a^{2} e^{2} g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a^{2} e^{2} g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+\sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,d^{2} g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,d^{2} g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,e^{2} f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,e^{2} f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+\sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2} d^{2} f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2} d^{2} f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-2 \sqrt{-a c}\, \sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a d e \,g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-2 \sqrt{-a c}\, \sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a d e \,g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+2 \sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a \,e^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-2 \sqrt{-a c}\, \sqrt{e g}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c d e \,f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-2 \sqrt{-a c}\, \sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c d e \,f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+2 \sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c \,e^{2} f^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)\right)}{2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \left(c f -\sqrt{-a c}\, g \right) \sqrt{-a c}\, \sqrt{e g}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \left(c f +\sqrt{-a c}\, g \right) \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}}"," ",0,"1/2*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*a*e^2*g^2*(-a*c)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*e^2*f^2*(-a*c)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a^2*e^2*g^2*(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a*c*d^2*g^2*(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a*c*e^2*f^2*(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-2*ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a*d*e*g^2*(-a*c)^(1/2)*(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*c^2*d^2*f^2*(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-2*ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*c*d*e*f^2*(-a*c)^(1/2)*(e*g)^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a^2*e^2*g^2*(e*g)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a*c*d^2*g^2*(e*g)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a*c*e^2*f^2*(e*g)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-2*ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a*d*e*g^2*(-a*c)^(1/2)*(e*g)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*c^2*d^2*f^2*(e*g)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-2*ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*c*d*e*f^2*(-a*c)^(1/2)*(e*g)^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2))/((e*x+d)*(g*x+f))^(1/2)/(c*f-g*(-a*c)^(1/2))/(-a*c)^(1/2)/(e*g)^(1/2)/(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)/(g*(-a*c)^(1/2)+c*f)/((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)","B"
611,1,1387,176,0.033000," ","int((e*x+d)^(1/2)/(c*x^2+a)/(g*x+f)^(1/2),x)","\frac{\sqrt{e x +d}\, \sqrt{g x +f}\, \left(\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c d \,g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c d \,g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)+\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2} d \,f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2} d \,f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, a e \,g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, a e \,g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, c e \,f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)-\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, c e \,f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)\right)}{2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \left(c f -\sqrt{-a c}\, g \right) \sqrt{-a c}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \left(c f +\sqrt{-a c}\, g \right) \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}}"," ",0,"1/2*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a*c*d*g^2*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a*e*g^2*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2)+ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*c^2*d*f^2*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*c*e*f^2*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a*c*d*g^2*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a*e*g^2*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*c^2*d*f^2*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*c*e*f^2*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*(-a*c)^(1/2))/((e*x+d)*(g*x+f))^(1/2)/(c*f-(-a*c)^(1/2)*g)/(-a*c)^(1/2)/(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)/(c*f+(-a*c)^(1/2)*g)/((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)","B"
612,1,1415,170,0.042000," ","int(1/(e*x+d)^(1/2)/(c*x^2+a)/(g*x+f)^(1/2),x)","-\frac{\left(-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a^{2} e^{2} g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a^{2} e^{2} g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,d^{2} g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,d^{2} g^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,e^{2} f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, a c \,e^{2} f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)-\sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2} d^{2} f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f -2 \sqrt{-a c}\, e g x -\sqrt{-a c}\, d g -\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x +\sqrt{-a c}}\right)+\sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c^{2} d^{2} f^{2} \ln \left(\frac{c d g x +c e f x +2 c d f +2 \sqrt{-a c}\, e g x +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, c}{c x -\sqrt{-a c}}\right)\right) \sqrt{g x +f}\, \sqrt{e x +d}\, c^{2}}{2 \sqrt{\frac{-a e g +c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \left(c f +\sqrt{-a c}\, g \right) \left(c d +\sqrt{-a c}\, e \right) \sqrt{-\frac{a e g -c d f +\sqrt{-a c}\, d g +\sqrt{-a c}\, e f}{c}}\, \sqrt{-a c}\, \left(c f -\sqrt{-a c}\, g \right) \left(c d -\sqrt{-a c}\, e \right) \sqrt{\left(e x +d \right) \left(g x +f \right)}}"," ",0,"-1/2*c^2*(ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a^2*e^2*g^2*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a*c*d^2*g^2*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*a*c*e^2*f^2*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)+ln((c*d*g*x+c*e*f*x+2*c*d*f+2*(-a*c)^(1/2)*e*g*x+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x-(-a*c)^(1/2)))*c^2*d^2*f^2*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a^2*e^2*g^2*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a*c*d^2*g^2*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*a*c*e^2*f^2*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)-ln((c*d*g*x+c*e*f*x+2*c*d*f-2*(-a*c)^(1/2)*e*g*x-(-a*c)^(1/2)*d*g-(-a*c)^(1/2)*e*f+2*((e*x+d)*(g*x+f))^(1/2)*(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)*c)/(c*x+(-a*c)^(1/2)))*c^2*d^2*f^2*((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2))*(g*x+f)^(1/2)*(e*x+d)^(1/2)/((-a*e*g+c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)/(c*f+(-a*c)^(1/2)*g)/(c*d+(-a*c)^(1/2)*e)/(-(a*e*g-c*d*f+(-a*c)^(1/2)*d*g+(-a*c)^(1/2)*e*f)/c)^(1/2)/(-a*c)^(1/2)/(c*f-(-a*c)^(1/2)*g)/(c*d-(-a*c)^(1/2)*e)/((e*x+d)*(g*x+f))^(1/2)","B"
613,1,10977,270,0.093000," ","int(1/(e*x+d)^(3/2)/(c*x^2+a)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
614,1,8264,497,0.072000," ","int((e*x+d)^(3/2)/(g*x+f)^(3/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
615,1,5383,279,0.056000," ","int((e*x+d)^(1/2)/(g*x+f)^(3/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
616,1,10977,270,0.090000," ","int(1/(e*x+d)^(1/2)/(g*x+f)^(3/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
617,1,30656,433,0.227000," ","int(1/(e*x+d)^(3/2)/(g*x+f)^(3/2)/(c*x^2+a),x)","\text{output too large to display}"," ",0,"result too large to display","B"
618,1,305,45,0.174000," ","int(x^(1/2)/(x^2+1)/(x+1)^(1/2),x)","\frac{\sqrt{\frac{\left(x +1\right) x}{\left(x +\sqrt{2}-1\right)^{2}}}\, \left(x +\sqrt{2}-1\right) \left(4 \sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, \sqrt{\frac{\left(x +1\right) x}{\left(x +\sqrt{2}-1\right)^{2}}}}{\sqrt{1+\sqrt{2}}}\right)-6 \arctanh \left(\frac{\sqrt{2}\, \sqrt{\frac{\left(x +1\right) x}{\left(x +\sqrt{2}-1\right)^{2}}}}{\sqrt{1+\sqrt{2}}}\right)+\sqrt{-2+2 \sqrt{2}}\, \sqrt{1+\sqrt{2}}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{\left(3 \sqrt{2}-4\right) \left(x +1\right) \left(4+3 \sqrt{2}\right) x}{\left(x +\sqrt{2}-1\right)^{2}}}\, \sqrt{-2+2 \sqrt{2}}\, \left(3+2 \sqrt{2}\right) \left(-x +\sqrt{2}+1\right) \left(3 \sqrt{2}-4\right) \left(x +\sqrt{2}-1\right)}{4 \left(x +1\right) x}\right)-2 \sqrt{-2+2 \sqrt{2}}\, \sqrt{1+\sqrt{2}}\, \arctan \left(\frac{\sqrt{\frac{\left(3 \sqrt{2}-4\right) \left(x +1\right) \left(4+3 \sqrt{2}\right) x}{\left(x +\sqrt{2}-1\right)^{2}}}\, \sqrt{-2+2 \sqrt{2}}\, \left(3+2 \sqrt{2}\right) \left(-x +\sqrt{2}+1\right) \left(3 \sqrt{2}-4\right) \left(x +\sqrt{2}-1\right)}{4 \left(x +1\right) x}\right)\right) \sqrt{2}}{4 \sqrt{x +1}\, \left(3 \sqrt{2}-4\right) \sqrt{1+\sqrt{2}}\, \sqrt{x}}"," ",0,"1/4/x^(1/2)/(x+1)^(1/2)*(x*(x+1)/(2^(1/2)-1+x)^2)^(1/2)*(2^(1/2)-1+x)*((-2+2*2^(1/2))^(1/2)*arctan(1/4*((3*2^(1/2)-4)*x*(x+1)*(4+3*2^(1/2))/(2^(1/2)-1+x)^2)^(1/2)*(-2+2*2^(1/2))^(1/2)*(3+2*2^(1/2))*(2^(1/2)+1-x)*(3*2^(1/2)-4)*(2^(1/2)-1+x)/x/(x+1))*(1+2^(1/2))^(1/2)*2^(1/2)-2*(-2+2*2^(1/2))^(1/2)*arctan(1/4*((3*2^(1/2)-4)*x*(x+1)*(4+3*2^(1/2))/(2^(1/2)-1+x)^2)^(1/2)*(-2+2*2^(1/2))^(1/2)*(3+2*2^(1/2))*(2^(1/2)+1-x)*(3*2^(1/2)-4)*(2^(1/2)-1+x)/x/(x+1))*(1+2^(1/2))^(1/2)+4*arctanh(2^(1/2)*(x*(x+1)/(2^(1/2)-1+x)^2)^(1/2)/(1+2^(1/2))^(1/2))*2^(1/2)-6*arctanh(2^(1/2)*(x*(x+1)/(2^(1/2)-1+x)^2)^(1/2)/(1+2^(1/2))^(1/2)))*2^(1/2)/(3*2^(1/2)-4)/(1+2^(1/2))^(1/2)","B"
619,1,125,70,0.018000," ","int((g*x+f)^2*(-x^2+1)^(1/2)/(1-x)^4,x)","\left(-\arcsin \left(x \right)+\frac{\left(-2 x -\left(x -1\right)^{2}+2\right)^{\frac{3}{2}}}{\left(x -1\right)^{2}}+\sqrt{-2 x -\left(x -1\right)^{2}+2}\right) g^{2}+\frac{2 \left(f +g \right) \left(-2 x -\left(x -1\right)^{2}+2\right)^{\frac{3}{2}} g}{3 \left(x -1\right)^{3}}+\left(f^{2}+2 f g +g^{2}\right) \left(\frac{\left(-2 x -\left(x -1\right)^{2}+2\right)^{\frac{3}{2}}}{5 \left(x -1\right)^{4}}-\frac{\left(-2 x -\left(x -1\right)^{2}+2\right)^{\frac{3}{2}}}{15 \left(x -1\right)^{3}}\right)"," ",0,"2/3*g*(f+g)/(x-1)^3*(-(x-1)^2-2*x+2)^(3/2)+g^2*(1/(x-1)^2*(-(x-1)^2-2*x+2)^(3/2)+(-(x-1)^2-2*x+2)^(1/2)-arcsin(x))+(f^2+2*f*g+g^2)*(1/5/(x-1)^4*(-(x-1)^2-2*x+2)^(3/2)-1/15/(x-1)^3*(-(x-1)^2-2*x+2)^(3/2))","A"
620,1,1178,99,0.038000," ","int((-a^2*x^2+1)^(3/2)/(-a*x+1)^2/(d*x+c),x)","-\frac{a^{4} c^{4} \ln \left(\frac{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\frac{2 \left(a^{2} c^{2}-d^{2}\right)}{d^{2}}+2 \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, \sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}{x +\frac{c}{d}}\right)}{\left(a c +d \right)^{2} \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, d^{3}}-\frac{a^{4} c^{3} \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}\right)}{\left(a c +d \right)^{2} \sqrt{a^{2}}\, d^{2}}+\frac{2 a^{2} c^{2} \ln \left(\frac{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\frac{2 \left(a^{2} c^{2}-d^{2}\right)}{d^{2}}+2 \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, \sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}{x +\frac{c}{d}}\right)}{\left(a c +d \right)^{2} \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, d}+\frac{\sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, a^{2} c x}{2 \left(a c +d \right)^{2}}+\frac{3 a^{2} c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}\right)}{2 \left(a c +d \right)^{2} \sqrt{a^{2}}}-\frac{\sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, a^{2} c^{2}}{\left(a c +d \right)^{2} d}+\frac{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}\, a d x}{2 \left(a c +d \right)^{2}}+\frac{a d \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}}\right)}{2 \left(a c +d \right)^{2} \sqrt{a^{2}}}+\frac{3 \sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}\, a x}{2 \left(a c +d \right)}+\frac{3 a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a}}\right)}{2 \left(a c +d \right) \sqrt{a^{2}}}-\frac{d \ln \left(\frac{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\frac{2 \left(a^{2} c^{2}-d^{2}\right)}{d^{2}}+2 \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, \sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}{x +\frac{c}{d}}\right)}{\left(a c +d \right)^{2} \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}-\frac{\left(-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a \right)^{\frac{3}{2}} d}{3 \left(a c +d \right)^{2}}+\frac{\left(\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}\right)^{\frac{3}{2}} d}{3 \left(a c +d \right)^{2}}+\frac{\sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, d}{\left(a c +d \right)^{2}}-\frac{\left(-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a \right)^{\frac{5}{2}}}{\left(a c +d \right) \left(x -\frac{1}{a}\right)^{2} a^{2}}-\frac{\left(-\left(x -\frac{1}{a}\right)^{2} a^{2}-2 \left(x -\frac{1}{a}\right) a \right)^{\frac{3}{2}}}{a c +d}"," ",0,"-1/a^2/(a*c+d)/(x-1/a)^2*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(5/2)-1/(a*c+d)*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(3/2)+3/2*a/(a*c+d)*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)*x+3/2*a/(a*c+d)/(a^2)^(1/2)*arctan((a^2)^(1/2)/(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)*x)-1/3*d/(a*c+d)^2*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(3/2)+1/2*d/(a*c+d)^2*a*(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)*x+1/2*d/(a*c+d)^2*a/(a^2)^(1/2)*arctan((a^2)^(1/2)/(-(x-1/a)^2*a^2-2*(x-1/a)*a)^(1/2)*x)+1/3*d/(a*c+d)^2*(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(3/2)+1/2/(a*c+d)^2*a^2*c*(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(1/2)*x+3/2/(a*c+d)^2*a^2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(1/2))-1/d/(a*c+d)^2*(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(1/2)*a^2*c^2+d/(a*c+d)^2*(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(1/2)-1/d^2/(a*c+d)^2*a^4*c^3/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(1/2))-1/d^3/(a*c+d)^2/(-(a^2*c^2-d^2)/d^2)^(1/2)*ln((-2*(a^2*c^2-d^2)/d^2+2*a^2*c/d*(x+c/d)+2*(-(a^2*c^2-d^2)/d^2)^(1/2)*(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(1/2))/(x+c/d))*a^4*c^4+2/d/(a*c+d)^2/(-(a^2*c^2-d^2)/d^2)^(1/2)*ln((-2*(a^2*c^2-d^2)/d^2+2*a^2*c/d*(x+c/d)+2*(-(a^2*c^2-d^2)/d^2)^(1/2)*(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(1/2))/(x+c/d))*a^2*c^2-d/(a*c+d)^2/(-(a^2*c^2-d^2)/d^2)^(1/2)*ln((-2*(a^2*c^2-d^2)/d^2+2*a^2*c/d*(x+c/d)+2*(-(a^2*c^2-d^2)/d^2)^(1/2)*(-(x+c/d)^2*a^2+2*a^2*c/d*(x+c/d)-(a^2*c^2-d^2)/d^2)^(1/2))/(x+c/d))","B"
621,1,524,99,0.021000," ","int((a*x+1)^2/(d*x+c)/(-a^2*x^2+1)^(1/2),x)","-\frac{a^{2} c^{2} \ln \left(\frac{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\frac{2 \left(a^{2} c^{2}-d^{2}\right)}{d^{2}}+2 \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, \sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}{x +\frac{c}{d}}\right)}{\sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, d^{3}}-\frac{a^{2} c \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}\, d^{2}}+\frac{2 a c \ln \left(\frac{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\frac{2 \left(a^{2} c^{2}-d^{2}\right)}{d^{2}}+2 \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, \sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}{x +\frac{c}{d}}\right)}{\sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, d^{2}}+\frac{2 a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}\, d}-\frac{\ln \left(\frac{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\frac{2 \left(a^{2} c^{2}-d^{2}\right)}{d^{2}}+2 \sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, \sqrt{\frac{2 \left(x +\frac{c}{d}\right) a^{2} c}{d}-\left(x +\frac{c}{d}\right)^{2} a^{2}-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}}{x +\frac{c}{d}}\right)}{\sqrt{-\frac{a^{2} c^{2}-d^{2}}{d^{2}}}\, d}-\frac{\sqrt{-a^{2} x^{2}+1}}{d}"," ",0,"-(-a^2*x^2+1)^(1/2)/d-a^2/d^2*c/(a^2)^(1/2)*arctan((a^2)^(1/2)/(-a^2*x^2+1)^(1/2)*x)+2*a/d/(a^2)^(1/2)*arctan((a^2)^(1/2)/(-a^2*x^2+1)^(1/2)*x)-1/d^3/(-(a^2*c^2-d^2)/d^2)^(1/2)*ln((2*(x+c/d)*a^2*c/d-2*(a^2*c^2-d^2)/d^2+2*(-(a^2*c^2-d^2)/d^2)^(1/2)*(2*(x+c/d)*a^2*c/d-(x+c/d)^2*a^2-(a^2*c^2-d^2)/d^2)^(1/2))/(x+c/d))*a^2*c^2+2/d^2/(-(a^2*c^2-d^2)/d^2)^(1/2)*ln((2*(x+c/d)*a^2*c/d-2*(a^2*c^2-d^2)/d^2+2*(-(a^2*c^2-d^2)/d^2)^(1/2)*(2*(x+c/d)*a^2*c/d-(x+c/d)^2*a^2-(a^2*c^2-d^2)/d^2)^(1/2))/(x+c/d))*a*c-1/d/(-(a^2*c^2-d^2)/d^2)^(1/2)*ln((2*(x+c/d)*a^2*c/d-2*(a^2*c^2-d^2)/d^2+2*(-(a^2*c^2-d^2)/d^2)^(1/2)*(2*(x+c/d)*a^2*c/d-(x+c/d)^2*a^2-(a^2*c^2-d^2)/d^2)^(1/2))/(x+c/d))","B"
622,1,6457,761,0.161000," ","int((e*x+d)^3*(g*x+f)^(1/2)*(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
623,1,4351,551,0.038000," ","int((e*x+d)^2*(g*x+f)^(1/2)*(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"-2/315*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(24*a*c^2*d*e*f^3*g^3-60*a^2*c*d*e*f*g^5-35*x^6*c^3*e^2*g^6-63*x^4*c^3*d^2*g^6+42*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^3*e^2*g^6-42*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^3*e^2*g^6-16*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*e^2*f^6-168*x^2*a*c^2*d*e*f*g^5+6*x*a*c^2*d*e*f^2*g^4-90*x^5*c^3*d*e*g^6-60*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*e^2*f^2*g^4+84*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d^2*f^2*g^4-34*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*e^2*f^4*g^2+48*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d*e*f^5*g-60*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a^2*d*e*g^6+6*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a^2*e^2*f*g^5+126*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d^2*g^6-42*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d^2*f^4*g^2-40*x^5*c^3*e^2*f*g^5-49*x^4*a*c^2*e^2*g^6+x^4*c^3*e^2*f^2*g^4-84*x^3*c^3*d^2*f*g^5-2*x^3*c^3*e^2*f^3*g^3-14*x^2*a^2*c*e^2*g^6-63*x^2*a*c^2*d^2*g^6-21*x^2*c^3*d^2*f^2*g^4-8*x^2*c^3*e^2*f^4*g^2-126*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d^2*g^6-108*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*d*e*f^2*g^4+42*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*d^2*f^3*g^3+16*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*e^2*f^5*g+54*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*e^2*f^2*g^4-126*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d^2*f^2*g^4+12*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*e^2*f^4*g^2-62*x^3*a*c^2*e^2*f*g^5-8*a^2*c*e^2*f^2*g^4-21*a*c^2*d^2*f^2*g^4-8*a*c^2*e^2*f^4*g^2+6*x^3*c^3*d*e*f^2*g^4-7*x^2*a*c^2*e^2*f^2*g^4+24*x^2*c^3*d*e*f^3*g^3-60*x*a^2*c*d*e*g^6-22*x*a^2*c*e^2*f*g^5-84*x*a*c^2*d^2*f*g^5-2*x*a*c^2*e^2*f^3*g^3-108*x^4*c^3*d*e*f*g^5-150*x^3*a*c^2*d*e*g^6+96*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d*e*f*g^5+144*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d*e*f^3*g^3+42*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*d^2*f*g^5+22*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*e^2*f^3*g^3-48*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*d*e*f^4*g^2-36*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d*e*f*g^5-36*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d*e*f^3*g^3)/c^2/(c*g*x^3+c*f*x^2+a*g*x+a*f)/g^5","B"
624,1,2549,362,0.026000," ","int((e*x+d)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2),x)","-\frac{2 \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \left(-15 c^{3} e \,g^{5} x^{5}-21 c^{3} d \,g^{5} x^{4}-18 c^{3} e f \,g^{4} x^{4}-25 a \,c^{2} e \,g^{5} x^{3}-28 c^{3} d f \,g^{4} x^{3}+c^{3} e \,f^{2} g^{3} x^{3}-21 a \,c^{2} d \,g^{5} x^{2}-28 a \,c^{2} e f \,g^{4} x^{2}-7 c^{3} d \,f^{2} g^{3} x^{2}+4 c^{3} e \,f^{3} g^{2} x^{2}+42 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} c d \,g^{5} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-42 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} c d \,g^{5} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+16 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} c e f \,g^{4} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} c e f \,g^{4} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-10 a^{2} c e \,g^{5} x +28 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a \,c^{2} d \,f^{2} g^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-42 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a \,c^{2} d \,f^{2} g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-28 a \,c^{2} d f \,g^{4} x +24 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a \,c^{2} e \,f^{3} g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a \,c^{2} e \,f^{3} g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a \,c^{2} e \,f^{2} g^{3} x -14 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{3} d \,f^{4} g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+8 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{3} e \,f^{5} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-10 a^{2} c e f \,g^{4}-10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a^{2} e \,g^{5} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-7 a \,c^{2} d \,f^{2} g^{3}+4 a \,c^{2} e \,f^{3} g^{2}+14 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a c d f \,g^{4} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-18 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a c e \,f^{2} g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+14 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c^{2} d \,f^{3} g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-8 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c^{2} e \,f^{4} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{105 \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c^{2} g^{4}}"," ",0,"-2/105*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(4*a*c^2*e*f^3*g^2-10*a^2*c*e*f*g^4-7*a*c^2*d*f^2*g^3-21*x^4*c^3*d*g^5-15*x^5*c^3*e*g^5-18*x^4*c^3*e*f*g^4+14*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*d*f*g^4-18*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*e*f^2*g^3+8*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*e*f^5+24*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*e*f^3*g^2+14*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*d*f^3*g^2-8*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*e*f^4*g+16*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*e*f*g^4+28*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d*f^2*g^3-6*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*e*f*g^4-42*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d*f^2*g^3-6*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*e*f^3*g^2-10*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a^2*e*g^5-25*x^3*a*c^2*e*g^5-28*x^3*c^3*d*f*g^4+x^3*c^3*e*f^2*g^3-21*x^2*a*c^2*d*g^5-7*x^2*c^3*d*f^2*g^3+4*x^2*c^3*e*f^3*g^2-10*x*a^2*c*e*g^5+x*a*c^2*e*f^2*g^3-28*x^2*a*c^2*e*f*g^4-28*x*a*c^2*d*f*g^4+42*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d*g^5-14*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticE((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d*f^4*g-42*(-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2)*((-c*x+(-a*c)^(1/2))*g/(c*f+(-a*c)^(1/2)*g))^(1/2)*((c*x+(-a*c)^(1/2))*g/((-a*c)^(1/2)*g-c*f))^(1/2)*EllipticF((-(g*x+f)*c/((-a*c)^(1/2)*g-c*f))^(1/2),(-((-a*c)^(1/2)*g-c*f)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d*g^5)/(c*g*x^3+c*f*x^2+a*g*x+a*f)/g^4/c^2","B"
625,1,1162,290,0.022000," ","int((g*x+f)^(1/2)*(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \left(3 c^{2} g^{4} x^{4}+4 c^{2} f \,g^{3} x^{3}+3 a c \,g^{4} x^{2}+c^{2} f^{2} g^{2} x^{2}-6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} g^{4} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} g^{4} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-4 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,f^{2} g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,f^{2} g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+4 a c f \,g^{3} x +2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} f^{4} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a c \,f^{2} g^{2}-2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a f \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c \,f^{3} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{15 \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c \,g^{3}}"," ",0,"2/15*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(6*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*a^2*g^4+6*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*a*c*f^2*g^2-2*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*(-a*c)^(1/2)*a*f*g^3-2*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*(-a*c)^(1/2)*c*f^3*g-6*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*a^2*g^4-4*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*a*c*f^2*g^2+2*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*c^2*f^4+3*x^4*c^2*g^4+4*x^3*c^2*f*g^3+3*x^2*a*c*g^4+x^2*c^2*f^2*g^2+4*x*a*c*f*g^3+a*c*f^2*g^2)/c/(c*g*x^3+c*f*x^2+a*g*x+a*f)/g^3","B"
626,1,2496,556,0.047000," ","int((g*x+f)^(1/2)*(c*x^2+a)^(1/2)/(e*x+d),x)","-\frac{2 \left(-c^{2} e^{2} g^{3} x^{3}-c^{2} e^{2} f \,g^{2} x^{2}-3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d e \,g^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d e \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,e^{2} f \,g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,e^{2} f \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,e^{2} f \,g^{2} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-a c \,e^{2} g^{3} x -3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d^{2} f \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d^{2} f \,g^{2} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d e \,f^{2} g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d e \,f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} e^{2} f^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-a c \,e^{2} f \,g^{2}+2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a \,e^{2} g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a \,e^{2} g^{3} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c \,d^{2} g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c \,d^{2} g^{3} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c \,e^{2} f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right) \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}}{3 \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c \,e^{3} g^{2}}"," ",0,"-2/3*(2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e^2*g^3+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^2*g^3-(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e^2*f^2*g+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*g^3-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*g^3+(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g+(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e^2*f^3-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)*e/c/(d*g-e*f),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e^2*g^3-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)*e/c/(d*g-e*f),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^2*g^3+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)*e/c/(d*g-e*f),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)*e/c/(d*g-e*f),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2-x^3*c^2*e^2*g^3-x^2*c^2*e^2*f*g^2-x*a*c*e^2*g^3-a*c*e^2*f*g^2)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)/e^3/c/g^2/(c*g*x^3+c*f*x^2+a*g*x+a*f)","B"
627,1,6044,531,0.059000," ","int((g*x+f)^(1/2)*(c*x^2+a)^(1/2)/(e*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
628,1,19181,1009,0.100000," ","int((g*x+f)^(1/2)*(c*x^2+a)^(1/2)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
629,1,5079,582,0.058000," ","int((e*x+d)^3*(c*x^2+a)^(1/2)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
630,1,3278,430,0.035000," ","int((e*x+d)^2*(c*x^2+a)^(1/2)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"2/105*(c*x^2+a)^(1/2)*(g*x+f)^(1/2)*(35*a*c^2*d^2*f*g^4+10*a^2*c*e^2*f*g^4+24*a*c^2*e^2*f^3*g^2+15*x^5*c^3*e^2*g^5+35*x^3*c^3*d^2*g^5-56*a*c^2*d*e*f^2*g^3-3*x^4*c^3*e^2*f*g^4+25*x^3*a*c^2*e^2*g^5+42*x^4*c^3*d*e*g^5+84*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d*e*g^5-36*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*e^2*f*g^4-36*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*e^2*f^3*g^2+26*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*e^2*f*g^4+70*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d^2*f*g^4+74*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*e^2*f^3*g^2-112*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d*e*f^4*g+6*x^3*c^3*e^2*f^2*g^3+35*x^2*c^3*d^2*f*g^4+70*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d^2*f^3*g^2+24*x^2*c^3*e^2*f^3*g^2+10*x*a^2*c*e^2*g^5+35*x*a*c^2*d^2*g^5+112*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*d*e*f*g^4+48*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*e^2*f^5-14*x*a*c^2*d*e*f*g^4-70*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*d^2*g^5-70*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*d^2*f^2*g^3-48*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*e^2*f^4*g-84*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d*e*g^5+6*x*a*c^2*e^2*f^2*g^3+112*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*d*e*f^3*g^2+84*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d*e*f^2*g^3-38*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*e^2*f^2*g^3-196*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d*e*f^2*g^3+10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a^2*e^2*g^5-14*x^3*c^3*d*e*f*g^4+42*x^2*a*c^2*d*e*g^5+7*x^2*a*c^2*e^2*f*g^4-56*x^2*c^3*d*e*f^2*g^3)/g^5/(c*g*x^3+c*f*x^2+a*g*x+a*f)/c^2","B"
631,1,1828,298,0.025000," ","int((e*x+d)*(c*x^2+a)^(1/2)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{g x +f}\, \left(3 c^{2} e \,g^{4} x^{4}+5 c^{2} d \,g^{4} x^{3}-c^{2} e f \,g^{3} x^{3}+3 a c e \,g^{4} x^{2}+5 c^{2} d f \,g^{3} x^{2}-4 c^{2} e \,f^{2} g^{2} x^{2}-6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} e \,g^{4} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} e \,g^{4} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d f \,g^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+5 a c d \,g^{4} x -14 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c e \,f^{2} g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c e \,f^{2} g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-a c e f \,g^{3} x +10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d \,f^{3} g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-8 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} e \,f^{4} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+5 a c d f \,g^{3}-4 a c e \,f^{2} g^{2}-10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a d \,g^{4} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+8 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a e f \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c d \,f^{2} g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+8 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c e \,f^{3} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{15 \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c \,g^{4}}"," ",0,"2/15*(c*x^2+a)^(1/2)*(g*x+f)^(1/2)*(6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*e*g^4+6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e*f^2*g^2-10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*d*g^4+8*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e*f*g^3-10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d*f^2*g^2+8*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e*f^3*g-6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*e*g^4+10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*f*g^3-14*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e*f^2*g^2+10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*f^3*g-8*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e*f^4+3*x^4*c^2*e*g^4+5*x^3*c^2*d*g^4-x^3*c^2*e*f*g^3+3*x^2*a*c*e*g^4+5*x^2*c^2*d*f*g^3-4*x^2*c^2*e*f^2*g^2+5*x*a*c*d*g^4-x*a*c*e*f*g^3+5*a*c*d*f*g^3-4*a*c*e*f^2*g^2)/c/(c*g*x^3+c*f*x^2+a*g*x+a*f)/g^4","B"
632,1,688,256,0.020000," ","int((c*x^2+a)^(1/2)/(g*x+f)^(1/2),x)","-\frac{2 \sqrt{c \,x^{2}+a}\, \sqrt{g x +f}\, \left(-c^{2} g^{3} x^{3}-c^{2} f \,g^{2} x^{2}-2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c f \,g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-a c \,g^{3} x -2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} f^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-a c f \,g^{2}+2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c \,f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{3 \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c \,g^{3}}"," ",0,"-2/3*(c*x^2+a)^(1/2)*(g*x+f)^(1/2)*(2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*g^3+2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*f^2*g-2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*f*g^2-2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*f^3-x^3*c^2*g^3-x^2*c^2*f*g^2-x*a*c*g^3-a*c*f*g^2)/c/(c*g*x^3+c*f*x^2+a*g*x+a*f)/g^3","B"
633,1,1216,386,0.033000," ","int((c*x^2+a)^(1/2)/(e*x+d)/(g*x+f)^(1/2),x)","\frac{2 \left(-a c d e \,g^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a c d e \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a c \,e^{2} f \,g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-a c \,e^{2} f \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a c \,e^{2} f \,g^{2} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-c^{2} d^{2} f \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+c^{2} d^{2} f \,g^{2} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-c^{2} d e \,f^{2} g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+c^{2} d e \,f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+c^{2} e^{2} f^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-a c}\, a \,e^{2} g^{3} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-a c}\, c \,d^{2} g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-a c}\, c \,d^{2} g^{3} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-a c}\, c \,e^{2} f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right) \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}}{\left(d g -e f \right) \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c \,e^{2} g^{2}}"," ",0,"2*(EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^2*g^3-EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e^2*f^2*g+EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*g^3-EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2+EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g-EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*g^3+EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g+EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e^2*f^3-EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e^2*g^3-EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^2*g^3+EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2+EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)/e^2/c/g^2/(d*g-e*f)/(c*g*x^3+c*f*x^2+a*g*x+a*f)","B"
634,1,6034,575,0.039000," ","int((c*x^2+a)^(1/2)/(e*x+d)^2/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
635,1,19187,1045,0.078000," ","int((c*x^2+a)^(1/2)/(e*x+d)^3/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
636,1,3924,453,0.056000," ","int((e*x+d)^3*(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"2/105*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(-25*a^2*c*e^3*f*g^4-4*a*c^2*e^3*f^3*g^2+15*x^5*c^3*e^3*g^5+84*x*a*c^2*d*e^2*f*g^4-8*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*e^3*f^5-42*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*d*e^2*f*g^4-189*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d*e^2*f^2*g^3+105*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*d^2*e*g^5-17*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*c*e^3*f^2*g^3-105*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d^2*e*f*g^4+231*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d*e^2*f^2*g^3+105*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*d^2*e*f^2*g^3-42*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*d*e^2*f^3*g^2-105*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d^3*g^5+6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*e^3*f^3*g^2+8*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c^2*e^3*f^4*g+11*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*e^3*f^3*g^2-105*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d^2*e*f^3*g^2+42*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d*e^2*f^4*g+19*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*e^3*f*g^4+189*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d*e^2*g^5-189*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*d*e^2*g^5+6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*c*e^3*f*g^4+63*x^4*c^3*d*e^2*g^5+63*x^2*a*c^2*d*e^2*g^5-7*x^2*a*c^2*e^3*f*g^4+105*x^2*c^3*d^2*e*f*g^4+21*x^2*c^3*d*e^2*f^2*g^3+105*x*a*c^2*d^2*e*g^5-x*a*c^2*e^3*f^2*g^3+84*x^3*c^3*d*e^2*f*g^4-105*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d^3*f^2*g^3+105*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c^2*d^3*g^5-25*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a^2*e^3*g^5+105*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^3*d^3*f^2*g^3+21*a*c^2*d*e^2*f^2*g^3+105*a*c^2*d^2*e*f*g^4+18*x^4*c^3*e^3*f*g^4-10*x^3*a*c^2*e^3*g^5+105*x^3*c^3*d^2*e*g^5-x^3*c^3*e^3*f^2*g^3-4*x^2*c^3*e^3*f^3*g^2-25*x*a^2*c*e^3*g^5)/(c*g*x^3+c*f*x^2+a*g*x+a*f)/c^3/g^4","B"
637,1,2470,338,0.049000," ","int((e*x+d)^2*(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","-\frac{2 \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \left(-3 c^{2} e^{2} g^{4} x^{4}-10 c^{2} d e \,g^{4} x^{3}-4 c^{2} e^{2} f \,g^{3} x^{3}-3 a c \,e^{2} g^{4} x^{2}-10 c^{2} d e f \,g^{3} x^{2}-c^{2} e^{2} f^{2} g^{2} x^{2}-9 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} e^{2} g^{4} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+9 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a^{2} e^{2} g^{4} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+15 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,d^{2} g^{4} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-15 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,d^{2} g^{4} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d e f \,g^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-10 a c d e \,g^{4} x -11 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,e^{2} f^{2} g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+9 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,e^{2} f^{2} g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-4 a c \,e^{2} f \,g^{3} x +15 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d^{2} f^{2} g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-15 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d^{2} f^{2} g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d e \,f^{3} g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} e^{2} f^{4} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-10 a c d e f \,g^{3}-a c \,e^{2} f^{2} g^{2}-10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a d e \,g^{4} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a \,e^{2} f \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-10 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c d e \,f^{2} g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c \,e^{2} f^{3} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{15 \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c^{2} g^{3}}"," ",0,"-2/15*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(-10*a*c*d*e*f*g^3-3*x^4*c^2*e^2*g^4-15*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d^2*g^4-a*c*e^2*f^2*g^2+9*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*e^2*g^4-9*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*e^2*g^4-2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e^2*f^4+9*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f^2*g^2-11*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f^2*g^2+10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^3*g-10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*d*e*g^4+2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e^2*f*g^3-15*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f^2*g^2+15*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d^2*g^4+15*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f^2*g^2+10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*f*g^3-10*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d*e*f^2*g^2+2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e^2*f^3*g-10*x^3*c^2*d*e*g^4-4*x*a*c*e^2*f*g^3-10*x*a*c*d*e*g^4-10*x^2*c^2*d*e*f*g^3-4*x^3*c^2*e^2*f*g^3-3*x^2*a*c*e^2*g^4-x^2*c^2*e^2*f^2*g^2)/c^2/(c*g*x^3+c*f*x^2+a*g*x+a*f)/g^3","B"
638,1,1286,265,0.039000," ","int((e*x+d)*(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \left(c^{2} e \,g^{3} x^{3}+c^{2} e f \,g^{2} x^{2}-3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d \,g^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c e f \,g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a c e \,g^{3} x -3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d \,f^{2} g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d \,f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} e \,f^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a c e f \,g^{2}+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a e \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c e \,f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{3 \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c^{2} g^{2}}"," ",0,"2/3*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e*g^3+(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e*f^2*g+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*g^3+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*f^2*g-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*g^3-(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e*f*g^2-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*f^2*g-(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e*f^3+x^3*c^2*e*g^3+x^2*c^2*e*f*g^2+x*a*c*e*g^3+a*c*e*f*g^2)/(c*g*x^3+c*f*x^2+a*g*x+a*f)/c^2/g^2","B"
639,1,396,108,0.036000," ","int((g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \left(c f -\sqrt{-a c}\, g \right) \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \left(-c f \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+c f \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-a c}\, g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-a c}\, g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{\left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c^{2} g}"," ",0,"2*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(c*f-(-a*c)^(1/2)*g)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((-a*c)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*g+f*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c-EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*g-EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*f)/g/(c*g*x^3+c*f*x^2+a*g*x+a*f)/c^2","B"
640,1,439,260,0.048000," ","int((g*x+f)^(1/2)/(e*x+d)/(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \left(c f \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-c f \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-a c}\, g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-a c}\, g \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{\left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c e}"," ",0,"2*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*(f*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c-(-a*c)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*g-EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*f+EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*g)/c/e/(c*g*x^3+c*f*x^2+a*g*x+a*f)","A"
641,1,5743,579,0.058000," ","int((g*x+f)^(1/2)/(e*x+d)^2/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
642,1,20359,1050,0.101000," ","int((g*x+f)^(1/2)/(e*x+d)^3/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
643,1,3164,493,0.054000," ","int((g*x+f)^(5/2)/(e*x+d)/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"-2/3*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*g^3-6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e^2*g^3-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2+9*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g-9*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e^2*f^3+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^2*g^3-6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d*e*f*g^2+2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e^2*f^2*g-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*g^3+7*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g+7*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e^2*f^3+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2-6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e^2*f^3-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^2*g^3+6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d*e*f*g^2-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e^2*f^2*g-c^2*e^2*g^3*x^3-c^2*e^2*f*g^2*x^2-a*c*e^2*g^3*x-a*c*e^2*f*g^2)/e^3/c^2/(c*g*x^3+c*f*x^2+a*g*x+a*f)","B"
644,1,959,382,0.048000," ","int((g*x+f)^(3/2)/(e*x+d)/(c*x^2+a)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \left(-a e \,g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a e \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-c d f g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+c d f g \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-c e \,f^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+2 c e \,f^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-c e \,f^{2} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-a c}\, d \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-a c}\, d \,g^{2} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-a c}\, e f g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-a c}\, e f g \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right)}{\left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c \,e^{2}}"," ",0,"2*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)/c*(EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*d*g^2-EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*e*f*g+EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*e*g^2-EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*d*f*g+2*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*e*f^2-EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*e*g^2-EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*e*f^2-EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*d*g^2+EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*e*f*g+EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*d*f*g-EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*e*f^2)/e^2/(c*g*x^3+c*f*x^2+a*g*x+a*f)","B"
645,1,2949,385,0.057000," ","int((e*x+d)^3/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"-2/15*(4*a*c*e^3*f^2*g^2-45*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^2*e*f*g^3+30*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d*e^2*f^2*g^2+45*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e^2*f*g^3-30*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e^2*f*g^3-3*x^4*c^2*e^3*g^4-15*x^2*c^2*d*e^2*f*g^3+15*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^3*g^4+45*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*e*f^2*g^2-30*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e^2*f^3*g-15*x*a*c*d*e^2*g^4+x*a*c*e^3*f*g^3-15*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*d*e^2*g^4+7*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e^3*f*g^3-8*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e^3*f^3*g-45*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d^2*e*g^4-6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^3*f^2*g^2+45*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d^2*e*g^4-(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^3*f^2*g^2-15*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^3*f*g^3-15*x^3*c^2*d*e^2*g^4+x^3*c^2*e^3*f*g^3-3*x^2*a*c*e^3*g^4+4*x^2*c^2*e^3*f^2*g^2+9*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*e^3*g^4-9*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a^2*e^3*g^4+8*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e^3*f^4-15*a*c*d*e^2*f*g^3)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)/c^2/g^4/(c*g*x^3+c*f*x^2+a*g*x+a*f)","B"
646,1,1769,290,0.050000," ","int((e*x+d)^2/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \left(c^{2} e^{2} g^{3} x^{3}+c^{2} e^{2} f \,g^{2} x^{2}-6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d e \,g^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d e \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,e^{2} f \,g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c \,e^{2} f \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a c \,e^{2} g^{3} x +3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d^{2} f \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d e \,f^{2} g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} e^{2} f^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a c \,e^{2} f \,g^{2}+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, a \,e^{2} g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-3 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c \,d^{2} g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+6 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c d e f \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-2 \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{-a c}\, c \,e^{2} f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right) \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}}{3 \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c^{2} g^{3}}"," ",0,"2/3*((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*a*e^2*g^3-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d^2*g^3+6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*d*e*f*g^2-2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*c*e^2*f^2*g+6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*g^3-3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2+3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2-6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*e*g^3+2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-6*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g+2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e^2*f^3+c^2*e^2*g^3*x^3+c^2*e^2*f*g^2*x^2+a*c*e^2*g^3*x+a*c*e^2*f*g^2)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)/c^2/g^3/(c*g*x^3+c*f*x^2+a*g*x+a*f)","B"
647,1,520,232,0.043000," ","int((e*x+d)/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \left(-a e \,g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+a e \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+c d f g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-c e \,f^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-a c}\, d \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-a c}\, e f g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right) \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}}{\left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c \,g^{2}}"," ",0,"2*(EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*e*g^2+EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*d*f*g-EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*d*g^2+EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*(-a*c)^(1/2)*e*f*g-EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*e*g^2-EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*e*f^2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)/c/g^2/(c*g*x^3+c*f*x^2+a*g*x+a*f)","B"
648,1,200,108,0.041000," ","int(1/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \left(c f -\sqrt{-a c}\, g \right) \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)}{\left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c g}"," ",0,"2*(c*f-(-a*c)^(1/2)*g)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)/g/c/(c*g*x^3+c*f*x^2+a*g*x+a*f)","A"
649,1,235,136,0.050000," ","int(1/(e*x+d)/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \left(c f -\sqrt{-a c}\, g \right) \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{c \,x^{2}+a}\, \sqrt{g x +f}\, \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)}{\left(d g -e f \right) \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c}"," ",0,"2*(c*f-(-a*c)^(1/2)*g)*EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*(c*x^2+a)^(1/2)*(g*x+f)^(1/2)/c/(d*g-e*f)/(c*g*x^3+c*f*x^2+a*g*x+a*f)","A"
650,1,5738,627,0.062000," ","int(1/(e*x+d)^2/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
651,1,20366,1061,0.131000," ","int(1/(e*x+d)^3/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
652,1,2011,324,0.084000," ","int(1/(e*x+d)/(g*x+f)^(3/2)/(c*x^2+a)^(1/2),x)","\frac{2 \left(-c^{2} d \,g^{3} x^{2}+c^{2} e f \,g^{2} x^{2}-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d \,g^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c d \,g^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c e f \,g^{2} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c e f \,g^{2} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a c e f \,g^{2} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d \,f^{2} g \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} d \,f^{2} g \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} e \,f^{3} \EllipticE \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} e \,f^{3} \EllipticF \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c^{2} e \,f^{3} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)-a c d \,g^{3}+a c e f \,g^{2}+\sqrt{-a c}\, \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, a e \,g^{3} \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)+\sqrt{-a c}\, \sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(-c x +\sqrt{-a c}\right) g}{c f +\sqrt{-a c}\, g}}\, \sqrt{\frac{\left(c x +\sqrt{-a c}\right) g}{-c f +\sqrt{-a c}\, g}}\, c e \,f^{2} g \EllipticPi \left(\sqrt{-\frac{\left(g x +f \right) c}{-c f +\sqrt{-a c}\, g}}, \frac{\left(-c f +\sqrt{-a c}\, g \right) e}{\left(d g -e f \right) c}, \sqrt{-\frac{-c f +\sqrt{-a c}\, g}{c f +\sqrt{-a c}\, g}}\right)\right) \sqrt{c \,x^{2}+a}\, \sqrt{g x +f}}{\left(d g -e f \right)^{2} \left(a \,g^{2}+c \,f^{2}\right) \left(c g \,x^{3}+c f \,x^{2}+a g x +a f \right) c}"," ",0,"2*((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*g^3-EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e*f*g^2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)+(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*f^2*g-EllipticF((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e*f^3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)-(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*d*g^3+(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e*f*g^2-(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*d*f^2*g+(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)*EllipticE((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e*f^3-EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*c*e*f*g^2*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)+EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*a*e*g^3*(-a*c)^(1/2)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)-EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c^2*e*f^3*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)+EllipticPi((-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2),(-c*f+(-a*c)^(1/2)*g)/(d*g-e*f)/c*e,(-(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g))^(1/2))*c*e*f^2*g*(-a*c)^(1/2)*(-(g*x+f)/(-c*f+(-a*c)^(1/2)*g)*c)^(1/2)*((-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)*g)^(1/2)*((c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)*g)^(1/2)-x^2*c^2*d*g^3+c^2*e*f*g^2*x^2-a*c*d*g^3+a*c*e*f*g^2)*(c*x^2+a)^(1/2)*(g*x+f)^(1/2)/c/(d*g-e*f)^2/(a*g^2+c*f^2)/(c*g*x^3+c*f*x^2+a*g*x+a*f)","B"
653,1,9409,683,0.116000," ","int(1/(e*x+d)/(g*x+f)^(5/2)/(c*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
654,1,215,95,0.116000," ","int(1/(e*x+d)/(g*x+f)^(1/2)/(c*x^2+1)^(1/2),x)","\frac{2 \left(\sqrt{-c}\, f +g \right) \sqrt{-\frac{\left(\sqrt{-c}\, x -1\right) g}{\sqrt{-c}\, f +g}}\, \sqrt{-\frac{\left(\sqrt{-c}\, x +1\right) g}{\sqrt{-c}\, f -g}}\, \sqrt{\frac{\left(g x +f \right) \sqrt{-c}}{\sqrt{-c}\, f +g}}\, \sqrt{c \,x^{2}+1}\, \sqrt{g x +f}\, \EllipticPi \left(\sqrt{\frac{\left(g x +f \right) \sqrt{-c}}{\sqrt{-c}\, f +g}}, -\frac{\left(\sqrt{-c}\, f +g \right) e}{\sqrt{-c}\, \left(d g -e f \right)}, \sqrt{\frac{\sqrt{-c}\, f +g}{\sqrt{-c}\, f -g}}\right)}{\sqrt{-c}\, \left(d g -e f \right) \left(c g \,x^{3}+c f \,x^{2}+g x +f \right)}"," ",0,"2*(g+f*(-c)^(1/2))/(-c)^(1/2)*EllipticPi(((g*x+f)*(-c)^(1/2)/(g+f*(-c)^(1/2)))^(1/2),-(g+f*(-c)^(1/2))*e/(-c)^(1/2)/(d*g-e*f),((g+f*(-c)^(1/2))/(f*(-c)^(1/2)-g))^(1/2))*(-(x*(-c)^(1/2)-1)*g/(g+f*(-c)^(1/2)))^(1/2)*(-(x*(-c)^(1/2)+1)*g/(f*(-c)^(1/2)-g))^(1/2)*((g*x+f)*(-c)^(1/2)/(g+f*(-c)^(1/2)))^(1/2)*(c*x^2+1)^(1/2)*(g*x+f)^(1/2)/(d*g-e*f)/(c*g*x^3+c*f*x^2+g*x+f)","B"
655,1,433,520,0.203000," ","int(1/(e*x+d)^(1/2)/(g*x+f)^(1/2)/(c*x^2+a)^(1/2),x)","\frac{2 \left(c \,e^{2} f \,x^{2}+2 c d e f x -\sqrt{-a c}\, e^{2} g \,x^{2}+c \,d^{2} f -2 \sqrt{-a c}\, d e g x -\sqrt{-a c}\, d^{2} g \right) \sqrt{\frac{\left(d g -e f \right) \left(c x +\sqrt{-a c}\right)}{\left(-c f +\sqrt{-a c}\, g \right) \left(e x +d \right)}}\, \sqrt{\frac{\left(d g -e f \right) \left(-c x +\sqrt{-a c}\right)}{\left(c f +\sqrt{-a c}\, g \right) \left(e x +d \right)}}\, \sqrt{\frac{\left(-c d +\sqrt{-a c}\, e \right) \left(g x +f \right)}{\left(-c f +\sqrt{-a c}\, g \right) \left(e x +d \right)}}\, \sqrt{e x +d}\, \sqrt{g x +f}\, \sqrt{c \,x^{2}+a}\, \EllipticF \left(\sqrt{\frac{\left(-c d +\sqrt{-a c}\, e \right) \left(g x +f \right)}{\left(-c f +\sqrt{-a c}\, g \right) \left(e x +d \right)}}, \sqrt{\frac{\left(c d +\sqrt{-a c}\, e \right) \left(-c f +\sqrt{-a c}\, g \right)}{\left(c f +\sqrt{-a c}\, g \right) \left(-c d +\sqrt{-a c}\, e \right)}}\right)}{\sqrt{-\frac{\left(g x +f \right) \left(e x +d \right) \left(-c x +\sqrt{-a c}\right) \left(c x +\sqrt{-a c}\right)}{c}}\, \left(d g -e f \right) \left(c d -\sqrt{-a c}\, e \right) \sqrt{c e g \,x^{4}+c d g \,x^{3}+c e f \,x^{3}+a e g \,x^{2}+c d f \,x^{2}+a d g x +a e f x +a d f}}"," ",0,"2*(c*e^2*f*x^2-(-a*c)^(1/2)*x^2*e^2*g+2*c*d*e*f*x-2*(-a*c)^(1/2)*x*d*e*g+c*d^2*f-(-a*c)^(1/2)*d^2*g)*EllipticF((((-a*c)^(1/2)*e-c*d)*(g*x+f)/(-c*f+(-a*c)^(1/2)*g)/(e*x+d))^(1/2),((c*d+(-a*c)^(1/2)*e)*(-c*f+(-a*c)^(1/2)*g)/(c*f+(-a*c)^(1/2)*g)/((-a*c)^(1/2)*e-c*d))^(1/2))*((d*g-e*f)*(c*x+(-a*c)^(1/2))/(-c*f+(-a*c)^(1/2)*g)/(e*x+d))^(1/2)*((d*g-e*f)*(-c*x+(-a*c)^(1/2))/(c*f+(-a*c)^(1/2)*g)/(e*x+d))^(1/2)*(((-a*c)^(1/2)*e-c*d)*(g*x+f)/(-c*f+(-a*c)^(1/2)*g)/(e*x+d))^(1/2)*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(c*x^2+a)^(1/2)/(-1/c*(g*x+f)*(e*x+d)*(-c*x+(-a*c)^(1/2))*(c*x+(-a*c)^(1/2)))^(1/2)/(d*g-e*f)/(c*d-(-a*c)^(1/2)*e)/(c*e*g*x^4+c*d*g*x^3+c*e*f*x^3+a*e*g*x^2+c*d*f*x^2+a*d*g*x+a*e*f*x+a*d*f)^(1/2)","A"
656,1,58,43,0.030000," ","int(1/(x-1)^(1/2)/(x+1)^(1/2)/(2*x^2-1)^(1/2),x)","\frac{\sqrt{x -1}\, \sqrt{x +1}\, \sqrt{2 x^{2}-1}\, \sqrt{-x^{2}+1}\, \sqrt{-2 x^{2}+1}\, \EllipticF \left(x , \sqrt{2}\right)}{2 x^{4}-3 x^{2}+1}"," ",0,"(x-1)^(1/2)*(x+1)^(1/2)*(2*x^2-1)^(1/2)/(2*x^4-3*x^2+1)*(-x^2+1)^(1/2)*(-2*x^2+1)^(1/2)*EllipticF(x,2^(1/2))","A"
657,1,188,245,0.009000," ","int((g*x+f)^3*(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-5 g^{3} x^{3} c^{3} d^{3}+6 a \,c^{2} d^{2} e \,g^{3} x^{2}-21 c^{3} d^{3} f \,g^{2} x^{2}-8 a^{2} c d \,e^{2} g^{3} x +28 a \,c^{2} d^{2} e f \,g^{2} x -35 c^{3} d^{3} f^{2} g x +16 a^{3} e^{3} g^{3}-56 a^{2} c d \,e^{2} f \,g^{2}+70 a \,c^{2} d^{2} e \,f^{2} g -35 f^{3} c^{3} d^{3}\right) \sqrt{e x +d}}{35 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{4} d^{4}}"," ",0,"-2/35*(c*d*x+a*e)*(-5*c^3*d^3*g^3*x^3+6*a*c^2*d^2*e*g^3*x^2-21*c^3*d^3*f*g^2*x^2-8*a^2*c*d*e^2*g^3*x+28*a*c^2*d^2*e*f*g^2*x-35*c^3*d^3*f^2*g*x+16*a^3*e^3*g^3-56*a^2*c*d*e^2*f*g^2+70*a*c^2*d^2*e*f^2*g-35*c^3*d^3*f^3)*(e*x+d)^(1/2)/c^4/d^4/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
658,1,116,182,0.008000," ","int((g*x+f)^2*(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(3 g^{2} x^{2} c^{2} d^{2}-4 a c d e \,g^{2} x +10 c^{2} d^{2} f g x +8 a^{2} e^{2} g^{2}-20 a c d e f g +15 f^{2} c^{2} d^{2}\right) \sqrt{e x +d}}{15 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{3} d^{3}}"," ",0,"2/15*(c*d*x+a*e)*(3*c^2*d^2*g^2*x^2-4*a*c*d*e*g^2*x+10*c^2*d^2*f*g*x+8*a^2*e^2*g^2-20*a*c*d*e*f*g+15*c^2*d^2*f^2)*(e*x+d)^(1/2)/c^3/d^3/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
659,1,67,113,0.007000," ","int((g*x+f)*(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-c d g x +2 a e g -3 c d f \right) \sqrt{e x +d}}{3 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{2} d^{2}}"," ",0,"-2/3*(c*d*x+a*e)*(-c*d*g*x+2*a*e*g-3*c*d*f)*(e*x+d)^(1/2)/c^2/d^2/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
660,1,50,42,0.005000," ","int((e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{2 \left(c d x +a e \right) \sqrt{e x +d}}{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c d}"," ",0,"2*(c*d*x+a*e)*(e*x+d)^(1/2)/c/d/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
661,1,87,68,0.030000," ","int((e*x+d)^(1/2)/(g*x+f)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}}"," ",0,"-2/(e*x+d)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*arctanh(g*(c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2))","A"
662,1,168,124,0.023000," ","int((e*x+d)^(1/2)/(g*x+f)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(c d g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+c d f \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\right)}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(a e g -c d f \right) \left(g x +f \right) \sqrt{\left(a e g -c d f \right) g}}"," ",0,"(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c*d*g+arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c*d*f-(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2))/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/(a*e*g-c*d*f)/(g*x+f)/((a*e*g-c*d*f)*g)^(1/2)","A"
663,1,285,187,0.023000," ","int((e*x+d)^(1/2)/(g*x+f)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{2} d^{2} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+6 c^{2} d^{2} f g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 c^{2} d^{2} f^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d g x +2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a e g -5 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d f \right)}{4 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(a e g -c d f \right)^{2} \left(g x +f \right)^{2} \sqrt{\left(a e g -c d f \right) g}}"," ",0,"-1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^2*d^2*g^2+6*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^2*d^2*f*g+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^2*d^2*f^2-3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*x*c*d*g+2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*e*g-5*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*f)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/(a*e*g-c*d*f)^2/(g*x+f)^2/((a*e*g-c*d*f)*g)^(1/2)","A"
664,1,450,248,0.024000," ","int((e*x+d)^(1/2)/(g*x+f)^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{3} d^{3} g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+45 c^{3} d^{3} f \,g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+45 c^{3} d^{3} f^{2} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 c^{3} d^{3} f^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} g^{2} x^{2}+10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e \,g^{2} x -40 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f g x -8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} e^{2} g^{2}+26 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e f g -33 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f^{2}\right)}{24 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(a e g -c d f \right)^{3} \left(g x +f \right)^{3} \sqrt{\left(a e g -c d f \right) g}}"," ",0,"1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^3*d^3*g^3+45*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^3*d^3*f*g^2+45*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^3*f^2*g+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^3*f^3-15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*x^2*c^2*d^2*g^2+10*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*x*a*c*d*e*g^2-40*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*x*c^2*d^2*f*g-8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^2*g^2+26*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*f*g-33*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/(a*e*g-c*d*f)^3/(g*x+f)^3/((a*e*g-c*d*f)*g)^(1/2)","A"
665,1,187,235,0.009000," ","int((e*x+d)^(3/2)*(g*x+f)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(g^{3} x^{3} c^{3} d^{3}-2 a \,c^{2} d^{2} e \,g^{3} x^{2}+5 c^{3} d^{3} f \,g^{2} x^{2}+8 a^{2} c d \,e^{2} g^{3} x -20 a \,c^{2} d^{2} e f \,g^{2} x +15 c^{3} d^{3} f^{2} g x +16 a^{3} e^{3} g^{3}-40 a^{2} c d \,e^{2} f \,g^{2}+30 a \,c^{2} d^{2} e \,f^{2} g -5 f^{3} c^{3} d^{3}\right) \left(e x +d \right)^{\frac{3}{2}}}{5 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}} c^{4} d^{4}}"," ",0,"2/5*(c*d*x+a*e)*(c^3*d^3*g^3*x^3-2*a*c^2*d^2*e*g^3*x^2+5*c^3*d^3*f*g^2*x^2+8*a^2*c*d*e^2*g^3*x-20*a*c^2*d^2*e*f*g^2*x+15*c^3*d^3*f^2*g*x+16*a^3*e^3*g^3-40*a^2*c*d*e^2*f*g^2+30*a*c^2*d^2*e*f^2*g-5*c^3*d^3*f^3)*(e*x+d)^(3/2)/c^4/d^4/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
666,1,116,165,0.007000," ","int((e*x+d)^(3/2)*(g*x+f)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-g^{2} x^{2} c^{2} d^{2}+4 a c d e \,g^{2} x -6 c^{2} d^{2} f g x +8 a^{2} e^{2} g^{2}-12 a c d e f g +3 f^{2} c^{2} d^{2}\right) \left(e x +d \right)^{\frac{3}{2}}}{3 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}} c^{3} d^{3}}"," ",0,"-2/3*(c*d*x+a*e)*(-c^2*d^2*g^2*x^2+4*a*c*d*e*g^2*x-6*c^2*d^2*f*g*x+8*a^2*e^2*g^2-12*a*c*d*e*f*g+3*c^2*d^2*f^2)*(e*x+d)^(3/2)/c^3/d^3/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
667,1,66,142,0.007000," ","int((e*x+d)^(3/2)*(g*x+f)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(c d g x +2 a e g -c d f \right) \left(e x +d \right)^{\frac{3}{2}}}{\left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}} c^{2} d^{2}}"," ",0,"2*(c*d*x+a*e)*(c*d*g*x+2*a*e*g-c*d*f)*(e*x+d)^(3/2)/c^2/d^2/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
668,1,50,42,0.003000," ","int((e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(e x +d \right)^{\frac{3}{2}}}{\left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}} c d}"," ",0,"-2*(c*d*x+a*e)*(e*x+d)^(3/2)/c/d/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
669,1,128,117,0.026000," ","int((e*x+d)^(3/2)/(g*x+f)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(\sqrt{c d x +a e}\, g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-\sqrt{\left(a e g -c d f \right) g}\right)}{\sqrt{e x +d}\, \left(c d x +a e \right) \left(a e g -c d f \right) \sqrt{\left(a e g -c d f \right) g}}"," ",0,"-2*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(g*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)-((a*e*g-c*d*f)*g)^(1/2))/(e*x+d)^(1/2)/(c*d*x+a*e)/(a*e*g-c*d*f)/((a*e*g-c*d*f)*g)^(1/2)","A"
670,1,225,182,0.030000," ","int((e*x+d)^(3/2)/(g*x+f)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 \sqrt{c d x +a e}\, c d \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 \sqrt{c d x +a e}\, c d f g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 \sqrt{\left(a e g -c d f \right) g}\, c d g x -\sqrt{\left(a e g -c d f \right) g}\, a e g -2 \sqrt{\left(a e g -c d f \right) g}\, c d f \right)}{\sqrt{e x +d}\, \left(c d x +a e \right) \left(a e g -c d f \right)^{2} \left(g x +f \right) \sqrt{\left(a e g -c d f \right) g}}"," ",0,"(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)*x*c*d*g^2+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)*c*d*f*g-3*((a*e*g-c*d*f)*g)^(1/2)*x*c*d*g-((a*e*g-c*d*f)*g)^(1/2)*a*e*g-2*((a*e*g-c*d*f)*g)^(1/2)*c*d*f)/(e*x+d)^(1/2)/(c*d*x+a*e)/(a*e*g-c*d*f)^2/(g*x+f)/((a*e*g-c*d*f)*g)^(1/2)","A"
671,1,379,244,0.035000," ","int((e*x+d)^(3/2)/(g*x+f)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 \sqrt{c d x +a e}\, c^{2} d^{2} g^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+30 \sqrt{c d x +a e}\, c^{2} d^{2} f \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 \sqrt{c d x +a e}\, c^{2} d^{2} f^{2} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} g^{2} x^{2}-5 \sqrt{\left(a e g -c d f \right) g}\, a c d e \,g^{2} x -25 \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} f g x +2 \sqrt{\left(a e g -c d f \right) g}\, a^{2} e^{2} g^{2}-9 \sqrt{\left(a e g -c d f \right) g}\, a c d e f g -8 \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} f^{2}\right)}{4 \sqrt{e x +d}\, \left(c d x +a e \right) \left(a e g -c d f \right)^{3} \left(g x +f \right)^{2} \sqrt{\left(a e g -c d f \right) g}}"," ",0,"-1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)*x^2*c^2*d^2*g^3+30*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)*x*c^2*d^2*f*g^2+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)*c^2*d^2*f^2*g-15*((a*e*g-c*d*f)*g)^(1/2)*x^2*c^2*d^2*g^2-5*((a*e*g-c*d*f)*g)^(1/2)*x*a*c*d*e*g^2-25*((a*e*g-c*d*f)*g)^(1/2)*x*c^2*d^2*f*g+2*((a*e*g-c*d*f)*g)^(1/2)*a^2*e^2*g^2-9*((a*e*g-c*d*f)*g)^(1/2)*a*c*d*e*f*g-8*((a*e*g-c*d*f)*g)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/(c*d*x+a*e)/(a*e*g-c*d*f)^3/(g*x+f)^2/((a*e*g-c*d*f)*g)^(1/2)","A"
672,1,187,217,0.009000," ","int((e*x+d)^(5/2)*(g*x+f)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(-g^{3} x^{3} c^{3} d^{3}+6 a \,c^{2} d^{2} e \,g^{3} x^{2}-9 c^{3} d^{3} f \,g^{2} x^{2}+24 a^{2} c d \,e^{2} g^{3} x -36 a \,c^{2} d^{2} e f \,g^{2} x +9 c^{3} d^{3} f^{2} g x +16 a^{3} e^{3} g^{3}-24 a^{2} c d \,e^{2} f \,g^{2}+6 a \,c^{2} d^{2} e \,f^{2} g +f^{3} c^{3} d^{3}\right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}} c^{4} d^{4}}"," ",0,"-2/3*(c*d*x+a*e)*(-c^3*d^3*g^3*x^3+6*a*c^2*d^2*e*g^3*x^2-9*c^3*d^3*f*g^2*x^2+24*a^2*c*d*e^2*g^3*x-36*a*c^2*d^2*e*f*g^2*x+9*c^3*d^3*f^2*g*x+16*a^3*e^3*g^3-24*a^2*c*d*e^2*f*g^2+6*a*c^2*d^2*e*f^2*g+c^3*d^3*f^3)*(e*x+d)^(5/2)/c^4/d^4/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
673,1,116,193,0.009000," ","int((e*x+d)^(5/2)*(g*x+f)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{2 \left(c d x +a e \right) \left(3 g^{2} x^{2} c^{2} d^{2}+12 a c d e \,g^{2} x -6 c^{2} d^{2} f g x +8 a^{2} e^{2} g^{2}-4 a c d e f g -f^{2} c^{2} d^{2}\right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}} c^{3} d^{3}}"," ",0,"2/3*(c*d*x+a*e)*(3*c^2*d^2*g^2*x^2+12*a*c*d*e*g^2*x-6*c^2*d^2*f*g*x+8*a^2*e^2*g^2-4*a*c*d*e*f*g-c^2*d^2*f^2)*(e*x+d)^(5/2)/c^3/d^3/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
674,1,66,142,0.007000," ","int((e*x+d)^(5/2)*(g*x+f)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(3 c d g x +2 a e g +c d f \right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}} c^{2} d^{2}}"," ",0,"-2/3*(c*d*x+a*e)*(3*c*d*g*x+2*a*e*g+c*d*f)*(e*x+d)^(5/2)/c^2/d^2/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
675,1,50,42,0.003000," ","int((e*x+d)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}} c d}"," ",0,"-2/3*(c*d*x+a*e)*(e*x+d)^(5/2)/c/d/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
676,1,219,166,0.030000," ","int((e*x+d)^(5/2)/(g*x+f)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 \sqrt{c d x +a e}\, c d \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 \sqrt{c d x +a e}\, a e \,g^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 \sqrt{\left(a e g -c d f \right) g}\, c d g x -4 \sqrt{\left(a e g -c d f \right) g}\, a e g +\sqrt{\left(a e g -c d f \right) g}\, c d f \right)}{3 \sqrt{e x +d}\, \left(c d x +a e \right)^{2} \left(a e g -c d f \right)^{2} \sqrt{\left(a e g -c d f \right) g}}"," ",0,"-2/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)*x*c*d*g^2+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*e*g^2*(c*d*x+a*e)^(1/2)-3*((a*e*g-c*d*f)*g)^(1/2)*c*d*g*x-4*((a*e*g-c*d*f)*g)^(1/2)*a*e*g+((a*e*g-c*d*f)*g)^(1/2)*c*d*f)/(e*x+d)^(1/2)/(c*d*x+a*e)^2/(a*e*g-c*d*f)^2/((a*e*g-c*d*f)*g)^(1/2)","A"
677,1,424,240,0.035000," ","int((e*x+d)^(5/2)/(g*x+f)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 \sqrt{c d x +a e}\, c^{2} d^{2} g^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 \sqrt{c d x +a e}\, a c d e \,g^{3} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 \sqrt{c d x +a e}\, c^{2} d^{2} f \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 \sqrt{c d x +a e}\, a c d e f \,g^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} g^{2} x^{2}-20 \sqrt{\left(a e g -c d f \right) g}\, a c d e \,g^{2} x -10 \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} f g x -3 \sqrt{\left(a e g -c d f \right) g}\, a^{2} e^{2} g^{2}-14 \sqrt{\left(a e g -c d f \right) g}\, a c d e f g +2 \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} f^{2}\right)}{3 \sqrt{e x +d}\, \left(c d x +a e \right)^{2} \left(a e g -c d f \right)^{3} \left(g x +f \right) \sqrt{\left(a e g -c d f \right) g}}"," ",0,"1/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)*x^2*c^2*d^2*g^3+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a*c*d*e*g^3*(c*d*x+a*e)^(1/2)+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*(c*d*x+a*e)^(1/2)*x*c^2*d^2*f*g^2+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c*d*e*f*g^2*(c*d*x+a*e)^(1/2)-15*((a*e*g-c*d*f)*g)^(1/2)*c^2*d^2*g^2*x^2-20*((a*e*g-c*d*f)*g)^(1/2)*a*c*d*e*g^2*x-10*((a*e*g-c*d*f)*g)^(1/2)*c^2*d^2*f*g*x-3*((a*e*g-c*d*f)*g)^(1/2)*a^2*e^2*g^2-14*((a*e*g-c*d*f)*g)^(1/2)*a*c*d*e*f*g+2*((a*e*g-c*d*f)*g)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^2/(a*e*g-c*d*f)^3/(g*x+f)/((a*e*g-c*d*f)*g)^(1/2)","A"
678,1,670,304,0.038000," ","int((e*x+d)^(5/2)/(g*x+f)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(105 \sqrt{c d x +a e}\, c^{3} d^{3} g^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+105 \sqrt{c d x +a e}\, a \,c^{2} d^{2} e \,g^{4} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+210 \sqrt{c d x +a e}\, c^{3} d^{3} f \,g^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+210 \sqrt{c d x +a e}\, a \,c^{2} d^{2} e f \,g^{3} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+105 \sqrt{c d x +a e}\, c^{3} d^{3} f^{2} g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-105 \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} g^{3} x^{3}+105 \sqrt{c d x +a e}\, a \,c^{2} d^{2} e \,f^{2} g^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-140 \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e \,g^{3} x^{2}-175 \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f \,g^{2} x^{2}-21 \sqrt{\left(a e g -c d f \right) g}\, a^{2} c d \,e^{2} g^{3} x -238 \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e f \,g^{2} x -56 \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f^{2} g x +6 \sqrt{\left(a e g -c d f \right) g}\, a^{3} e^{3} g^{3}-39 \sqrt{\left(a e g -c d f \right) g}\, a^{2} c d \,e^{2} f \,g^{2}-80 \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e \,f^{2} g +8 \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f^{3}\right)}{12 \sqrt{e x +d}\, \left(c d x +a e \right)^{2} \left(a e g -c d f \right)^{4} \left(g x +f \right)^{2} \sqrt{\left(a e g -c d f \right) g}}"," ",0,"-1/12*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(105*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^3*d^3*g^4*(c*d*x+a*e)^(1/2)+105*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*a*c^2*d^2*e*g^4*(c*d*x+a*e)^(1/2)+210*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^3*d^3*f*g^3*(c*d*x+a*e)^(1/2)+210*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a*c^2*d^2*e*f*g^3*(c*d*x+a*e)^(1/2)+105*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^3*f^2*g^2*(c*d*x+a*e)^(1/2)-105*((a*e*g-c*d*f)*g)^(1/2)*x^3*c^3*d^3*g^3+105*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c^2*d^2*e*f^2*g^2*(c*d*x+a*e)^(1/2)-140*((a*e*g-c*d*f)*g)^(1/2)*x^2*a*c^2*d^2*e*g^3-175*((a*e*g-c*d*f)*g)^(1/2)*x^2*c^3*d^3*f*g^2-21*((a*e*g-c*d*f)*g)^(1/2)*x*a^2*c*d*e^2*g^3-238*((a*e*g-c*d*f)*g)^(1/2)*x*a*c^2*d^2*e*f*g^2-56*((a*e*g-c*d*f)*g)^(1/2)*x*c^3*d^3*f^2*g+6*((a*e*g-c*d*f)*g)^(1/2)*a^3*e^3*g^3-39*((a*e*g-c*d*f)*g)^(1/2)*a^2*c*d*e^2*f*g^2-80*((a*e*g-c*d*f)*g)^(1/2)*a*c^2*d^2*e*f^2*g+8*((a*e*g-c*d*f)*g)^(1/2)*c^3*d^3*f^3)/(e*x+d)^(1/2)/(c*d*x+a*e)^2/(a*e*g-c*d*f)^4/(g*x+f)^2/((a*e*g-c*d*f)*g)^(1/2)","B"
679,1,283,306,0.009000," ","int((g*x+f)^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(315 g^{4} x^{4} c^{4} d^{4}-280 a \,c^{3} d^{3} e \,g^{4} x^{3}+1540 c^{4} d^{4} f \,g^{3} x^{3}+240 a^{2} c^{2} d^{2} e^{2} g^{4} x^{2}-1320 a \,c^{3} d^{3} e f \,g^{3} x^{2}+2970 c^{4} d^{4} f^{2} g^{2} x^{2}-192 a^{3} c d \,e^{3} g^{4} x +1056 a^{2} c^{2} d^{2} e^{2} f \,g^{3} x -2376 a \,c^{3} d^{3} e \,f^{2} g^{2} x +2772 c^{4} d^{4} f^{3} g x +128 a^{4} e^{4} g^{4}-704 a^{3} c d \,e^{3} f \,g^{3}+1584 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-1848 a \,c^{3} d^{3} e \,f^{3} g +1155 f^{4} c^{4} d^{4}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{3465 \sqrt{e x +d}\, c^{5} d^{5}}"," ",0,"2/3465*(c*d*x+a*e)*(315*c^4*d^4*g^4*x^4-280*a*c^3*d^3*e*g^4*x^3+1540*c^4*d^4*f*g^3*x^3+240*a^2*c^2*d^2*e^2*g^4*x^2-1320*a*c^3*d^3*e*f*g^3*x^2+2970*c^4*d^4*f^2*g^2*x^2-192*a^3*c*d*e^3*g^4*x+1056*a^2*c^2*d^2*e^2*f*g^3*x-2376*a*c^3*d^3*e*f^2*g^2*x+2772*c^4*d^4*f^3*g*x+128*a^4*e^4*g^4-704*a^3*c*d*e^3*f*g^3+1584*a^2*c^2*d^2*e^2*f^2*g^2-1848*a*c^3*d^3*e*f^3*g+1155*c^4*d^4*f^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c^5/d^5/(e*x+d)^(1/2)","A"
680,1,188,245,0.010000," ","int((g*x+f)^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-35 g^{3} x^{3} c^{3} d^{3}+30 a \,c^{2} d^{2} e \,g^{3} x^{2}-135 c^{3} d^{3} f \,g^{2} x^{2}-24 a^{2} c d \,e^{2} g^{3} x +108 a \,c^{2} d^{2} e f \,g^{2} x -189 c^{3} d^{3} f^{2} g x +16 a^{3} e^{3} g^{3}-72 a^{2} c d \,e^{2} f \,g^{2}+126 a \,c^{2} d^{2} e \,f^{2} g -105 f^{3} c^{3} d^{3}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{315 \sqrt{e x +d}\, c^{4} d^{4}}"," ",0,"-2/315*(c*d*x+a*e)*(-35*c^3*d^3*g^3*x^3+30*a*c^2*d^2*e*g^3*x^2-135*c^3*d^3*f*g^2*x^2-24*a^2*c*d*e^2*g^3*x+108*a*c^2*d^2*e*f*g^2*x-189*c^3*d^3*f^2*g*x+16*a^3*e^3*g^3-72*a^2*c*d*e^2*f*g^2+126*a*c^2*d^2*e*f^2*g-105*c^3*d^3*f^3)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c^4/d^4/(e*x+d)^(1/2)","A"
681,1,116,182,0.007000," ","int((g*x+f)^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(15 g^{2} x^{2} c^{2} d^{2}-12 a c d e \,g^{2} x +42 c^{2} d^{2} f g x +8 a^{2} e^{2} g^{2}-28 a c d e f g +35 f^{2} c^{2} d^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{105 \sqrt{e x +d}\, c^{3} d^{3}}"," ",0,"2/105*(c*d*x+a*e)*(15*c^2*d^2*g^2*x^2-12*a*c*d*e*g^2*x+42*c^2*d^2*f*g*x+8*a^2*e^2*g^2-28*a*c*d*e*f*g+35*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c^3/d^3/(e*x+d)^(1/2)","A"
682,1,67,113,0.006000," ","int((g*x+f)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-3 c d g x +2 a e g -5 c d f \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{15 \sqrt{e x +d}\, c^{2} d^{2}}"," ",0,"-2/15*(c*d*x+a*e)*(-3*c*d*g*x+2*a*e*g-5*c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c^2/d^2/(e*x+d)^(1/2)","A"
683,1,50,42,0.003000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","\frac{2 \left(c d x +a e \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{3 \sqrt{e x +d}\, c d}"," ",0,"2/3*(c*d*x+a*e)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/c/d/(e*x+d)^(1/2)","A"
684,1,153,108,0.022000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)/(e*x+d)^(1/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(a e g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-c d f \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\right)}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, g}"," ",0,"-2*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*e*g-arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c*d*f-(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2))/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g/((a*e*g-c*d*f)*g)^(1/2)","A"
685,1,161,116,0.025000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^2/(e*x+d)^(1/2),x)","\frac{\left(-c d g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-c d f \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(g x +f \right) \sqrt{\left(a e g -c d f \right) g}\, g}"," ",0,"(-arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c*d*g-arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c*d*f-(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2))*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g/(g*x+f)/((a*e*g-c*d*f)*g)^(1/2)","A"
686,1,285,181,0.030000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^3/(e*x+d)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(c^{2} d^{2} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+2 c^{2} d^{2} f g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+c^{2} d^{2} f^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-\sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d g x -2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a e g +\sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d f \right)}{4 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(a e g -c d f \right) \left(g x +f \right)^{2} \sqrt{\left(a e g -c d f \right) g}\, g}"," ",0,"1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^2*d^2*g^2+2*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^2*d^2*f*g+arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^2*d^2*f^2-((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*g*x-2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*e*g+((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*f)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/(a*e*g-c*d*f)/g/(g*x+f)^2/((a*e*g-c*d*f)*g)^(1/2)","A"
687,1,453,245,0.036000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^4/(e*x+d)^(1/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{3} d^{3} g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+9 c^{3} d^{3} f \,g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+9 c^{3} d^{3} f^{2} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 c^{3} d^{3} f^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} g^{2} x^{2}+2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e \,g^{2} x -8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f g x +8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} e^{2} g^{2}-14 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e f g +3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f^{2}\right)}{24 \sqrt{e x +d}\, \sqrt{\left(a e g -c d f \right) g}\, \left(g x +f \right)^{3} \left(a e g -c d f \right)^{2} \sqrt{c d x +a e}\, g}"," ",0,"-1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^3*d^3*g^3+9*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^3*d^3*f*g^2+9*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^3*f^2*g+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^3*f^3-3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*g^2*x^2+2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*g^2*x-8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f*g*x+8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^2*g^2-14*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*f*g+3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)/(g*x+f)^3/g/(a*e*g-c*d*f)^2/(c*d*x+a*e)^(1/2)","A"
688,1,696,309,0.035000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^5/(e*x+d)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{4} d^{4} g^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+60 c^{4} d^{4} f \,g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+90 c^{4} d^{4} f^{2} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+60 c^{4} d^{4} f^{3} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 c^{4} d^{4} f^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} g^{3} x^{3}+10 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e \,g^{3} x^{2}-55 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f \,g^{2} x^{2}-8 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} c d \,e^{2} g^{3} x +36 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e f \,g^{2} x -73 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f^{2} g x -48 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{3} e^{3} g^{3}+136 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c d \,e^{2} f \,g^{2}-118 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{2} d^{2} e \,f^{2} g +15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{3} d^{3} f^{3}\right)}{192 \sqrt{e x +d}\, \sqrt{\left(a e g -c d f \right) g}\, \left(g x +f \right)^{4} \left(a e g -c d f \right) \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \sqrt{c d x +a e}\, g}"," ",0,"1/192*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^4*c^4*d^4*g^4+60*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^4*d^4*f*g^3+90*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^4*d^4*f^2*g^2+60*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^4*d^4*f^3*g-15*x^3*c^3*d^3*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^4*d^4*f^4+10*x^2*a*c^2*d^2*e*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-55*x^2*c^3*d^3*f*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-8*x*a^2*c*d*e^2*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+36*x*a*c^2*d^2*e*f*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-73*x*c^3*d^3*f^2*g*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-48*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*e^3*g^3+136*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c*d*e^2*f*g^2-118*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^2*d^2*e*f^2*g+15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^3*d^3*f^3)/(e*x+d)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)/(g*x+f)^4/g/(a*e*g-c*d*f)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(c*d*x+a*e)^(1/2)","B"
689,1,283,306,0.010000," ","int((g*x+f)^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(1155 g^{4} x^{4} c^{4} d^{4}-840 a \,c^{3} d^{3} e \,g^{4} x^{3}+5460 c^{4} d^{4} f \,g^{3} x^{3}+560 a^{2} c^{2} d^{2} e^{2} g^{4} x^{2}-3640 a \,c^{3} d^{3} e f \,g^{3} x^{2}+10010 c^{4} d^{4} f^{2} g^{2} x^{2}-320 a^{3} c d \,e^{3} g^{4} x +2080 a^{2} c^{2} d^{2} e^{2} f \,g^{3} x -5720 a \,c^{3} d^{3} e \,f^{2} g^{2} x +8580 c^{4} d^{4} f^{3} g x +128 a^{4} e^{4} g^{4}-832 a^{3} c d \,e^{3} f \,g^{3}+2288 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-3432 a \,c^{3} d^{3} e \,f^{3} g +3003 f^{4} c^{4} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{15015 \left(e x +d \right)^{\frac{3}{2}} c^{5} d^{5}}"," ",0,"2/15015*(c*d*x+a*e)*(1155*c^4*d^4*g^4*x^4-840*a*c^3*d^3*e*g^4*x^3+5460*c^4*d^4*f*g^3*x^3+560*a^2*c^2*d^2*e^2*g^4*x^2-3640*a*c^3*d^3*e*f*g^3*x^2+10010*c^4*d^4*f^2*g^2*x^2-320*a^3*c*d*e^3*g^4*x+2080*a^2*c^2*d^2*e^2*f*g^3*x-5720*a*c^3*d^3*e*f^2*g^2*x+8580*c^4*d^4*f^3*g*x+128*a^4*e^4*g^4-832*a^3*c*d*e^3*f*g^3+2288*a^2*c^2*d^2*e^2*f^2*g^2-3432*a*c^3*d^3*e*f^3*g+3003*c^4*d^4*f^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c^5/d^5/(e*x+d)^(3/2)","A"
690,1,188,245,0.009000," ","int((g*x+f)^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-105 g^{3} x^{3} c^{3} d^{3}+70 a \,c^{2} d^{2} e \,g^{3} x^{2}-385 c^{3} d^{3} f \,g^{2} x^{2}-40 a^{2} c d \,e^{2} g^{3} x +220 a \,c^{2} d^{2} e f \,g^{2} x -495 c^{3} d^{3} f^{2} g x +16 a^{3} e^{3} g^{3}-88 a^{2} c d \,e^{2} f \,g^{2}+198 a \,c^{2} d^{2} e \,f^{2} g -231 f^{3} c^{3} d^{3}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{1155 \left(e x +d \right)^{\frac{3}{2}} c^{4} d^{4}}"," ",0,"-2/1155*(c*d*x+a*e)*(-105*c^3*d^3*g^3*x^3+70*a*c^2*d^2*e*g^3*x^2-385*c^3*d^3*f*g^2*x^2-40*a^2*c*d*e^2*g^3*x+220*a*c^2*d^2*e*f*g^2*x-495*c^3*d^3*f^2*g*x+16*a^3*e^3*g^3-88*a^2*c*d*e^2*f*g^2+198*a*c^2*d^2*e*f^2*g-231*c^3*d^3*f^3)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c^4/d^4/(e*x+d)^(3/2)","A"
691,1,116,182,0.009000," ","int((g*x+f)^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(35 g^{2} x^{2} c^{2} d^{2}-20 a c d e \,g^{2} x +90 c^{2} d^{2} f g x +8 a^{2} e^{2} g^{2}-36 a c d e f g +63 f^{2} c^{2} d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{315 \left(e x +d \right)^{\frac{3}{2}} c^{3} d^{3}}"," ",0,"2/315*(c*d*x+a*e)*(35*c^2*d^2*g^2*x^2-20*a*c*d*e*g^2*x+90*c^2*d^2*f*g*x+8*a^2*e^2*g^2-36*a*c*d*e*f*g+63*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c^3/d^3/(e*x+d)^(3/2)","A"
692,1,67,113,0.005000," ","int((g*x+f)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-5 c d g x +2 a e g -7 c d f \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{35 \left(e x +d \right)^{\frac{3}{2}} c^{2} d^{2}}"," ",0,"-2/35*(c*d*x+a*e)*(-5*c*d*g*x+2*a*e*g-7*c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c^2/d^2/(e*x+d)^(3/2)","A"
693,1,50,42,0.005000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","\frac{2 \left(c d x +a e \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{5 \left(e x +d \right)^{\frac{3}{2}} c d}"," ",0,"2/5*(c*d*x+a*e)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/c/d/(e*x+d)^(3/2)","A"
694,1,263,157,0.023000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 a^{2} e^{2} g^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-6 a c d e f g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 c^{2} d^{2} f^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-\sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d g x -4 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a e g +3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d f \right)}{3 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, g^{2}}"," ",0,"-2/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a^2*e^2*g^2-6*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c*d*e*f*g+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^2*d^2*f^2-((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*g*x-4*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*e*g+3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*f)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g^2/((a*e*g-c*d*f)*g)^(1/2)","A"
695,1,306,158,0.030000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^2,x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(-3 a c d e \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 c^{2} d^{2} f g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 a c d e f g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 c^{2} d^{2} f^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d g x -\sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a e g +3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d f \right)}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(g x +f \right) \sqrt{\left(a e g -c d f \right) g}\, g^{2}}"," ",0,"(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^(1/2)*(-3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a*c*d*e*g^2+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^2*d^2*f*g-3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c*d*e*f*g+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^2*d^2*f^2+2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*g*x-((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*e*g+3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*f)/(c*d*x+a*e)^(1/2)/g^2/(g*x+f)/((a*e*g-c*d*f)*g)^(1/2)","A"
696,1,276,169,0.029000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^3,x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{2} d^{2} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+6 c^{2} d^{2} f g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 c^{2} d^{2} f^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+5 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d g x +2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a e g +3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c d f \right)}{4 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(g x +f \right)^{2} \sqrt{\left(a e g -c d f \right) g}\, g^{2}}"," ",0,"-1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^2*d^2*g^2+6*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^2*d^2*f*g+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^2*d^2*f^2+5*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*g*x+2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*e*g+3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c*d*f)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g^2/(g*x+f)^2/((a*e*g-c*d*f)*g)^(1/2)","A"
697,1,453,233,0.032000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^4,x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{3} d^{3} g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+9 c^{3} d^{3} f \,g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+9 c^{3} d^{3} f^{2} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 c^{3} d^{3} f^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} g^{2} x^{2}-14 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e \,g^{2} x +8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f g x -8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} e^{2} g^{2}+2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e f g +3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f^{2}\right)}{24 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(a e g -c d f \right) \left(g x +f \right)^{3} \sqrt{\left(a e g -c d f \right) g}\, g^{2}}"," ",0,"1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^3*d^3*g^3+9*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^3*d^3*f*g^2+9*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^3*f^2*g+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^3*f^3-3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*g^2*x^2-14*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*g^2*x+8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f*g*x-8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^2*g^2+2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*f*g+3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/(a*e*g-c*d*f)/g^2/(g*x+f)^3/((a*e*g-c*d*f)*g)^(1/2)","A"
698,1,665,297,0.041000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^5,x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{4} d^{4} g^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+12 c^{4} d^{4} f \,g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+18 c^{4} d^{4} f^{2} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+12 c^{4} d^{4} f^{3} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+3 c^{4} d^{4} f^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} g^{3} x^{3}+2 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e \,g^{3} x^{2}-11 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f \,g^{2} x^{2}+24 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} c d \,e^{2} g^{3} x -44 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e f \,g^{2} x +11 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f^{2} g x +16 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{3} e^{3} g^{3}-24 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c d \,e^{2} f \,g^{2}+2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{2} d^{2} e \,f^{2} g +3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{3} d^{3} f^{3}\right)}{64 \sqrt{e x +d}\, \sqrt{\left(a e g -c d f \right) g}\, \left(g x +f \right)^{4} \left(a e g -c d f \right)^{2} \sqrt{c d x +a e}\, g^{2}}"," ",0,"-1/64*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^4*c^4*d^4*g^4+12*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^4*d^4*f*g^3+18*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^4*d^4*f^2*g^2+12*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^4*d^4*f^3*g-3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*c^3*d^3*g^3*x^3+3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^4*d^4*f^4+2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*a*c^2*d^2*e*g^3*x^2-11*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*c^3*d^3*f*g^2*x^2+24*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*a^2*c*d*e^2*g^3*x-44*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*a*c^2*d^2*e*f*g^2*x+11*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*c^3*d^3*f^2*g*x+16*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*e^3*g^3-24*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c*d*e^2*f*g^2+2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^2*d^2*e*f^2*g+3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^3*d^3*f^3)/(e*x+d)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)/(g*x+f)^4/g^2/(a*e*g-c*d*f)^2/(c*d*x+a*e)^(1/2)","B"
699,1,955,361,0.039000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^6,x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{5} d^{5} g^{5} x^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+75 c^{5} d^{5} f \,g^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+150 c^{5} d^{5} f^{2} g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+150 c^{5} d^{5} f^{3} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+75 c^{5} d^{5} f^{4} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 c^{5} d^{5} f^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} g^{4} x^{4}+10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{3} d^{3} e \,g^{4} x^{3}-70 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} f \,g^{3} x^{3}-8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c^{2} d^{2} e^{2} g^{4} x^{2}+46 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{3} d^{3} e f \,g^{3} x^{2}-128 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} f^{2} g^{2} x^{2}-176 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{3} c d \,e^{3} g^{4} x +512 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c^{2} d^{2} e^{2} f \,g^{3} x -466 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{3} d^{3} e \,f^{2} g^{2} x +70 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} f^{3} g x -128 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{4} e^{4} g^{4}+336 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{3} c d \,e^{3} f \,g^{3}-248 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}+10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{3} d^{3} e \,f^{3} g +15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} f^{4}\right)}{640 \sqrt{e x +d}\, \sqrt{\left(a e g -c d f \right) g}\, \left(g x +f \right)^{5} \left(a e g -c d f \right) \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \sqrt{c d x +a e}\, g^{2}}"," ",0,"1/640*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^5*c^5*d^5*g^5+75*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^4*c^5*d^5*f*g^4+150*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^5*d^5*f^2*g^3+150*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^5*d^5*f^3*g^2-15*x^4*c^4*d^4*g^4*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)+75*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^5*d^5*f^4*g+10*x^3*a*c^3*d^3*e*g^4*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)-70*x^3*c^4*d^4*f*g^3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^5*d^5*f^5-8*x^2*a^2*c^2*d^2*e^2*g^4*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)+46*x^2*a*c^3*d^3*e*f*g^3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)-128*x^2*c^4*d^4*f^2*g^2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)-176*x*a^3*c*d*e^3*g^4*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)+512*x*a^2*c^2*d^2*e^2*f*g^3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)-466*x*a*c^3*d^3*e*f^2*g^2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)+70*x*c^4*d^4*f^3*g*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)-128*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^4*e^4*g^4+336*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*c*d*e^3*f*g^3-248*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c^2*d^2*e^2*f^2*g^2+10*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^3*d^3*e*f^3*g+15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^4*d^4*f^4)/(e*x+d)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)/(g*x+f)^5/g^2/(a*e*g-c*d*f)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(c*d*x+a*e)^(1/2)","B"
700,1,283,306,0.010000," ","int((g*x+f)^4*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","\frac{2 \left(c d x +a e \right) \left(3003 g^{4} x^{4} c^{4} d^{4}-1848 a \,c^{3} d^{3} e \,g^{4} x^{3}+13860 c^{4} d^{4} f \,g^{3} x^{3}+1008 a^{2} c^{2} d^{2} e^{2} g^{4} x^{2}-7560 a \,c^{3} d^{3} e f \,g^{3} x^{2}+24570 c^{4} d^{4} f^{2} g^{2} x^{2}-448 a^{3} c d \,e^{3} g^{4} x +3360 a^{2} c^{2} d^{2} e^{2} f \,g^{3} x -10920 a \,c^{3} d^{3} e \,f^{2} g^{2} x +20020 c^{4} d^{4} f^{3} g x +128 a^{4} e^{4} g^{4}-960 a^{3} c d \,e^{3} f \,g^{3}+3120 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-5720 a \,c^{3} d^{3} e \,f^{3} g +6435 f^{4} c^{4} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{45045 \left(e x +d \right)^{\frac{5}{2}} c^{5} d^{5}}"," ",0,"2/45045*(c*d*x+a*e)*(3003*c^4*d^4*g^4*x^4-1848*a*c^3*d^3*e*g^4*x^3+13860*c^4*d^4*f*g^3*x^3+1008*a^2*c^2*d^2*e^2*g^4*x^2-7560*a*c^3*d^3*e*f*g^3*x^2+24570*c^4*d^4*f^2*g^2*x^2-448*a^3*c*d*e^3*g^4*x+3360*a^2*c^2*d^2*e^2*f*g^3*x-10920*a*c^3*d^3*e*f^2*g^2*x+20020*c^4*d^4*f^3*g*x+128*a^4*e^4*g^4-960*a^3*c*d*e^3*f*g^3+3120*a^2*c^2*d^2*e^2*f^2*g^2-5720*a*c^3*d^3*e*f^3*g+6435*c^4*d^4*f^4)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c^5/d^5/(e*x+d)^(5/2)","A"
701,1,188,245,0.011000," ","int((g*x+f)^3*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(-231 g^{3} x^{3} c^{3} d^{3}+126 a \,c^{2} d^{2} e \,g^{3} x^{2}-819 c^{3} d^{3} f \,g^{2} x^{2}-56 a^{2} c d \,e^{2} g^{3} x +364 a \,c^{2} d^{2} e f \,g^{2} x -1001 c^{3} d^{3} f^{2} g x +16 a^{3} e^{3} g^{3}-104 a^{2} c d \,e^{2} f \,g^{2}+286 a \,c^{2} d^{2} e \,f^{2} g -429 f^{3} c^{3} d^{3}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{3003 \left(e x +d \right)^{\frac{5}{2}} c^{4} d^{4}}"," ",0,"-2/3003*(c*d*x+a*e)*(-231*c^3*d^3*g^3*x^3+126*a*c^2*d^2*e*g^3*x^2-819*c^3*d^3*f*g^2*x^2-56*a^2*c*d*e^2*g^3*x+364*a*c^2*d^2*e*f*g^2*x-1001*c^3*d^3*f^2*g*x+16*a^3*e^3*g^3-104*a^2*c*d*e^2*f*g^2+286*a*c^2*d^2*e*f^2*g-429*c^3*d^3*f^3)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c^4/d^4/(e*x+d)^(5/2)","A"
702,1,116,182,0.009000," ","int((g*x+f)^2*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","\frac{2 \left(c d x +a e \right) \left(63 g^{2} x^{2} c^{2} d^{2}-28 a c d e \,g^{2} x +154 c^{2} d^{2} f g x +8 a^{2} e^{2} g^{2}-44 a c d e f g +99 f^{2} c^{2} d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{693 \left(e x +d \right)^{\frac{5}{2}} c^{3} d^{3}}"," ",0,"2/693*(c*d*x+a*e)*(63*c^2*d^2*g^2*x^2-28*a*c*d*e*g^2*x+154*c^2*d^2*f*g*x+8*a^2*e^2*g^2-44*a*c*d*e*f*g+99*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c^3/d^3/(e*x+d)^(5/2)","A"
703,1,67,113,0.005000," ","int((g*x+f)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(-7 c d g x +2 a e g -9 c d f \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{63 \left(e x +d \right)^{\frac{5}{2}} c^{2} d^{2}}"," ",0,"-2/63*(c*d*x+a*e)*(-7*c*d*g*x+2*a*e*g-9*c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c^2/d^2/(e*x+d)^(5/2)","A"
704,1,50,42,0.005000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","\frac{2 \left(c d x +a e \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{7 \left(e x +d \right)^{\frac{5}{2}} c d}"," ",0,"2/7*(c*d*x+a*e)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/c/d/(e*x+d)^(5/2)","A"
705,1,431,208,0.023000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a^{3} e^{3} g^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-45 a^{2} c d \,e^{2} f \,g^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+45 a \,c^{2} d^{2} e \,f^{2} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 c^{3} d^{3} f^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} g^{2} x^{2}-11 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e \,g^{2} x +5 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f g x -23 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} e^{2} g^{2}+35 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e f g -15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f^{2}\right)}{15 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, g^{3}}"," ",0,"-2/15*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a^3*e^3*g^3-45*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a^2*c*d*e^2*f*g^2+45*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c^2*d^2*e*f^2*g-15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^3*f^3-3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*g^2*x^2-11*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*g^2*x+5*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f*g*x-23*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^2*g^2+35*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*f*g-15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g^3/((a*e*g-c*d*f)*g)^(1/2)","B"
706,1,523,209,0.031000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^2,x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a^{2} c d \,e^{2} g^{3} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-30 a \,c^{2} d^{2} e f \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 c^{3} d^{3} f^{2} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 a^{2} c d \,e^{2} f \,g^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-30 a \,c^{2} d^{2} e \,f^{2} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 c^{3} d^{3} f^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} g^{2} x^{2}-14 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e \,g^{2} x +10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f g x +3 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} e^{2} g^{2}-20 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e f g +15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f^{2}\right)}{3 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(g x +f \right) \sqrt{\left(a e g -c d f \right) g}\, g^{3}}"," ",0,"-1/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a^2*c*d*e^2*g^3-30*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a*c^2*d^2*e*f*g^2+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^3*f^2*g+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a^2*c*d*e^2*f*g^2-30*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c^2*d^2*e*f^2*g+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^3*f^3-2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*g^2*x^2-14*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*g^2*x+10*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f*g*x+3*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^2*g^2-20*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*f*g+15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g^3/(g*x+f)/((a*e*g-c*d*f)*g)^(1/2)","B"
707,1,526,214,0.033000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^3,x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a \,c^{2} d^{2} e \,g^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 c^{3} d^{3} f \,g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+30 a \,c^{2} d^{2} e f \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-30 c^{3} d^{3} f^{2} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 a \,c^{2} d^{2} e \,f^{2} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 c^{3} d^{3} f^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} g^{2} x^{2}+9 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e \,g^{2} x -25 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f g x +2 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} e^{2} g^{2}+5 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e f g -15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f^{2}\right)}{4 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(g x +f \right)^{2} \sqrt{\left(a e g -c d f \right) g}\, g^{3}}"," ",0,"-1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*a*c^2*d^2*e*g^3-15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^3*d^3*f*g^2+30*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a*c^2*d^2*e*f*g^2-30*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^3*f^2*g+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c^2*d^2*e*f^2*g-15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^3*f^3-8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*g^2*x^2+9*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*g^2*x-25*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f*g*x+2*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^2*g^2+5*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*f*g-15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g^3/(g*x+f)^2/((a*e*g-c*d*f)*g)^(1/2)","B"
708,1,441,221,0.033000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^4,x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{3} d^{3} g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+45 c^{3} d^{3} f \,g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+45 c^{3} d^{3} f^{2} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 c^{3} d^{3} f^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+33 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} g^{2} x^{2}+26 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e \,g^{2} x +40 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f g x +8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} e^{2} g^{2}+10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a c d e f g +15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{2} d^{2} f^{2}\right)}{24 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(g x +f \right)^{3} \sqrt{\left(a e g -c d f \right) g}\, g^{3}}"," ",0,"-1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^3*d^3*g^3+45*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^3*d^3*f*g^2+45*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^3*f^2*g+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^3*f^3+33*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*g^2*x^2+26*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*g^2*x+40*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f*g*x+8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*e^2*g^2+10*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c*d*e*f*g+15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g^3/(g*x+f)^3/((a*e*g-c*d*f)*g)^(1/2)","A"
709,1,665,285,0.035000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^5,x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{4} d^{4} g^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+60 c^{4} d^{4} f \,g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+90 c^{4} d^{4} f^{2} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+60 c^{4} d^{4} f^{3} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 c^{4} d^{4} f^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} g^{3} x^{3}-118 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e \,g^{3} x^{2}+73 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f \,g^{2} x^{2}-136 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} c d \,e^{2} g^{3} x +36 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{2} d^{2} e f \,g^{2} x +55 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{3} d^{3} f^{2} g x -48 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{3} e^{3} g^{3}+8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c d \,e^{2} f \,g^{2}+10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{2} d^{2} e \,f^{2} g +15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{3} d^{3} f^{3}\right)}{192 \sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(a e g -c d f \right) \left(g x +f \right)^{4} \sqrt{\left(a e g -c d f \right) g}\, g^{3}}"," ",0,"1/192*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^4*c^4*d^4*g^4+60*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^4*d^4*f*g^3+90*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^4*d^4*f^2*g^2+60*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^4*d^4*f^3*g-15*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*c^3*d^3*g^3*x^3+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^4*d^4*f^4-118*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*a*c^2*d^2*e*g^3*x^2+73*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*c^3*d^3*f*g^2*x^2-136*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*a^2*c*d*e^2*g^3*x+36*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*a*c^2*d^2*e*f*g^2*x+55*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)*c^3*d^3*f^2*g*x-48*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*e^3*g^3+8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c*d*e^2*f*g^2+10*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^2*d^2*e*f^2*g+15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^3*d^3*f^3)/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/g^3/(a*e*g-c*d*f)/(g*x+f)^4/((a*e*g-c*d*f)*g)^(1/2)","B"
710,1,924,349,0.043000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^6,x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{5} d^{5} g^{5} x^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+75 c^{5} d^{5} f \,g^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+150 c^{5} d^{5} f^{2} g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+150 c^{5} d^{5} f^{3} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+75 c^{5} d^{5} f^{4} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+15 c^{5} d^{5} f^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} g^{4} x^{4}+10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{3} d^{3} e \,g^{4} x^{3}-70 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} f \,g^{3} x^{3}+248 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c^{2} d^{2} e^{2} g^{4} x^{2}-466 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{3} d^{3} e f \,g^{3} x^{2}+128 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} f^{2} g^{2} x^{2}+336 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{3} c d \,e^{3} g^{4} x -512 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c^{2} d^{2} e^{2} f \,g^{3} x +46 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{3} d^{3} e \,f^{2} g^{2} x +70 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} f^{3} g x +128 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{4} e^{4} g^{4}-176 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{3} c d \,e^{3} f \,g^{3}+8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}+10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{3} d^{3} e \,f^{3} g +15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{4} d^{4} f^{4}\right)}{640 \sqrt{e x +d}\, \sqrt{\left(a e g -c d f \right) g}\, \left(g x +f \right)^{5} \left(a e g -c d f \right)^{2} \sqrt{c d x +a e}\, g^{3}}"," ",0,"-1/640*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^5*c^5*d^5*g^5+75*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^4*c^5*d^5*f*g^4+150*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^5*d^5*f^2*g^3+150*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^5*d^5*f^3*g^2-15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^4*d^4*g^4*x^4+75*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^5*d^5*f^4*g+10*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^3*d^3*e*g^4*x^3-70*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^4*d^4*f*g^3*x^3+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^5*d^5*f^5+248*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c^2*d^2*e^2*g^4*x^2-466*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^3*d^3*e*f*g^3*x^2+128*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^4*d^4*f^2*g^2*x^2+336*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*c*d*e^3*g^4*x-512*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c^2*d^2*e^2*f*g^3*x+46*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^3*d^3*e*f^2*g^2*x+70*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^4*d^4*f^3*g*x+128*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^4*e^4*g^4-176*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*c*d*e^3*f*g^3+8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c^2*d^2*e^2*f^2*g^2+10*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^3*d^3*e*f^3*g+15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^4*d^4*f^4)/(e*x+d)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)/(g*x+f)^5/g^3/(a*e*g-c*d*f)^2/(c*d*x+a*e)^(1/2)","B"
711,1,1261,413,0.042000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^7,x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{6} d^{6} g^{6} x^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+90 c^{6} d^{6} f \,g^{5} x^{5} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+225 c^{6} d^{6} f^{2} g^{4} x^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+300 c^{6} d^{6} f^{3} g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+225 c^{6} d^{6} f^{4} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+90 c^{6} d^{6} f^{5} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{5} d^{5} g^{5} x^{5}+10 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{4} d^{4} e \,g^{5} x^{4}+15 c^{6} d^{6} f^{6} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-85 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{5} d^{5} f \,g^{4} x^{4}-8 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} c^{3} d^{3} e^{2} g^{5} x^{3}+56 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{4} d^{4} e f \,g^{4} x^{3}-198 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{5} d^{5} f^{2} g^{3} x^{3}-432 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{3} c^{2} d^{2} e^{3} g^{5} x^{2}+1272 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} c^{3} d^{3} e^{2} f \,g^{4} x^{2}-1188 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{4} d^{4} e \,f^{2} g^{3} x^{2}+198 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{5} d^{5} f^{3} g^{2} x^{2}-640 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{4} c d \,e^{4} g^{5} x +1696 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{3} c^{2} d^{2} e^{3} f \,g^{4} x -1272 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} c^{3} d^{3} e^{2} f^{2} g^{3} x +56 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,c^{4} d^{4} e \,f^{3} g^{2} x +85 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{5} d^{5} f^{4} g x -256 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{5} e^{5} g^{5}+640 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{4} c d \,e^{4} f \,g^{4}-432 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{3} c^{2} d^{2} e^{3} f^{2} g^{3}+8 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a^{2} c^{3} d^{3} e^{2} f^{3} g^{2}+10 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, a \,c^{4} d^{4} e \,f^{4} g +15 \sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, c^{5} d^{5} f^{5}\right)}{1536 \sqrt{e x +d}\, \sqrt{\left(a e g -c d f \right) g}\, \left(g x +f \right)^{6} \left(a e g -c d f \right) \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \sqrt{c d x +a e}\, g^{3}}"," ",0,"1/1536*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^6*d^6*f^6-15*x^5*c^5*d^5*g^5*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-85*x^4*c^5*d^5*f*g^4*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-198*x^3*c^5*d^5*f^2*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+198*x^2*c^5*d^5*f^3*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+85*x*c^5*d^5*f^4*g*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+10*x^4*a*c^4*d^4*e*g^5*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^6*c^6*d^6*g^6+90*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^5*c^6*d^6*f*g^5+225*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^4*c^6*d^6*f^2*g^4+300*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^6*d^6*f^3*g^3+225*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^6*d^6*f^4*g^2+90*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^6*d^6*f^5*g-8*x^3*a^2*c^3*d^3*e^2*g^5*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-432*x^2*a^3*c^2*d^2*e^3*g^5*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-640*x*a^4*c*d*e^4*g^5*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+640*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^4*c*d*e^4*f*g^4-432*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^3*c^2*d^2*e^3*f^2*g^3+8*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^2*c^3*d^3*e^2*f^3*g^2+10*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a*c^4*d^4*e*f^4*g+56*x^3*a*c^4*d^4*e*f*g^4*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+1272*x^2*a^2*c^3*d^3*e^2*f*g^4*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-1188*x^2*a*c^4*d^4*e*f^2*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+1696*x*a^3*c^2*d^2*e^3*f*g^4*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-1272*x*a^2*c^3*d^3*e^2*f^2*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+56*x*a*c^4*d^4*e*f^3*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-256*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*a^5*e^5*g^5+15*((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*c^5*d^5*f^5)/(e*x+d)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)/(g*x+f)^6/g^3/(a*e*g-c*d*f)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(c*d*x+a*e)^(1/2)","B"
712,1,511,265,0.045000," ","int((g*x+f)^(5/2)*(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a^{3} e^{3} g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-45 a^{2} c d \,e^{2} f \,g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+45 a \,c^{2} d^{2} e \,f^{2} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-15 c^{3} d^{3} f^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-16 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} g^{2} x^{2}+20 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a c d e \,g^{2} x -52 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c^{2} d^{2} f g x -30 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a^{2} e^{2} g^{2}+80 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a c d e f g -66 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} f^{2}\right)}{48 \sqrt{e x +d}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{3} d^{3}}"," ",0,"-1/48*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(d*g*c)^(1/2))/(d*g*c)^(1/2))*a^3*e^3*g^3-45*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(d*g*c)^(1/2))/(d*g*c)^(1/2))*a^2*c*d*e^2*f*g^2+45*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(d*g*c)^(1/2))/(d*g*c)^(1/2))*a*c^2*d^2*e*f^2*g-15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(d*g*c)^(1/2))/(d*g*c)^(1/2))*c^3*d^3*f^3-16*x^2*c^2*d^2*g^2*((g*x+f)*(c*d*x+a*e))^(1/2)*(d*g*c)^(1/2)+20*(d*g*c)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*x*a*c*d*e*g^2-52*(d*g*c)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*x*c^2*d^2*f*g-30*((g*x+f)*(c*d*x+a*e))^(1/2)*(d*g*c)^(1/2)*a^2*e^2*g^2+80*((g*x+f)*(c*d*x+a*e))^(1/2)*(d*g*c)^(1/2)*a*c*d*e*f*g-66*((g*x+f)*(c*d*x+a*e))^(1/2)*(d*g*c)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/c^3/d^3/((g*x+f)*(c*d*x+a*e))^(1/2)/(d*g*c)^(1/2)","A"
713,1,328,204,0.029000," ","int((g*x+f)^(3/2)*(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 a^{2} e^{2} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-6 a c d e f g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+3 c^{2} d^{2} f^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+4 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d g x -6 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a e g +10 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d f \right)}{8 \sqrt{e x +d}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2}}"," ",0,"1/8*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^2*e^2*g^2-6*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a*c*d*e*f*g+3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*c^2*d^2*f^2+4*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*x*c*d*g-6*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*e*g+10*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*f)/(e*x+d)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/c^2/d^2/(c*d*g)^(1/2)","A"
714,1,201,141,0.025000," ","int((g*x+f)^(1/2)*(e*x+d)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(a e g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-c d f \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\right)}{2 \sqrt{e x +d}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c d}"," ",0,"-1/2*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a*e*g-ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*c*d*f-2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(e*x+d)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/c/d/(c*d*g)^(1/2)","A"
715,1,120,83,0.030000," ","int((e*x+d)^(1/2)/(g*x+f)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)}{\sqrt{e x +d}\, \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}}"," ",0,"1/(e*x+d)^(1/2)*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))/(c*d*g)^(1/2)/(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)","A"
716,1,63,55,0.007000," ","int((e*x+d)^(1/2)/(g*x+f)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \sqrt{e x +d}}{\sqrt{g x +f}\, \left(a e g -c d f \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2/(g*x+f)^(1/2)*(c*d*x+a*e)/(a*e*g-c*d*f)*(e*x+d)^(1/2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
717,1,98,113,0.008000," ","int((e*x+d)^(1/2)/(g*x+f)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-2 c d g x +a e g -3 c d f \right) \sqrt{e x +d}}{3 \left(g x +f \right)^{\frac{3}{2}} \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2/3*(c*d*x+a*e)*(-2*c*d*g*x+a*e*g-3*c*d*f)*(e*x+d)^(1/2)/(g*x+f)^(3/2)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
718,1,169,174,0.010000," ","int((e*x+d)^(1/2)/(g*x+f)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(8 g^{2} x^{2} c^{2} d^{2}-4 a c d e \,g^{2} x +20 c^{2} d^{2} f g x +3 a^{2} e^{2} g^{2}-10 a c d e f g +15 f^{2} c^{2} d^{2}\right) \sqrt{e x +d}}{15 \left(g x +f \right)^{\frac{5}{2}} \left(a^{3} e^{3} g^{3}-3 a^{2} c d \,e^{2} f \,g^{2}+3 a \,c^{2} d^{2} e \,f^{2} g -f^{3} c^{3} d^{3}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2/15*(c*d*x+a*e)*(8*c^2*d^2*g^2*x^2-4*a*c*d*e*g^2*x+20*c^2*d^2*f*g*x+3*a^2*e^2*g^2-10*a*c*d*e*f*g+15*c^2*d^2*f^2)*(e*x+d)^(1/2)/(g*x+f)^(5/2)/(a^3*e^3*g^3-3*a^2*c*d*e^2*f*g^2+3*a*c^2*d^2*e*f^2*g-c^3*d^3*f^3)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
719,1,260,235,0.012000," ","int((e*x+d)^(1/2)/(g*x+f)^(9/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-16 g^{3} x^{3} c^{3} d^{3}+8 a \,c^{2} d^{2} e \,g^{3} x^{2}-56 c^{3} d^{3} f \,g^{2} x^{2}-6 a^{2} c d \,e^{2} g^{3} x +28 a \,c^{2} d^{2} e f \,g^{2} x -70 c^{3} d^{3} f^{2} g x +5 a^{3} e^{3} g^{3}-21 a^{2} c d \,e^{2} f \,g^{2}+35 a \,c^{2} d^{2} e \,f^{2} g -35 f^{3} c^{3} d^{3}\right) \sqrt{e x +d}}{35 \left(g x +f \right)^{\frac{7}{2}} \left(g^{4} e^{4} a^{4}-4 a^{3} c d \,e^{3} f \,g^{3}+6 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-4 a \,c^{3} d^{3} e \,f^{3} g +f^{4} c^{4} d^{4}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}"," ",0,"-2/35*(c*d*x+a*e)*(-16*c^3*d^3*g^3*x^3+8*a*c^2*d^2*e*g^3*x^2-56*c^3*d^3*f*g^2*x^2-6*a^2*c*d*e^2*g^3*x+28*a*c^2*d^2*e*f*g^2*x-70*c^3*d^3*f^2*g*x+5*a^3*e^3*g^3-21*a^2*c*d*e^2*f*g^2+35*a*c^2*d^2*e*f^2*g-35*c^3*d^3*f^3)*(e*x+d)^(1/2)/(g*x+f)^(7/2)/(a^4*e^4*g^4-4*a^3*c*d*e^3*f*g^3+6*a^2*c^2*d^2*e^2*f^2*g^2-4*a*c^3*d^3*e*f^3*g+c^4*d^4*f^4)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
720,1,648,255,0.038000," ","int((e*x+d)^(3/2)*(g*x+f)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{\left(15 a^{2} c d \,e^{2} g^{3} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-30 a \,c^{2} d^{2} e f \,g^{2} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 c^{3} d^{3} f^{2} g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 a^{3} e^{3} g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-30 a^{2} c d \,e^{2} f \,g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 a \,c^{2} d^{2} e \,f^{2} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+4 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} g^{2} x^{2}-10 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a c d e \,g^{2} x +18 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c^{2} d^{2} f g x -30 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a^{2} e^{2} g^{2}+50 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a c d e f g -16 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} f^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \sqrt{g x +f}}{8 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, \left(c d x +a e \right) \sqrt{e x +d}\, c^{3} d^{3}}"," ",0,"1/8*(15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x*a^2*c*d*e^2*g^3-30*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x*a*c^2*d^2*e*f*g^2+15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x*c^3*d^3*f^2*g+15*a^3*e^3*g^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-30*a^2*c*d*e^2*f*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+15*a*c^2*d^2*e*f^2*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+4*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*g^2*x^2-10*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*c*d*e*g^2*x+18*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c^2*d^2*f*g*x-30*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a^2*e^2*g^2+50*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a*c*d*e*f*g-16*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(g*x+f)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/(c*d*g)^(1/2)/(c*d*x+a*e)/c^3/d^3/(e*x+d)^(1/2)","B"
721,1,396,193,0.030000," ","int((e*x+d)^(3/2)*(g*x+f)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{\left(3 a c d e \,g^{2} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-3 c^{2} d^{2} f g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+3 a^{2} e^{2} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-3 a c d e f g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-2 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d g x -6 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a e g +4 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d f \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \sqrt{g x +f}}{2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \left(c d x +a e \right) \sqrt{c d g}\, \sqrt{e x +d}\, c^{2} d^{2}}"," ",0,"-1/2*(3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x*a*c*d*e*g^2-3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x*c^2*d^2*f*g+3*a^2*e^2*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-3*a*c*d*e*f*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-2*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*g*x-6*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*e*g+4*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(g*x+f)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/(c*d*x+a*e)/(c*d*g)^(1/2)/c^2/d^2/(e*x+d)^(1/2)","B"
722,1,210,133,0.027000," ","int((e*x+d)^(3/2)*(g*x+f)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(c d g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+a e g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\right)}{\sqrt{c d g}\, \left(c d x +a e \right) \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{e x +d}\, c d}"," ",0,"(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x*c*d*g+a*e*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2)/(c*d*x+a*e)/((g*x+f)*(c*d*x+a*e))^(1/2)/d/c/(e*x+d)^(1/2)","A"
723,1,63,55,0.006000," ","int((e*x+d)^(3/2)/(g*x+f)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\frac{2 \sqrt{g x +f}\, \left(c d x +a e \right) \left(e x +d \right)^{\frac{3}{2}}}{\left(a e g -c d f \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"2*(g*x+f)^(1/2)*(c*d*x+a*e)/(a*e*g-c*d*f)*(e*x+d)^(3/2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
724,1,97,112,0.007000," ","int((e*x+d)^(3/2)/(g*x+f)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(2 c d g x +a e g +c d f \right) \left(e x +d \right)^{\frac{3}{2}}}{\sqrt{g x +f}\, \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2*(c*d*x+a*e)*(2*c*d*g*x+a*e*g+c*d*f)*(e*x+d)^(3/2)/(g*x+f)^(1/2)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
725,1,168,170,0.010000," ","int((e*x+d)^(3/2)/(g*x+f)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(-8 g^{2} x^{2} c^{2} d^{2}-4 a c d e \,g^{2} x -12 c^{2} d^{2} f g x +a^{2} e^{2} g^{2}-6 a c d e f g -3 f^{2} c^{2} d^{2}\right) \left(e x +d \right)^{\frac{3}{2}}}{3 \left(g x +f \right)^{\frac{3}{2}} \left(a^{3} e^{3} g^{3}-3 a^{2} c d \,e^{2} f \,g^{2}+3 a \,c^{2} d^{2} e \,f^{2} g -f^{3} c^{3} d^{3}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2/3*(c*d*x+a*e)*(-8*c^2*d^2*g^2*x^2-4*a*c*d*e*g^2*x-12*c^2*d^2*f*g*x+a^2*e^2*g^2-6*a*c*d*e*f*g-3*c^2*d^2*f^2)*(e*x+d)^(3/2)/(g*x+f)^(3/2)/(a^3*e^3*g^3-3*a^2*c*d*e^2*f*g^2+3*a*c^2*d^2*e*f^2*g-c^3*d^3*f^3)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
726,1,259,232,0.013000," ","int((e*x+d)^(3/2)/(g*x+f)^(7/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","-\frac{2 \left(c d x +a e \right) \left(16 g^{3} x^{3} c^{3} d^{3}+8 a \,c^{2} d^{2} e \,g^{3} x^{2}+40 c^{3} d^{3} f \,g^{2} x^{2}-2 a^{2} c d \,e^{2} g^{3} x +20 a \,c^{2} d^{2} e f \,g^{2} x +30 c^{3} d^{3} f^{2} g x +a^{3} e^{3} g^{3}-5 a^{2} c d \,e^{2} f \,g^{2}+15 a \,c^{2} d^{2} e \,f^{2} g +5 f^{3} c^{3} d^{3}\right) \left(e x +d \right)^{\frac{3}{2}}}{5 \left(g x +f \right)^{\frac{5}{2}} \left(g^{4} e^{4} a^{4}-4 a^{3} c d \,e^{3} f \,g^{3}+6 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-4 a \,c^{3} d^{3} e \,f^{3} g +f^{4} c^{4} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}"," ",0,"-2/5*(c*d*x+a*e)*(16*c^3*d^3*g^3*x^3+8*a*c^2*d^2*e*g^3*x^2+40*c^3*d^3*f*g^2*x^2-2*a^2*c*d*e^2*g^3*x+20*a*c^2*d^2*e*f*g^2*x+30*c^3*d^3*f^2*g*x+a^3*e^3*g^3-5*a^2*c*d*e^2*f*g^2+15*a*c^2*d^2*e*f^2*g+5*c^3*d^3*f^3)*(e*x+d)^(3/2)/(g*x+f)^(5/2)/(a^4*e^4*g^4-4*a^3*c*d*e^3*f*g^3+6*a^2*c^2*d^2*e^2*f^2*g^2-4*a*c^3*d^3*e*f^3*g+c^4*d^4*f^4)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)","A"
727,1,652,245,0.044000," ","int((e*x+d)^(5/2)*(g*x+f)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{\left(15 a \,c^{2} d^{2} e \,g^{3} x^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-15 c^{3} d^{3} f \,g^{2} x^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+30 a^{2} c d \,e^{2} g^{3} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-30 a \,c^{2} d^{2} e f \,g^{2} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 a^{3} e^{3} g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-15 a^{2} c d \,e^{2} f \,g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-6 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} g^{2} x^{2}-40 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a c d e \,g^{2} x +28 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c^{2} d^{2} f g x -30 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a^{2} e^{2} g^{2}+20 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a c d e f g +4 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} f^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \sqrt{g x +f}}{6 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \left(c d x +a e \right)^{2} \sqrt{c d g}\, \sqrt{e x +d}\, c^{3} d^{3}}"," ",0,"-1/6*(15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x^2*a*c^2*d^2*e*g^3-15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x^2*c^3*d^3*f*g^2+30*a^2*c*d*e^2*g^3*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-30*a*c^2*d^2*e*f*g^2*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+15*a^3*e^3*g^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-15*a^2*c*d*e^2*f*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-6*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*g^2*x^2-40*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*c*d*e*g^2*x+28*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c^2*d^2*f*g*x-30*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a^2*e^2*g^2+20*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a*c*d*e*f*g+4*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(g*x+f)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/(c*d*x+a*e)^2/(c*d*g)^(1/2)/c^3/d^3/(e*x+d)^(1/2)","B"
728,1,343,183,0.030000," ","int((e*x+d)^(5/2)*(g*x+f)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{2} d^{2} g^{2} x^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+6 a c d e \,g^{2} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+3 a^{2} e^{2} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-8 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d g x -6 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a e g -2 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d f \right)}{3 \sqrt{c d g}\, \left(c d x +a e \right)^{2} \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{e x +d}\, c^{2} d^{2}}"," ",0,"1/3*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x^2*c^2*d^2*g^2+6*a*c*d*e*g^2*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+3*a^2*e^2*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-8*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*g*x-6*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*e*g-2*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*f)/(c*d*g)^(1/2)/(c*d*x+a*e)^2/((g*x+f)*(c*d*x+a*e))^(1/2)/d^2/c^2/(e*x+d)^(1/2)","A"
729,1,63,55,0.008000," ","int((e*x+d)^(5/2)*(g*x+f)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{2 \left(g x +f \right)^{\frac{3}{2}} \left(c d x +a e \right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(a e g -c d f \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"2/3*(g*x+f)^(3/2)*(c*d*x+a*e)/(a*e*g-c*d*f)*(e*x+d)^(5/2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
730,1,99,112,0.008000," ","int((e*x+d)^(5/2)/(g*x+f)^(1/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\frac{2 \sqrt{g x +f}\, \left(c d x +a e \right) \left(2 c d g x +3 a e g -c d f \right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"2/3*(g*x+f)^(1/2)*(c*d*x+a*e)*(2*c*d*g*x+3*a*e*g-c*d*f)*(e*x+d)^(5/2)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
731,1,169,170,0.010000," ","int((e*x+d)^(5/2)/(g*x+f)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(8 g^{2} x^{2} c^{2} d^{2}+12 a c d e \,g^{2} x +4 c^{2} d^{2} f g x +3 a^{2} e^{2} g^{2}+6 a c d e f g -f^{2} c^{2} d^{2}\right) \left(e x +d \right)^{\frac{5}{2}}}{3 \sqrt{g x +f}\, \left(a^{3} e^{3} g^{3}-3 a^{2} c d \,e^{2} f \,g^{2}+3 a \,c^{2} d^{2} e \,f^{2} g -f^{3} c^{3} d^{3}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"-2/3*(c*d*x+a*e)*(8*c^2*d^2*g^2*x^2+12*a*c*d*e*g^2*x+4*c^2*d^2*f*g*x+3*a^2*e^2*g^2+6*a*c*d*e*f*g-c^2*d^2*f^2)*(e*x+d)^(5/2)/(g*x+f)^(1/2)/(a^3*e^3*g^3-3*a^2*c*d*e^2*f*g^2+3*a*c^2*d^2*e*f^2*g-c^3*d^3*f^3)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
732,1,258,230,0.012000," ","int((e*x+d)^(5/2)/(g*x+f)^(5/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","-\frac{2 \left(c d x +a e \right) \left(-16 g^{3} x^{3} c^{3} d^{3}-24 a \,c^{2} d^{2} e \,g^{3} x^{2}-24 c^{3} d^{3} f \,g^{2} x^{2}-6 a^{2} c d \,e^{2} g^{3} x -36 a \,c^{2} d^{2} e f \,g^{2} x -6 c^{3} d^{3} f^{2} g x +a^{3} e^{3} g^{3}-9 a^{2} c d \,e^{2} f \,g^{2}-9 a \,c^{2} d^{2} e \,f^{2} g +f^{3} c^{3} d^{3}\right) \left(e x +d \right)^{\frac{5}{2}}}{3 \left(g x +f \right)^{\frac{3}{2}} \left(g^{4} e^{4} a^{4}-4 a^{3} c d \,e^{3} f \,g^{3}+6 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-4 a \,c^{3} d^{3} e \,f^{3} g +f^{4} c^{4} d^{4}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}"," ",0,"-2/3*(c*d*x+a*e)*(-16*c^3*d^3*g^3*x^3-24*a*c^2*d^2*e*g^3*x^2-24*c^3*d^3*f*g^2*x^2-6*a^2*c*d*e^2*g^3*x-36*a*c^2*d^2*e*f*g^2*x-6*c^3*d^3*f^2*g*x+a^3*e^3*g^3-9*a^2*c*d*e^2*f*g^2-9*a*c^2*d^2*e*f^2*g+c^3*d^3*f^3)*(e*x+d)^(5/2)/(g*x+f)^(3/2)/(a^4*e^4*g^4-4*a^3*c*d*e^3*f*g^3+6*a^2*c^2*d^2*e^2*f^2*g^2-4*a*c^3*d^3*e*f^3*g+c^4*d^4*f^4)/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)","A"
733,1,870,329,0.031000," ","int((g*x+f)^(5/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a^{4} e^{4} g^{4} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-60 a^{3} c d \,e^{3} f \,g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+90 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-60 a \,c^{3} d^{3} e \,f^{3} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 c^{4} d^{4} f^{4} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-96 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{3} d^{3} g^{3} x^{3}-16 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, a \,c^{2} d^{2} e \,g^{3} x^{2}-272 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{3} d^{3} f \,g^{2} x^{2}+20 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} c d \,e^{2} g^{3} x -72 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a \,c^{2} d^{2} e f \,g^{2} x -236 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{3} d^{3} f^{2} g x -30 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{3} e^{3} g^{3}+110 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} c d \,e^{2} f \,g^{2}-146 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a \,c^{2} d^{2} e \,f^{2} g -30 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{3} d^{3} f^{3}\right)}{384 \sqrt{e x +d}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{3} d^{3} g}"," ",0,"-1/384*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(-96*x^3*c^3*d^3*g^3*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)+15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^4*e^4*g^4-60*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^3*c*d*e^3*f*g^3+90*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^2*c^2*d^2*e^2*f^2*g^2-60*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a*c^3*d^3*e*f^3*g+15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*c^4*d^4*f^4-16*x^2*a*c^2*d^2*e*g^3*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)-272*x^2*c^3*d^3*f*g^2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)+20*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*a^2*c*d*e^2*g^3-72*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*a*c^2*d^2*e*f*g^2-236*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*c^3*d^3*f^2*g-30*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^3*e^3*g^3+110*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^2*c*d*e^2*f*g^2-146*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*c^2*d^2*e*f^2*g-30*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^3*d^3*f^3)/(e*x+d)^(1/2)/g/(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)/c^3/d^3/(c*d*g)^(1/2)","B"
734,1,602,265,0.028000," ","int((g*x+f)^(3/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 a^{3} e^{3} g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-9 a^{2} c d \,e^{2} f \,g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+9 a \,c^{2} d^{2} e \,f^{2} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-3 c^{3} d^{3} f^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+16 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{2} d^{2} g^{2} x^{2}+4 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a c d e \,g^{2} x +28 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{2} d^{2} f g x -6 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} e^{2} g^{2}+16 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a c d e f g +6 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{2} d^{2} f^{2}\right)}{48 \sqrt{e x +d}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{2} d^{2} g}"," ",0,"1/48*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^3*e^3*g^3-9*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^2*c*d*e^2*f*g^2+9*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a*c^2*d^2*e*f^2*g-3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*c^3*d^3*f^3+16*x^2*c^2*d^2*g^2*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)+4*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*a*c*d*e*g^2+28*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*c^2*d^2*f*g-6*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^2*e^2*g^2+16*a*c*d*e*f*g*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)+6*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/g/(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)/d^2/c^2/(c*d*g)^(1/2)","B"
735,1,385,201,0.022000," ","int((g*x+f)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","-\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(a^{2} e^{2} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-2 a c d e f g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+c^{2} d^{2} f^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-4 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c d g x -2 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a e g -2 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c d f \right)}{8 \sqrt{e x +d}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c d g}"," ",0,"-1/8*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^2*e^2*g^2-2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a*c*d*e*f*g+ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*c^2*d^2*f^2-4*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*c*d*g-2*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*e*g-2*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c*d*f)/(e*x+d)^(1/2)/(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)/d/g/c/(c*d*g)^(1/2)","A"
736,1,198,139,0.023000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^(1/2)/(e*x+d)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \sqrt{g x +f}\, \left(a e g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-c d f \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\right)}{2 \sqrt{e x +d}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, g}"," ",0,"1/2*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(g*x+f)^(1/2)/(e*x+d)^(1/2)*(a*e*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-c*d*f*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/((g*x+f)*(c*d*x+a*e))^(1/2)/g/(c*d*g)^(1/2)","A"
737,1,197,130,0.031000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^(3/2)/(e*x+d)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(c d g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+c d f \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\right)}{\sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{e x +d}\, \sqrt{g x +f}\, g}"," ",0,"(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(c*d*g*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+c*d*f*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/g/(e*x+d)^(1/2)/(g*x+f)^(1/2)","A"
738,1,63,55,0.007000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^(5/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{3 \left(g x +f \right)^{\frac{3}{2}} \left(a e g -c d f \right) \sqrt{e x +d}}"," ",0,"-2/3/(g*x+f)^(3/2)*(c*d*x+a*e)/(a*e*g-c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(e*x+d)^(1/2)","A"
739,1,99,113,0.008000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^(7/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-2 c d g x +3 a e g -5 c d f \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{15 \left(g x +f \right)^{\frac{5}{2}} \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \sqrt{e x +d}}"," ",0,"-2/15*(c*d*x+a*e)*(-2*c*d*g*x+3*a*e*g-5*c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(g*x+f)^(5/2)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(e*x+d)^(1/2)","A"
740,1,169,174,0.009000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^(9/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(8 g^{2} x^{2} c^{2} d^{2}-12 a c d e \,g^{2} x +28 c^{2} d^{2} f g x +15 a^{2} e^{2} g^{2}-42 a c d e f g +35 f^{2} c^{2} d^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{105 \left(g x +f \right)^{\frac{7}{2}} \left(a^{3} e^{3} g^{3}-3 a^{2} c d \,e^{2} f \,g^{2}+3 a \,c^{2} d^{2} e \,f^{2} g -f^{3} c^{3} d^{3}\right) \sqrt{e x +d}}"," ",0,"-2/105*(c*d*x+a*e)*(8*c^2*d^2*g^2*x^2-12*a*c*d*e*g^2*x+28*c^2*d^2*f*g*x+15*a^2*e^2*g^2-42*a*c*d*e*f*g+35*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(g*x+f)^(7/2)/(a^3*e^3*g^3-3*a^2*c*d*e^2*f*g^2+3*a*c^2*d^2*e*f^2*g-c^3*d^3*f^3)/(e*x+d)^(1/2)","A"
741,1,260,235,0.013000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(g*x+f)^(11/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-16 g^{3} x^{3} c^{3} d^{3}+24 a \,c^{2} d^{2} e \,g^{3} x^{2}-72 c^{3} d^{3} f \,g^{2} x^{2}-30 a^{2} c d \,e^{2} g^{3} x +108 a \,c^{2} d^{2} e f \,g^{2} x -126 c^{3} d^{3} f^{2} g x +35 a^{3} e^{3} g^{3}-135 a^{2} c d \,e^{2} f \,g^{2}+189 a \,c^{2} d^{2} e \,f^{2} g -105 f^{3} c^{3} d^{3}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{315 \left(g x +f \right)^{\frac{9}{2}} \left(g^{4} e^{4} a^{4}-4 a^{3} c d \,e^{3} f \,g^{3}+6 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-4 a \,c^{3} d^{3} e \,f^{3} g +f^{4} c^{4} d^{4}\right) \sqrt{e x +d}}"," ",0,"-2/315*(c*d*x+a*e)*(-16*c^3*d^3*g^3*x^3+24*a*c^2*d^2*e*g^3*x^2-72*c^3*d^3*f*g^2*x^2-30*a^2*c*d*e^2*g^3*x+108*a*c^2*d^2*e*f*g^2*x-126*c^3*d^3*f^2*g*x+35*a^3*e^3*g^3-135*a^2*c*d*e^2*f*g^2+189*a*c^2*d^2*e*f^2*g-105*c^3*d^3*f^3)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(g*x+f)^(9/2)/(a^4*e^4*g^4-4*a^3*c*d*e^3*f*g^3+6*a^2*c^2*d^2*e^2*f^2*g^2-4*a*c^3*d^3*e*f^3*g+c^4*d^4*f^4)/(e*x+d)^(1/2)","A"
742,1,870,326,0.025000," ","int((g*x+f)^(3/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 a^{4} e^{4} g^{4} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-12 a^{3} c d \,e^{3} f \,g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+18 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-12 a \,c^{3} d^{3} e \,f^{3} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+3 c^{4} d^{4} f^{4} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+32 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{3} d^{3} g^{3} x^{3}+48 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, a \,c^{2} d^{2} e \,g^{3} x^{2}+48 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{3} d^{3} f \,g^{2} x^{2}+4 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} c d \,e^{2} g^{3} x +88 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a \,c^{2} d^{2} e f \,g^{2} x +4 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{3} d^{3} f^{2} g x -6 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{3} e^{3} g^{3}+22 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} c d \,e^{2} f \,g^{2}+22 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a \,c^{2} d^{2} e \,f^{2} g -6 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{3} d^{3} f^{3}\right)}{128 \sqrt{e x +d}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{2} d^{2} g^{2}}"," ",0,"1/128*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(32*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)*c^3*d^3*g^3*x^3+3*a^4*e^4*g^4*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-12*a^3*c*d*e^3*f*g^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+18*a^2*c^2*d^2*e^2*f^2*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-12*a*c^3*d^3*e*f^3*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+3*c^4*d^4*f^4*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+48*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)*a*c^2*d^2*e*g^3*x^2+48*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)*c^3*d^3*f*g^2*x^2+4*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^2*c*d*e^2*g^3*x+88*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*c^2*d^2*e*f*g^2*x+4*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^3*d^3*f^2*g*x-6*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^3*e^3*g^3+22*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^2*c*d*e^2*f*g^2+22*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*c^2*d^2*e*f^2*g-6*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^3*d^3*f^3)/(e*x+d)^(1/2)/c^2/d^2/g^2/(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)/(c*d*g)^(1/2)","B"
743,1,602,262,0.024000," ","int((g*x+f)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","-\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 a^{3} e^{3} g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-9 a^{2} c d \,e^{2} f \,g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+9 a \,c^{2} d^{2} e \,f^{2} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-3 c^{3} d^{3} f^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-16 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{2} d^{2} g^{2} x^{2}-28 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a c d e \,g^{2} x -4 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{2} d^{2} f g x -6 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} e^{2} g^{2}-16 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a c d e f g +6 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{2} d^{2} f^{2}\right)}{48 \sqrt{e x +d}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c d \,g^{2}}"," ",0,"-1/48*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*a^3*e^3*g^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-9*a^2*c*d*e^2*f*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+9*a*c^2*d^2*e*f^2*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-3*c^3*d^3*f^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-16*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^2*d^2*g^2*x^2-28*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*c*d*e*g^2*x-4*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^2*d^2*f*g*x-6*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^2*e^2*g^2-16*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*c*d*e*f*g+6*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/c/d/(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)/g^2/(c*d*g)^(1/2)","B"
744,1,325,198,0.027000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \sqrt{g x +f}\, \left(3 a^{2} e^{2} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-6 a c d e f g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+3 c^{2} d^{2} f^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+4 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d g x +10 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a e g -6 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d f \right)}{8 \sqrt{e x +d}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, g^{2}}"," ",0,"1/8*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(g*x+f)^(1/2)*(3*a^2*e^2*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-6*a*c*d*e*f*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+3*c^2*d^2*f^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+4*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*g*x+10*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*e*g-6*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*f)/(e*x+d)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/g^2/(c*d*g)^(1/2)","A"
745,1,383,188,0.031000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(3/2),x)","\frac{\left(3 a c d e \,g^{2} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-3 c^{2} d^{2} f g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+3 a c d e f g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-3 c^{2} d^{2} f^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+2 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d g x -4 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a e g +6 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d f \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, \sqrt{g x +f}\, \sqrt{e x +d}\, g^{2}}"," ",0,"1/2*(3*a*c*d*e*g^2*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-3*c^2*d^2*f*g*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+3*a*c*d*e*f*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-3*c^2*d^2*f^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+2*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*g*x-4*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*e*g+6*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/(c*d*g)^(1/2)/g^2/(g*x+f)^(1/2)/(e*x+d)^(1/2)","B"
746,1,331,178,0.034000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(5/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(3 c^{2} d^{2} g^{2} x^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+6 c^{2} d^{2} f g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+3 c^{2} d^{2} f^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-8 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d g x -2 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a e g -6 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c d f \right)}{3 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \left(g x +f \right)^{\frac{3}{2}} \sqrt{e x +d}\, g^{2}}"," ",0,"1/3*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(3*c^2*d^2*g^2*x^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+6*c^2*d^2*f*g*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+3*c^2*d^2*f^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-8*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*g*x-2*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*e*g-6*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c*d*f)/(c*d*g)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/g^2/(g*x+f)^(3/2)/(e*x+d)^(1/2)","A"
747,1,63,55,0.008000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(7/2),x)","-\frac{2 \left(c d x +a e \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{5 \left(g x +f \right)^{\frac{5}{2}} \left(a e g -c d f \right) \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"-2/5/(g*x+f)^(5/2)*(c*d*x+a*e)/(a*e*g-c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/(e*x+d)^(3/2)","A"
748,1,99,113,0.008000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(9/2),x)","-\frac{2 \left(c d x +a e \right) \left(-2 c d g x +5 a e g -7 c d f \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{35 \left(g x +f \right)^{\frac{7}{2}} \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"-2/35*(c*d*x+a*e)*(-2*c*d*g*x+5*a*e*g-7*c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/(g*x+f)^(7/2)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(e*x+d)^(3/2)","A"
749,1,169,174,0.010000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(11/2),x)","-\frac{2 \left(c d x +a e \right) \left(8 g^{2} x^{2} c^{2} d^{2}-20 a c d e \,g^{2} x +36 c^{2} d^{2} f g x +35 a^{2} e^{2} g^{2}-90 a c d e f g +63 f^{2} c^{2} d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{315 \left(g x +f \right)^{\frac{9}{2}} \left(a^{3} e^{3} g^{3}-3 a^{2} c d \,e^{2} f \,g^{2}+3 a \,c^{2} d^{2} e \,f^{2} g -f^{3} c^{3} d^{3}\right) \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"-2/315*(c*d*x+a*e)*(8*c^2*d^2*g^2*x^2-20*a*c*d*e*g^2*x+36*c^2*d^2*f*g*x+35*a^2*e^2*g^2-90*a*c*d*e*f*g+63*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/(g*x+f)^(9/2)/(a^3*e^3*g^3-3*a^2*c*d*e^2*f*g^2+3*a*c^2*d^2*e*f^2*g-c^3*d^3*f^3)/(e*x+d)^(3/2)","A"
750,1,260,235,0.013000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2)/(g*x+f)^(13/2),x)","-\frac{2 \left(c d x +a e \right) \left(-16 g^{3} x^{3} c^{3} d^{3}+40 a \,c^{2} d^{2} e \,g^{3} x^{2}-88 c^{3} d^{3} f \,g^{2} x^{2}-70 a^{2} c d \,e^{2} g^{3} x +220 a \,c^{2} d^{2} e f \,g^{2} x -198 c^{3} d^{3} f^{2} g x +105 a^{3} e^{3} g^{3}-385 a^{2} c d \,e^{2} f \,g^{2}+495 a \,c^{2} d^{2} e \,f^{2} g -231 f^{3} c^{3} d^{3}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{3}{2}}}{1155 \left(g x +f \right)^{\frac{11}{2}} \left(g^{4} e^{4} a^{4}-4 a^{3} c d \,e^{3} f \,g^{3}+6 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-4 a \,c^{3} d^{3} e \,f^{3} g +f^{4} c^{4} d^{4}\right) \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"-2/1155*(c*d*x+a*e)*(-16*c^3*d^3*g^3*x^3+40*a*c^2*d^2*e*g^3*x^2-88*c^3*d^3*f*g^2*x^2-70*a^2*c*d*e^2*g^3*x+220*a*c^2*d^2*e*f*g^2*x-198*c^3*d^3*f^2*g*x+105*a^3*e^3*g^3-385*a^2*c*d*e^2*f*g^2+495*a*c^2*d^2*e*f^2*g-231*c^3*d^3*f^3)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(3/2)/(g*x+f)^(11/2)/(a^4*e^4*g^4-4*a^3*c*d*e^3*f*g^3+6*a^2*c^2*d^2*e^2*f^2*g^2-4*a*c^3*d^3*e*f^3*g+c^4*d^4*f^4)/(e*x+d)^(3/2)","A"
751,1,1191,384,0.031000," ","int((g*x+f)^(3/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a^{5} e^{5} g^{5} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-75 a^{4} c d \,e^{4} f \,g^{4} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+150 a^{3} c^{2} d^{2} e^{3} f^{2} g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-150 a^{2} c^{3} d^{3} e^{2} f^{3} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+75 a \,c^{4} d^{4} e \,f^{4} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-15 c^{5} d^{5} f^{5} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+256 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{4} d^{4} g^{4} x^{4}+672 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, a \,c^{3} d^{3} e \,g^{4} x^{3}+352 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{4} d^{4} f \,g^{3} x^{3}+496 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, a^{2} c^{2} d^{2} e^{2} g^{4} x^{2}+1024 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, a \,c^{3} d^{3} e f \,g^{3} x^{2}+16 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{4} d^{4} f^{2} g^{2} x^{2}+20 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{3} c d \,e^{3} g^{4} x +932 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} c^{2} d^{2} e^{2} f \,g^{3} x +92 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a \,c^{3} d^{3} e \,f^{2} g^{2} x -20 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{4} d^{4} f^{3} g x -30 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{4} e^{4} g^{4}+140 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{3} c d \,e^{3} f \,g^{3}+256 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-140 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a \,c^{3} d^{3} e \,f^{3} g +30 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{4} d^{4} f^{4}\right)}{1280 \sqrt{e x +d}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{2} d^{2} g^{3}}"," ",0,"1/1280*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(256*x^4*c^4*d^4*g^4*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)+672*x^3*a*c^3*d^3*e*g^4*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)+352*x^3*c^4*d^4*f*g^3*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)+15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^5*e^5*g^5-75*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^4*c*d*e^4*f*g^4+150*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^3*c^2*d^2*e^3*f^2*g^3-150*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a^2*c^3*d^3*e^2*f^3*g^2+75*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*a*c^4*d^4*e*f^4*g-15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*c^5*d^5*f^5+496*x^2*a^2*c^2*d^2*e^2*g^4*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)+1024*x^2*a*c^3*d^3*e*f*g^3*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)+16*x^2*c^4*d^4*f^2*g^2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)+20*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*a^3*c*d*e^3*g^4+932*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*a^2*c^2*d^2*e^2*f*g^3+92*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*a*c^3*d^3*e*f^2*g^2-20*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*x*c^4*d^4*f^3*g-30*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^4*e^4*g^4+140*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^3*c*d*e^3*f*g^3+256*a^2*c^2*d^2*e^2*f^2*g^2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)-140*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*c^3*d^3*e*f^3*g+30*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^4*d^4*f^4)/(e*x+d)^(1/2)/g^3/c^2/d^2/(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)/(c*d*g)^(1/2)","B"
752,1,870,320,0.025000," ","int((g*x+f)^(1/2)*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","-\frac{\sqrt{g x +f}\, \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 a^{4} e^{4} g^{4} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-60 a^{3} c d \,e^{3} f \,g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+90 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-60 a \,c^{3} d^{3} e \,f^{3} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 c^{4} d^{4} f^{4} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-96 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{3} d^{3} g^{3} x^{3}-272 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, a \,c^{2} d^{2} e \,g^{3} x^{2}-16 \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c^{3} d^{3} f \,g^{2} x^{2}-236 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} c d \,e^{2} g^{3} x -72 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a \,c^{2} d^{2} e f \,g^{2} x +20 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{3} d^{3} f^{2} g x -30 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{3} e^{3} g^{3}-146 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a^{2} c d \,e^{2} f \,g^{2}+110 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, a \,c^{2} d^{2} e \,f^{2} g -30 \sqrt{c d g}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, c^{3} d^{3} f^{3}\right)}{384 \sqrt{e x +d}\, \sqrt{c d g \,x^{2}+a e g x +c d f x +a e f}\, \sqrt{c d g}\, c d \,g^{3}}"," ",0,"-1/384*(g*x+f)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(-96*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)*c^3*d^3*g^3*x^3+15*a^4*e^4*g^4*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-60*a^3*c*d*e^3*f*g^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+90*a^2*c^2*d^2*e^2*f^2*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-60*a*c^3*d^3*e*f^3*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+15*c^4*d^4*f^4*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-272*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)*a*c^2*d^2*e*g^3*x^2-16*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*(c*d*g)^(1/2)*c^3*d^3*f*g^2*x^2-236*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^2*c*d*e^2*g^3*x-72*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*c^2*d^2*e*f*g^2*x+20*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^3*d^3*f^2*g*x-30*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^3*e^3*g^3-146*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a^2*c*d*e^2*f*g^2+110*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*a*c^2*d^2*e*f^2*g-30*(c*d*g)^(1/2)*(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)*c^3*d^3*f^3)/(e*x+d)^(1/2)/c/d/(c*d*g*x^2+a*e*g*x+c*d*f*x+a*e*f)^(1/2)/g^3/(c*d*g)^(1/2)","B"
753,1,508,256,0.031000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \sqrt{g x +f}\, \left(15 a^{3} e^{3} g^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-45 a^{2} c d \,e^{2} f \,g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+45 a \,c^{2} d^{2} e \,f^{2} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-15 c^{3} d^{3} f^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+16 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} g^{2} x^{2}+52 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a c d e \,g^{2} x -20 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c^{2} d^{2} f g x +66 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a^{2} e^{2} g^{2}-80 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a c d e f g +30 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} f^{2}\right)}{48 \sqrt{e x +d}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, g^{3}}"," ",0,"1/48*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(g*x+f)^(1/2)*(15*a^3*e^3*g^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-45*a^2*c*d*e^2*f*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+45*a*c^2*d^2*e*f^2*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-15*c^3*d^3*f^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+16*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*g^2*x^2+52*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*c*d*e*g^2*x-20*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c^2*d^2*f*g*x+66*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a^2*e^2*g^2-80*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a*c*d*e*f*g+30*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*f^2)/(e*x+d)^(1/2)/g^3/((g*x+f)*(c*d*x+a*e))^(1/2)/(c*d*g)^(1/2)","A"
754,1,635,248,0.033000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(3/2),x)","\frac{\left(15 a^{2} c d \,e^{2} g^{3} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-30 a \,c^{2} d^{2} e f \,g^{2} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 c^{3} d^{3} f^{2} g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 a^{2} c d \,e^{2} f \,g^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-30 a \,c^{2} d^{2} e \,f^{2} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 c^{3} d^{3} f^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+4 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} g^{2} x^{2}+18 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a c d e \,g^{2} x -10 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c^{2} d^{2} f g x -16 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a^{2} e^{2} g^{2}+50 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a c d e f g -30 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} f^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{8 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, \sqrt{g x +f}\, \sqrt{e x +d}\, g^{3}}"," ",0,"1/8*(15*a^2*c*d*e^2*g^3*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-30*a*c^2*d^2*e*f*g^2*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+15*c^3*d^3*f^2*g*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+15*a^2*c*d*e^2*f*g^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-30*a*c^2*d^2*e*f^2*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+15*c^3*d^3*f^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+4*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*g^2*x^2+18*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*c*d*e*g^2*x-10*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c^2*d^2*f*g*x-16*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a^2*e^2*g^2+50*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a*c*d*e*f*g-30*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/(c*d*g)^(1/2)/g^3/(g*x+f)^(1/2)/(e*x+d)^(1/2)","B"
755,1,638,240,0.032000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(5/2),x)","\frac{\left(15 a \,c^{2} d^{2} e \,g^{3} x^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-15 c^{3} d^{3} f \,g^{2} x^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+30 a \,c^{2} d^{2} e f \,g^{2} x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-30 c^{3} d^{3} f^{2} g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 a \,c^{2} d^{2} e \,f^{2} g \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-15 c^{3} d^{3} f^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+6 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} g^{2} x^{2}-28 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a c d e \,g^{2} x +40 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c^{2} d^{2} f g x -4 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a^{2} e^{2} g^{2}-20 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a c d e f g +30 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} f^{2}\right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{6 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, \left(g x +f \right)^{\frac{3}{2}} \sqrt{e x +d}\, g^{3}}"," ",0,"1/6*(15*a*c^2*d^2*e*g^3*x^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-15*c^3*d^3*f*g^2*x^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+30*a*c^2*d^2*e*f*g^2*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-30*c^3*d^3*f^2*g*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+15*a*c^2*d^2*e*f^2*g*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-15*c^3*d^3*f^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+6*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*g^2*x^2-28*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*c*d*e*g^2*x+40*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c^2*d^2*f*g*x-4*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a^2*e^2*g^2-20*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a*c*d*e*f*g+30*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/((g*x+f)*(c*d*x+a*e))^(1/2)/(c*d*g)^(1/2)/g^3/(g*x+f)^(3/2)/(e*x+d)^(1/2)","B"
756,1,511,230,0.037000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(7/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(15 c^{3} d^{3} g^{3} x^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+45 c^{3} d^{3} f \,g^{2} x^{2} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+45 c^{3} d^{3} f^{2} g x \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)+15 c^{3} d^{3} f^{3} \ln \left(\frac{2 c d g x +a e g +c d f +2 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}}{2 \sqrt{c d g}}\right)-46 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} g^{2} x^{2}-22 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, a c d e \,g^{2} x -70 \sqrt{c d g}\, \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, c^{2} d^{2} f g x -6 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a^{2} e^{2} g^{2}-10 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, a c d e f g -30 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, c^{2} d^{2} f^{2}\right)}{15 \sqrt{\left(g x +f \right) \left(c d x +a e \right)}\, \sqrt{c d g}\, \left(g x +f \right)^{\frac{5}{2}} \sqrt{e x +d}\, g^{3}}"," ",0,"1/15*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(15*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))*x^3*c^3*d^3*g^3+45*c^3*d^3*f*g^2*x^2*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+45*c^3*d^3*f^2*g*x*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))+15*c^3*d^3*f^3*ln(1/2*(2*c*d*g*x+a*e*g+c*d*f+2*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2))/(c*d*g)^(1/2))-46*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*g^2*x^2-22*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*a*c*d*e*g^2*x-70*(c*d*g)^(1/2)*((g*x+f)*(c*d*x+a*e))^(1/2)*c^2*d^2*f*g*x-6*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a^2*e^2*g^2-10*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*a*c*d*e*f*g-30*((g*x+f)*(c*d*x+a*e))^(1/2)*(c*d*g)^(1/2)*c^2*d^2*f^2)/((g*x+f)*(c*d*x+a*e))^(1/2)/(c*d*g)^(1/2)/g^3/(g*x+f)^(5/2)/(e*x+d)^(1/2)","B"
757,1,63,55,0.008000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(9/2),x)","-\frac{2 \left(c d x +a e \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{7 \left(g x +f \right)^{\frac{7}{2}} \left(a e g -c d f \right) \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-2/7/(g*x+f)^(7/2)*(c*d*x+a*e)/(a*e*g-c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/(e*x+d)^(5/2)","A"
758,1,99,113,0.009000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(11/2),x)","-\frac{2 \left(c d x +a e \right) \left(-2 c d g x +7 a e g -9 c d f \right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{63 \left(g x +f \right)^{\frac{9}{2}} \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-2/63*(c*d*x+a*e)*(-2*c*d*g*x+7*a*e*g-9*c*d*f)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/(g*x+f)^(9/2)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(e*x+d)^(5/2)","A"
759,1,169,174,0.011000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(13/2),x)","-\frac{2 \left(c d x +a e \right) \left(8 g^{2} x^{2} c^{2} d^{2}-28 a c d e \,g^{2} x +44 c^{2} d^{2} f g x +63 a^{2} e^{2} g^{2}-154 a c d e f g +99 f^{2} c^{2} d^{2}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{693 \left(g x +f \right)^{\frac{11}{2}} \left(a^{3} e^{3} g^{3}-3 a^{2} c d \,e^{2} f \,g^{2}+3 a \,c^{2} d^{2} e \,f^{2} g -f^{3} c^{3} d^{3}\right) \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-2/693*(c*d*x+a*e)*(8*c^2*d^2*g^2*x^2-28*a*c*d*e*g^2*x+44*c^2*d^2*f*g*x+63*a^2*e^2*g^2-154*a*c*d*e*f*g+99*c^2*d^2*f^2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/(g*x+f)^(11/2)/(a^3*e^3*g^3-3*a^2*c*d*e^2*f*g^2+3*a*c^2*d^2*e*f^2*g-c^3*d^3*f^3)/(e*x+d)^(5/2)","A"
760,1,260,235,0.014000," ","int((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2)/(g*x+f)^(15/2),x)","-\frac{2 \left(c d x +a e \right) \left(-16 g^{3} x^{3} c^{3} d^{3}+56 a \,c^{2} d^{2} e \,g^{3} x^{2}-104 c^{3} d^{3} f \,g^{2} x^{2}-126 a^{2} c d \,e^{2} g^{3} x +364 a \,c^{2} d^{2} e f \,g^{2} x -286 c^{3} d^{3} f^{2} g x +231 a^{3} e^{3} g^{3}-819 a^{2} c d \,e^{2} f \,g^{2}+1001 a \,c^{2} d^{2} e \,f^{2} g -429 f^{3} c^{3} d^{3}\right) \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{\frac{5}{2}}}{3003 \left(g x +f \right)^{\frac{13}{2}} \left(g^{4} e^{4} a^{4}-4 a^{3} c d \,e^{3} f \,g^{3}+6 a^{2} c^{2} d^{2} e^{2} f^{2} g^{2}-4 a \,c^{3} d^{3} e \,f^{3} g +f^{4} c^{4} d^{4}\right) \left(e x +d \right)^{\frac{5}{2}}}"," ",0,"-2/3003*(c*d*x+a*e)*(-16*c^3*d^3*g^3*x^3+56*a*c^2*d^2*e*g^3*x^2-104*c^3*d^3*f*g^2*x^2-126*a^2*c*d*e^2*g^3*x+364*a*c^2*d^2*e*f*g^2*x-286*c^3*d^3*f^2*g*x+231*a^3*e^3*g^3-819*a^2*c*d*e^2*f*g^2+1001*a*c^2*d^2*e*f^2*g-429*c^3*d^3*f^3)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(5/2)/(g*x+f)^(13/2)/(a^4*e^4*g^4-4*a^3*c*d*e^3*f*g^3+6*a^2*c^2*d^2*e^2*f^2*g^2-4*a*c^3*d^3*e*f^3*g+c^4*d^4*f^4)/(e*x+d)^(5/2)","A"
761,0,0,100,0.128000," ","int((e*x+d)^(5/2)*(g*x+f)^n/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","\int \frac{\left(e x +d \right)^{\frac{5}{2}} \left(g x +f \right)^{n}}{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*x+d)^(5/2)*(g*x+f)^n/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2),x)","F"
762,0,0,100,0.108000," ","int((e*x+d)^(3/2)*(g*x+f)^n/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","\int \frac{\left(e x +d \right)^{\frac{3}{2}} \left(g x +f \right)^{n}}{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d)^(3/2)*(g*x+f)^n/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2),x)","F"
763,0,0,100,0.104000," ","int((e*x+d)^(1/2)*(g*x+f)^n/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\int \frac{\sqrt{e x +d}\, \left(g x +f \right)^{n}}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}\, dx"," ",0,"int((e*x+d)^(1/2)*(g*x+f)^n/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","F"
764,0,0,100,0.109000," ","int((g*x+f)^n*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","\int \frac{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}\, \left(g x +f \right)^{n}}{\sqrt{e x +d}}\, dx"," ",0,"int((g*x+f)^n*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2)/(e*x+d)^(1/2),x)","F"
765,0,0,100,0.105000," ","int((g*x+f)^n*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{3}{2}} \left(g x +f \right)^{n}}{\left(e x +d \right)^{\frac{3}{2}}}\, dx"," ",0,"int((g*x+f)^n*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(3/2)/(e*x+d)^(3/2),x)","F"
766,0,0,100,0.105000," ","int((g*x+f)^n*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{\frac{5}{2}} \left(g x +f \right)^{n}}{\left(e x +d \right)^{\frac{5}{2}}}\, dx"," ",0,"int((g*x+f)^n*(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(5/2)/(e*x+d)^(5/2),x)","F"
767,0,0,105,0.205000," ","int((e*x+d)^m*(g*x+f)^n/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m} \left(g x +f \right)^{n}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)^n/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
768,1,527,335,0.011000," ","int((e*x+d)^m*(g*x+f)^3/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","-\frac{\left(c^{3} d^{3} g^{3} m^{3} x^{3}+3 c^{3} d^{3} f \,g^{2} m^{3} x^{2}-6 c^{3} d^{3} g^{3} m^{2} x^{3}+3 a \,c^{2} d^{2} e \,g^{3} m^{2} x^{2}+3 c^{3} d^{3} f^{2} g \,m^{3} x -21 c^{3} d^{3} f \,g^{2} m^{2} x^{2}+11 c^{3} d^{3} g^{3} m \,x^{3}+6 a \,c^{2} d^{2} e f \,g^{2} m^{2} x -9 a \,c^{2} d^{2} e \,g^{3} m \,x^{2}+c^{3} d^{3} f^{3} m^{3}-24 c^{3} d^{3} f^{2} g \,m^{2} x +42 c^{3} d^{3} f \,g^{2} m \,x^{2}-6 g^{3} x^{3} c^{3} d^{3}+6 a^{2} c d \,e^{2} g^{3} m x +3 a \,c^{2} d^{2} e \,f^{2} g \,m^{2}-30 a \,c^{2} d^{2} e f \,g^{2} m x +6 a \,c^{2} d^{2} e \,g^{3} x^{2}-9 c^{3} d^{3} f^{3} m^{2}+57 c^{3} d^{3} f^{2} g m x -24 c^{3} d^{3} f \,g^{2} x^{2}+6 a^{2} c d \,e^{2} f \,g^{2} m -6 a^{2} c d \,e^{2} g^{3} x -21 a \,c^{2} d^{2} e \,f^{2} g m +24 a \,c^{2} d^{2} e f \,g^{2} x +26 c^{3} d^{3} f^{3} m -36 c^{3} d^{3} f^{2} g x +6 a^{3} e^{3} g^{3}-24 a^{2} c d \,e^{2} f \,g^{2}+36 a \,c^{2} d^{2} e \,f^{2} g -24 f^{3} c^{3} d^{3}\right) \left(c d x +a e \right) \left(e x +d \right)^{m} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{-m}}{\left(m^{4}-10 m^{3}+35 m^{2}-50 m +24\right) c^{4} d^{4}}"," ",0,"-(e*x+d)^m*(c^3*d^3*g^3*m^3*x^3+3*c^3*d^3*f*g^2*m^3*x^2-6*c^3*d^3*g^3*m^2*x^3+3*a*c^2*d^2*e*g^3*m^2*x^2+3*c^3*d^3*f^2*g*m^3*x-21*c^3*d^3*f*g^2*m^2*x^2+11*c^3*d^3*g^3*m*x^3+6*a*c^2*d^2*e*f*g^2*m^2*x-9*a*c^2*d^2*e*g^3*m*x^2+c^3*d^3*f^3*m^3-24*c^3*d^3*f^2*g*m^2*x+42*c^3*d^3*f*g^2*m*x^2-6*c^3*d^3*g^3*x^3+6*a^2*c*d*e^2*g^3*m*x+3*a*c^2*d^2*e*f^2*g*m^2-30*a*c^2*d^2*e*f*g^2*m*x+6*a*c^2*d^2*e*g^3*x^2-9*c^3*d^3*f^3*m^2+57*c^3*d^3*f^2*g*m*x-24*c^3*d^3*f*g^2*x^2+6*a^2*c*d*e^2*f*g^2*m-6*a^2*c*d*e^2*g^3*x-21*a*c^2*d^2*e*f^2*g*m+24*a*c^2*d^2*e*f*g^2*x+26*c^3*d^3*f^3*m-36*c^3*d^3*f^2*g*x+6*a^3*e^3*g^3-24*a^2*c*d*e^2*f*g^2+36*a*c^2*d^2*e*f^2*g-24*c^3*d^3*f^3)*(c*d*x+a*e)/((c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^m)/c^4/d^4/(m^4-10*m^3+35*m^2-50*m+24)","A"
769,1,235,246,0.010000," ","int((e*x+d)^m*(g*x+f)^2/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","-\frac{\left(c d x +a e \right) \left(c^{2} d^{2} g^{2} m^{2} x^{2}+2 c^{2} d^{2} f g \,m^{2} x -3 c^{2} d^{2} g^{2} m \,x^{2}+2 a c d e \,g^{2} m x +c^{2} d^{2} f^{2} m^{2}-8 c^{2} d^{2} f g m x +2 g^{2} x^{2} c^{2} d^{2}+2 a c d e f g m -2 a c d e \,g^{2} x -5 c^{2} d^{2} f^{2} m +6 c^{2} d^{2} f g x +2 a^{2} e^{2} g^{2}-6 a c d e f g +6 f^{2} c^{2} d^{2}\right) \left(e x +d \right)^{m} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{-m}}{\left(m^{3}-6 m^{2}+11 m -6\right) c^{3} d^{3}}"," ",0,"-(c*d*x+a*e)*(c^2*d^2*g^2*m^2*x^2+2*c^2*d^2*f*g*m^2*x-3*c^2*d^2*g^2*m*x^2+2*a*c*d*e*g^2*m*x+c^2*d^2*f^2*m^2-8*c^2*d^2*f*g*m*x+2*c^2*d^2*g^2*x^2+2*a*c*d*e*f*g*m-2*a*c*d*e*g^2*x-5*c^2*d^2*f^2*m+6*c^2*d^2*f*g*x+2*a^2*e^2*g^2-6*a*c*d*e*f*g+6*c^2*d^2*f^2)*(e*x+d)^m/((c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^m)/c^3/d^3/(m^3-6*m^2+11*m-6)","A"
770,1,89,150,0.005000," ","int((e*x+d)^m*(g*x+f)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","-\frac{\left(c d g m x +c d f m -c d g x +a e g -2 c d f \right) \left(c d x +a e \right) \left(e x +d \right)^{m} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{-m}}{\left(m^{2}-3 m +2\right) c^{2} d^{2}}"," ",0,"-(e*x+d)^m*(c*d*g*m*x+c*d*f*m-c*d*g*x+a*e*g-2*c*d*f)*(c*d*x+a*e)/((c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^m)/c^2/d^2/(m^2-3*m+2)","A"
771,1,57,54,0.003000," ","int((e*x+d)^m/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","-\frac{\left(c d x +a e \right) \left(e x +d \right)^{m} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{-m}}{\left(m -1\right) c d}"," ",0,"-(c*d*x+a*e)/c/d/(-1+m)*(e*x+d)^m/((c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^m)","A"
772,0,0,101,0.118000," ","int((e*x+d)^m/(g*x+f)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m}}{g x +f}\, dx"," ",0,"int((e*x+d)^m/(g*x+f)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
773,0,0,103,0.123000," ","int((e*x+d)^m/(g*x+f)^2/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m}}{\left(g x +f \right)^{2}}\, dx"," ",0,"int((e*x+d)^m/(g*x+f)^2/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
774,0,0,107,0.129000," ","int((e*x+d)^m/(g*x+f)^3/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m}}{\left(g x +f \right)^{3}}\, dx"," ",0,"int((e*x+d)^m/(g*x+f)^3/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
775,0,0,99,0.107000," ","int((e*x+d)^m*(g*x+f)^(3/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \left(g x +f \right)^{\frac{3}{2}} \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)^(3/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
776,0,0,99,0.113000," ","int((e*x+d)^m*(g*x+f)^(1/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \sqrt{g x +f}\, \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)^(1/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
777,0,0,99,0.107000," ","int((e*x+d)^m/(g*x+f)^(1/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m}}{\sqrt{g x +f}}\, dx"," ",0,"int((e*x+d)^m/(g*x+f)^(1/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
778,0,0,99,0.107000," ","int((e*x+d)^m/(g*x+f)^(3/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m}}{\left(g x +f \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d)^m/(g*x+f)^(3/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
779,0,0,99,0.106000," ","int((e*x+d)^m/(g*x+f)^(5/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \frac{\left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(e x +d \right)^{m}}{\left(g x +f \right)^{\frac{5}{2}}}\, dx"," ",0,"int((e*x+d)^m/(g*x+f)^(5/2)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
780,1,64,65,0.003000," ","int((c*d*x+a*e)^n*(e*x+d)^m/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","-\frac{\left(e x +d \right)^{m} \left(c d x +a e \right)^{n +1} \left(c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e \right)^{-m}}{\left(m -n -1\right) c d}"," ",0,"-(c*d*x+a*e)^(n+1)/c/d/(-1+m-n)*(e*x+d)^m/((c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^m)","A"
781,0,0,78,0.242000," ","int((e*x+d)^m*(c*d^2*e*g-e*(a*e^2+c*d^2)*g-c*d*e^2*g*x)^(m-1)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","\int \left(c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x \right)^{-m} \left(-c d \,e^{2} g x +c \,d^{2} e g -\left(a \,e^{2}+c \,d^{2}\right) e g \right)^{m -1} \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*d^2*e*g-e*(a*e^2+c*d^2)*g-c*d*e^2*g*x)^(m-1)/((c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^m),x)","F"
782,0,0,205,0.106000," ","int((e*x+d)^(3/2)*(g*x+f)^n/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\int \frac{\left(e x +d \right)^{\frac{3}{2}} \left(g x +f \right)^{n}}{\sqrt{c d e \,x^{2}+a d e +\left(a \,e^{2}+c \,d^{2}\right) x}}\, dx"," ",0,"int((e*x+d)^(3/2)*(g*x+f)^n/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","F"
783,1,641,465,0.011000," ","int((e*x+d)^(3/2)*(g*x+f)^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-315 e \,g^{4} x^{5} c^{5} d^{5}+350 a \,c^{4} d^{4} e^{2} g^{4} x^{4}-385 c^{5} d^{6} g^{4} x^{4}-1540 c^{5} d^{5} e f \,g^{3} x^{4}-400 a^{2} c^{3} d^{3} e^{3} g^{4} x^{3}+440 a \,c^{4} d^{5} e \,g^{4} x^{3}+1760 a \,c^{4} d^{4} e^{2} f \,g^{3} x^{3}-1980 c^{5} d^{6} f \,g^{3} x^{3}-2970 c^{5} d^{5} e \,f^{2} g^{2} x^{3}+480 a^{3} c^{2} d^{2} e^{4} g^{4} x^{2}-528 a^{2} c^{3} d^{4} e^{2} g^{4} x^{2}-2112 a^{2} c^{3} d^{3} e^{3} f \,g^{3} x^{2}+2376 a \,c^{4} d^{5} e f \,g^{3} x^{2}+3564 a \,c^{4} d^{4} e^{2} f^{2} g^{2} x^{2}-4158 c^{5} d^{6} f^{2} g^{2} x^{2}-2772 c^{5} d^{5} e \,f^{3} g \,x^{2}-640 a^{4} c d \,e^{5} g^{4} x +704 a^{3} c^{2} d^{3} e^{3} g^{4} x +2816 a^{3} c^{2} d^{2} e^{4} f \,g^{3} x -3168 a^{2} c^{3} d^{4} e^{2} f \,g^{3} x -4752 a^{2} c^{3} d^{3} e^{3} f^{2} g^{2} x +5544 a \,c^{4} d^{5} e \,f^{2} g^{2} x +3696 a \,c^{4} d^{4} e^{2} f^{3} g x -4620 c^{5} d^{6} f^{3} g x -1155 c^{5} d^{5} e \,f^{4} x +1280 a^{5} e^{6} g^{4}-1408 a^{4} c \,d^{2} e^{4} g^{4}-5632 a^{4} c d \,e^{5} f \,g^{3}+6336 a^{3} c^{2} d^{3} e^{3} f \,g^{3}+9504 a^{3} c^{2} d^{2} e^{4} f^{2} g^{2}-11088 a^{2} c^{3} d^{4} e^{2} f^{2} g^{2}-7392 a^{2} c^{3} d^{3} e^{3} f^{3} g +9240 a \,c^{4} d^{5} e \,f^{3} g +2310 a \,c^{4} d^{4} e^{2} f^{4}-3465 d^{6} f^{4} c^{5}\right) \sqrt{e x +d}}{3465 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{6} d^{6}}"," ",0,"-2/3465*(c*d*x+a*e)*(-315*c^5*d^5*e*g^4*x^5+350*a*c^4*d^4*e^2*g^4*x^4-385*c^5*d^6*g^4*x^4-1540*c^5*d^5*e*f*g^3*x^4-400*a^2*c^3*d^3*e^3*g^4*x^3+440*a*c^4*d^5*e*g^4*x^3+1760*a*c^4*d^4*e^2*f*g^3*x^3-1980*c^5*d^6*f*g^3*x^3-2970*c^5*d^5*e*f^2*g^2*x^3+480*a^3*c^2*d^2*e^4*g^4*x^2-528*a^2*c^3*d^4*e^2*g^4*x^2-2112*a^2*c^3*d^3*e^3*f*g^3*x^2+2376*a*c^4*d^5*e*f*g^3*x^2+3564*a*c^4*d^4*e^2*f^2*g^2*x^2-4158*c^5*d^6*f^2*g^2*x^2-2772*c^5*d^5*e*f^3*g*x^2-640*a^4*c*d*e^5*g^4*x+704*a^3*c^2*d^3*e^3*g^4*x+2816*a^3*c^2*d^2*e^4*f*g^3*x-3168*a^2*c^3*d^4*e^2*f*g^3*x-4752*a^2*c^3*d^3*e^3*f^2*g^2*x+5544*a*c^4*d^5*e*f^2*g^2*x+3696*a*c^4*d^4*e^2*f^3*g*x-4620*c^5*d^6*f^3*g*x-1155*c^5*d^5*e*f^4*x+1280*a^5*e^6*g^4-1408*a^4*c*d^2*e^4*g^4-5632*a^4*c*d*e^5*f*g^3+6336*a^3*c^2*d^3*e^3*f*g^3+9504*a^3*c^2*d^2*e^4*f^2*g^2-11088*a^2*c^3*d^4*e^2*f^2*g^2-7392*a^2*c^3*d^3*e^3*f^3*g+9240*a*c^4*d^5*e*f^3*g+2310*a*c^4*d^4*e^2*f^4-3465*c^5*d^6*f^4)*(e*x+d)^(1/2)/c^6/d^6/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
784,1,425,382,0.010000," ","int((e*x+d)^(3/2)*(g*x+f)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(35 e \,g^{3} x^{4} c^{4} d^{4}-40 a \,c^{3} d^{3} e^{2} g^{3} x^{3}+45 c^{4} d^{5} g^{3} x^{3}+135 c^{4} d^{4} e f \,g^{2} x^{3}+48 a^{2} c^{2} d^{2} e^{3} g^{3} x^{2}-54 a \,c^{3} d^{4} e \,g^{3} x^{2}-162 a \,c^{3} d^{3} e^{2} f \,g^{2} x^{2}+189 c^{4} d^{5} f \,g^{2} x^{2}+189 c^{4} d^{4} e \,f^{2} g \,x^{2}-64 a^{3} c d \,e^{4} g^{3} x +72 a^{2} c^{2} d^{3} e^{2} g^{3} x +216 a^{2} c^{2} d^{2} e^{3} f \,g^{2} x -252 a \,c^{3} d^{4} e f \,g^{2} x -252 a \,c^{3} d^{3} e^{2} f^{2} g x +315 c^{4} d^{5} f^{2} g x +105 c^{4} d^{4} e \,f^{3} x +128 a^{4} e^{5} g^{3}-144 a^{3} c \,d^{2} e^{3} g^{3}-432 a^{3} c d \,e^{4} f \,g^{2}+504 a^{2} c^{2} d^{3} e^{2} f \,g^{2}+504 a^{2} c^{2} d^{2} e^{3} f^{2} g -630 a \,c^{3} d^{4} e \,f^{2} g -210 a \,c^{3} d^{3} e^{2} f^{3}+315 d^{5} f^{3} c^{4}\right) \sqrt{e x +d}}{315 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{5} d^{5}}"," ",0,"2/315*(c*d*x+a*e)*(35*c^4*d^4*e*g^3*x^4-40*a*c^3*d^3*e^2*g^3*x^3+45*c^4*d^5*g^3*x^3+135*c^4*d^4*e*f*g^2*x^3+48*a^2*c^2*d^2*e^3*g^3*x^2-54*a*c^3*d^4*e*g^3*x^2-162*a*c^3*d^3*e^2*f*g^2*x^2+189*c^4*d^5*f*g^2*x^2+189*c^4*d^4*e*f^2*g*x^2-64*a^3*c*d*e^4*g^3*x+72*a^2*c^2*d^3*e^2*g^3*x+216*a^2*c^2*d^2*e^3*f*g^2*x-252*a*c^3*d^4*e*f*g^2*x-252*a*c^3*d^3*e^2*f^2*g*x+315*c^4*d^5*f^2*g*x+105*c^4*d^4*e*f^3*x+128*a^4*e^5*g^3-144*a^3*c*d^2*e^3*g^3-432*a^3*c*d*e^4*f*g^2+504*a^2*c^2*d^3*e^2*f*g^2+504*a^2*c^2*d^2*e^3*f^2*g-630*a*c^3*d^4*e*f^2*g-210*a*c^3*d^3*e^2*f^3+315*c^4*d^5*f^3)*(e*x+d)^(1/2)/c^5/d^5/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
785,1,255,297,0.010000," ","int((e*x+d)^(3/2)*(g*x+f)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-15 e \,g^{2} x^{3} c^{3} d^{3}+18 a \,c^{2} d^{2} e^{2} g^{2} x^{2}-21 c^{3} d^{4} g^{2} x^{2}-42 c^{3} d^{3} e f g \,x^{2}-24 a^{2} c d \,e^{3} g^{2} x +28 a \,c^{2} d^{3} e \,g^{2} x +56 a \,c^{2} d^{2} e^{2} f g x -70 c^{3} d^{4} f g x -35 c^{3} d^{3} e \,f^{2} x +48 a^{3} e^{4} g^{2}-56 a^{2} c \,d^{2} e^{2} g^{2}-112 a^{2} c d \,e^{3} f g +140 a \,c^{2} d^{3} e f g +70 a \,c^{2} d^{2} e^{2} f^{2}-105 d^{4} f^{2} c^{3}\right) \sqrt{e x +d}}{105 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{4} d^{4}}"," ",0,"-2/105*(c*d*x+a*e)*(-15*c^3*d^3*e*g^2*x^3+18*a*c^2*d^2*e^2*g^2*x^2-21*c^3*d^4*g^2*x^2-42*c^3*d^3*e*f*g*x^2-24*a^2*c*d*e^3*g^2*x+28*a*c^2*d^3*e*g^2*x+56*a*c^2*d^2*e^2*f*g*x-70*c^3*d^4*f*g*x-35*c^3*d^3*e*f^2*x+48*a^3*e^4*g^2-56*a^2*c*d^2*e^2*g^2-112*a^2*c*d*e^3*f*g+140*a*c^2*d^3*e*f*g+70*a*c^2*d^2*e^2*f^2-105*c^3*d^4*f^2)*(e*x+d)^(1/2)/c^4/d^4/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
786,1,131,191,0.005000," ","int((e*x+d)^(3/2)*(g*x+f)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{2 \left(c d x +a e \right) \left(3 e g \,x^{2} c^{2} d^{2}-4 a c d \,e^{2} g x +5 c^{2} d^{3} g x +5 c^{2} d^{2} e f x +8 a^{2} e^{3} g -10 a c \,d^{2} e g -10 a c d \,e^{2} f +15 d^{3} f \,c^{2}\right) \sqrt{e x +d}}{15 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{3} d^{3}}"," ",0,"2/15*(c*d*x+a*e)*(3*c^2*d^2*e*g*x^2-4*a*c*d*e^2*g*x+5*c^2*d^3*g*x+5*c^2*d^2*e*f*x+8*a^2*e^3*g-10*a*c*d^2*e*g-10*a*c*d*e^2*f+15*c^2*d^3*f)*(e*x+d)^(1/2)/c^3/d^3/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
787,1,69,97,0.003000," ","int((e*x+d)^(3/2)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \left(c d x +a e \right) \left(-c d e x +2 a \,e^{2}-3 c \,d^{2}\right) \sqrt{e x +d}}{3 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, c^{2} d^{2}}"," ",0,"-2/3*(c*d*x+a*e)*(-c*d*e*x+2*a*e^2-3*c*d^2)*(e*x+d)^(1/2)/c^2/d^2/(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)","A"
788,1,163,123,0.024000," ","int((e*x+d)^(3/2)/(g*x+f)/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{2 \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(c \,d^{2} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-c d e f \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-\sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, e \right)}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c d g}"," ",0,"-2*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c*d^2*g-arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c*d*e*f-(c*d*x+a*e)^(1/2)*e*((a*e*g-c*d*f)*g)^(1/2))/(e*x+d)^(1/2)/(c*d*x+a*e)^(1/2)/c/d/g/((a*e*g-c*d*f)*g)^(1/2)","A"
789,1,347,154,0.028000," ","int((e*x+d)^(3/2)/(g*x+f)^2/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\left(-2 a \,e^{2} g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+c \,d^{2} g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+c d e f g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-2 a \,e^{2} f g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+c \,d^{2} f g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+c d e \,f^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-\sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, d g +\sqrt{\left(a e g -c d f \right) g}\, \sqrt{c d x +a e}\, e f \right) \sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}}{\sqrt{e x +d}\, \sqrt{c d x +a e}\, \left(a e g -c d f \right) \left(g x +f \right) \sqrt{\left(a e g -c d f \right) g}\, g}"," ",0,"(-2*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a*e^2*g^2+arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c*d^2*g^2+arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c*d*e*f*g-2*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*e^2*f*g+arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c*d^2*f*g+arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c*d*e*f^2-((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*d*g+((a*e*g-c*d*f)*g)^(1/2)*(c*d*x+a*e)^(1/2)*e*f)/(e*x+d)^(1/2)*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)/(c*d*x+a*e)^(1/2)/(a*e*g-c*d*f)/g/(g*x+f)/((a*e*g-c*d*f)*g)^(1/2)","B"
790,1,673,235,0.042000," ","int((e*x+d)^(3/2)/(g*x+f)^3/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(4 a c d \,e^{2} g^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 c^{2} d^{3} g^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-c^{2} d^{2} e f \,g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+8 a c d \,e^{2} f \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-6 c^{2} d^{3} f \,g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-2 c^{2} d^{2} e \,f^{2} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+4 a c d \,e^{2} f^{2} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 c^{2} d^{3} f^{2} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-c^{2} d^{2} e \,f^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-4 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,e^{2} g^{2} x +3 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c \,d^{2} g^{2} x +\sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c d e f g x -2 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a d e \,g^{2}-2 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a \,e^{2} f g +5 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c \,d^{2} f g -\sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c d e \,f^{2}\right)}{4 \sqrt{e x +d}\, \sqrt{\left(a e g -c d f \right) g}\, \left(g x +f \right)^{2} \left(a e g -c d f \right)^{2} \sqrt{c d x +a e}\, g}"," ",0,"1/4*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(4*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*a*c*d*e^2*g^3-3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^2*d^3*g^3-arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^2*d^2*e*f*g^2+8*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a*c*d*e^2*f*g^2-6*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^2*d^3*f*g^2-2*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^2*d^2*e*f^2*g+4*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c*d*e^2*f^2*g-3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^2*d^3*f^2*g-arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^2*d^2*e*f^3-4*x*a*e^2*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+3*x*c*d^2*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+x*c*d*e*f*g*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-2*a*d*e*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-2*a*e^2*f*g*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+5*c*d^2*f*g*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-c*d*e*f^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2))/(e*x+d)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)/(g*x+f)^2/g/(a*e*g-c*d*f)^2/(c*d*x+a*e)^(1/2)","B"
791,1,1142,319,0.047000," ","int((e*x+d)^(3/2)/(g*x+f)^4/(c*d*e*x^2+a*d*e+(a*e^2+c*d^2)*x)^(1/2),x)","-\frac{\sqrt{c d e \,x^{2}+a \,e^{2} x +c \,d^{2} x +a d e}\, \left(18 a \,c^{2} d^{2} e^{2} g^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 c^{3} d^{4} g^{4} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 c^{3} d^{3} e f \,g^{3} x^{3} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+54 a \,c^{2} d^{2} e^{2} f \,g^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-45 c^{3} d^{4} f \,g^{3} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-9 c^{3} d^{3} e \,f^{2} g^{2} x^{2} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+54 a \,c^{2} d^{2} e^{2} f^{2} g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-45 c^{3} d^{4} f^{2} g^{2} x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-9 c^{3} d^{3} e \,f^{3} g x \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)+18 a \,c^{2} d^{2} e^{2} f^{3} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-15 c^{3} d^{4} f^{3} g \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-3 c^{3} d^{3} e \,f^{4} \arctanh \left(\frac{\sqrt{c d x +a e}\, g}{\sqrt{\left(a e g -c d f \right) g}}\right)-18 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a c d \,e^{2} g^{3} x^{2}+15 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{3} g^{3} x^{2}+3 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} e f \,g^{2} x^{2}+12 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} e^{3} g^{3} x -10 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a c \,d^{2} e \,g^{3} x -50 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a c d \,e^{2} f \,g^{2} x +40 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{3} f \,g^{2} x +8 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} e \,f^{2} g x +8 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} d \,e^{2} g^{3}+4 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a^{2} e^{3} f \,g^{2}-26 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a c \,d^{2} e f \,g^{2}-16 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, a c d \,e^{2} f^{2} g +33 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{3} f^{2} g -3 \sqrt{c d x +a e}\, \sqrt{\left(a e g -c d f \right) g}\, c^{2} d^{2} e \,f^{3}\right)}{24 \sqrt{e x +d}\, \sqrt{\left(a e g -c d f \right) g}\, \left(g x +f \right)^{3} \left(a e g -c d f \right) \left(a^{2} e^{2} g^{2}-2 a c d e f g +f^{2} c^{2} d^{2}\right) \sqrt{c d x +a e}\, g}"," ",0,"-1/24*(c*d*e*x^2+a*e^2*x+c*d^2*x+a*d*e)^(1/2)*(-3*c^2*d^2*e*f^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^3*d^4*g^4-15*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^4*f^3*g-3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*c^3*d^3*e*f^4-50*x*a*c*d*e^2*f*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-45*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^3*d^4*f*g^3-45*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^4*f^2*g^2+15*x^2*c^2*d^3*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+12*x*a^2*e^3*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+8*a^2*d*e^2*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+4*a^2*e^3*f*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+33*c^2*d^3*f^2*g*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-18*x^2*a*c*d*e^2*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+40*x*c^2*d^3*f*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+18*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*a*c^2*d^2*e^2*g^4-3*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^3*c^3*d^3*e*f*g^3-9*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*c^3*d^3*e*f^2*g^2-9*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*c^3*d^3*e*f^3*g+18*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*a*c^2*d^2*e^2*f^3*g+3*x^2*c^2*d^2*e*f*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-10*x*a*c*d^2*e*g^3*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+8*x*c^2*d^2*e*f^2*g*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-26*a*c*d^2*e*f*g^2*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)-16*a*c*d*e^2*f^2*g*(c*d*x+a*e)^(1/2)*((a*e*g-c*d*f)*g)^(1/2)+54*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x^2*a*c^2*d^2*e^2*f*g^3+54*arctanh((c*d*x+a*e)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)*g)*x*a*c^2*d^2*e^2*f^2*g^2)/(e*x+d)^(1/2)/((a*e*g-c*d*f)*g)^(1/2)/(g*x+f)^3/g/(a*e*g-c*d*f)/(a^2*e^2*g^2-2*a*c*d*e*f*g+c^2*d^2*f^2)/(c*d*x+a*e)^(1/2)","B"
792,1,602,298,0.059000," ","int((c*x^2+b*x+a)^3/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(40 \sqrt{-d^{2} x^{2}+1}\, c^{3} d^{5} x^{5} \mathrm{csgn}\left(d \right)+144 \sqrt{-d^{2} x^{2}+1}\, b \,c^{2} d^{5} x^{4} \mathrm{csgn}\left(d \right)+180 \sqrt{-d^{2} x^{2}+1}\, a \,c^{2} d^{5} x^{3} \mathrm{csgn}\left(d \right)+180 \sqrt{-d^{2} x^{2}+1}\, b^{2} c \,d^{5} x^{3} \mathrm{csgn}\left(d \right)+480 \sqrt{-d^{2} x^{2}+1}\, a b c \,d^{5} x^{2} \mathrm{csgn}\left(d \right)+80 \sqrt{-d^{2} x^{2}+1}\, b^{3} d^{5} x^{2} \mathrm{csgn}\left(d \right)-240 a^{3} d^{6} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+360 \sqrt{-d^{2} x^{2}+1}\, a^{2} c \,d^{5} x \,\mathrm{csgn}\left(d \right)+360 \sqrt{-d^{2} x^{2}+1}\, a \,b^{2} d^{5} x \,\mathrm{csgn}\left(d \right)+50 \sqrt{-d^{2} x^{2}+1}\, c^{3} d^{3} x^{3} \mathrm{csgn}\left(d \right)+720 \sqrt{-d^{2} x^{2}+1}\, a^{2} b \,d^{5} \mathrm{csgn}\left(d \right)+192 \sqrt{-d^{2} x^{2}+1}\, b \,c^{2} d^{3} x^{2} \mathrm{csgn}\left(d \right)-360 a^{2} c \,d^{4} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-360 a \,b^{2} d^{4} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+270 \sqrt{-d^{2} x^{2}+1}\, a \,c^{2} d^{3} x \,\mathrm{csgn}\left(d \right)+270 \sqrt{-d^{2} x^{2}+1}\, b^{2} c \,d^{3} x \,\mathrm{csgn}\left(d \right)+960 \sqrt{-d^{2} x^{2}+1}\, a b c \,d^{3} \mathrm{csgn}\left(d \right)+160 \sqrt{-d^{2} x^{2}+1}\, b^{3} d^{3} \mathrm{csgn}\left(d \right)-270 a \,c^{2} d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-270 b^{2} c \,d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+75 \sqrt{-d^{2} x^{2}+1}\, c^{3} d x \,\mathrm{csgn}\left(d \right)+384 \sqrt{-d^{2} x^{2}+1}\, b \,c^{2} d \,\mathrm{csgn}\left(d \right)-75 c^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{240 \sqrt{-d^{2} x^{2}+1}\, d^{7}}"," ",0,"-1/240*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(40*csgn(d)*x^5*c^3*d^5*(-d^2*x^2+1)^(1/2)+144*csgn(d)*x^4*b*c^2*d^5*(-d^2*x^2+1)^(1/2)+180*csgn(d)*x^3*a*c^2*d^5*(-d^2*x^2+1)^(1/2)+180*csgn(d)*x^3*b^2*c*d^5*(-d^2*x^2+1)^(1/2)+480*csgn(d)*x^2*a*b*c*d^5*(-d^2*x^2+1)^(1/2)+80*csgn(d)*x^2*b^3*d^5*(-d^2*x^2+1)^(1/2)+50*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x^3*c^3+360*csgn(d)*d^5*(-d^2*x^2+1)^(1/2)*x*a^2*c+360*csgn(d)*d^5*(-d^2*x^2+1)^(1/2)*x*a*b^2+192*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x^2*b*c^2+720*(-d^2*x^2+1)^(1/2)*csgn(d)*d^5*a^2*b-240*arctan(csgn(d)*d*x/(-d^2*x^2+1)^(1/2))*a^3*d^6+270*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x*a*c^2+270*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x*b^2*c+960*(-d^2*x^2+1)^(1/2)*csgn(d)*d^3*a*b*c+160*(-d^2*x^2+1)^(1/2)*csgn(d)*d^3*b^3-360*arctan(csgn(d)*d*x/(-d^2*x^2+1)^(1/2))*a^2*c*d^4-360*arctan(csgn(d)*d*x/(-d^2*x^2+1)^(1/2))*a*b^2*d^4+75*csgn(d)*d*(-d^2*x^2+1)^(1/2)*x*c^3+384*(-d^2*x^2+1)^(1/2)*csgn(d)*d*b*c^2-270*arctan(csgn(d)*d*x/(-d^2*x^2+1)^(1/2))*a*c^2*d^2-270*arctan(csgn(d)*d*x/(-d^2*x^2+1)^(1/2))*b^2*c*d^2-75*arctan(csgn(d)*d*x/(-d^2*x^2+1)^(1/2))*c^3)*csgn(d)/d^7/(-d^2*x^2+1)^(1/2)","C"
793,1,291,148,0.027000," ","int((c*x^2+b*x+a)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(6 \sqrt{-d^{2} x^{2}+1}\, c^{2} d^{3} x^{3} \mathrm{csgn}\left(d \right)+16 \sqrt{-d^{2} x^{2}+1}\, b c \,d^{3} x^{2} \mathrm{csgn}\left(d \right)-24 a^{2} d^{4} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+24 \sqrt{-d^{2} x^{2}+1}\, a c \,d^{3} x \,\mathrm{csgn}\left(d \right)+12 \sqrt{-d^{2} x^{2}+1}\, b^{2} d^{3} x \,\mathrm{csgn}\left(d \right)+48 \sqrt{-d^{2} x^{2}+1}\, a b \,d^{3} \mathrm{csgn}\left(d \right)-24 a c \,d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-12 b^{2} d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+9 \sqrt{-d^{2} x^{2}+1}\, c^{2} d x \,\mathrm{csgn}\left(d \right)+32 \sqrt{-d^{2} x^{2}+1}\, b c d \,\mathrm{csgn}\left(d \right)-9 c^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{24 \sqrt{-d^{2} x^{2}+1}\, d^{5}}"," ",0,"-1/24*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*(6*csgn(d)*x^3*c^2*d^3*(-d^2*x^2+1)^(1/2)+16*csgn(d)*x^2*b*c*d^3*(-d^2*x^2+1)^(1/2)+24*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x*a*c+12*csgn(d)*d^3*(-d^2*x^2+1)^(1/2)*x*b^2+48*(-d^2*x^2+1)^(1/2)*csgn(d)*d^3*a*b-24*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*a^2*d^4+9*csgn(d)*d*(-d^2*x^2+1)^(1/2)*x*c^2+32*(-d^2*x^2+1)^(1/2)*csgn(d)*d*b*c-24*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*a*c*d^2-12*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*b^2*d^2-9*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*c^2)*csgn(d)/d^5/(-d^2*x^2+1)^(1/2)","C"
794,1,117,55,0.018000," ","int((c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{\sqrt{-d x +1}\, \sqrt{d x +1}\, \left(-2 a \,d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+\sqrt{-d^{2} x^{2}+1}\, c d x \,\mathrm{csgn}\left(d \right)+2 \sqrt{-d^{2} x^{2}+1}\, b d \,\mathrm{csgn}\left(d \right)-c \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{2 \sqrt{-d^{2} x^{2}+1}\, d^{3}}"," ",0,"-1/2*(-d*x+1)^(1/2)*(d*x+1)^(1/2)/d^3*(csgn(d)*d*(-d^2*x^2+1)^(1/2)*x*c-2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*a*d^2+2*csgn(d)*d*(-d^2*x^2+1)^(1/2)*b-arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*c)/(-d^2*x^2+1)^(1/2)*csgn(d)","C"
795,1,1759,248,0.141000," ","int(1/(c*x^2+b*x+a)/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","-\frac{32 \sqrt{-d x +1}\, \sqrt{d x +1}\, \left(\sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, a^{2} d^{4} \ln \left(\frac{2 b \,d^{2} x -2 \sqrt{-4 a c +b^{2}}\, d^{2} x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c +4 c}{2 c x +b -\sqrt{-4 a c +b^{2}}}\right)-\sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, a^{2} d^{4} \ln \left(\frac{2 b \,d^{2} x +2 \sqrt{-4 a c +b^{2}}\, d^{2} x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c +4 c}{2 c x +b +\sqrt{-4 a c +b^{2}}}\right)+2 \sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, a c \,d^{2} \ln \left(\frac{2 b \,d^{2} x -2 \sqrt{-4 a c +b^{2}}\, d^{2} x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c +4 c}{2 c x +b -\sqrt{-4 a c +b^{2}}}\right)-2 \sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, a c \,d^{2} \ln \left(\frac{2 b \,d^{2} x +2 \sqrt{-4 a c +b^{2}}\, d^{2} x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c +4 c}{2 c x +b +\sqrt{-4 a c +b^{2}}}\right)-\sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, b^{2} d^{2} \ln \left(\frac{2 b \,d^{2} x -2 \sqrt{-4 a c +b^{2}}\, d^{2} x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c +4 c}{2 c x +b -\sqrt{-4 a c +b^{2}}}\right)+\sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, b^{2} d^{2} \ln \left(\frac{2 b \,d^{2} x +2 \sqrt{-4 a c +b^{2}}\, d^{2} x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c +4 c}{2 c x +b +\sqrt{-4 a c +b^{2}}}\right)+\sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c^{2} \ln \left(\frac{2 b \,d^{2} x -2 \sqrt{-4 a c +b^{2}}\, d^{2} x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c +4 c}{2 c x +b -\sqrt{-4 a c +b^{2}}}\right)-\sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c^{2} \ln \left(\frac{2 b \,d^{2} x +2 \sqrt{-4 a c +b^{2}}\, d^{2} x +2 \sqrt{-d^{2} x^{2}+1}\, \sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, c +4 c}{2 c x +b +\sqrt{-4 a c +b^{2}}}\right)\right) c^{2} \mathrm{csgn}\left(d \right)^{2}}{\sqrt{-d^{2} x^{2}+1}\, \left(b d +2 c -\sqrt{-4 a c +b^{2}}\, d \right) \left(b d +2 c +\sqrt{-4 a c +b^{2}}\, d \right) \left(b d -2 c -\sqrt{-4 a c +b^{2}}\, d \right) \sqrt{-4 a c +b^{2}}\, \sqrt{-\frac{\left(2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(-2 a^{2} d^{2}-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}\, \left(b d -2 c +\sqrt{-4 a c +b^{2}}\, d \right) \sqrt{-\frac{\left(-2 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b \right) \left(2 a^{2} d^{2}+2 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b \right)}{a^{2} c^{2}}}}"," ",0,"-32*(-d*x+1)^(1/2)*(d*x+1)^(1/2)*csgn(d)^2*c^2*(ln(2*(x*b*d^2-(-4*a*c+b^2)^(1/2)*x*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)*c+2*c)/(2*c*x-(-4*a*c+b^2)^(1/2)+b))*a^2*d^4*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)-ln(2*((-4*a*c+b^2)^(1/2)*x*d^2+x*b*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)*c+2*c)/(b+2*c*x+(-4*a*c+b^2)^(1/2)))*a^2*d^4*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)+2*ln(2*(x*b*d^2-(-4*a*c+b^2)^(1/2)*x*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)*c+2*c)/(2*c*x-(-4*a*c+b^2)^(1/2)+b))*a*c*d^2*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)-ln(2*(x*b*d^2-(-4*a*c+b^2)^(1/2)*x*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)*c+2*c)/(2*c*x-(-4*a*c+b^2)^(1/2)+b))*b^2*d^2*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)-2*ln(2*((-4*a*c+b^2)^(1/2)*x*d^2+x*b*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)*c+2*c)/(b+2*c*x+(-4*a*c+b^2)^(1/2)))*a*c*d^2*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)+ln(2*((-4*a*c+b^2)^(1/2)*x*d^2+x*b*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)*c+2*c)/(b+2*c*x+(-4*a*c+b^2)^(1/2)))*b^2*d^2*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)+ln(2*(x*b*d^2-(-4*a*c+b^2)^(1/2)*x*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)*c+2*c)/(2*c*x-(-4*a*c+b^2)^(1/2)+b))*c^2*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)-ln(2*((-4*a*c+b^2)^(1/2)*x*d^2+x*b*d^2+(-d^2*x^2+1)^(1/2)*(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)*c+2*c)/(b+2*c*x+(-4*a*c+b^2)^(1/2)))*c^2*(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2))/(-d^2*x^2+1)^(1/2)/(b*d-d*(-4*a*c+b^2)^(1/2)+2*c)/(d*(-4*a*c+b^2)^(1/2)+b*d+2*c)/(b*d-d*(-4*a*c+b^2)^(1/2)-2*c)/(-4*a*c+b^2)^(1/2)/(-(b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)*(-2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)/a^2/c^2)^(1/2)/(d*(-4*a*c+b^2)^(1/2)+b*d-2*c)/(-(b*(-4*a*c+b^2)^(1/2)-2*a*c+b^2)*(2*a^2*d^2+b*(-4*a*c+b^2)^(1/2)+2*a*c-b^2)/a^2/c^2)^(1/2)","C"
796,1,41837,530,0.814000," ","int(1/(c*x^2+b*x+a)^2/(-d*x+1)^(1/2)/(d*x+1)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
797,1,755,260,0.040000," ","int((c*x^2+b*x+a)^3/(-d*x+1)^(3/2)/(d*x+1)^(3/2),x)","\frac{\sqrt{-d x +1}\, \left(2 \sqrt{-d^{2} x^{2}+1}\, c^{3} d^{5} x^{5} \mathrm{csgn}\left(d \right)+8 \sqrt{-d^{2} x^{2}+1}\, b \,c^{2} d^{5} x^{4} \mathrm{csgn}\left(d \right)-8 \sqrt{-d^{2} x^{2}+1}\, a^{3} d^{7} x \,\mathrm{csgn}\left(d \right)-24 a^{2} c \,d^{6} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-24 a \,b^{2} d^{6} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+12 \sqrt{-d^{2} x^{2}+1}\, a \,c^{2} d^{5} x^{3} \mathrm{csgn}\left(d \right)+12 \sqrt{-d^{2} x^{2}+1}\, b^{2} c \,d^{5} x^{3} \mathrm{csgn}\left(d \right)+48 \sqrt{-d^{2} x^{2}+1}\, a b c \,d^{5} x^{2} \mathrm{csgn}\left(d \right)+8 \sqrt{-d^{2} x^{2}+1}\, b^{3} d^{5} x^{2} \mathrm{csgn}\left(d \right)-24 \sqrt{-d^{2} x^{2}+1}\, a^{2} c \,d^{5} x \,\mathrm{csgn}\left(d \right)-24 \sqrt{-d^{2} x^{2}+1}\, a \,b^{2} d^{5} x \,\mathrm{csgn}\left(d \right)-36 a \,c^{2} d^{4} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-36 b^{2} c \,d^{4} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+5 \sqrt{-d^{2} x^{2}+1}\, c^{3} d^{3} x^{3} \mathrm{csgn}\left(d \right)-24 \sqrt{-d^{2} x^{2}+1}\, a^{2} b \,d^{5} \mathrm{csgn}\left(d \right)+32 \sqrt{-d^{2} x^{2}+1}\, b \,c^{2} d^{3} x^{2} \mathrm{csgn}\left(d \right)+24 a^{2} c \,d^{4} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+24 a \,b^{2} d^{4} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-36 \sqrt{-d^{2} x^{2}+1}\, a \,c^{2} d^{3} x \,\mathrm{csgn}\left(d \right)-36 \sqrt{-d^{2} x^{2}+1}\, b^{2} c \,d^{3} x \,\mathrm{csgn}\left(d \right)-15 c^{3} d^{2} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-96 \sqrt{-d^{2} x^{2}+1}\, a b c \,d^{3} \mathrm{csgn}\left(d \right)-16 \sqrt{-d^{2} x^{2}+1}\, b^{3} d^{3} \mathrm{csgn}\left(d \right)+36 a \,c^{2} d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+36 b^{2} c \,d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-15 \sqrt{-d^{2} x^{2}+1}\, c^{3} d x \,\mathrm{csgn}\left(d \right)-64 \sqrt{-d^{2} x^{2}+1}\, b \,c^{2} d \,\mathrm{csgn}\left(d \right)+15 c^{3} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{8 \left(d x -1\right) \sqrt{-d^{2} x^{2}+1}\, \sqrt{d x +1}\, d^{7}}"," ",0,"1/8*(-d*x+1)^(1/2)*(-16*(-d^2*x^2+1)^(1/2)*b^3*d^3*csgn(d)+24*a^2*c*d^4*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+24*a*b^2*d^4*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+36*a*c^2*d^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+36*b^2*c*d^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+15*c^3*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))-15*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x^2*c^3*d^2+2*(-d^2*x^2+1)^(1/2)*c^3*d^5*x^5*csgn(d)-36*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x^2*a*c^2*d^4-36*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x^2*b^2*c*d^4-24*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x^2*a^2*c*d^6-24*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x^2*a*b^2*d^6-8*csgn(d)*d^7*(-d^2*x^2+1)^(1/2)*x*a^3-15*(-d^2*x^2+1)^(1/2)*c^3*d*x*csgn(d)-64*(-d^2*x^2+1)^(1/2)*b*c^2*d*csgn(d)+8*(-d^2*x^2+1)^(1/2)*b^3*d^5*x^2*csgn(d)+5*(-d^2*x^2+1)^(1/2)*c^3*d^3*x^3*csgn(d)-24*(-d^2*x^2+1)^(1/2)*a^2*b*d^5*csgn(d)+8*(-d^2*x^2+1)^(1/2)*b*c^2*d^5*x^4*csgn(d)+12*(-d^2*x^2+1)^(1/2)*a*c^2*d^5*x^3*csgn(d)+12*(-d^2*x^2+1)^(1/2)*b^2*c*d^5*x^3*csgn(d)-24*(-d^2*x^2+1)^(1/2)*a^2*c*d^5*x*csgn(d)-24*(-d^2*x^2+1)^(1/2)*a*b^2*d^5*x*csgn(d)+32*(-d^2*x^2+1)^(1/2)*b*c^2*d^3*x^2*csgn(d)-36*(-d^2*x^2+1)^(1/2)*a*c^2*d^3*x*csgn(d)-36*(-d^2*x^2+1)^(1/2)*b^2*c*d^3*x*csgn(d)-96*(-d^2*x^2+1)^(1/2)*a*b*c*d^3*csgn(d)+48*(-d^2*x^2+1)^(1/2)*a*b*c*d^5*x^2*csgn(d))*csgn(d)/(d*x-1)/(-d^2*x^2+1)^(1/2)/d^7/(d*x+1)^(1/2)","C"
798,1,380,125,0.030000," ","int((c*x^2+b*x+a)^2/(-d*x+1)^(3/2)/(d*x+1)^(3/2),x)","\frac{\sqrt{-d x +1}\, \left(-2 \sqrt{-d^{2} x^{2}+1}\, a^{2} d^{5} x \,\mathrm{csgn}\left(d \right)-4 a c \,d^{4} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-2 b^{2} d^{4} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+\sqrt{-d^{2} x^{2}+1}\, c^{2} d^{3} x^{3} \mathrm{csgn}\left(d \right)+4 \sqrt{-d^{2} x^{2}+1}\, b c \,d^{3} x^{2} \mathrm{csgn}\left(d \right)-4 \sqrt{-d^{2} x^{2}+1}\, a c \,d^{3} x \,\mathrm{csgn}\left(d \right)-2 \sqrt{-d^{2} x^{2}+1}\, b^{2} d^{3} x \,\mathrm{csgn}\left(d \right)-3 c^{2} d^{2} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-4 \sqrt{-d^{2} x^{2}+1}\, a b \,d^{3} \mathrm{csgn}\left(d \right)+4 a c \,d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)+2 b^{2} d^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)-3 \sqrt{-d^{2} x^{2}+1}\, c^{2} d x \,\mathrm{csgn}\left(d \right)-8 \sqrt{-d^{2} x^{2}+1}\, b c d \,\mathrm{csgn}\left(d \right)+3 c^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-d^{2} x^{2}+1}}\right)\right) \mathrm{csgn}\left(d \right)}{2 \left(d x -1\right) \sqrt{-d^{2} x^{2}+1}\, \sqrt{d x +1}\, d^{5}}"," ",0,"1/2*(-d*x+1)^(1/2)*((-d^2*x^2+1)^(1/2)*c^2*d^3*x^3*csgn(d)-2*csgn(d)*d^5*(-d^2*x^2+1)^(1/2)*x*a^2+4*(-d^2*x^2+1)^(1/2)*b*c*d^3*x^2*csgn(d)-4*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x^2*a*c*d^4-2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x^2*b^2*d^4-4*(-d^2*x^2+1)^(1/2)*a*c*d^3*x*csgn(d)-2*(-d^2*x^2+1)^(1/2)*b^2*d^3*x*csgn(d)-4*(-d^2*x^2+1)^(1/2)*a*b*d^3*csgn(d)-3*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))*x^2*c^2*d^2-3*(-d^2*x^2+1)^(1/2)*c^2*d*x*csgn(d)-8*(-d^2*x^2+1)^(1/2)*b*c*d*csgn(d)+4*a*c*d^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+2*b^2*d^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d))+3*c^2*arctan(1/(-d^2*x^2+1)^(1/2)*d*x*csgn(d)))*csgn(d)/(d*x-1)/(-d^2*x^2+1)^(1/2)/d^5/(d*x+1)^(1/2)","C"
799,1,151,38,0.026000," ","int((c*x^2+b*x+a)/(-d*x+1)^(3/2)/(d*x+1)^(3/2),x)","\frac{\left(-\sqrt{-d^{2} x^{2}+1}\, a \,d^{3} x \,\mathrm{csgn}\left(d \right)-c \,d^{2} x^{2} \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-\left(d x -1\right) \left(d x +1\right)}}\right)-\sqrt{-d^{2} x^{2}+1}\, c d x \,\mathrm{csgn}\left(d \right)-\sqrt{-d^{2} x^{2}+1}\, b d \,\mathrm{csgn}\left(d \right)+c \arctan \left(\frac{d x \,\mathrm{csgn}\left(d \right)}{\sqrt{-\left(d x -1\right) \left(d x +1\right)}}\right)\right) \sqrt{-d x +1}\, \mathrm{csgn}\left(d \right)}{\left(d x -1\right) \sqrt{-d^{2} x^{2}+1}\, \sqrt{d x +1}\, d^{3}}"," ",0,"(-(-d^2*x^2+1)^(1/2)*csgn(d)*d^3*x*a-arctan(csgn(d)*d*x/(-(d*x-1)*(d*x+1))^(1/2))*x^2*c*d^2-(-d^2*x^2+1)^(1/2)*c*d*x*csgn(d)-(-d^2*x^2+1)^(1/2)*b*d*csgn(d)+arctan(csgn(d)*d*x/(-(d*x-1)*(d*x+1))^(1/2))*c)*(-d*x+1)^(1/2)*csgn(d)/(d*x-1)/(-d^2*x^2+1)^(1/2)/d^3/(d*x+1)^(1/2)","C"
800,1,11141,404,0.125000," ","int(1/(-d*x+1)^(3/2)/(d*x+1)^(3/2)/(c*x^2+b*x+a),x)","\text{output too large to display}"," ",0,"result too large to display","C"
801,1,108974,887,4.138000," ","int(1/(-d*x+1)^(3/2)/(d*x+1)^(3/2)/(c*x^2+b*x+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","C"
802,0,0,50,0.164000," ","int((-e*x+1)^m*(e*x+1)^m*(c*x^2+a)^p,x)","\int \left(-e x +1\right)^{m} \left(e x +1\right)^{m} \left(c \,x^{2}+a \right)^{p}\, dx"," ",0,"int((-e*x+1)^m*(e*x+1)^m*(c*x^2+a)^p,x)","F"
803,0,0,85,0.168000," ","int((-e*x+d)^m*(e*x+d)^m*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(-e x +d \right)^{m} \left(e x +d \right)^{m}\, dx"," ",0,"int((-e*x+d)^m*(e*x+d)^m*(c*x^2+a)^p,x)","F"
804,0,0,88,0.165000," ","int((e*x+d)^m*(-e*f*x+d*f)^m*(c*x^2+a)^p,x)","\int \left(c \,x^{2}+a \right)^{p} \left(e x +d \right)^{m} \left(-e f x +d f \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(-e*f*x+d*f)^m*(c*x^2+a)^p,x)","F"
805,1,2017,275,0.019000," ","int((e*x+d)^3*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x)","\frac{\left(c \,e^{4} g^{5} n^{5} x^{5}+5 c d \,e^{3} g^{5} n^{5} x^{4}+15 c \,e^{4} g^{5} n^{4} x^{5}+9 c \,d^{2} e^{2} g^{5} n^{5} x^{3}+80 c d \,e^{3} g^{5} n^{4} x^{4}-5 c \,e^{4} f \,g^{4} n^{4} x^{4}+85 c \,e^{4} g^{5} n^{3} x^{5}+a \,e^{3} g^{5} n^{5} x^{3}+7 c \,d^{3} e \,g^{5} n^{5} x^{2}+153 c \,d^{2} e^{2} g^{5} n^{4} x^{3}-20 c d \,e^{3} f \,g^{4} n^{4} x^{3}+475 c d \,e^{3} g^{5} n^{3} x^{4}-50 c \,e^{4} f \,g^{4} n^{3} x^{4}+225 c \,e^{4} g^{5} n^{2} x^{5}+3 a d \,e^{2} g^{5} n^{5} x^{2}+17 a \,e^{3} g^{5} n^{4} x^{3}+2 c \,d^{4} g^{5} n^{5} x +126 c \,d^{3} e \,g^{5} n^{4} x^{2}-27 c \,d^{2} e^{2} f \,g^{4} n^{4} x^{2}+963 c \,d^{2} e^{2} g^{5} n^{3} x^{3}-240 c d \,e^{3} f \,g^{4} n^{3} x^{3}+1300 c d \,e^{3} g^{5} n^{2} x^{4}+20 c \,e^{4} f^{2} g^{3} n^{3} x^{3}-175 c \,e^{4} f \,g^{4} n^{2} x^{4}+274 c \,e^{4} g^{5} n \,x^{5}+3 a \,d^{2} e \,g^{5} n^{5} x +54 a d \,e^{2} g^{5} n^{4} x^{2}-3 a \,e^{3} f \,g^{4} n^{4} x^{2}+107 a \,e^{3} g^{5} n^{3} x^{3}+38 c \,d^{4} g^{5} n^{4} x -14 c \,d^{3} e f \,g^{4} n^{4} x +847 c \,d^{3} e \,g^{5} n^{3} x^{2}-378 c \,d^{2} e^{2} f \,g^{4} n^{3} x^{2}+2763 c \,d^{2} e^{2} g^{5} n^{2} x^{3}+60 c d \,e^{3} f^{2} g^{3} n^{3} x^{2}-940 c d \,e^{3} f \,g^{4} n^{2} x^{3}+1620 c d \,e^{3} g^{5} n \,x^{4}+120 c \,e^{4} f^{2} g^{3} n^{2} x^{3}-250 c \,e^{4} f \,g^{4} n \,x^{4}+120 c \,e^{4} x^{5} g^{5}+a \,d^{3} g^{5} n^{5}+57 a \,d^{2} e \,g^{5} n^{4} x -6 a d \,e^{2} f \,g^{4} n^{4} x +363 a d \,e^{2} g^{5} n^{3} x^{2}-42 a \,e^{3} f \,g^{4} n^{3} x^{2}+307 a \,e^{3} g^{5} n^{2} x^{3}-2 c \,d^{4} f \,g^{4} n^{4}+274 c \,d^{4} g^{5} n^{3} x -224 c \,d^{3} e f \,g^{4} n^{3} x +2604 c \,d^{3} e \,g^{5} n^{2} x^{2}+54 c \,d^{2} e^{2} f^{2} g^{3} n^{3} x -1755 c \,d^{2} e^{2} f \,g^{4} n^{2} x^{2}+3564 c \,d^{2} e^{2} g^{5} n \,x^{3}+540 c d \,e^{3} f^{2} g^{3} n^{2} x^{2}-1440 c d \,e^{3} f \,g^{4} n \,x^{3}+720 c d \,e^{3} g^{5} x^{4}-60 c \,e^{4} f^{3} g^{2} n^{2} x^{2}+220 c \,e^{4} f^{2} g^{3} n \,x^{3}-120 c \,e^{4} f \,g^{4} x^{4}+20 a \,d^{3} g^{5} n^{4}-3 a \,d^{2} e f \,g^{4} n^{4}+411 a \,d^{2} e \,g^{5} n^{3} x -96 a d \,e^{2} f \,g^{4} n^{3} x +1116 a d \,e^{2} g^{5} n^{2} x^{2}+6 a \,e^{3} f^{2} g^{3} n^{3} x -195 a \,e^{3} f \,g^{4} n^{2} x^{2}+396 a \,e^{3} g^{5} n \,x^{3}-36 c \,d^{4} f \,g^{4} n^{3}+922 c \,d^{4} g^{5} n^{2} x +14 c \,d^{3} e \,f^{2} g^{3} n^{3}-1246 c \,d^{3} e f \,g^{4} n^{2} x +3556 c \,d^{3} e \,g^{5} n \,x^{2}+648 c \,d^{2} e^{2} f^{2} g^{3} n^{2} x -3024 c \,d^{2} e^{2} f \,g^{4} n \,x^{2}+1620 c \,d^{2} e^{2} g^{5} x^{3}-120 c d \,e^{3} f^{3} g^{2} n^{2} x +1200 c d \,e^{3} f^{2} g^{3} n \,x^{2}-720 c d \,e^{3} f \,g^{4} x^{3}-180 c \,e^{4} f^{3} g^{2} n \,x^{2}+120 c \,e^{4} f^{2} g^{3} x^{3}+155 a \,d^{3} g^{5} n^{3}-54 a \,d^{2} e f \,g^{4} n^{3}+1383 a \,d^{2} e \,g^{5} n^{2} x +6 a d \,e^{2} f^{2} g^{3} n^{3}-534 a d \,e^{2} f \,g^{4} n^{2} x +1524 a d \,e^{2} g^{5} n \,x^{2}+72 a \,e^{3} f^{2} g^{3} n^{2} x -336 a \,e^{3} f \,g^{4} n \,x^{2}+180 a \,e^{3} g^{5} x^{3}-238 c \,d^{4} f \,g^{4} n^{2}+1404 c \,d^{4} g^{5} n x +210 c \,d^{3} e \,f^{2} g^{3} n^{2}-2716 c \,d^{3} e f \,g^{4} n x +1680 c \,d^{3} e \,g^{5} x^{2}-54 c \,d^{2} e^{2} f^{3} g^{2} n^{2}+2214 c \,d^{2} e^{2} f^{2} g^{3} n x -1620 c \,d^{2} e^{2} f \,g^{4} x^{2}-840 c d \,e^{3} f^{3} g^{2} n x +720 c d \,e^{3} f^{2} g^{3} x^{2}+120 c \,e^{4} f^{4} g n x -120 c \,e^{4} f^{3} g^{2} x^{2}+580 a \,d^{3} g^{5} n^{2}-357 a \,d^{2} e f \,g^{4} n^{2}+2106 a \,d^{2} e \,g^{5} n x +90 a d \,e^{2} f^{2} g^{3} n^{2}-1164 a d \,e^{2} f \,g^{4} n x +720 a d \,e^{2} g^{5} x^{2}-6 a \,e^{3} f^{3} g^{2} n^{2}+246 a \,e^{3} f^{2} g^{3} n x -180 a \,e^{3} f \,g^{4} x^{2}-684 c \,d^{4} f \,g^{4} n +720 c \,d^{4} g^{5} x +1036 c \,d^{3} e \,f^{2} g^{3} n -1680 c \,d^{3} e f \,g^{4} x -594 c \,d^{2} e^{2} f^{3} g^{2} n +1620 c \,d^{2} e^{2} f^{2} g^{3} x +120 c d \,e^{3} f^{4} g n -720 c d \,e^{3} f^{3} g^{2} x +120 c \,e^{4} f^{4} g x +1044 a \,d^{3} g^{5} n -1026 a \,d^{2} e f \,g^{4} n +1080 a \,d^{2} e \,g^{5} x +444 a d \,e^{2} f^{2} g^{3} n -720 a d \,e^{2} f \,g^{4} x -66 a \,e^{3} f^{3} g^{2} n +180 a \,e^{3} f^{2} g^{3} x -720 c \,d^{4} f \,g^{4}+1680 c \,d^{3} e \,f^{2} g^{3}-1620 c \,d^{2} e^{2} f^{3} g^{2}+720 c d \,e^{3} f^{4} g -120 c \,e^{4} f^{5}+720 a \,d^{3} g^{5}-1080 a \,d^{2} e f \,g^{4}+720 a d \,e^{2} f^{2} g^{3}-180 a \,e^{3} f^{3} g^{2}\right) \left(g x +f \right)^{n +1}}{\left(n^{6}+21 n^{5}+175 n^{4}+735 n^{3}+1624 n^{2}+1764 n +720\right) g^{6}}"," ",0,"(g*x+f)^(n+1)*(c*e^4*g^5*n^5*x^5+5*c*d*e^3*g^5*n^5*x^4+15*c*e^4*g^5*n^4*x^5+9*c*d^2*e^2*g^5*n^5*x^3+80*c*d*e^3*g^5*n^4*x^4-5*c*e^4*f*g^4*n^4*x^4+85*c*e^4*g^5*n^3*x^5+a*e^3*g^5*n^5*x^3+7*c*d^3*e*g^5*n^5*x^2+153*c*d^2*e^2*g^5*n^4*x^3-20*c*d*e^3*f*g^4*n^4*x^3+475*c*d*e^3*g^5*n^3*x^4-50*c*e^4*f*g^4*n^3*x^4+225*c*e^4*g^5*n^2*x^5+3*a*d*e^2*g^5*n^5*x^2+17*a*e^3*g^5*n^4*x^3+2*c*d^4*g^5*n^5*x+126*c*d^3*e*g^5*n^4*x^2-27*c*d^2*e^2*f*g^4*n^4*x^2+963*c*d^2*e^2*g^5*n^3*x^3-240*c*d*e^3*f*g^4*n^3*x^3+1300*c*d*e^3*g^5*n^2*x^4+20*c*e^4*f^2*g^3*n^3*x^3-175*c*e^4*f*g^4*n^2*x^4+274*c*e^4*g^5*n*x^5+3*a*d^2*e*g^5*n^5*x+54*a*d*e^2*g^5*n^4*x^2-3*a*e^3*f*g^4*n^4*x^2+107*a*e^3*g^5*n^3*x^3+38*c*d^4*g^5*n^4*x-14*c*d^3*e*f*g^4*n^4*x+847*c*d^3*e*g^5*n^3*x^2-378*c*d^2*e^2*f*g^4*n^3*x^2+2763*c*d^2*e^2*g^5*n^2*x^3+60*c*d*e^3*f^2*g^3*n^3*x^2-940*c*d*e^3*f*g^4*n^2*x^3+1620*c*d*e^3*g^5*n*x^4+120*c*e^4*f^2*g^3*n^2*x^3-250*c*e^4*f*g^4*n*x^4+120*c*e^4*g^5*x^5+a*d^3*g^5*n^5+57*a*d^2*e*g^5*n^4*x-6*a*d*e^2*f*g^4*n^4*x+363*a*d*e^2*g^5*n^3*x^2-42*a*e^3*f*g^4*n^3*x^2+307*a*e^3*g^5*n^2*x^3-2*c*d^4*f*g^4*n^4+274*c*d^4*g^5*n^3*x-224*c*d^3*e*f*g^4*n^3*x+2604*c*d^3*e*g^5*n^2*x^2+54*c*d^2*e^2*f^2*g^3*n^3*x-1755*c*d^2*e^2*f*g^4*n^2*x^2+3564*c*d^2*e^2*g^5*n*x^3+540*c*d*e^3*f^2*g^3*n^2*x^2-1440*c*d*e^3*f*g^4*n*x^3+720*c*d*e^3*g^5*x^4-60*c*e^4*f^3*g^2*n^2*x^2+220*c*e^4*f^2*g^3*n*x^3-120*c*e^4*f*g^4*x^4+20*a*d^3*g^5*n^4-3*a*d^2*e*f*g^4*n^4+411*a*d^2*e*g^5*n^3*x-96*a*d*e^2*f*g^4*n^3*x+1116*a*d*e^2*g^5*n^2*x^2+6*a*e^3*f^2*g^3*n^3*x-195*a*e^3*f*g^4*n^2*x^2+396*a*e^3*g^5*n*x^3-36*c*d^4*f*g^4*n^3+922*c*d^4*g^5*n^2*x+14*c*d^3*e*f^2*g^3*n^3-1246*c*d^3*e*f*g^4*n^2*x+3556*c*d^3*e*g^5*n*x^2+648*c*d^2*e^2*f^2*g^3*n^2*x-3024*c*d^2*e^2*f*g^4*n*x^2+1620*c*d^2*e^2*g^5*x^3-120*c*d*e^3*f^3*g^2*n^2*x+1200*c*d*e^3*f^2*g^3*n*x^2-720*c*d*e^3*f*g^4*x^3-180*c*e^4*f^3*g^2*n*x^2+120*c*e^4*f^2*g^3*x^3+155*a*d^3*g^5*n^3-54*a*d^2*e*f*g^4*n^3+1383*a*d^2*e*g^5*n^2*x+6*a*d*e^2*f^2*g^3*n^3-534*a*d*e^2*f*g^4*n^2*x+1524*a*d*e^2*g^5*n*x^2+72*a*e^3*f^2*g^3*n^2*x-336*a*e^3*f*g^4*n*x^2+180*a*e^3*g^5*x^3-238*c*d^4*f*g^4*n^2+1404*c*d^4*g^5*n*x+210*c*d^3*e*f^2*g^3*n^2-2716*c*d^3*e*f*g^4*n*x+1680*c*d^3*e*g^5*x^2-54*c*d^2*e^2*f^3*g^2*n^2+2214*c*d^2*e^2*f^2*g^3*n*x-1620*c*d^2*e^2*f*g^4*x^2-840*c*d*e^3*f^3*g^2*n*x+720*c*d*e^3*f^2*g^3*x^2+120*c*e^4*f^4*g*n*x-120*c*e^4*f^3*g^2*x^2+580*a*d^3*g^5*n^2-357*a*d^2*e*f*g^4*n^2+2106*a*d^2*e*g^5*n*x+90*a*d*e^2*f^2*g^3*n^2-1164*a*d*e^2*f*g^4*n*x+720*a*d*e^2*g^5*x^2-6*a*e^3*f^3*g^2*n^2+246*a*e^3*f^2*g^3*n*x-180*a*e^3*f*g^4*x^2-684*c*d^4*f*g^4*n+720*c*d^4*g^5*x+1036*c*d^3*e*f^2*g^3*n-1680*c*d^3*e*f*g^4*x-594*c*d^2*e^2*f^3*g^2*n+1620*c*d^2*e^2*f^2*g^3*x+120*c*d*e^3*f^4*g*n-720*c*d*e^3*f^3*g^2*x+120*c*e^4*f^4*g*x+1044*a*d^3*g^5*n-1026*a*d^2*e*f*g^4*n+1080*a*d^2*e*g^5*x+444*a*d*e^2*f^2*g^3*n-720*a*d*e^2*f*g^4*x-66*a*e^3*f^3*g^2*n+180*a*e^3*f^2*g^3*x-720*c*d^4*f*g^4+1680*c*d^3*e*f^2*g^3-1620*c*d^2*e^2*f^3*g^2+720*c*d*e^3*f^4*g-120*c*e^4*f^5+720*a*d^3*g^5-1080*a*d^2*e*f*g^4+720*a*d*e^2*f^2*g^3-180*a*e^3*f^3*g^2)/g^6/(n^6+21*n^5+175*n^4+735*n^3+1624*n^2+1764*n+720)","B"
806,1,1048,208,0.013000," ","int((e*x+d)^2*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x)","\frac{\left(c \,e^{3} g^{4} n^{4} x^{4}+4 c d \,e^{2} g^{4} n^{4} x^{3}+10 c \,e^{3} g^{4} n^{3} x^{4}+5 c \,d^{2} e \,g^{4} n^{4} x^{2}+44 c d \,e^{2} g^{4} n^{3} x^{3}-4 c \,e^{3} f \,g^{3} n^{3} x^{3}+35 c \,e^{3} g^{4} n^{2} x^{4}+a \,e^{2} g^{4} n^{4} x^{2}+2 c \,d^{3} g^{4} n^{4} x +60 c \,d^{2} e \,g^{4} n^{3} x^{2}-12 c d \,e^{2} f \,g^{3} n^{3} x^{2}+164 c d \,e^{2} g^{4} n^{2} x^{3}-24 c \,e^{3} f \,g^{3} n^{2} x^{3}+50 c \,e^{3} g^{4} n \,x^{4}+2 a d e \,g^{4} n^{4} x +12 a \,e^{2} g^{4} n^{3} x^{2}+26 c \,d^{3} g^{4} n^{3} x -10 c \,d^{2} e f \,g^{3} n^{3} x +245 c \,d^{2} e \,g^{4} n^{2} x^{2}-96 c d \,e^{2} f \,g^{3} n^{2} x^{2}+244 c d \,e^{2} g^{4} n \,x^{3}+12 c \,e^{3} f^{2} g^{2} n^{2} x^{2}-44 c \,e^{3} f \,g^{3} n \,x^{3}+24 c \,e^{3} x^{4} g^{4}+a \,d^{2} g^{4} n^{4}+26 a d e \,g^{4} n^{3} x -2 a \,e^{2} f \,g^{3} n^{3} x +49 a \,e^{2} g^{4} n^{2} x^{2}-2 c \,d^{3} f \,g^{3} n^{3}+118 c \,d^{3} g^{4} n^{2} x -100 c \,d^{2} e f \,g^{3} n^{2} x +390 c \,d^{2} e \,g^{4} n \,x^{2}+24 c d \,e^{2} f^{2} g^{2} n^{2} x -204 c d \,e^{2} f \,g^{3} n \,x^{2}+120 c d \,e^{2} g^{4} x^{3}+36 c \,e^{3} f^{2} g^{2} n \,x^{2}-24 c \,e^{3} f \,g^{3} x^{3}+14 a \,d^{2} g^{4} n^{3}-2 a d e f \,g^{3} n^{3}+118 a d e \,g^{4} n^{2} x -20 a \,e^{2} f \,g^{3} n^{2} x +78 a \,e^{2} g^{4} n \,x^{2}-24 c \,d^{3} f \,g^{3} n^{2}+214 c \,d^{3} g^{4} n x +10 c \,d^{2} e \,f^{2} g^{2} n^{2}-290 c \,d^{2} e f \,g^{3} n x +200 c \,d^{2} e \,g^{4} x^{2}+144 c d \,e^{2} f^{2} g^{2} n x -120 c d \,e^{2} f \,g^{3} x^{2}-24 c \,e^{3} f^{3} g n x +24 c \,e^{3} f^{2} g^{2} x^{2}+71 a \,d^{2} g^{4} n^{2}-24 a d e f \,g^{3} n^{2}+214 a d e \,g^{4} n x +2 a \,e^{2} f^{2} g^{2} n^{2}-58 a \,e^{2} f \,g^{3} n x +40 a \,e^{2} g^{4} x^{2}-94 c \,d^{3} f \,g^{3} n +120 c \,d^{3} g^{4} x +90 c \,d^{2} e \,f^{2} g^{2} n -200 c \,d^{2} e f \,g^{3} x -24 c d \,e^{2} f^{3} g n +120 c d \,e^{2} f^{2} g^{2} x -24 c \,e^{3} f^{3} g x +154 a \,d^{2} g^{4} n -94 a d e f \,g^{3} n +120 a d e \,g^{4} x +18 a \,e^{2} f^{2} g^{2} n -40 a \,e^{2} f \,g^{3} x -120 c \,d^{3} f \,g^{3}+200 c \,d^{2} e \,f^{2} g^{2}-120 c d \,e^{2} f^{3} g +24 c \,e^{3} f^{4}+120 a \,d^{2} g^{4}-120 a d e f \,g^{3}+40 a \,e^{2} f^{2} g^{2}\right) \left(g x +f \right)^{n +1}}{\left(n^{5}+15 n^{4}+85 n^{3}+225 n^{2}+274 n +120\right) g^{5}}"," ",0,"(g*x+f)^(n+1)*(c*e^3*g^4*n^4*x^4+4*c*d*e^2*g^4*n^4*x^3+10*c*e^3*g^4*n^3*x^4+5*c*d^2*e*g^4*n^4*x^2+44*c*d*e^2*g^4*n^3*x^3-4*c*e^3*f*g^3*n^3*x^3+35*c*e^3*g^4*n^2*x^4+a*e^2*g^4*n^4*x^2+2*c*d^3*g^4*n^4*x+60*c*d^2*e*g^4*n^3*x^2-12*c*d*e^2*f*g^3*n^3*x^2+164*c*d*e^2*g^4*n^2*x^3-24*c*e^3*f*g^3*n^2*x^3+50*c*e^3*g^4*n*x^4+2*a*d*e*g^4*n^4*x+12*a*e^2*g^4*n^3*x^2+26*c*d^3*g^4*n^3*x-10*c*d^2*e*f*g^3*n^3*x+245*c*d^2*e*g^4*n^2*x^2-96*c*d*e^2*f*g^3*n^2*x^2+244*c*d*e^2*g^4*n*x^3+12*c*e^3*f^2*g^2*n^2*x^2-44*c*e^3*f*g^3*n*x^3+24*c*e^3*g^4*x^4+a*d^2*g^4*n^4+26*a*d*e*g^4*n^3*x-2*a*e^2*f*g^3*n^3*x+49*a*e^2*g^4*n^2*x^2-2*c*d^3*f*g^3*n^3+118*c*d^3*g^4*n^2*x-100*c*d^2*e*f*g^3*n^2*x+390*c*d^2*e*g^4*n*x^2+24*c*d*e^2*f^2*g^2*n^2*x-204*c*d*e^2*f*g^3*n*x^2+120*c*d*e^2*g^4*x^3+36*c*e^3*f^2*g^2*n*x^2-24*c*e^3*f*g^3*x^3+14*a*d^2*g^4*n^3-2*a*d*e*f*g^3*n^3+118*a*d*e*g^4*n^2*x-20*a*e^2*f*g^3*n^2*x+78*a*e^2*g^4*n*x^2-24*c*d^3*f*g^3*n^2+214*c*d^3*g^4*n*x+10*c*d^2*e*f^2*g^2*n^2-290*c*d^2*e*f*g^3*n*x+200*c*d^2*e*g^4*x^2+144*c*d*e^2*f^2*g^2*n*x-120*c*d*e^2*f*g^3*x^2-24*c*e^3*f^3*g*n*x+24*c*e^3*f^2*g^2*x^2+71*a*d^2*g^4*n^2-24*a*d*e*f*g^3*n^2+214*a*d*e*g^4*n*x+2*a*e^2*f^2*g^2*n^2-58*a*e^2*f*g^3*n*x+40*a*e^2*g^4*x^2-94*c*d^3*f*g^3*n+120*c*d^3*g^4*x+90*c*d^2*e*f^2*g^2*n-200*c*d^2*e*f*g^3*x-24*c*d*e^2*f^3*g*n+120*c*d*e^2*f^2*g^2*x-24*c*e^3*f^3*g*x+154*a*d^2*g^4*n-94*a*d*e*f*g^3*n+120*a*d*e*g^4*x+18*a*e^2*f^2*g^2*n-40*a*e^2*f*g^3*x-120*c*d^3*f*g^3+200*c*d^2*e*f^2*g^2-120*c*d*e^2*f^3*g+24*c*e^3*f^4+120*a*d^2*g^4-120*a*d*e*f*g^3+40*a*e^2*f^2*g^2)/g^5/(n^5+15*n^4+85*n^3+225*n^2+274*n+120)","B"
807,1,449,146,0.007000," ","int((e*x+d)*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x)","\frac{\left(c \,e^{2} g^{3} n^{3} x^{3}+3 c d e \,g^{3} n^{3} x^{2}+6 c \,e^{2} g^{3} n^{2} x^{3}+2 c \,d^{2} g^{3} n^{3} x +21 c d e \,g^{3} n^{2} x^{2}-3 c \,e^{2} f \,g^{2} n^{2} x^{2}+11 c \,e^{2} g^{3} n \,x^{3}+a e \,g^{3} n^{3} x +16 c \,d^{2} g^{3} n^{2} x -6 c d e f \,g^{2} n^{2} x +42 c d e \,g^{3} n \,x^{2}-9 c \,e^{2} f \,g^{2} n \,x^{2}+6 c \,e^{2} x^{3} g^{3}+a d \,g^{3} n^{3}+8 a e \,g^{3} n^{2} x -2 c \,d^{2} f \,g^{2} n^{2}+38 c \,d^{2} g^{3} n x -30 c d e f \,g^{2} n x +24 c d e \,g^{3} x^{2}+6 c \,e^{2} f^{2} g n x -6 c \,e^{2} f \,g^{2} x^{2}+9 a d \,g^{3} n^{2}-a e f \,g^{2} n^{2}+19 a e \,g^{3} n x -14 c \,d^{2} f \,g^{2} n +24 c \,d^{2} g^{3} x +6 c d e \,f^{2} g n -24 c d e f \,g^{2} x +6 c \,e^{2} f^{2} g x +26 a d \,g^{3} n -7 a e f \,g^{2} n +12 a e \,g^{3} x -24 c \,d^{2} f \,g^{2}+24 c d e \,f^{2} g -6 c \,e^{2} f^{3}+24 a d \,g^{3}-12 a e f \,g^{2}\right) \left(g x +f \right)^{n +1}}{\left(n^{4}+10 n^{3}+35 n^{2}+50 n +24\right) g^{4}}"," ",0,"(g*x+f)^(n+1)*(c*e^2*g^3*n^3*x^3+3*c*d*e*g^3*n^3*x^2+6*c*e^2*g^3*n^2*x^3+2*c*d^2*g^3*n^3*x+21*c*d*e*g^3*n^2*x^2-3*c*e^2*f*g^2*n^2*x^2+11*c*e^2*g^3*n*x^3+a*e*g^3*n^3*x+16*c*d^2*g^3*n^2*x-6*c*d*e*f*g^2*n^2*x+42*c*d*e*g^3*n*x^2-9*c*e^2*f*g^2*n*x^2+6*c*e^2*g^3*x^3+a*d*g^3*n^3+8*a*e*g^3*n^2*x-2*c*d^2*f*g^2*n^2+38*c*d^2*g^3*n*x-30*c*d*e*f*g^2*n*x+24*c*d*e*g^3*x^2+6*c*e^2*f^2*g*n*x-6*c*e^2*f*g^2*x^2+9*a*d*g^3*n^2-a*e*f*g^2*n^2+19*a*e*g^3*n*x-14*c*d^2*f*g^2*n+24*c*d^2*g^3*x+6*c*d*e*f^2*g*n-24*c*d*e*f*g^2*x+6*c*e^2*f^2*g*x+26*a*d*g^3*n-7*a*e*f*g^2*n+12*a*e*g^3*x-24*c*d^2*f*g^2+24*c*d*e*f^2*g-6*c*e^2*f^3+24*a*d*g^3-12*a*e*f*g^2)/g^4/(n^4+10*n^3+35*n^2+50*n+24)","B"
808,1,147,84,0.005000," ","int((g*x+f)^n*(c*e*x^2+2*c*d*x+a),x)","\frac{\left(c e \,g^{2} n^{2} x^{2}+2 c d \,g^{2} n^{2} x +3 c e \,g^{2} n \,x^{2}+8 c d \,g^{2} n x -2 c e f g n x +2 c e \,x^{2} g^{2}+a \,g^{2} n^{2}-2 c d f g n +6 c d \,g^{2} x -2 c e f g x +5 a \,g^{2} n -6 c d f g +2 c e \,f^{2}+6 a \,g^{2}\right) \left(g x +f \right)^{n +1}}{\left(n^{3}+6 n^{2}+11 n +6\right) g^{3}}"," ",0,"(g*x+f)^(n+1)*(c*e*g^2*n^2*x^2+2*c*d*g^2*n^2*x+3*c*e*g^2*n*x^2+8*c*d*g^2*n*x-2*c*e*f*g*n*x+2*c*e*g^2*x^2+a*g^2*n^2-2*c*d*f*g*n+6*c*d*g^2*x-2*c*e*f*g*x+5*a*g^2*n-6*c*d*f*g+2*c*e*f^2+6*a*g^2)/g^3/(n^3+6*n^2+11*n+6)","A"
809,0,0,116,0.058000," ","int((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d),x)","\int \frac{\left(c e \,x^{2}+2 c d x +a \right) \left(g x +f \right)^{n}}{e x +d}\, dx"," ",0,"int((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d),x)","F"
810,0,0,90,0.065000," ","int((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^2,x)","\int \frac{\left(c e \,x^{2}+2 c d x +a \right) \left(g x +f \right)^{n}}{\left(e x +d \right)^{2}}\, dx"," ",0,"int((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^2,x)","F"
811,0,0,189,0.090000," ","int((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^3,x)","\int \frac{\left(c e \,x^{2}+2 c d x +a \right) \left(g x +f \right)^{n}}{\left(e x +d \right)^{3}}\, dx"," ",0,"int((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^3,x)","F"
812,0,0,193,0.167000," ","int((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^4,x)","\int \frac{\left(c e \,x^{2}+2 c d x +a \right) \left(g x +f \right)^{n}}{\left(e x +d \right)^{4}}\, dx"," ",0,"int((g*x+f)^n*(c*e*x^2+2*c*d*x+a)/(e*x+d)^4,x)","F"
813,0,0,233,0.072000," ","int((e*x+d)^m*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x)","\int \left(c e \,x^{2}+2 c d x +a \right) \left(e x +d \right)^{m} \left(g x +f \right)^{n}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)^n*(c*e*x^2+2*c*d*x+a),x)","F"
814,1,142,83,0.008000," ","int((c*x^2+b*x+a)/(e*x+d)/(g*x+f),x)","-\frac{a \ln \left(e x +d \right)}{d g -e f}+\frac{a \ln \left(g x +f \right)}{d g -e f}+\frac{b d \ln \left(e x +d \right)}{\left(d g -e f \right) e}-\frac{b f \ln \left(g x +f \right)}{\left(d g -e f \right) g}-\frac{c \,d^{2} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{2}}+\frac{c \,f^{2} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{2}}+\frac{c x}{e g}"," ",0,"c*x/e/g+1/(d*g-e*f)*ln(g*x+f)*a-1/g/(d*g-e*f)*ln(g*x+f)*b*f+1/g^2/(d*g-e*f)*ln(g*x+f)*c*f^2-1/(d*g-e*f)*ln(e*x+d)*a+1/(d*g-e*f)/e*ln(e*x+d)*b*d-1/(d*g-e*f)/e^2*ln(e*x+d)*c*d^2","A"
815,1,444,180,0.012000," ","int((c*x^2+b*x+a)^2/(e*x+d)/(g*x+f),x)","-\frac{a^{2} \ln \left(e x +d \right)}{d g -e f}+\frac{a^{2} \ln \left(g x +f \right)}{d g -e f}+\frac{2 a b d \ln \left(e x +d \right)}{\left(d g -e f \right) e}-\frac{2 a b f \ln \left(g x +f \right)}{\left(d g -e f \right) g}-\frac{2 a c \,d^{2} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{2}}+\frac{2 a c \,f^{2} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{2}}-\frac{b^{2} d^{2} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{2}}+\frac{b^{2} f^{2} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{2}}+\frac{2 b c \,d^{3} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{3}}-\frac{2 b c \,f^{3} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{3}}-\frac{c^{2} d^{4} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{4}}+\frac{c^{2} x^{3}}{3 e g}+\frac{c^{2} f^{4} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{4}}+\frac{b c \,x^{2}}{e g}-\frac{c^{2} d \,x^{2}}{2 e^{2} g}-\frac{c^{2} f \,x^{2}}{2 e \,g^{2}}+\frac{2 a c x}{e g}+\frac{b^{2} x}{e g}-\frac{2 b c d x}{e^{2} g}-\frac{2 b c f x}{e \,g^{2}}+\frac{c^{2} d^{2} x}{e^{3} g}+\frac{c^{2} d f x}{e^{2} g^{2}}+\frac{c^{2} f^{2} x}{e \,g^{3}}"," ",0,"1/3*c^2*x^3/e/g+1/e/g*x^2*b*c-1/2/e^2/g*x^2*c^2*d-1/2/e/g^2*x^2*c^2*f+2/e/g*a*c*x+1/e/g*b^2*x-2/e^2/g*b*c*d*x-2/e/g^2*b*c*f*x+1/e^3/g*c^2*d^2*x+1/e^2/g^2*c^2*d*f*x+1/e/g^3*c^2*f^2*x+1/(d*g-e*f)*ln(g*x+f)*a^2-2/g/(d*g-e*f)*ln(g*x+f)*a*b*f+2/g^2/(d*g-e*f)*ln(g*x+f)*a*c*f^2+1/g^2/(d*g-e*f)*ln(g*x+f)*b^2*f^2-2/g^3/(d*g-e*f)*ln(g*x+f)*b*c*f^3+1/g^4/(d*g-e*f)*ln(g*x+f)*c^2*f^4-1/(d*g-e*f)*ln(e*x+d)*a^2+2/e/(d*g-e*f)*ln(e*x+d)*a*b*d-2/e^2/(d*g-e*f)*ln(e*x+d)*a*c*d^2-1/e^2/(d*g-e*f)*ln(e*x+d)*b^2*d^2+2/e^3/(d*g-e*f)*ln(e*x+d)*b*c*d^3-1/e^4/(d*g-e*f)*ln(e*x+d)*c^2*d^4","B"
816,1,1232,523,0.020000," ","int((c*x^2+b*x+a)^3/(e*x+d)/(g*x+f),x)","\frac{c^{3} x^{5}}{5 e g}+\frac{3 b \,c^{2} x^{4}}{4 e g}-\frac{c^{3} d \,x^{4}}{4 e^{2} g}-\frac{c^{3} f \,x^{4}}{4 e \,g^{2}}-\frac{a^{3} \ln \left(e x +d \right)}{d g -e f}+\frac{a^{3} \ln \left(g x +f \right)}{d g -e f}+\frac{3 a^{2} b d \ln \left(e x +d \right)}{\left(d g -e f \right) e}-\frac{3 a^{2} b f \ln \left(g x +f \right)}{\left(d g -e f \right) g}-\frac{3 a^{2} c \,d^{2} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{2}}+\frac{3 a^{2} c \,f^{2} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{2}}-\frac{3 a \,b^{2} d^{2} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{2}}+\frac{3 a \,b^{2} f^{2} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{2}}+\frac{6 a b c \,d^{3} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{3}}-\frac{6 a b c \,f^{3} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{3}}-\frac{3 a \,c^{2} d^{4} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{4}}+\frac{a \,c^{2} x^{3}}{e g}+\frac{3 a \,c^{2} f^{4} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{4}}+\frac{b^{3} d^{3} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{3}}-\frac{b^{3} f^{3} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{3}}-\frac{3 b^{2} c \,d^{4} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{4}}+\frac{b^{2} c \,x^{3}}{e g}+\frac{3 b^{2} c \,f^{4} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{4}}+\frac{3 b \,c^{2} d^{5} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{5}}-\frac{b \,c^{2} d \,x^{3}}{e^{2} g}-\frac{b \,c^{2} f \,x^{3}}{e \,g^{2}}-\frac{3 b \,c^{2} f^{5} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{5}}-\frac{c^{3} d^{6} \ln \left(e x +d \right)}{\left(d g -e f \right) e^{6}}+\frac{c^{3} d^{2} x^{3}}{3 e^{3} g}+\frac{c^{3} d f \,x^{3}}{3 e^{2} g^{2}}+\frac{c^{3} f^{2} x^{3}}{3 e \,g^{3}}+\frac{c^{3} f^{6} \ln \left(g x +f \right)}{\left(d g -e f \right) g^{6}}+\frac{3 a b c \,x^{2}}{e g}-\frac{3 a \,c^{2} d \,x^{2}}{2 e^{2} g}-\frac{3 a \,c^{2} f \,x^{2}}{2 e \,g^{2}}+\frac{b^{3} x^{2}}{2 e g}-\frac{3 b^{2} c d \,x^{2}}{2 e^{2} g}-\frac{3 b^{2} c f \,x^{2}}{2 e \,g^{2}}+\frac{3 b \,c^{2} d^{2} x^{2}}{2 e^{3} g}+\frac{3 b \,c^{2} d f \,x^{2}}{2 e^{2} g^{2}}+\frac{3 b \,c^{2} f^{2} x^{2}}{2 e \,g^{3}}-\frac{c^{3} d^{3} x^{2}}{2 e^{4} g}-\frac{c^{3} d^{2} f \,x^{2}}{2 e^{3} g^{2}}-\frac{c^{3} d \,f^{2} x^{2}}{2 e^{2} g^{3}}-\frac{c^{3} f^{3} x^{2}}{2 e \,g^{4}}+\frac{3 a^{2} c x}{e g}+\frac{3 a \,b^{2} x}{e g}-\frac{6 a b c d x}{e^{2} g}-\frac{6 a b c f x}{e \,g^{2}}+\frac{3 a \,c^{2} d^{2} x}{e^{3} g}+\frac{3 a \,c^{2} d f x}{e^{2} g^{2}}+\frac{3 a \,c^{2} f^{2} x}{e \,g^{3}}-\frac{b^{3} d x}{e^{2} g}-\frac{b^{3} f x}{e \,g^{2}}+\frac{3 b^{2} c \,d^{2} x}{e^{3} g}+\frac{3 b^{2} c d f x}{e^{2} g^{2}}+\frac{3 b^{2} c \,f^{2} x}{e \,g^{3}}-\frac{3 b \,c^{2} d^{3} x}{e^{4} g}-\frac{3 b \,c^{2} d^{2} f x}{e^{3} g^{2}}-\frac{3 b \,c^{2} d \,f^{2} x}{e^{2} g^{3}}-\frac{3 b \,c^{2} f^{3} x}{e \,g^{4}}+\frac{c^{3} d^{4} x}{e^{5} g}+\frac{c^{3} d^{3} f x}{e^{4} g^{2}}+\frac{c^{3} d^{2} f^{2} x}{e^{3} g^{3}}+\frac{c^{3} d \,f^{3} x}{e^{2} g^{4}}+\frac{c^{3} f^{4} x}{e \,g^{5}}"," ",0,"1/5*c^3*x^5/e/g+1/2/g/e*x^2*b^3-6/g/e^2*a*b*c*d*x-6/g^2/e*a*b*c*f*x+3/g^2/e^2*a*c^2*d*f*x+3/g^2/e^2*b^2*c*d*f*x-3/g^2/e^3*b*c^2*d^2*f*x-6/g^3/(d*g-e*f)*ln(g*x+f)*a*b*c*f^3+6/e^3/(d*g-e*f)*ln(e*x+d)*a*b*c*d^3+1/(d*g-e*f)*ln(g*x+f)*a^3-1/(d*g-e*f)*ln(e*x+d)*a^3-3/g/(d*g-e*f)*ln(g*x+f)*a^2*b*f+3/e/(d*g-e*f)*ln(e*x+d)*a^2*b*d-3/e^2/(d*g-e*f)*ln(e*x+d)*a^2*c*d^2-3/e^2/(d*g-e*f)*ln(e*x+d)*a*b^2*d^2-3/e^4/(d*g-e*f)*ln(e*x+d)*a*c^2*d^4-3/e^4/(d*g-e*f)*ln(e*x+d)*b^2*c*d^4+3/e^5/(d*g-e*f)*ln(e*x+d)*b*c^2*d^5+3/2/g^3/e*x^2*b*c^2*f^2-1/2/g^2/e^3*x^2*c^3*d^2*f-1/2/g^3/e^2*x^2*c^3*d*f^2+3/g/e^3*a*c^2*d^2*x+3/g^3/e*a*c^2*f^2*x+3/g/e^3*b^2*c*d^2*x+3/g^3/e*b^2*c*f^2*x+3/g^2/(d*g-e*f)*ln(g*x+f)*a^2*c*f^2+3/g^2/(d*g-e*f)*ln(g*x+f)*a*b^2*f^2+3/g^4/(d*g-e*f)*ln(g*x+f)*a*c^2*f^4+3/g^4/(d*g-e*f)*ln(g*x+f)*b^2*c*f^4-3/g^5/(d*g-e*f)*ln(g*x+f)*b*c^2*f^5-1/g/e^2*x^3*b*c^2*d-1/g^2/e*x^3*b*c^2*f+1/3/g^2/e^2*x^3*c^3*d*f+1/g/e*x^3*a*c^2+1/g^5/e*c^3*f^4*x-3/g/e^4*b*c^2*d^3*x-3/g^4/e*b*c^2*f^3*x+1/g^2/e^4*c^3*d^3*f*x+1/g^3/e^3*c^3*d^2*f^2*x+1/g^4/e^2*c^3*d*f^3*x+1/g/e^5*c^3*d^4*x+3/4/g/e*x^4*b*c^2-1/4/g/e^2*x^4*c^3*d-1/4/g^2/e*x^4*c^3*f+1/3/g/e^3*x^3*c^3*d^2+1/3/g^3/e*x^3*c^3*f^2-1/2/g/e^4*x^2*c^3*d^3-1/2/g^4/e*x^2*c^3*f^3+3/g/e*a^2*c*x+3/g/e*a*b^2*x-1/g/e^2*b^3*d*x-1/g^2/e*b^3*f*x+1/g/e*x^3*b^2*c-1/g^3/(d*g-e*f)*ln(g*x+f)*b^3*f^3+1/g^6/(d*g-e*f)*ln(g*x+f)*c^3*f^6+1/e^3/(d*g-e*f)*ln(e*x+d)*b^3*d^3-1/e^6/(d*g-e*f)*ln(e*x+d)*c^3*d^6+3/g/e*x^2*a*b*c-3/2/g/e^2*x^2*a*c^2*d-3/2/g^2/e*x^2*a*c^2*f-3/2/g/e^2*x^2*b^2*c*d-3/2/g^2/e*x^2*b^2*c*f+3/2/g/e^3*x^2*b*c^2*d^2-3/g^3/e^2*b*c^2*d*f^2*x+3/2/g^2/e^2*x^2*b*c^2*d*f","B"
817,1,606,240,0.012000," ","int(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a),x)","-\frac{2 a c e g \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{b^{2} e g \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{b c d g \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{4 a c -b^{2}}}-\frac{b c e f \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{2 c^{2} d f \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{4 a c -b^{2}}}+\frac{b e g \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(a \,g^{2}-b f g +c \,f^{2}\right)}-\frac{c d g \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(a \,g^{2}-b f g +c \,f^{2}\right)}-\frac{c e f \ln \left(c \,x^{2}+b x +a \right)}{2 \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(a \,g^{2}-b f g +c \,f^{2}\right)}-\frac{e^{2} \ln \left(e x +d \right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(d g -e f \right)}+\frac{g^{2} \ln \left(g x +f \right)}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right)}"," ",0,"1/2/(a*e^2-b*d*e+c*d^2)/(a*g^2-b*f*g+c*f^2)*ln(c*x^2+b*x+a)*g*e*b-1/2/(a*e^2-b*d*e+c*d^2)/(a*g^2-b*f*g+c*f^2)*c*ln(c*x^2+b*x+a)*g*d-1/2/(a*e^2-b*d*e+c*d^2)/(a*g^2-b*f*g+c*f^2)*c*ln(c*x^2+b*x+a)*f*e-2/(a*e^2-b*d*e+c*d^2)/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c*e*g+1/(a*e^2-b*d*e+c*d^2)/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*e*g-1/(a*e^2-b*d*e+c*d^2)/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c*d*g-1/(a*e^2-b*d*e+c*d^2)/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c*e*f+2/(a*e^2-b*d*e+c*d^2)/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2*d*f+g^2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)*ln(g*x+f)-e^2/(a*e^2-b*d*e+c*d^2)/(d*g-e*f)*ln(e*x+d)","B"
818,1,9103,635,0.050000," ","int(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
819,1,540,265,0.009000," ","int((e*x+d)^3*(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(315 e^{3} c \,x^{5} g^{5}+385 b \,e^{3} g^{5} x^{4}+1155 c d \,e^{2} g^{5} x^{4}-350 c \,e^{3} f \,g^{4} x^{4}+495 a \,e^{3} g^{5} x^{3}+1485 b d \,e^{2} g^{5} x^{3}-440 b \,e^{3} f \,g^{4} x^{3}+1485 c \,d^{2} e \,g^{5} x^{3}-1320 c d \,e^{2} f \,g^{4} x^{3}+400 c \,e^{3} f^{2} g^{3} x^{3}+2079 a d \,e^{2} g^{5} x^{2}-594 a \,e^{3} f \,g^{4} x^{2}+2079 b \,d^{2} e \,g^{5} x^{2}-1782 b d \,e^{2} f \,g^{4} x^{2}+528 b \,e^{3} f^{2} g^{3} x^{2}+693 c \,d^{3} g^{5} x^{2}-1782 c \,d^{2} e f \,g^{4} x^{2}+1584 c d \,e^{2} f^{2} g^{3} x^{2}-480 c \,e^{3} f^{3} g^{2} x^{2}+3465 a \,d^{2} e \,g^{5} x -2772 a d \,e^{2} f \,g^{4} x +792 a \,e^{3} f^{2} g^{3} x +1155 b \,d^{3} g^{5} x -2772 b \,d^{2} e f \,g^{4} x +2376 b d \,e^{2} f^{2} g^{3} x -704 b \,e^{3} f^{3} g^{2} x -924 c \,d^{3} f \,g^{4} x +2376 c \,d^{2} e \,f^{2} g^{3} x -2112 c d \,e^{2} f^{3} g^{2} x +640 c \,e^{3} f^{4} g x +3465 d^{3} a \,g^{5}-6930 a \,d^{2} e f \,g^{4}+5544 a d \,e^{2} f^{2} g^{3}-1584 a \,e^{3} f^{3} g^{2}-2310 b \,d^{3} f \,g^{4}+5544 b \,d^{2} e \,f^{2} g^{3}-4752 b d \,e^{2} f^{3} g^{2}+1408 b \,e^{3} f^{4} g +1848 c \,d^{3} f^{2} g^{3}-4752 c \,d^{2} e \,f^{3} g^{2}+4224 c d \,e^{2} f^{4} g -1280 c \,e^{3} f^{5}\right)}{3465 g^{6}}"," ",0,"2/3465*(g*x+f)^(1/2)*(315*c*e^3*g^5*x^5+385*b*e^3*g^5*x^4+1155*c*d*e^2*g^5*x^4-350*c*e^3*f*g^4*x^4+495*a*e^3*g^5*x^3+1485*b*d*e^2*g^5*x^3-440*b*e^3*f*g^4*x^3+1485*c*d^2*e*g^5*x^3-1320*c*d*e^2*f*g^4*x^3+400*c*e^3*f^2*g^3*x^3+2079*a*d*e^2*g^5*x^2-594*a*e^3*f*g^4*x^2+2079*b*d^2*e*g^5*x^2-1782*b*d*e^2*f*g^4*x^2+528*b*e^3*f^2*g^3*x^2+693*c*d^3*g^5*x^2-1782*c*d^2*e*f*g^4*x^2+1584*c*d*e^2*f^2*g^3*x^2-480*c*e^3*f^3*g^2*x^2+3465*a*d^2*e*g^5*x-2772*a*d*e^2*f*g^4*x+792*a*e^3*f^2*g^3*x+1155*b*d^3*g^5*x-2772*b*d^2*e*f*g^4*x+2376*b*d*e^2*f^2*g^3*x-704*b*e^3*f^3*g^2*x-924*c*d^3*f*g^4*x+2376*c*d^2*e*f^2*g^3*x-2112*c*d*e^2*f^3*g^2*x+640*c*e^3*f^4*g*x+3465*a*d^3*g^5-6930*a*d^2*e*f*g^4+5544*a*d*e^2*f^2*g^3-1584*a*e^3*f^3*g^2-2310*b*d^3*f*g^4+5544*b*d^2*e*f^2*g^3-4752*b*d*e^2*f^3*g^2+1408*b*e^3*f^4*g+1848*c*d^3*f^2*g^3-4752*c*d^2*e*f^3*g^2+4224*c*d*e^2*f^4*g-1280*c*e^3*f^5)/g^6","B"
820,1,315,194,0.009000," ","int((e*x+d)^2*(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(35 e^{2} c \,x^{4} g^{4}+45 b \,e^{2} g^{4} x^{3}+90 c d e \,g^{4} x^{3}-40 c \,e^{2} f \,g^{3} x^{3}+63 a \,e^{2} g^{4} x^{2}+126 b d e \,g^{4} x^{2}-54 b \,e^{2} f \,g^{3} x^{2}+63 c \,d^{2} g^{4} x^{2}-108 c d e f \,g^{3} x^{2}+48 c \,e^{2} f^{2} g^{2} x^{2}+210 a d e \,g^{4} x -84 a \,e^{2} f \,g^{3} x +105 b \,d^{2} g^{4} x -168 b d e f \,g^{3} x +72 b \,e^{2} f^{2} g^{2} x -84 c \,d^{2} f \,g^{3} x +144 c d e \,f^{2} g^{2} x -64 c \,e^{2} f^{3} g x +315 a \,d^{2} g^{4}-420 a d e f \,g^{3}+168 a \,e^{2} f^{2} g^{2}-210 b \,d^{2} f \,g^{3}+336 b d e \,f^{2} g^{2}-144 b \,e^{2} f^{3} g +168 c \,d^{2} f^{2} g^{2}-288 c d e \,f^{3} g +128 c \,e^{2} f^{4}\right)}{315 g^{5}}"," ",0,"2/315*(g*x+f)^(1/2)*(35*c*e^2*g^4*x^4+45*b*e^2*g^4*x^3+90*c*d*e*g^4*x^3-40*c*e^2*f*g^3*x^3+63*a*e^2*g^4*x^2+126*b*d*e*g^4*x^2-54*b*e^2*f*g^3*x^2+63*c*d^2*g^4*x^2-108*c*d*e*f*g^3*x^2+48*c*e^2*f^2*g^2*x^2+210*a*d*e*g^4*x-84*a*e^2*f*g^3*x+105*b*d^2*g^4*x-168*b*d*e*f*g^3*x+72*b*e^2*f^2*g^2*x-84*c*d^2*f*g^3*x+144*c*d*e*f^2*g^2*x-64*c*e^2*f^3*g*x+315*a*d^2*g^4-420*a*d*e*f*g^3+168*a*e^2*f^2*g^2-210*b*d^2*f*g^3+336*b*d*e*f^2*g^2-144*b*e^2*f^3*g+168*c*d^2*f^2*g^2-288*c*d*e*f^3*g+128*c*e^2*f^4)/g^5","A"
821,1,144,123,0.006000," ","int((e*x+d)*(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(15 c e \,x^{3} g^{3}+21 b e \,g^{3} x^{2}+21 c d \,g^{3} x^{2}-18 c e f \,g^{2} x^{2}+35 a e \,g^{3} x +35 b d \,g^{3} x -28 b e f \,g^{2} x -28 c d f \,g^{2} x +24 c e \,f^{2} g x +105 a d \,g^{3}-70 a e f \,g^{2}-70 b d f \,g^{2}+56 b e \,f^{2} g +56 c d \,f^{2} g -48 c e \,f^{3}\right)}{105 g^{4}}"," ",0,"2/105*(g*x+f)^(1/2)*(15*c*e*g^3*x^3+21*b*e*g^3*x^2+21*c*d*g^3*x^2-18*c*e*f*g^2*x^2+35*a*e*g^3*x+35*b*d*g^3*x-28*b*e*f*g^2*x-28*c*d*f*g^2*x+24*c*e*f^2*g*x+105*a*d*g^3-70*a*e*f*g^2-70*b*d*f*g^2+56*b*e*f^2*g+56*c*d*f^2*g-48*c*e*f^3)/g^4","A"
822,1,53,63,0.003000," ","int((c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(3 c \,x^{2} g^{2}+5 b \,g^{2} x -4 c f g x +15 a \,g^{2}-10 b f g +8 c \,f^{2}\right)}{15 g^{3}}"," ",0,"2/15*(g*x+f)^(1/2)*(3*c*g^2*x^2+5*b*g^2*x-4*c*f*g*x+15*a*g^2-10*b*f*g+8*c*f^2)/g^3","A"
823,1,189,100,0.013000," ","int((c*x^2+b*x+a)/(e*x+d)/(g*x+f)^(1/2),x)","\frac{2 a \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\sqrt{\left(d g -e f \right) e}}-\frac{2 b d \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\sqrt{\left(d g -e f \right) e}\, e}+\frac{2 c \,d^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\sqrt{\left(d g -e f \right) e}\, e^{2}}+\frac{2 \sqrt{g x +f}\, b}{e g}-\frac{2 \sqrt{g x +f}\, c d}{e^{2} g}-\frac{2 \sqrt{g x +f}\, c f}{e \,g^{2}}+\frac{2 \left(g x +f \right)^{\frac{3}{2}} c}{3 e \,g^{2}}"," ",0,"2/3*(g*x+f)^(3/2)*c/e/g^2+2/g/e*b*(g*x+f)^(1/2)-2*(g*x+f)^(1/2)*c*d/e^2/g-2*(g*x+f)^(1/2)*c/e*f/g^2+2/((d*g-e*f)*e)^(1/2)*a*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)-2/e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*d+2/((d*g-e*f)*e)^(1/2)*c*d^2/e^2*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)","A"
824,1,371,126,0.019000," ","int((c*x^2+b*x+a)/(e*x+d)^2/(g*x+f)^(1/2),x)","\frac{a g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}}+\frac{b d g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}\, e}-\frac{2 b f \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}}-\frac{3 c \,d^{2} g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}\, e^{2}}+\frac{4 c d f \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}\, e}+\frac{\sqrt{g x +f}\, a g}{\left(d g -e f \right) \left(e g x +d g \right)}-\frac{\sqrt{g x +f}\, b d g}{\left(d g -e f \right) \left(e g x +d g \right) e}+\frac{\sqrt{g x +f}\, c \,d^{2} g}{\left(d g -e f \right) \left(e g x +d g \right) e^{2}}+\frac{2 \sqrt{g x +f}\, c}{e^{2} g}"," ",0,"2*(g*x+f)^(1/2)*c/e^2/g+g/(d*g-e*f)*(g*x+f)^(1/2)/(e*g*x+d*g)*a-g/e/(d*g-e*f)*(g*x+f)^(1/2)/(e*g*x+d*g)*b*d+g/e^2/(d*g-e*f)*(g*x+f)^(1/2)/(e*g*x+d*g)*c*d^2+g/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*a+g/e/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*d-2/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*f-3*g/e^2/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d^2+4/e/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*d*c*f","B"
825,1,538,186,0.021000," ","int((c*x^2+b*x+a)/(e*x+d)^3/(g*x+f)^(1/2),x)","\frac{3 a \,g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}}+\frac{b d \,g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}\, e}-\frac{b f g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}}+\frac{3 c \,d^{2} g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}\, e^{2}}-\frac{2 c d f g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}\, e}+\frac{2 c \,f^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) \sqrt{\left(d g -e f \right) e}}+\frac{\frac{\left(3 a \,e^{2} g +b d e g -4 b \,e^{2} f -5 c \,d^{2} g +8 d e c f \right) \left(g x +f \right)^{\frac{3}{2}} g}{4 \left(d^{2} g^{2}-2 d e f g +e^{2} f^{2}\right) e}+\frac{\left(5 a \,e^{2} g -b d e g -4 b \,e^{2} f -3 c \,d^{2} g +8 d e c f \right) \sqrt{g x +f}\, g}{4 \left(d g -e f \right) e^{2}}}{\left(d g -e f +\left(g x +f \right) e \right)^{2}}"," ",0,"2*(1/8*g*(3*a*e^2*g+b*d*e*g-4*b*e^2*f-5*c*d^2*g+8*c*d*e*f)/e/(d^2*g^2-2*d*e*f*g+e^2*f^2)*(g*x+f)^(3/2)+1/8*(5*a*e^2*g-b*d*e*g-4*b*e^2*f-3*c*d^2*g+8*c*d*e*f)/e^2*g/(d*g-e*f)*(g*x+f)^(1/2))/(d*g-e*f+(g*x+f)*e)^2+3/4/(d^2*g^2-2*d*e*f*g+e^2*f^2)/((d*g-e*f)*e)^(1/2)*a*g^2*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)+1/4/(d^2*g^2-2*d*e*f*g+e^2*f^2)/e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*d*g^2-1/(d^2*g^2-2*d*e*f*g+e^2*f^2)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*f*g+3/4/(d^2*g^2-2*d*e*f*g+e^2*f^2)/((d*g-e*f)*e)^(1/2)*c*d^2/e^2*g^2*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)-2/(d^2*g^2-2*d*e*f*g+e^2*f^2)/((d*g-e*f)*e)^(1/2)*c*d/e*f*g*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)+2/(d^2*g^2-2*d*e*f*g+e^2*f^2)/((d*g-e*f)*e)^(1/2)*c*f^2*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)","B"
826,1,540,265,0.009000," ","int((e*x+d)^3*(c*x^2+b*x+a)/(g*x+f)^(3/2),x)","-\frac{2 \left(-35 e^{3} c \,x^{5} g^{5}-45 b \,e^{3} g^{5} x^{4}-135 c d \,e^{2} g^{5} x^{4}+50 c \,e^{3} f \,g^{4} x^{4}-63 a \,e^{3} g^{5} x^{3}-189 b d \,e^{2} g^{5} x^{3}+72 b \,e^{3} f \,g^{4} x^{3}-189 c \,d^{2} e \,g^{5} x^{3}+216 c d \,e^{2} f \,g^{4} x^{3}-80 c \,e^{3} f^{2} g^{3} x^{3}-315 a d \,e^{2} g^{5} x^{2}+126 a \,e^{3} f \,g^{4} x^{2}-315 b \,d^{2} e \,g^{5} x^{2}+378 b d \,e^{2} f \,g^{4} x^{2}-144 b \,e^{3} f^{2} g^{3} x^{2}-105 c \,d^{3} g^{5} x^{2}+378 c \,d^{2} e f \,g^{4} x^{2}-432 c d \,e^{2} f^{2} g^{3} x^{2}+160 c \,e^{3} f^{3} g^{2} x^{2}-945 a \,d^{2} e \,g^{5} x +1260 a d \,e^{2} f \,g^{4} x -504 a \,e^{3} f^{2} g^{3} x -315 b \,d^{3} g^{5} x +1260 b \,d^{2} e f \,g^{4} x -1512 b d \,e^{2} f^{2} g^{3} x +576 b \,e^{3} f^{3} g^{2} x +420 c \,d^{3} f \,g^{4} x -1512 c \,d^{2} e \,f^{2} g^{3} x +1728 c d \,e^{2} f^{3} g^{2} x -640 c \,e^{3} f^{4} g x +315 d^{3} a \,g^{5}-1890 a \,d^{2} e f \,g^{4}+2520 a d \,e^{2} f^{2} g^{3}-1008 a \,e^{3} f^{3} g^{2}-630 b \,d^{3} f \,g^{4}+2520 b \,d^{2} e \,f^{2} g^{3}-3024 b d \,e^{2} f^{3} g^{2}+1152 b \,e^{3} f^{4} g +840 c \,d^{3} f^{2} g^{3}-3024 c \,d^{2} e \,f^{3} g^{2}+3456 c d \,e^{2} f^{4} g -1280 c \,e^{3} f^{5}\right)}{315 \sqrt{g x +f}\, g^{6}}"," ",0,"-2/315/(g*x+f)^(1/2)*(-35*c*e^3*g^5*x^5-45*b*e^3*g^5*x^4-135*c*d*e^2*g^5*x^4+50*c*e^3*f*g^4*x^4-63*a*e^3*g^5*x^3-189*b*d*e^2*g^5*x^3+72*b*e^3*f*g^4*x^3-189*c*d^2*e*g^5*x^3+216*c*d*e^2*f*g^4*x^3-80*c*e^3*f^2*g^3*x^3-315*a*d*e^2*g^5*x^2+126*a*e^3*f*g^4*x^2-315*b*d^2*e*g^5*x^2+378*b*d*e^2*f*g^4*x^2-144*b*e^3*f^2*g^3*x^2-105*c*d^3*g^5*x^2+378*c*d^2*e*f*g^4*x^2-432*c*d*e^2*f^2*g^3*x^2+160*c*e^3*f^3*g^2*x^2-945*a*d^2*e*g^5*x+1260*a*d*e^2*f*g^4*x-504*a*e^3*f^2*g^3*x-315*b*d^3*g^5*x+1260*b*d^2*e*f*g^4*x-1512*b*d*e^2*f^2*g^3*x+576*b*e^3*f^3*g^2*x+420*c*d^3*f*g^4*x-1512*c*d^2*e*f^2*g^3*x+1728*c*d*e^2*f^3*g^2*x-640*c*e^3*f^4*g*x+315*a*d^3*g^5-1890*a*d^2*e*f*g^4+2520*a*d*e^2*f^2*g^3-1008*a*e^3*f^3*g^2-630*b*d^3*f*g^4+2520*b*d^2*e*f^2*g^3-3024*b*d*e^2*f^3*g^2+1152*b*e^3*f^4*g+840*c*d^3*f^2*g^3-3024*c*d^2*e*f^3*g^2+3456*c*d*e^2*f^4*g-1280*c*e^3*f^5)/g^6","B"
827,1,315,194,0.008000," ","int((e*x+d)^2*(c*x^2+b*x+a)/(g*x+f)^(3/2),x)","-\frac{2 \left(-15 e^{2} c \,x^{4} g^{4}-21 b \,e^{2} g^{4} x^{3}-42 c d e \,g^{4} x^{3}+24 c \,e^{2} f \,g^{3} x^{3}-35 a \,e^{2} g^{4} x^{2}-70 b d e \,g^{4} x^{2}+42 b \,e^{2} f \,g^{3} x^{2}-35 c \,d^{2} g^{4} x^{2}+84 c d e f \,g^{3} x^{2}-48 c \,e^{2} f^{2} g^{2} x^{2}-210 a d e \,g^{4} x +140 a \,e^{2} f \,g^{3} x -105 b \,d^{2} g^{4} x +280 b d e f \,g^{3} x -168 b \,e^{2} f^{2} g^{2} x +140 c \,d^{2} f \,g^{3} x -336 c d e \,f^{2} g^{2} x +192 c \,e^{2} f^{3} g x +105 a \,d^{2} g^{4}-420 a d e f \,g^{3}+280 a \,e^{2} f^{2} g^{2}-210 b \,d^{2} f \,g^{3}+560 b d e \,f^{2} g^{2}-336 b \,e^{2} f^{3} g +280 c \,d^{2} f^{2} g^{2}-672 c d e \,f^{3} g +384 c \,e^{2} f^{4}\right)}{105 \sqrt{g x +f}\, g^{5}}"," ",0,"-2/105/(g*x+f)^(1/2)*(-15*c*e^2*g^4*x^4-21*b*e^2*g^4*x^3-42*c*d*e*g^4*x^3+24*c*e^2*f*g^3*x^3-35*a*e^2*g^4*x^2-70*b*d*e*g^4*x^2+42*b*e^2*f*g^3*x^2-35*c*d^2*g^4*x^2+84*c*d*e*f*g^3*x^2-48*c*e^2*f^2*g^2*x^2-210*a*d*e*g^4*x+140*a*e^2*f*g^3*x-105*b*d^2*g^4*x+280*b*d*e*f*g^3*x-168*b*e^2*f^2*g^2*x+140*c*d^2*f*g^3*x-336*c*d*e*f^2*g^2*x+192*c*e^2*f^3*g*x+105*a*d^2*g^4-420*a*d*e*f*g^3+280*a*e^2*f^2*g^2-210*b*d^2*f*g^3+560*b*d*e*f^2*g^2-336*b*e^2*f^3*g+280*c*d^2*f^2*g^2-672*c*d*e*f^3*g+384*c*e^2*f^4)/g^5","A"
828,1,144,123,0.005000," ","int((e*x+d)*(c*x^2+b*x+a)/(g*x+f)^(3/2),x)","-\frac{2 \left(-3 c e \,x^{3} g^{3}-5 b e \,g^{3} x^{2}-5 c d \,g^{3} x^{2}+6 c e f \,g^{2} x^{2}-15 a e \,g^{3} x -15 b d \,g^{3} x +20 b e f \,g^{2} x +20 c d f \,g^{2} x -24 c e \,f^{2} g x +15 a d \,g^{3}-30 a e f \,g^{2}-30 b d f \,g^{2}+40 b e \,f^{2} g +40 c d \,f^{2} g -48 c e \,f^{3}\right)}{15 \sqrt{g x +f}\, g^{4}}"," ",0,"-2/15/(g*x+f)^(1/2)*(-3*c*e*g^3*x^3-5*b*e*g^3*x^2-5*c*d*g^3*x^2+6*c*e*f*g^2*x^2-15*a*e*g^3*x-15*b*d*g^3*x+20*b*e*f*g^2*x+20*c*d*f*g^2*x-24*c*e*f^2*g*x+15*a*d*g^3-30*a*e*f*g^2-30*b*d*f*g^2+40*b*e*f^2*g+40*c*d*f^2*g-48*c*e*f^3)/g^4","A"
829,1,53,63,0.004000," ","int((c*x^2+b*x+a)/(g*x+f)^(3/2),x)","-\frac{2 \left(-c \,x^{2} g^{2}-3 b \,g^{2} x +4 c f g x +3 a \,g^{2}-6 b f g +8 c \,f^{2}\right)}{3 \sqrt{g x +f}\, g^{3}}"," ",0,"-2/3/(g*x+f)^(1/2)*(-c*g^2*x^2-3*b*g^2*x+4*c*f*g*x+3*a*g^2-6*b*f*g+8*c*f^2)/g^3","A"
830,1,237,108,0.014000," ","int((c*x^2+b*x+a)/(e*x+d)/(g*x+f)^(3/2),x)","-\frac{2 a e \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}}+\frac{2 b d \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}}-\frac{2 c \,d^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right) \sqrt{\left(d g -e f \right) e}\, e}-\frac{2 a}{\left(d g -e f \right) \sqrt{g x +f}}+\frac{2 b f}{\left(d g -e f \right) \sqrt{g x +f}\, g}-\frac{2 c \,f^{2}}{\left(d g -e f \right) \sqrt{g x +f}\, g^{2}}+\frac{2 \sqrt{g x +f}\, c}{e \,g^{2}}"," ",0,"2*(g*x+f)^(1/2)*c/e/g^2-2/(d*g-e*f)*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*a+2/(d*g-e*f)/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*d-2/(d*g-e*f)/e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d^2-2/(d*g-e*f)/(g*x+f)^(1/2)*a+2/g/(d*g-e*f)/(g*x+f)^(1/2)*b*f-2/g^2/(d*g-e*f)/(g*x+f)^(1/2)*c*f^2","B"
831,1,418,151,0.022000," ","int((c*x^2+b*x+a)/(e*x+d)^2/(g*x+f)^(3/2),x)","-\frac{3 a e g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\left(d g -e f \right) e}}+\frac{b d g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\left(d g -e f \right) e}}+\frac{2 b e f \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\left(d g -e f \right) e}}+\frac{c \,d^{2} g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\left(d g -e f \right) e}\, e}-\frac{4 c d f \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\left(d g -e f \right) e}}-\frac{\sqrt{g x +f}\, a e g}{\left(d g -e f \right)^{2} \left(e g x +d g \right)}+\frac{\sqrt{g x +f}\, b d g}{\left(d g -e f \right)^{2} \left(e g x +d g \right)}-\frac{\sqrt{g x +f}\, c \,d^{2} g}{\left(d g -e f \right)^{2} \left(e g x +d g \right) e}-\frac{2 a g}{\left(d g -e f \right)^{2} \sqrt{g x +f}}+\frac{2 b f}{\left(d g -e f \right)^{2} \sqrt{g x +f}}-\frac{2 c \,f^{2}}{\left(d g -e f \right)^{2} \sqrt{g x +f}\, g}"," ",0,"-1/(d*g-e*f)^2*(g*x+f)^(1/2)/(e*g*x+d*g)*a*e*g+g/(d*g-e*f)^2*(g*x+f)^(1/2)/(e*g*x+d*g)*b*d-1/(d*g-e*f)^2*(g*x+f)^(1/2)/(e*g*x+d*g)*c*d^2/e*g-3/(d*g-e*f)^2/((d*g-e*f)*e)^(1/2)*a*e*g*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)+g/(d*g-e*f)^2/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*d+2/(d*g-e*f)^2*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*f+1/(d*g-e*f)^2/((d*g-e*f)*e)^(1/2)*c*d^2/e*g*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)-4/(d*g-e*f)^2/((d*g-e*f)*e)^(1/2)*c*d*f*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)-2/(d*g-e*f)^2/(g*x+f)^(1/2)*a*g+2/(d*g-e*f)^2/(g*x+f)^(1/2)*b*f-2/(d*g-e*f)^2/(g*x+f)^(1/2)*c*f^2/g","B"
832,1,847,226,0.026000," ","int((c*x^2+b*x+a)/(e*x+d)^3/(g*x+f)^(3/2),x)","-\frac{9 \sqrt{g x +f}\, a d e \,g^{3}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}+\frac{9 \sqrt{g x +f}\, a \,e^{2} f \,g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}+\frac{5 \sqrt{g x +f}\, b \,d^{2} g^{3}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{\sqrt{g x +f}\, b d e f \,g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{\sqrt{g x +f}\, b \,e^{2} f^{2} g}{\left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{\sqrt{g x +f}\, c \,d^{3} g^{3}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2} e}-\frac{7 \sqrt{g x +f}\, c \,d^{2} f \,g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}+\frac{2 \sqrt{g x +f}\, c d e \,f^{2} g}{\left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{7 \left(g x +f \right)^{\frac{3}{2}} a \,e^{2} g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{15 a e \,g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}}+\frac{3 \left(g x +f \right)^{\frac{3}{2}} b d e \,g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}+\frac{3 b d \,g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}}+\frac{\left(g x +f \right)^{\frac{3}{2}} b \,e^{2} f g}{\left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}+\frac{3 b e f g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}}+\frac{c \,d^{2} g^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{4 \left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}\, e}+\frac{\left(g x +f \right)^{\frac{3}{2}} c \,d^{2} g^{2}}{4 \left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{2 \left(g x +f \right)^{\frac{3}{2}} c d e f g}{\left(d g -e f \right)^{3} \left(e g x +d g \right)^{2}}-\frac{2 c d f g \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}}-\frac{2 c e \,f^{2} \arctan \left(\frac{\sqrt{g x +f}\, e}{\sqrt{\left(d g -e f \right) e}}\right)}{\left(d g -e f \right)^{3} \sqrt{\left(d g -e f \right) e}}-\frac{2 a \,g^{2}}{\left(d g -e f \right)^{3} \sqrt{g x +f}}+\frac{2 b f g}{\left(d g -e f \right)^{3} \sqrt{g x +f}}-\frac{2 c \,f^{2}}{\left(d g -e f \right)^{3} \sqrt{g x +f}}"," ",0,"-7/4/(d*g-e*f)^3/(e*g*x+d*g)^2*(g*x+f)^(3/2)*a*e^2*g^2+3/4/(d*g-e*f)^3/(e*g*x+d*g)^2*(g*x+f)^(3/2)*b*d*e*g^2+1/(d*g-e*f)^3/(e*g*x+d*g)^2*(g*x+f)^(3/2)*b*e^2*f*g+1/4/(d*g-e*f)^3/(e*g*x+d*g)^2*(g*x+f)^(3/2)*c*d^2*g^2-2/(d*g-e*f)^3/(e*g*x+d*g)^2*(g*x+f)^(3/2)*c*d*e*f*g-9/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^3*e*(g*x+f)^(1/2)*a*d+9/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^2*e^2*(g*x+f)^(1/2)*a*f+5/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^3*(g*x+f)^(1/2)*b*d^2-1/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^2*e*(g*x+f)^(1/2)*f*d*b-1/(d*g-e*f)^3/(e*g*x+d*g)^2*g*e^2*(g*x+f)^(1/2)*b*f^2-1/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^3/e*(g*x+f)^(1/2)*c*d^3-7/4/(d*g-e*f)^3/(e*g*x+d*g)^2*g^2*(g*x+f)^(1/2)*c*d^2*f+2/(d*g-e*f)^3/(e*g*x+d*g)^2*g*e*(g*x+f)^(1/2)*c*d*f^2-15/4/(d*g-e*f)^3*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*a*g^2+3/4/(d*g-e*f)^3/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*d*g^2+3/(d*g-e*f)^3*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*b*f*g+1/4/(d*g-e*f)^3/e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d^2*g^2-2/(d*g-e*f)^3/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*d*f*g-2/(d*g-e*f)^3*e/((d*g-e*f)*e)^(1/2)*arctan((g*x+f)^(1/2)/((d*g-e*f)*e)^(1/2)*e)*c*f^2-2/(d*g-e*f)^3/(g*x+f)^(1/2)*a*g^2+2/(d*g-e*f)^3/(g*x+f)^(1/2)*b*f*g-2/(d*g-e*f)^3/(g*x+f)^(1/2)*c*f^2","B"
833,1,231,65,0.086000," ","int((x-1)^(1/2)*(x+1)^(1/2)/(-x^2+x+1),x)","-\frac{\sqrt{x -1}\, \sqrt{x +1}\, \sqrt{5}\, \left(-\sqrt{5}\, \sqrt{-2+2 \sqrt{5}}\, \arctanh \left(\frac{\sqrt{5}\, x +x -2}{\sqrt{2 \sqrt{5}+2}\, \sqrt{x^{2}-1}}\right)-\sqrt{-2+2 \sqrt{5}}\, \arctanh \left(\frac{\sqrt{5}\, x +x -2}{\sqrt{2 \sqrt{5}+2}\, \sqrt{x^{2}-1}}\right)-\sqrt{5}\, \sqrt{2 \sqrt{5}+2}\, \arctan \left(\frac{\sqrt{5}\, x -x +2}{\sqrt{-2+2 \sqrt{5}}\, \sqrt{x^{2}-1}}\right)+\sqrt{2 \sqrt{5}+2}\, \arctan \left(\frac{\sqrt{5}\, x -x +2}{\sqrt{-2+2 \sqrt{5}}\, \sqrt{x^{2}-1}}\right)+\sqrt{5}\, \sqrt{2 \sqrt{5}+2}\, \sqrt{-2+2 \sqrt{5}}\, \ln \left(x +\sqrt{x^{2}-1}\right)\right)}{5 \sqrt{x^{2}-1}\, \sqrt{2 \sqrt{5}+2}\, \sqrt{-2+2 \sqrt{5}}}"," ",0,"-1/5*(x-1)^(1/2)*(x+1)^(1/2)*5^(1/2)*(5^(1/2)*ln(x+(x^2-1)^(1/2))*(2*5^(1/2)+2)^(1/2)*(-2+2*5^(1/2))^(1/2)-5^(1/2)*arctan((x*5^(1/2)-x+2)/(-2+2*5^(1/2))^(1/2)/(x^2-1)^(1/2))*(2*5^(1/2)+2)^(1/2)-5^(1/2)*arctanh((x*5^(1/2)+x-2)/(2*5^(1/2)+2)^(1/2)/(x^2-1)^(1/2))*(-2+2*5^(1/2))^(1/2)+arctan((x*5^(1/2)-x+2)/(-2+2*5^(1/2))^(1/2)/(x^2-1)^(1/2))*(2*5^(1/2)+2)^(1/2)-arctanh((x*5^(1/2)+x-2)/(2*5^(1/2)+2)^(1/2)/(x^2-1)^(1/2))*(-2+2*5^(1/2))^(1/2))/(x^2-1)^(1/2)/(2*5^(1/2)+2)^(1/2)/(-2+2*5^(1/2))^(1/2)","B"
834,1,425,138,0.029000," ","int((c*x^2+b*x+a)/(e*x+d)^(1/2)/(g*x+f)^(1/2),x)","\frac{\left(8 a \,e^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-4 b d e \,g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-4 b \,e^{2} f g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,d^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+2 c d e f g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,e^{2} f^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+4 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c e g x +8 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b e g -6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c d g -6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c e f \right) \sqrt{e x +d}\, \sqrt{g x +f}}{8 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, e^{2} g^{2}}"," ",0,"1/8*(8*a*e^2*g^2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))-4*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*d*e*g^2-4*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*e^2*f*g+3*c*d^2*g^2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))+2*c*d*e*f*g*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))+3*c*e^2*f^2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))+4*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*e*g*x+8*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*b*e*g-6*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)*c*d*g-6*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)*c*e*f)*(e*x+d)^(1/2)*(g*x+f)^(1/2)/(e*g)^(1/2)/g^2/e^2/((e*x+d)*(g*x+f))^(1/2)","B"
835,1,1207,295,0.032000," ","int((e*x+d)^(3/2)*(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\frac{\sqrt{e x +d}\, \sqrt{g x +f}\, \left(144 a \,d^{2} e^{2} g^{4} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-288 a d \,e^{3} f \,g^{3} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+144 a \,e^{4} f^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-24 b \,d^{3} e \,g^{4} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-72 b \,d^{2} e^{2} f \,g^{3} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+216 b d \,e^{3} f^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-120 b \,e^{4} f^{3} g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+9 c \,d^{4} g^{4} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+12 c \,d^{3} e f \,g^{3} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+54 c \,d^{2} e^{2} f^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-180 c d \,e^{3} f^{3} g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+105 c \,e^{4} f^{4} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+96 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c \,e^{3} g^{3} x^{3}+128 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, b \,e^{3} g^{3} x^{2}+144 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c d \,e^{2} g^{3} x^{2}-112 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c \,e^{3} f \,g^{2} x^{2}+192 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, a \,e^{3} g^{3} x +224 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b d \,e^{2} g^{3} x -160 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b \,e^{3} f \,g^{2} x +12 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c \,d^{2} e \,g^{3} x -184 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c d \,e^{2} f \,g^{2} x +140 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c \,e^{3} f^{2} g x +480 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, a d \,e^{2} g^{3}-288 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, a \,e^{3} f \,g^{2}+48 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b \,d^{2} e \,g^{3}-352 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b d \,e^{2} f \,g^{2}+240 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b \,e^{3} f^{2} g -18 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c \,d^{3} g^{3}-30 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c \,d^{2} e f \,g^{2}+290 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c d \,e^{2} f^{2} g -210 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c \,e^{3} f^{3}\right)}{384 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, e^{2} g^{4}}"," ",0,"1/384*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(9*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^4*g^4+105*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*e^4*f^4-72*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*d^2*e^2*f*g^3-30*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*d^2*e*f*g^2+224*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*b*d*e^2*g^3-160*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*b*e^3*f*g^2+12*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*c*d^2*e*g^3+140*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*c*e^3*f^2*g-112*x^2*c*e^3*f*g^2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-352*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*b*d*e^2*f*g^2+290*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*d*e^2*f^2*g+144*x^2*c*d*e^2*g^3*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+144*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*a*d^2*e^2*g^4-184*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*c*d*e^2*f*g^2+144*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*a*e^4*f^2*g^2-120*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*e^4*f^3*g-210*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*e^3*f^3-24*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*d^3*e*g^4-18*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*d^3*g^3+216*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*d*e^3*f^2*g^2+54*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^2*e^2*f^2*g^2-180*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d*e^3*f^3*g+480*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*a*d*e^2*g^3-288*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*a*e^3*f*g^2+240*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*b*e^3*f^2*g-288*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*a*d*e^3*f*g^3+48*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*b*d^2*e*g^3+192*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*a*e^3*g^3+96*x^3*c*e^3*g^3*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+128*x^2*b*e^3*g^3*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+12*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^3*e*f*g^3)/e^2/g^4/((e*x+d)*(g*x+f))^(1/2)/(e*g)^(1/2)","B"
836,1,763,214,0.023000," ","int((e*x+d)^(1/2)*(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\frac{\sqrt{e x +d}\, \sqrt{g x +f}\, \left(24 a d \,e^{2} g^{3} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-24 a \,e^{3} f \,g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-6 b \,d^{2} e \,g^{3} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-12 b d \,e^{2} f \,g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+18 b \,e^{3} f^{2} g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,d^{3} g^{3} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,d^{2} e f \,g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+9 c d \,e^{2} f^{2} g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-15 c \,e^{3} f^{3} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+16 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c \,e^{2} g^{2} x^{2}+24 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b \,e^{2} g^{2} x +4 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c d e \,g^{2} x -20 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c \,e^{2} f g x +48 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, a \,e^{2} g^{2}+12 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b d e \,g^{2}-36 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b \,e^{2} f g -6 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c \,d^{2} g^{2}-8 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c d e f g +30 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c \,e^{2} f^{2}\right)}{48 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, e^{2} g^{3}}"," ",0,"1/48*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(16*x^2*c*e^2*g^2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+24*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*a*d*e^2*g^3-24*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*a*e^3*f*g^2-6*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*d^2*e*g^3-12*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*d*e^2*f*g^2+18*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*e^3*f^2*g+3*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^3*g^3+3*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^2*e*f*g^2+9*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d*e^2*f^2*g-15*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*e^3*f^3+24*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*b*e^2*g^2+4*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*c*d*e*g^2-20*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*x*c*e^2*f*g+48*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*a*e^2*g^2+12*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*b*d*e*g^2-36*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*b*e^2*f*g-6*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*d^2*g^2-8*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*d*e*f*g+30*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*e^2*f^2)/g^3/((e*x+d)*(g*x+f))^(1/2)/e^2/(e*g)^(1/2)","B"
837,1,425,138,0.000000," ","int((c*x^2+b*x+a)/(e*x+d)^(1/2)/(g*x+f)^(1/2),x)","\frac{\left(8 a \,e^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-4 b d e \,g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-4 b \,e^{2} f g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,d^{2} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+2 c d e f g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,e^{2} f^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+4 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, c e g x +8 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, b e g -6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c d g -6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c e f \right) \sqrt{e x +d}\, \sqrt{g x +f}}{8 \sqrt{e g}\, \sqrt{\left(e x +d \right) \left(g x +f \right)}\, e^{2} g^{2}}"," ",0,"1/8*(8*a*e^2*g^2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))-4*b*d*e*g^2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))-4*b*e^2*f*g*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))+3*c*d^2*g^2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))+2*c*d*e*f*g*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))+3*c*e^2*f^2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))+4*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*c*e*g*x+8*(e*g)^(1/2)*((e*x+d)*(g*x+f))^(1/2)*b*e*g-6*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)*c*d*g-6*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)*c*e*f)*(e*x+d)^(1/2)*(g*x+f)^(1/2)/(e*g)^(1/2)/((e*x+d)*(g*x+f))^(1/2)/e^2/g^2","B"
838,1,697,109,0.029000," ","int((c*x^2+b*x+a)/(e*x+d)^(3/2)/(g*x+f)^(1/2),x)","\frac{\sqrt{g x +f}\, \left(2 b d \,e^{2} g^{2} x \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-2 b \,e^{3} f g x \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-3 c \,d^{2} e \,g^{2} x \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+2 c d \,e^{2} f g x \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+c \,e^{3} f^{2} x \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+2 b \,d^{2} e \,g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-2 b d \,e^{2} f g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-3 c \,d^{3} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+2 c \,d^{2} e f g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+c d \,e^{2} f^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c d e g x -2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c \,e^{2} f x +4 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, a \,e^{2} g -4 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, b d e g +6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c \,d^{2} g -2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c d e f \right)}{2 \sqrt{e g}\, \left(d g -e f \right) \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e x +d}\, e^{2} g}"," ",0,"1/2*(g*x+f)^(1/2)*(2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x*b*d*e^2*g^2-2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x*b*e^3*f*g-3*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x*c*d^2*e*g^2+2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x*c*d*e^2*f*g+ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x*c*e^3*f^2+2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*d^2*e*g^2-2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*b*d*e^2*f*g-3*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^3*g^2+2*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^2*e*f*g+ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d*e^2*f^2+2*x*c*d*e*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-2*x*c*e^2*f*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+4*a*e^2*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-4*b*d*e*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+6*c*d^2*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-2*c*d*e*f*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2)/g/(d*g-e*f)/((e*x+d)*(g*x+f))^(1/2)/e^2/(e*x+d)^(1/2)","B"
839,1,773,136,0.028000," ","int((c*x^2+b*x+a)/(e*x+d)^(5/2)/(g*x+f)^(1/2),x)","\frac{\sqrt{g x +f}\, \left(3 c \,d^{2} e^{2} g^{2} x^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-6 c d \,e^{3} f g \,x^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,e^{4} f^{2} x^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+6 c \,d^{3} e \,g^{2} x \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-12 c \,d^{2} e^{2} f g x \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+6 c d \,e^{3} f^{2} x \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,d^{4} g^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)-6 c \,d^{3} e f g \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+3 c \,d^{2} e^{2} f^{2} \ln \left(\frac{2 e g x +d g +e f +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}}{2 \sqrt{e g}}\right)+4 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, a \,e^{3} g x +2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, b d \,e^{2} g x -6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, b \,e^{3} f x -8 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c \,d^{2} e g x +12 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c d \,e^{2} f x +6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, a d \,e^{2} g -2 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, a \,e^{3} f -4 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, b d \,e^{2} f -6 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c \,d^{3} g +10 \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \sqrt{e g}\, c \,d^{2} e f \right)}{3 \sqrt{e g}\, \left(d g -e f \right)^{2} \sqrt{\left(e x +d \right) \left(g x +f \right)}\, \left(e x +d \right)^{\frac{3}{2}} e^{2}}"," ",0,"1/3*(g*x+f)^(1/2)*(3*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x^2*c*d^2*e^2*g^2-6*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x^2*c*d*e^3*f*g+3*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x^2*c*e^4*f^2+6*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x*c*d^3*e*g^2-12*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x*c*d^2*e^2*f*g+6*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*x*c*d*e^3*f^2+3*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^4*g^2-6*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^3*e*f*g+3*ln(1/2*(2*e*g*x+d*g+e*f+2*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2))*c*d^2*e^2*f^2+4*x*a*e^3*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+2*x*b*d*e^2*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-6*x*b*e^3*f*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-8*x*c*d^2*e*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+12*x*c*d*e^2*f*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+6*a*d*e^2*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-2*a*e^3*f*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-4*b*d*e^2*f*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)-6*c*d^3*g*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2)+10*c*d^2*e*f*((e*x+d)*(g*x+f))^(1/2)*(e*g)^(1/2))/(e*g)^(1/2)/(d*g-e*f)^2/((e*x+d)*(g*x+f))^(1/2)/e^2/(e*x+d)^(3/2)","B"
840,1,238,180,0.010000," ","int((c*x^2+b*x+a)/(e*x+d)^(7/2)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(8 a \,e^{2} g^{2} x^{2}+2 b d e \,g^{2} x^{2}-10 b \,e^{2} f g \,x^{2}+3 c \,d^{2} g^{2} x^{2}-10 c d e f g \,x^{2}+15 c \,e^{2} f^{2} x^{2}+20 a d e \,g^{2} x -4 a \,e^{2} f g x +5 b \,d^{2} g^{2} x -26 b d e f g x +5 b \,e^{2} f^{2} x -4 c \,d^{2} f g x +20 c d e \,f^{2} x +15 a \,d^{2} g^{2}-10 a d e f g +3 a \,e^{2} f^{2}-10 b \,d^{2} f g +2 b d e \,f^{2}+8 c \,d^{2} f^{2}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} \left(g^{3} d^{3}-3 d^{2} e f \,g^{2}+3 d \,e^{2} f^{2} g -e^{3} f^{3}\right)}"," ",0,"2/15*(g*x+f)^(1/2)*(8*a*e^2*g^2*x^2+2*b*d*e*g^2*x^2-10*b*e^2*f*g*x^2+3*c*d^2*g^2*x^2-10*c*d*e*f*g*x^2+15*c*e^2*f^2*x^2+20*a*d*e*g^2*x-4*a*e^2*f*g*x+5*b*d^2*g^2*x-26*b*d*e*f*g*x+5*b*e^2*f^2*x-4*c*d^2*f*g*x+20*c*d*e*f^2*x+15*a*d^2*g^2-10*a*d*e*f*g+3*a*e^2*f^2-10*b*d^2*f*g+2*b*d*e*f^2+8*c*d^2*f^2)/(e*x+d)^(5/2)/(d^3*g^3-3*d^2*e*f*g^2+3*d*e^2*f^2*g-e^3*f^3)","A"
841,1,468,257,0.010000," ","int((c*x^2+b*x+a)/(e*x+d)^(9/2)/(g*x+f)^(1/2),x)","\frac{2 \sqrt{g x +f}\, \left(48 a \,e^{3} g^{3} x^{3}+8 b d \,e^{2} g^{3} x^{3}-56 b \,e^{3} f \,g^{2} x^{3}+6 c \,d^{2} e \,g^{3} x^{3}-28 c d \,e^{2} f \,g^{2} x^{3}+70 c \,e^{3} f^{2} g \,x^{3}+168 a d \,e^{2} g^{3} x^{2}-24 a \,e^{3} f \,g^{2} x^{2}+28 b \,d^{2} e \,g^{3} x^{2}-200 b d \,e^{2} f \,g^{2} x^{2}+28 b \,e^{3} f^{2} g \,x^{2}+21 c \,d^{3} g^{3} x^{2}-101 c \,d^{2} e f \,g^{2} x^{2}+259 c d \,e^{2} f^{2} g \,x^{2}-35 c \,e^{3} f^{3} x^{2}+210 a \,d^{2} e \,g^{3} x -84 a d \,e^{2} f \,g^{2} x +18 a \,e^{3} f^{2} g x +35 b \,d^{3} g^{3} x -259 b \,d^{2} e f \,g^{2} x +101 b d \,e^{2} f^{2} g x -21 b \,e^{3} f^{3} x -28 c \,d^{3} f \,g^{2} x +200 c \,d^{2} e \,f^{2} g x -28 c d \,e^{2} f^{3} x +105 a \,d^{3} g^{3}-105 a \,d^{2} e f \,g^{2}+63 a d \,e^{2} f^{2} g -15 a \,e^{3} f^{3}-70 b \,d^{3} f \,g^{2}+28 b \,d^{2} e \,f^{2} g -6 b d \,e^{2} f^{3}+56 c \,d^{3} f^{2} g -8 c \,d^{2} e \,f^{3}\right)}{105 \left(e x +d \right)^{\frac{7}{2}} \left(g^{4} d^{4}-4 e \,g^{3} f \,d^{3}+6 d^{2} e^{2} f^{2} g^{2}-4 d \,e^{3} f^{3} g +e^{4} f^{4}\right)}"," ",0,"2/105*(g*x+f)^(1/2)*(48*a*e^3*g^3*x^3+8*b*d*e^2*g^3*x^3-56*b*e^3*f*g^2*x^3+6*c*d^2*e*g^3*x^3-28*c*d*e^2*f*g^2*x^3+70*c*e^3*f^2*g*x^3+168*a*d*e^2*g^3*x^2-24*a*e^3*f*g^2*x^2+28*b*d^2*e*g^3*x^2-200*b*d*e^2*f*g^2*x^2+28*b*e^3*f^2*g*x^2+21*c*d^3*g^3*x^2-101*c*d^2*e*f*g^2*x^2+259*c*d*e^2*f^2*g*x^2-35*c*e^3*f^3*x^2+210*a*d^2*e*g^3*x-84*a*d*e^2*f*g^2*x+18*a*e^3*f^2*g*x+35*b*d^3*g^3*x-259*b*d^2*e*f*g^2*x+101*b*d*e^2*f^2*g*x-21*b*e^3*f^3*x-28*c*d^3*f*g^2*x+200*c*d^2*e*f^2*g*x-28*c*d*e^2*f^3*x+105*a*d^3*g^3-105*a*d^2*e*f*g^2+63*a*d*e^2*f^2*g-15*a*e^3*f^3-70*b*d^3*f*g^2+28*b*d^2*e*f^2*g-6*b*d*e^2*f^3+56*c*d^3*f^2*g-8*c*d^2*e*f^3)/(e*x+d)^(7/2)/(d^4*g^4-4*d^3*e*f*g^3+6*d^2*e^2*f^2*g^2-4*d*e^3*f^3*g+e^4*f^4)","A"
842,1,834,219,0.042000," ","int((e*x+d)^(1/2)*(c*x^2+b*x+a)/(f*x+e)^(3/2),x)","\frac{\sqrt{e x +d}\, \left(8 a \,e^{2} f^{3} x \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)+4 b d e \,f^{3} x \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)-12 b \,e^{3} f^{2} x \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)-c \,d^{2} f^{3} x \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)-6 c d \,e^{2} f^{2} x \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)+15 c \,e^{4} f x \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)+8 a \,e^{3} f^{2} \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)+4 b d \,e^{2} f^{2} \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)-12 b \,e^{4} f \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)-c \,d^{2} e \,f^{2} \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)-6 c d \,e^{3} f \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)+15 c \,e^{5} \ln \left(\frac{2 e f x +d f +e^{2}+2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}}{2 \sqrt{e f}}\right)+4 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}\, c e \,f^{2} x^{2}+8 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}\, b e \,f^{2} x +2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}\, c d \,f^{2} x -10 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}\, c \,e^{2} f x -16 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}\, a e \,f^{2}+24 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}\, b \,e^{2} f +2 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}\, c d e f -30 \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{e f}\, c \,e^{3}\right)}{8 \sqrt{e f}\, \sqrt{\left(e x +d \right) \left(f x +e \right)}\, \sqrt{f x +e}\, e \,f^{3}}"," ",0,"1/8*(e*x+d)^(1/2)*(8*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*x*a*e^2*f^3+4*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*x*b*d*e*f^3-12*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*x*b*e^3*f^2-ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*x*c*d^2*f^3-6*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*x*c*d*e^2*f^2+15*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*x*c*e^4*f+4*x^2*c*e*f^2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+8*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*a*e^3*f^2+4*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*b*d*e^2*f^2-12*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*b*e^4*f-ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*c*d^2*e*f^2-6*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*c*d*e^3*f+15*ln(1/2*(2*e*f*x+2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+d*f+e^2)/(e*f)^(1/2))*c*e^5+8*x*b*e*f^2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+2*x*c*d*f^2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)-10*x*c*e^2*f*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)-16*a*e*f^2*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+24*b*e^2*f*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)+2*c*d*e*f*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2)-30*c*e^3*((e*x+d)*(f*x+e))^(1/2)*(e*f)^(1/2))/(e*f)^(1/2)/e/((e*x+d)*(f*x+e))^(1/2)/f^3/(f*x+e)^(1/2)","B"
843,1,571,204,0.044000," ","int((e*x+d)^(3/2)*(8*e^2*x^2+20*d*e*x+15*d^2)/(b*x+a)^(1/2),x)","\frac{\sqrt{e x +d}\, \sqrt{b x +a}\, \left(105 a^{4} e^{4} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-480 a^{3} b d \,e^{3} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+864 a^{2} b^{2} d^{2} e^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-708 a \,b^{3} d^{3} e \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+219 b^{4} d^{4} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+96 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b^{3} e^{3} x^{3}-112 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, a \,b^{2} e^{3} x^{2}+464 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b^{3} d \,e^{2} x^{2}+140 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, a^{2} b \,e^{3} x -584 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, a \,b^{2} d \,e^{2} x +932 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, b^{3} d^{2} e x -210 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, a^{3} e^{3}+890 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, a^{2} b d \,e^{2}-1450 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, a \,b^{2} d^{2} e +1002 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b^{3} d^{3}\right)}{48 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b^{4}}"," ",0,"1/48*(e*x+d)^(1/2)*(b*x+a)^(1/2)*(96*x^3*b^3*e^3*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)-112*x^2*a*b^2*e^3*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+464*x^2*b^3*d*e^2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+105*ln(1/2*(2*b*e*x+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+a*e+b*d)/(b*e)^(1/2))*a^4*e^4-480*ln(1/2*(2*b*e*x+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+a*e+b*d)/(b*e)^(1/2))*a^3*b*d*e^3+864*ln(1/2*(2*b*e*x+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+a*e+b*d)/(b*e)^(1/2))*a^2*b^2*d^2*e^2-708*ln(1/2*(2*b*e*x+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+a*e+b*d)/(b*e)^(1/2))*a*b^3*d^3*e+219*ln(1/2*(2*b*e*x+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+a*e+b*d)/(b*e)^(1/2))*b^4*d^4+140*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*x*a^2*b*e^3-584*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*x*a*b^2*d*e^2+932*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*x*b^3*d^2*e-210*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)*a^3*e^3+890*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)*a^2*b*d*e^2-1450*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)*a*b^2*d^2*e+1002*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)*b^3*d^3)/b^4/((b*x+a)*(e*x+d))^(1/2)/(b*e)^(1/2)","B"
844,1,392,150,0.025000," ","int((e*x+d)^(1/2)*(8*e^2*x^2+20*d*e*x+15*d^2)/(b*x+a)^(1/2),x)","-\frac{\sqrt{e x +d}\, \sqrt{b x +a}\, \left(15 a^{3} e^{3} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-54 a^{2} b d \,e^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+72 a \,b^{2} d^{2} e \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-33 b^{3} d^{3} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-16 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b^{2} e^{2} x^{2}+20 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, a b \,e^{2} x -64 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, b^{2} d e x -30 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, a^{2} e^{2}+98 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, a b d e -114 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, b^{2} d^{2}\right)}{6 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b^{3}}"," ",0,"-1/6*(e*x+d)^(1/2)*(b*x+a)^(1/2)*(-16*x^2*b^2*e^2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+15*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a^3*e^3-54*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a^2*b*d*e^2+72*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a*b^2*d^2*e-33*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*b^3*d^3+20*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*x*a*b*e^2-64*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*x*b^2*d*e-30*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*a^2*e^2+98*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*a*b*d*e-114*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*b^2*d^2)/b^3/((b*x+a)*(e*x+d))^(1/2)/(b*e)^(1/2)","B"
845,1,247,102,0.029000," ","int((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(1/2)/(b*x+a)^(1/2),x)","\frac{\left(3 a^{2} e^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-8 a b d e \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+8 b^{2} d^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+4 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, b e x -6 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, a e +14 \sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, b d \right) \sqrt{e x +d}\, \sqrt{b x +a}}{\sqrt{b e}\, \sqrt{\left(b x +a \right) \left(e x +d \right)}\, b^{2}}"," ",0,"(3*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a^2*e^2-8*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a*b*d*e+8*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*b^2*d^2+4*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*x*b*e-6*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*a*e+14*(b*e)^(1/2)*((b*x+a)*(e*x+d))^(1/2)*b*d)*(e*x+d)^(1/2)*(b*x+a)^(1/2)/(b*e)^(1/2)/b^2/((b*x+a)*(e*x+d))^(1/2)","B"
846,1,438,88,0.032000," ","int((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(3/2)/(b*x+a)^(1/2),x)","-\frac{2 \sqrt{b x +a}\, \left(2 a^{2} e^{3} x \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-6 a b d \,e^{2} x \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+4 b^{2} d^{2} e x \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+2 a^{2} d \,e^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-6 a b \,d^{2} e \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+4 b^{2} d^{3} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-4 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, a \,e^{2} x +4 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b d e x -4 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, a d e +7 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b \,d^{2}\right)}{\sqrt{b e}\, \left(a e -b d \right) \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{e x +d}\, b}"," ",0,"-2*(b*x+a)^(1/2)*(2*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x*a^2*e^3-6*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x*a*b*d*e^2+4*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x*b^2*d^2*e+2*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a^2*d*e^2-6*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a*b*d^2*e+4*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*b^2*d^3-4*x*a*e^2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+4*x*b*d*e*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)-4*a*d*e*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+7*b*d^2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/b/(b*e)^(1/2)/(a*e-b*d)/((b*x+a)*(e*x+d))^(1/2)/(e*x+d)^(1/2)","B"
847,1,601,96,0.032000," ","int((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(5/2)/(b*x+a)^(1/2),x)","\frac{2 \sqrt{b x +a}\, \left(4 a^{2} e^{4} x^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-8 a b d \,e^{3} x^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+4 b^{2} d^{2} e^{2} x^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+8 a^{2} d \,e^{3} x \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-16 a b \,d^{2} e^{2} x \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+8 b^{2} d^{3} e x \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+4 a^{2} d^{2} e^{2} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-8 a b \,d^{3} e \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)+4 b^{2} d^{4} \ln \left(\frac{2 b e x +a e +b d +2 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}}{2 \sqrt{b e}}\right)-4 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, a d \,e^{2} x +6 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b \,d^{2} e x -5 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, a \,d^{2} e +7 \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \sqrt{b e}\, b \,d^{3}\right)}{\sqrt{b e}\, \left(a e -b d \right)^{2} \sqrt{\left(b x +a \right) \left(e x +d \right)}\, \left(e x +d \right)^{\frac{3}{2}}}"," ",0,"2*(b*x+a)^(1/2)*(4*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x^2*a^2*e^4-8*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x^2*a*b*d*e^3+4*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x^2*b^2*d^2*e^2+8*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x*a^2*d*e^3-16*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x*a*b*d^2*e^2+8*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*x*b^2*d^3*e+4*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a^2*d^2*e^2-8*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*a*b*d^3*e+4*ln(1/2*(2*b*e*x+a*e+b*d+2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2))*b^2*d^4-4*x*a*d*e^2*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+6*x*b*d^2*e*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)-5*a*d^2*e*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2)+7*b*d^3*((b*x+a)*(e*x+d))^(1/2)*(b*e)^(1/2))/(b*e)^(1/2)/(a*e-b*d)^2/((b*x+a)*(e*x+d))^(1/2)/(e*x+d)^(3/2)","B"
848,1,150,115,0.012000," ","int((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(7/2)/(b*x+a)^(1/2),x)","-\frac{2 \sqrt{b x +a}\, \left(120 a^{2} e^{4} x^{2}-280 a b d \,e^{3} x^{2}+184 b^{2} d^{2} e^{2} x^{2}+260 a^{2} d \,e^{3} x -612 a b \,d^{2} e^{2} x +400 b^{2} d^{3} e x +149 a^{2} d^{2} e^{2}-350 a b \,d^{3} e +225 b^{2} d^{4}\right)}{15 \left(e x +d \right)^{\frac{5}{2}} \left(a^{3} e^{3}-3 a^{2} b d \,e^{2}+3 a \,b^{2} d^{2} e -b^{3} d^{3}\right)}"," ",0,"-2/15*(b*x+a)^(1/2)*(120*a^2*e^4*x^2-280*a*b*d*e^3*x^2+184*b^2*d^2*e^2*x^2+260*a^2*d*e^3*x-612*a*b*d^2*e^2*x+400*b^2*d^3*e*x+149*a^2*d^2*e^2-350*a*b*d^3*e+225*b^2*d^4)/(e*x+d)^(5/2)/(a^3*e^3-3*a^2*b*d*e^2+3*a*b^2*d^2*e-b^3*d^3)","A"
849,1,248,165,0.013000," ","int((8*e^2*x^2+20*d*e*x+15*d^2)/(e*x+d)^(9/2)/(b*x+a)^(1/2),x)","-\frac{2 \sqrt{b x +a}\, \left(-560 a^{2} b \,e^{5} x^{3}+1344 a \,b^{2} d \,e^{4} x^{3}-928 b^{3} d^{2} e^{3} x^{3}+280 a^{3} e^{5} x^{2}-2632 a^{2} b d \,e^{4} x^{2}+5168 a \,b^{2} d^{2} e^{3} x^{2}-3248 b^{3} d^{3} e^{2} x^{2}+644 a^{3} d \,e^{4} x -3890 a^{2} b \,d^{2} e^{3} x +6664 a \,b^{2} d^{3} e^{2} x -3850 b^{3} d^{4} e x +409 a^{3} d^{2} e^{3}-1953 a^{2} b \,d^{3} e^{2}+2975 a \,b^{2} d^{4} e -1575 b^{3} d^{5}\right)}{105 \left(e x +d \right)^{\frac{7}{2}} \left(e^{4} a^{4}-4 b \,e^{3} d \,a^{3}+6 a^{2} b^{2} d^{2} e^{2}-4 a \,b^{3} d^{3} e +b^{4} d^{4}\right)}"," ",0,"-2/105*(b*x+a)^(1/2)*(-560*a^2*b*e^5*x^3+1344*a*b^2*d*e^4*x^3-928*b^3*d^2*e^3*x^3+280*a^3*e^5*x^2-2632*a^2*b*d*e^4*x^2+5168*a*b^2*d^2*e^3*x^2-3248*b^3*d^3*e^2*x^2+644*a^3*d*e^4*x-3890*a^2*b*d^2*e^3*x+6664*a*b^2*d^3*e^2*x-3850*b^3*d^4*e*x+409*a^3*d^2*e^3-1953*a^2*b*d^3*e^2+2975*a*b^2*d^4*e-1575*b^3*d^5)/(e*x+d)^(7/2)/(a^4*e^4-4*a^3*b*d*e^3+6*a^2*b^2*d^2*e^2-4*a*b^3*d^3*e+b^4*d^4)","A"
850,1,11688,361,0.179000," ","int((e*x+d)^(3/2)/(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
851,1,5482,241,0.047000," ","int((e*x+d)^(1/2)/(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
852,1,5507,243,0.065000," ","int(1/(e*x+d)^(1/2)/(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
853,1,47351,369,0.343000," ","int(1/(e*x+d)^(3/2)/(c*x^2+b*x+a)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
854,1,3941,500,0.038000," ","int((g*x+f)^3*(c*x^2+b*x+a)^(1/2)/(e*x+d),x)","\text{output too large to display}"," ",0,"-1/e^4*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*g^3*d^3+1/e*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*f^3+3/e^3*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d^2*f*g^2-1/16*g^3/e/c^2*a*(c*x^2+b*x+a)^(1/2)*b+1/8*g^3/e^2*b^2/c^2*(c*x^2+b*x+a)^(1/2)*d-3/8*g^2/e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*f-3/8*g/e*f^2/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2-3/2/e^2*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*d*f^2*g-3/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d^2*f*g^2+3/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d*f^2*g+3/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^3*f*g^2-3/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^2*f^2*g-3/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^4*f*g^2+3/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^3*f^2*g-3/4*g^2/e^2*d*f/c*(c*x^2+b*x+a)^(1/2)*b-3/2*g^2/e^2*d*f/c^(1/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+3/8*g^2/e^2*d*f/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2-3/4*g^2/e*b/c*x*(c*x^2+b*x+a)^(1/2)*f+1/4*g^3/e^2*b/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a*d-1/2/e^4*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*g^3*d^3-3/e^4*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^3*f*g^2+3/e^3*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*f^2*g+1/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*g^3*d^3-1/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^4*g^3+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d*f^3+1/e^6/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^5*g^3-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2*f^3+3/16*g^2/e*b^3/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f-3/2*g^2/e^2*d*f*x*(c*x^2+b*x+a)^(1/2)-1/8*g^3/e/c*a*x*(c*x^2+b*x+a)^(1/2)-3/e^2*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d*f^2*g+1/2/e*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*f^3+1/e^5*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^4*g^3-1/e^2*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*f^3-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*f^3+5/32*g^3/e*b^2/c^2*x*(c*x^2+b*x+a)^(1/2)+3/16*g^3/e*b^2/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/4*g^3/e^3*d^2/c*(c*x^2+b*x+a)^(1/2)*b+1/2*g^3/e^3*d^2/c^(1/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/8*g^3/e^3*d^2/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2+3/4*g/e*f^2/c*(c*x^2+b*x+a)^(1/2)*b+3/2*g/e*f^2/c^(1/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/16*g^3/e^2*b^3/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d-3/4*g^2/e*b/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a*f+1/4*g^3/e^2*b/c*x*(c*x^2+b*x+a)^(1/2)*d+3/2/e^3*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*d^2*f*g^2+3/2*g/e*f^2*x*(c*x^2+b*x+a)^(1/2)+1/2*g^3/e^3*d^2*x*(c*x^2+b*x+a)^(1/2)+1/4*g^3/e*x*(c*x^2+b*x+a)^(3/2)/c-5/24*g^3/e*b/c^2*(c*x^2+b*x+a)^(3/2)+5/64*g^3/e*b^3/c^3*(c*x^2+b*x+a)^(1/2)-5/128*g^3/e*b^4/c^(7/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/8*g^3/e/c^(3/2)*a^2*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/3*g^3/e^2*(c*x^2+b*x+a)^(3/2)/c*d+g^2/e*(c*x^2+b*x+a)^(3/2)/c*f","B"
855,1,2602,299,0.016000," ","int((g*x+f)^2*(c*x^2+b*x+a)^(1/2)/(e*x+d),x)","\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} g^{2}}{3 c e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, d^{2} g^{2}}{e^{3}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, f^{2}}{e}-\frac{b d f g \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{\sqrt{c}\, e^{2}}-\frac{2 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, d f g}{e^{2}}+\frac{b \,f^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 \sqrt{c}\, e}-\frac{\sqrt{c}\, d^{3} g^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{4}}-\frac{\sqrt{c}\, d \,f^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, d \,g^{2} x}{2 e^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b \,g^{2} x}{4 c e}-\frac{a b \,g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{3}{2}} e}-\frac{\sqrt{c \,x^{2}+b x +a}\, b d \,g^{2}}{4 c \,e^{2}}-\frac{a d \,g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}\, e^{2}}+\frac{b^{2} d \,g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}} e^{2}}+\frac{b \,d^{2} g^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 \sqrt{c}\, e^{3}}+\frac{2 \sqrt{c}\, d^{2} f g \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{3}}+\frac{\sqrt{c \,x^{2}+b x +a}\, b f g}{2 c e}+\frac{a f g \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e}-\frac{b^{2} f g \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{3}{2}} e}-\frac{a \,f^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{a \,d^{2} g^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{b \,d^{3} g^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{4}}+\frac{b d \,f^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{c \,d^{4} g^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{5}}-\frac{c \,d^{2} f^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{2 a d f g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{2 b \,d^{2} f g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{2 c \,d^{3} f g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{4}}+\frac{\sqrt{c \,x^{2}+b x +a}\, f g x}{e}-\frac{\sqrt{c \,x^{2}+b x +a}\, b^{2} g^{2}}{8 c^{2} e}+\frac{b^{3} g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}} e}"," ",0,"1/3*g^2*(c*x^2+b*x+a)^(3/2)/c/e+1/e^3*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d^2*g^2+2/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^3*f*g+1/e*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*f^2-1/e^2*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*d*f*g+2/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d*f*g-2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^2*f*g-2/e^2*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d*f*g+1/2/e*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*f^2-1/e^4*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^3*g^2-1/e^2*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*f^2-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*f^2-1/2*g^2/e^2*d*(c*x^2+b*x+a)^(1/2)*x-1/4*g^2/e*b/c*(c*x^2+b*x+a)^(1/2)*x-1/4*g^2/e*b/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/4*g^2/e^2*d/c*(c*x^2+b*x+a)^(1/2)*b-1/2*g^2/e^2*d/c^(1/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/8*g^2/e^2*d/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2+1/2/e^3*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*d^2*g^2+2/e^3*ln((1/2*(b*e-2*c*d)/e+(x+d/e)*c)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*f*g-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d^2*g^2+1/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^3*g^2+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d*f^2-1/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^4*g^2-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln((2*(a*e^2-b*d*e+c*d^2)/e^2+(b*e-2*c*d)/e*(x+d/e)+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)/e*(x+d/e)+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2*f^2+1/2*g/e*f/c*(c*x^2+b*x+a)^(1/2)*b+g/e*f/c^(1/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/4*g/e*f/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2+g/e*f*(c*x^2+b*x+a)^(1/2)*x-1/8*g^2/e*b^2/c^2*(c*x^2+b*x+a)^(1/2)+1/16*g^2/e*b^3/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))","B"
856,1,1559,197,0.010000," ","int((g*x+f)*(c*x^2+b*x+a)^(1/2)/(e*x+d),x)","\frac{a d g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{a f \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{b \,d^{2} g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{b d f \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{c \,d^{3} g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{c \,d^{2} f \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{a g \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}\, e}-\frac{b^{2} g \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}} e}-\frac{b d g \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 \sqrt{c}\, e^{2}}+\frac{b f \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 \sqrt{c}\, e}+\frac{\sqrt{c}\, d^{2} g \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{3}}-\frac{\sqrt{c}\, d f \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, g x}{2 e}+\frac{\sqrt{c \,x^{2}+b x +a}\, b g}{4 c e}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, d g}{e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, f}{e}"," ",0,"1/2/e*g*(c*x^2+b*x+a)^(1/2)*x+1/4/e*g/c*(c*x^2+b*x+a)^(1/2)*b+1/2/e*g/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/8/e*g/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2-1/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d*g+1/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*f-1/2/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*d*g+1/2/e*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b*f+1/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*g-1/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*f+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*d*g-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*f-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^2*g+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d*f+1/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^3*g-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2*f","B"
857,1,715,132,0.006000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d),x)","-\frac{a \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{b d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{b \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 \sqrt{c}\, e}-\frac{\sqrt{c}\, d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{e}"," ",0,"1/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+1/2/e*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b-1/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2","B"
858,1,1529,204,0.031000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f),x)","\frac{a \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(d g -e f \right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{a \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{b d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(d g -e f \right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{b f \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, g}+\frac{c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(d g -e f \right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{c \,f^{2} \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, g^{2}}-\frac{b \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 \left(d g -e f \right) \sqrt{c}}+\frac{b \ln \left(\frac{\left(x +\frac{f}{g}\right) c +\frac{b g -2 c f}{2 g}}{\sqrt{c}}+\sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\right)}{2 \left(d g -e f \right) \sqrt{c}}+\frac{\sqrt{c}\, d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{\left(d g -e f \right) e}-\frac{\sqrt{c}\, f \ln \left(\frac{\left(x +\frac{f}{g}\right) c +\frac{b g -2 c f}{2 g}}{\sqrt{c}}+\sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\right)}{\left(d g -e f \right) g}+\frac{\sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{d g -e f}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{d g -e f}"," ",0,"1/(d*g-e*f)*((x+f/g)^2*c+(b*g-2*c*f)/g*(x+f/g)+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)+1/2/(d*g-e*f)*ln((1/2*(b*g-2*c*f)/g+c*(x+f/g))/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)/g*(x+f/g)+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/c^(1/2)*b-1/(d*g-e*f)/g*ln((1/2*(b*g-2*c*f)/g+c*(x+f/g))/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)/g*(x+f/g)+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*c^(1/2)*f-1/(d*g-e*f)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln((2*(a*g^2-b*f*g+c*f^2)/g^2+(b*g-2*c*f)/g*(x+f/g)+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)/g*(x+f/g)+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*a+1/(d*g-e*f)/g/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln((2*(a*g^2-b*f*g+c*f^2)/g^2+(b*g-2*c*f)/g*(x+f/g)+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)/g*(x+f/g)+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b*f-1/(d*g-e*f)/g^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln((2*(a*g^2-b*f*g+c*f^2)/g^2+(b*g-2*c*f)/g*(x+f/g)+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)/g*(x+f/g)+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*c*f^2-1/(d*g-e*f)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-1/2/(d*g-e*f)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b+1/(d*g-e*f)/e*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d+1/(d*g-e*f)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a-1/(d*g-e*f)/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d+1/(d*g-e*f)/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2","B"
859,1,3162,434,0.020000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f)^2,x)","\text{output too large to display}"," ",0,"-g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/(x+f/g)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(3/2)+g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b-1/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*c*f-1/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*c^(1/2)*f*b+1/g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*c^(3/2)*f^2-1/2*g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*a*b+1/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*a*c*f+1/2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b^2*f-3/2/g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b*f^2*c+1/g^2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*c^2*f^3+g/(d*g-e*f)*c/(a*g^2-b*f*g+c*f^2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x+g/(d*g-e*f)*c^(1/2)/(a*g^2-b*f*g+c*f^2)*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*a-1/(d*g-e*f)^2*e*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)-1/2/(d*g-e*f)^2*e*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/c^(1/2)*b+1/(d*g-e*f)^2*e/g*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*c^(1/2)*f+1/(d*g-e*f)^2*e/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*a-1/(d*g-e*f)^2*e/g/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b*f+1/(d*g-e*f)^2*e/g^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*c*f^2+1/(d*g-e*f)^2*e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+1/2/(d*g-e*f)^2*e*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b-1/(d*g-e*f)^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d-1/(d*g-e*f)^2*e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a+1/(d*g-e*f)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d-1/(d*g-e*f)^2/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c*d^2","B"
860,1,6714,603,0.021000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
861,1,11995,845,0.024000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
862,1,10058,1055,0.027000," ","int((g*x+f)^3*(c*x^2+b*x+a)^(3/2)/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
863,1,6860,632,0.017000," ","int((g*x+f)^2*(c*x^2+b*x+a)^(3/2)/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
864,1,4188,415,0.009000," ","int((g*x+f)*(c*x^2+b*x+a)^(3/2)/(e*x+d),x)","\text{output too large to display}"," ",0,"1/3/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*f+1/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a*f+1/4/e*g*(c*x^2+b*x+a)^(3/2)*x-1/3/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)*d*g-1/e^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^3*f-1/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a*d*g-1/16/e/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^3*f-5/4/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d*f+1/4/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*f-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*f+1/8/e*g/c*(c*x^2+b*x+a)^(3/2)*b+3/8/e*g*(c*x^2+b*x+a)^(1/2)*x*a-3/64/e*g/c^2*(c*x^2+b*x+a)^(1/2)*b^3+3/8/e*g/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+3/128/e*g/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4-1/e^4*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d^3*g+1/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d^2*f+1/e^5*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^4*g+1/8/e/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*f+5/4/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d^2*g+1/16/e^2/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^3*d*g-3/2/e^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^3*b*g-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^2*f-3/8/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b^2*d*f-2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*d^2*g-2/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^4*c*g+2/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^3*c*f+2/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*d*f+2/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c*d^3*g-2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c*d^2*f-3/4/e^2/c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b*d*g+1/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^3*g+3/2/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*a*g-3/2/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*a*f-1/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^4*f+1/e^6/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^5*g-1/2/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c*d*f+3/4/e/c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b*f-3/16/e*g/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a+3/16/e*g/c*(c*x^2+b*x+a)^(1/2)*b*a-3/32/e*g/c*(c*x^2+b*x+a)^(1/2)*x*b^2+3/2/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*b*f+3/8/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b^2*d^2*g-1/8/e^2/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d*g+1/2/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c*d^2*g-1/4/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*d*g+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2*d*g","B"
865,1,1946,226,0.007000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d),x)","-\frac{a^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{2 a b d \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{2 a c \,d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}-\frac{b^{2} d^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{2 b c \,d^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{c^{2} d^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{5}}+\frac{3 a b \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{4 \sqrt{c}\, e}-\frac{3 a \sqrt{c}\, d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 e^{2}}-\frac{b^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{16 c^{\frac{3}{2}} e}-\frac{3 b^{2} d \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{8 \sqrt{c}\, e^{2}}+\frac{3 b \sqrt{c}\, d^{2} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{2 e^{3}}-\frac{c^{\frac{3}{2}} d^{3} \ln \left(\frac{\left(x +\frac{d}{e}\right) c +\frac{b e -2 c d}{2 e}}{\sqrt{c}}+\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\right)}{e^{4}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b x}{4 e}-\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c d x}{2 e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, a}{e}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b^{2}}{8 c e}-\frac{5 \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, b d}{4 e^{2}}+\frac{\sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, c \,d^{2}}{e^{3}}+\frac{\left(\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}\right)^{\frac{3}{2}}}{3 e}"," ",0,"1/3/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)+1/4/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b-1/2/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c*d+1/8/e/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-5/4/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d+3/4/e/c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b-3/2/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*a-1/16/e/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^3-3/8/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b^2*d+1/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a+1/e^3*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d^2+3/2/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*b-1/e^4*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^3-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+2/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*d-2/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c*d^2-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^2+2/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^3*c-1/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^4","B"
866,1,4226,449,0.018000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)/(g*x+f),x)","\text{output too large to display}"," ",0,"-1/4/(d*g-e*f)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b-1/8/(d*g-e*f)/c*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2+1/16/(d*g-e*f)/c^(3/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*b^3+1/(d*g-e*f)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a^2+1/4/(d*g-e*f)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*b+1/8/(d*g-e*f)/c*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b^2-1/16/(d*g-e*f)/c^(3/2)*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*b^3-1/(d*g-e*f)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*a^2-1/3/(d*g-e*f)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(3/2)+1/3/(d*g-e*f)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(3/2)+1/(d*g-e*f)/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b^2*d^2+1/(d*g-e*f)/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*c^2*d^4+1/2/(d*g-e*f)/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c*d+3/2/(d*g-e*f)/e*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d*a+3/8/(d*g-e*f)/e*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/c^(1/2)*b^2*d-3/2/(d*g-e*f)/e^2*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(1/2)*d^2*b-1/2/(d*g-e*f)/g*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*c*f-3/2/(d*g-e*f)/g*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*c^(1/2)*f*a-3/8/(d*g-e*f)/g*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/c^(1/2)*b^2*f-1/(d*g-e*f)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*a+1/(d*g-e*f)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*a+2/(d*g-e*f)/g^3/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b*f^3*c-2/(d*g-e*f)/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*b*d-2/(d*g-e*f)/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*b*d^3*c-2/(d*g-e*f)/g^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*a*c*f^2+3/2/(d*g-e*f)/g^2*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*c^(1/2)*f^2*b-1/(d*g-e*f)/g^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b^2*f^2-1/(d*g-e*f)/g^4/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*c^2*f^4-5/4/(d*g-e*f)/g*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b*f+3/4/(d*g-e*f)/c^(1/2)*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*a*b+2/(d*g-e*f)/g/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*a*b*f+2/(d*g-e*f)/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*a*c*d^2+1/(d*g-e*f)/g^2*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*c*f^2-1/(d*g-e*f)/g^3*ln(((x+f/g)*c+1/2*(b*g-2*c*f)/g)/c^(1/2)+((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))*c^(3/2)*f^3+5/4/(d*g-e*f)/e*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*d-3/4/(d*g-e*f)/c^(1/2)*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*a*b-1/(d*g-e*f)/e^2*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*c*d^2+1/(d*g-e*f)/e^3*ln(((x+d/e)*c+1/2*(b*e-2*c*d)/e)/c^(1/2)+((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))*c^(3/2)*d^3","B"
867,1,7959,717,0.021000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)/(g*x+f)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
868,1,15927,968,0.024000," ","int((c*x^2+b*x+a)^(3/2)/(e*x+d)/(g*x+f)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
869,1,9052,834,0.022000," ","int((c*x^2+b*x+a)^(5/2)/(e*x+d)/(g*x+f),x)","\text{output too large to display}"," ",0,"result too large to display","B"
870,1,1597,401,0.029000," ","int((g*x+f)^4/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","-\frac{f^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{2 b d f \,g^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}} e^{2}}+\frac{4 d^{3} f \,g^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{6 d^{2} f^{2} g^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{4 d \,f^{3} g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{2 \sqrt{c \,x^{2}+b x +a}\, f \,g^{3} x}{c e}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b d \,g^{4}}{4 c^{2} e^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b f \,g^{3}}{c^{2} e}-\frac{3 b^{2} d \,g^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}} e^{2}}+\frac{3 b^{2} f \,g^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{5}{2}} e}+\frac{a d \,g^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}} e^{2}}-\frac{2 a f \,g^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}} e}-\frac{4 \sqrt{c \,x^{2}+b x +a}\, d f \,g^{3}}{c \,e^{2}}-\frac{b \,d^{2} g^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}} e^{3}}-\frac{3 b \,f^{2} g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}} e}+\frac{4 d^{2} f \,g^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e^{3}}-\frac{6 d \,f^{2} g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e^{2}}-\frac{d^{4} g^{4} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{5}}+\frac{\sqrt{c \,x^{2}+b x +a}\, g^{4} x^{2}}{3 c e}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b \,g^{4} x}{12 c^{2} e}+\frac{3 a b \,g^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{5}{2}} e}-\frac{\sqrt{c \,x^{2}+b x +a}\, d \,g^{4} x}{2 c \,e^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} g^{4}}{8 c^{3} e}-\frac{5 b^{3} g^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}} e}-\frac{2 \sqrt{c \,x^{2}+b x +a}\, a \,g^{4}}{3 c^{2} e}+\frac{\sqrt{c \,x^{2}+b x +a}\, d^{2} g^{4}}{c \,e^{3}}+\frac{6 \sqrt{c \,x^{2}+b x +a}\, f^{2} g^{2}}{c e}-\frac{d^{3} g^{4} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e^{4}}+\frac{4 f^{3} g \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e}"," ",0,"-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*f^4+2*g^3/e^2*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f+2*g^3/e*x/c*(c*x^2+b*x+a)^(1/2)*f+3/4*g^4/e^2*b/c^2*(c*x^2+b*x+a)^(1/2)*d-3*g^3/e*b/c^2*(c*x^2+b*x+a)^(1/2)*f-3/8*g^4/e^2*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d+3/2*g^3/e*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f+1/2*g^4/e^2*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d-2*g^3/e*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f-4*g^3/e^2/c*(c*x^2+b*x+a)^(1/2)*d*f-1/2*g^4/e^3*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d^2-3*g^2/e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f^2+4*g^3/e^3*d^2*f*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-6*g^2/e^2*d*f^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)+4/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*g^3*f*d^3-6/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2*f^2*g^2+4/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d*f^3*g-1/e^5/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*g^4*d^4+1/3*g^4/e*x^2/c*(c*x^2+b*x+a)^(1/2)-5/12*g^4/e*b/c^2*x*(c*x^2+b*x+a)^(1/2)+3/4*g^4/e*b/c^(5/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/2*g^4/e^2*x/c*(c*x^2+b*x+a)^(1/2)*d+5/8*g^4/e*b^2/c^3*(c*x^2+b*x+a)^(1/2)-5/16*g^4/e*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-2/3*g^4/e/c^2*a*(c*x^2+b*x+a)^(1/2)+g^4/e^3/c*(c*x^2+b*x+a)^(1/2)*d^2+6*g^2/e/c*(c*x^2+b*x+a)^(1/2)*f^2-g^4/e^4*d^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)+4*g/e*f^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)","B"
871,1,1007,244,0.016000," ","int((g*x+f)^3/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","\frac{d^{3} g^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{4}}-\frac{3 d^{2} f \,g^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{3 d \,f^{2} g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{f^{3} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{a \,g^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}} e}+\frac{3 b^{2} g^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}} e}+\frac{b d \,g^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}} e^{2}}-\frac{3 b f \,g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}} e}+\frac{d^{2} g^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e^{3}}-\frac{3 d f \,g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e^{2}}+\frac{3 f^{2} g \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e}+\frac{\sqrt{c \,x^{2}+b x +a}\, g^{3} x}{2 c e}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b \,g^{3}}{4 c^{2} e}-\frac{\sqrt{c \,x^{2}+b x +a}\, d \,g^{3}}{c \,e^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, f \,g^{2}}{c e}"," ",0,"1/2*g^3/e*x/c*(c*x^2+b*x+a)^(1/2)-3/4*g^3/e*b/c^2*(c*x^2+b*x+a)^(1/2)+3/8*g^3/e*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/2*g^3/e*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-g^3/e^2/c*(c*x^2+b*x+a)^(1/2)*d+3*g^2/e/c*(c*x^2+b*x+a)^(1/2)*f+1/2*g^3/e^2*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d-3/2*g^2/e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f+g^3/e^3*d^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-3*g^2/e^2*d*f*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)+3*g/e*f^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)+1/e^4/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*g^3*d^3-3/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2*f*g^2+3/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d*f^2*g-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*f^3","B"
872,1,613,156,0.015000," ","int((g*x+f)^2/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","-\frac{d^{2} g^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{3}}+\frac{2 d f g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{f^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{b \,g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}} e}-\frac{d \,g^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e^{2}}+\frac{2 f g \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e}+\frac{\sqrt{c \,x^{2}+b x +a}\, g^{2}}{c e}"," ",0,"g^2*(c*x^2+b*x+a)^(1/2)/c/e-1/2*g^2/e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-g^2/e^2*d*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)+2*g/e*f*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-1/e^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2*g^2+2/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d*f*g-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*f^2","B"
873,1,349,115,0.008000," ","int((g*x+f)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","\frac{d g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{f \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{g \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}\, e}"," ",0,"1/e*g*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)+1/e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d*g-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*f","B"
874,1,157,71,0.006000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","-\frac{\ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}"," ",0,"-1/e/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
875,1,327,166,0.017000," ","int(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^(1/2),x)","\frac{\ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(d g -e f \right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{\ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}"," ",0,"-1/(d*g-e*f)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))+1/(d*g-e*f)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","A"
876,1,788,312,0.020000," ","int(1/(e*x+d)/(g*x+f)^2/(c*x^2+b*x+a)^(1/2),x)","\frac{b g \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{2 \left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{c f \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(d g -e f \right)^{2} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{e \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right)^{2} \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{\sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, g}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \left(x +\frac{f}{g}\right)}"," ",0,"-g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/(x+f/g)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)+1/2*g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b-1/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*c*f+e/(d*g-e*f)^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))-e/(d*g-e*f)^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
877,1,1817,541,0.024000," ","int(1/(e*x+d)/(g*x+f)^3/(c*x^2+b*x+a)^(1/2),x)","-\frac{3 b^{2} g^{2} \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{8 \left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right)^{2} \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}+\frac{3 b c f g \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{2 \left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right)^{2} \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{3 c^{2} f^{2} \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{2 \left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right)^{2} \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{b e g \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{2 \left(d g -e f \right)^{2} \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}+\frac{c e f \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right)^{2} \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}+\frac{3 \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, b \,g^{2}}{4 \left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right)^{2} \left(x +\frac{f}{g}\right)}-\frac{3 \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, c f g}{2 \left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right)^{2} \left(x +\frac{f}{g}\right)}+\frac{e^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(d g -e f \right)^{3} \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{e^{2} \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right)^{3} \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}+\frac{c \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{2 \left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}+\frac{\sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, e g}{\left(d g -e f \right)^{2} \left(a \,g^{2}-b f g +c \,f^{2}\right) \left(x +\frac{f}{g}\right)}-\frac{\sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{2 \left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \left(x +\frac{f}{g}\right)^{2}}"," ",0,"-1/2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/(x+f/g)^2*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)+3/4*g^2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/(x+f/g)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b-3/2*g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/(x+f/g)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*c*f-3/8*g^2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b^2+3/2*g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b*c*f-3/2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*c^2*f^2+1/2/(d*g-e*f)*c/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))+g*e/(d*g-e*f)^2/(a*g^2-b*f*g+c*f^2)/(x+f/g)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)-1/2*g*e/(d*g-e*f)^2/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b+e/(d*g-e*f)^2/(a*g^2-b*f*g+c*f^2)/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*c*f-e^2/(d*g-e*f)^3/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))+e^2/(d*g-e*f)^3/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
878,1,4453,474,0.025000," ","int((g*x+f)^4/(e*x+d)/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*f^4+6/e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d^2*f^2*g^2-e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*f^4-1/e^3/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*g^4*d^4-2*g^4/e^4*d^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b+4/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d*f^3*g+4*g^3/e^2/c/(c*x^2+b*x+a)^(1/2)*d*f+3/2*g^4/e*b/c^2*x/(c*x^2+b*x+a)^(1/2)-3/4*g^4/e*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+8*g/e*f^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b+g^4/e^2*x/c/(c*x^2+b*x+a)^(1/2)*d-4*g^3/e*x/c/(c*x^2+b*x+a)^(1/2)*f-1/2*g^4/e^2*b/c^2/(c*x^2+b*x+a)^(1/2)*d+2*g^3/e*b/c^2/(c*x^2+b*x+a)^(1/2)*f-4/e^2/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*g^3*f*d^3-e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*f^4+1/e^3/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*g^4*d^4-4/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d*f^3*g+g^4/e*x^2/c/(c*x^2+b*x+a)^(1/2)-3/4*g^4/e*b^2/c^3/(c*x^2+b*x+a)^(1/2)-3/2*g^4/e*b/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+2*g^4/e/c^2*a/(c*x^2+b*x+a)^(1/2)-g^4/e^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d+4*g^3/e/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f-g^4/e^3/c/(c*x^2+b*x+a)^(1/2)*d^2-6*g^2/e/c/(c*x^2+b*x+a)^(1/2)*f^2+12/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^3*f^2*g^2-2/e^3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*g^4*d^4-16/e^3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^4*g^3*f+8/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d*f^3*g-8/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^2*f^3*g+24/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^3*f^2*g^2-16/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^2*f^3*g-8/e^3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^4*g^3*f-6/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d^2*f^2*g^2+2/e^4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^5*g^4-2*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*f^4+4/e^4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^5*g^4+4/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*g^3*f*d^3+4*g^4/e/c*a*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-g^4/e^2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d+4*g^3/e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*f+8*g^3/e^2*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d*f+4*g^3/e^2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d*f-24*g^2/e^2*d*f^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x+16*g^3/e^3*d^2*f/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x+8/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*g^3*f*d^3-12/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d^2*f^2*g^2+8*g^3/e^3*d^2*f/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b-12*g^2/e^2*d*f^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b-3/2*g^4/e*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+2*g^4/e/c^2*a*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+16*g/e*f^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x-4*g^4/e^4*d^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x-g^4/e^3*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d^2-6*g^2/e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*f^2+2*g^3/e*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*f-2*g^4/e^3*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d^2-12*g^2/e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*f^2-1/e^3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*g^4*d^4+4/e^2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*g^3*f*d^3-6/e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2*f^2*g^2-1/2*g^4/e^2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d+4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d*f^3*g+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d*f^4+4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d*f^4","B"
879,1,3127,339,0.016000," ","int((g*x+f)^3/(e*x+d)/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*f^3+g^3/e/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+6/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^3*f*g^2+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d*f^3-6*g^2/e^2*d*f/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b+12*g/e*f^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x+1/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*g^3*d^3+3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d*f^2*g-3/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d^2*f*g^2-2/e^3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^4*g^3-12*g^2/e^2*d*f/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x-2*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*f^3-4/e^3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^4*g^3+2/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*g^3*d^3-6/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d^2*f*g^2-6/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^2*f^2*g-3*g^2/e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*f+4*g^3/e^3*d^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x+1/2*g^3/e*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+2*g^3/e^3*d^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b+6*g/e*f^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b+3/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d*f^2*g-e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*f^3+1/e^2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*g^3*d^3+g^3/e^2/c/(c*x^2+b*x+a)^(1/2)*d-3*g^2/e/c/(c*x^2+b*x+a)^(1/2)*f-1/e^2/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*g^3*d^3+g^3/e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+2*g^3/e^2*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d-6*g^2/e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*f+g^3/e^2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d+4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d*f^3-3/e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2*f*g^2+3/e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d^2*f*g^2-3/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d*f^2*g-e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*f^3-g^3/e*x/c/(c*x^2+b*x+a)^(1/2)+1/2*g^3/e*b/c^2/(c*x^2+b*x+a)^(1/2)+6/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d*f^2*g+12/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^3*f*g^2-12/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^2*f^2*g","B"
880,1,2123,230,0.016000," ","int((g*x+f)^2/(e*x+d)/(c*x^2+b*x+a)^(3/2),x)","-\frac{b^{2} e \,f^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{e \,f^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{g^{2}}{\sqrt{c \,x^{2}+b x +a}\, c e}+\frac{d^{2} g^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{4 c^{2} d^{3} g^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}+\frac{2 b c \,d^{3} g^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e^{2}}-\frac{2 d f g}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{4 b c \,d^{2} f g}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{d^{2} g^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{2 d f g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{2 b c \,d^{2} g^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{4 b c d f g x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{e \,f^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{2 b^{2} d f g}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{2 b c d \,f^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{4 c d \,g^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, e^{2}}+\frac{8 c f g x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, e}+\frac{4 c^{2} d \,f^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{b^{2} d^{2} g^{2}}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{2 b d \,g^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, e^{2}}+\frac{4 b f g}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, e}-\frac{2 b \,g^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, e}-\frac{b^{2} g^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c e}-\frac{8 c^{2} d^{2} f g x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}-\frac{2 b c e \,f^{2} x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}"," ",0,"2/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d*f*g-1/e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d^2*g^2-e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*f^2+e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*f^2-g^2/e/c/(c*x^2+b*x+a)^(1/2)+1/e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d^2*g^2+4/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^3*g^2+2/e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^3*g^2-2/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d*f*g-e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*f^2-4/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^2*f*g-2/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d^2*g^2+4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d*f*g+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d*f*g+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d*f^2-4*g^2/e^2*d/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x+8*g/e*f/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*c*x+4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d*f^2-1/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d^2*g^2-2*g^2/e^2*d/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b+4*g/e*f/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*b-2*g^2/e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-g^2/e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-8/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^2*f*g-2*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*f^2","B"
881,1,1261,177,0.009000," ","int((g*x+f)/(e*x+d)/(c*x^2+b*x+a)^(3/2),x)","\frac{2 b c d g x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{2 b c e f x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{4 c^{2} d^{2} g x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{4 c^{2} d f x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{b^{2} d g}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{b^{2} e f}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{2 b c \,d^{2} g}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, e}+\frac{2 b c d f}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{d g \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{e f \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{d g}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{e f}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{2 \left(2 c x +b \right) g}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, e}"," ",0,"2/e*g*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-1/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*d*g+e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*f+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*d*g-2*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c*f-4/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d^2*g+4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d*f+1/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*d*g-e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2*f-2/e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d^2*g+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d*f+1/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*d*g-e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))*f","B"
882,1,603,145,0.008000," ","int(1/(e*x+d)/(c*x^2+b*x+a)^(3/2),x)","-\frac{2 b c e x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{4 c^{2} d x}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{b^{2} e}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{2 b c d}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{e \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{e}{\left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}"," ",0,"e/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)-2*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c+4/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d-e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2+2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d-e/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
883,1,1343,332,0.021000," ","int(1/(e*x+d)/(g*x+f)/(c*x^2+b*x+a)^(3/2),x)","\frac{2 b c \,e^{2} x}{\left(d g -e f \right) \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{2 b c \,g^{2} x}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{4 c^{2} d e x}{\left(d g -e f \right) \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{4 c^{2} f g x}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}+\frac{b^{2} e^{2}}{\left(d g -e f \right) \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{b^{2} g^{2}}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{2 b c d e}{\left(d g -e f \right) \left(a \,e^{2}-b d e +c \,d^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{2 b c f g}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \left(4 a c -b^{2}\right) \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}+\frac{e^{2} \ln \left(\frac{\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{2 a \,e^{2}-2 b d e +2 c \,d^{2}}{e^{2}}+2 \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}\, \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}{x +\frac{d}{e}}\right)}{\left(d g -e f \right) \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}-\frac{g^{2} \ln \left(\frac{\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{2 a \,g^{2}-2 b f g +2 c \,f^{2}}{g^{2}}+2 \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}\, \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}{x +\frac{f}{g}}\right)}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}-\frac{e^{2}}{\left(d g -e f \right) \left(a \,e^{2}-b d e +c \,d^{2}\right) \sqrt{\left(x +\frac{d}{e}\right)^{2} c +\frac{\left(b e -2 c d \right) \left(x +\frac{d}{e}\right)}{e}+\frac{a \,e^{2}-b d e +c \,d^{2}}{e^{2}}}}+\frac{g^{2}}{\left(d g -e f \right) \left(a \,g^{2}-b f g +c \,f^{2}\right) \sqrt{\left(x +\frac{f}{g}\right)^{2} c +\frac{\left(b g -2 c f \right) \left(x +\frac{f}{g}\right)}{g}+\frac{a \,g^{2}-b f g +c \,f^{2}}{g^{2}}}}"," ",0,"1/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)*g^2/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)-2/(d*g-e*f)*g^2/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*b*c+4/(d*g-e*f)*g/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*c^2*f-1/(d*g-e*f)*g^2/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b^2+2/(d*g-e*f)*g/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b*c*f-1/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)*g^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))-1/(d*g-e*f)/(a*e^2-b*d*e+c*d^2)*e^2/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+2/(d*g-e*f)*e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c-4/(d*g-e*f)*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d+1/(d*g-e*f)*e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2-2/(d*g-e*f)*e/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d+1/(d*g-e*f)/(a*e^2-b*d*e+c*d^2)*e^2/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))","B"
884,1,2807,608,0.026000," ","int(1/(e*x+d)/(g*x+f)^2/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"1/(d*g-e*f)^2*e^3/(a*e^2-b*d*e+c*d^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)+1/(d*g-e*f)^2*e/(a*g^2-b*f*g+c*f^2)*g^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))-1/(d*g-e*f)^2*e^3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b^2+3/2*g^3/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b^3+3*g^2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*c*f-1/(d*g-e*f)^2*e^3/(a*e^2-b*d*e+c*d^2)/((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*ln(((b*e-2*c*d)*(x+d/e)/e+2*(a*e^2-b*d*e+c*d^2)/e^2+2*((a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2))/(x+d/e))-g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)/(x+f/g)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)+3*g^3/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*b^2*c+12*g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*c^3*f^2-6*g^2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b^2*c*f+6*g/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b*c^2*f^2-2/(d*g-e*f)^2*e^3/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*b*c+4/(d*g-e*f)^2*e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*x*c^2*d+2/(d*g-e*f)^2*e^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)/((x+d/e)^2*c+(b*e-2*c*d)*(x+d/e)/e+(a*e^2-b*d*e+c*d^2)/e^2)^(1/2)*b*c*d-12*g^2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*b*c^2*f-2/(d*g-e*f)^2*e*g/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b*c*f+2/(d*g-e*f)^2*e*g^2/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*b*c-3/2*g^3/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b-1/(d*g-e*f)^2*e/(a*g^2-b*f*g+c*f^2)*g^2/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)-4/(d*g-e*f)^2*e*g/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x*c^2*f-3*g^2/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*c*f-8*g/(d*g-e*f)*c^2/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*x-4*g/(d*g-e*f)*c/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b+1/(d*g-e*f)^2*e*g^2/(a*g^2-b*f*g+c*f^2)/(4*a*c-b^2)/((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*b^2+3/2*g^3/(d*g-e*f)/(a*g^2-b*f*g+c*f^2)^2/((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*ln(((b*g-2*c*f)*(x+f/g)/g+2*(a*g^2-b*f*g+c*f^2)/g^2+2*((a*g^2-b*f*g+c*f^2)/g^2)^(1/2)*((x+f/g)^2*c+(b*g-2*c*f)*(x+f/g)/g+(a*g^2-b*f*g+c*f^2)/g^2)^(1/2))/(x+f/g))*b","B"
885,1,5459,1010,0.035000," ","int(1/(e*x+d)/(g*x+f)^3/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
886,1,32647,1469,0.260000," ","int((e*x+d)^3*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
887,1,20224,939,0.090000," ","int((e*x+d)^2*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
888,1,10711,588,0.056000," ","int((e*x+d)*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
889,1,4356,449,0.037000," ","int((g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"1/15*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/c^2*(8*x*a*c^2*f*g^3+8*x^3*b*c^2*g^4+8*x^3*c^3*f*g^3+6*x^2*a*c^2*g^4+2*x^2*b^2*c*g^4+2*x^2*c^3*f^2*g^2+2*a*c^2*f^2*g^2+6*x^4*c^3*g^4+2*a*b*c*f*g^3-3*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b^2*g^4+3*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*b^3*f*g^3-4*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*b^3*f*g^3+12*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a^2*c*g^4-12*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a^2*c*g^4+4*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b^2*g^4-8*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a*c^2*f^2*g^2+12*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a*c^2*f^2*g^2-12*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b*c*f*g^3+3*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*b*c*f^2*g^2-2*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*a*c*f*g^3+8*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b*c*f*g^3+2*x*b^2*c*f*g^3+2*x*b*c^2*f^2*g^2+10*x^2*b*c^2*f*g^3+2*x*a*b*c*g^4+8*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*b^2*c*f^2*g^2+2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*a*b*g^4-8*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*b*c^2*f^3*g-2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*b^2*f*g^3-2*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*c^2*f^3*g-3*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*b^2*c*f^2*g^2+4*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*c^3*f^4)/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)/g^3","B"
890,1,6812,674,0.062000," ","int((g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/(e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
891,1,16688,660,0.086000," ","int((g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
892,1,55368,934,0.209000," ","int((g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/(e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
893,1,22215,1022,0.108000," ","int((e*x+d)^3*(c*x^2+b*x+a)^(1/2)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
894,1,12923,685,0.075000," ","int((e*x+d)^2*(c*x^2+b*x+a)^(1/2)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
895,1,6207,461,0.046000," ","int((e*x+d)*(c*x^2+b*x+a)^(1/2)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
896,1,1854,386,0.030000," ","int((c*x^2+b*x+a)^(1/2)/(g*x+f)^(1/2),x)","-\frac{2 \sqrt{c \,x^{2}+b x +a}\, \sqrt{g x +f}\, \left(-c^{2} g^{3} x^{3}-b c \,g^{3} x^{2}-c^{2} f \,g^{2} x^{2}+\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, a b \,g^{3} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-2 \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, a c f \,g^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-a c \,g^{3} x -\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, b^{2} f \,g^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+3 \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, b c \,f^{2} g \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-b c f \,g^{2} x -2 \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, c^{2} f^{3} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-a c f \,g^{2}+\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{-4 a c +b^{2}}\, a \,g^{3} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{-4 a c +b^{2}}\, b f \,g^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{-4 a c +b^{2}}\, c \,f^{2} g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)\right)}{3 \left(c g \,x^{3}+b g \,x^{2}+c f \,x^{2}+a g x +b f x +a f \right) c \,g^{3}}"," ",0,"-2/3*(c*x^2+b*x+a)^(1/2)*(g*x+f)^(1/2)/c*(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*a*g^3-2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*b*f*g^2+2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*(-4*a*c+b^2)^(1/2)*c*f^2*g+2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a*b*g^3-2*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*a*c*f*g^2-2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*b^2*f*g^2+3*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*b*c*f^2*g-2*2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*((-2*c*x+(-4*a*c+b^2)^(1/2)-b)*g/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))*g/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)*c/(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f))^(1/2),(-(g*(-4*a*c+b^2)^(1/2)+b*g-2*c*f)/(2*c*f-b*g+g*(-4*a*c+b^2)^(1/2)))^(1/2))*c^2*f^3-x^3*c^2*g^3-x^2*b*c*g^3-x^2*c^2*f*g^2-x*a*c*g^3-x*b*c*f*g^2-a*c*f*g^2)/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)/g^3","B"
897,1,3126,617,0.039000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"(2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*e^2*f^3-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*e^2*f^2*g+EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*c*d^2*g^3+2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d*e*f*g^2-2*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d*e*f*g^2-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b^2*d*e*g^3+EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b^2*e^2*f*g^2+EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d^2*g^3-2*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2-EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*a*e^2*g^3-EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*c*d^2*g^3-EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*b*e^2*g^3+EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b^2*d*e*g^3-EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d^2*g^3+2*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2+2*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g+EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*b*d*e*g^3+2*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*d*e*g^3+2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*e^2*f^2*g-2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g+2*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*d*e*g^3-2*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*b*d*e*g^3+EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*b*e^2*f*g^2-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*c*e^2*f^2*g)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/c/g^2/e^2/(d*g-e*f)/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)","B"
898,1,13872,653,0.071000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^2/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
899,1,57841,949,0.221000," ","int((c*x^2+b*x+a)^(1/2)/(e*x+d)^3/(g*x+f)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
900,1,14978,704,0.092000," ","int((e*x+d)^3*(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
901,1,8248,503,0.067000," ","int((e*x+d)^2*(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
902,1,3805,394,0.049000," ","int((e*x+d)*(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"-1/3*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)*(3*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*b*e*g^3-6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*d*g^3-2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*a*e*g^3-3*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b^2*e*f*g^2+6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d*f*g^2+3*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*e*f^2*g+2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*b*e*f*g^2-6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d*f^2*g-2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*c*e*f^2*g-4*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*b*e*g^3+6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*d*g^3+2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e*f*g^2+4*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b^2*e*f*g^2-6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d*f*g^2-6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*e*f^2*g+6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d*f^2*g+2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*e*f^3-2*c^2*e*g^3*x^3-2*x^2*b*c*e*g^3-2*c^2*e*f*g^2*x^2-2*a*c*e*g^3*x-2*x*b*c*e*f*g^2-2*a*c*e*f*g^2)/c^2/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)/g^2","B"
903,1,747,164,0.035000," ","int((g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c \,x^{2}+b x +a}\, \left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \left(-b g \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+b g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+2 c f \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-2 c f \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+\sqrt{-4 a c +b^{2}}\, g \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-\sqrt{-4 a c +b^{2}}\, g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)\right)}{2 \left(c g \,x^{3}+b g \,x^{2}+c f \,x^{2}+a g x +b f x +a f \right) c^{2} g}"," ",0,"1/2*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*(EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*g*b-2*f*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*g*(-4*a*c+b^2)^(1/2)-EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*g+2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*f+EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*g)/g/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)/c^2","B"
904,1,834,408,0.044000," ","int((g*x+f)^(1/2)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","\frac{\left(-b g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+b g \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+2 c f \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-2 c f \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-\sqrt{-4 a c +b^{2}}\, g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+\sqrt{-4 a c +b^{2}}\, g \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)\right) \sqrt{g x +f}\, \sqrt{c \,x^{2}+b x +a}\, \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}}{\left(c g \,x^{3}+b g \,x^{2}+c f \,x^{2}+a g x +b f x +a f \right) c e}"," ",0,"(-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*g*(-4*a*c+b^2)^(1/2)-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*g*b+2*f*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c+EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*g+EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*g-2*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/c/(d*g-e*f),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*f)*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/e*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)/c/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)","B"
905,1,13017,885,0.080000," ","int((g*x+f)^(1/2)/(e*x+d)^2/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
906,1,59522,1601,0.249000," ","int((g*x+f)^(1/2)/(e*x+d)^3/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
907,1,1879,592,0.048000," ","int((g*x+f)^(3/2)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{g x +f}\, \sqrt{c \,x^{2}+b x +a}\, \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \left(-2 a e \,g^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+2 a e \,g^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+b d \,g^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-b d \,g^{2} \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+2 b e f g \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-3 b e f g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+b e f g \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-2 c d f g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+2 c d f g \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-2 c e \,f^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+4 c e \,f^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-2 c e \,f^{2} \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+\sqrt{-4 a c +b^{2}}\, d \,g^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-\sqrt{-4 a c +b^{2}}\, d \,g^{2} \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-\sqrt{-4 a c +b^{2}}\, e f g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+\sqrt{-4 a c +b^{2}}\, e f g \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)\right)}{\left(c g \,x^{3}+b g \,x^{2}+c f \,x^{2}+a g x +b f x +a f \right) c \,e^{2}}"," ",0,"(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)/c*(EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*d*g^2-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*e*f*g+2*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*e*g^2+EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*d*g^2-3*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*e*f*g-2*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*d*f*g+4*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*e*f^2-2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*e*g^2+2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*e*f*g-2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*e*f^2-EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*d*g^2+EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*e*f*g-EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*d*g^2+EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*e*f*g+2*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*d*f*g-2*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*e*f^2)/e^2/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)","B"
908,1,7464,997,0.066000," ","int((g*x+f)^(5/2)/(e*x+d)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
909,1,8755,567,0.078000," ","int((e*x+d)^3/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
910,1,4295,421,0.058000," ","int((e*x+d)^2/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"1/3/c^2*(2*c^2*e^2*g^3*x^3+2*x*b*c*e^2*f*g^2+2*c^2*e^2*f*g^2*x^2+2*x^2*b*c*e^2*g^3-6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*b*e^2*f*g^2+12*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d*e*f*g^2+6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*c*d*e*f*g^2-6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d*e*f*g^2+12*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*d*e*g^3+2*a*c*e^2*g^3*x-12*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*d*e*g^3+4*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e^2*f*g^2-12*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d*e*f^2*g-2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*c*e^2*f^2*g+4*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*e^2*f^3+2*a*c*e^2*f*g^2-3*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*b*e^2*g^3-4*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b^2*e^2*f*g^2+2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*a*e^2*g^3-3*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*c*d^2*g^3+3*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b^2*e^2*f*g^2-3*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d^2*g^3+6*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d^2*f*g^2+4*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*b*e^2*g^3)*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/g^3/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)","B"
911,1,1014,345,0.044000," ","int((e*x+d)/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\left(-2 a e \,g^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+2 a e \,g^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-b d \,g^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+2 b e f g \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-b e f g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+2 c d f g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-2 c e \,f^{2} \EllipticE \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)-\sqrt{-4 a c +b^{2}}\, d \,g^{2} \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)+\sqrt{-4 a c +b^{2}}\, e f g \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)\right) \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{g x +f}\, \sqrt{c \,x^{2}+b x +a}}{\left(c g \,x^{3}+b g \,x^{2}+c f \,x^{2}+a g x +b f x +a f \right) c \,g^{2}}"," ",0,"(2*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*e*g^2-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*d*g^2-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*e*f*g+2*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*d*f*g-EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*d*g^2+EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*(-4*a*c+b^2)^(1/2)*e*f*g-2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*e*g^2+2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*e*f*g-2*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*e*f^2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/c/g^2/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)","B"
912,1,287,165,0.039000," ","int(1/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\left(-b g +2 c f -\sqrt{-4 a c +b^{2}}\, g \right) \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{g x +f}\, \sqrt{c \,x^{2}+b x +a}\, \EllipticF \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)}{\left(c g \,x^{3}+b g \,x^{2}+c f \,x^{2}+a g x +b f x +a f \right) c g}"," ",0,"(-(-4*a*c+b^2)^(1/2)*g-b*g+2*c*f)/c*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)/g*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)","A"
913,1,330,245,0.048000," ","int(1/(e*x+d)/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{\left(-b g +2 c f -\sqrt{-4 a c +b^{2}}\, g \right) \sqrt{\frac{\left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) g}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{\frac{\left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}\, \sqrt{c \,x^{2}+b x +a}\, \sqrt{g x +f}\, \EllipticPi \left(\sqrt{2}\, \sqrt{-\frac{\left(g x +f \right) c}{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{2 \left(d g -e f \right) c}, \sqrt{-\frac{b g -2 c f +\sqrt{-4 a c +b^{2}}\, g}{-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g}}\right)}{\left(d g -e f \right) \left(c g \,x^{3}+b g \,x^{2}+c f \,x^{2}+a g x +b f x +a f \right) c}"," ",0,"(-b*g+2*c*f-(-4*a*c+b^2)^(1/2)*g)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)/c*(c*x^2+b*x+a)^(1/2)*(g*x+f)^(1/2)/(d*g-e*f)/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)","A"
914,1,14048,927,0.098000," ","int(1/(e*x+d)^2/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
915,1,64947,1014,0.344000," ","int(1/(e*x+d)^3/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
916,1,4757,490,0.095000," ","int(1/(e*x+d)/(g*x+f)^(3/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"(-2*c^2*d*g^3*x^2-2*a*c*d*g^3+2*a*c*e*f*g^2-2*2^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e*f*g^2*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)-2*2^(1/2)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e*f*g^2*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)+3*2^(1/2)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*e*f^2*g*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)-2^(1/2)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*e*f*g^2*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*(-4*a*c+b^2)^(1/2)+2^(1/2)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c*e*f^2*g*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*(-4*a*c+b^2)^(1/2)+2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*e*f^3-2*x*b*c*d*g^3+2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*e*f^2*g+2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*e*f*g^2+2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d*f*g^2+2*c^2*e*f*g^2*x^2-2*2^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*e*f^3*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)-2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*d*f*g^2-2*2^(1/2)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*e*f^3*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)-2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b*c*e*f^2*g+2^(1/2)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*b*e*g^3*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)+2^(1/2)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*e*g^3*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*(-4*a*c+b^2)^(1/2)-2^(1/2)*EllipticPi(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),1/2*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(d*g-e*f)/c*e,(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*b^2*e*f*g^2*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)+2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*d*g^3+2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticF(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d*f^2*g-2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*a*c*d*g^3-2*2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2)*((-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*((2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*g)^(1/2)*EllipticE(2^(1/2)*(-(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*c)^(1/2),(-(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g))^(1/2))*c^2*d*f^2*g+2*x*b*c*e*f*g^2)*(c*x^2+b*x+a)^(1/2)*(g*x+f)^(1/2)/c/(d*g-e*f)^2/(a*g^2-b*f*g+c*f^2)/(c*g*x^3+b*g*x^2+c*f*x^2+a*g*x+b*f*x+a*f)","B"
917,1,27597,998,0.214000," ","int(1/(e*x+d)/(g*x+f)^(5/2)/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
918,1,645,420,0.198000," ","int((e*x+d)^(1/2)/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{4 \sqrt{e x +d}\, \sqrt{g x +f}\, \sqrt{c \,x^{2}+b x +a}\, \sqrt{\frac{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(g x +f \right)}{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(e x +d \right)}}\, \sqrt{\frac{\left(d g -e f \right) \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right)}{\left(-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(e x +d \right)}}\, \sqrt{\frac{\left(d g -e f \right) \left(2 c x +b +\sqrt{-4 a c +b^{2}}\right)}{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(e x +d \right)}}\, \left(b \,e^{2} g \,x^{2}-2 c \,e^{2} f \,x^{2}+2 b d e g x -4 c d e f x +\sqrt{-4 a c +b^{2}}\, e^{2} g \,x^{2}+b \,d^{2} g -2 c \,d^{2} f +2 \sqrt{-4 a c +b^{2}}\, d e g x +\sqrt{-4 a c +b^{2}}\, d^{2} g \right) \EllipticPi \left(\sqrt{\frac{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(g x +f \right)}{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(e x +d \right)}}, \frac{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) e}{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) g}, \sqrt{\frac{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right)}{\left(-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right)}}\right)}{\sqrt{-\frac{\left(g x +f \right) \left(e x +d \right) \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) \left(2 c x +b +\sqrt{-4 a c +b^{2}}\right)}{c}}\, \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{c e g \,x^{4}+b e g \,x^{3}+c d g \,x^{3}+c e f \,x^{3}+a e g \,x^{2}+b d g \,x^{2}+b e f \,x^{2}+c d f \,x^{2}+a d g x +a e f x +b d f x +a d f}\, g}"," ",0,"4*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/g*((e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)*(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*x+d))^(1/2)*((d*g-e*f)*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*x+d))^(1/2)*((d*g-e*f)*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*x+d))^(1/2)*EllipticPi(((e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)*(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*x+d))^(1/2),(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)*e/g/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d),((e*(-4*a*c+b^2)^(1/2)-b*e+2*c*d)*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d))^(1/2))*((-4*a*c+b^2)^(1/2)*x^2*e^2*g+b*e^2*g*x^2-2*c*e^2*f*x^2+2*(-4*a*c+b^2)^(1/2)*x*d*e*g+2*b*d*e*g*x-4*c*d*e*f*x+(-4*a*c+b^2)^(1/2)*d^2*g+b*d^2*g-2*c*d^2*f)/(-1/c*(g*x+f)*(e*x+d)*(-2*c*x-b+(-4*a*c+b^2)^(1/2))*(2*c*x+b+(-4*a*c+b^2)^(1/2)))^(1/2)/(e*(-4*a*c+b^2)^(1/2)+b*e-2*c*d)/(c*e*g*x^4+b*e*g*x^3+c*d*g*x^3+c*e*f*x^3+a*e*g*x^2+b*d*g*x^2+b*e*f*x^2+c*d*f*x^2+a*d*g*x+a*e*f*x+b*d*f*x+a*d*f)^(1/2)","A"
919,1,605,673,0.102000," ","int(1/(e*x+d)^(1/2)/(g*x+f)^(1/2)/(c*x^2+b*x+a)^(1/2),x)","\frac{4 \left(b \,e^{2} g \,x^{2}-2 c \,e^{2} f \,x^{2}+2 b d e g x -4 c d e f x +\sqrt{-4 a c +b^{2}}\, e^{2} g \,x^{2}+b \,d^{2} g -2 c \,d^{2} f +2 \sqrt{-4 a c +b^{2}}\, d e g x +\sqrt{-4 a c +b^{2}}\, d^{2} g \right) \sqrt{\frac{\left(d g -e f \right) \left(2 c x +b +\sqrt{-4 a c +b^{2}}\right)}{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(e x +d \right)}}\, \sqrt{\frac{\left(d g -e f \right) \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right)}{\left(-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(e x +d \right)}}\, \sqrt{\frac{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(g x +f \right)}{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(e x +d \right)}}\, \sqrt{e x +d}\, \sqrt{g x +f}\, \sqrt{c \,x^{2}+b x +a}\, \EllipticF \left(\sqrt{\frac{\left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(g x +f \right)}{\left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(e x +d \right)}}, \sqrt{\frac{\left(-b e +2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \left(b g -2 c f +\sqrt{-4 a c +b^{2}}\, g \right)}{\left(-b g +2 c f +\sqrt{-4 a c +b^{2}}\, g \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right)}}\right)}{\sqrt{-\frac{\left(g x +f \right) \left(e x +d \right) \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) \left(2 c x +b +\sqrt{-4 a c +b^{2}}\right)}{c}}\, \left(d g -e f \right) \left(b e -2 c d +\sqrt{-4 a c +b^{2}}\, e \right) \sqrt{c e g \,x^{4}+b e g \,x^{3}+c d g \,x^{3}+c e f \,x^{3}+a e g \,x^{2}+b d g \,x^{2}+b e f \,x^{2}+c d f \,x^{2}+a d g x +a e f x +b d f x +a d f}}"," ",0,"4*(b*e^2*g*x^2-2*c*e^2*f*x^2+2*b*d*e*g*x-4*c*d*e*f*x+(-4*a*c+b^2)^(1/2)*e^2*g*x^2+b*d^2*g-2*c*d^2*f+2*(-4*a*c+b^2)^(1/2)*d*e*g*x+(-4*a*c+b^2)^(1/2)*d^2*g)*EllipticF(((b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*x+d))^(1/2),((-b*e+2*c*d+(-4*a*c+b^2)^(1/2)*e)*(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e))^(1/2))*((d*g-e*f)*(2*c*x+b+(-4*a*c+b^2)^(1/2))/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*x+d))^(1/2)*((d*g-e*f)*(-2*c*x-b+(-4*a*c+b^2)^(1/2))/(-b*g+2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*x+d))^(1/2)*((b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)*(g*x+f)/(b*g-2*c*f+(-4*a*c+b^2)^(1/2)*g)/(e*x+d))^(1/2)*(e*x+d)^(1/2)*(g*x+f)^(1/2)*(c*x^2+b*x+a)^(1/2)/(-(g*x+f)*(e*x+d)*(-2*c*x-b+(-4*a*c+b^2)^(1/2))*(2*c*x+b+(-4*a*c+b^2)^(1/2))/c)^(1/2)/(d*g-e*f)/(b*e-2*c*d+(-4*a*c+b^2)^(1/2)*e)/(c*e*g*x^4+b*e*g*x^3+c*d*g*x^3+c*e*f*x^3+a*e*g*x^2+b*d*g*x^2+b*e*f*x^2+c*d*f*x^2+a*d*g*x+a*e*f*x+b*d*f*x+a*d*f)^(1/2)","A"
920,1,1347,220,0.016000," ","int((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a),x)","\frac{\left(c \,e^{4} g^{2} m^{4} x^{4}+b \,e^{4} g^{2} m^{4} x^{3}+2 c \,e^{4} f g \,m^{4} x^{3}+10 c \,e^{4} g^{2} m^{3} x^{4}+a \,e^{4} g^{2} m^{4} x^{2}+2 b \,e^{4} f g \,m^{4} x^{2}+11 b \,e^{4} g^{2} m^{3} x^{3}-4 c d \,e^{3} g^{2} m^{3} x^{3}+c \,e^{4} f^{2} m^{4} x^{2}+22 c \,e^{4} f g \,m^{3} x^{3}+35 c \,e^{4} g^{2} m^{2} x^{4}+2 a \,e^{4} f g \,m^{4} x +12 a \,e^{4} g^{2} m^{3} x^{2}-3 b d \,e^{3} g^{2} m^{3} x^{2}+b \,e^{4} f^{2} m^{4} x +24 b \,e^{4} f g \,m^{3} x^{2}+41 b \,e^{4} g^{2} m^{2} x^{3}-6 c d \,e^{3} f g \,m^{3} x^{2}-24 c d \,e^{3} g^{2} m^{2} x^{3}+12 c \,e^{4} f^{2} m^{3} x^{2}+82 c \,e^{4} f g \,m^{2} x^{3}+50 c \,e^{4} g^{2} m \,x^{4}-2 a d \,e^{3} g^{2} m^{3} x +a \,e^{4} f^{2} m^{4}+26 a \,e^{4} f g \,m^{3} x +49 a \,e^{4} g^{2} m^{2} x^{2}-4 b d \,e^{3} f g \,m^{3} x -24 b d \,e^{3} g^{2} m^{2} x^{2}+13 b \,e^{4} f^{2} m^{3} x +98 b \,e^{4} f g \,m^{2} x^{2}+61 b \,e^{4} g^{2} m \,x^{3}+12 c \,d^{2} e^{2} g^{2} m^{2} x^{2}-2 c d \,e^{3} f^{2} m^{3} x -48 c d \,e^{3} f g \,m^{2} x^{2}-44 c d \,e^{3} g^{2} m \,x^{3}+49 c \,e^{4} f^{2} m^{2} x^{2}+122 c \,e^{4} f g m \,x^{3}+24 c \,g^{2} x^{4} e^{4}-2 a d \,e^{3} f g \,m^{3}-20 a d \,e^{3} g^{2} m^{2} x +14 a \,e^{4} f^{2} m^{3}+118 a \,e^{4} f g \,m^{2} x +78 a \,e^{4} g^{2} m \,x^{2}+6 b \,d^{2} e^{2} g^{2} m^{2} x -b d \,e^{3} f^{2} m^{3}-40 b d \,e^{3} f g \,m^{2} x -51 b d \,e^{3} g^{2} m \,x^{2}+59 b \,e^{4} f^{2} m^{2} x +156 b \,e^{4} f g m \,x^{2}+30 b \,e^{4} g^{2} x^{3}+12 c \,d^{2} e^{2} f g \,m^{2} x +36 c \,d^{2} e^{2} g^{2} m \,x^{2}-20 c d \,e^{3} f^{2} m^{2} x -102 c d \,e^{3} f g m \,x^{2}-24 c d \,e^{3} g^{2} x^{3}+78 c \,e^{4} f^{2} m \,x^{2}+60 c \,e^{4} f g \,x^{3}+2 a \,d^{2} e^{2} g^{2} m^{2}-24 a d \,e^{3} f g \,m^{2}-58 a d \,e^{3} g^{2} m x +71 a \,e^{4} f^{2} m^{2}+214 a \,e^{4} f g m x +40 a \,e^{4} g^{2} x^{2}+4 b \,d^{2} e^{2} f g \,m^{2}+36 b \,d^{2} e^{2} g^{2} m x -12 b d \,e^{3} f^{2} m^{2}-116 b d \,e^{3} f g m x -30 b d \,e^{3} g^{2} x^{2}+107 b \,e^{4} f^{2} m x +80 b \,e^{4} f g \,x^{2}-24 c \,d^{3} e \,g^{2} m x +2 c \,d^{2} e^{2} f^{2} m^{2}+72 c \,d^{2} e^{2} f g m x +24 c \,d^{2} e^{2} g^{2} x^{2}-58 c d \,e^{3} f^{2} m x -60 c d \,e^{3} f g \,x^{2}+40 c \,e^{4} f^{2} x^{2}+18 a \,d^{2} e^{2} g^{2} m -94 a d \,e^{3} f g m -40 a d \,e^{3} g^{2} x +154 a \,e^{4} f^{2} m +120 a \,e^{4} f g x -6 b \,d^{3} e \,g^{2} m +36 b \,d^{2} e^{2} f g m +30 b \,d^{2} e^{2} g^{2} x -47 b d \,e^{3} f^{2} m -80 b d \,e^{3} f g x +60 b \,e^{4} f^{2} x -12 c \,d^{3} e f g m -24 c \,d^{3} e \,g^{2} x +18 c \,d^{2} e^{2} f^{2} m +60 c \,d^{2} e^{2} f g x -40 c d \,e^{3} f^{2} x +40 a \,d^{2} e^{2} g^{2}-120 a d \,e^{3} f g +120 a \,e^{4} f^{2}-30 b \,d^{3} e \,g^{2}+80 b \,d^{2} e^{2} f g -60 b d \,e^{3} f^{2}+24 c \,d^{4} g^{2}-60 c \,d^{3} e f g +40 c \,d^{2} e^{2} f^{2}\right) \left(e x +d \right)^{m +1}}{\left(m^{5}+15 m^{4}+85 m^{3}+225 m^{2}+274 m +120\right) e^{5}}"," ",0,"(e*x+d)^(1+m)*(c*e^4*g^2*m^4*x^4+b*e^4*g^2*m^4*x^3+2*c*e^4*f*g*m^4*x^3+10*c*e^4*g^2*m^3*x^4+a*e^4*g^2*m^4*x^2+2*b*e^4*f*g*m^4*x^2+11*b*e^4*g^2*m^3*x^3-4*c*d*e^3*g^2*m^3*x^3+c*e^4*f^2*m^4*x^2+22*c*e^4*f*g*m^3*x^3+35*c*e^4*g^2*m^2*x^4+2*a*e^4*f*g*m^4*x+12*a*e^4*g^2*m^3*x^2-3*b*d*e^3*g^2*m^3*x^2+b*e^4*f^2*m^4*x+24*b*e^4*f*g*m^3*x^2+41*b*e^4*g^2*m^2*x^3-6*c*d*e^3*f*g*m^3*x^2-24*c*d*e^3*g^2*m^2*x^3+12*c*e^4*f^2*m^3*x^2+82*c*e^4*f*g*m^2*x^3+50*c*e^4*g^2*m*x^4-2*a*d*e^3*g^2*m^3*x+a*e^4*f^2*m^4+26*a*e^4*f*g*m^3*x+49*a*e^4*g^2*m^2*x^2-4*b*d*e^3*f*g*m^3*x-24*b*d*e^3*g^2*m^2*x^2+13*b*e^4*f^2*m^3*x+98*b*e^4*f*g*m^2*x^2+61*b*e^4*g^2*m*x^3+12*c*d^2*e^2*g^2*m^2*x^2-2*c*d*e^3*f^2*m^3*x-48*c*d*e^3*f*g*m^2*x^2-44*c*d*e^3*g^2*m*x^3+49*c*e^4*f^2*m^2*x^2+122*c*e^4*f*g*m*x^3+24*c*e^4*g^2*x^4-2*a*d*e^3*f*g*m^3-20*a*d*e^3*g^2*m^2*x+14*a*e^4*f^2*m^3+118*a*e^4*f*g*m^2*x+78*a*e^4*g^2*m*x^2+6*b*d^2*e^2*g^2*m^2*x-b*d*e^3*f^2*m^3-40*b*d*e^3*f*g*m^2*x-51*b*d*e^3*g^2*m*x^2+59*b*e^4*f^2*m^2*x+156*b*e^4*f*g*m*x^2+30*b*e^4*g^2*x^3+12*c*d^2*e^2*f*g*m^2*x+36*c*d^2*e^2*g^2*m*x^2-20*c*d*e^3*f^2*m^2*x-102*c*d*e^3*f*g*m*x^2-24*c*d*e^3*g^2*x^3+78*c*e^4*f^2*m*x^2+60*c*e^4*f*g*x^3+2*a*d^2*e^2*g^2*m^2-24*a*d*e^3*f*g*m^2-58*a*d*e^3*g^2*m*x+71*a*e^4*f^2*m^2+214*a*e^4*f*g*m*x+40*a*e^4*g^2*x^2+4*b*d^2*e^2*f*g*m^2+36*b*d^2*e^2*g^2*m*x-12*b*d*e^3*f^2*m^2-116*b*d*e^3*f*g*m*x-30*b*d*e^3*g^2*x^2+107*b*e^4*f^2*m*x+80*b*e^4*f*g*x^2-24*c*d^3*e*g^2*m*x+2*c*d^2*e^2*f^2*m^2+72*c*d^2*e^2*f*g*m*x+24*c*d^2*e^2*g^2*x^2-58*c*d*e^3*f^2*m*x-60*c*d*e^3*f*g*x^2+40*c*e^4*f^2*x^2+18*a*d^2*e^2*g^2*m-94*a*d*e^3*f*g*m-40*a*d*e^3*g^2*x+154*a*e^4*f^2*m+120*a*e^4*f*g*x-6*b*d^3*e*g^2*m+36*b*d^2*e^2*f*g*m+30*b*d^2*e^2*g^2*x-47*b*d*e^3*f^2*m-80*b*d*e^3*f*g*x+60*b*e^4*f^2*x-12*c*d^3*e*f*g*m-24*c*d^3*e*g^2*x+18*c*d^2*e^2*f^2*m+60*c*d^2*e^2*f*g*x-40*c*d*e^3*f^2*x+40*a*d^2*e^2*g^2-120*a*d*e^3*f*g+120*a*e^4*f^2-30*b*d^3*e*g^2+80*b*d^2*e^2*f*g-60*b*d*e^3*f^2+24*c*d^4*g^2-60*c*d^3*e*f*g+40*c*d^2*e^2*f^2)/e^5/(m^5+15*m^4+85*m^3+225*m^2+274*m+120)","B"
921,1,503,144,0.008000," ","int((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a),x)","-\frac{\left(-c \,e^{3} g \,m^{3} x^{3}-b \,e^{3} g \,m^{3} x^{2}-c \,e^{3} f \,m^{3} x^{2}-6 c \,e^{3} g \,m^{2} x^{3}-a \,e^{3} g \,m^{3} x -b \,e^{3} f \,m^{3} x -7 b \,e^{3} g \,m^{2} x^{2}+3 c d \,e^{2} g \,m^{2} x^{2}-7 c \,e^{3} f \,m^{2} x^{2}-11 c \,e^{3} g m \,x^{3}-a \,e^{3} f \,m^{3}-8 a \,e^{3} g \,m^{2} x +2 b d \,e^{2} g \,m^{2} x -8 b \,e^{3} f \,m^{2} x -14 b \,e^{3} g m \,x^{2}+2 c d \,e^{2} f \,m^{2} x +9 c d \,e^{2} g m \,x^{2}-14 c \,e^{3} f m \,x^{2}-6 c g \,x^{3} e^{3}+a d \,e^{2} g \,m^{2}-9 a \,e^{3} f \,m^{2}-19 a \,e^{3} g m x +b d \,e^{2} f \,m^{2}+10 b d \,e^{2} g m x -19 b \,e^{3} f m x -8 b \,e^{3} g \,x^{2}-6 c \,d^{2} e g m x +10 c d \,e^{2} f m x +6 c d \,e^{2} g \,x^{2}-8 c \,e^{3} f \,x^{2}+7 a d \,e^{2} g m -26 a \,e^{3} f m -12 a \,e^{3} g x -2 b \,d^{2} e g m +7 b d \,e^{2} f m +8 b d \,e^{2} g x -12 b \,e^{3} f x -2 c \,d^{2} e f m -6 c \,d^{2} e g x +8 c d \,e^{2} f x +12 a d \,e^{2} g -24 a \,e^{3} f -8 b \,d^{2} e g +12 b d \,e^{2} f +6 c \,d^{3} g -8 c \,d^{2} e f \right) \left(e x +d \right)^{m +1}}{\left(m^{4}+10 m^{3}+35 m^{2}+50 m +24\right) e^{4}}"," ",0,"-(e*x+d)^(m+1)*(-c*e^3*g*m^3*x^3-b*e^3*g*m^3*x^2-c*e^3*f*m^3*x^2-6*c*e^3*g*m^2*x^3-a*e^3*g*m^3*x-b*e^3*f*m^3*x-7*b*e^3*g*m^2*x^2+3*c*d*e^2*g*m^2*x^2-7*c*e^3*f*m^2*x^2-11*c*e^3*g*m*x^3-a*e^3*f*m^3-8*a*e^3*g*m^2*x+2*b*d*e^2*g*m^2*x-8*b*e^3*f*m^2*x-14*b*e^3*g*m*x^2+2*c*d*e^2*f*m^2*x+9*c*d*e^2*g*m*x^2-14*c*e^3*f*m*x^2-6*c*e^3*g*x^3+a*d*e^2*g*m^2-9*a*e^3*f*m^2-19*a*e^3*g*m*x+b*d*e^2*f*m^2+10*b*d*e^2*g*m*x-19*b*e^3*f*m*x-8*b*e^3*g*x^2-6*c*d^2*e*g*m*x+10*c*d*e^2*f*m*x+6*c*d*e^2*g*x^2-8*c*e^3*f*x^2+7*a*d*e^2*g*m-26*a*e^3*f*m-12*a*e^3*g*x-2*b*d^2*e*g*m+7*b*d*e^2*f*m+8*b*d*e^2*g*x-12*b*e^3*f*x-2*c*d^2*e*f*m-6*c*d^2*e*g*x+8*c*d*e^2*f*x+12*a*d*e^2*g-24*a*e^3*f-8*b*d^2*e*g+12*b*d*e^2*f+6*c*d^3*g-8*c*d^2*e*f)/e^4/(m^4+10*m^3+35*m^2+50*m+24)","B"
922,0,0,131,0.062000," ","int((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f),x)","\int \frac{\left(c \,x^{2}+b x +a \right) \left(e x +d \right)^{m}}{g x +f}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f),x)","F"
923,0,0,159,0.063000," ","int((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f)^2,x)","\int \frac{\left(c \,x^{2}+b x +a \right) \left(e x +d \right)^{m}}{\left(g x +f \right)^{2}}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f)^2,x)","F"
924,0,0,241,0.097000," ","int((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f)^3,x)","\int \frac{\left(c \,x^{2}+b x +a \right) \left(e x +d \right)^{m}}{\left(g x +f \right)^{3}}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)/(g*x+f)^3,x)","F"
925,1,5890,525,0.035000," ","int((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
926,1,2563,311,0.020000," ","int((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a)^2,x)","-\frac{\left(-c^{2} e^{5} g \,m^{5} x^{5}-2 b c \,e^{5} g \,m^{5} x^{4}-c^{2} e^{5} f \,m^{5} x^{4}-15 c^{2} e^{5} g \,m^{4} x^{5}-2 a c \,e^{5} g \,m^{5} x^{3}-b^{2} e^{5} g \,m^{5} x^{3}-2 b c \,e^{5} f \,m^{5} x^{3}-32 b c \,e^{5} g \,m^{4} x^{4}+5 c^{2} d \,e^{4} g \,m^{4} x^{4}-16 c^{2} e^{5} f \,m^{4} x^{4}-85 c^{2} e^{5} g \,m^{3} x^{5}-2 a b \,e^{5} g \,m^{5} x^{2}-2 a c \,e^{5} f \,m^{5} x^{2}-34 a c \,e^{5} g \,m^{4} x^{3}-b^{2} e^{5} f \,m^{5} x^{2}-17 b^{2} e^{5} g \,m^{4} x^{3}+8 b c d \,e^{4} g \,m^{4} x^{3}-34 b c \,e^{5} f \,m^{4} x^{3}-190 b c \,e^{5} g \,m^{3} x^{4}+4 c^{2} d \,e^{4} f \,m^{4} x^{3}+50 c^{2} d \,e^{4} g \,m^{3} x^{4}-95 c^{2} e^{5} f \,m^{3} x^{4}-225 c^{2} e^{5} g \,m^{2} x^{5}-a^{2} e^{5} g \,m^{5} x -2 a b \,e^{5} f \,m^{5} x -36 a b \,e^{5} g \,m^{4} x^{2}+6 a c d \,e^{4} g \,m^{4} x^{2}-36 a c \,e^{5} f \,m^{4} x^{2}-214 a c \,e^{5} g \,m^{3} x^{3}+3 b^{2} d \,e^{4} g \,m^{4} x^{2}-18 b^{2} e^{5} f \,m^{4} x^{2}-107 b^{2} e^{5} g \,m^{3} x^{3}+6 b c d \,e^{4} f \,m^{4} x^{2}+96 b c d \,e^{4} g \,m^{3} x^{3}-214 b c \,e^{5} f \,m^{3} x^{3}-520 b c \,e^{5} g \,m^{2} x^{4}-20 c^{2} d^{2} e^{3} g \,m^{3} x^{3}+48 c^{2} d \,e^{4} f \,m^{3} x^{3}+175 c^{2} d \,e^{4} g \,m^{2} x^{4}-260 c^{2} e^{5} f \,m^{2} x^{4}-274 c^{2} e^{5} g m \,x^{5}-a^{2} e^{5} f \,m^{5}-19 a^{2} e^{5} g \,m^{4} x +4 a b d \,e^{4} g \,m^{4} x -38 a b \,e^{5} f \,m^{4} x -242 a b \,e^{5} g \,m^{3} x^{2}+4 a c d \,e^{4} f \,m^{4} x +84 a c d \,e^{4} g \,m^{3} x^{2}-242 a c \,e^{5} f \,m^{3} x^{2}-614 a c \,e^{5} g \,m^{2} x^{3}+2 b^{2} d \,e^{4} f \,m^{4} x +42 b^{2} d \,e^{4} g \,m^{3} x^{2}-121 b^{2} e^{5} f \,m^{3} x^{2}-307 b^{2} e^{5} g \,m^{2} x^{3}-24 b c \,d^{2} e^{3} g \,m^{3} x^{2}+84 b c d \,e^{4} f \,m^{3} x^{2}+376 b c d \,e^{4} g \,m^{2} x^{3}-614 b c \,e^{5} f \,m^{2} x^{3}-648 b c \,e^{5} g m \,x^{4}-12 c^{2} d^{2} e^{3} f \,m^{3} x^{2}-120 c^{2} d^{2} e^{3} g \,m^{2} x^{3}+188 c^{2} d \,e^{4} f \,m^{2} x^{3}+250 c^{2} d \,e^{4} g m \,x^{4}-324 c^{2} e^{5} f m \,x^{4}-120 g \,c^{2} x^{5} e^{5}+a^{2} d \,e^{4} g \,m^{4}-20 a^{2} e^{5} f \,m^{4}-137 a^{2} e^{5} g \,m^{3} x +2 a b d \,e^{4} f \,m^{4}+64 a b d \,e^{4} g \,m^{3} x -274 a b \,e^{5} f \,m^{3} x -744 a b \,e^{5} g \,m^{2} x^{2}-12 a c \,d^{2} e^{3} g \,m^{3} x +64 a c d \,e^{4} f \,m^{3} x +390 a c d \,e^{4} g \,m^{2} x^{2}-744 a c \,e^{5} f \,m^{2} x^{2}-792 a c \,e^{5} g m \,x^{3}-6 b^{2} d^{2} e^{3} g \,m^{3} x +32 b^{2} d \,e^{4} f \,m^{3} x +195 b^{2} d \,e^{4} g \,m^{2} x^{2}-372 b^{2} e^{5} f \,m^{2} x^{2}-396 b^{2} e^{5} g m \,x^{3}-12 b c \,d^{2} e^{3} f \,m^{3} x -216 b c \,d^{2} e^{3} g \,m^{2} x^{2}+390 b c d \,e^{4} f \,m^{2} x^{2}+576 b c d \,e^{4} g m \,x^{3}-792 b c \,e^{5} f m \,x^{3}-288 b c \,e^{5} g \,x^{4}+60 c^{2} d^{3} e^{2} g \,m^{2} x^{2}-108 c^{2} d^{2} e^{3} f \,m^{2} x^{2}-220 c^{2} d^{2} e^{3} g m \,x^{3}+288 c^{2} d \,e^{4} f m \,x^{3}+120 c^{2} d \,e^{4} g \,x^{4}-144 c^{2} e^{5} f \,x^{4}+18 a^{2} d \,e^{4} g \,m^{3}-155 a^{2} e^{5} f \,m^{3}-461 a^{2} e^{5} g \,m^{2} x -4 a b \,d^{2} e^{3} g \,m^{3}+36 a b d \,e^{4} f \,m^{3}+356 a b d \,e^{4} g \,m^{2} x -922 a b \,e^{5} f \,m^{2} x -1016 a b \,e^{5} g m \,x^{2}-4 a c \,d^{2} e^{3} f \,m^{3}-144 a c \,d^{2} e^{3} g \,m^{2} x +356 a c d \,e^{4} f \,m^{2} x +672 a c d \,e^{4} g m \,x^{2}-1016 a c \,e^{5} f m \,x^{2}-360 a c \,e^{5} g \,x^{3}-2 b^{2} d^{2} e^{3} f \,m^{3}-72 b^{2} d^{2} e^{3} g \,m^{2} x +178 b^{2} d \,e^{4} f \,m^{2} x +336 b^{2} d \,e^{4} g m \,x^{2}-508 b^{2} e^{5} f m \,x^{2}-180 b^{2} e^{5} g \,x^{3}+48 b c \,d^{3} e^{2} g \,m^{2} x -144 b c \,d^{2} e^{3} f \,m^{2} x -480 b c \,d^{2} e^{3} g m \,x^{2}+672 b c d \,e^{4} f m \,x^{2}+288 b c d \,e^{4} g \,x^{3}-360 b c \,e^{5} f \,x^{3}+24 c^{2} d^{3} e^{2} f \,m^{2} x +180 c^{2} d^{3} e^{2} g m \,x^{2}-240 c^{2} d^{2} e^{3} f m \,x^{2}-120 c^{2} d^{2} e^{3} g \,x^{3}+144 c^{2} d \,e^{4} f \,x^{3}+119 a^{2} d \,e^{4} g \,m^{2}-580 a^{2} e^{5} f \,m^{2}-702 a^{2} e^{5} g m x -60 a b \,d^{2} e^{3} g \,m^{2}+238 a b d \,e^{4} f \,m^{2}+776 a b d \,e^{4} g m x -1404 a b \,e^{5} f m x -480 a b \,e^{5} g \,x^{2}+12 a c \,d^{3} e^{2} g \,m^{2}-60 a c \,d^{2} e^{3} f \,m^{2}-492 a c \,d^{2} e^{3} g m x +776 a c d \,e^{4} f m x +360 a c d \,e^{4} g \,x^{2}-480 a c \,e^{5} f \,x^{2}+6 b^{2} d^{3} e^{2} g \,m^{2}-30 b^{2} d^{2} e^{3} f \,m^{2}-246 b^{2} d^{2} e^{3} g m x +388 b^{2} d \,e^{4} f m x +180 b^{2} d \,e^{4} g \,x^{2}-240 b^{2} e^{5} f \,x^{2}+12 b c \,d^{3} e^{2} f \,m^{2}+336 b c \,d^{3} e^{2} g m x -492 b c \,d^{2} e^{3} f m x -288 b c \,d^{2} e^{3} g \,x^{2}+360 b c d \,e^{4} f \,x^{2}-120 c^{2} d^{4} e g m x +168 c^{2} d^{3} e^{2} f m x +120 c^{2} d^{3} e^{2} g \,x^{2}-144 c^{2} d^{2} e^{3} f \,x^{2}+342 a^{2} d \,e^{4} g m -1044 a^{2} e^{5} f m -360 a^{2} e^{5} g x -296 a b \,d^{2} e^{3} g m +684 a b d \,e^{4} f m +480 a b d \,e^{4} g x -720 a b \,e^{5} f x +132 a c \,d^{3} e^{2} g m -296 a c \,d^{2} e^{3} f m -360 a c \,d^{2} e^{3} g x +480 a c d \,e^{4} f x +66 b^{2} d^{3} e^{2} g m -148 b^{2} d^{2} e^{3} f m -180 b^{2} d^{2} e^{3} g x +240 b^{2} d \,e^{4} f x -48 b c \,d^{4} e g m +132 b c \,d^{3} e^{2} f m +288 b c \,d^{3} e^{2} g x -360 b c \,d^{2} e^{3} f x -24 c^{2} d^{4} e f m -120 c^{2} d^{4} e g x +144 c^{2} d^{3} e^{2} f x +360 a^{2} d \,e^{4} g -720 a^{2} e^{5} f -480 a b \,d^{2} e^{3} g +720 a b d \,e^{4} f +360 a c \,d^{3} e^{2} g -480 a c \,d^{2} e^{3} f +180 b^{2} d^{3} e^{2} g -240 b^{2} d^{2} e^{3} f -288 b c \,d^{4} e g +360 b c \,d^{3} e^{2} f +120 c^{2} d^{5} g -144 c^{2} d^{4} e f \right) \left(e x +d \right)^{m +1}}{\left(m^{6}+21 m^{5}+175 m^{4}+735 m^{3}+1624 m^{2}+1764 m +720\right) e^{6}}"," 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927,0,0,289,0.125000," ","int((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f),x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{2} \left(e x +d \right)^{m}}{g x +f}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f),x)","F"
928,0,0,300,0.128000," ","int((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f)^2,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{2} \left(e x +d \right)^{m}}{\left(g x +f \right)^{2}}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f)^2,x)","F"
929,0,0,457,0.171000," ","int((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f)^3,x)","\int \frac{\left(c \,x^{2}+b x +a \right)^{2} \left(e x +d \right)^{m}}{\left(g x +f \right)^{3}}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^2/(g*x+f)^3,x)","F"
930,0,0,165,0.186000," ","int((2+3*x)^4*(1+4*x)^m/(3*x^2-5*x+1),x)","\int \frac{\left(3 x +2\right)^{4} \left(4 x +1\right)^{m}}{3 x^{2}-5 x +1}\, dx"," ",0,"int((2+3*x)^4*(1+4*x)^m/(3*x^2-5*x+1),x)","F"
931,0,0,149,0.125000," ","int((3*x+2)^3*(4*x+1)^m/(3*x^2-5*x+1),x)","\int \frac{\left(3 x +2\right)^{3} \left(4 x +1\right)^{m}}{3 x^{2}-5 x +1}\, dx"," ",0,"int((3*x+2)^3*(4*x+1)^m/(3*x^2-5*x+1),x)","F"
932,0,0,133,0.123000," ","int((3*x+2)^2*(4*x+1)^m/(3*x^2-5*x+1),x)","\int \frac{\left(3 x +2\right)^{2} \left(4 x +1\right)^{m}}{3 x^{2}-5 x +1}\, dx"," ",0,"int((3*x+2)^2*(4*x+1)^m/(3*x^2-5*x+1),x)","F"
933,0,0,117,0.119000," ","int((3*x+2)*(4*x+1)^m/(3*x^2-5*x+1),x)","\int \frac{\left(3 x +2\right) \left(4 x +1\right)^{m}}{3 x^{2}-5 x +1}\, dx"," ",0,"int((3*x+2)*(4*x+1)^m/(3*x^2-5*x+1),x)","F"
934,0,0,109,0.138000," ","int((4*x+1)^m/(3*x^2-5*x+1),x)","\int \frac{\left(4 x +1\right)^{m}}{3 x^{2}-5 x +1}\, dx"," ",0,"int((4*x+1)^m/(3*x^2-5*x+1),x)","F"
935,0,0,148,0.126000," ","int((4*x+1)^m/(3*x+2)/(3*x^2-5*x+1),x)","\int \frac{\left(4 x +1\right)^{m}}{\left(3 x +2\right) \left(3 x^{2}-5 x +1\right)}\, dx"," ",0,"int((4*x+1)^m/(3*x+2)/(3*x^2-5*x+1),x)","F"
936,0,0,179,0.133000," ","int((4*x+1)^m/(3*x+2)^2/(3*x^2-5*x+1),x)","\int \frac{\left(4 x +1\right)^{m}}{\left(3 x +2\right)^{2} \left(3 x^{2}-5 x +1\right)}\, dx"," ",0,"int((4*x+1)^m/(3*x+2)^2/(3*x^2-5*x+1),x)","F"
937,0,0,182,0.158000," ","int((3*x+2)^4*(4*x+1)^m/(3*x^2-5*x+1)^2,x)","\int \frac{\left(3 x +2\right)^{4} \left(4 x +1\right)^{m}}{\left(3 x^{2}-5 x +1\right)^{2}}\, dx"," ",0,"int((3*x+2)^4*(4*x+1)^m/(3*x^2-5*x+1)^2,x)","F"
938,0,0,162,0.149000," ","int((3*x+2)^3*(4*x+1)^m/(3*x^2-5*x+1)^2,x)","\int \frac{\left(3 x +2\right)^{3} \left(4 x +1\right)^{m}}{\left(3 x^{2}-5 x +1\right)^{2}}\, dx"," ",0,"int((3*x+2)^3*(4*x+1)^m/(3*x^2-5*x+1)^2,x)","F"
939,0,0,161,0.145000," ","int((3*x+2)^2*(4*x+1)^m/(3*x^2-5*x+1)^2,x)","\int \frac{\left(3 x +2\right)^{2} \left(4 x +1\right)^{m}}{\left(3 x^{2}-5 x +1\right)^{2}}\, dx"," ",0,"int((3*x+2)^2*(4*x+1)^m/(3*x^2-5*x+1)^2,x)","F"
940,0,0,161,0.139000," ","int((3*x+2)*(4*x+1)^m/(3*x^2-5*x+1)^2,x)","\int \frac{\left(3 x +2\right) \left(4 x +1\right)^{m}}{\left(3 x^{2}-5 x +1\right)^{2}}\, dx"," ",0,"int((3*x+2)*(4*x+1)^m/(3*x^2-5*x+1)^2,x)","F"
941,0,0,159,0.137000," ","int((4*x+1)^m/(3*x^2-5*x+1)^2,x)","\int \frac{\left(4 x +1\right)^{m}}{\left(3 x^{2}-5 x +1\right)^{2}}\, dx"," ",0,"int((4*x+1)^m/(3*x^2-5*x+1)^2,x)","F"
942,0,0,306,0.159000," ","int((4*x+1)^m/(3*x+2)/(3*x^2-5*x+1)^2,x)","\int \frac{\left(4 x +1\right)^{m}}{\left(3 x +2\right) \left(3 x^{2}-5 x +1\right)^{2}}\, dx"," ",0,"int((4*x+1)^m/(3*x+2)/(3*x^2-5*x+1)^2,x)","F"
943,0,0,338,0.167000," ","int((4*x+1)^m/(3*x+2)^2/(3*x^2-5*x+1)^2,x)","\int \frac{\left(4 x +1\right)^{m}}{\left(3 x +2\right)^{2} \left(3 x^{2}-5 x +1\right)^{2}}\, dx"," ",0,"int((4*x+1)^m/(3*x+2)^2/(3*x^2-5*x+1)^2,x)","F"
944,0,0,229,0.063000," ","int((e*x+d)^m*(c*x^2+b*x+a)/(f*x+e)^(3/2),x)","\int \frac{\left(c \,x^{2}+b x +a \right) \left(e x +d \right)^{m}}{\left(f x +e \right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)/(f*x+e)^(3/2),x)","F"
945,0,0,469,0.139000," ","int((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a)^(1/2),x)","\int \left(g x +f \right)^{2} \sqrt{c \,x^{2}+b x +a}\, \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a)^(1/2),x)","F"
946,0,0,352,0.120000," ","int((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a)^(1/2),x)","\int \left(g x +f \right) \sqrt{c \,x^{2}+b x +a}\, \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a)^(1/2),x)","F"
947,0,0,171,0.121000," ","int((e*x+d)^m*(c*x^2+b*x+a)^(1/2),x)","\int \sqrt{c \,x^{2}+b x +a}\, \left(e x +d \right)^{m}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^(1/2),x)","F"
948,0,0,29,0.129000," ","int((e*x+d)^m*(c*x^2+b*x+a)^(1/2)/(g*x+f),x)","\int \frac{\sqrt{c \,x^{2}+b x +a}\, \left(e x +d \right)^{m}}{g x +f}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^(1/2)/(g*x+f),x)","F"
949,0,0,462,0.131000," ","int((e*x+d)^m*(g*x+f)^2/(c*x^2+b*x+a)^(1/2),x)","\int \frac{\left(g x +f \right)^{2} \left(e x +d \right)^{m}}{\sqrt{c \,x^{2}+b x +a}}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)^2/(c*x^2+b*x+a)^(1/2),x)","F"
950,0,0,352,0.133000," ","int((e*x+d)^m*(g*x+f)/(c*x^2+b*x+a)^(1/2),x)","\int \frac{\left(g x +f \right) \left(e x +d \right)^{m}}{\sqrt{c \,x^{2}+b x +a}}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)/(c*x^2+b*x+a)^(1/2),x)","F"
951,0,0,171,0.130000," ","int((e*x+d)^m/(c*x^2+b*x+a)^(1/2),x)","\int \frac{\left(e x +d \right)^{m}}{\sqrt{c \,x^{2}+b x +a}}\, dx"," ",0,"int((e*x+d)^m/(c*x^2+b*x+a)^(1/2),x)","F"
952,0,0,29,0.131000," ","int((e*x+d)^m/(g*x+f)/(c*x^2+b*x+a)^(1/2),x)","\int \frac{\left(e x +d \right)^{m}}{\left(g x +f \right) \sqrt{c \,x^{2}+b x +a}}\, dx"," ",0,"int((e*x+d)^m/(g*x+f)/(c*x^2+b*x+a)^(1/2),x)","F"
953,0,0,267,0.074000," ","int((e*x+d)^m*(g*x+f)^n*(c*x^2+b*x+a),x)","\int \left(c \,x^{2}+b x +a \right) \left(e x +d \right)^{m} \left(g x +f \right)^{n}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)^n*(c*x^2+b*x+a),x)","F"
954,0,0,509,0.140000," ","int((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a)^p,x)","\int \left(g x +f \right)^{2} \left(e x +d \right)^{m} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)^2*(c*x^2+b*x+a)^p,x)","F"
955,0,0,368,0.119000," ","int((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a)^p,x)","\int \left(g x +f \right) \left(e x +d \right)^{m} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^m*(g*x+f)*(c*x^2+b*x+a)^p,x)","F"
956,0,0,179,0.172000," ","int((e*x+d)^m*(c*x^2+b*x+a)^p,x)","\int \left(e x +d \right)^{m} \left(c \,x^{2}+b x +a \right)^{p}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^p,x)","F"
957,0,0,29,0.133000," ","int((e*x+d)^m*(c*x^2+b*x+a)^p/(g*x+f),x)","\int \frac{\left(e x +d \right)^{m} \left(c \,x^{2}+b x +a \right)^{p}}{g x +f}\, dx"," ",0,"int((e*x+d)^m*(c*x^2+b*x+a)^p/(g*x+f),x)","F"
958,1,148,82,0.143000," ","int(1/x^2/(1-1/c^2/x^2)^(1/2)/(e*x+d)^(1/2),x)","-\frac{2 \left(c d -e \right) \sqrt{-\frac{\left(c x +1\right) e}{c d -e}}\, \sqrt{-\frac{\left(c x -1\right) e}{c d +e}}\, \sqrt{\frac{\left(e x +d \right) c}{c d -e}}\, \EllipticPi \left(\sqrt{\frac{\left(e x +d \right) c}{c d -e}}, \frac{c d -e}{c d}, \sqrt{\frac{c d -e}{c d +e}}\right)}{\sqrt{\frac{c^{2} x^{2}-1}{c^{2} x^{2}}}\, \sqrt{e x +d}\, c d x}"," ",0,"-2/((c^2*x^2-1)/c^2/x^2)^(1/2)/x*(c*d-e)*EllipticPi(((e*x+d)*c/(c*d-e))^(1/2),(c*d-e)/c/d,((c*d-e)/(c*d+e))^(1/2))*(-(c*x+1)*e/(c*d-e))^(1/2)*(-(c*x-1)*e/(c*d+e))^(1/2)*((e*x+d)*c/(c*d-e))^(1/2)/(e*x+d)^(1/2)/c/d","A"