1,1,139,114,0.152000," ","int(1/(2^(2/3)+x)/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{2^{\frac{2}{3}}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(2^{\frac{2}{3}}-1\right)}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)/(2^(2/3)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(2^(2/3)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
2,1,143,129,0.092000," ","int(1/(2^(2/3)-x)/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
3,1,143,127,0.057000," ","int(1/(2^(2/3)-x)/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-2^{\frac{2}{3}}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-2^{\frac{2}{3}}+1\right)}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)/(-2^(2/3)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-2^(2/3)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
4,1,139,124,0.053000," ","int(1/(2^(2/3)+x)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
5,0,0,201,0.101000," ","int(1/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x)","\int \frac{1}{\left(b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int(1/(2^(2/3)*a^(1/3)+b^(1/3)*x)/(b*x^3+a)^(1/2),x)","F"
6,0,0,209,0.074000," ","int(1/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x)","\int \frac{1}{\left(-b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int(1/(2^(2/3)*a^(1/3)-b^(1/3)*x)/(-b*x^3+a)^(1/2),x)","F"
7,0,0,216,0.060000," ","int(1/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{1}{\left(-b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int(1/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
8,0,0,212,0.061000," ","int(1/(b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{1}{\left(b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int(1/(b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
9,1,495,200,0.206000," ","int(1/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x)","\frac{2 \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}\right) \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \sqrt{\frac{x +\frac{2^{\frac{1}{3}} c}{2 d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}, \frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{c}{d}}, \sqrt{\frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\right)}{\sqrt{4 d^{3} x^{3}+c^{3}}\, \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{c}{d}\right) d}"," ",0,"2/d*((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)*((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)*((x+1/2*2^(1/3)*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2)*((x-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)/(4*d^3*x^3+c^3)^(1/2)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+c/d)*EllipticPi(((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2),((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+c/d),(((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2))","B"
10,1,132,118,0.053000," ","int(1/(1+x+3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}"," ",0,"2/3*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*3^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
11,1,143,135,0.056000," ","int(1/(1-x+3^(1/2))/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-3/2+1/2*I*3^(1/2)-3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-3/2+1/2*I*3^(1/2)-3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
12,1,132,133,0.045000," ","int(1/(1-x+3^(1/2))/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}"," ",0,"2/3*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*3^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
13,1,139,128,0.052000," ","int(1/(1+x+3^(1/2))/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(3/2+3^(1/2)+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(3/2+3^(1/2)+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
14,1,123,269,0.020000," ","int(1/(x+3)/(x^3+1)^(1/2),x)","\frac{\left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3}{4}+\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}"," ",0,"(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),-3/4+1/4*I*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
15,1,133,306,0.026000," ","int(1/(x+3)/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{5}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{5}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(5/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(5/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
16,1,124,295,0.021000," ","int(1/(x+3)/(x^3-1)^(1/2),x)","\frac{\left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{8}+\frac{i \sqrt{3}}{8}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}"," ",0,"1/2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),3/8+1/8*I*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
17,1,133,283,0.025000," ","int(1/(x+3)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{7}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{7}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(7/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(7/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
18,0,0,116,0.075000," ","int(1/(d*x+c)/(d^3*x^3-c^3)^(1/3),x)","\int \frac{1}{\left(d x +c \right) \left(d^{3} x^{3}-c^{3}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(d*x+c)/(d^3*x^3-c^3)^(1/3),x)","F"
19,0,0,162,0.061000," ","int(1/(d*x+c)/(d^3*x^3+2*c^3)^(1/3),x)","\int \frac{1}{\left(d x +c \right) \left(d^{3} x^{3}+2 c^{3}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(d*x+c)/(d^3*x^3+2*c^3)^(1/3),x)","F"
20,0,0,163,0.059000," ","int(1/(d*x+c)/(d^3*x^3+2*c^3)^(2/3),x)","\int \frac{1}{\left(d x +c \right) \left(d^{3} x^{3}+2 c^{3}\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(d*x+c)/(d^3*x^3+2*c^3)^(2/3),x)","F"
21,1,3064,112,42.609000," ","int(1/(1+2^(1/3)*x)/(x^3+1)^(2/3),x)","\text{output too large to display}"," ",0,"-1/6*ln(-(-15559137585059152-12498127505504256*2^(1/3)*(x^3+1)^(1/3)-1604954020235328*2^(1/3)*x^4-1604954020235328*2^(2/3)*x^2-23004340956706368*2^(1/3)*x-936223178470608*x^6+14712078518823840*x^3-4279877387294208*x^5*2^(2/3)+840505690860402*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^2-11688730639030284*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x+6471910353179844*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^3+1203809884289286*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^4-3218487773589102*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^5-72607968203490*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^4-1560939140169318*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^5+3775614346581480*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^2-3842311729647552*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^3-10498622607665136*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^4-7759251414704196*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x-3531674097632562*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^2+2613886855325640*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x+6150800763487380*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^5+6434683875648336*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^2-5504178119120758*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)-10391133689698608*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x+7959206999356368*x^4*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)-10107087250606332*(x^3+1)^(2/3)*2^(2/3)-9125490357912936*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)-2960082830251008*(x^3+1)^(1/3)*x^5-32590199706036744*(x^3+1)^(2/3)*x-12827025597754368*(x^3+1)^(1/3)*x^2+3712807561447224*(x^3+1)^(2/3)*x^4+7959206999356368*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^2+5665414413224496*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^5+2321435374812274*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^6+3532767618003008*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^3+10197714008127436*2^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+1876782797064098*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^6+2613886855325640*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^3+2884227944870616*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^2-8123294120973864*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+3217341937824168*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^4+2081809489180344*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x-11138422684341672*(x^3+1)^(2/3)*2^(1/3)*x^2+3919074648194292*(x^3+1)^(2/3)*2^(2/3)*x^3-1315592369000448*(x^3+1)^(1/3)*2^(2/3)*x^4-6964190009986188*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^4+3288980922501120*(x^3+1)^(1/3)*2^(1/3)*x^3-20062783627256832*(x^3+1)^(1/3)*2^(2/3)*x-7115580883942020*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)+2161300347926748*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x)/(1+2^(1/3)*x)^6)*2^(1/3)-1/6*ln(-(-15559137585059152-12498127505504256*2^(1/3)*(x^3+1)^(1/3)-1604954020235328*2^(1/3)*x^4-1604954020235328*2^(2/3)*x^2-23004340956706368*2^(1/3)*x-936223178470608*x^6+14712078518823840*x^3-4279877387294208*x^5*2^(2/3)+840505690860402*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^2-11688730639030284*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x+6471910353179844*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^3+1203809884289286*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^4-3218487773589102*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^5-72607968203490*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^4-1560939140169318*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^5+3775614346581480*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^2-3842311729647552*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^3-10498622607665136*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^4-7759251414704196*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x-3531674097632562*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^2+2613886855325640*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x+6150800763487380*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^5+6434683875648336*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^2-5504178119120758*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)-10391133689698608*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x+7959206999356368*x^4*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)-10107087250606332*(x^3+1)^(2/3)*2^(2/3)-9125490357912936*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)-2960082830251008*(x^3+1)^(1/3)*x^5-32590199706036744*(x^3+1)^(2/3)*x-12827025597754368*(x^3+1)^(1/3)*x^2+3712807561447224*(x^3+1)^(2/3)*x^4+7959206999356368*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^2+5665414413224496*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^5+2321435374812274*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^6+3532767618003008*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^3+10197714008127436*2^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+1876782797064098*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^6+2613886855325640*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^3+2884227944870616*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^2-8123294120973864*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+3217341937824168*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^4+2081809489180344*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x-11138422684341672*(x^3+1)^(2/3)*2^(1/3)*x^2+3919074648194292*(x^3+1)^(2/3)*2^(2/3)*x^3-1315592369000448*(x^3+1)^(1/3)*2^(2/3)*x^4-6964190009986188*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^4+3288980922501120*(x^3+1)^(1/3)*2^(1/3)*x^3-20062783627256832*(x^3+1)^(1/3)*2^(2/3)*x-7115580883942020*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)+2161300347926748*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x)/(1+2^(1/3)*x)^6)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)+1/6*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*ln(-(-4550781346817636-3372637147591320*2^(1/3)*(x^3+1)^(1/3)-3129477143943360*2^(1/3)*x^4-3129477143943360*2^(2/3)*x^2-8449588288647072*2^(1/3)*x-1825528333966960*x^6+1382185738574984*x^3-3794491037031324*x^5*2^(2/3)+840505690860402*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^2+16011331334883780*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x-1244136642528564*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^3-1349025820696266*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^4+96609493250466*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^5-72607968203490*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^4-1560939140169318*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^5+3775614346581480*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^2-3842311729647552*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^3-3429757412307240*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^4+12987025125355476*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x+5212685479353366*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^2+2613886855325640*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x+6150800763487380*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^5+6434683875648336*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^2+5504178119120758*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)+18718371646419984*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x+4910160751940304*x^4*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)-2991506366664312*(x^3+1)^(2/3)*2^(2/3)+9125490357912936*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)+355014436588560*(x^3+1)^(1/3)*x^5-11843923165977072*(x^3+1)^(2/3)*x-4082666020768440*(x^3+1)^(1/3)*x^2+1159971856461672*(x^3+1)^(2/3)*x^4+4910160751940304*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^2+6636187113750264*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^5+1432130219315922*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^6+3532767618003008*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^3-3132178772121420*2^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+1876782797064098*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^6+2613886855325640*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^3+12218229441455304*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^2-7245952797616344*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+3217341937824168*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^4+2081809489180344*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x-6471421936049328*(x^3+1)^(2/3)*2^(1/3)*x^2+61051150340088*(x^3+1)^(2/3)*2^(2/3)*x^3+2218840228678500*(x^3+1)^(1/3)*2^(2/3)*x^4-6964190009986188*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^4+3727651584179880*(x^3+1)^(1/3)*2^(1/3)*x^3-6212752640299800*(x^3+1)^(1/3)*2^(2/3)*x+7115580883942020*(x^3+1)^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)+2161300347926748*(x^3+1)^(1/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x)/(1+2^(1/3)*x)^6)","C"
22,1,3250,125,41.368000," ","int(1/(1-2^(1/3)*x)/(-x^3+1)^(2/3),x)","\text{output too large to display}"," ",0,"-1/6*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*ln(-(-4550781346817636-3372637147591320*2^(1/3)*(-x^3+1)^(1/3)-3129477143943360*2^(1/3)*x^4-3129477143943360*2^(2/3)*x^2+8449588288647072*2^(1/3)*x-1825528333966960*x^6-1382185738574984*x^3+3794491037031324*x^5*2^(2/3)-6150800763487380*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^5+6434683875648336*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^2+5504178119120758*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)-18718371646419984*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x+4910160751940304*x^4*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)+4910160751940304*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^2-6636187113750264*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^5+1432130219315922*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^6-3532767618003008*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^3+3132178772121420*2^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+1876782797064098*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^6+3217341937824168*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^4-2081809489180344*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x-2991506366664312*2^(2/3)*(-x^3+1)^(2/3)+9125490357912936*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(1/3)+1159971856461672*(-x^3+1)^(2/3)*x^4-355014436588560*(-x^3+1)^(1/3)*x^5+11843923165977072*(-x^3+1)^(2/3)*x-4082666020768440*(-x^3+1)^(1/3)*x^2-6471421936049328*2^(1/3)*(-x^3+1)^(2/3)*x^2-61051150340088*2^(2/3)*(-x^3+1)^(2/3)*x^3+2218840228678500*2^(2/3)*(-x^3+1)^(1/3)*x^4-6964190009986188*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(1/3)*x^4-3727651584179880*2^(1/3)*(-x^3+1)^(1/3)*x^3+7245952797616344*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(1/3)*x^3+6212752640299800*2^(2/3)*(-x^3+1)^(1/3)*x+7115580883942020*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(2/3)-2161300347926748*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(1/3)*x-2613886855325640*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(2/3)*x^3+12218229441455304*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(2/3)*x^2+3775614346581480*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*(-x^3+1)^(2/3)*x^2+3842311729647552*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*(-x^3+1)^(1/3)*x^3-3429757412307240*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(1/3)*x^4-12987025125355476*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(2/3)*x+5212685479353366*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(1/3)*x^2-2613886855325640*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(2/3)*x+840505690860402*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(1/3)*x^2-16011331334883780*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(1/3)*x+1244136642528564*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(2/3)*x^3-1349025820696266*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(2/3)*x^4-96609493250466*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(1/3)*x^5-72607968203490*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(2/3)*x^4+1560939140169318*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(1/3)*x^5)/(2^(1/3)*x-1)^6)+1/6*ln(-(-15559137585059152-12498127505504256*2^(1/3)*(-x^3+1)^(1/3)-1604954020235328*2^(1/3)*x^4-1604954020235328*2^(2/3)*x^2+23004340956706368*2^(1/3)*x-936223178470608*x^6-14712078518823840*x^3+4279877387294208*x^5*2^(2/3)-6150800763487380*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^5+6434683875648336*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^2-5504178119120758*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)+10391133689698608*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x+7959206999356368*x^4*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)+7959206999356368*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^2-5665414413224496*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^5+2321435374812274*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^6-3532767618003008*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^3-10197714008127436*2^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+1876782797064098*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^6+3217341937824168*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^4-2081809489180344*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x-10107087250606332*2^(2/3)*(-x^3+1)^(2/3)-9125490357912936*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(1/3)+3712807561447224*(-x^3+1)^(2/3)*x^4+2960082830251008*(-x^3+1)^(1/3)*x^5+32590199706036744*(-x^3+1)^(2/3)*x-12827025597754368*(-x^3+1)^(1/3)*x^2-11138422684341672*2^(1/3)*(-x^3+1)^(2/3)*x^2-3919074648194292*2^(2/3)*(-x^3+1)^(2/3)*x^3-1315592369000448*2^(2/3)*(-x^3+1)^(1/3)*x^4-6964190009986188*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(1/3)*x^4-3288980922501120*2^(1/3)*(-x^3+1)^(1/3)*x^3+8123294120973864*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(1/3)*x^3+20062783627256832*2^(2/3)*(-x^3+1)^(1/3)*x-7115580883942020*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(2/3)-2161300347926748*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(1/3)*x-2613886855325640*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(2/3)*x^3+2884227944870616*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(2/3)*x^2+3775614346581480*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*(-x^3+1)^(2/3)*x^2+3842311729647552*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*(-x^3+1)^(1/3)*x^3-10498622607665136*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(1/3)*x^4+7759251414704196*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(2/3)*x-3531674097632562*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(1/3)*x^2-2613886855325640*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(2/3)*x+840505690860402*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(1/3)*x^2+11688730639030284*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(1/3)*x-6471910353179844*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(2/3)*x^3+1203809884289286*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(2/3)*x^4+3218487773589102*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(1/3)*x^5-72607968203490*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(2/3)*x^4+1560939140169318*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(1/3)*x^5)/(2^(1/3)*x-1)^6)*2^(1/3)+1/6*ln(-(-15559137585059152-12498127505504256*2^(1/3)*(-x^3+1)^(1/3)-1604954020235328*2^(1/3)*x^4-1604954020235328*2^(2/3)*x^2+23004340956706368*2^(1/3)*x-936223178470608*x^6-14712078518823840*x^3+4279877387294208*x^5*2^(2/3)-6150800763487380*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^5+6434683875648336*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*x^2-5504178119120758*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)+10391133689698608*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x+7959206999356368*x^4*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)+7959206999356368*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^2-5665414413224496*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*x^5+2321435374812274*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*x^6-3532767618003008*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^3-10197714008127436*2^(2/3)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*x^3+1876782797064098*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*x^6+3217341937824168*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x^4-2081809489180344*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*x-10107087250606332*2^(2/3)*(-x^3+1)^(2/3)-9125490357912936*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(1/3)+3712807561447224*(-x^3+1)^(2/3)*x^4+2960082830251008*(-x^3+1)^(1/3)*x^5+32590199706036744*(-x^3+1)^(2/3)*x-12827025597754368*(-x^3+1)^(1/3)*x^2-11138422684341672*2^(1/3)*(-x^3+1)^(2/3)*x^2-3919074648194292*2^(2/3)*(-x^3+1)^(2/3)*x^3-1315592369000448*2^(2/3)*(-x^3+1)^(1/3)*x^4-6964190009986188*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(1/3)*x^4-3288980922501120*2^(1/3)*(-x^3+1)^(1/3)*x^3+8123294120973864*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(1/3)*x^3+20062783627256832*2^(2/3)*(-x^3+1)^(1/3)*x-7115580883942020*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(2/3)-2161300347926748*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(1/3)*x-2613886855325640*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*(-x^3+1)^(2/3)*x^3+2884227944870616*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*(-x^3+1)^(2/3)*x^2+3775614346581480*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*(-x^3+1)^(2/3)*x^2+3842311729647552*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(2/3)*(-x^3+1)^(1/3)*x^3-10498622607665136*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(1/3)*x^4+7759251414704196*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(2/3)*x-3531674097632562*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(1/3)*x^2-2613886855325640*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(2/3)*x+840505690860402*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(1/3)*x^2+11688730639030284*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(1/3)*x-6471910353179844*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(1/3)*(-x^3+1)^(2/3)*x^3+1203809884289286*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(2/3)*x^4+3218487773589102*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)*2^(2/3)*(-x^3+1)^(1/3)*x^5-72607968203490*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(2/3)*x^4+1560939140169318*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)^2*2^(1/3)*(-x^3+1)^(1/3)*x^5)/(2^(1/3)*x-1)^6)*RootOf(2^(2/3)+2^(1/3)*_Z+_Z^2)","C"
23,0,0,317,0.079000," ","int((d*x+c)^4*(b*x^3+a)^(1/3),x)","\int \left(d x +c \right)^{4} \left(b \,x^{3}+a \right)^{\frac{1}{3}}\, dx"," ",0,"int((d*x+c)^4*(b*x^3+a)^(1/3),x)","F"
24,0,0,203,0.057000," ","int((d*x+c)^3*(b*x^3+a)^(1/3),x)","\int \left(d x +c \right)^{3} \left(b \,x^{3}+a \right)^{\frac{1}{3}}\, dx"," ",0,"int((d*x+c)^3*(b*x^3+a)^(1/3),x)","F"
25,0,0,155,0.061000," ","int((d*x+c)^2*(b*x^3+a)^(1/3),x)","\int \left(d x +c \right)^{2} \left(b \,x^{3}+a \right)^{\frac{1}{3}}\, dx"," ",0,"int((d*x+c)^2*(b*x^3+a)^(1/3),x)","F"
26,0,0,122,0.052000," ","int((d*x+c)*(b*x^3+a)^(1/3),x)","\int \left(d x +c \right) \left(b \,x^{3}+a \right)^{\frac{1}{3}}\, dx"," ",0,"int((d*x+c)*(b*x^3+a)^(1/3),x)","F"
27,0,0,370,0.079000," ","int((b*x^3+a)^(1/3)/(d*x+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{d x +c}\, dx"," ",0,"int((b*x^3+a)^(1/3)/(d*x+c),x)","F"
28,0,0,708,0.069000," ","int((b*x^3+a)^(1/3)/(d*x+c)^2,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/(d*x+c)^2,x)","F"
29,0,0,251,0.061000," ","int((d*x+c)^4/(b*x^3+a)^(1/3),x)","\int \frac{\left(d x +c \right)^{4}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*x+c)^4/(b*x^3+a)^(1/3),x)","F"
30,0,0,202,0.055000," ","int((d*x+c)^3/(b*x^3+a)^(1/3),x)","\int \frac{\left(d x +c \right)^{3}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*x+c)^3/(b*x^3+a)^(1/3),x)","F"
31,0,0,119,0.061000," ","int((d*x+c)^2/(b*x^3+a)^(1/3),x)","\int \frac{\left(d x +c \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*x+c)^2/(b*x^3+a)^(1/3),x)","F"
32,0,0,98,0.049000," ","int((d*x+c)/(b*x^3+a)^(1/3),x)","\int \frac{d x +c}{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*x+c)/(b*x^3+a)^(1/3),x)","F"
33,0,0,284,0.058000," ","int(1/(d*x+c)/(b*x^3+a)^(1/3),x)","\int \frac{1}{\left(d x +c \right) \left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(d*x+c)/(b*x^3+a)^(1/3),x)","F"
34,0,0,668,0.063000," ","int(1/(d*x+c)^2/(b*x^3+a)^(1/3),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(d*x+c)^2/(b*x^3+a)^(1/3),x)","F"
35,0,0,1346,0.066000," ","int(1/(d*x+c)^3/(b*x^3+a)^(1/3),x)","\int \frac{1}{\left(d x +c \right)^{3} \left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(d*x+c)^3/(b*x^3+a)^(1/3),x)","F"
36,0,0,250,0.062000," ","int((d*x+c)^4/(b*x^3+a)^(2/3),x)","\int \frac{\left(d x +c \right)^{4}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int((d*x+c)^4/(b*x^3+a)^(2/3),x)","F"
37,0,0,154,0.059000," ","int((d*x+c)^3/(b*x^3+a)^(2/3),x)","\int \frac{\left(d x +c \right)^{3}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int((d*x+c)^3/(b*x^3+a)^(2/3),x)","F"
38,0,0,116,0.057000," ","int((d*x+c)^2/(b*x^3+a)^(2/3),x)","\int \frac{\left(d x +c \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int((d*x+c)^2/(b*x^3+a)^(2/3),x)","F"
39,0,0,96,0.048000," ","int((d*x+c)/(b*x^3+a)^(2/3),x)","\int \frac{d x +c}{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int((d*x+c)/(b*x^3+a)^(2/3),x)","F"
40,0,0,285,0.057000," ","int(1/(d*x+c)/(b*x^3+a)^(2/3),x)","\int \frac{1}{\left(d x +c \right) \left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(d*x+c)/(b*x^3+a)^(2/3),x)","F"
41,0,0,669,0.061000," ","int(1/(d*x+c)^2/(b*x^3+a)^(2/3),x)","\int \frac{1}{\left(d x +c \right)^{2} \left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(d*x+c)^2/(b*x^3+a)^(2/3),x)","F"
42,0,0,1207,0.074000," ","int(1/(d*x+c)^3/(b*x^3+a)^(2/3),x)","\int \frac{1}{\left(d x +c \right)^{3} \left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(d*x+c)^3/(b*x^3+a)^(2/3),x)","F"
43,1,258,27,0.069000," ","int((2^(2/3)-2*x)/(2^(2/3)+x)/(x^3+1)^(1/2),x)","-\frac{4 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{6 \,2^{\frac{2}{3}} \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{2^{\frac{2}{3}}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(2^{\frac{2}{3}}-1\right)}"," ",0,"-4*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+6*2^(2/3)*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)/(2^(2/3)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(2^(2/3)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","C"
44,1,253,30,0.061000," ","int((2^(2/3)+2*x)/(2^(2/3)-x)/(-x^3+1)^(1/2),x)","\frac{4 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}+\frac{2 i 2^{\frac{2}{3}} \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}\right)}"," ",0,"4/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+2*I*2^(2/3)*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","C"
45,1,262,28,0.059000," ","int((2^(2/3)+2*x)/(2^(2/3)-x)/(x^3-1)^(1/2),x)","-\frac{4 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{6 \,2^{\frac{2}{3}} \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-2^{\frac{2}{3}}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-2^{\frac{2}{3}}+1\right)}"," ",0,"-4*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-6*2^(2/3)*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)/(-2^(2/3)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-2^(2/3)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","C"
46,1,249,29,0.056000," ","int((2^(2/3)-2*x)/(2^(2/3)+x)/(-x^3-1)^(1/2),x)","\frac{4 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 i 2^{\frac{2}{3}} \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}\, \left(2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"4/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2*I*2^(2/3)*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","C"
47,0,0,43,0.368000," ","int((2^(2/3)*a^(1/3)-2*b^(1/3)*x)/(b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3+a)^(1/2),x)","\int \frac{-2 b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}}{\left(b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((2^(2/3)*a^(1/3)-2*b^(1/3)*x)/(b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3+a)^(1/2),x)","F"
48,0,0,45,0.353000," ","int((2^(2/3)*a^(1/3)+2*b^(1/3)*x)/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{2 b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}}{\left(-b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((2^(2/3)*a^(1/3)+2*b^(1/3)*x)/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
49,0,0,46,0.153000," ","int((2*b^(1/3)*x+2^(2/3)*a^(1/3))/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{2 b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}}{\left(-b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((2*b^(1/3)*x+2^(2/3)*a^(1/3))/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
50,0,0,46,0.156000," ","int((-2*b^(1/3)*x+2^(2/3)*a^(1/3))/(b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{-2 b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}}{\left(b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int((-2*b^(1/3)*x+2^(2/3)*a^(1/3))/(b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
51,1,889,39,0.073000," ","int((-2*d*x+c)/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x)","\frac{6 \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}\right) \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \sqrt{\frac{x +\frac{2^{\frac{1}{3}} c}{2 d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, c \EllipticPi \left(\sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}, \frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{c}{d}}, \sqrt{\frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\right)}{\sqrt{4 d^{3} x^{3}+c^{3}}\, \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{c}{d}\right) d}-\frac{4 \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}\right) \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \sqrt{\frac{x +\frac{2^{\frac{1}{3}} c}{2 d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}, \sqrt{\frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\right)}{\sqrt{4 d^{3} x^{3}+c^{3}}}"," ",0,"-4*((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)*((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)*((x+1/2*2^(1/3)*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2)*((x-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)/(4*d^3*x^3+c^3)^(1/2)*EllipticF(((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2),(((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2))+6*c/d*((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)*((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)*((x+1/2*2^(1/3)*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2)*((x-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)/(4*d^3*x^3+c^3)^(1/2)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+c/d)*EllipticPi(((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2),((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+c/d),(((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2))","C"
52,1,262,125,0.044000," ","int((3*x+2)/(2^(2/3)+x)/(x^3+1)^(1/2),x)","\frac{6 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(2-3 \,2^{\frac{2}{3}}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{2^{\frac{2}{3}}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(2^{\frac{2}{3}}-1\right)}"," ",0,"6*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*(2-3*2^(2/3))*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)/(2^(2/3)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(2^(2/3)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
53,1,257,140,0.045000," ","int((3*x+2)/(2^(2/3)-x)/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}}-\frac{2 i \left(-2-3 \,2^{\frac{2}{3}}\right) \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}\right)}"," ",0,"2*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(-2-3*2^(2/3))*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
54,1,266,138,0.036000," ","int((3*x+2)/(2^(2/3)-x)/(x^3-1)^(1/2),x)","-\frac{6 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \left(-2-3 \,2^{\frac{2}{3}}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-2^{\frac{2}{3}}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-2^{\frac{2}{3}}+1\right)}"," ",0,"-6*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2*(-2-3*2^(2/3))*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)/(-2^(2/3)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-2^(2/3)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
55,1,253,135,0.036000," ","int((3*x+2)/(2^(2/3)+x)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}}-\frac{2 i \left(2-3 \,2^{\frac{2}{3}}\right) \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(2-3*2^(2/3))*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
56,1,264,126,0.039000," ","int((f*x+e)/(2^(2/3)+x)/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(e -2^{\frac{2}{3}} f \right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{2^{\frac{2}{3}}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(2^{\frac{2}{3}}-1\right)}"," ",0,"2*f*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*(e-2^(2/3)*f)*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)/(2^(2/3)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(2^(2/3)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
57,1,261,142,0.040000," ","int((f*x+e)/(2^(2/3)-x)/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \left(-e -2^{\frac{2}{3}} f \right) \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}\right)}"," ",0,"2/3*I*f*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(-e-2^(2/3)*f)*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
58,1,270,140,0.036000," ","int((f*x+e)/(2^(2/3)-x)/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \left(-e -2^{\frac{2}{3}} f \right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-2^{\frac{2}{3}}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-2^{\frac{2}{3}}+1\right)}"," ",0,"-2*f*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2*(-e-2^(2/3)*f)*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)/(-2^(2/3)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-2^(2/3)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
59,1,255,136,0.039000," ","int((f*x+e)/(2^(2/3)+x)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 i \left(e -2^{\frac{2}{3}} f \right) \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*f*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(e-2^(2/3)*f)*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
60,0,0,227,0.113000," ","int((f*x+e)/(b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3+a)^(1/2),x)","\int \frac{f x +e}{\left(b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((f*x+e)/(b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3+a)^(1/2),x)","F"
61,0,0,235,0.108000," ","int((f*x+e)/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{f x +e}{\left(-b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((f*x+e)/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
62,0,0,242,0.099000," ","int((f*x+e)/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{f x +e}{\left(-b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((f*x+e)/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
63,0,0,238,0.105000," ","int((f*x+e)/(b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{f x +e}{\left(b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int((f*x+e)/(b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
64,1,900,216,0.013000," ","int((f*x+e)/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x)","\frac{2 \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}\right) \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \sqrt{\frac{x +\frac{2^{\frac{1}{3}} c}{2 d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, f \EllipticF \left(\sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}, \sqrt{\frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\right)}{\sqrt{4 d^{3} x^{3}+c^{3}}\, d}+\frac{2 \left(-c f +d e \right) \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}\right) \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \sqrt{\frac{x +\frac{2^{\frac{1}{3}} c}{2 d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}, \frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{c}{d}}, \sqrt{\frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\right)}{\sqrt{4 d^{3} x^{3}+c^{3}}\, \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{c}{d}\right) d^{2}}"," ",0,"2*f/d*((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)*((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)*((x+1/2*2^(1/3)*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2)*((x-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)/(4*d^3*x^3+c^3)^(1/2)*EllipticF(((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2),(((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2))+2*(-c*f+d*e)/d^2*((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)*((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)*((x+1/2*2^(1/3)*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2)*((x-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)/(4*d^3*x^3+c^3)^(1/2)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+c/d)*EllipticPi(((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2),((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+c/d),(((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2))","B"
65,1,258,114,0.037000," ","int(x/(2^(2/3)+x)/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 \,2^{\frac{2}{3}} \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{2^{\frac{2}{3}}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(2^{\frac{2}{3}}-1\right)}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-2*2^(2/3)*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)/(2^(2/3)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(2^(2/3)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
66,1,253,129,0.038000," ","int(x/(2^(2/3)-x)/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}+\frac{2 i 2^{\frac{2}{3}} \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}-2^{\frac{2}{3}}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*2^(2/3)*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)-2^(2/3)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
67,1,262,127,0.032000," ","int(x/(2^(2/3)-x)/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \,2^{\frac{2}{3}} \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-2^{\frac{2}{3}}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-2^{\frac{2}{3}}+1\right)}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2*2^(2/3)*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)/(-2^(2/3)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-2^(2/3)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","B"
68,1,249,124,0.032000," ","int(x/(2^(2/3)+x)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{2 i 2^{\frac{2}{3}} \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(2^{\frac{2}{3}}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*2^(2/3)*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(2^(2/3)+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
69,0,0,198,0.095000," ","int(x/(b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3+a)^(1/2),x)","\int \frac{x}{\left(b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int(x/(b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3+a)^(1/2),x)","F"
70,0,0,206,0.102000," ","int(x/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{x}{\left(-b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int(x/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
71,0,0,213,0.094000," ","int(x/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{x}{\left(-b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int(x/(-b^(1/3)*x+2^(2/3)*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
72,0,0,209,0.093000," ","int(x/(b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{x}{\left(b^{\frac{1}{3}} x +2^{\frac{2}{3}} a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int(x/(b^(1/3)*x+2^(2/3)*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
73,1,892,197,0.013000," ","int(x/(d*x+c)/(4*d^3*x^3+c^3)^(1/2),x)","-\frac{2 \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}\right) \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \sqrt{\frac{x +\frac{2^{\frac{1}{3}} c}{2 d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, c \EllipticPi \left(\sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}, \frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{c}{d}}, \sqrt{\frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\right)}{\sqrt{4 d^{3} x^{3}+c^{3}}\, \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{c}{d}\right) d^{2}}+\frac{2 \left(\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}\right) \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \sqrt{\frac{x +\frac{2^{\frac{1}{3}} c}{2 d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}}, \sqrt{\frac{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}-\frac{\left(\frac{2^{\frac{1}{3}}}{4}-\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}}{\frac{\left(\frac{2^{\frac{1}{3}}}{4}+\frac{i \sqrt{3}\, 2^{\frac{1}{3}}}{4}\right) c}{d}+\frac{2^{\frac{1}{3}} c}{2 d}}}\right)}{\sqrt{4 d^{3} x^{3}+c^{3}}\, d}"," ",0,"2/d*((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)*((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)*((x+1/2*2^(1/3)*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2)*((x-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)/(4*d^3*x^3+c^3)^(1/2)*EllipticF(((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2),(((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2))-2*c/d^2*((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)*((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)*((x+1/2*2^(1/3)*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2)*((x-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2)/(4*d^3*x^3+c^3)^(1/2)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+c/d)*EllipticPi(((x-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d))^(1/2),((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+c/d),(((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d-(1/4*2^(1/3)-1/4*I*3^(1/2)*2^(1/3))*c/d)/((1/4*2^(1/3)+1/4*I*3^(1/2)*2^(1/3))*c/d+1/2*2^(1/3)*c/d))^(1/2))","B"
74,1,240,17,0.045000," ","int((x+1)/(2-x)/(x^3+1)^(1/2),x)","-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-\frac{i \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}"," ",0,"-2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),1/2-1/6*I*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","C"
75,1,240,21,0.038000," ","int((1-x)/(x+2)/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}\, \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(3/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(3/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","C"
76,1,240,19,0.042000," ","int((1-x)/(x+2)/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/2+1/6*I*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","C"
77,1,240,19,0.037000," ","int((x+1)/(2-x)/(-x^3-1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}\, \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(-3/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-3/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","C"
78,0,0,34,0.132000," ","int((a^(1/3)+b^(1/3)*x)/(2*a^(1/3)-b^(1/3)*x)/(b*x^3+a)^(1/2),x)","\int \frac{b^{\frac{1}{3}} x +a^{\frac{1}{3}}}{\left(-b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((a^(1/3)+b^(1/3)*x)/(2*a^(1/3)-b^(1/3)*x)/(b*x^3+a)^(1/2),x)","F"
79,0,0,36,0.128000," ","int((a^(1/3)-b^(1/3)*x)/(2*a^(1/3)+b^(1/3)*x)/(-b*x^3+a)^(1/2),x)","\int \frac{-b^{\frac{1}{3}} x +a^{\frac{1}{3}}}{\left(b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((a^(1/3)-b^(1/3)*x)/(2*a^(1/3)+b^(1/3)*x)/(-b*x^3+a)^(1/2),x)","F"
80,0,0,37,0.119000," ","int((-b^(1/3)*x+a^(1/3))/(b^(1/3)*x+2*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{-b^{\frac{1}{3}} x +a^{\frac{1}{3}}}{\left(b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((-b^(1/3)*x+a^(1/3))/(b^(1/3)*x+2*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
81,0,0,37,0.122000," ","int((b^(1/3)*x+a^(1/3))/(-b^(1/3)*x+2*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{b^{\frac{1}{3}} x +a^{\frac{1}{3}}}{\left(-b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int((b^(1/3)*x+a^(1/3))/(-b^(1/3)*x+2*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
82,1,650,36,0.195000," ","int((-2*d*x+c)/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x)","\frac{6 \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}\right) \sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \sqrt{\frac{x -\frac{c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, c \EllipticPi \left(\sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}, \frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}+\frac{c}{d}}, \sqrt{\frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\right)}{\sqrt{-8 d^{3} x^{3}+c^{3}}\, \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}+\frac{c}{d}\right) d}-\frac{4 \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}\right) \sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \sqrt{\frac{x -\frac{c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}, \sqrt{\frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\right)}{\sqrt{-8 d^{3} x^{3}+c^{3}}}"," ",0,"-4*(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d)*((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2)*((x-1/2*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2)*((x-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d))^(1/2)/(-8*d^3*x^3+c^3)^(1/2)*EllipticF(((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2),((1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2))+6*c/d*(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d)*((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2)*((x-1/2*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2)*((x-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d))^(1/2)/(-8*d^3*x^3+c^3)^(1/2)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d+c/d)*EllipticPi(((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2),(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d+c/d),((1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2))","C"
83,1,246,114,0.011000," ","int((f*x+e)/(2-x)/(x^3+1)^(1/2),x)","-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(e +2 f \right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-\frac{i \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}"," ",0,"-2*f*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2/3*(e+2*f)*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),1/2-1/6*I*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
84,1,246,128,0.011000," ","int((f*x+e)/(x+2)/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \left(e -2 f \right) \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*f*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(e-2*f)*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(3/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(3/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
85,1,246,126,0.012000," ","int((f*x+e)/(x+2)/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \left(e -2 f \right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}"," ",0,"2*f*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2/3*(e-2*f)*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/2+1/6*I*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
86,1,246,124,0.010000," ","int((f*x+e)/(2-x)/(-x^3-1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{2 i \left(e +2 f \right) \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"2/3*I*f*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*(e+2*f)*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(-3/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-3/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
87,0,0,216,0.097000," ","int((f*x+e)/(-b^(1/3)*x+2*a^(1/3))/(b*x^3+a)^(1/2),x)","\int \frac{f x +e}{\left(-b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((f*x+e)/(-b^(1/3)*x+2*a^(1/3))/(b*x^3+a)^(1/2),x)","F"
88,0,0,223,0.094000," ","int((f*x+e)/(b^(1/3)*x+2*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{f x +e}{\left(b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((f*x+e)/(b^(1/3)*x+2*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
89,0,0,230,0.086000," ","int((f*x+e)/(b^(1/3)*x+2*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{f x +e}{\left(b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((f*x+e)/(b^(1/3)*x+2*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
90,0,0,227,0.095000," ","int((f*x+e)/(-b^(1/3)*x+2*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{f x +e}{\left(-b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int((f*x+e)/(-b^(1/3)*x+2*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
91,1,661,192,0.013000," ","int((f*x+e)/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x)","\frac{2 \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}\right) \sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \sqrt{\frac{x -\frac{c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, f \EllipticF \left(\sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}, \sqrt{\frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\right)}{\sqrt{-8 d^{3} x^{3}+c^{3}}\, d}+\frac{2 \left(-c f +d e \right) \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}\right) \sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \sqrt{\frac{x -\frac{c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \EllipticPi \left(\sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}, \frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}+\frac{c}{d}}, \sqrt{\frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\right)}{\sqrt{-8 d^{3} x^{3}+c^{3}}\, \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}+\frac{c}{d}\right) d^{2}}"," ",0,"2*f/d*(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d)*((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2)*((x-1/2*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2)*((x-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d))^(1/2)/(-8*d^3*x^3+c^3)^(1/2)*EllipticF(((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2),((1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2))+2*(-c*f+d*e)/d^2*(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d)*((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2)*((x-1/2*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2)*((x-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d))^(1/2)/(-8*d^3*x^3+c^3)^(1/2)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d+c/d)*EllipticPi(((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2),(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d+c/d),((1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2))","B"
92,1,240,104,0.010000," ","int(x/(2-x)/(x^3+1)^(1/2),x)","-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{4 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{2}-\frac{i \sqrt{3}}{6}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}"," ",0,"-2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+4/3*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),1/2-1/6*I*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
93,1,240,120,0.008000," ","int(x/(x+2)/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}+\frac{4 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+4/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(3/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(3/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
94,1,240,118,0.010000," ","int(x/(x+2)/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{4 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{1}{2}+\frac{i \sqrt{3}}{6}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}"," ",0,"2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-4/3*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/2+1/6*I*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","B"
95,1,240,114,0.010000," ","int(x/(2-x)/(-x^3-1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{4 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+4/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(-3/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-3/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","B"
96,0,0,189,0.086000," ","int(x/(-b^(1/3)*x+2*a^(1/3))/(b*x^3+a)^(1/2),x)","\int \frac{x}{\left(-b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int(x/(-b^(1/3)*x+2*a^(1/3))/(b*x^3+a)^(1/2),x)","F"
97,0,0,197,0.086000," ","int(x/(b^(1/3)*x+2*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{x}{\left(b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int(x/(b^(1/3)*x+2*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
98,0,0,204,0.078000," ","int(x/(b^(1/3)*x+2*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{x}{\left(b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int(x/(b^(1/3)*x+2*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
99,0,0,200,0.086000," ","int(x/(-b^(1/3)*x+2*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{x}{\left(-b^{\frac{1}{3}} x +2 a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int(x/(-b^(1/3)*x+2*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
100,1,653,173,0.012000," ","int(x/(d*x+c)/(-8*d^3*x^3+c^3)^(1/2),x)","-\frac{2 \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}\right) \sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \sqrt{\frac{x -\frac{c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, c \EllipticPi \left(\sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}, \frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}+\frac{c}{d}}, \sqrt{\frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\right)}{\sqrt{-8 d^{3} x^{3}+c^{3}}\, \left(\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}+\frac{c}{d}\right) d^{2}}+\frac{2 \left(\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}\right) \sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \sqrt{\frac{x -\frac{c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\, \sqrt{\frac{x -\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}}\, \EllipticF \left(\sqrt{\frac{x -\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}}}, \sqrt{\frac{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) c}{2 d}}{\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) c}{2 d}-\frac{c}{2 d}}}\right)}{\sqrt{-8 d^{3} x^{3}+c^{3}}\, d}"," ",0,"2/d*(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d)*((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2)*((x-1/2*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2)*((x-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d))^(1/2)/(-8*d^3*x^3+c^3)^(1/2)*EllipticF(((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2),((1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2))-2*c/d^2*(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d)*((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2)*((x-1/2*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2)*((x-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d))^(1/2)/(-8*d^3*x^3+c^3)^(1/2)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d+c/d)*EllipticPi(((x-1/2*(-1/2-1/2*I*3^(1/2))*c/d)/(1/2*(-1/2+1/2*I*3^(1/2))*c/d-1/2*(-1/2-1/2*I*3^(1/2))*c/d))^(1/2),(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d+c/d),((1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*(-1/2+1/2*I*3^(1/2))*c/d)/(1/2*(-1/2-1/2*I*3^(1/2))*c/d-1/2*c/d))^(1/2))","B"
101,1,245,32,0.085000," ","int((1+x+3^(1/2))/(1+x-3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{4 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-4*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","C"
102,1,243,36,0.075000," ","int((1-x+3^(1/2))/(1-x-3^(1/2))/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}+\frac{4 i \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}\, \left(-\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+4*I*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-3/2+3^(1/2)+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-3/2+3^(1/2)+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","C"
103,1,245,34,0.063000," ","int((1-x+3^(1/2))/(1-x-3^(1/2))/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{4 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}"," ",0,"2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-4*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","C"
104,1,247,34,0.070000," ","int((1+x+3^(1/2))/(1+x-3^(1/2))/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{4 i \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}\, \left(\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-4*I*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(3/2+1/2*I*3^(1/2)-3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(3/2+1/2*I*3^(1/2)-3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","C"
105,0,0,49,0.223000," ","int((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x)","\int \frac{b^{\frac{1}{3}} x +\left(1+\sqrt{3}\right) a^{\frac{1}{3}}}{\left(b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x)","F"
106,0,0,51,0.219000," ","int((-b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{-b^{\frac{1}{3}} x +\left(1+\sqrt{3}\right) a^{\frac{1}{3}}}{\left(-b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((-b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
107,0,0,52,0.138000," ","int((-b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{-b^{\frac{1}{3}} x +\left(1+\sqrt{3}\right) a^{\frac{1}{3}}}{\left(-b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((-b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
108,0,0,52,0.145000," ","int((b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{b^{\frac{1}{3}} x +\left(1+\sqrt{3}\right) a^{\frac{1}{3}}}{\left(b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int((b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
109,0,0,55,0.195000," ","int((1+(1/a*b)^(1/3)*x+3^(1/2))/(1+(1/a*b)^(1/3)*x-3^(1/2))/(b*x^3+a)^(1/2),x)","\int \frac{\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1+\sqrt{3}}{\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1-\sqrt{3}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((1+(1/a*b)^(1/3)*x+3^(1/2))/(1+(1/a*b)^(1/3)*x-3^(1/2))/(b*x^3+a)^(1/2),x)","F"
110,0,0,57,0.186000," ","int((1-(1/a*b)^(1/3)*x+3^(1/2))/(1-(1/a*b)^(1/3)*x-3^(1/2))/(-b*x^3+a)^(1/2),x)","\int \frac{-\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1+\sqrt{3}}{\left(-\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1-\sqrt{3}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((1-(1/a*b)^(1/3)*x+3^(1/2))/(1-(1/a*b)^(1/3)*x-3^(1/2))/(-b*x^3+a)^(1/2),x)","F"
111,0,0,58,0.127000," ","int((-(1/a*b)^(1/3)*x+1+3^(1/2))/(-(1/a*b)^(1/3)*x+1-3^(1/2))/(b*x^3-a)^(1/2),x)","\int \frac{-\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1+\sqrt{3}}{\left(-\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1-\sqrt{3}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((-(1/a*b)^(1/3)*x+1+3^(1/2))/(-(1/a*b)^(1/3)*x+1-3^(1/2))/(b*x^3-a)^(1/2),x)","F"
112,0,0,58,0.136000," ","int(((1/a*b)^(1/3)*x+1+3^(1/2))/((1/a*b)^(1/3)*x+1-3^(1/2))/(-b*x^3-a)^(1/2),x)","\int \frac{\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1+\sqrt{3}}{\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1-\sqrt{3}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int(((1/a*b)^(1/3)*x+1+3^(1/2))/((1/a*b)^(1/3)*x+1-3^(1/2))/(-b*x^3-a)^(1/2),x)","F"
113,1,245,32,0.033000," ","int((1+x-3^(1/2))/(1+x+3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{4 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-4*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","C"
114,1,247,36,0.037000," ","int((1-x-3^(1/2))/(1-x+3^(1/2))/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{4 i \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}\, \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-4*I*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-3/2+1/2*I*3^(1/2)-3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-3/2+1/2*I*3^(1/2)-3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","C"
115,1,245,34,0.034000," ","int((1-x-3^(1/2))/(1-x+3^(1/2))/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{4 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}"," ",0,"2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-4*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","C"
116,1,243,34,0.028000," ","int((1+x-3^(1/2))/(1+x+3^(1/2))/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{4 i \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}\, \left(\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+4*I*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(3/2+3^(1/2)+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(3/2+3^(1/2)+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","C"
117,0,0,49,0.187000," ","int((b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(b*x^3+a)^(1/2),x)","\int \frac{b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}}{\left(b^{\frac{1}{3}} x +\left(1+\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(b*x^3+a)^(1/2),x)","F"
118,0,0,51,0.189000," ","int((-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{-b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}}{\left(-b^{\frac{1}{3}} x +\left(1+\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
119,0,0,52,0.129000," ","int((-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{-b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}}{\left(-b^{\frac{1}{3}} x +\left(1+\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
120,0,0,52,0.136000," ","int((b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}}{\left(b^{\frac{1}{3}} x +\left(1+\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int((b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b^(1/3)*x+(1+3^(1/2))*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
121,0,0,55,0.174000," ","int(((1/a*b)^(1/3)*x+1-3^(1/2))/((1/a*b)^(1/3)*x+1+3^(1/2))/(b*x^3+a)^(1/2),x)","\int \frac{\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1-\sqrt{3}}{\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1+\sqrt{3}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int(((1/a*b)^(1/3)*x+1-3^(1/2))/((1/a*b)^(1/3)*x+1+3^(1/2))/(b*x^3+a)^(1/2),x)","F"
122,0,0,57,0.179000," ","int((-(1/a*b)^(1/3)*x+1-3^(1/2))/(-(1/a*b)^(1/3)*x+1+3^(1/2))/(-b*x^3+a)^(1/2),x)","\int \frac{-\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1-\sqrt{3}}{\left(-\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1+\sqrt{3}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((-(1/a*b)^(1/3)*x+1-3^(1/2))/(-(1/a*b)^(1/3)*x+1+3^(1/2))/(-b*x^3+a)^(1/2),x)","F"
123,0,0,58,0.125000," ","int((-(1/a*b)^(1/3)*x+1-3^(1/2))/(-(1/a*b)^(1/3)*x+1+3^(1/2))/(b*x^3-a)^(1/2),x)","\int \frac{-\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1-\sqrt{3}}{\left(-\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1+\sqrt{3}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((-(1/a*b)^(1/3)*x+1-3^(1/2))/(-(1/a*b)^(1/3)*x+1+3^(1/2))/(b*x^3-a)^(1/2),x)","F"
124,0,0,58,0.129000," ","int(((1/a*b)^(1/3)*x+1-3^(1/2))/((1/a*b)^(1/3)*x+1+3^(1/2))/(-b*x^3-a)^(1/2),x)","\int \frac{\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1-\sqrt{3}}{\left(\left(\frac{b}{a}\right)^{\frac{1}{3}} x +1+\sqrt{3}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int(((1/a*b)^(1/3)*x+1-3^(1/2))/((1/a*b)^(1/3)*x+1+3^(1/2))/(-b*x^3-a)^(1/2),x)","F"
125,1,245,119,0.036000," ","int((x+1)/(1+x+3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
126,1,245,119,0.038000," ","int((x+1)/(1+x-3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
127,1,260,141,0.039000," ","int((f*x+e)/(1+x+3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(e -f -\sqrt{3}\, f \right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}"," ",0,"2*f*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2/3*(e-f-f*3^(1/2))*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*3^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
128,1,264,154,0.041000," ","int((f*x+e)/(1-x+3^(1/2))/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \left(-e -f -\sqrt{3}\, f \right) \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}\right)}"," ",0,"2/3*I*f*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(-e-f-3^(1/2)*f)*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-3/2+1/2*I*3^(1/2)-3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-3/2+1/2*I*3^(1/2)-3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
129,1,262,152,0.040000," ","int((f*x+e)/(1-x+3^(1/2))/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \left(-e -f -\sqrt{3}\, f \right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}"," ",0,"-2*f*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2/3*(-e-f-3^(1/2)*f)*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*3^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
130,1,258,150,0.039000," ","int((f*x+e)/(1+x+3^(1/2))/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 i \left(e -f -\sqrt{3}\, f \right) \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*f*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(e-f-3^(1/2)*f)*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(3/2+3^(1/2)+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(3/2+3^(1/2)+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
131,0,0,243,0.116000," ","int((f*x+e)/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3+a)^(1/2),x)","\int \frac{f x +e}{\left(b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int((f*x+e)/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3+a)^(1/2),x)","F"
132,0,0,248,0.115000," ","int((f*x+e)/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{f x +e}{\left(-b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int((f*x+e)/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
133,0,0,255,0.102000," ","int((f*x+e)/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{f x +e}{\left(-b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int((f*x+e)/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
134,0,0,254,0.112000," ","int((f*x+e)/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{f x +e}{\left(b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int((f*x+e)/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
135,1,255,108,0.036000," ","int(x/(1+x+3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(-1-\sqrt{3}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2/3*(-1-3^(1/2))*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*3^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
136,1,257,124,0.037000," ","int(x/(1-x+3^(1/2))/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \left(-1-\sqrt{3}\right) \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}-\sqrt{3}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(-1-3^(1/2))*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-3/2+1/2*I*3^(1/2)-3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-3/2+1/2*I*3^(1/2)-3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","B"
137,1,255,130,0.034000," ","int(x/(1-x+3^(1/2))/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \left(-1-\sqrt{3}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}-1}}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2/3*(-1-3^(1/2))*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*3^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(3/2+1/2*I*3^(1/2))*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
138,1,253,126,0.033000," ","int(x/(1+x+3^(1/2))/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 i \left(-1-\sqrt{3}\right) \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{3}{2}+\sqrt{3}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(-1-3^(1/2))*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(3/2+3^(1/2)+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(3/2+3^(1/2)+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
139,1,255,116,0.036000," ","int(x/(1+x-3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(1-\sqrt{3}\right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}{3}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2/3*(1-3^(1/2))*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*3^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),-1/3*(-3/2+1/2*I*3^(1/2))*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
140,0,0,201,0.115000," ","int(x/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3+a)^(1/2),x)","\int \frac{x}{\left(b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}+a}}\, dx"," ",0,"int(x/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3+a)^(1/2),x)","F"
141,0,0,209,0.105000," ","int(x/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3+a)^(1/2),x)","\int \frac{x}{\left(-b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}+a}}\, dx"," ",0,"int(x/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3+a)^(1/2),x)","F"
142,0,0,208,0.092000," ","int(x/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3-a)^(1/2),x)","\int \frac{x}{\left(-b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{b \,x^{3}-a}}\, dx"," ",0,"int(x/(-b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(b*x^3-a)^(1/2),x)","F"
143,0,0,204,0.102000," ","int(x/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3-a)^(1/2),x)","\int \frac{x}{\left(b^{\frac{1}{3}} x +\left(1-\sqrt{3}\right) a^{\frac{1}{3}}\right) \sqrt{-b \,x^{3}-a}}\, dx"," ",0,"int(x/(b^(1/3)*x+(1-3^(1/2))*a^(1/3))/(-b*x^3-a)^(1/2),x)","F"
144,1,275,262,0.069000," ","int((1+x+3^(1/2))/(d*x+c)/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, d}+\frac{2 \left(-c +\sqrt{3}\, d +d \right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{c}{d}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(\frac{c}{d}-1\right) d^{2}}"," ",0,"2/d*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*(d*3^(1/2)-c+d)/d^2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)/(-1+c/d)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+c/d),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
145,1,264,270,0.066000," ","int((1-x+3^(1/2))/(d*x+c)/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, d}-\frac{2 i \left(c +d +\sqrt{3}\, d \right) \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{c}{d}-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{c}{d}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) d^{2}}"," ",0,"2/3*I/d*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(c+d+3^(1/2)*d)/d^2*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+c/d)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+c/d),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
146,1,273,266,0.068000," ","int((1-x+3^(1/2))/(d*x+c)/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, d}+\frac{2 \left(c +d +\sqrt{3}\, d \right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{c}{d}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(\frac{c}{d}+1\right) d^{2}}"," ",0,"-2/d*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2*(c+d+3^(1/2)*d)/d^2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)/(1+c/d)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+c/d),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
147,1,266,266,0.063000," ","int((1+x+3^(1/2))/(d*x+c)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, d}-\frac{2 i \left(-c +\sqrt{3}\, d +d \right) \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{c}{d}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{c}{d}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) d^{2}}"," ",0,"-2/3*I/d*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(-c+3^(1/2)*d+d)/d^2*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+c/d)*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+c/d),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
148,1,275,304,0.033000," ","int((1+x-3^(1/2))/(d*x+c)/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, d}-\frac{2 \left(c +\sqrt{3}\, d -d \right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{c}{d}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(\frac{c}{d}-1\right) d^{2}}"," ",0,"2/d*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-2*(3^(1/2)*d+c-d)/d^2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)/(c/d-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(c/d-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
149,1,268,280,0.031000," ","int((1-x-3^(1/2))/(d*x+c)/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, d}+\frac{2 i \left(-c +\sqrt{3}\, d -d \right) \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{c}{d}-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{c}{d}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) d^{2}}"," ",0,"2/3*I/d*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*(3^(1/2)*d-c-d)/d^2*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(c/d-1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(c/d-1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
150,1,277,276,0.031000," ","int((1-x-3^(1/2))/(d*x+c)/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, d}-\frac{2 \left(-c +\sqrt{3}\, d -d \right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{c}{d}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(\frac{c}{d}+1\right) d^{2}}"," ",0,"-2/d*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2*(-c+3^(1/2)*d-d)/d^2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)/(c/d+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(c/d+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
151,1,266,308,0.033000," ","int((1+x-3^(1/2))/(d*x+c)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, d}+\frac{2 i \left(c +\sqrt{3}\, d -d \right) \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{c}{d}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{c}{d}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) d^{2}}"," ",0,"-2/3*I/d*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*(c+3^(1/2)*d-d)/d^2*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(c/d+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(c/d+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
152,1,132,102,0.061000," ","int((1+x+3^(1/2))/x/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 \left(1+\sqrt{3}\right) \arctanh \left(\sqrt{x^{3}+1}\right)}{3}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-2/3*arctanh((x^3+1)^(1/2))*(1+3^(1/2))","A"
153,1,125,116,0.056000," ","int((1-x+3^(1/2))/x/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 \left(1+\sqrt{3}\right) \arctanh \left(\sqrt{-x^{3}+1}\right)}{3}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*arctanh((-x^3+1)^(1/2))*(1+3^(1/2))","A"
154,1,140,114,0.053000," ","int((1-x+3^(1/2))/x/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \sqrt{3}\, \arctan \left(\sqrt{x^{3}-1}\right)}{3}+\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2/3*arctan((x^3-1)^(1/2))*3^(1/2)+2/3*arctan((x^3-1)^(1/2))","A"
155,1,135,112,0.049000," ","int((1+x+3^(1/2))/x/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{2 \sqrt{3}\, \arctan \left(\sqrt{-x^{3}-1}\right)}{3}+\frac{2 \arctan \left(\sqrt{-x^{3}-1}\right)}{3}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*arctan((-x^3-1)^(1/2))*3^(1/2)+2/3*arctan((-x^3-1)^(1/2))","A"
156,1,132,104,0.031000," ","int((1+x-3^(1/2))/x/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(\sqrt{3}-1\right) \arctanh \left(\sqrt{x^{3}+1}\right)}{3}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2/3*(3^(1/2)-1)*arctanh((x^3+1)^(1/2))","A"
157,1,125,118,0.027000," ","int((1-x-3^(1/2))/x/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}+\frac{2 \left(\sqrt{3}-1\right) \arctanh \left(\sqrt{-x^{3}+1}\right)}{3}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+2/3*(3^(1/2)-1)*arctanh((-x^3+1)^(1/2))","A"
158,1,140,116,0.023000," ","int((1-x-3^(1/2))/x/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \sqrt{3}\, \arctan \left(\sqrt{x^{3}-1}\right)}{3}+\frac{2 \arctan \left(\sqrt{x^{3}-1}\right)}{3}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2/3*3^(1/2)*arctan((x^3-1)^(1/2))+2/3*arctan((x^3-1)^(1/2))","A"
159,1,135,114,0.026000," ","int((1+x-3^(1/2))/x/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 \sqrt{3}\, \arctan \left(\sqrt{-x^{3}-1}\right)}{3}+\frac{2 \arctan \left(\sqrt{-x^{3}-1}\right)}{3}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*3^(1/2)*arctan((-x^3-1)^(1/2))+2/3*arctan((-x^3-1)^(1/2))","A"
160,1,240,269,0.009000," ","int(x/(x+3)/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{3 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, -\frac{3}{4}+\frac{i \sqrt{3}}{4}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-3*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),-3/4+1/4*I*3^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
161,1,240,299,0.010000," ","int(x/(x+3)/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}+\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{5}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}\, \left(\frac{5}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+2*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(5/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(5/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
162,1,240,294,0.010000," ","int(x/(x+3)/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{3 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{3}{8}+\frac{i \sqrt{3}}{8}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{2 \sqrt{x^{3}-1}}"," ",0,"2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-3/2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),3/8+1/8*I*3^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
163,1,240,279,0.009000," ","int(x/(x+3)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{7}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}\, \left(\frac{7}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(7/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(7/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
164,1,274,378,0.013000," ","int((f*x+e)/(d*x+c)/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, d}+\frac{2 \left(-c f +d e \right) \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{c}{d}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(\frac{c}{d}-1\right) d^{2}}"," ",0,"2*f/d*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*(-c*f+d*e)/d^2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)/(c/d-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(c/d-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
165,1,265,398,0.012000," ","int((f*x+e)/(d*x+c)/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, d}-\frac{2 i \left(-c f +d e \right) \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{c}{d}-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{c}{d}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) d^{2}}"," ",0,"-2/3*I*f/d*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(-c*f+d*e)/d^2*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)/(c/d-1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(c/d-1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
166,1,274,394,0.011000," ","int((f*x+e)/(d*x+c)/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, d}+\frac{2 \left(-c f +d e \right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{c}{d}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(\frac{c}{d}+1\right) d^{2}}"," ",0,"2*f/d*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2*(-c*f+d*e)/d^2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)/(c/d+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(c/d+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
167,1,265,390,0.011000," ","int((f*x+e)/(d*x+c)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, d}-\frac{2 i \left(-c f +d e \right) \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{c}{d}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{c}{d}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) d^{2}}"," ",0,"-2/3*I*f/d*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*(-c*f+d*e)/d^2*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)/(c/d+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(c/d+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
168,1,129,99,0.009000," ","int((f*x+e)/x/(x^3+1)^(1/2),x)","-\frac{2 e \arctanh \left(\sqrt{x^{3}+1}\right)}{3}+\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}"," ",0,"2*f*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-2/3*e*arctanh((x^3+1)^(1/2))","A"
169,1,122,113,0.009000," ","int((f*x+e)/x/(-x^3+1)^(1/2),x)","-\frac{2 e \arctanh \left(\sqrt{-x^{3}+1}\right)}{3}-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}"," ",0,"-2/3*I*f*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*e*arctanh((-x^3+1)^(1/2))","A"
170,1,129,111,0.009000," ","int((f*x+e)/x/(x^3-1)^(1/2),x)","\frac{2 e \arctan \left(\sqrt{x^{3}-1}\right)}{3}+\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, f \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}"," ",0,"2*f*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2/3*e*arctan((x^3-1)^(1/2))","A"
171,1,122,109,0.009000," ","int((f*x+e)/x/(-x^3-1)^(1/2),x)","\frac{2 e \arctan \left(\sqrt{-x^{3}-1}\right)}{3}-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, f \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}"," ",0,"-2/3*I*f*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*e*arctan((-x^3-1)^(1/2))","A"
172,0,0,86,0.070000," ","int((-d*x+c)/(d*x+c)/(d^3*x^3+2*c^3)^(1/3),x)","\int \frac{-d x +c}{\left(d x +c \right) \left(d^{3} x^{3}+2 c^{3}\right)^{\frac{1}{3}}}\, dx"," ",0,"int((-d*x+c)/(d*x+c)/(d^3*x^3+2*c^3)^(1/3),x)","F"
173,0,0,203,0.066000," ","int((f*x+e)/(d*x+c)/(d^3*x^3-c^3)^(1/3),x)","\int \frac{f x +e}{\left(d x +c \right) \left(d^{3} x^{3}-c^{3}\right)^{\frac{1}{3}}}\, dx"," ",0,"int((f*x+e)/(d*x+c)/(d^3*x^3-c^3)^(1/3),x)","F"
174,1,451,160,0.010000," ","int(x^2*(b*x+a)^n*(d*x^3+c),x)","-\frac{\left(-b^{5} d \,n^{5} x^{5}-15 b^{5} d \,n^{4} x^{5}+5 a \,b^{4} d \,n^{4} x^{4}-85 b^{5} d \,n^{3} x^{5}+50 a \,b^{4} d \,n^{3} x^{4}-b^{5} c \,n^{5} x^{2}-225 b^{5} d \,n^{2} x^{5}-20 a^{2} b^{3} d \,n^{3} x^{3}+175 a \,b^{4} d \,n^{2} x^{4}-18 b^{5} c \,n^{4} x^{2}-274 b^{5} d n \,x^{5}-120 a^{2} b^{3} d \,n^{2} x^{3}+2 a \,b^{4} c \,n^{4} x +250 a \,b^{4} d n \,x^{4}-121 b^{5} c \,n^{3} x^{2}-120 d \,x^{5} b^{5}+60 a^{3} b^{2} d \,n^{2} x^{2}-220 a^{2} b^{3} d n \,x^{3}+32 a \,b^{4} c \,n^{3} x +120 a d \,x^{4} b^{4}-372 b^{5} c \,n^{2} x^{2}+180 a^{3} b^{2} d n \,x^{2}-2 a^{2} b^{3} c \,n^{3}-120 d \,a^{2} x^{3} b^{3}+178 a \,b^{4} c \,n^{2} x -508 b^{5} c n \,x^{2}-120 a^{4} b d n x +120 a^{3} b^{2} d \,x^{2}-30 a^{2} b^{3} c \,n^{2}+388 a \,b^{4} c n x -240 b^{5} c \,x^{2}-120 a^{4} b d x -148 a^{2} b^{3} c n +240 a \,b^{4} c x +120 a^{5} d -240 a^{2} b^{3} c \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*n^5*x^5-15*b^5*d*n^4*x^5+5*a*b^4*d*n^4*x^4-85*b^5*d*n^3*x^5+50*a*b^4*d*n^3*x^4-b^5*c*n^5*x^2-225*b^5*d*n^2*x^5-20*a^2*b^3*d*n^3*x^3+175*a*b^4*d*n^2*x^4-18*b^5*c*n^4*x^2-274*b^5*d*n*x^5-120*a^2*b^3*d*n^2*x^3+2*a*b^4*c*n^4*x+250*a*b^4*d*n*x^4-121*b^5*c*n^3*x^2-120*b^5*d*x^5+60*a^3*b^2*d*n^2*x^2-220*a^2*b^3*d*n*x^3+32*a*b^4*c*n^3*x+120*a*b^4*d*x^4-372*b^5*c*n^2*x^2+180*a^3*b^2*d*n*x^2-2*a^2*b^3*c*n^3-120*a^2*b^3*d*x^3+178*a*b^4*c*n^2*x-508*b^5*c*n*x^2-120*a^4*b*d*n*x+120*a^3*b^2*d*x^2-30*a^2*b^3*c*n^2+388*a*b^4*c*n*x-240*b^5*c*x^2-120*a^4*b*d*x-148*a^2*b^3*c*n+240*a*b^4*c*x+120*a^5*d-240*a^2*b^3*c)/b^6/(n^6+21*n^5+175*n^4+735*n^3+1624*n^2+1764*n+720)","B"
175,1,283,126,0.007000," ","int(x*(b*x+a)^n*(d*x^3+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}+35 b^{4} d \,n^{2} x^{4}-24 a \,b^{3} d \,n^{2} x^{3}+b^{4} c \,n^{4} x +50 b^{4} d n \,x^{4}+12 a^{2} b^{2} d \,n^{2} x^{2}-44 a \,b^{3} d n \,x^{3}+13 b^{4} c \,n^{3} x +24 d \,x^{4} b^{4}+36 a^{2} b^{2} d n \,x^{2}-a \,b^{3} c \,n^{3}-24 a d \,x^{3} b^{3}+59 b^{4} c \,n^{2} x -24 a^{3} b d n x +24 d \,a^{2} x^{2} b^{2}-12 a \,b^{3} c \,n^{2}+107 b^{4} c n x -24 a^{3} b d x -47 a \,b^{3} c n +60 b^{4} c x +24 a^{4} d -60 a \,b^{3} 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)^(n+1)*(b^4*d*n^4*x^4+10*b^4*d*n^3*x^4-4*a*b^3*d*n^3*x^3+35*b^4*d*n^2*x^4-24*a*b^3*d*n^2*x^3+b^4*c*n^4*x+50*b^4*d*n*x^4+12*a^2*b^2*d*n^2*x^2-44*a*b^3*d*n*x^3+13*b^4*c*n^3*x+24*b^4*d*x^4+36*a^2*b^2*d*n*x^2-a*b^3*c*n^3-24*a*b^3*d*x^3+59*b^4*c*n^2*x-24*a^3*b*d*n*x+24*a^2*b^2*d*x^2-12*a*b^3*c*n^2+107*b^4*c*n*x-24*a^3*b*d*x-47*a*b^3*c*n+60*b^4*c*x+24*a^4*d-60*a*b^3*c)/b^5/(n^5+15*n^4+85*n^3+225*n^2+274*n+120)","B"
176,1,167,94,0.004000," ","int((b*x+a)^n*(d*x^3+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}-11 b^{3} d n \,x^{3}+9 a \,b^{2} d n \,x^{2}-b^{3} c \,n^{3}-6 d \,x^{3} b^{3}-6 a^{2} b d n x +6 a d \,x^{2} b^{2}-9 b^{3} c \,n^{2}-6 d \,a^{2} x b -26 b^{3} c n +6 a^{3} d -24 b^{3} 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^2-11*b^3*d*n*x^3+9*a*b^2*d*n*x^2-b^3*c*n^3-6*b^3*d*x^3-6*a^2*b*d*n*x+6*a*b^2*d*x^2-9*b^3*c*n^2-6*a^2*b*d*x-26*b^3*c*n+6*a^3*d-24*b^3*c)/b^4/(n^4+10*n^3+35*n^2+50*n+24)","A"
177,0,0,101,0.038000," ","int((b*x+a)^n*(d*x^3+c)/x,x)","\int \frac{\left(d \,x^{3}+c \right) \left(b x +a \right)^{n}}{x}\, dx"," ",0,"int((b*x+a)^n*(d*x^3+c)/x,x)","F"
178,1,1565,294,0.021000," ","int(x^2*(b*x+a)^n*(d*x^3+c)^2,x)","\frac{\left(b^{8} d^{2} n^{8} x^{8}+36 b^{8} d^{2} n^{7} x^{8}-8 a \,b^{7} d^{2} n^{7} x^{7}+546 b^{8} d^{2} n^{6} x^{8}-224 a \,b^{7} d^{2} n^{6} x^{7}+2 b^{8} c d \,n^{8} x^{5}+4536 b^{8} d^{2} n^{5} x^{8}+56 a^{2} b^{6} d^{2} n^{6} x^{6}-2576 a \,b^{7} d^{2} n^{5} x^{7}+78 b^{8} c d \,n^{7} x^{5}+22449 b^{8} d^{2} n^{4} x^{8}+1176 a^{2} b^{6} d^{2} n^{5} x^{6}-10 a \,b^{7} c d \,n^{7} x^{4}-15680 a \,b^{7} d^{2} n^{4} x^{7}+1272 b^{8} c d \,n^{6} x^{5}+67284 b^{8} d^{2} n^{3} x^{8}-336 a^{3} b^{5} d^{2} n^{5} x^{5}+9800 a^{2} b^{6} d^{2} n^{4} x^{6}-340 a \,b^{7} c d \,n^{6} x^{4}-54152 a \,b^{7} d^{2} n^{3} x^{7}+b^{8} c^{2} n^{8} x^{2}+11268 b^{8} c d \,n^{5} x^{5}+118124 b^{8} d^{2} n^{2} x^{8}-5040 a^{3} b^{5} d^{2} n^{4} x^{5}+40 a^{2} b^{6} c d \,n^{6} x^{3}+41160 a^{2} b^{6} d^{2} n^{3} x^{6}-4660 a \,b^{7} c d \,n^{5} x^{4}-105056 a \,b^{7} d^{2} n^{2} x^{7}+42 b^{8} c^{2} n^{7} x^{2}+58938 b^{8} c d \,n^{4} x^{5}+109584 b^{8} d^{2} n \,x^{8}+1680 a^{4} b^{4} d^{2} n^{4} x^{4}-28560 a^{3} b^{5} d^{2} n^{3} x^{5}+1200 a^{2} b^{6} c d \,n^{5} x^{3}+90944 a^{2} b^{6} d^{2} n^{2} x^{6}-2 a \,b^{7} c^{2} n^{7} x -33040 a \,b^{7} c d \,n^{4} x^{4}-104544 a \,b^{7} d^{2} n \,x^{7}+744 b^{8} c^{2} n^{6} x^{2}+185022 b^{8} c d \,n^{3} x^{5}+40320 d^{2} x^{8} b^{8}+16800 a^{4} b^{4} d^{2} n^{3} x^{4}-120 a^{3} b^{5} c d \,n^{5} x^{2}-75600 a^{3} b^{5} d^{2} n^{2} x^{5}+13840 a^{2} b^{6} c d \,n^{4} x^{3}+98784 a^{2} b^{6} d^{2} n \,x^{6}-80 a \,b^{7} c^{2} n^{6} x -129490 a \,b^{7} c d \,n^{3} x^{4}-40320 a \,d^{2} x^{7} b^{7}+7218 b^{8} c^{2} n^{5} x^{2}+337228 b^{8} c d \,n^{2} x^{5}-6720 a^{5} b^{3} d^{2} n^{3} x^{3}+58800 a^{4} b^{4} d^{2} n^{2} x^{4}-3240 a^{3} b^{5} c d \,n^{4} x^{2}-92064 a^{3} b^{5} d^{2} n \,x^{5}+2 a^{2} b^{6} c^{2} n^{6}+76800 a^{2} b^{6} c d \,n^{3} x^{3}+40320 a^{2} d^{2} x^{6} b^{6}-1328 a \,b^{7} c^{2} n^{5} x -277660 a \,b^{7} c d \,n^{2} x^{4}+41619 b^{8} c^{2} n^{4} x^{2}+322032 b^{8} c d n \,x^{5}-40320 a^{5} b^{3} d^{2} n^{2} x^{3}+240 a^{4} b^{4} c d \,n^{4} x +84000 a^{4} b^{4} d^{2} n \,x^{4}-31800 a^{3} b^{5} c d \,n^{3} x^{2}-40320 a^{3} b^{5} d^{2} x^{5}+78 a^{2} b^{6} c^{2} n^{5}+210760 a^{2} b^{6} c d \,n^{2} x^{3}-11780 a \,b^{7} c^{2} n^{4} x -297840 a \,b^{7} c d n \,x^{4}+144468 b^{8} c^{2} n^{3} x^{2}+120960 b^{8} c d \,x^{5}+20160 a^{6} b^{2} d^{2} n^{2} x^{2}-73920 a^{5} b^{3} d^{2} n \,x^{3}+6000 a^{4} b^{4} c d \,n^{3} x +40320 a^{4} b^{4} d^{2} x^{4}-135000 a^{3} b^{5} c d \,n^{2} x^{2}+1250 a^{2} b^{6} c^{2} n^{4}+267600 a^{2} b^{6} c d n \,x^{3}-59678 a \,b^{7} c^{2} n^{3} x -120960 a \,b^{7} c d \,x^{4}+290276 b^{8} c^{2} n^{2} x^{2}+60480 a^{6} b^{2} d^{2} n \,x^{2}-240 a^{5} b^{3} c d \,n^{3}-40320 a^{5} b^{3} d^{2} x^{3}+51600 a^{4} b^{4} c d \,n^{2} x -227280 a^{3} b^{5} c d n \,x^{2}+10530 a^{2} b^{6} c^{2} n^{3}+120960 a^{2} b^{6} c d \,x^{3}-169580 a \,b^{7} c^{2} n^{2} x +301872 b^{8} c^{2} n \,x^{2}-40320 a^{7} b \,d^{2} n x +40320 a^{6} b^{2} d^{2} x^{2}-5760 a^{5} b^{3} c d \,n^{2}+166800 a^{4} b^{4} c d n x -120960 a^{3} b^{5} c d \,x^{2}+49148 a^{2} b^{6} c^{2} n^{2}-241392 a \,b^{7} c^{2} n x +120960 b^{8} c^{2} x^{2}-40320 a^{7} b \,d^{2} x -45840 a^{5} b^{3} c d n +120960 a^{4} b^{4} c d x +120432 a^{2} b^{6} c^{2} n -120960 a \,b^{7} c^{2} x +40320 a^{8} d^{2}-120960 a^{5} b^{3} c d +120960 a^{2} b^{6} c^{2}\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^2*n^8*x^8+36*b^8*d^2*n^7*x^8-8*a*b^7*d^2*n^7*x^7+546*b^8*d^2*n^6*x^8-224*a*b^7*d^2*n^6*x^7+2*b^8*c*d*n^8*x^5+4536*b^8*d^2*n^5*x^8+56*a^2*b^6*d^2*n^6*x^6-2576*a*b^7*d^2*n^5*x^7+78*b^8*c*d*n^7*x^5+22449*b^8*d^2*n^4*x^8+1176*a^2*b^6*d^2*n^5*x^6-10*a*b^7*c*d*n^7*x^4-15680*a*b^7*d^2*n^4*x^7+1272*b^8*c*d*n^6*x^5+67284*b^8*d^2*n^3*x^8-336*a^3*b^5*d^2*n^5*x^5+9800*a^2*b^6*d^2*n^4*x^6-340*a*b^7*c*d*n^6*x^4-54152*a*b^7*d^2*n^3*x^7+b^8*c^2*n^8*x^2+11268*b^8*c*d*n^5*x^5+118124*b^8*d^2*n^2*x^8-5040*a^3*b^5*d^2*n^4*x^5+40*a^2*b^6*c*d*n^6*x^3+41160*a^2*b^6*d^2*n^3*x^6-4660*a*b^7*c*d*n^5*x^4-105056*a*b^7*d^2*n^2*x^7+42*b^8*c^2*n^7*x^2+58938*b^8*c*d*n^4*x^5+109584*b^8*d^2*n*x^8+1680*a^4*b^4*d^2*n^4*x^4-28560*a^3*b^5*d^2*n^3*x^5+1200*a^2*b^6*c*d*n^5*x^3+90944*a^2*b^6*d^2*n^2*x^6-2*a*b^7*c^2*n^7*x-33040*a*b^7*c*d*n^4*x^4-104544*a*b^7*d^2*n*x^7+744*b^8*c^2*n^6*x^2+185022*b^8*c*d*n^3*x^5+40320*b^8*d^2*x^8+16800*a^4*b^4*d^2*n^3*x^4-120*a^3*b^5*c*d*n^5*x^2-75600*a^3*b^5*d^2*n^2*x^5+13840*a^2*b^6*c*d*n^4*x^3+98784*a^2*b^6*d^2*n*x^6-80*a*b^7*c^2*n^6*x-129490*a*b^7*c*d*n^3*x^4-40320*a*b^7*d^2*x^7+7218*b^8*c^2*n^5*x^2+337228*b^8*c*d*n^2*x^5-6720*a^5*b^3*d^2*n^3*x^3+58800*a^4*b^4*d^2*n^2*x^4-3240*a^3*b^5*c*d*n^4*x^2-92064*a^3*b^5*d^2*n*x^5+2*a^2*b^6*c^2*n^6+76800*a^2*b^6*c*d*n^3*x^3+40320*a^2*b^6*d^2*x^6-1328*a*b^7*c^2*n^5*x-277660*a*b^7*c*d*n^2*x^4+41619*b^8*c^2*n^4*x^2+322032*b^8*c*d*n*x^5-40320*a^5*b^3*d^2*n^2*x^3+240*a^4*b^4*c*d*n^4*x+84000*a^4*b^4*d^2*n*x^4-31800*a^3*b^5*c*d*n^3*x^2-40320*a^3*b^5*d^2*x^5+78*a^2*b^6*c^2*n^5+210760*a^2*b^6*c*d*n^2*x^3-11780*a*b^7*c^2*n^4*x-297840*a*b^7*c*d*n*x^4+144468*b^8*c^2*n^3*x^2+120960*b^8*c*d*x^5+20160*a^6*b^2*d^2*n^2*x^2-73920*a^5*b^3*d^2*n*x^3+6000*a^4*b^4*c*d*n^3*x+40320*a^4*b^4*d^2*x^4-135000*a^3*b^5*c*d*n^2*x^2+1250*a^2*b^6*c^2*n^4+267600*a^2*b^6*c*d*n*x^3-59678*a*b^7*c^2*n^3*x-120960*a*b^7*c*d*x^4+290276*b^8*c^2*n^2*x^2+60480*a^6*b^2*d^2*n*x^2-240*a^5*b^3*c*d*n^3-40320*a^5*b^3*d^2*x^3+51600*a^4*b^4*c*d*n^2*x-227280*a^3*b^5*c*d*n*x^2+10530*a^2*b^6*c^2*n^3+120960*a^2*b^6*c*d*x^3-169580*a*b^7*c^2*n^2*x+301872*b^8*c^2*n*x^2-40320*a^7*b*d^2*n*x+40320*a^6*b^2*d^2*x^2-5760*a^5*b^3*c*d*n^2+166800*a^4*b^4*c*d*n*x-120960*a^3*b^5*c*d*x^2+49148*a^2*b^6*c^2*n^2-241392*a*b^7*c^2*n*x+120960*b^8*c^2*x^2-40320*a^7*b*d^2*x-45840*a^5*b^3*c*d*n+120960*a^4*b^4*c*d*x+120432*a^2*b^6*c^2*n-120960*a*b^7*c^2*x+40320*a^8*d^2-120960*a^5*b^3*c*d+120960*a^2*b^6*c^2)/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"
179,1,1142,248,0.018000," ","int(x*(b*x+a)^n*(d*x^3+c)^2,x)","-\frac{\left(-b^{7} d^{2} n^{7} x^{7}-28 b^{7} d^{2} n^{6} x^{7}+7 a \,b^{6} d^{2} n^{6} x^{6}-322 b^{7} d^{2} n^{5} x^{7}+147 a \,b^{6} d^{2} n^{5} x^{6}-2 b^{7} c d \,n^{7} x^{4}-1960 b^{7} d^{2} n^{4} x^{7}-42 a^{2} b^{5} d^{2} n^{5} x^{5}+1225 a \,b^{6} d^{2} n^{4} x^{6}-62 b^{7} c d \,n^{6} x^{4}-6769 b^{7} d^{2} n^{3} x^{7}-630 a^{2} b^{5} d^{2} n^{4} x^{5}+8 a \,b^{6} c d \,n^{6} x^{3}+5145 a \,b^{6} d^{2} n^{3} x^{6}-782 b^{7} c d \,n^{5} x^{4}-13132 b^{7} d^{2} n^{2} x^{7}+210 a^{3} b^{4} d^{2} n^{4} x^{4}-3570 a^{2} b^{5} d^{2} n^{3} x^{5}+216 a \,b^{6} c d \,n^{5} x^{3}+11368 a \,b^{6} d^{2} n^{2} x^{6}-b^{7} c^{2} n^{7} x -5162 b^{7} c d \,n^{4} x^{4}-13068 b^{7} d^{2} n \,x^{7}+2100 a^{3} b^{4} d^{2} n^{3} x^{4}-24 a^{2} b^{5} c d \,n^{5} x^{2}-9450 a^{2} b^{5} d^{2} n^{2} x^{5}+2264 a \,b^{6} c d \,n^{4} x^{3}+12348 a \,b^{6} d^{2} n \,x^{6}-34 b^{7} c^{2} n^{6} x -19088 b^{7} c d \,n^{3} x^{4}-5040 d^{2} x^{7} b^{7}-840 a^{4} b^{3} d^{2} n^{3} x^{3}+7350 a^{3} b^{4} d^{2} n^{2} x^{4}-576 a^{2} b^{5} c d \,n^{4} x^{2}-11508 a^{2} b^{5} d^{2} n \,x^{5}+a \,b^{6} c^{2} n^{6}+11592 a \,b^{6} c d \,n^{3} x^{3}+5040 a \,d^{2} x^{6} b^{6}-478 b^{7} c^{2} n^{5} x -39128 b^{7} c d \,n^{2} x^{4}-5040 a^{4} b^{3} d^{2} n^{2} x^{3}+48 a^{3} b^{4} c d \,n^{4} x +10500 a^{3} b^{4} d^{2} n \,x^{4}-5064 a^{2} b^{5} c d \,n^{3} x^{2}-5040 a^{2} d^{2} x^{5} b^{5}+33 a \,b^{6} c^{2} n^{5}+29984 a \,b^{6} c d \,n^{2} x^{3}-3580 b^{7} c^{2} n^{4} x -40608 b^{7} c d n \,x^{4}+2520 a^{5} b^{2} d^{2} n^{2} x^{2}-9240 a^{4} b^{3} d^{2} n \,x^{3}+1056 a^{3} b^{4} c d \,n^{3} x +5040 a^{3} b^{4} d^{2} x^{4}-19584 a^{2} b^{5} c d \,n^{2} x^{2}+445 a \,b^{6} c^{2} n^{4}+36576 a \,b^{6} c d n \,x^{3}-15289 b^{7} c^{2} n^{3} x -16128 b^{7} c d \,x^{4}+7560 a^{5} b^{2} d^{2} n \,x^{2}-48 a^{4} b^{3} c d \,n^{3}-5040 a^{4} b^{3} d^{2} x^{3}+8016 a^{3} b^{4} c d \,n^{2} x -31200 a^{2} b^{5} c d n \,x^{2}+3135 a \,b^{6} c^{2} n^{3}+16128 a \,b^{6} c d \,x^{3}-36706 b^{7} c^{2} n^{2} x -5040 a^{6} b \,d^{2} n x +5040 a^{5} b^{2} d^{2} x^{2}-1008 a^{4} b^{3} c d \,n^{2}+23136 a^{3} b^{4} c d n x -16128 a^{2} b^{5} c d \,x^{2}+12154 a \,b^{6} c^{2} n^{2}-44712 b^{7} c^{2} n x -5040 a^{6} b \,d^{2} x -7008 a^{4} b^{3} c d n +16128 a^{3} b^{4} c d x +24552 a \,b^{6} c^{2} n -20160 b^{7} c^{2} x +5040 a^{7} d^{2}-16128 a^{4} b^{3} c d +20160 a \,b^{6} c^{2}\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^2*n^7*x^7-28*b^7*d^2*n^6*x^7+7*a*b^6*d^2*n^6*x^6-322*b^7*d^2*n^5*x^7+147*a*b^6*d^2*n^5*x^6-2*b^7*c*d*n^7*x^4-1960*b^7*d^2*n^4*x^7-42*a^2*b^5*d^2*n^5*x^5+1225*a*b^6*d^2*n^4*x^6-62*b^7*c*d*n^6*x^4-6769*b^7*d^2*n^3*x^7-630*a^2*b^5*d^2*n^4*x^5+8*a*b^6*c*d*n^6*x^3+5145*a*b^6*d^2*n^3*x^6-782*b^7*c*d*n^5*x^4-13132*b^7*d^2*n^2*x^7+210*a^3*b^4*d^2*n^4*x^4-3570*a^2*b^5*d^2*n^3*x^5+216*a*b^6*c*d*n^5*x^3+11368*a*b^6*d^2*n^2*x^6-b^7*c^2*n^7*x-5162*b^7*c*d*n^4*x^4-13068*b^7*d^2*n*x^7+2100*a^3*b^4*d^2*n^3*x^4-24*a^2*b^5*c*d*n^5*x^2-9450*a^2*b^5*d^2*n^2*x^5+2264*a*b^6*c*d*n^4*x^3+12348*a*b^6*d^2*n*x^6-34*b^7*c^2*n^6*x-19088*b^7*c*d*n^3*x^4-5040*b^7*d^2*x^7-840*a^4*b^3*d^2*n^3*x^3+7350*a^3*b^4*d^2*n^2*x^4-576*a^2*b^5*c*d*n^4*x^2-11508*a^2*b^5*d^2*n*x^5+a*b^6*c^2*n^6+11592*a*b^6*c*d*n^3*x^3+5040*a*b^6*d^2*x^6-478*b^7*c^2*n^5*x-39128*b^7*c*d*n^2*x^4-5040*a^4*b^3*d^2*n^2*x^3+48*a^3*b^4*c*d*n^4*x+10500*a^3*b^4*d^2*n*x^4-5064*a^2*b^5*c*d*n^3*x^2-5040*a^2*b^5*d^2*x^5+33*a*b^6*c^2*n^5+29984*a*b^6*c*d*n^2*x^3-3580*b^7*c^2*n^4*x-40608*b^7*c*d*n*x^4+2520*a^5*b^2*d^2*n^2*x^2-9240*a^4*b^3*d^2*n*x^3+1056*a^3*b^4*c*d*n^3*x+5040*a^3*b^4*d^2*x^4-19584*a^2*b^5*c*d*n^2*x^2+445*a*b^6*c^2*n^4+36576*a*b^6*c*d*n*x^3-15289*b^7*c^2*n^3*x-16128*b^7*c*d*x^4+7560*a^5*b^2*d^2*n*x^2-48*a^4*b^3*c*d*n^3-5040*a^4*b^3*d^2*x^3+8016*a^3*b^4*c*d*n^2*x-31200*a^2*b^5*c*d*n*x^2+3135*a*b^6*c^2*n^3+16128*a*b^6*c*d*x^3-36706*b^7*c^2*n^2*x-5040*a^6*b*d^2*n*x+5040*a^5*b^2*d^2*x^2-1008*a^4*b^3*c*d*n^2+23136*a^3*b^4*c*d*n*x-16128*a^2*b^5*c*d*x^2+12154*a*b^6*c^2*n^2-44712*b^7*c^2*n*x-5040*a^6*b*d^2*x-7008*a^4*b^3*c*d*n+16128*a^3*b^4*c*d*x+24552*a*b^6*c^2*n-20160*b^7*c^2*x+5040*a^7*d^2-16128*a^4*b^3*c*d+20160*a*b^6*c^2)/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"
180,1,793,203,0.013000," ","int((b*x+a)^n*(d*x^3+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}+175 b^{6} d^{2} n^{4} x^{6}-90 a \,b^{5} d^{2} n^{4} x^{5}+2 b^{6} c d \,n^{6} x^{3}+735 b^{6} d^{2} n^{3} x^{6}+30 a^{2} b^{4} d^{2} n^{4} x^{4}-510 a \,b^{5} d^{2} n^{3} x^{5}+48 b^{6} c d \,n^{5} x^{3}+1624 b^{6} d^{2} n^{2} x^{6}+300 a^{2} b^{4} d^{2} n^{3} x^{4}-6 a \,b^{5} c d \,n^{5} x^{2}-1350 a \,b^{5} d^{2} n^{2} x^{5}+452 b^{6} c d \,n^{4} x^{3}+1764 b^{6} d^{2} n \,x^{6}-120 a^{3} b^{3} d^{2} n^{3} x^{3}+1050 a^{2} b^{4} d^{2} n^{2} x^{4}-126 a \,b^{5} c d \,n^{4} x^{2}-1644 a \,b^{5} d^{2} n \,x^{5}+b^{6} c^{2} n^{6}+2112 b^{6} c d \,n^{3} x^{3}+720 d^{2} x^{6} b^{6}-720 a^{3} b^{3} d^{2} n^{2} x^{3}+12 a^{2} b^{4} c d \,n^{4} x +1500 a^{2} b^{4} d^{2} n \,x^{4}-978 a \,b^{5} c d \,n^{3} x^{2}-720 a \,d^{2} x^{5} b^{5}+27 b^{6} c^{2} n^{5}+5090 b^{6} c d \,n^{2} x^{3}+360 a^{4} b^{2} d^{2} n^{2} x^{2}-1320 a^{3} b^{3} d^{2} n \,x^{3}+228 a^{2} b^{4} c d \,n^{3} x +720 a^{2} d^{2} x^{4} b^{4}-3402 a \,b^{5} c d \,n^{2} x^{2}+295 b^{6} c^{2} n^{4}+5904 b^{6} c d n \,x^{3}+1080 a^{4} b^{2} d^{2} n \,x^{2}-12 a^{3} b^{3} c d \,n^{3}-720 a^{3} b^{3} d^{2} x^{3}+1500 a^{2} b^{4} c d \,n^{2} x -5064 a \,b^{5} c d n \,x^{2}+1665 b^{6} c^{2} n^{3}+2520 b^{6} c d \,x^{3}-720 a^{5} b \,d^{2} n x +720 a^{4} b^{2} d^{2} x^{2}-216 a^{3} b^{3} c d \,n^{2}+3804 a^{2} b^{4} c d n x -2520 a \,b^{5} c d \,x^{2}+5104 b^{6} c^{2} n^{2}-720 a^{5} b \,d^{2} x -1284 a^{3} b^{3} c d n +2520 a^{2} b^{4} c d x +8028 b^{6} c^{2} n +720 a^{6} d^{2}-2520 a^{3} b^{3} c d +5040 b^{6} 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+175*b^6*d^2*n^4*x^6-90*a*b^5*d^2*n^4*x^5+2*b^6*c*d*n^6*x^3+735*b^6*d^2*n^3*x^6+30*a^2*b^4*d^2*n^4*x^4-510*a*b^5*d^2*n^3*x^5+48*b^6*c*d*n^5*x^3+1624*b^6*d^2*n^2*x^6+300*a^2*b^4*d^2*n^3*x^4-6*a*b^5*c*d*n^5*x^2-1350*a*b^5*d^2*n^2*x^5+452*b^6*c*d*n^4*x^3+1764*b^6*d^2*n*x^6-120*a^3*b^3*d^2*n^3*x^3+1050*a^2*b^4*d^2*n^2*x^4-126*a*b^5*c*d*n^4*x^2-1644*a*b^5*d^2*n*x^5+b^6*c^2*n^6+2112*b^6*c*d*n^3*x^3+720*b^6*d^2*x^6-720*a^3*b^3*d^2*n^2*x^3+12*a^2*b^4*c*d*n^4*x+1500*a^2*b^4*d^2*n*x^4-978*a*b^5*c*d*n^3*x^2-720*a*b^5*d^2*x^5+27*b^6*c^2*n^5+5090*b^6*c*d*n^2*x^3+360*a^4*b^2*d^2*n^2*x^2-1320*a^3*b^3*d^2*n*x^3+228*a^2*b^4*c*d*n^3*x+720*a^2*b^4*d^2*x^4-3402*a*b^5*c*d*n^2*x^2+295*b^6*c^2*n^4+5904*b^6*c*d*n*x^3+1080*a^4*b^2*d^2*n*x^2-12*a^3*b^3*c*d*n^3-720*a^3*b^3*d^2*x^3+1500*a^2*b^4*c*d*n^2*x-5064*a*b^5*c*d*n*x^2+1665*b^6*c^2*n^3+2520*b^6*c*d*x^3-720*a^5*b*d^2*n*x+720*a^4*b^2*d^2*x^2-216*a^3*b^3*c*d*n^2+3804*a^2*b^4*c*d*n*x-2520*a*b^5*c*d*x^2+5104*b^6*c^2*n^2-720*a^5*b*d^2*x-1284*a^3*b^3*c*d*n+2520*a^2*b^4*c*d*x+8028*b^6*c^2*n+720*a^6*d^2-2520*a^3*b^3*c*d+5040*b^6*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"
181,0,0,211,0.043000," ","int((b*x+a)^n*(d*x^3+c)^2/x,x)","\int \frac{\left(d \,x^{3}+c \right)^{2} \left(b x +a \right)^{n}}{x}\, dx"," ",0,"int((b*x+a)^n*(d*x^3+c)^2/x,x)","F"
182,1,3780,459,0.056000," ","int(x^2*(b*x+a)^n*(d*x^3+c)^3,x)","\text{output too large to display}"," 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183,1,2972,396,0.037000," ","int(x*(b*x+a)^n*(d*x^3+c)^3,x)","\text{output too large to display}"," ",0,"(b*x+a)^(n+1)*(b^10*d^3*n^10*x^10+55*b^10*d^3*n^9*x^10-10*a*b^9*d^3*n^9*x^9+1320*b^10*d^3*n^8*x^10-450*a*b^9*d^3*n^8*x^9+3*b^10*c*d^2*n^10*x^7+18150*b^10*d^3*n^7*x^10+90*a^2*b^8*d^3*n^8*x^8-8700*a*b^9*d^3*n^7*x^9+174*b^10*c*d^2*n^9*x^7+157773*b^10*d^3*n^6*x^10+3240*a^2*b^8*d^3*n^7*x^8-21*a*b^9*c*d^2*n^9*x^6-94500*a*b^9*d^3*n^6*x^9+4383*b^10*c*d^2*n^8*x^7+902055*b^10*d^3*n^5*x^10-720*a^3*b^7*d^3*n^7*x^7+49140*a^2*b^8*d^3*n^6*x^8-1071*a*b^9*c*d^2*n^8*x^6-632730*a*b^9*d^3*n^5*x^9+3*b^10*c^2*d*n^10*x^4+62946*b^10*c*d^2*n^7*x^7+3416930*b^10*d^3*n^4*x^10-20160*a^3*b^7*d^3*n^6*x^7+126*a^2*b^8*c*d^2*n^8*x^5+408240*a^2*b^8*d^3*n^5*x^8-23184*a*b^9*c*d^2*n^7*x^6-2693250*a*b^9*d^3*n^4*x^9+183*b^10*c^2*d*n^9*x^4+568701*b^10*c*d^2*n^6*x^7+8409500*b^10*d^3*n^3*x^10+5040*a^4*b^6*d^3*n^6*x^6-231840*a^3*b^7*d^3*n^5*x^7+5670*a^2*b^8*c*d^2*n^7*x^5+2020410*a^2*b^8*d^3*n^4*x^8-12*a*b^9*c^2*d*n^9*x^3-278334*a*b^9*c*d^2*n^6*x^6-7236800*a*b^9*d^3*n^3*x^9+4860*b^10*c^2*d*n^8*x^4+3363066*b^10*c*d^2*n^5*x^7+12753576*b^10*d^3*n^2*x^10+105840*a^4*b^6*d^3*n^5*x^6-630*a^3*b^7*c*d^2*n^7*x^4-1411200*a^3*b^7*d^3*n^4*x^7+105084*a^2*b^8*c*d^2*n^6*x^5+6055560*a^2*b^8*d^3*n^3*x^8-684*a*b^9*c^2*d*n^8*x^3-2032569*a*b^9*c*d^2*n^5*x^6-11727000*a*b^9*d^3*n^2*x^9+b^10*c^3*n^10*x+73710*b^10*c^2*d*n^7*x^4+13114077*b^10*c*d^2*n^4*x^7+10628640*b^10*d^3*n*x^10-30240*a^5*b^5*d^3*n^5*x^5+882000*a^4*b^6*d^3*n^4*x^6-25200*a^3*b^7*c*d^2*n^6*x^4-4873680*a^3*b^7*d^3*n^3*x^7+36*a^2*b^8*c^2*d*n^8*x^2+1039500*a^2*b^8*c*d^2*n^5*x^5+10631160*a^2*b^8*d^3*n^2*x^8-16704*a*b^9*c^2*d*n^7*x^3-9313479*a*b^9*c*d^2*n^4*x^6-10265760*a*b^9*d^3*n*x^9+64*b^10*c^3*n^9*x+703719*b^10*c^2*d*n^6*x^4+33074574*b^10*c*d^2*n^3*x^7+3628800*b^10*d^3*x^10-453600*a^5*b^5*d^3*n^4*x^5+2520*a^4*b^6*c*d^2*n^6*x^3+3704400*a^4*b^6*d^3*n^3*x^6-399420*a^3*b^7*c*d^2*n^5*x^4-9455040*a^3*b^7*d^3*n^2*x^7+1944*a^2*b^8*c^2*d*n^7*x^2+5958414*a^2*b^8*c*d^2*n^4*x^5+9862560*a^2*b^8*d^3*n*x^8-a*b^9*c^3*n^9-228024*a*b^9*c^2*d*n^6*x^3-26604186*a*b^9*c*d^2*n^3*x^6-3628800*a*b^9*d^3*x^9+1797*b^10*c^3*n^8*x+4394079*b^10*c^2*d*n^5*x^4+51177636*b^10*c*d^2*n^2*x^7+151200*a^6*b^4*d^3*n^4*x^4-2570400*a^5*b^5*d^3*n^3*x^5+90720*a^4*b^6*c*d^2*n^5*x^3+8184960*a^4*b^6*d^3*n^2*x^6-72*a^3*b^7*c^2*d*n^7*x-3200400*a^3*b^7*c*d^2*n^4*x^4-9408960*a^3*b^7*d^3*n*x^7+44280*a^2*b^8*c^2*d*n^6*x^2+20130390*a^2*b^8*c*d^2*n^3*x^5+3628800*a^2*b^8*d^3*x^8-63*a*b^9*c^3*n^8-1902780*a*b^9*c^2*d*n^5*x^3-45292716*a*b^9*c*d^2*n^2*x^6+29076*b^10*c^3*n^7*x+18048210*b^10*c^2*d*n^4*x^4+43332840*b^10*c*d^2*n*x^7+1512000*a^6*b^4*d^3*n^3*x^4-7560*a^5*b^5*c*d^2*n^5*x^2-6804000*a^5*b^5*d^3*n^2*x^5+1234800*a^4*b^6*c*d^2*n^4*x^3+8890560*a^4*b^6*d^3*n*x^6-3744*a^3*b^7*c^2*d*n^6*x-13790070*a^3*b^7*c*d^2*n^3*x^4-3628800*a^3*b^7*d^3*x^7+551232*a^2*b^8*c^2*d*n^5*x^2+38842776*a^2*b^8*c*d^2*n^2*x^5-1734*a*b^9*c^3*n^7-9965196*a*b^9*c^2*d*n^4*x^3-41194440*a*b^9*c*d^2*n*x^6+299271*b^10*c^3*n^6*x+47746140*b^10*c^2*d*n^3*x^4+14968800*b^10*c*d^2*x^7-604800*a^7*b^3*d^3*n^3*x^3+5292000*a^6*b^4*d^3*n^2*x^4-249480*a^5*b^5*c*d^2*n^4*x^2-8285760*a^5*b^5*d^3*n*x^5+72*a^4*b^6*c^2*d*n^6+7862400*a^4*b^6*c*d^2*n^3*x^3+3628800*a^4*b^6*d^3*x^6-81072*a^3*b^7*c^2*d*n^5*x-31701600*a^3*b^7*c*d^2*n^2*x^4+4054644*a^2*b^8*c^2*d*n^4*x^2+38699640*a^2*b^8*c*d^2*n*x^5-27342*a*b^9*c^3*n^6-32332056*a*b^9*c^2*d*n^3*x^3-14968800*a*b^9*c*d^2*x^6+2039016*b^10*c^3*n^5*x+77043528*b^10*c^2*d*n^2*x^4-3628800*a^7*b^3*d^3*n^2*x^3+15120*a^6*b^4*c*d^2*n^4*x+7560000*a^6*b^4*d^3*n*x^4-2955960*a^5*b^5*c*d^2*n^3*x^2-3628800*a^5*b^5*d^3*x^5+3672*a^4*b^6*c^2*d*n^5+23710680*a^4*b^6*c*d^2*n^2*x^3-940320*a^3*b^7*c^2*d*n^4*x-35705880*a^3*b^7*c*d^2*n*x^4+17731656*a^2*b^8*c^2*d*n^3*x^2+14968800*a^2*b^8*c*d^2*x^5-271929*a*b^9*c^3*n^5-61656336*a*b^9*c^2*d*n^2*x^3+9261503*b^10*c^3*n^4*x+67536288*b^10*c^2*d*n*x^4+1814400*a^8*b^2*d^3*n^2*x^2-6652800*a^7*b^3*d^3*n*x^3+468720*a^6*b^4*c*d^2*n^3*x+3628800*a^6*b^4*d^3*x^4-14719320*a^5*b^5*c*d^2*n^2*x^2+77400*a^4*b^6*c^2*d*n^4+31963680*a^4*b^6*c*d^2*n*x^3-6228648*a^3*b^7*c^2*d*n^3*x-14968800*a^3*b^7*c*d^2*x^4+43801200*a^2*b^8*c^2*d*n^2*x^2-1767087*a*b^9*c^3*n^4-61548768*a*b^9*c^2*d*n*x^3+27472724*b^10*c^3*n^3*x+23950080*b^10*c^2*d*x^4+5443200*a^8*b^2*d^3*n*x^2-15120*a^7*b^3*c*d^2*n^3-3628800*a^7*b^3*d^3*x^3+4974480*a^6*b^4*c*d^2*n^2*x-26974080*a^5*b^5*c*d^2*n*x^2+862920*a^4*b^6*c^2*d*n^3+14968800*a^4*b^6*c*d^2*x^3-23006016*a^3*b^7*c^2*d*n^2*x+53565408*a^2*b^8*c^2*d*n*x^2-7494416*a*b^9*c^3*n^3-23950080*a*b^9*c^2*d*x^3+50312628*b^10*c^3*n^2*x-3628800*a^9*b*d^3*n*x+3628800*a^8*b^2*d^3*x^2-453600*a^7*b^3*c*d^2*n^2+19489680*a^6*b^4*c*d^2*n*x-14968800*a^5*b^5*c*d^2*x^2+5365728*a^4*b^6*c^2*d*n^2-41590368*a^3*b^7*c^2*d*n*x+23950080*a^2*b^8*c^2*d*x^2-19978308*a*b^9*c^3*n^2+50292720*b^10*c^3*n*x-3628800*a^9*b*d^3*x-4520880*a^7*b^3*c*d^2*n+14968800*a^6*b^4*c*d^2*x+17640288*a^4*b^6*c^2*d*n-23950080*a^3*b^7*c^2*d*x-30334320*a*b^9*c^3*n+19958400*b^10*c^3*x+3628800*a^10*d^3-14968800*a^7*b^3*c*d^2+23950080*a^4*b^6*c^2*d-19958400*a*b^9*c^3)/b^11/(n^11+66*n^10+1925*n^9+32670*n^8+357423*n^7+2637558*n^6+13339535*n^5+45995730*n^4+105258076*n^3+150917976*n^2+120543840*n+39916800)","B"
184,1,2280,337,0.028000," ","int((b*x+a)^n*(d*x^3+c)^3,x)","-\frac{\left(-b^{9} d^{3} n^{9} x^{9}-45 b^{9} d^{3} n^{8} x^{9}+9 a \,b^{8} d^{3} n^{8} x^{8}-870 b^{9} d^{3} n^{7} x^{9}+324 a \,b^{8} d^{3} n^{7} x^{8}-3 b^{9} c \,d^{2} n^{9} x^{6}-9450 b^{9} d^{3} n^{6} x^{9}-72 a^{2} b^{7} d^{3} n^{7} x^{7}+4914 a \,b^{8} d^{3} n^{6} x^{8}-144 b^{9} c \,d^{2} n^{8} x^{6}-63273 b^{9} d^{3} n^{5} x^{9}-2016 a^{2} b^{7} d^{3} n^{6} x^{7}+18 a \,b^{8} c \,d^{2} n^{8} x^{5}+40824 a \,b^{8} d^{3} n^{5} x^{8}-2952 b^{9} c \,d^{2} n^{7} x^{6}-269325 b^{9} d^{3} n^{4} x^{9}+504 a^{3} b^{6} d^{3} n^{6} x^{6}-23184 a^{2} b^{7} d^{3} n^{5} x^{7}+756 a \,b^{8} c \,d^{2} n^{7} x^{5}+202041 a \,b^{8} d^{3} n^{4} x^{8}-3 b^{9} c^{2} d \,n^{9} x^{3}-33786 b^{9} c \,d^{2} n^{6} x^{6}-723680 b^{9} d^{3} n^{3} x^{9}+10584 a^{3} b^{6} d^{3} n^{5} x^{6}-90 a^{2} b^{7} c \,d^{2} n^{7} x^{4}-141120 a^{2} b^{7} d^{3} n^{4} x^{7}+13176 a \,b^{8} c \,d^{2} n^{6} x^{5}+605556 a \,b^{8} d^{3} n^{3} x^{8}-153 b^{9} c^{2} d \,n^{8} x^{3}-236817 b^{9} c \,d^{2} n^{5} x^{6}-1172700 b^{9} d^{3} n^{2} x^{9}-3024 a^{4} b^{5} d^{3} n^{5} x^{5}+88200 a^{3} b^{6} d^{3} n^{4} x^{6}-3330 a^{2} b^{7} c \,d^{2} n^{6} x^{4}-487368 a^{2} b^{7} d^{3} n^{3} x^{7}+9 a \,b^{8} c^{2} d \,n^{8} x^{2}+123660 a \,b^{8} c \,d^{2} n^{5} x^{5}+1063116 a \,b^{8} d^{3} n^{2} x^{8}-3348 b^{9} c^{2} d \,n^{7} x^{3}-1048446 b^{9} c \,d^{2} n^{4} x^{6}-1026576 b^{9} d^{3} n \,x^{9}-45360 a^{4} b^{5} d^{3} n^{4} x^{5}+360 a^{3} b^{6} c \,d^{2} n^{6} x^{3}+370440 a^{3} b^{6} d^{3} n^{3} x^{6}-49230 a^{2} b^{7} c \,d^{2} n^{5} x^{4}-945504 a^{2} b^{7} d^{3} n^{2} x^{7}+432 a \,b^{8} c^{2} d \,n^{7} x^{2}+678942 a \,b^{8} c \,d^{2} n^{4} x^{5}+986256 a \,b^{8} d^{3} n \,x^{8}-b^{9} c^{3} n^{9}-41058 b^{9} c^{2} d \,n^{6} x^{3}-2911668 b^{9} c \,d^{2} n^{3} x^{6}-362880 d^{3} x^{9} b^{9}+15120 a^{5} b^{4} d^{3} n^{4} x^{4}-257040 a^{4} b^{5} d^{3} n^{3} x^{5}+11880 a^{3} b^{6} c \,d^{2} n^{5} x^{3}+818496 a^{3} b^{6} d^{3} n^{2} x^{6}-18 a^{2} b^{7} c^{2} d \,n^{7} x -372150 a^{2} b^{7} c \,d^{2} n^{4} x^{4}-940896 a^{2} b^{7} d^{3} n \,x^{7}+8748 a \,b^{8} c^{2} d \,n^{6} x^{2}+2217024 a \,b^{8} c \,d^{2} n^{3} x^{5}+362880 d^{3} a \,x^{8} b^{8}-54 b^{9} c^{3} n^{8}-309087 b^{9} c^{2} d \,n^{5} x^{3}-4846824 b^{9} c \,d^{2} n^{2} x^{6}+151200 a^{5} b^{4} d^{3} n^{3} x^{4}-1080 a^{4} b^{5} c \,d^{2} n^{5} x^{2}-680400 a^{4} b^{5} d^{3} n^{2} x^{5}+149400 a^{3} b^{6} c \,d^{2} n^{4} x^{3}+889056 a^{3} b^{6} d^{3} n \,x^{6}-828 a^{2} b^{7} c^{2} d \,n^{6} x -1533960 a^{2} b^{7} c \,d^{2} n^{3} x^{4}-362880 a^{2} d^{3} x^{7} b^{7}+96930 a \,b^{8} c^{2} d \,n^{5} x^{2}+4167864 a \,b^{8} c \,d^{2} n^{2} x^{5}-1266 b^{9} c^{3} n^{7}-1469817 b^{9} c^{2} d \,n^{4} x^{3}-4332960 b^{9} c \,d^{2} n \,x^{6}-60480 a^{6} b^{3} d^{3} n^{3} x^{3}+529200 a^{5} b^{4} d^{3} n^{2} x^{4}-32400 a^{4} b^{5} c \,d^{2} n^{4} x^{2}-828576 a^{4} b^{5} d^{3} n \,x^{5}+18 a^{3} b^{6} c^{2} d \,n^{6}+891000 a^{3} b^{6} c \,d^{2} n^{3} x^{3}+362880 a^{3} b^{6} d^{3} x^{6}-15840 a^{2} b^{7} c^{2} d \,n^{5} x -3415320 a^{2} b^{7} c \,d^{2} n^{2} x^{4}+636471 a \,b^{8} c^{2} d \,n^{4} x^{2}+4073760 a \,b^{8} c \,d^{2} n \,x^{5}-16884 b^{9} c^{3} n^{6}-4371522 b^{9} c^{2} d \,n^{3} x^{3}-1555200 b^{9} c \,d^{2} x^{6}-362880 a^{6} b^{3} d^{3} n^{2} x^{3}+2160 a^{5} b^{4} c \,d^{2} n^{4} x +756000 a^{5} b^{4} d^{3} n \,x^{4}-351000 a^{4} b^{5} c \,d^{2} n^{3} x^{2}-362880 a^{4} b^{5} d^{3} x^{5}+810 a^{3} b^{6} c^{2} d \,n^{5}+2571840 a^{3} b^{6} c \,d^{2} n^{2} x^{3}-162180 a^{2} b^{7} c^{2} d \,n^{4} x -3762720 a^{2} b^{7} c \,d^{2} n \,x^{4}+2500038 a \,b^{8} c^{2} d \,n^{3} x^{2}+1555200 a \,b^{8} c \,d^{2} x^{5}-140889 b^{9} c^{3} n^{5}-7742412 b^{9} c^{2} d \,n^{2} x^{3}+181440 a^{7} b^{2} d^{3} n^{2} x^{2}-665280 a^{6} b^{3} d^{3} n \,x^{3}+60480 a^{5} b^{4} c \,d^{2} n^{3} x +362880 a^{5} b^{4} d^{3} x^{4}-1620000 a^{4} b^{5} c \,d^{2} n^{2} x^{2}+15030 a^{3} b^{6} c^{2} d \,n^{4}+3373920 a^{3} b^{6} c \,d^{2} n \,x^{3}-948582 a^{2} b^{7} c^{2} d \,n^{3} x -1555200 a^{2} b^{7} c \,d^{2} x^{4}+5614452 a \,b^{8} c^{2} d \,n^{2} x^{2}-761166 b^{9} c^{3} n^{4}-7291080 b^{9} c^{2} d n \,x^{3}+544320 a^{7} b^{2} d^{3} n \,x^{2}-2160 a^{6} b^{3} c \,d^{2} n^{3}-362880 a^{6} b^{3} d^{3} x^{3}+581040 a^{5} b^{4} c \,d^{2} n^{2} x -2855520 a^{4} b^{5} c \,d^{2} n \,x^{2}+147150 a^{3} b^{6} c^{2} d \,n^{3}+1555200 a^{3} b^{6} c \,d^{2} x^{3}-3102912 a^{2} b^{7} c^{2} d \,n^{2} x +6383880 a \,b^{8} c^{2} d n \,x^{2}-2655764 b^{9} c^{3} n^{3}-2721600 b^{9} c^{2} d \,x^{3}-362880 a^{8} b \,d^{3} n x +362880 a^{7} b^{2} d^{3} x^{2}-58320 a^{6} b^{3} c \,d^{2} n^{2}+2077920 a^{5} b^{4} c \,d^{2} n x -1555200 a^{4} b^{5} c \,d^{2} x^{2}+801432 a^{3} b^{6} c^{2} d \,n^{2}-5023080 a^{2} b^{7} c^{2} d n x +2721600 a \,b^{8} c^{2} d \,x^{2}-5753736 b^{9} c^{3} n^{2}-362880 a^{8} b \,d^{3} x -522720 a^{6} b^{3} c \,d^{2} n +1555200 a^{5} b^{4} c \,d^{2} x +2301480 a^{3} b^{6} c^{2} d n -2721600 a^{2} b^{7} c^{2} d x -6999840 b^{9} c^{3} n +362880 a^{9} d^{3}-1555200 a^{6} b^{3} c \,d^{2}+2721600 a^{3} b^{6} c^{2} d -3628800 b^{9} c^{3}\right) \left(b x +a \right)^{n +1}}{\left(n^{10}+55 n^{9}+1320 n^{8}+18150 n^{7}+157773 n^{6}+902055 n^{5}+3416930 n^{4}+8409500 n^{3}+12753576 n^{2}+10628640 n +3628800\right) b^{10}}"," ",0,"-(b*x+a)^(n+1)*(-b^9*d^3*n^9*x^9-45*b^9*d^3*n^8*x^9+9*a*b^8*d^3*n^8*x^8-870*b^9*d^3*n^7*x^9+324*a*b^8*d^3*n^7*x^8-3*b^9*c*d^2*n^9*x^6-9450*b^9*d^3*n^6*x^9-72*a^2*b^7*d^3*n^7*x^7+4914*a*b^8*d^3*n^6*x^8-144*b^9*c*d^2*n^8*x^6-63273*b^9*d^3*n^5*x^9-2016*a^2*b^7*d^3*n^6*x^7+18*a*b^8*c*d^2*n^8*x^5+40824*a*b^8*d^3*n^5*x^8-2952*b^9*c*d^2*n^7*x^6-269325*b^9*d^3*n^4*x^9+504*a^3*b^6*d^3*n^6*x^6-23184*a^2*b^7*d^3*n^5*x^7+756*a*b^8*c*d^2*n^7*x^5+202041*a*b^8*d^3*n^4*x^8-3*b^9*c^2*d*n^9*x^3-33786*b^9*c*d^2*n^6*x^6-723680*b^9*d^3*n^3*x^9+10584*a^3*b^6*d^3*n^5*x^6-90*a^2*b^7*c*d^2*n^7*x^4-141120*a^2*b^7*d^3*n^4*x^7+13176*a*b^8*c*d^2*n^6*x^5+605556*a*b^8*d^3*n^3*x^8-153*b^9*c^2*d*n^8*x^3-236817*b^9*c*d^2*n^5*x^6-1172700*b^9*d^3*n^2*x^9-3024*a^4*b^5*d^3*n^5*x^5+88200*a^3*b^6*d^3*n^4*x^6-3330*a^2*b^7*c*d^2*n^6*x^4-487368*a^2*b^7*d^3*n^3*x^7+9*a*b^8*c^2*d*n^8*x^2+123660*a*b^8*c*d^2*n^5*x^5+1063116*a*b^8*d^3*n^2*x^8-3348*b^9*c^2*d*n^7*x^3-1048446*b^9*c*d^2*n^4*x^6-1026576*b^9*d^3*n*x^9-45360*a^4*b^5*d^3*n^4*x^5+360*a^3*b^6*c*d^2*n^6*x^3+370440*a^3*b^6*d^3*n^3*x^6-49230*a^2*b^7*c*d^2*n^5*x^4-945504*a^2*b^7*d^3*n^2*x^7+432*a*b^8*c^2*d*n^7*x^2+678942*a*b^8*c*d^2*n^4*x^5+986256*a*b^8*d^3*n*x^8-b^9*c^3*n^9-41058*b^9*c^2*d*n^6*x^3-2911668*b^9*c*d^2*n^3*x^6-362880*b^9*d^3*x^9+15120*a^5*b^4*d^3*n^4*x^4-257040*a^4*b^5*d^3*n^3*x^5+11880*a^3*b^6*c*d^2*n^5*x^3+818496*a^3*b^6*d^3*n^2*x^6-18*a^2*b^7*c^2*d*n^7*x-372150*a^2*b^7*c*d^2*n^4*x^4-940896*a^2*b^7*d^3*n*x^7+8748*a*b^8*c^2*d*n^6*x^2+2217024*a*b^8*c*d^2*n^3*x^5+362880*a*b^8*d^3*x^8-54*b^9*c^3*n^8-309087*b^9*c^2*d*n^5*x^3-4846824*b^9*c*d^2*n^2*x^6+151200*a^5*b^4*d^3*n^3*x^4-1080*a^4*b^5*c*d^2*n^5*x^2-680400*a^4*b^5*d^3*n^2*x^5+149400*a^3*b^6*c*d^2*n^4*x^3+889056*a^3*b^6*d^3*n*x^6-828*a^2*b^7*c^2*d*n^6*x-1533960*a^2*b^7*c*d^2*n^3*x^4-362880*a^2*b^7*d^3*x^7+96930*a*b^8*c^2*d*n^5*x^2+4167864*a*b^8*c*d^2*n^2*x^5-1266*b^9*c^3*n^7-1469817*b^9*c^2*d*n^4*x^3-4332960*b^9*c*d^2*n*x^6-60480*a^6*b^3*d^3*n^3*x^3+529200*a^5*b^4*d^3*n^2*x^4-32400*a^4*b^5*c*d^2*n^4*x^2-828576*a^4*b^5*d^3*n*x^5+18*a^3*b^6*c^2*d*n^6+891000*a^3*b^6*c*d^2*n^3*x^3+362880*a^3*b^6*d^3*x^6-15840*a^2*b^7*c^2*d*n^5*x-3415320*a^2*b^7*c*d^2*n^2*x^4+636471*a*b^8*c^2*d*n^4*x^2+4073760*a*b^8*c*d^2*n*x^5-16884*b^9*c^3*n^6-4371522*b^9*c^2*d*n^3*x^3-1555200*b^9*c*d^2*x^6-362880*a^6*b^3*d^3*n^2*x^3+2160*a^5*b^4*c*d^2*n^4*x+756000*a^5*b^4*d^3*n*x^4-351000*a^4*b^5*c*d^2*n^3*x^2-362880*a^4*b^5*d^3*x^5+810*a^3*b^6*c^2*d*n^5+2571840*a^3*b^6*c*d^2*n^2*x^3-162180*a^2*b^7*c^2*d*n^4*x-3762720*a^2*b^7*c*d^2*n*x^4+2500038*a*b^8*c^2*d*n^3*x^2+1555200*a*b^8*c*d^2*x^5-140889*b^9*c^3*n^5-7742412*b^9*c^2*d*n^2*x^3+181440*a^7*b^2*d^3*n^2*x^2-665280*a^6*b^3*d^3*n*x^3+60480*a^5*b^4*c*d^2*n^3*x+362880*a^5*b^4*d^3*x^4-1620000*a^4*b^5*c*d^2*n^2*x^2+15030*a^3*b^6*c^2*d*n^4+3373920*a^3*b^6*c*d^2*n*x^3-948582*a^2*b^7*c^2*d*n^3*x-1555200*a^2*b^7*c*d^2*x^4+5614452*a*b^8*c^2*d*n^2*x^2-761166*b^9*c^3*n^4-7291080*b^9*c^2*d*n*x^3+544320*a^7*b^2*d^3*n*x^2-2160*a^6*b^3*c*d^2*n^3-362880*a^6*b^3*d^3*x^3+581040*a^5*b^4*c*d^2*n^2*x-2855520*a^4*b^5*c*d^2*n*x^2+147150*a^3*b^6*c^2*d*n^3+1555200*a^3*b^6*c*d^2*x^3-3102912*a^2*b^7*c^2*d*n^2*x+6383880*a*b^8*c^2*d*n*x^2-2655764*b^9*c^3*n^3-2721600*b^9*c^2*d*x^3-362880*a^8*b*d^3*n*x+362880*a^7*b^2*d^3*x^2-58320*a^6*b^3*c*d^2*n^2+2077920*a^5*b^4*c*d^2*n*x-1555200*a^4*b^5*c*d^2*x^2+801432*a^3*b^6*c^2*d*n^2-5023080*a^2*b^7*c^2*d*n*x+2721600*a*b^8*c^2*d*x^2-5753736*b^9*c^3*n^2-362880*a^8*b*d^3*x-522720*a^6*b^3*c*d^2*n+1555200*a^5*b^4*c*d^2*x+2301480*a^3*b^6*c^2*d*n-2721600*a^2*b^7*c^2*d*x-6999840*b^9*c^3*n+362880*a^9*d^3-1555200*a^6*b^3*c*d^2+2721600*a^3*b^6*c^2*d-3628800*b^9*c^3)/b^10/(n^10+55*n^9+1320*n^8+18150*n^7+157773*n^6+902055*n^5+3416930*n^4+8409500*n^3+12753576*n^2+10628640*n+3628800)","B"
185,0,0,360,0.043000," ","int((b*x+a)^n*(d*x^3+c)^3/x,x)","\int \frac{\left(d \,x^{3}+c \right)^{3} \left(b x +a \right)^{n}}{x}\, dx"," ",0,"int((b*x+a)^n*(d*x^3+c)^3/x,x)","F"
186,0,0,280,0.072000," ","int(x^5*(f*x+e)^n/(b*x^3+a),x)","\int \frac{x^{5} \left(f x +e \right)^{n}}{b \,x^{3}+a}\, dx"," ",0,"int(x^5*(f*x+e)^n/(b*x^3+a),x)","F"
187,0,0,274,0.063000," ","int(x^4*(f*x+e)^n/(b*x^3+a),x)","\int \frac{x^{4} \left(f x +e \right)^{n}}{b \,x^{3}+a}\, dx"," ",0,"int(x^4*(f*x+e)^n/(b*x^3+a),x)","F"
188,0,0,245,0.058000," ","int(x^3*(f*x+e)^n/(b*x^3+a),x)","\int \frac{x^{3} \left(f x +e \right)^{n}}{b \,x^{3}+a}\, dx"," ",0,"int(x^3*(f*x+e)^n/(b*x^3+a),x)","F"
189,0,0,209,0.053000," ","int(x^2*(f*x+e)^n/(b*x^3+a),x)","\int \frac{x^{2} \left(f x +e \right)^{n}}{b \,x^{3}+a}\, dx"," ",0,"int(x^2*(f*x+e)^n/(b*x^3+a),x)","F"
190,0,0,230,0.056000," ","int(x*(f*x+e)^n/(b*x^3+a),x)","\int \frac{x \left(f x +e \right)^{n}}{b \,x^{3}+a}\, dx"," ",0,"int(x*(f*x+e)^n/(b*x^3+a),x)","F"
191,0,0,215,0.055000," ","int((f*x+e)^n/(b*x^3+a),x)","\int \frac{\left(f x +e \right)^{n}}{b \,x^{3}+a}\, dx"," ",0,"int((f*x+e)^n/(b*x^3+a),x)","F"
192,0,0,258,0.049000," ","int((f*x+e)^n/x/(b*x^3+a),x)","\int \frac{\left(f x +e \right)^{n}}{\left(b \,x^{3}+a \right) x}\, dx"," ",0,"int((f*x+e)^n/x/(b*x^3+a),x)","F"
193,0,0,270,0.067000," ","int((f*x+e)^n/x^2/(b*x^3+a),x)","\int \frac{\left(f x +e \right)^{n}}{\left(b \,x^{3}+a \right) x^{2}}\, dx"," ",0,"int((f*x+e)^n/x^2/(b*x^3+a),x)","F"
194,0,0,209,0.059000," ","int(x^2*(d*x+c)^(n+1)/(b*x^3+a),x)","\int \frac{x^{2} \left(d x +c \right)^{n +1}}{b \,x^{3}+a}\, dx"," ",0,"int(x^2*(d*x+c)^(n+1)/(b*x^3+a),x)","F"
195,0,0,189,0.061000," ","int(x^m*(f*x+e)^n/(b*x^3+a),x)","\int \frac{x^{m} \left(f x +e \right)^{n}}{b \,x^{3}+a}\, dx"," ",0,"int(x^m*(f*x+e)^n/(b*x^3+a),x)","F"
196,1,1126,1109,0.225000," ","int((d*x^3+c)^(1/2)/(b*x+a),x)","-\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, b^{3}}+\frac{2 i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)+\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{d}\right) a}{3 \sqrt{d \,x^{3}+c}\, b^{2}}+\frac{2 \sqrt{d \,x^{3}+c}}{3 b}+\frac{2 i \left(a^{3} d -b^{3} c \right) \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{d}}{-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}-\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) \sqrt{3}\, d}{\left(-c \,d^{2}\right)^{\frac{1}{3}}}}}{3}, \frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(\frac{a}{b}-\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}, \sqrt{\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) d}}\right)}{3 \sqrt{d \,x^{3}+c}\, \left(\frac{a}{b}-\frac{\left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}+\frac{i \sqrt{3}\, \left(-c \,d^{2}\right)^{\frac{1}{3}}}{2 d}\right) b^{4} d}"," ",0,"2/3*(d*x^3+c)^(1/2)/b-2/3*I*a^2/b^3*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2/d*(-c*d^2)^(1/3)-1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2)*((x-1/d*(-c*d^2)^(1/3))/(-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)))^(1/2)*(-I*(x+1/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2)/(d*x^3+c)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/d*(-c*d^2)^(1/3)-1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2),(I*3^(1/2)/d*(-c*d^2)^(1/3)/(-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)))^(1/2))+2/3*I*a/b^2*3^(1/2)*(-c*d^2)^(1/3)*(I*(x+1/2/d*(-c*d^2)^(1/3)-1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2)*((x-1/d*(-c*d^2)^(1/3))/(-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)))^(1/2)*(-I*(x+1/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2)/(d*x^3+c)^(1/2)*((-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*EllipticE(1/3*3^(1/2)*(I*(x+1/2/d*(-c*d^2)^(1/3)-1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2),(I*3^(1/2)/d*(-c*d^2)^(1/3)/(-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)))^(1/2))+1/d*(-c*d^2)^(1/3)*EllipticF(1/3*3^(1/2)*(I*(x+1/2/d*(-c*d^2)^(1/3)-1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2),(I*3^(1/2)/d*(-c*d^2)^(1/3)/(-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)))^(1/2)))+2/3*I*(a^3*d-b^3*c)/b^4*3^(1/2)/d*(-c*d^2)^(1/3)*(I*(x+1/2/d*(-c*d^2)^(1/3)-1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2)*((x-1/d*(-c*d^2)^(1/3))/(-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)))^(1/2)*(-I*(x+1/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2)/(d*x^3+c)^(1/2)/(-1/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)+a/b)*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/d*(-c*d^2)^(1/3)-1/2*I*3^(1/2)/d*(-c*d^2)^(1/3))*3^(1/2)*d/(-c*d^2)^(1/3))^(1/2),I*3^(1/2)/d*(-c*d^2)^(1/3)/(-1/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)+a/b),(I*3^(1/2)/d*(-c*d^2)^(1/3)/(-3/2/d*(-c*d^2)^(1/3)+1/2*I*3^(1/2)/d*(-c*d^2)^(1/3)))^(1/2))","A"
197,0,0,123,0.066000," ","int((e^3*x^3+d^3)^p/(e*x+d),x)","\int \frac{\left(e^{3} x^{3}+d^{3}\right)^{p}}{e x +d}\, dx"," ",0,"int((e^3*x^3+d^3)^p/(e*x+d),x)","F"
198,1,1640,14,0.072000," ","int((-x^2-2*x+2)/(x^2+2)/(x^3+1)^(1/2),x)","-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{3 i \sqrt{2}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-1-i \sqrt{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(-1-i \sqrt{2}\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-1-i \sqrt{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(-1-i \sqrt{2}\right)}-\frac{3 \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-1-i \sqrt{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(-1-i \sqrt{2}\right)}+\frac{i \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-1-i \sqrt{2}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(-1-i \sqrt{2}\right)}+\frac{3 i \sqrt{2}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{i \sqrt{2}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(i \sqrt{2}-1\right)}+\frac{\sqrt{2}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{i \sqrt{2}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(i \sqrt{2}-1\right)}-\frac{3 \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{i \sqrt{2}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(i \sqrt{2}-1\right)}+\frac{i \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}-\frac{i \sqrt{3}}{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{2 \left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{i \sqrt{3}}{-3+i \sqrt{3}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{i \sqrt{2}-1}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}\, \left(i \sqrt{2}-1\right)}"," ",0,"-2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-3*I*2^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1-I*2^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1-I*2^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-2^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1-I*2^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1-I*2^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-3*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1-I*2^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1-I*2^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+I*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1-I*2^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1-I*2^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+3*I*2^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(I*2^(1/2)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(I*2^(1/2)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(I*2^(1/2)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(I*2^(1/2)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-3*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(I*2^(1/2)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(I*2^(1/2)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+I*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(I*2^(1/2)-1)*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(I*2^(1/2)-1),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)","C"
199,1,732,18,0.062000," ","int((-x^2+2*x+2)/(x^2+2)/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}-i \sqrt{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}-i \sqrt{2}\right)}-\frac{2 \sqrt{2}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{-\frac{1}{2}+\frac{i \sqrt{3}}{2}-i \sqrt{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}-i \sqrt{2}\right)}-\frac{2 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{i \sqrt{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(i \sqrt{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{2 \sqrt{2}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{i \sqrt{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(i \sqrt{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)-I*2^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)-I*2^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*2^(1/2)*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)-I*2^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)-I*2^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(I*2^(1/2)-1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(I*2^(1/2)-1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+2/3*2^(1/2)*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(I*2^(1/2)-1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(I*2^(1/2)-1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","C"
200,1,1656,16,0.063000," ","int((-x^2+2*x+2)/(x^2+2)/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{3 \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-i \sqrt{2}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-i \sqrt{2}+1\right)}-\frac{i \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-i \sqrt{2}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-i \sqrt{2}+1\right)}+\frac{3 i \sqrt{2}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-i \sqrt{2}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-i \sqrt{2}+1\right)}-\frac{\sqrt{2}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-i \sqrt{2}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(-i \sqrt{2}+1\right)}-\frac{3 \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{i \sqrt{2}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(i \sqrt{2}+1\right)}-\frac{i \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{i \sqrt{2}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(i \sqrt{2}+1\right)}-\frac{3 i \sqrt{2}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{i \sqrt{2}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(i \sqrt{2}+1\right)}+\frac{\sqrt{2}\, \sqrt{\frac{x}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}+\frac{1}{3-i \sqrt{3}}-\frac{i \sqrt{3}}{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{3+i \sqrt{3}}+\frac{i \sqrt{3}}{3+i \sqrt{3}}}\, \sqrt{3}\, \EllipticPi \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{i \sqrt{2}+1}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}\, \left(i \sqrt{2}+1\right)}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-3*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(-I*2^(1/2)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-I*2^(1/2)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-I*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(-I*2^(1/2)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-I*2^(1/2)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+3*I*2^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(-I*2^(1/2)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-I*2^(1/2)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(-I*2^(1/2)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(-I*2^(1/2)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-3*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(I*2^(1/2)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(I*2^(1/2)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-I*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(I*2^(1/2)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(I*2^(1/2)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-3*I*2^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(I*2^(1/2)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(I*2^(1/2)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(I*2^(1/2)+1)*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(I*2^(1/2)+1),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)","C"
201,1,724,16,0.061000," ","int((-x^2-2*x+2)/(x^2+2)/(-x^3-1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 \sqrt{2}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}-i \sqrt{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}-i \sqrt{2}\right)}+\frac{2 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{1}{2}+\frac{i \sqrt{3}}{2}-i \sqrt{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{1}{2}+\frac{i \sqrt{3}}{2}-i \sqrt{2}\right)}+\frac{2 \sqrt{2}\, \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{i \sqrt{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(i \sqrt{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}+\frac{2 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{i \sqrt{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(i \sqrt{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*2^(1/2)*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)-I*2^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)-I*2^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)-I*2^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)-I*2^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*2^(1/2)*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(I*2^(1/2)+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(I*2^(1/2)+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(I*2^(1/2)+1/2+1/2*I*3^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(I*2^(1/2)+1/2+1/2*I*3^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","C"
202,1,4397,24,0.071000," ","int((-x^2-2*x+2)/(d*x+x^2+d+2)/(x^3+1)^(1/2),x)","\text{output too large to display}"," ",0,"-2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-3/2/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d^2-1/2*I*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d*3^(1/2)+3/2*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d-4*I/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+6/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d+2*I/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d*3^(1/2)-3*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+4*I/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+12/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+1/2*I/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d^2*3^(1/2)+3/2/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d^2+I*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)+3/2*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d-1/2*I*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d*3^(1/2)-6/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d-2*I/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d-1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d*3^(1/2)-3*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+I*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-12/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-1/2*I/(d^2-4*d-8)^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/(3/2-1/2*I*3^(1/2)))^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/2/(-3/2-1/2*I*3^(1/2))-1/2*I/(-3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/2/(-3/2+1/2*I*3^(1/2))+1/2*I/(-3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3+1)^(1/2)/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),(-3/2+1/2*I*3^(1/2))/(-1+1/2*d+1/2*(d^2-4*d-8)^(1/2)),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))*d^2*3^(1/2)","C"
203,1,1908,32,0.071000," ","int((-x^2+2*x+2)/(d*x+x^2-d+2)/(-x^3+1)^(1/2),x)","\frac{i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d^{2} \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}+4 d -8}\, \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}-\frac{i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d^{2} \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}+4 d -8}\, \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}-\frac{i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}+\frac{4 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}+4 d -8}\, \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}-\frac{i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}-\frac{4 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}+4 d -8}\, \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}+\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}-\frac{8 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}+4 d -8}\, \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}-\frac{2 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}+\frac{8 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}-\frac{1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}+4 d -8}\, \sqrt{-x^{3}+1}\, \left(\frac{d}{2}-\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}+4 d -8}}{2}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+1/3*I/(d^2+4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))*d^2-1/3*I*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))*d+4/3*I/(d^2+4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))*d-2/3*I*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-8/3*I/(d^2+4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-1/3*I/(d^2+4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))*d^2-1/3*I*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))*d-4/3*I/(d^2+4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))*d-2/3*I*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+8/3*I/(d^2+4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)*(1/(-3/2+1/2*I*3^(1/2))*x-1/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3+1)^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(-1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2+4*d-8)^(1/2)),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","C"
204,1,4437,30,0.052000," ","int((-x^2+2*x+2)/(d*x+x^2-d+2)/(x^3-1)^(1/2),x)","\text{output too large to display}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+3/2/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d^2+2*I/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d*3^(1/2)-3/2*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d-1/2*I*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d*3^(1/2)+6/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d-1/2*I*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d*3^(1/2)-3*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-I*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-12/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+4*I/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-3/2/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d^2+1/2*I/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d^2*3^(1/2)-3/2*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d-I*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-6/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d-4*I/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d-1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*3^(1/2)-3*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-1/2*I/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d^2*3^(1/2)+12/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2*I/(d^2+4*d-8)^(1/2)*(1/(-3/2-1/2*I*3^(1/2))*x-1/(-3/2-1/2*I*3^(1/2)))^(1/2)*(1/(3/2-1/2*I*3^(1/2))*x+1/2/(3/2-1/2*I*3^(1/2))-1/2*I/(3/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/2/(3/2+1/2*I*3^(1/2))+1/2*I/(3/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(x^3-1)^(1/2)/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2))*EllipticPi(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),(3/2+1/2*I*3^(1/2))/(1+1/2*d+1/2*(d^2+4*d-8)^(1/2)),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))*d*3^(1/2)","C"
205,1,1888,26,0.059000," ","int((-x^2-2*x+2)/(d*x+x^2+d+2)/(-x^3-1)^(1/2),x)","\frac{i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d^{2} \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}-4 d -8}\, \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}-\frac{i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d^{2} \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}-4 d -8}\, \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}-\frac{i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}-\frac{4 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}-4 d -8}\, \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}-\frac{i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}+\frac{4 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, d \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}-4 d -8}\, \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}+\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{2 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}-\frac{8 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}-4 d -8}\, \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}-\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}+\frac{2 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}+\frac{8 i \sqrt{3}\, \sqrt{i \sqrt{3}\, x -\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \sqrt{\frac{x}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}+\frac{1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \sqrt{3}\, x +\frac{i \sqrt{3}}{2}+\frac{3}{2}}\, \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \frac{i \sqrt{3}}{\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{d^{2}-4 d -8}\, \sqrt{-x^{3}-1}\, \left(\frac{d}{2}+\frac{1}{2}+\frac{i \sqrt{3}}{2}+\frac{\sqrt{d^{2}-4 d -8}}{2}\right)}"," ",0,"2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+1/3*I/(d^2-4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))*d^2-1/3*I*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))*d-4/3*I/(d^2-4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))*d+2/3*I*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-8/3*I/(d^2-4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d-1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-1/3*I/(d^2-4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))*d^2-1/3*I*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))*d+4/3*I/(d^2-4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))*d+2/3*I*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+8/3*I/(d^2-4*d-8)^(1/2)*3^(1/2)*(I*3^(1/2)*x-1/2*I*3^(1/2)+3/2)^(1/2)*(1/(3/2+1/2*I*3^(1/2))*x+1/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*3^(1/2)*x+1/2*I*3^(1/2)+3/2)^(1/2)/(-x^3-1)^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2))*EllipticPi(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),I*3^(1/2)/(1/2+1/2*I*3^(1/2)+1/2*d+1/2*(d^2-4*d-8)^(1/2)),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","C"
206,1,334,343,0.064000," ","int((e*x+d)^3*(c*x^4+a)^(1/2),x)","\frac{3 \sqrt{c \,x^{4}+a}\, d \,e^{2} x^{3}}{5}-\frac{6 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} d \,e^{2} \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}+\frac{6 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} d \,e^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}+\frac{2 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,d^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{3 \sqrt{c \,x^{4}+a}\, d^{2} e \,x^{2}}{4}+\frac{3 a \,d^{2} e \ln \left(\sqrt{c}\, x^{2}+\sqrt{c \,x^{4}+a}\right)}{4 \sqrt{c}}+\frac{\sqrt{c \,x^{4}+a}\, d^{3} x}{3}+\frac{\left(c \,x^{4}+a \right)^{\frac{3}{2}} e^{3}}{6 c}"," ",0,"1/6*e^3*(c*x^4+a)^(3/2)/c+3/5*d*e^2*x^3*(c*x^4+a)^(1/2)+6/5*I*d*e^2*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(1-I/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*c^(1/2)*x^2)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*EllipticF(x*(I/a^(1/2)*c^(1/2))^(1/2),I)-6/5*I*d*e^2*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(1-I/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*c^(1/2)*x^2)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*EllipticE(x*(I/a^(1/2)*c^(1/2))^(1/2),I)+3/4*d^2*e*x^2*(c*x^4+a)^(1/2)+3/4*e*d^2*a/c^(1/2)*ln(x^2*c^(1/2)+(c*x^4+a)^(1/2))+1/3*d^3*x*(c*x^4+a)^(1/2)+2/3*d^3*a/(I/a^(1/2)*c^(1/2))^(1/2)*(1-I/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*c^(1/2)*x^2)^(1/2)/(c*x^4+a)^(1/2)*EllipticF(x*(I/a^(1/2)*c^(1/2))^(1/2),I)","C"
207,1,310,318,0.016000," ","int((e*x+d)^2*(c*x^4+a)^(1/2),x)","\frac{\sqrt{c \,x^{4}+a}\, e^{2} x^{3}}{5}-\frac{2 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} e^{2} \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}+\frac{2 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} e^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}+\frac{2 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,d^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, d e \,x^{2}}{2}+\frac{a d e \ln \left(\sqrt{c}\, x^{2}+\sqrt{c \,x^{4}+a}\right)}{2 \sqrt{c}}+\frac{\sqrt{c \,x^{4}+a}\, d^{2} x}{3}"," ",0,"1/5*e^2*x^3*(c*x^4+a)^(1/2)+2/5*I*e^2*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-2/5*I*e^2*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*d*e*x^2*(c*x^4+a)^(1/2)+1/2*d*e*a/c^(1/2)*ln(c^(1/2)*x^2+(c*x^4+a)^(1/2))+1/3*d^2*x*(c*x^4+a)^(1/2)+2/3*d^2*a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
208,1,127,153,0.010000," ","int((e*x+d)*(c*x^4+a)^(1/2),x)","\frac{2 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e \,x^{2}}{4}+\frac{a e \ln \left(\sqrt{c}\, x^{2}+\sqrt{c \,x^{4}+a}\right)}{4 \sqrt{c}}+\frac{\sqrt{c \,x^{4}+a}\, d x}{3}"," ",0,"1/4*e*x^2*(c*x^4+a)^(1/2)+1/4*e*a/c^(1/2)*ln(c^(1/2)*x^2+(c*x^4+a)^(1/2))+1/3*d*x*(c*x^4+a)^(1/2)+2/3*d*a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
209,1,85,112,0.003000," ","int((c*x^4+a)^(1/2),x)","\frac{2 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, x}{3}"," ",0,"1/3*x*(c*x^4+a)^(1/2)+2/3*a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
210,1,565,714,0.025000," ","int((c*x^4+a)^(1/2)/(e*x+d),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{a \arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+a}}\right)}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, e}-\frac{c \,d^{4} \arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+a}}\right)}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, e^{5}}-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,d^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, e^{4}}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,d^{3} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, e^{4}}+\frac{\sqrt{c}\, d^{2} \ln \left(2 \sqrt{c}\, x^{2}+2 \sqrt{c \,x^{4}+a}\right)}{2 e^{3}}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, \sqrt{c}\, d}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, e^{2}}+\frac{\sqrt{c \,x^{4}+a}}{2 e}"," ",0,"1/2*(c*x^4+a)^(1/2)/e-c*d^3/e^4/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*c^(1/2)*d^2/e^3*ln(2*c^(1/2)*x^2+2*(c*x^4+a)^(1/2))-I*c^(1/2)*d/e^2*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))-1/2/e/(c*d^4/e^4+a)^(1/2)*arctanh(1/2*(2*c*x^2*d^2/e^2+2*a)/(c*d^4/e^4+a)^(1/2)/(c*x^4+a)^(1/2))*a-1/2/e^5/(c*d^4/e^4+a)^(1/2)*arctanh(1/2*(2*c*x^2*d^2/e^2+2*a)/(c*d^4/e^4+a)^(1/2)/(c*x^4+a)^(1/2))*c*d^4+1/(I/a^(1/2)*c^(1/2))^(1/2)/d*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)/d^2*e^2,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a+1/e^4/(I/a^(1/2)*c^(1/2))^(1/2)*d^3*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)/d^2*e^2,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c","C"
211,1,402,1212,0.029000," ","int((c*x^4+a)^(1/2)/(e*x+d)^2,x)","\frac{c \,d^{3} \arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+a}}\right)}{\sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, e^{5}}+\frac{2 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,d^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, e^{4}}-\frac{2 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,d^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, e^{4}}-\frac{\sqrt{c}\, d \ln \left(2 \sqrt{c}\, x^{2}+2 \sqrt{c \,x^{4}+a}\right)}{e^{3}}+\frac{2 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, \sqrt{c}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, e^{2}}-\frac{\sqrt{c \,x^{4}+a}}{\left(e x +d \right) e}"," ",0,"-1/e*(c*x^4+a)^(1/2)/(e*x+d)+2*c*d^2/e^4/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-c^(1/2)*d/e^3*ln(2*c^(1/2)*x^2+2*(c*x^4+a)^(1/2))+2*I*c^(1/2)/e^2*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+c*d^3/e^5/(a+c*d^4/e^4)^(1/2)*arctanh(1/2*(2*c*d^2/e^2*x^2+2*a)/(a+c*d^4/e^4)^(1/2)/(c*x^4+a)^(1/2))-2*c*d^2/e^4/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)/d^2*e^2,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))","C"
212,1,218,295,0.025000," ","int((e*x+d)^3/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{3 d^{2} e \ln \left(\sqrt{c}\, x^{2}+\sqrt{c \,x^{4}+a}\right)}{2 \sqrt{c}}+\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, d \,e^{2}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}+\frac{\sqrt{c \,x^{4}+a}\, e^{3}}{2 c}"," ",0,"1/2*e^3*(c*x^4+a)^(1/2)/c+3*I*d*e^2*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+3/2*e*d^2*ln(c^(1/2)*x^2+(c*x^4+a)^(1/2))/c^(1/2)+d^3/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
213,1,197,269,0.015000," ","int((e*x+d)^2/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{d e \ln \left(\sqrt{c}\, x^{2}+\sqrt{c \,x^{4}+a}\right)}{\sqrt{c}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, e^{2}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}"," ",0,"I*e^2*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+d*e*ln(c^(1/2)*x^2+(c*x^4+a)^(1/2))/c^(1/2)+d^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
214,1,96,124,0.010000," ","int((e*x+d)/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{e \ln \left(\sqrt{c}\, x^{2}+\sqrt{c \,x^{4}+a}\right)}{2 \sqrt{c}}"," ",0,"1/2*e*ln(c^(1/2)*x^2+(c*x^4+a)^(1/2))/c^(1/2)+d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
215,1,70,99,0.003000," ","int(1/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}"," ",0,"1/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
216,1,169,389,0.016000," ","int(1/(e*x+d)/(c*x^4+a)^(1/2),x)","\frac{\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{\arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+a}}\right)}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}}}{e}"," ",0,"1/e*(-1/2/(a+c*d^4/e^4)^(1/2)*arctanh(1/2*(2*c*d^2/e^2*x^2+2*a)/(a+c*d^4/e^4)^(1/2)/(c*x^4+a)^(1/2))+1/(I/a^(1/2)*c^(1/2))^(1/2)/d*e*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)/d^2*e^2,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)))","C"
217,1,421,601,0.026000," ","int(1/(e*x+d)^2/(c*x^4+a)^(1/2),x)","-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,d^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\left(a \,e^{4}+c \,d^{4}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, \sqrt{c}\, e^{2}}{\left(a \,e^{4}+c \,d^{4}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{2 \left(\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{\arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+a}}\right)}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}}\right) c \,d^{3}}{\left(a \,e^{4}+c \,d^{4}\right) e}-\frac{\sqrt{c \,x^{4}+a}\, e^{3}}{\left(a \,e^{4}+c \,d^{4}\right) \left(e x +d \right)}"," ",0,"-e^3*(c*x^4+a)^(1/2)/(a*e^4+c*d^4)/(e*x+d)-c*d^2/(a*e^4+c*d^4)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+I*c^(1/2)*e^2/(a*e^4+c*d^4)*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+2*c*d^3/(a*e^4+c*d^4)/e*(-1/2/(a+c*d^4/e^4)^(1/2)*arctanh(1/2*(2*c*d^2/e^2*x^2+2*a)/(a+c*d^4/e^4)^(1/2)/(c*x^4+a)^(1/2))+1/(I/a^(1/2)*c^(1/2))^(1/2)/d*e*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)/d^2*e^2,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)))","C"
218,1,483,650,0.026000," ","int(1/(e*x+d)^3/(c*x^4+a)^(1/2),x)","\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, c^{\frac{3}{2}} d^{3} e^{2}}{\left(a \,e^{4}+c \,d^{4}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}-\frac{3 \sqrt{c \,x^{4}+a}\, c \,d^{3} e^{3}}{\left(a \,e^{4}+c \,d^{4}\right)^{2} \left(e x +d \right)}+\frac{\left(a \,e^{4}-2 c \,d^{4}\right) \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\left(a \,e^{4}+c \,d^{4}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}-\frac{\sqrt{c \,x^{4}+a}\, e^{3}}{2 \left(a \,e^{4}+c \,d^{4}\right) \left(e x +d \right)^{2}}-\frac{3 \left(a \,e^{4}-c \,d^{4}\right) \left(\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{\arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+a}}\right)}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}}\right) c \,d^{2}}{\left(a \,e^{4}+c \,d^{4}\right)^{2} e}"," ",0,"-1/2*e^3*(c*x^4+a)^(1/2)/(a*e^4+c*d^4)/(e*x+d)^2-3*c*d^3*e^3*(c*x^4+a)^(1/2)/(a*e^4+c*d^4)^2/(e*x+d)+c*d*(a*e^4-2*c*d^4)/(a*e^4+c*d^4)^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+3*I*c^(3/2)*e^2*d^3/(a*e^4+c*d^4)^2*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))-3*c*d^2*(a*e^4-c*d^4)/(a*e^4+c*d^4)^2/e*(-1/2/(a+c*d^4/e^4)^(1/2)*arctanh(1/2*(2*c*d^2/e^2*x^2+2*a)/(a+c*d^4/e^4)^(1/2)/(c*x^4+a)^(1/2))+1/(I/a^(1/2)*c^(1/2))^(1/2)/d*e*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)/d^2*e^2,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)))","C"
219,1,261,302,0.033000," ","int((e*x+d)^3/(c*x^4+a)^(3/2),x)","\frac{3 d^{2} e \,x^{2}}{2 \sqrt{c \,x^{4}+a}\, a}+\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}\right) d^{3}+3 \left(\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}\, \sqrt{c}}\right) d \,e^{2}-\frac{e^{3}}{2 \sqrt{c \,x^{4}+a}\, c}"," ",0,"-1/2*e^3/c/(c*x^4+a)^(1/2)+3*d*e^2*(1/2*x^3/a/((x^4+a/c)*c)^(1/2)-1/2*I/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+3/2*e*d^2/(c*x^4+a)^(1/2)/a*x^2+d^3*(1/2*x/a/((x^4+a/c)*c)^(1/2)+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
220,1,239,274,0.016000," ","int((e*x+d)^2/(c*x^4+a)^(3/2),x)","\frac{d e \,x^{2}}{\sqrt{c \,x^{4}+a}\, a}+\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}\right) d^{2}+\left(\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}\, \sqrt{c}}\right) e^{2}"," ",0,"e^2*(1/2/((x^4+a/c)*c)^(1/2)/a*x^3-1/2*I/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+d*e/(c*x^4+a)^(1/2)/a*x^2+d^2*(1/2/((x^4+a/c)*c)^(1/2)/a*x+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
221,1,115,121,0.011000," ","int((e*x+d)/(c*x^4+a)^(3/2),x)","\frac{e \,x^{2}}{2 \sqrt{c \,x^{4}+a}\, a}+\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}\right) d"," ",0,"1/2*e/(c*x^4+a)^(1/2)/a*x^2+d*(1/2/((x^4+a/c)*c)^(1/2)/a*x+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
222,1,94,115,0.005000," ","int(1/(c*x^4+a)^(3/2),x)","\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}"," ",0,"1/2/((x^4+a/c)*c)^(1/2)/a*x+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
223,1,496,802,0.022000," ","int(1/(e*x+d)/(c*x^4+a)^(3/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,d^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{4}+c \,d^{4}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{c}\, d \,e^{2}}{2 \left(a \,e^{4}+c \,d^{4}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}}+\frac{\left(\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , -\frac{i \sqrt{a}\, e^{2}}{\sqrt{c}\, d^{2}}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{\arctanh \left(\frac{\frac{2 c \,d^{2} x^{2}}{e^{2}}+2 a}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}\, \sqrt{c \,x^{4}+a}}\right)}{2 \sqrt{a +\frac{c \,d^{4}}{e^{4}}}}\right) e^{3}}{a \,e^{4}+c \,d^{4}}-\frac{2 \left(-\frac{d \,e^{2} x^{3}}{4 \left(a \,e^{4}+c \,d^{4}\right) a}+\frac{d^{2} e \,x^{2}}{4 \left(a \,e^{4}+c \,d^{4}\right) a}-\frac{d^{3} x}{4 \left(a \,e^{4}+c \,d^{4}\right) a}-\frac{e^{3}}{4 \left(a \,e^{4}+c \,d^{4}\right) c}\right) c}{\sqrt{\left(x^{4}+\frac{a}{c}\right) c}}"," ",0,"-2*c*(-1/4/a*e^2*d/(a*e^4+c*d^4)*x^3+1/4/a*e*d^2/(a*e^4+c*d^4)*x^2-1/4/a*d^3/(a*e^4+c*d^4)*x-1/4*e^3/(a*e^4+c*d^4)/c)/((x^4+a/c)*c)^(1/2)+1/2/a*c*d^3/(a*e^4+c*d^4)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-1/2*I/a^(1/2)*c^(1/2)*e^2*d/(a*e^4+c*d^4)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+e^3/(a*e^4+c*d^4)*(-1/2/(a+c*d^4/e^4)^(1/2)*arctanh(1/2*(2*c*d^2/e^2*x^2+2*a)/(a+c*d^4/e^4)^(1/2)/(c*x^4+a)^(1/2))+1/(I/a^(1/2)*c^(1/2))^(1/2)/d*e*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,-I*a^(1/2)/c^(1/2)/d^2*e^2,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)))","C"
224,0,0,293,0.061000," ","int(x^3*(d*x+c)^n/(b*x^4+a),x)","\int \frac{x^{3} \left(d x +c \right)^{n}}{b \,x^{4}+a}\, dx"," ",0,"int(x^3*(d*x+c)^n/(b*x^4+a),x)","F"
225,0,0,293,0.059000," ","int(x^3*(d*x+c)^(n+1)/(b*x^4+a),x)","\int \frac{x^{3} \left(d x +c \right)^{n +1}}{b \,x^{4}+a}\, dx"," ",0,"int(x^3*(d*x+c)^(n+1)/(b*x^4+a),x)","F"
226,1,1153,1491,0.102000," ","int(1/(e*x^2+d*x+c)/(b*x^4+a)^(1/2),x)","-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticPi \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , -\frac{4 i \sqrt{a}\, e^{2}}{\left(-d +\sqrt{-4 c e +d^{2}}\right)^{2} \sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{-4 c e +d^{2}}\, \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \left(-d +\sqrt{-4 c e +d^{2}}\right) \sqrt{b \,x^{4}+a}}-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticPi \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , -\frac{4 i \sqrt{a}\, e^{2}}{\left(d +\sqrt{-4 c e +d^{2}}\right)^{2} \sqrt{b}}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{-4 c e +d^{2}}\, \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \left(d +\sqrt{-4 c e +d^{2}}\right) \sqrt{b \,x^{4}+a}}-\frac{\arctanh \left(-\frac{b c \,x^{2}}{\sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}+\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}-\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}\, \sqrt{b \,x^{4}+a}\, e}+\frac{b \,d^{2} x^{2}}{2 \sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}+\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}-\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}\, \sqrt{b \,x^{4}+a}\, e^{2}}-\frac{\sqrt{-4 c e +d^{2}}\, b d \,x^{2}}{2 \sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}+\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}-\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}\, \sqrt{b \,x^{4}+a}\, e^{2}}+\frac{a}{\sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}+\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}-\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}\, \sqrt{b \,x^{4}+a}}\right)}{2 \sqrt{-4 c e +d^{2}}\, \sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}+\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}-\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}}+\frac{\arctanh \left(-\frac{b c \,x^{2}}{\sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}-\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}+\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}\, \sqrt{b \,x^{4}+a}\, e}+\frac{b \,d^{2} x^{2}}{2 \sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}-\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}+\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}\, \sqrt{b \,x^{4}+a}\, e^{2}}+\frac{\sqrt{-4 c e +d^{2}}\, b d \,x^{2}}{2 \sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}-\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}+\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}\, \sqrt{b \,x^{4}+a}\, e^{2}}+\frac{a}{\sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}-\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}+\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}\, \sqrt{b \,x^{4}+a}}\right)}{2 \sqrt{-4 c e +d^{2}}\, \sqrt{a +\frac{b \,c^{2}}{e^{2}}-\frac{2 b c \,d^{2}}{e^{3}}+\frac{b \,d^{4}}{2 e^{4}}-\frac{\sqrt{-4 c e +d^{2}}\, b c d}{e^{3}}+\frac{\sqrt{-4 c e +d^{2}}\, b \,d^{3}}{2 e^{4}}}}"," ",0,"-1/2/(-4*c*e+d^2)^(1/2)/(1/2*b/e^4*d^4-1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2+b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)*arctanh(1/2/(1/2*b/e^4*d^4-1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2+b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)/(b*x^4+a)^(1/2)*b*x^2/e^2*d^2-1/2/(1/2*b/e^4*d^4-1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2+b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)/(b*x^4+a)^(1/2)*b*x^2/e^2*d*(-4*c*e+d^2)^(1/2)-1/(1/2*b/e^4*d^4-1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2+b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)/(b*x^4+a)^(1/2)*b*x^2/e*c+1/(1/2*b/e^4*d^4-1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2+b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)/(b*x^4+a)^(1/2)*a)-2/(-4*c*e+d^2)^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*e/(-d+(-4*c*e+d^2)^(1/2))*(1-I/a^(1/2)*b^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*x^2)^(1/2)/(b*x^4+a)^(1/2)*EllipticPi(x*(I/a^(1/2)*b^(1/2))^(1/2),-4*I*a^(1/2)/b^(1/2)*e^2/(-d+(-4*c*e+d^2)^(1/2))^2,(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))+1/2/(-4*c*e+d^2)^(1/2)/(1/2*b/e^4*d^4+1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2-b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)*arctanh(1/2/(1/2*b/e^4*d^4+1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2-b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)/(b*x^4+a)^(1/2)*b*x^2/e^2*d^2+1/2/(1/2*b/e^4*d^4+1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2-b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)/(b*x^4+a)^(1/2)*b*x^2/e^2*d*(-4*c*e+d^2)^(1/2)-1/(1/2*b/e^4*d^4+1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2-b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)/(b*x^4+a)^(1/2)*b*x^2/e*c+1/(1/2*b/e^4*d^4+1/2*b/e^4*d^3*(-4*c*e+d^2)^(1/2)-2*b/e^3*c*d^2-b/e^3*c*d*(-4*c*e+d^2)^(1/2)+b/e^2*c^2+a)^(1/2)/(b*x^4+a)^(1/2)*a)-2/(-4*c*e+d^2)^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)/(d+(-4*c*e+d^2)^(1/2))*e*(1-I/a^(1/2)*b^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*x^2)^(1/2)/(b*x^4+a)^(1/2)*EllipticPi(x*(I/a^(1/2)*b^(1/2))^(1/2),-4*I*a^(1/2)/b^(1/2)/(d+(-4*c*e+d^2)^(1/2))^2*e^2,(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))","C"
227,1,200,153,0.009000," ","int(x^m*(c*(b*x^2+a)^2)^(3/2),x)","\frac{\left(b^{3} m^{3} x^{6}+9 b^{3} m^{2} x^{6}+3 a \,b^{2} m^{3} x^{4}+23 b^{3} m \,x^{6}+33 a \,b^{2} m^{2} x^{4}+15 b^{3} x^{6}+3 a^{2} b \,m^{3} x^{2}+93 a \,b^{2} m \,x^{4}+39 a^{2} b \,m^{2} x^{2}+63 a \,b^{2} x^{4}+a^{3} m^{3}+141 a^{2} b m \,x^{2}+15 a^{3} m^{2}+105 a^{2} b \,x^{2}+71 a^{3} m +105 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} x^{m +1}}{\left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right) \left(b \,x^{2}+a \right)^{3}}"," ",0,"x^(m+1)*(b^3*m^3*x^6+9*b^3*m^2*x^6+3*a*b^2*m^3*x^4+23*b^3*m*x^6+33*a*b^2*m^2*x^4+15*b^3*x^6+3*a^2*b*m^3*x^2+93*a*b^2*m*x^4+39*a^2*b*m^2*x^2+63*a*b^2*x^4+a^3*m^3+141*a^2*b*m*x^2+15*a^3*m^2+105*a^2*b*x^2+71*a^3*m+105*a^3)*(c*(b*x^2+a)^2)^(3/2)/(7+m)/(5+m)/(3+m)/(m+1)/(b*x^2+a)^3","A"
228,1,60,127,0.009000," ","int(x^5*((b*x^2+a)^2*c)^(3/2),x)","\frac{\left(10 b^{3} x^{6}+36 a \,b^{2} x^{4}+45 a^{2} b \,x^{2}+20 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} x^{6}}{120 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/120*x^6*(10*b^3*x^6+36*a*b^2*x^4+45*a^2*b*x^2+20*a^3)*((b*x^2+a)^2*c)^(3/2)/(b*x^2+a)^3","A"
229,1,60,127,0.008000," ","int(x^4*((b*x^2+a)^2*c)^(3/2),x)","\frac{\left(105 b^{3} x^{6}+385 a \,b^{2} x^{4}+495 a^{2} b \,x^{2}+231 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} x^{5}}{1155 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/1155*x^5*(105*b^3*x^6+385*a*b^2*x^4+495*a^2*b*x^2+231*a^3)*((b*x^2+a)^2*c)^(3/2)/(b*x^2+a)^3","A"
230,1,60,58,0.006000," ","int(x^3*((b*x^2+a)^2*c)^(3/2),x)","\frac{\left(4 b^{3} x^{6}+15 a \,b^{2} x^{4}+20 a^{2} b \,x^{2}+10 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} x^{4}}{40 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/40*x^4*(4*b^3*x^6+15*a*b^2*x^4+20*a^2*b*x^2+10*a^3)*((b*x^2+a)^2*c)^(3/2)/(b*x^2+a)^3","A"
231,1,60,127,0.008000," ","int(x^2*((b*x^2+a)^2*c)^(3/2),x)","\frac{\left(35 b^{3} x^{6}+135 a \,b^{2} x^{4}+189 a^{2} b \,x^{2}+105 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} x^{3}}{315 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/315*x^3*(35*b^3*x^6+135*a*b^2*x^4+189*a^2*b*x^2+105*a^3)*((b*x^2+a)^2*c)^(3/2)/(b*x^2+a)^3","A"
232,1,59,28,0.007000," ","int(x*((b*x^2+a)^2*c)^(3/2),x)","\frac{\left(b^{3} x^{6}+4 a \,b^{2} x^{4}+6 a^{2} b \,x^{2}+4 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} x^{2}}{8 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/8*x^2*(b^3*x^6+4*a*b^2*x^4+6*a^2*b*x^2+4*a^3)*((b*x^2+a)^2*c)^(3/2)/(b*x^2+a)^3","B"
233,1,58,123,0.003000," ","int(((b*x^2+a)^2*c)^(3/2),x)","\frac{\left(5 b^{3} x^{6}+21 a \,b^{2} x^{4}+35 a^{2} b \,x^{2}+35 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} x}{35 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/35*x*(5*b^3*x^6+21*a*b^2*x^4+35*a^2*b*x^2+35*a^3)*((b*x^2+a)^2*c)^(3/2)/(b*x^2+a)^3","A"
234,1,59,125,0.023000," ","int(((b*x^2+a)^2*c)^(3/2)/x,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} \left(2 b^{3} x^{6}+9 a \,b^{2} x^{4}+18 a^{2} b \,x^{2}+12 a^{3} \ln \left(x \right)\right)}{12 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/12*((b*x^2+a)^2*c)^(3/2)*(2*b^3*x^6+9*a*b^2*x^4+18*a^2*b*x^2+12*a^3*ln(x))/(b*x^2+a)^3","A"
235,1,60,124,0.008000," ","int(((b*x^2+a)^2*c)^(3/2)/x^2,x)","-\frac{\left(-b^{3} x^{6}-5 a \,b^{2} x^{4}-15 a^{2} b \,x^{2}+5 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}}}{5 \left(b \,x^{2}+a \right)^{3} x}"," ",0,"-1/5*(-b^3*x^6-5*a*b^2*x^4-15*a^2*b*x^2+5*a^3)*((b*x^2+a)^2*c)^(3/2)/x/(b*x^2+a)^3","A"
236,1,61,126,0.017000," ","int(((b*x^2+a)^2*c)^(3/2)/x^3,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2} c \right)^{\frac{3}{2}} \left(b^{3} x^{6}+6 a \,b^{2} x^{4}+12 a^{2} b \,x^{2} \ln \left(x \right)-2 a^{3}\right)}{4 \left(b \,x^{2}+a \right)^{3} x^{2}}"," ",0,"1/4*((b*x^2+a)^2*c)^(3/2)*(b^3*x^6+6*a*b^2*x^4+12*b*a^2*ln(x)*x^2-2*a^3)/(b*x^2+a)^3/x^2","A"
237,1,236,215,0.036000," ","int(x^2*(c*(b*x^2+a)^3)^(3/2),x)","-\frac{\left(\left(b \,x^{2}+a \right)^{3} c \right)^{\frac{3}{2}} \left(315 a^{6} c^{3} \ln \left(\frac{b c x +\sqrt{b c \,x^{2}+a c}\, \sqrt{b c}}{\sqrt{b c}}\right)-1280 \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} \sqrt{b c}\, b^{3} x^{7}+315 \sqrt{b c}\, \sqrt{b c \,x^{2}+a c}\, a^{5} c^{2} x -3712 \sqrt{b c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} a \,b^{2} x^{5}+210 \sqrt{b c}\, \left(b c \,x^{2}+a c \right)^{\frac{3}{2}} a^{4} c x -3440 \sqrt{b c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} a^{2} b \,x^{3}-840 \sqrt{b c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} a^{3} x \right)}{15360 \left(b \,x^{2}+a \right)^{3} \left(\left(b \,x^{2}+a \right) c \right)^{\frac{3}{2}} \sqrt{b c}\, b c}"," ",0,"-1/15360*(c*(b*x^2+a)^3)^(3/2)/b*(-1280*x^7*(b*c*x^2+a*c)^(5/2)*b^3*(b*c)^(1/2)-3712*(b*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*x^5*a*b^2-3440*(b*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*x^3*a^2*b+315*ln((b*c*x+(b*c*x^2+a*c)^(1/2)*(b*c)^(1/2))/(b*c)^(1/2))*a^6*c^3-840*(b*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*x*a^3+210*(b*c)^(1/2)*(b*c*x^2+a*c)^(3/2)*x*a^4*c+315*(b*c)^(1/2)*(b*c*x^2+a*c)^(1/2)*x*a^5*c^2)/(b*x^2+a)^3/(c*(b*x^2+a))^(3/2)/c/(b*c)^(1/2)","A"
238,1,26,28,0.006000," ","int(x*((b*x^2+a)^3*c)^(3/2),x)","\frac{\left(b \,x^{2}+a \right) \left(\left(b \,x^{2}+a \right)^{3} c \right)^{\frac{3}{2}}}{11 b}"," ",0,"1/11*(b*x^2+a)/b*((b*x^2+a)^3*c)^(3/2)","A"
239,1,205,173,0.018000," ","int(((b*x^2+a)^3*c)^(3/2),x)","\frac{\left(\left(b \,x^{2}+a \right)^{3} c \right)^{\frac{3}{2}} \left(315 a^{5} c^{3} \ln \left(\frac{b c x +\sqrt{b c \,x^{2}+a c}\, \sqrt{b c}}{\sqrt{b c}}\right)+315 \sqrt{b c \,x^{2}+a c}\, \sqrt{b c}\, a^{4} c^{2} x +128 \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} \sqrt{b c}\, b^{2} x^{5}+210 \left(b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{b c}\, a^{3} c x +400 \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} \sqrt{b c}\, a b \,x^{3}+440 \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} \sqrt{b c}\, a^{2} x \right)}{1280 \left(b \,x^{2}+a \right)^{3} \left(\left(b \,x^{2}+a \right) c \right)^{\frac{3}{2}} \sqrt{b c}\, c}"," ",0,"1/1280*((b*x^2+a)^3*c)^(3/2)*(128*x^5*(b*c*x^2+a*c)^(5/2)*b^2*(b*c)^(1/2)+400*(b*c*x^2+a*c)^(5/2)*(b*c)^(1/2)*x^3*a*b+440*(b*c*x^2+a*c)^(5/2)*(b*c)^(1/2)*x*a^2+210*(b*c*x^2+a*c)^(3/2)*(b*c)^(1/2)*x*a^3*c+315*(b*c*x^2+a*c)^(1/2)*(b*c)^(1/2)*x*a^4*c^2+315*ln((b*c*x+(b*c*x^2+a*c)^(1/2)*(b*c)^(1/2))/(b*c)^(1/2))*a^5*c^3)/(b*x^2+a)^3/((b*x^2+a)*c)^(3/2)/c/(b*c)^(1/2)","A"
240,1,221,168,0.019000," ","int(((b*x^2+a)^3*c)^(3/2)/x,x)","-\frac{\left(\left(b \,x^{2}+a \right)^{3} c \right)^{\frac{3}{2}} \left(315 a^{5} c^{3} \ln \left(\frac{2 a c +2 \sqrt{a c}\, \sqrt{b c \,x^{2}+a c}}{x}\right)-315 \sqrt{a c}\, \sqrt{b c \,x^{2}+a c}\, a^{4} c^{2}-35 \sqrt{a c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} b^{2} x^{4}-105 \sqrt{a c}\, \left(b c \,x^{2}+a c \right)^{\frac{3}{2}} a^{3} c -115 \sqrt{a c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} a b \,x^{2}-189 \left(\left(b \,x^{2}+a \right) c \right)^{\frac{5}{2}} \sqrt{a c}\, a^{2}+46 \sqrt{a c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} a^{2}\right)}{315 \left(b \,x^{2}+a \right)^{3} \left(\left(b \,x^{2}+a \right) c \right)^{\frac{3}{2}} \sqrt{a c}\, c}"," ",0,"-1/315*((b*x^2+a)^3*c)^(3/2)*(-35*(a*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*x^4*b^2-115*(a*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*x^2*a*b+315*ln(2*((a*c)^(1/2)*(b*c*x^2+a*c)^(1/2)+a*c)/x)*a^5*c^3-189*a^2*((b*x^2+a)*c)^(5/2)*(a*c)^(1/2)+46*(a*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*a^2-105*(a*c)^(1/2)*(b*c*x^2+a*c)^(3/2)*a^3*c-315*(a*c)^(1/2)*(b*c*x^2+a*c)^(1/2)*a^4*c^2)/(b*x^2+a)^3/((b*x^2+a)*c)^(3/2)/c/(a*c)^(1/2)","A"
241,1,215,176,0.019000," ","int(((b*x^2+a)^3*c)^(3/2)/x^2,x)","\frac{\left(\left(b \,x^{2}+a \right)^{3} c \right)^{\frac{3}{2}} \left(315 a^{4} b \,c^{3} x \ln \left(\frac{b c x +\sqrt{b c \,x^{2}+a c}\, \sqrt{b c}}{\sqrt{b c}}\right)+315 \sqrt{b c \,x^{2}+a c}\, \sqrt{b c}\, a^{3} b \,c^{2} x^{2}+210 \left(b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{b c}\, a^{2} b c \,x^{2}+16 \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} \sqrt{b c}\, b^{2} x^{4}+56 \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} \sqrt{b c}\, a b \,x^{2}-128 \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} \sqrt{b c}\, a^{2}\right)}{128 \left(b \,x^{2}+a \right)^{3} \left(\left(b \,x^{2}+a \right) c \right)^{\frac{3}{2}} \sqrt{b c}\, c x}"," ",0,"1/128*((b*x^2+a)^3*c)^(3/2)*(16*(b*c*x^2+a*c)^(5/2)*(b*c)^(1/2)*x^4*b^2+56*(b*c*x^2+a*c)^(5/2)*(b*c)^(1/2)*x^2*a*b+210*(b*c*x^2+a*c)^(3/2)*(b*c)^(1/2)*x^2*a^2*b*c+315*(b*c*x^2+a*c)^(1/2)*(b*c)^(1/2)*x^2*a^3*b*c^2+315*ln((b*c*x+(b*c*x^2+a*c)^(1/2)*(b*c)^(1/2))/(b*c)^(1/2))*x*a^4*b*c^3-128*(b*c*x^2+a*c)^(5/2)*(b*c)^(1/2)*a^2)/(b*x^2+a)^3/((b*x^2+a)*c)^(3/2)/c/(b*c)^(1/2)/x","A"
242,1,238,174,0.021000," ","int(((b*x^2+a)^3*c)^(3/2)/x^3,x)","\frac{\left(\left(b \,x^{2}+a \right)^{3} c \right)^{\frac{3}{2}} \left(-315 a^{4} b \,c^{3} x^{2} \ln \left(\frac{2 a c +2 \sqrt{a c}\, \sqrt{b c \,x^{2}+a c}}{x}\right)+315 \sqrt{b c \,x^{2}+a c}\, \sqrt{a c}\, a^{3} b \,c^{2} x^{2}+105 \left(b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} b c \,x^{2}+10 \sqrt{a c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} b^{2} x^{4}-4 \sqrt{a c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} a b \,x^{2}+42 \left(\left(b \,x^{2}+a \right) c \right)^{\frac{5}{2}} \sqrt{a c}\, a b \,x^{2}-35 \sqrt{a c}\, \left(b c \,x^{2}+a c \right)^{\frac{5}{2}} a^{2}\right)}{70 \left(b \,x^{2}+a \right)^{3} \left(\left(b \,x^{2}+a \right) c \right)^{\frac{3}{2}} \sqrt{a c}\, c \,x^{2}}"," ",0,"1/70*((b*x^2+a)^3*c)^(3/2)*(10*(a*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*b^2*x^4-315*ln(2*(a*c+(a*c)^(1/2)*(b*c*x^2+a*c)^(1/2))/x)*x^2*a^4*b*c^3-4*(a*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*a*b*x^2+105*(b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*a^2*b*c+315*(b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^2*a^3*b*c^2+42*a*b*((b*x^2+a)*c)^(5/2)*x^2*(a*c)^(1/2)-35*(a*c)^(1/2)*(b*c*x^2+a*c)^(5/2)*a^2)/(b*x^2+a)^3/((b*x^2+a)*c)^(3/2)/c/x^2/(a*c)^(1/2)","A"
243,1,60,63,0.013000," ","int(x^2*(c/(b*x^2+a))^(3/2),x)","-\frac{\left(\frac{c}{b \,x^{2}+a}\right)^{\frac{3}{2}} \left(b \,x^{2}+a \right) \left(b^{\frac{3}{2}} x -\sqrt{b \,x^{2}+a}\, b \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)\right)}{b^{\frac{5}{2}}}"," ",0,"-(c/(b*x^2+a))^(3/2)*(b*x^2+a)*(x*b^(3/2)-ln(b^(1/2)*x+(b*x^2+a)^(1/2))*b*(b*x^2+a)^(1/2))/b^(5/2)","A"
244,1,26,19,0.005000," ","int(x*(1/(b*x^2+a)*c)^(3/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(\frac{c}{b \,x^{2}+a}\right)^{\frac{3}{2}}}{b}"," ",0,"-(b*x^2+a)/b*(1/(b*x^2+a)*c)^(3/2)","A"
245,1,26,19,0.002000," ","int((1/(b*x^2+a)*c)^(3/2),x)","\frac{\left(b \,x^{2}+a \right) \left(\frac{c}{b \,x^{2}+a}\right)^{\frac{3}{2}} x}{a}"," ",0,"(b*x^2+a)/a*x*(1/(b*x^2+a)*c)^(3/2)","A"
246,1,64,63,0.010000," ","int((1/(b*x^2+a)*c)^(3/2)/x,x)","-\frac{\left(\frac{c}{b \,x^{2}+a}\right)^{\frac{3}{2}} \left(b \,x^{2}+a \right) \left(\sqrt{b \,x^{2}+a}\, a \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-a^{\frac{3}{2}}\right)}{a^{\frac{5}{2}}}"," ",0,"-(1/(b*x^2+a)*c)^(3/2)*(b*x^2+a)*(ln(2*(a^(1/2)*(b*x^2+a)^(1/2)+a)/x)*a*(b*x^2+a)^(1/2)-a^(3/2))/a^(5/2)","A"
247,1,37,44,0.006000," ","int((1/(b*x^2+a)*c)^(3/2)/x^2,x)","-\frac{\left(b \,x^{2}+a \right) \left(2 b \,x^{2}+a \right) \left(\frac{c}{b \,x^{2}+a}\right)^{\frac{3}{2}}}{a^{2} x}"," ",0,"-(b*x^2+a)*(2*b*x^2+a)*(1/(b*x^2+a)*c)^(3/2)/a^2/x","A"
248,1,81,88,0.010000," ","int((1/(b*x^2+a)*c)^(3/2)/x^3,x)","\frac{\left(\frac{c}{b \,x^{2}+a}\right)^{\frac{3}{2}} \left(b \,x^{2}+a \right) \left(3 \sqrt{b \,x^{2}+a}\, a b \,x^{2} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)-3 a^{\frac{3}{2}} b \,x^{2}-a^{\frac{5}{2}}\right)}{2 a^{\frac{7}{2}} x^{2}}"," ",0,"1/2*(1/(b*x^2+a)*c)^(3/2)*(b*x^2+a)*(3*(b*x^2+a)^(1/2)*ln(2*(a+(b*x^2+a)^(1/2)*a^(1/2))/x)*x^2*a*b-3*a^(3/2)*x^2*b-a^(5/2))/a^(7/2)/x^2","A"
249,1,58,114,0.008000," ","int(x^7*(c*(b*x^2+a)^(1/2))^(3/2),x)","-\frac{2 \left(b \,x^{2}+a \right) \left(-385 b^{3} x^{6}+308 a \,b^{2} x^{4}-224 a^{2} b \,x^{2}+128 a^{3}\right) \left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}}{7315 b^{4}}"," ",0,"-2/7315*(b*x^2+a)*(-385*b^3*x^6+308*a*b^2*x^4-224*a^2*b*x^2+128*a^3)*(c*(b*x^2+a)^(1/2))^(3/2)/b^4","A"
250,1,47,84,0.007000," ","int(x^5*((b*x^2+a)^(1/2)*c)^(3/2),x)","\frac{2 \left(b \,x^{2}+a \right) \left(77 x^{4} b^{2}-56 a b \,x^{2}+32 a^{2}\right) \left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}}{1155 b^{3}}"," ",0,"2/1155*(b*x^2+a)*(77*b^2*x^4-56*a*b*x^2+32*a^2)*((b*x^2+a)^(1/2)*c)^(3/2)/b^3","A"
251,1,36,54,0.007000," ","int(x^3*((b*x^2+a)^(1/2)*c)^(3/2),x)","-\frac{2 \left(b \,x^{2}+a \right) \left(-7 b \,x^{2}+4 a \right) \left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}}{77 b^{2}}"," ",0,"-2/77*(b*x^2+a)*(-7*b*x^2+4*a)*((b*x^2+a)^(1/2)*c)^(3/2)/b^2","A"
252,1,26,28,0.004000," ","int(x*((b*x^2+a)^(1/2)*c)^(3/2),x)","\frac{2 \left(b \,x^{2}+a \right) \left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}}{7 b}"," ",0,"2/7*(b*x^2+a)*((b*x^2+a)^(1/2)*c)^(3/2)/b","A"
253,0,0,95,0.033000," ","int(((b*x^2+a)^(1/2)*c)^(3/2)/x,x)","\int \frac{\left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int(((b*x^2+a)^(1/2)*c)^(3/2)/x,x)","F"
254,0,0,107,0.015000," ","int(((b*x^2+a)^(1/2)*c)^(3/2)/x^3,x)","\int \frac{\left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"int(((b*x^2+a)^(1/2)*c)^(3/2)/x^3,x)","F"
255,0,0,149,0.012000," ","int(x^2*((b*x^2+a)^(1/2)*c)^(3/2),x)","\int \left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}} x^{2}\, dx"," ",0,"int(x^2*((b*x^2+a)^(1/2)*c)^(3/2),x)","F"
256,0,0,122,0.008000," ","int(((b*x^2+a)^(1/2)*c)^(3/2),x)","\int \left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}\, dx"," ",0,"int(((b*x^2+a)^(1/2)*c)^(3/2),x)","F"
257,0,0,124,0.013000," ","int(((b*x^2+a)^(1/2)*c)^(3/2)/x^2,x)","\int \frac{\left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int(((b*x^2+a)^(1/2)*c)^(3/2)/x^2,x)","F"
258,0,0,151,0.013000," ","int(((b*x^2+a)^(1/2)*c)^(3/2)/x^4,x)","\int \frac{\left(\sqrt{b \,x^{2}+a}\, c \right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"int(((b*x^2+a)^(1/2)*c)^(3/2)/x^4,x)","F"
259,1,122,61,0.015000," ","int(((b-x)*(-a+x))^(1/2),x)","\frac{a^{2} \arctan \left(\frac{-\frac{a}{2}-\frac{b}{2}+x}{\sqrt{-a b -x^{2}+\left(a +b \right) x}}\right)}{8}-\frac{a b \arctan \left(\frac{-\frac{a}{2}-\frac{b}{2}+x}{\sqrt{-a b -x^{2}+\left(a +b \right) x}}\right)}{4}+\frac{b^{2} \arctan \left(\frac{-\frac{a}{2}-\frac{b}{2}+x}{\sqrt{-a b -x^{2}+\left(a +b \right) x}}\right)}{8}-\frac{\left(a +b -2 x \right) \sqrt{-a b -x^{2}+\left(a +b \right) x}}{4}"," ",0,"-1/4*(a+b-2*x)*(-a*b+(a+b)*x-x^2)^(1/2)-1/4*arctan((x-1/2*b-1/2*a)/(-a*b+(a+b)*x-x^2)^(1/2))*a*b+1/8*arctan((x-1/2*b-1/2*a)/(-a*b+(a+b)*x-x^2)^(1/2))*a^2+1/8*arctan((x-1/2*b-1/2*a)/(-a*b+(a+b)*x-x^2)^(1/2))*b^2","A"
260,1,114,44,0.022000," ","int(((-x^2+1)*(x^2+3))^(1/2),x)","\frac{\sqrt{-x^{4}-2 x^{2}+3}\, x}{3}+\frac{2 \sqrt{-x^{2}+1}\, \sqrt{3 x^{2}+9}\, \EllipticF \left(x , \frac{i \sqrt{3}}{3}\right)}{3 \sqrt{-x^{4}-2 x^{2}+3}}+\frac{2 \sqrt{-x^{2}+1}\, \sqrt{3 x^{2}+9}\, \left(-\EllipticE \left(x , \frac{i \sqrt{3}}{3}\right)+\EllipticF \left(x , \frac{i \sqrt{3}}{3}\right)\right)}{3 \sqrt{-x^{4}-2 x^{2}+3}}"," ",0,"1/3*x*(-x^4-2*x^2+3)^(1/2)+2/3*(-x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-x^4-2*x^2+3)^(1/2)*EllipticF(x,1/3*I*3^(1/2))+2/3*(-x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-x^4-2*x^2+3)^(1/2)*(EllipticF(x,1/3*I*3^(1/2))-EllipticE(x,1/3*I*3^(1/2)))","B"
261,1,28,28,0.007000," ","int(1/((b-x)*(-a+x))^(1/2),x)","\arctan \left(\frac{-\frac{a}{2}-\frac{b}{2}+x}{\sqrt{-a b -x^{2}+\left(a +b \right) x}}\right)"," ",0,"arctan((-1/2*a-1/2*b+x)/(-a*b-x^2+(a+b)*x)^(1/2))","A"
262,1,43,13,0.010000," ","int(1/((-x^2+1)*(x^2+3))^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{3 x^{2}+9}\, \EllipticF \left(x , \frac{i \sqrt{3}}{3}\right)}{3 \sqrt{-x^{4}-2 x^{2}+3}}"," ",0,"1/3*(-x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-x^4-2*x^2+3)^(1/2)*EllipticF(x,1/3*I*3^(1/2))","B"
263,1,527,216,0.067000," ","int(x^5*(e*(b*x^2+a)/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(3 a^{3} d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 a^{2} b c \,d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+9 a \,b^{2} c^{2} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-15 b^{3} c^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-12 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b \,d^{2} x^{2}-36 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c d \,x^{2}-6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} d^{2}-24 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b c d +30 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c^{2}+16 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{b d}\, b d \right)}{96 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, b^{2} d^{3}}"," ",0,"1/96*(e*(b*x^2+a)/(d*x^2+c))^(1/2)*(d*x^2+c)/d^3*(-12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*a*b*d^2*(b*d)^(1/2)-36*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^2*c*b^2*d*(b*d)^(1/2)+3*d^3*ln(1/2*(2*b*d*x^2+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*a^3+3*ln(1/2*(2*b*d*x^2+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*a^2*c*b*d^2+9*ln(1/2*(2*b*d*x^2+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*a*c^2*b^2*d-15*b^3*ln(1/2*(2*b*d*x^2+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*c^3+16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*b*d*(b*d)^(1/2)-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a^2*d^2*(b*d)^(1/2)-24*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*a*c*b*d*(b*d)^(1/2)+30*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*c^2*b^2*(b*d)^(1/2))/((d*x^2+c)*(b*x^2+a))^(1/2)/b^2/(b*d)^(1/2)","B"
264,1,342,137,0.038000," ","int(x^3*((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-a^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 a b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+4 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b d \,x^{2}+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a d -6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b c \right)}{16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, b \,d^{2}}"," ",0,"1/16*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*b*d-d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2-2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*c*b*d+3*b^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*c^2+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*d-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b*c)/((d*x^2+c)*(b*x^2+a))^(1/2)/d^2/b/(b*d)^(1/2)","B"
265,1,200,83,0.025000," ","int(x*((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(a d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-b c \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\right)}{4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, d}"," ",0,"1/4*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(a*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*d-b*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/((d*x^2+c)*(b*x^2+a))^(1/2)/d/(b*d)^(1/2)","B"
266,1,179,84,0.042000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(1/2)/x,x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-\sqrt{b d}\, a \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+\sqrt{a c}\, b \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)\right)}{2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, \sqrt{a c}}"," ",0,"1/2*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*b*(a*c)^(1/2)-a*ln((a*d*x^2+b*c*x^2+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)+2*a*c)/x^2)*(b*d)^(1/2))/((d*x^2+c)*(b*x^2+a))^(1/2)/(b*d)^(1/2)/(a*c)^(1/2)","B"
267,1,326,107,0.053000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(1/2)/x^3,x)","-\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-a^{2} c d \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+a b \,c^{2} x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b d \,x^{4}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a d \,x^{2}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b c \,x^{2}+2 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\right)}{4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a \,c^{2} x^{2}}"," ",0,"-1/4*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(-2*b*d*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^4*(a*c)^(1/2)-a^2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*d*c*x^2+c^2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*b*a*x^2-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*d*a*x^2*(a*c)^(1/2)-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b*c*x^2*(a*c)^(1/2)+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2))/((d*x^2+c)*(b*x^2+a))^(1/2)/c^2/a/x^2/(a*c)^(1/2)","B"
268,1,558,184,0.066000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(1/2)/x^5,x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-3 a^{3} c \,d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+2 a^{2} b \,c^{2} d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+a \,b^{2} c^{3} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b \,d^{2} x^{6}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} c d \,x^{6}-10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} d^{2} x^{4}-8 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b c d \,x^{4}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} c^{2} x^{4}+10 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a d \,x^{2}+2 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b c \,x^{2}-4 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a c \right)}{16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a^{2} c^{3} x^{4}}"," ",0,"1/16*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(-10*b*d^2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^6*a*(a*c)^(1/2)-2*b^2*d*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^6*c*(a*c)^(1/2)-3*a^3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*d^2*c*x^4+2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*d*b*a^2*c^2*x^4+c^3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*b^2*a*x^4-10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*d^2*a^2*x^4*(a*c)^(1/2)-8*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a*b*c*d-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b^2*c^2*x^4*(a*c)^(1/2)+10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*d*a*x^2*(a*c)^(1/2)+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*b*c*x^2*(a*c)^(1/2)-4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*a*c*(a*c)^(1/2))/((d*x^2+c)*(b*x^2+a))^(1/2)/c^3/a^2/x^4/(a*c)^(1/2)","B"
269,1,849,290,0.077000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(1/2)/x^7,x)","-\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-15 a^{4} c \,d^{3} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+9 a^{3} b \,c^{2} d^{2} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 a^{2} b^{2} c^{3} d \,x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 a \,b^{3} c^{4} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-66 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} b \,d^{3} x^{8}-24 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,b^{2} c \,d^{2} x^{8}-6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{3} c^{2} d \,x^{8}-66 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{3} d^{3} x^{6}-54 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} b c \,d^{2} x^{6}-18 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,b^{2} c^{2} d \,x^{6}-6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{3} c^{3} x^{6}+66 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} d^{2} x^{4}+24 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a b c d \,x^{4}+6 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b^{2} c^{2} x^{4}-36 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} c d \,x^{2}-12 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a b \,c^{2} x^{2}+16 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} c^{2}\right)}{96 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a^{3} c^{4} x^{6}}"," ",0,"-1/96*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(-66*b*d^3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^8*a^2*(a*c)^(1/2)-24*b^2*d^2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^8*a*c*(a*c)^(1/2)-6*b^3*d*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^8*c^2*(a*c)^(1/2)-15*a^4*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*d^3*c*x^6+9*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*d^2*b*a^3*c^2*x^6+3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*d*b^2*a^2*c^3*x^6+3*c^4*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*b^3*a*x^6-66*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*d^3*a^3*x^6*(a*c)^(1/2)-54*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*d^2*b*a^2*c*x^6*(a*c)^(1/2)-18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b^2*d*a*c^2*x^6*(a*c)^(1/2)-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b^3*c^3*x^6*(a*c)^(1/2)+66*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*d^2*a^2*x^4*(a*c)^(1/2)+24*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*d*b*a*c*x^4*(a*c)^(1/2)+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*b^2*c^2*x^4*(a*c)^(1/2)-36*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*d*a^2*c*x^2*(a*c)^(1/2)-12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*b*a*c^2*x^2*(a*c)^(1/2)+16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*a^2*c^2*(a*c)^(1/2))/((d*x^2+c)*(b*x^2+a))^(1/2)/c^4/a^3/x^6/(a*c)^(1/2)","B"
270,1,552,395,0.046000," ","int(x^4*((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(3 \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}+4 \sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}-\sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}-4 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}+\sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x -3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{15 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, b \,d^{3}}"," ",0,"1/15*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(3*(-1/a*b)^(1/2)*x^7*b^2*d^3+4*(-1/a*b)^(1/2)*x^5*a*b*d^3-(-1/a*b)^(1/2)*x^5*b^2*c*d^2+(-1/a*b)^(1/2)*x^3*a^2*d^3-4*(-1/a*b)^(1/2)*x^3*b^2*c^2*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*a^2*c*d^2+7*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*a*b*c^2*d-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*b^2*c^3-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*a^2*c*d^2-3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*a*b*c^2*d+8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*b^2*c^3+(-1/a*b)^(1/2)*x*a^2*c*d^2-4*(-1/a*b)^(1/2)*x*a*b*c^2*d)/d^3/((d*x^2+c)*(b*x^2+a))^(1/2)/b/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
271,1,356,308,0.020000," ","int(x^2*((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(\sqrt{-\frac{b}{a}}\, b \,d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b c d \,x^{3}+\sqrt{-\frac{b}{a}}\, a c d x +\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, d^{2}}"," ",0,"1/3*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*((-1/a*b)^(1/2)*x^5*b*d^2+(-1/a*b)^(1/2)*x^3*a*d^2+(-1/a*b)^(1/2)*x^3*b*c*d-2*a*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+(-1/a*b)^(1/2)*x*a*c*d)/((d*x^2+c)*(b*x^2+a))^(1/2)/d^2/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
272,1,184,246,0.016000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \left(a d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-b c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, d}"," ",0,"((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*(a*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d-b*c*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))+b*c*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2)))/((d*x^2+c)*(b*x^2+a))^(1/2)/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/d","A"
273,1,192,289,0.034000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(1/2)/x^2,x)","-\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(\sqrt{-\frac{b}{a}}\, b d \,x^{4}+\sqrt{-\frac{b}{a}}\, a d \,x^{2}+\sqrt{-\frac{b}{a}}\, b c \,x^{2}-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a c \right)}{\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, c x}"," ",0,"-((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*((-1/a*b)^(1/2)*x^4*b*d-b*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*x*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))+(-1/a*b)^(1/2)*x^2*a*d+(-1/a*b)^(1/2)*x^2*b*c+(-1/a*b)^(1/2)*a*c)/((d*x^2+c)*(b*x^2+a))^(1/2)/c/x/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
274,1,444,359,0.036000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(1/2)/x^4,x)","\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(2 \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}-\sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}+2 \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{4}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{4}+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a^{2} c d \,x^{2}-2 \sqrt{-\frac{b}{a}}\, a b \,c^{2} x^{2}-\sqrt{-\frac{b}{a}}\, a^{2} c^{2}\right)}{3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, a \,c^{2} x^{3}}"," ",0,"1/3*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(2*(-1/a*b)^(1/2)*x^6*a*b*d^2-(-1/a*b)^(1/2)*x^6*b^2*c*d+b*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*c-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2+2*(-1/a*b)^(1/2)*x^4*a^2*d^2-(-1/a*b)^(1/2)*x^4*b^2*c^2+(-1/a*b)^(1/2)*x^2*a^2*c*d-2*(-1/a*b)^(1/2)*x^2*a*b*c^2-(-1/a*b)^(1/2)*a^2*c^2)/((d*x^2+c)*(b*x^2+a))^(1/2)/c^2/x^3/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/a","A"
275,1,708,458,0.044000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(1/2)/x^6,x)","-\frac{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(8 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{3} x^{8}-3 \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{2} x^{8}-2 \sqrt{-\frac{b}{a}}\, b^{3} c^{2} d \,x^{8}+8 \sqrt{-\frac{b}{a}}\, a^{3} d^{3} x^{6}+\sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{2} x^{6}-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} x^{5} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} x^{5} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d \,x^{6}+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \,x^{5} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \,x^{5} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{-\frac{b}{a}}\, b^{3} c^{3} x^{6}+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} x^{5} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} x^{5} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{-\frac{b}{a}}\, a^{3} c \,d^{2} x^{4}-3 \sqrt{-\frac{b}{a}}\, a^{2} b \,c^{2} d \,x^{4}-\sqrt{-\frac{b}{a}}\, a \,b^{2} c^{3} x^{4}-\sqrt{-\frac{b}{a}}\, a^{3} c^{2} d \,x^{2}+4 \sqrt{-\frac{b}{a}}\, a^{2} b \,c^{3} x^{2}+3 \sqrt{-\frac{b}{a}}\, a^{3} c^{3}\right)}{15 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, a^{2} c^{3} x^{5}}"," ",0,"-1/15*((b*x^2+a)/(d*x^2+c)*e)^(1/2)*(d*x^2+c)*(8*(-1/a*b)^(1/2)*x^8*a^2*b*d^3-3*(-1/a*b)^(1/2)*x^8*a*b^2*c*d^2-2*(-1/a*b)^(1/2)*x^8*b^3*c^2*d+4*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*a^2*b*c*d^2-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*a*b^2*c^2*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*b^3*c^3-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*a^2*b*c*d^2+3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*a*b^2*c^2*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*b^3*c^3+8*(-1/a*b)^(1/2)*x^6*a^3*d^3+(-1/a*b)^(1/2)*x^6*a^2*b*c*d^2-4*(-1/a*b)^(1/2)*x^6*a*b^2*c^2*d-2*(-1/a*b)^(1/2)*x^6*b^3*c^3+4*(-1/a*b)^(1/2)*x^4*a^3*c*d^2-3*(-1/a*b)^(1/2)*x^4*a^2*b*c^2*d-(-1/a*b)^(1/2)*x^4*a*b^2*c^3-(-1/a*b)^(1/2)*x^2*a^3*c^2*d+4*(-1/a*b)^(1/2)*x^2*a^2*b*c^3+3*(-1/a*b)^(1/2)*a^3*c^3)/((d*x^2+c)*(b*x^2+a))^(1/2)/c^3/x^5/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/a^2","A"
276,1,1027,252,0.076000," ","int(x^5*((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(-3 a^{3} d^{4} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-27 a^{2} b c \,d^{3} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+135 a \,b^{2} c^{2} d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-105 b^{3} c^{3} d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+12 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b \,d^{3} x^{4}-60 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c \,d^{2} x^{4}-3 a^{3} c \,d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-27 a^{2} b \,c^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+135 a \,b^{2} c^{3} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-105 b^{3} c^{4} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} d^{3} x^{2}-108 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b c \,d^{2} x^{2}+54 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c^{2} d \,x^{2}+6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} c \,d^{2}-120 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b \,c^{2} d -96 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, a b \,c^{2} d +114 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c^{3}+96 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, b^{2} c^{3}+16 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{b d}\, b \,d^{2} x^{2}+16 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{b d}\, b c d \right) \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}}}{96 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(b \,x^{2}+a \right) b \,d^{4}}"," ",0,"1/96*(12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^4*a*b*d^3-60*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^4*b^2*c*d^2-3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a^3*d^4-27*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a^2*b*c*d^3+135*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b^2*c^2*d^2-105*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^3*c^3*d+16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(b*d)^(1/2)*x^2*b*d^2+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*a^2*d^3-108*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*a*b*c*d^2+54*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*b^2*c^2*d-3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^3*c*d^3-27*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*b*c^2*d^2+135*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*b^2*c^3*d-105*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*b^3*c^4+16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(b*d)^(1/2)*b*c*d+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^2*c*d^2-120*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b*c^2*d+114*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*c^3-96*(b*d)^(1/2)*((d*x^2+c)*(b*x^2+a))^(1/2)*a*b*c^2*d+96*(b*d)^(1/2)*((d*x^2+c)*(b*x^2+a))^(1/2)*b^2*c^3)/d^4/b*(d*x^2+c)*((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(b*d)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(b*x^2+a)","B"
277,1,679,173,0.057000," ","int(x^3*((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(3 a^{2} d^{3} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-18 a b c \,d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+15 b^{2} c^{2} d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+4 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b \,d^{2} x^{4}+3 a^{2} c \,d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-18 a b \,c^{2} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+15 b^{2} c^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,d^{2} x^{2}-10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b c d \,x^{2}+16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, a c d +10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a c d -16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, b \,c^{2}-14 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b \,c^{2}\right) \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}}}{16 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(b \,x^{2}+a \right) d^{3}}"," ",0,"1/16*(4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^4*b*d^2+3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a^2*d^3-18*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b*c*d^2+15*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^2*c^2*d+10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*a*d^2-10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*b*c*d+3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*c*d^2-18*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*b*c^2*d+15*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*b^2*c^3+16*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*a*c*d-16*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*b*c^2+10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*c*d-14*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b*c^2)/d^3*(d*x^2+c)*((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(b*d)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(b*x^2+a)","B"
278,1,432,117,0.048000," ","int(x*((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","-\frac{\left(-3 a b \,d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 b^{2} c d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-3 a b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b d \,x^{2}+4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, a d -4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, b c -2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b c \right) \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}}}{4 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(b \,x^{2}+a \right) d^{2}}"," ",0,"-1/4*(-3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b*d^2+3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^2*c*d-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b*d*x^2-3*a*b*c*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+3*b^2*c^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+4*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*a*d-4*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*b*c-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b*c)/d^2*(d*x^2+c)*((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(b*d)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(b*x^2+a)","B"
279,1,401,121,0.060000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(3/2)/x,x)","\frac{\left(-\sqrt{b d}\, a^{2} d^{2} x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+\sqrt{a c}\, b^{2} c d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-\sqrt{b d}\, a^{2} c d \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+\sqrt{a c}\, b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, \sqrt{a c}\, a d -2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, \sqrt{a c}\, b c \right) \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}}}{2 \sqrt{a c}\, \sqrt{b d}\, \left(b \,x^{2}+a \right) \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, c d}"," ",0,"1/2*(ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*x^2*b^2*c*d-(b*d)^(1/2)*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a^2*d^2+ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*b^2*c^2-(b*d)^(1/2)*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*a^2*c*d+2*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*(a*c)^(1/2)*a*d-2*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*(a*c)^(1/2)*b*c)/c/d*(d*x^2+c)*((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(a*c)^(1/2)/(b*d)^(1/2)/(b*x^2+a)/((d*x^2+c)*(b*x^2+a))^(1/2)","B"
280,1,641,141,0.076000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(3/2)/x^3,x)","-\frac{\left(-3 a^{2} c \,d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 a b \,c^{2} d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b \,d^{2} x^{6}-3 a^{2} c^{2} d \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 a b \,c^{3} x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,d^{2} x^{4}-4 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b c d \,x^{4}+4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a c d \,x^{2}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a c d \,x^{2}-4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, b \,c^{2} x^{2}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b \,c^{2} x^{2}+2 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, d \,x^{2}+2 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, c \right) \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}}}{4 \sqrt{a c}\, \left(b \,x^{2}+a \right) \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, c^{3} x^{2}}"," ",0,"-1/4*(-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*b*d^2-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^2*c*d^2+3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a*b*c^2*d-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a*d^2-4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*b*c*d-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a^2*c^2*d+3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a*b*c^3+4*((d*x^2+c)*(b*x^2+a))^(1/2)*(a*c)^(1/2)*x^2*a*c*d-4*((d*x^2+c)*(b*x^2+a))^(1/2)*(a*c)^(1/2)*x^2*b*c^2+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*d-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^2*a*c*d-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^2*b*c^2+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*c)*(d*x^2+c)*((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(a*c)^(1/2)/x^2/c^3/(b*x^2+a)/((d*x^2+c)*(b*x^2+a))^(1/2)","B"
281,1,1042,230,0.066000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(3/2)/x^5,x)","\frac{\left(-15 a^{3} c \,d^{3} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+18 a^{2} b \,c^{2} d^{2} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-3 a \,b^{2} c^{3} d \,x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-18 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b \,d^{3} x^{8}+6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} c \,d^{2} x^{8}-15 a^{3} c^{2} d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+18 a^{2} b \,c^{3} d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-3 a \,b^{2} c^{4} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-18 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} d^{3} x^{6}-26 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b c \,d^{2} x^{6}+12 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} c^{2} d \,x^{6}+16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a^{2} c \,d^{2} x^{4}-18 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} c \,d^{2} x^{4}-16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a b \,c^{2} d \,x^{4}-8 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b \,c^{2} d \,x^{4}+6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} c^{3} x^{4}+18 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a \,d^{2} x^{4}-6 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b c d \,x^{4}+14 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a c d \,x^{2}-6 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b \,c^{2} x^{2}-4 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a \,c^{2}\right) \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}}}{16 \sqrt{a c}\, \left(b \,x^{2}+a \right) \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, a \,c^{4} x^{4}}"," ",0,"1/16*(-18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^8*a*b*d^3+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^8*b^2*c*d^2-15*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a^3*c*d^3+18*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a^2*b*c^2*d^2-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a*b^2*c^3*d-18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*a^2*d^3-26*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*a*b*c*d^2+12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*b^2*c^2*d-15*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^3*c^2*d^2+18*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^2*b*c^3*d-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a*b^2*c^4+16*((d*x^2+c)*(b*x^2+a))^(1/2)*(a*c)^(1/2)*x^4*a^2*c*d^2-16*((d*x^2+c)*(b*x^2+a))^(1/2)*(a*c)^(1/2)*x^4*a*b*c^2*d+18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^4*a*d^2-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^4*b*c*d-18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a^2*c*d^2-8*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a*b*c^2*d+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*b^2*c^3+14*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*a*c*d-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*b*c^2-4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*a*c^2)/a*(d*x^2+c)*((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(a*c)^(1/2)/x^4/c^4/(b*x^2+a)/((d*x^2+c)*(b*x^2+a))^(1/2)","B"
282,1,1498,336,0.095000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(3/2)/x^7,x)","-\frac{\left(-105 a^{4} c \,d^{4} x^{8} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+135 a^{3} b \,c^{2} d^{3} x^{8} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-27 a^{2} b^{2} c^{3} d^{2} x^{8} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-3 a \,b^{3} c^{4} d \,x^{8} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-174 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} b \,d^{4} x^{10}+72 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,b^{2} c \,d^{3} x^{10}+6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{3} c^{2} d^{2} x^{10}-105 a^{4} c^{2} d^{3} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+135 a^{3} b \,c^{3} d^{2} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-27 a^{2} b^{2} c^{4} d \,x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-3 a \,b^{3} c^{5} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-174 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{3} d^{4} x^{8}-216 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} b c \,d^{3} x^{8}+138 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,b^{2} c^{2} d^{2} x^{8}+12 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{3} c^{3} d \,x^{8}-174 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{3} c \,d^{3} x^{6}+96 \sqrt{a c}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, a^{3} c \,d^{3} x^{6}-42 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} b \,c^{2} d^{2} x^{6}-96 \sqrt{a c}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, a^{2} b \,c^{2} d^{2} x^{6}+66 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,b^{2} c^{3} d \,x^{6}+6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{3} c^{4} x^{6}+174 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} d^{3} x^{6}-72 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a b c \,d^{2} x^{6}-6 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b^{2} c^{2} d \,x^{6}+114 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} c \,d^{2} x^{4}-60 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a b \,c^{2} d \,x^{4}-6 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b^{2} c^{3} x^{4}-44 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} c^{2} d \,x^{2}+12 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a b \,c^{3} x^{2}+16 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} c^{3}\right) \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}}}{96 \sqrt{a c}\, \left(b \,x^{2}+a \right) \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, a^{2} c^{5} x^{6}}"," ",0,"-1/96*(-174*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^10*a^2*b*d^4+72*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^10*a*b^2*c*d^3-216*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^8*a^2*b*c*d^3+138*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^8*a*b^2*c^2*d^2-72*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^6*a*b*c*d^2-42*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*a^2*b*c^2*d^2+66*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*a*b^2*c^3*d-96*(a*c)^(1/2)*((d*x^2+c)*(b*x^2+a))^(1/2)*x^6*a^2*b*c^2*d^2-60*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^4*a*b*c^2*d-105*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a^4*c^2*d^3-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a*b^3*c^5+174*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^6*a^2*d^3+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*b^3*c^4-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^4*b^2*c^3-105*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^8*a^4*c*d^4-174*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^8*a^3*d^4+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^10*b^3*c^2*d^2+135*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^8*a^3*b*c^2*d^3-27*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^8*a^2*b^2*c^3*d^2-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^8*a*b^3*c^4*d+12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^8*b^3*c^3*d+135*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a^3*b*c^3*d^2-27*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a^2*b^2*c^4*d-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^6*b^2*c^2*d-174*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*a^3*c*d^3+96*(a*c)^(1/2)*((d*x^2+c)*(b*x^2+a))^(1/2)*x^6*a^3*c*d^3+114*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^4*a^2*c*d^2-44*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*a^2*c^2*d+12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*a*b*c^3+16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*a^2*c^3)/a^2*(d*x^2+c)*((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(a*c)^(1/2)/x^6/c^5/(b*x^2+a)/((d*x^2+c)*(b*x^2+a))^(1/2)","B"
283,1,933,427,0.053000," ","int(x^4*((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right) \left(\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}+3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}-2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}+5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b c \,d^{2} x^{3}-3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}-5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x +5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x +\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x -5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x -16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+24 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{5 \left(b \,x^{2}+a \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, d^{4}}"," ",0,"1/5*((b*x^2+a)/(d*x^2+c)*e)^(3/2)*(d*x^2+c)*(((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^7*b^2*d^3+3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^5*a*b*d^3-2*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^5*b^2*c*d^2+2*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^3*a^2*d^3-3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^3*b^2*c^2*d+5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^3*a*b*c*d^2-5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^3*b^2*c^2*d-8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2+24*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d-16*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3+((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2-16*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d+16*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3+2*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x*a^2*c*d^2-3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x*a*b*c^2*d+5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x*a^2*c*d^2-5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x*a*b*c^2*d)/d^4/(b*x^2+a)^2/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
284,1,734,350,0.033000," ","int(x^2*((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right) \left(\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} d^{2} x^{5}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{3}-3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{3}+3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{3}-3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x +3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b c d x +3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b c d x +7 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-11 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \left(b \,x^{2}+a \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, d^{3}}"," ",0,"1/3*((b*x^2+a)/(d*x^2+c)*e)^(3/2)*(d*x^2+c)*(((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^5*b^2*d^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^3*a*b*d^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^3*b^2*c*d-3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^3*a*b*d^2+3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^3*b^2*c*d+3*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*d^2-11*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d+8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2+7*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d-8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x*a*b*c*d-3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x*a^2*d^2+3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x*a*b*c*d)/(b*x^2+a)^2/d^3/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
285,1,527,312,0.029000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right) \left(\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{3}-\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{3}+\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x -\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b c d x -\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\left(b \,x^{2}+a \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, c \,d^{2}}"," ",0,"((b*x^2+a)/(d*x^2+c)*e)^(3/2)*(d*x^2+c)*((b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a*b*d^2*x^3-(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*b^2*c*d*x^3+2*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d-2*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2-((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d+2*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2+(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a^2*d^2*x-(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a*b*c*d*x)/(b*x^2+a)^2/d^2/c/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
286,1,670,355,0.033000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(3/2)/x^2,x)","-\frac{\left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right) \left(\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{4}+\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{4}-\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{4}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{2}+\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{2}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b c d \,x^{2}-\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b c d \,x^{2}-2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} c d \right)}{\left(b \,x^{2}+a \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, c^{2} d x}"," ",0,"-((b*x^2+a)/(d*x^2+c)*e)^(3/2)*(d*x^2+c)*(((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^4*a*b*d^2+(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^4*a*b*d^2-(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^4*b^2*c*d+((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*b*c*d-((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*b^2*c^2-2*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*b*c*d+((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*b^2*c^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^2*a^2*d^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^2*a*b*c*d+(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^2*a^2*d^2-(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^2*a*b*c*d+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a^2*c*d)/(b*x^2+a)^2/c^2/x/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/d","A"
287,1,791,419,0.036000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(3/2)/x^4,x)","\frac{\left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right) \left(5 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}+3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}-4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}-3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}+5 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{4}+3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{4}-3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b c d \,x^{4}-8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{4}+7 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} c d \,x^{2}-5 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,c^{2} x^{2}-\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} c^{2}\right)}{3 \left(b \,x^{2}+a \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, c^{3} x^{3}}"," ",0,"1/3*((b*x^2+a)/(d*x^2+c)*e)^(3/2)*(d*x^2+c)*(5*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^6*a*b*d^2-4*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^6*b^2*c*d+3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^6*a*b*d^2-3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^6*b^2*c*d+4*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d-4*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2-8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d+7*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2+5*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^4*a^2*d^2-4*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^4*b^2*c^2+3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^4*a^2*d^2-3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^4*a*b*c*d+4*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^2*a^2*c*d-5*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^2*a*b*c^2-((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a^2*c^2)/(b*x^2+a)^2/c^3/x^3/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
288,1,1197,512,0.038000," ","int(((b*x^2+a)/(d*x^2+c)*e)^(3/2)/x^6,x)","-\frac{\left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right) \left(11 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{3} x^{8}+5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{3} x^{8}-11 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{2} x^{8}-5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{2} x^{8}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{3} c^{2} d \,x^{8}+11 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{3} d^{3} x^{6}+5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{3} d^{3} x^{6}-3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{2} x^{6}-5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{2} x^{6}-16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} x^{5} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} x^{5} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d \,x^{6}+16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \,x^{5} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-9 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \,x^{5} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{3} c^{3} x^{6}-\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} x^{5} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} x^{5} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{3} c \,d^{2} x^{4}-11 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} b \,c^{2} d \,x^{4}+3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{3} x^{4}-2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{3} c^{2} d \,x^{2}+3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} b \,c^{3} x^{2}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{3} c^{3}\right)}{5 \left(b \,x^{2}+a \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, a \,c^{4} x^{5}}"," ",0,"-1/5*((b*x^2+a)/(d*x^2+c)*e)^(3/2)*(d*x^2+c)*(11*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^8*a^2*b*d^3-11*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^8*a*b^2*c*d^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^8*b^3*c^2*d+5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^8*a^2*b*d^3-5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^8*a*b^2*c*d^2+8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*a^2*b*c*d^2-9*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*a*b^2*c^2*d+((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*b^3*c^3-16*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*a^2*b*c*d^2+16*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*a*b^2*c^2*d-((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^5*b^3*c^3+11*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^6*a^3*d^3-3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^6*a^2*b*c*d^2-8*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^6*a*b^2*c^2*d+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^6*b^3*c^3+5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^6*a^3*d^3-5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^6*a^2*b*c*d^2+8*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^4*a^3*c*d^2-11*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^4*a^2*b*c^2*d+3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^4*a*b^2*c^3-2*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^2*a^3*c^2*d+3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^2*a^2*b*c^3+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a^3*c^3)/a/(b*x^2+a)^2/c^4/x^5/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","B"
289,1,52,45,0.025000," ","int(x*((-x^2+1)/(x^2+1))^(1/2),x)","\frac{\sqrt{-\frac{x^{2}-1}{x^{2}+1}}\, \left(x^{2}+1\right) \left(\arcsin \left(x^{2}\right)+\sqrt{-x^{4}+1}\right)}{2 \sqrt{-\left(x^{2}-1\right) \left(x^{2}+1\right)}}"," ",0,"1/2*(-(x^2-1)/(x^2+1))^(1/2)*(x^2+1)*((-x^4+1)^(1/2)+arcsin(x^2))/(-(x^2-1)*(x^2+1))^(1/2)","A"
290,1,78,59,0.028000," ","int(x*((-7*x^2+5)/(5*x^2+7))^(1/2),x)","\frac{\sqrt{-\frac{7 x^{2}-5}{5 x^{2}+7}}\, \left(5 x^{2}+7\right) \left(37 \sqrt{35}\, \arcsin \left(\frac{35 x^{2}}{37}+\frac{12}{37}\right)+35 \sqrt{-35 x^{4}-24 x^{2}+35}\right)}{350 \sqrt{-\left(7 x^{2}-5\right) \left(5 x^{2}+7\right)}}"," ",0,"1/350*(-(7*x^2-5)/(5*x^2+7))^(1/2)*(5*x^2+7)*(37*35^(1/2)*arcsin(35/37*x^2+12/37)+35*(-35*x^4-24*x^2+35)^(1/2))/(-(7*x^2-5)*(5*x^2+7))^(1/2)","A"
291,1,68,45,0.101000," ","int(x^2*((-x^3+1)/(x^3+1))^(1/2),x)","-\frac{\sqrt{-\frac{x^{3}-1}{x^{3}+1}}\, \sqrt{-\left(x^{3}+1\right) \left(x^{3}-1\right)}\, \arcsin \left(x^{3}\right)}{3 \left(x^{3}-1\right)}+\frac{\left(x^{3}+1\right) \sqrt{-\frac{x^{3}-1}{x^{3}+1}}}{3}"," ",0,"1/3*(x^3+1)*(-(x^3-1)/(x^3+1))^(1/2)-1/3*arcsin(x^3)*(-(x^3-1)/(x^3+1))^(1/2)*(-(x^3+1)*(x^3-1))^(1/2)/(x^3-1)","A"
292,1,80,97,0.069000," ","int(x^8*((-x^3+1)/(x^3+1))^(1/2),x)","-\frac{\sqrt{-\frac{x^{3}-1}{x^{3}+1}}\, \sqrt{-\left(x^{3}+1\right) \left(x^{3}-1\right)}\, \arcsin \left(x^{3}\right)}{6 \left(x^{3}-1\right)}+\frac{\left(2 x^{6}-3 x^{3}+4\right) \left(x^{3}+1\right) \sqrt{-\frac{x^{3}-1}{x^{3}+1}}}{18}"," ",0,"1/18*(2*x^6-3*x^3+4)*(x^3+1)*(-(x^3-1)/(x^3+1))^(1/2)-1/6*(-(x^3-1)/(x^3+1))^(1/2)*(-(x^3+1)*(x^3-1))^(1/2)/(x^3-1)*arcsin(x^3)","A"
293,1,130,89,0.282000," ","int(x^9*((-7*x^5+5)/(5*x^5+7))^(1/2),x)","-\frac{2257 \sqrt{-\frac{7 x^{5}-5}{5 x^{5}+7}}\, \sqrt{-\left(5 x^{5}+7\right) \left(7 x^{5}-5\right)}\, \RootOf \left(\textit{\_Z}^{2}+35\right) \ln \left(35 x^{5} \RootOf \left(\textit{\_Z}^{2}+35\right)+12 \RootOf \left(\textit{\_Z}^{2}+35\right)+35 \sqrt{-35 x^{10}-24 x^{5}+35}\right)}{61250 \left(7 x^{5}-5\right)}+\frac{\left(35 x^{5}-86\right) \left(5 x^{5}+7\right) \sqrt{-\frac{7 x^{5}-5}{5 x^{5}+7}}}{1750}"," ",0,"1/1750*(35*x^5-86)*(5*x^5+7)*(-(7*x^5-5)/(5*x^5+7))^(1/2)-2257/61250*RootOf(_Z^2+35)*ln(35*RootOf(_Z^2+35)*x^5+12*RootOf(_Z^2+35)+35*(-35*x^10-24*x^5+35)^(1/2))*(-(7*x^5-5)/(5*x^5+7))^(1/2)*(-(5*x^5+7)*(7*x^5-5))^(1/2)/(7*x^5-5)","C"
294,1,42,44,0.016000," ","int((x^2/(x^2-1))^(1/2)/(x^2+1),x)","\frac{\sqrt{\frac{x^{2}}{x^{2}-1}}\, \sqrt{x^{2}-1}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{x^{2}-1}\, \sqrt{2}}{2}\right)}{2 x}"," ",0,"1/2*(x^2/(x^2-1))^(1/2)/x*(x^2-1)^(1/2)*2^(1/2)*arctan(1/2*(x^2-1)^(1/2)*2^(1/2))","A"
295,1,60,60,0.040000," ","int((x^2/(-1+a+(1+a)*x^2))^(1/2)/(x^2+1),x)","\frac{\sqrt{\frac{x^{2}}{a \,x^{2}+x^{2}+a -1}}\, \sqrt{a \,x^{2}+x^{2}+a -1}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{a \,x^{2}+x^{2}+a -1}\, \sqrt{2}}{2}\right)}{2 x}"," ",0,"1/2*(x^2/(a*x^2+x^2+a-1))^(1/2)/x*(a*x^2+x^2+a-1)^(1/2)*2^(1/2)*arctan(1/2*(a*x^2+x^2+a-1)^(1/2)*2^(1/2))","A"
296,1,527,253,0.052000," ","int(x^5/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(-15 a^{3} d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+9 a^{2} b c \,d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 a \,b^{2} c^{2} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 b^{3} c^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-36 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b \,d^{2} x^{2}-12 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c d \,x^{2}+30 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} d^{2}-24 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b c d -6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c^{2}+16 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{b d}\, b d \right)}{96 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, b^{3} d^{2}}"," ",0,"1/96*(b*x^2+a)/b^3*(-36*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b*d^2*x^2-12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*c*d*x^2-15*a^3*d^3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+9*a^2*b*c*d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+3*a*b^2*c^2*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+3*b^3*c^3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(b*d)^(1/2)*b*d+30*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^2*d^2-24*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b*c*d-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b^2*c^2)/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/d^2/(b*d)^(1/2)","B"
297,1,342,145,0.040000," ","int(x^3/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(3 a^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-2 a b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+4 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b d \,x^{2}-6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a d +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b c \right)}{16 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, b^{2} d}"," ",0,"1/16*(b*x^2+a)*(4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b*d*x^2+3*d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2-2*a*b*c*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*b^2*c^2-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*d+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b*c)/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/b^2/d/(b*d)^(1/2)","B"
298,1,200,86,0.026000," ","int(x/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(-a d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+b c \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\right)}{4 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, b}"," ",0,"1/4*(b*x^2+a)*(-d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a+b*c*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/b/(b*d)^(1/2)","B"
299,1,179,84,0.043000," ","int(1/x/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(-\sqrt{b d}\, c \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+\sqrt{a c}\, d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)\right)}{2 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, \sqrt{a c}}"," ",0,"1/2*(b*x^2+a)*(d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)-c*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*(b*d)^(1/2))/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(b*d)^(1/2)/(a*c)^(1/2)","B"
300,1,326,110,0.053000," ","int(1/x^3/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(a^{2} c d \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-a b \,c^{2} x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b d \,x^{4}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a d \,x^{2}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b c \,x^{2}+2 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\right)}{4 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a^{2} c \,x^{2}}"," ",0,"-1/4*(b*x^2+a)*(-2*b*d*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^4*(a*c)^(1/2)+a^2*c*d*x^2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)-a*b*c^2*x^2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*d*a*x^2*(a*c)^(1/2)-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*b*c*x^2+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2))/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/a^2/c/x^2/(a*c)^(1/2)","B"
301,1,558,194,0.064000," ","int(1/x^5/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(a^{3} c \,d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+2 a^{2} b \,c^{2} d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-3 a \,b^{2} c^{3} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b \,d^{2} x^{6}-10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} c d \,x^{6}-2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} d^{2} x^{4}-8 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b c d \,x^{4}-10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} c^{2} x^{4}+2 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a d \,x^{2}+10 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b c \,x^{2}-4 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a c \right)}{16 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a^{3} c^{2} x^{4}}"," ",0,"1/16*(b*x^2+a)*(-2*b*d^2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^6*a*(a*c)^(1/2)-10*b^2*d*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*x^6*c*(a*c)^(1/2)+a^3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*d^2*c*x^4+2*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*d*b*a^2*c^2*x^4-3*c^3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*b^2*a*x^4-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*d^2*a^2*x^4*(a*c)^(1/2)-8*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a*b*c*d-10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*b^2*c^2*x^4*(a*c)^(1/2)+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*a*d*x^2+10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*b*c*x^2*(a*c)^(1/2)-4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*a*c)/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/a^3/c^2/x^4/(a*c)^(1/2)","B"
302,1,553,441,0.032000," ","int(x^4/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(3 \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}-\sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}+4 \sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}-4 \sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}+\sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}-4 \sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x +8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a b \,c^{2} d x -3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{15 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, b^{2} d^{2}}"," ",0,"1/15*(b*x^2+a)*(3*(-1/a*b)^(1/2)*b^2*d^3*x^7-(-1/a*b)^(1/2)*a*b*d^3*x^5+4*(-1/a*b)^(1/2)*b^2*c*d^2*x^5-4*(-1/a*b)^(1/2)*a^2*d^3*x^3+(-1/a*b)^(1/2)*b^2*c^2*d*x^3-4*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3+8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2-3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3-4*(-1/a*b)^(1/2)*a^2*c*d^2*x+(-1/a*b)^(1/2)*a*b*c^2*d*x)/b^2/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/d^2/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
303,1,358,354,0.020000," ","int(x^2/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(\sqrt{-\frac{b}{a}}\, b \,d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b c d \,x^{3}+\sqrt{-\frac{b}{a}}\, a c d x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, b d}"," ",0,"1/3*(b*x^2+a)*((-1/a*b)^(1/2)*x^5*b*d^2+(-1/a*b)^(1/2)*x^3*a*d^2+(-1/a*b)^(1/2)*x^3*b*c*d+a*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+(-1/a*b)^(1/2)*a*c*d*x)/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/b/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)/d","A"
304,1,127,304,0.015000," ","int(1/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}"," ",0,"(b*x^2+a)*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
305,1,297,341,0.023000," ","int(1/x^2/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(\sqrt{-\frac{b}{a}}\, b d \,x^{4}+\sqrt{-\frac{b}{a}}\, a d \,x^{2}-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a d x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, b c \,x^{2}-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a c \right)}{\sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, a x}"," ",0,"-(b*x^2+a)*((-1/a*b)^(1/2)*b*d*x^4-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*d+b*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*x*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))-b*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*x*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))+(-1/a*b)^(1/2)*x^2*a*d+(-1/a*b)^(1/2)*x^2*b*c+(-1/a*b)^(1/2)*a*c)/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/a/x/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
306,1,444,413,0.028000," ","int(1/x^4/((b*x^2+a)/(d*x^2+c)*e)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(\sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}-2 \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}+\sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{4}-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{4}+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{-\frac{b}{a}}\, a^{2} c d \,x^{2}-\sqrt{-\frac{b}{a}}\, a b \,c^{2} x^{2}+\sqrt{-\frac{b}{a}}\, a^{2} c^{2}\right)}{3 \sqrt{\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, a^{2} c \,x^{3}}"," ",0,"-1/3*(b*x^2+a)*((-1/a*b)^(1/2)*a*b*d^2*x^6-2*(-1/a*b)^(1/2)*b^2*c*d*x^6+2*b*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*c-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2+(-1/a*b)^(1/2)*a^2*d^2*x^4-2*(-1/a*b)^(1/2)*b^2*c^2*x^4+2*(-1/a*b)^(1/2)*a^2*c*d*x^2-(-1/a*b)^(1/2)*a*b*c^2*x^2+(-1/a*b)^(1/2)*a^2*c^2)/((b*x^2+a)/(d*x^2+c)*e)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/a^2/x^3/c/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
307,1,1027,324,0.074000," ","int(x^5/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(-105 a^{3} b \,d^{3} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+135 a^{2} b^{2} c \,d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-27 a \,b^{3} c^{2} d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-3 b^{4} c^{3} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-60 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} d^{2} x^{4}+12 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} c d \,x^{4}-105 a^{4} d^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+135 a^{3} b c \,d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-27 a^{2} b^{2} c^{2} d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-3 a \,b^{3} c^{3} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+54 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} b \,d^{2} x^{2}-108 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} c d \,x^{2}+6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{3} c^{2} x^{2}+114 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{3} d^{2}+96 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, a^{3} d^{2}-120 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} b c d -96 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, a^{2} b c d +6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a \,b^{2} c^{2}+16 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{b d}\, b^{2} d \,x^{2}+16 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{b d}\, a b d \right) \left(b \,x^{2}+a \right)}{96 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} b^{4} d}"," ",0,"1/96*(-60*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^4*a*b^2*d^2+12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^4*b^3*c*d-105*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a^3*b*d^3+135*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a^2*b^2*c*d^2-27*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b^3*c^2*d-3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^4*c^3+16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(b*d)^(1/2)*x^2*b^2*d+54*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*a^2*b*d^2-108*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*a*b^2*c*d+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*b^3*c^2-105*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^4*d^3+135*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^3*b*c*d^2-27*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*b^2*c^2*d-3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*b^3*c^3+16*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(b*d)^(1/2)*a*b*d+114*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^3*d^2-120*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^2*b*c*d+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b^2*c^2+96*(b*d)^(1/2)*((d*x^2+c)*(b*x^2+a))^(1/2)*a^3*d^2-96*(b*d)^(1/2)*((d*x^2+c)*(b*x^2+a))^(1/2)*a^2*b*c*d)/d/b^4*(b*x^2+a)/(b*d)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(d*x^2+c)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)","B"
308,1,679,176,0.062000," ","int(x^3/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","-\frac{\left(-15 a^{2} b \,d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+18 a \,b^{2} c d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-3 b^{3} c^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-4 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} d \,x^{4}-15 a^{3} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+18 a^{2} b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-3 a \,b^{2} c^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b d \,x^{2}-10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b^{2} c \,x^{2}+16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, a^{2} d +14 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a^{2} d -16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, a b c -10 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a b c \right) \left(b \,x^{2}+a \right)}{16 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} b^{3}}"," ",0,"-1/16*(-4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^4*b^2*d-15*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a^2*b*d^2+18*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b^2*c*d-3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*b^3*c^2+10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*a*b*d-10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*x^2*b^2*c-15*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^3*d^2+18*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a^2*b*c*d-3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*b^2*c^2+16*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*a^2*d-16*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*a*b*c+14*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a^2*d-10*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*b*c)/b^3*(b*x^2+a)/(b*d)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(d*x^2+c)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)","B"
309,1,432,122,0.050000," ","int(x/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(-3 a b \,d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 b^{2} c d \,x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-3 a^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+3 a b c d \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, b d \,x^{2}+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}\, a d +4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, a d -4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, b c \right) \left(b \,x^{2}+a \right)}{4 \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} b^{2}}"," ",0,"1/4*(-3*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*x^2*a*b*d^2+3*b^2*c*d*x^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*b*d*x^2-3*a^2*d^2*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+3*a*b*c*d*ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2)*a*d+4*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*a*d-4*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*b*c)/b^2*(b*x^2+a)/(b*d)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(d*x^2+c)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)","B"
310,1,401,122,0.062000," ","int(1/x/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","-\frac{\left(-\sqrt{a c}\, a b \,d^{2} x^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+\sqrt{b d}\, b^{2} c^{2} x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-\sqrt{a c}\, a^{2} d^{2} \ln \left(\frac{2 b d \,x^{2}+a d +b c +2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+\sqrt{b d}\, a b \,c^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, \sqrt{a c}\, a d -2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{b d}\, \sqrt{a c}\, b c \right) \left(b \,x^{2}+a \right)}{2 \sqrt{a c}\, \sqrt{b d}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} a b}"," ",0,"-1/2*(-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*x^2*a*b*d^2+(b*d)^(1/2)*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*b^2*c^2-ln(1/2*(2*b*d*x^2+a*d+b*c+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*(a*c)^(1/2)*a^2*d^2+(b*d)^(1/2)*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*a*b*c^2+2*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*(a*c)^(1/2)*a*d-2*((d*x^2+c)*(b*x^2+a))^(1/2)*(b*d)^(1/2)*(a*c)^(1/2)*b*c)/a/b*(b*x^2+a)/(a*c)^(1/2)/(b*d)^(1/2)/((d*x^2+c)*(b*x^2+a))^(1/2)/(d*x^2+c)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)","B"
311,1,641,146,0.072000," ","int(1/x^3/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(-3 a^{2} b c d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 a \,b^{2} c^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} d \,x^{6}-3 a^{3} c d \,x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+3 a^{2} b \,c^{2} x^{2} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+4 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b d \,x^{4}+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{2} c \,x^{4}+4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a^{2} d \,x^{2}+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} d \,x^{2}-4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a b c \,x^{2}+2 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a b c \,x^{2}-2 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b \,x^{2}-2 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a \right) \left(b \,x^{2}+a \right)}{4 \sqrt{a c}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} a^{3} x^{2}}"," ",0,"1/4*(2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*b^2*d-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^2*b*c*d+3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a*b^2*c^2+4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a*b*d+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*b^2*c-3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a^3*c*d+3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^2*a^2*b*c^2+4*((d*x^2+c)*(b*x^2+a))^(1/2)*(a*c)^(1/2)*x^2*a^2*d-4*((d*x^2+c)*(b*x^2+a))^(1/2)*(a*c)^(1/2)*x^2*a*b*c-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*b+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^2*a^2*d+2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^2*a*b*c-2*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*a)*(b*x^2+a)/(a*c)^(1/2)/x^2/a^3/((d*x^2+c)*(b*x^2+a))^(1/2)/(d*x^2+c)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)","B"
312,1,1042,229,0.081000," ","int(1/x^5/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","-\frac{\left(3 a^{3} b c \,d^{2} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-18 a^{2} b^{2} c^{2} d \,x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+15 a \,b^{3} c^{3} x^{6} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,b^{2} d^{2} x^{8}+18 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{3} c d \,x^{8}+3 a^{4} c \,d^{2} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-18 a^{3} b \,c^{2} d \,x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)+15 a^{2} b^{2} c^{3} x^{4} \ln \left(\frac{a d \,x^{2}+b c \,x^{2}+2 a c +2 \sqrt{a c}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}}{x^{2}}\right)-12 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} b \,d^{2} x^{6}+26 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,b^{2} c d \,x^{6}+18 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, b^{3} c^{2} x^{6}-6 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{3} d^{2} x^{4}+16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a^{2} b c d \,x^{4}+8 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a^{2} b c d \,x^{4}-16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{a c}\, a \,b^{2} c^{2} x^{4}+18 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{a c}\, a \,b^{2} c^{2} x^{4}+6 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a b d \,x^{4}-18 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, b^{2} c \,x^{4}+6 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} d \,x^{2}-14 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a b c \,x^{2}+4 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)^{\frac{3}{2}} \sqrt{a c}\, a^{2} c \right) \left(b \,x^{2}+a \right)}{16 \sqrt{a c}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \left(d \,x^{2}+c \right) \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} a^{4} c \,x^{4}}"," ",0,"-1/16*(-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^8*a*b^2*d^2+18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^8*b^3*c*d+3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a^3*b*c*d^2-18*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a^2*b^2*c^2*d+15*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^6*a*b^3*c^3-12*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*a^2*b*d^2+26*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*a*b^2*c*d+18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^6*b^3*c^2+3*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^4*c*d^2-18*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^3*b*c^2*d+15*ln((a*d*x^2+b*c*x^2+2*a*c+2*(a*c)^(1/2)*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2))/x^2)*x^4*a^2*b^2*c^3+16*((d*x^2+c)*(b*x^2+a))^(1/2)*(a*c)^(1/2)*x^4*a^2*b*c*d-16*((d*x^2+c)*(b*x^2+a))^(1/2)*(a*c)^(1/2)*x^4*a*b^2*c^2+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^4*a*b*d-18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^4*b^2*c-6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a^3*d^2+8*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a^2*b*c*d+18*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(a*c)^(1/2)*x^4*a*b^2*c^2+6*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*a^2*d-14*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*x^2*a*b*c+4*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(3/2)*(a*c)^(1/2)*a^2*c)/c*(b*x^2+a)/(a*c)^(1/2)/x^4/a^4/((d*x^2+c)*(b*x^2+a))^(1/2)/(d*x^2+c)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)","B"
313,1,935,489,0.055000," ","int(x^4/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(b \,x^{2}+a \right) \left(\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}-2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}+3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}-3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}-5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}+5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b c \,d^{2} x^{3}+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}-3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x -5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x +16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x +5 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x -16 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+9 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{5 \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, b^{3} d}"," ",0,"1/5*(b*x^2+a)*(((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^7*b^2*d^3-2*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^5*a*b*d^3+3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^5*b^2*c*d^2-3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a^2*d^3*x^3+2*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^3*b^2*c^2*d-5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^3*a^2*d^3+5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^3*a*b*c*d^2-8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2+9*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d-((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3+16*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2-16*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d+((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3-3*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x*a^2*c*d^2+2*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x*a*b*c^2*d-5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a^2*c*d^2*x+5*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a*b*c^2*d*x)/b^3/d/((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(d*x^2+c)^2/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
314,1,643,418,0.034000," ","int(x^2/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","\frac{\left(b \,x^{2}+a \right) \left(\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b \,d^{2} x^{5}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}+3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b c d \,x^{3}-3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b c d \,x^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a c d x +3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a c d x -8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b \,c^{2} x +7 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, b^{2}}"," ",0,"1/3*(b*x^2+a)*(((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^5*b*d^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^3*a*d^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^3*b*c*d+3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^3*a*d^2-3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^3*b*c*d+4*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d-4*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2-8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d+7*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x*a*c*d+3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x*a*c*d-3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x*b*c^2)/b^2/((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(d*x^2+c)^2/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
315,1,514,377,0.027000," ","int(1/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}-\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b c d \,x^{3}+\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a c d x -2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b \,c^{2} x +\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, a b}"," ",0,"-(b*x^2+a)/b*((b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a*d^2*x^3-(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*b*c*d*x^3+((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d-((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2-2*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d+((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a*c*d*x-(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*b*c^2*x)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(d*x^2+c)^2/a/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
316,1,650,428,0.035000," ","int(1/x^2/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(-\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a \,d^{2} x^{4}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b c d \,x^{4}+\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b c d \,x^{4}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a c d \,x^{2}-\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a c d \,x^{2}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b \,c^{2} x^{2}+\sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b \,c^{2} x^{2}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, b \,c^{2} x \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} x \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a \,c^{2}\right)}{\left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, a^{2} x}"," ",0,"-(b*x^2+a)*(((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^4*b*c*d-(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^4*a*d^2+(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^4*b*c*d-2*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*c*d+2*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*b*c^2+((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*a*c*d-2*b*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x*((d*x^2+c)*(b*x^2+a))^(1/2)+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^2*a*c*d+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*x^2*b*c^2-(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^2*a*c*d+(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^2*b*c^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a*c^2)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(d*x^2+c)^2/a^2/x/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
317,1,866,480,0.038000," ","int(1/x^4/((b*x^2+a)/(d*x^2+c)*e)^(3/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}+3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{6}-5 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}-3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{6}+4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{4}-3 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} d^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, a b c d \,x^{4}-7 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+11 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-5 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{4}-3 \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, \sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{4}+8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+5 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} c d \,x^{2}-4 \sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a b \,c^{2} x^{2}+\sqrt{\left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)}\, \sqrt{-\frac{b}{a}}\, a^{2} c^{2}\right)}{3 \left(\frac{\left(b \,x^{2}+a \right) e}{d \,x^{2}+c}\right)^{\frac{3}{2}} \left(d \,x^{2}+c \right)^{2} \sqrt{-\frac{b}{a}}\, \sqrt{b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c}\, a^{3} x^{3}}"," ",0,"-1/3*(b*x^2+a)*(4*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a*b*d^2*x^6-5*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*b^2*c*d*x^6+3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a*b*d^2*x^6-3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*b^2*c*d*x^6-3*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a^2*d^2+11*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d-8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2-7*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*a*b*c*d+8*((d*x^2+c)*(b*x^2+a))^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^3*b^2*c^2+4*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a^2*d^2*x^4-5*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*b^2*c^2*x^4+3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*a*b*c*d*x^4-3*(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)*(-1/a*b)^(1/2)*x^4*b^2*c^2+5*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a^2*c*d*x^2-4*((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a*b*c^2*x^2+((d*x^2+c)*(b*x^2+a))^(1/2)*(-1/a*b)^(1/2)*a^2*c^2)/((b*x^2+a)/(d*x^2+c)*e)^(3/2)/(d*x^2+c)^2/a^3/x^3/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)^(1/2)","A"
318,1,533,196,0.063000," ","int(x^5*(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(24 a^{2} b \,c^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-48 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{2} c d \,x^{2}+12 a \,b^{2} c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-12 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b d \,x^{2}+3 b^{3} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-36 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b c -6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b^{2}+16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,d^{2}}\, a \right)}{96 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a^{2} d^{3}}"," ",0,"1/96*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)/d^3*(-48*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^2*c*a^2*d*(a*d^2)^(1/2)+24*ln(1/2*(2*a*d^2*x^2+2*a*c*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)+b*d)/(a*d^2)^(1/2))*a^2*b*c^2*d-12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^2*b*a*d*(a*d^2)^(1/2)+12*ln(1/2*(2*a*d^2*x^2+2*a*c*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)+b*d)/(a*d^2)^(1/2))*b^2*c*a*d+3*ln(1/2*(2*a*d^2*x^2+2*a*c*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)+b*d)/(a*d^2)^(1/2))*b^3*d+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*a*(a*d^2)^(1/2)-36*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*c*b*a*(a*d^2)^(1/2)-6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*b^2*(a*d^2)^(1/2))/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/a^2/(a*d^2)^(1/2)","B"
319,1,354,125,0.036000," ","int(x^3*(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-4 a b c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a d \,x^{2}-b^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a c +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b \right)}{16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a \,d^{2}}"," ",0,"1/16*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)/d^2*(4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^2*a*d-4*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a*b*c*d-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*c-ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*b^2*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*b)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/a/(a*d^2)^(1/2)","B"
320,1,180,57,0.024000," ","int(x*(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(b d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\right)}{4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, d}"," ",0,"1/4*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(b*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/d/(a*d^2)^(1/2)","B"
321,1,235,80,0.042000," ","int((a+b/(d*x^2+c))^(1/2)/x,x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-a c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+\sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)\right)}{2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, c}"," ",0,"-1/2*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(-ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a*c*d+(a*c^2+b*c)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)+2*b*c)/x^2)*(a*d^2)^(1/2))/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/c/(a*d^2)^(1/2)","B"
322,1,454,88,0.050000," ","int((a+b/(d*x^2+c))^(1/2)/x^3,x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-a b \,c^{2} d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a \,d^{2} x^{4}-b^{2} c d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a c d \,x^{2}-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, b d \,x^{2}+2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,c^{2}+b c}\right)}{4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right) \sqrt{a \,c^{2}+b c}\, c^{2} x^{2}}"," ",0,"-1/4*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(-2*a*d^2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^4*(a*c^2+b*c)^(1/2)-ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*a*b*c^2*d-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*a*c*d*x^2*(a*c^2+b*c)^(1/2)-ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*b^2*c*d-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*b*d*x^2*(a*c^2+b*c)^(1/2)+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(1/2))/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/c^2/(a*c+b)/x^2/(a*c^2+b*c)^(1/2)","B"
323,1,923,154,0.062000," ","int((a+b/(d*x^2+c))^(1/2)/x^5,x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-4 a^{3} b \,c^{5} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-11 a^{2} b^{2} c^{4} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-10 a \,b^{3} c^{3} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-3 b^{4} c^{2} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-12 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c \,d^{3} x^{6}-10 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b \,d^{3} x^{6}-20 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c^{2} d^{2} x^{4}-28 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b c \,d^{2} x^{4}-10 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b^{2} d^{2} x^{4}+12 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a c d \,x^{2}+10 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b d \,x^{2}-4 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a \,c^{2}-4 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b c \right)}{16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right)^{2} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} c^{3} x^{4}}"," ",0,"1/16*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(-12*a^2*d^3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^6*c*(a*c^2+b*c)^(3/2)-4*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a^3*b*c^5*d^2-10*a*d^3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^6*b*(a*c^2+b*c)^(3/2)-11*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a^2*b^2*c^4*d^2-20*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*a^2*c^2*d^2*x^4*(a*c^2+b*c)^(3/2)-10*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a*b^3*c^3*d^2-28*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*a*c*d^2*b*x^4*(a*c^2+b*c)^(3/2)-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*b^4*c^2*d^2-10*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*b^2*d^2*x^4*(a*c^2+b*c)^(3/2)+12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*a*c*d*x^2*(a*c^2+b*c)^(3/2)+10*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*b*d*x^2*(a*c^2+b*c)^(3/2)-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*a*c^2-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*b*c)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/c^3/(a*c+b)^2/x^4/(a*c^2+b*c)^(3/2)","B"
324,1,1518,241,0.076000," ","int((a+b/(d*x^2+c))^(1/2)/x^7,x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-24 a^{5} b \,c^{8} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-108 a^{4} b^{2} c^{7} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-195 a^{3} b^{3} c^{6} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-177 a^{2} b^{4} c^{5} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-81 a \,b^{5} c^{4} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-15 b^{6} c^{3} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-96 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{3} c^{2} d^{4} x^{8}-156 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} b c \,d^{4} x^{8}-144 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{3} c^{3} d^{3} x^{6}-66 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a \,b^{2} d^{4} x^{8}-324 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} b \,c^{2} d^{3} x^{6}-252 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a \,b^{2} c \,d^{3} x^{6}-66 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{3} d^{3} x^{6}+96 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} c^{2} d^{2} x^{4}+156 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a b c \,d^{2} x^{4}-48 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} c^{3} d \,x^{2}+66 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{2} d^{2} x^{4}-84 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a b \,c^{2} d \,x^{2}+16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} c^{4}-36 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{2} c d \,x^{2}+32 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a b \,c^{3}+16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{2} c^{2}\right)}{96 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right)^{3} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} c^{4} x^{6}}"," ",0,"-1/96*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(-24*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^5*b*c^8*d^3-96*a^3*d^4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^8*c^2*(a*c^2+b*c)^(5/2)-108*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^4*b^2*c^7*d^3-156*a^2*d^4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^8*c*b*(a*c^2+b*c)^(5/2)-195*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^3*b^3*c^6*d^3-66*a*d^4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^8*b^2*(a*c^2+b*c)^(5/2)-144*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*a^3*c^3*d^3*(a*c^2+b*c)^(5/2)*x^6-177*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^2*b^4*c^5*d^3-324*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*a^2*c^2*d^3*b*(a*c^2+b*c)^(5/2)*x^6-81*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a*b^5*c^4*d^3-252*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*a*c*d^3*b^2*(a*c^2+b*c)^(5/2)*x^6-15*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*b^6*c^3*d^3+96*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*a^2*c^2*d^2*(a*c^2+b*c)^(5/2)*x^4-66*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*b^3*d^3*(a*c^2+b*c)^(5/2)*x^6+156*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*a*c*d^2*b*(a*c^2+b*c)^(5/2)*x^4+66*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*b^2*d^2*(a*c^2+b*c)^(5/2)*x^4-48*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^2*a^2*c^3*d-84*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^2*a*b*c^2*d-36*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^2*b^2*c*d+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*a^2*c^4+32*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*a*b*c^3+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*b^2*c^2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/c^4/(a*c+b)^3/x^6/(a*c^2+b*c)^(5/2)","B"
325,1,662,406,0.044000," ","int(x^4*(a+b/(d*x^2+c))^(1/2),x)","\frac{\left(3 \sqrt{-\frac{a d}{a c +b}}\, a^{2} d^{3} x^{7}+3 \sqrt{-\frac{a d}{a c +b}}\, a^{2} c \,d^{2} x^{5}+4 \sqrt{-\frac{a d}{a c +b}}\, a b \,d^{2} x^{5}-3 \sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{2} d \,x^{3}+2 \sqrt{-\frac{a d}{a c +b}}\, a b c d \,x^{3}-3 \sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{3} x +3 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{-\frac{a d}{a c +b}}\, b^{2} d \,x^{3}-2 \sqrt{-\frac{a d}{a c +b}}\, a b \,c^{2} x -7 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+9 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{-\frac{a d}{a c +b}}\, b^{2} c x -2 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{15 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a \,d^{2}}"," ",0,"1/15*(3*(-a*d/(a*c+b))^(1/2)*x^7*a^2*d^3+3*(-a*d/(a*c+b))^(1/2)*x^5*a^2*c*d^2+4*(-a*d/(a*c+b))^(1/2)*x^5*a*b*d^2-3*(-a*d/(a*c+b))^(1/2)*x^3*a^2*c^2*d+3*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-a*d/(a*c+b))^(1/2),((a*c+b)/a/c)^(1/2))*a^2*c^3+2*(-a*d/(a*c+b))^(1/2)*x^3*a*b*c*d+9*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-a*d/(a*c+b))^(1/2),((a*c+b)/a/c)^(1/2))*a*b*c^2-7*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-a*d/(a*c+b))^(1/2),((a*c+b)/a/c)^(1/2))*a*b*c^2+(-a*d/(a*c+b))^(1/2)*x^3*b^2*d-3*(-a*d/(a*c+b))^(1/2)*x*a^2*c^3+((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-a*d/(a*c+b))^(1/2),((a*c+b)/a/c)^(1/2))*b^2*c-2*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-a*d/(a*c+b))^(1/2),((a*c+b)/a/c)^(1/2))*b^2*c-2*(-a*d/(a*c+b))^(1/2)*x*a*b*c^2+(-a*d/(a*c+b))^(1/2)*x*b^2*c)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/d^2/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-a*d/(a*c+b))^(1/2)/a/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
326,1,406,324,0.023000," ","int(x^2*(a+b/(d*x^2+c))^(1/2),x)","\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, a \,d^{2} x^{5}+2 \sqrt{-\frac{a d}{a c +b}}\, a c d \,x^{3}+\sqrt{-\frac{a d}{a c +b}}\, b d \,x^{3}+\sqrt{-\frac{a d}{a c +b}}\, a \,c^{2} x -\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{-\frac{a d}{a c +b}}\, b c x +\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-2 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, d}"," ",0,"1/3*((-1/(a*c+b)*a*d)^(1/2)*x^5*a*d^2+2*(-1/(a*c+b)*a*d)^(1/2)*x^3*a*c*d+(-1/(a*c+b)*a*d)^(1/2)*x^3*b*d-((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*c^2+(-1/(a*c+b)*a*d)^(1/2)*x*a*c^2-2*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b*c+((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b*c+(-1/(a*c+b)*a*d)^(1/2)*x*b*c)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/d/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
327,1,199,265,0.017000," ","int((a+b/(d*x^2+c))^(1/2),x)","\frac{\left(a c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+b \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}}"," ",0,"(a*c*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))+EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b)*((d*x^2+c)/c)^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
328,1,272,315,0.033000," ","int((a+b/(d*x^2+c))^(1/2)/x^2,x)","-\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, a \,d^{2} x^{4}+2 \sqrt{-\frac{a d}{a c +b}}\, a c d \,x^{2}-\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d x \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{-\frac{a d}{a c +b}}\, b d \,x^{2}+\sqrt{-\frac{a d}{a c +b}}\, a \,c^{2}+\sqrt{-\frac{a d}{a c +b}}\, b c \right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, c x}"," ",0,"-((-1/(a*c+b)*a*d)^(1/2)*x^4*a*d^2-a*d*c*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*x*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))+2*(-1/(a*c+b)*a*d)^(1/2)*x^2*a*c*d+(-1/(a*c+b)*a*d)^(1/2)*x^2*b*d+(-1/(a*c+b)*a*d)^(1/2)*a*c^2+(-1/(a*c+b)*a*d)^(1/2)*b*c)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/x/c/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
329,1,571,400,0.039000," ","int((a+b/(d*x^2+c))^(1/2)/x^4,x)","\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, a^{2} c \,d^{3} x^{6}+2 \sqrt{-\frac{a d}{a c +b}}\, a b \,d^{3} x^{6}+\sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{2} d^{2} x^{4}-\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{2} d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+4 \sqrt{-\frac{a d}{a c +b}}\, a b c \,d^{2} x^{4}-2 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \,d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \,d^{2} x^{3} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-\sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{3} d \,x^{2}+2 \sqrt{-\frac{a d}{a c +b}}\, b^{2} d^{2} x^{4}-\sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{4}+\sqrt{-\frac{a d}{a c +b}}\, b^{2} c d \,x^{2}-2 \sqrt{-\frac{a d}{a c +b}}\, a b \,c^{3}-\sqrt{-\frac{a d}{a c +b}}\, b^{2} c^{2}\right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a c +b \right) \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, c^{2} x^{3}}"," ",0,"1/3*((-1/(a*c+b)*a*d)^(1/2)*x^6*a^2*c*d^3+2*(-1/(a*c+b)*a*d)^(1/2)*x^6*a*b*d^3-((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a^2*c^2*d^2+(-1/(a*c+b)*a*d)^(1/2)*x^4*a^2*c^2*d^2+((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a*b*c*d^2-2*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a*b*c*d^2+4*(-1/(a*c+b)*a*d)^(1/2)*x^4*a*b*c*d^2+2*(-1/(a*c+b)*a*d)^(1/2)*x^4*b^2*d^2-(-1/(a*c+b)*a*d)^(1/2)*x^2*a^2*c^3*d+(-1/(a*c+b)*a*d)^(1/2)*x^2*b^2*c*d-(-1/(a*c+b)*a*d)^(1/2)*a^2*c^4-2*(-1/(a*c+b)*a*d)^(1/2)*a*b*c^3-(-1/(a*c+b)*a*d)^(1/2)*b^2*c^2)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/(a*c+b)/x^3/c^2/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
330,1,955,500,0.047000," ","int((a+b/(d*x^2+c))^(1/2)/x^6,x)","-\frac{\left(3 \sqrt{-\frac{a d}{a c +b}}\, a^{3} c^{2} d^{4} x^{8}+13 \sqrt{-\frac{a d}{a c +b}}\, a^{2} b c \,d^{4} x^{8}+3 \sqrt{-\frac{a d}{a c +b}}\, a^{3} c^{3} d^{3} x^{6}-3 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} c^{3} d^{3} x^{5} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+8 \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} d^{4} x^{8}+22 \sqrt{-\frac{a d}{a c +b}}\, a^{2} b \,c^{2} d^{3} x^{6}-13 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{3} x^{5} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+6 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{3} x^{5} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+25 \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c \,d^{3} x^{6}-8 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c \,d^{3} x^{5} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+4 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c \,d^{3} x^{5} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+5 \sqrt{-\frac{a d}{a c +b}}\, a^{2} b \,c^{3} d^{2} x^{4}+8 \sqrt{-\frac{a d}{a c +b}}\, b^{3} d^{3} x^{6}+3 \sqrt{-\frac{a d}{a c +b}}\, a^{3} c^{5} d \,x^{2}+9 \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c^{2} d^{2} x^{4}+5 \sqrt{-\frac{a d}{a c +b}}\, a^{2} b \,c^{4} d \,x^{2}+4 \sqrt{-\frac{a d}{a c +b}}\, b^{3} c \,d^{2} x^{4}+3 \sqrt{-\frac{a d}{a c +b}}\, a^{3} c^{6}+\sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c^{3} d \,x^{2}+9 \sqrt{-\frac{a d}{a c +b}}\, a^{2} b \,c^{5}-\sqrt{-\frac{a d}{a c +b}}\, b^{3} c^{2} d \,x^{2}+9 \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c^{4}+3 \sqrt{-\frac{a d}{a c +b}}\, b^{3} c^{3}\right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{15 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a c +b \right)^{2} \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, c^{3} x^{5}}"," ",0,"-1/15*(3*(-1/(a*c+b)*a*d)^(1/2)*x^8*a^3*c^2*d^4+13*(-1/(a*c+b)*a*d)^(1/2)*x^8*a^2*b*c*d^4-3*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a^3*c^3*d^3+8*(-1/(a*c+b)*a*d)^(1/2)*x^8*a*b^2*d^4+3*(-1/(a*c+b)*a*d)^(1/2)*x^6*a^3*c^3*d^3+6*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a^2*b*c^2*d^3-13*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a^2*b*c^2*d^3+22*(-1/(a*c+b)*a*d)^(1/2)*x^6*a^2*b*c^2*d^3+4*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a*b^2*c*d^3-8*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a*b^2*c*d^3+25*(-1/(a*c+b)*a*d)^(1/2)*x^6*a*b^2*c*d^3+8*(-1/(a*c+b)*a*d)^(1/2)*x^6*b^3*d^3+5*(-1/(a*c+b)*a*d)^(1/2)*x^4*a^2*b*c^3*d^2+9*(-1/(a*c+b)*a*d)^(1/2)*x^4*a*b^2*c^2*d^2+3*(-1/(a*c+b)*a*d)^(1/2)*x^2*a^3*c^5*d+4*(-1/(a*c+b)*a*d)^(1/2)*x^4*b^3*c*d^2+5*(-1/(a*c+b)*a*d)^(1/2)*x^2*a^2*b*c^4*d+(-1/(a*c+b)*a*d)^(1/2)*x^2*a*b^2*c^3*d+3*(-1/(a*c+b)*a*d)^(1/2)*a^3*c^6-(-1/(a*c+b)*a*d)^(1/2)*x^2*b^3*c^2*d+9*(-1/(a*c+b)*a*d)^(1/2)*a^2*b*c^5+9*(-1/(a*c+b)*a*d)^(1/2)*a*b^2*c^4+3*(-1/(a*c+b)*a*d)^(1/2)*b^3*c^3)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/(a*c+b)^2/x^5/c^3/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
331,1,1018,227,0.069000," ","int(x^5*(a+b/(d*x^2+c))^(3/2),x)","-\frac{\left(-72 a^{2} b \,c^{2} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+48 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{2} c \,d^{2} x^{4}+36 a \,b^{2} c \,d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-72 a^{2} b \,c^{3} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-12 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b \,d^{2} x^{4}+3 b^{3} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+48 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{2} c^{2} d \,x^{2}+36 a \,b^{2} c^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+96 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b c d \,x^{2}+3 b^{3} c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b^{2} d \,x^{2}+96 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a b \,c^{2}+108 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b \,c^{2}-16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,d^{2}}\, a d \,x^{2}-6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b^{2} c -16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,d^{2}}\, a c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{96 \sqrt{a \,d^{2}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a \,d^{3}}"," ",0,"-1/96*(48*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^4*a^2*c*d^2-12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^4*a*b*d^2-72*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a^2*b*c^2*d^2+48*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^2*a^2*c^2*d+36*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a*b^2*c*d^2-16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*d^2)^(1/2)*x^2*a*d+96*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^2*a*b*c*d+3*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*b^3*d^2-72*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a^2*b*c^3*d-6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^2*b^2*d+36*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a*b^2*c^2*d+96*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*a*b*c^2-16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*d^2)^(1/2)*a*c+108*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*b*c^2+3*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*b^3*c*d-6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*b^2*c)/d^3/a*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2)^(1/2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","B"
332,1,593,154,0.056000," ","int(x^3*(a+b/(d*x^2+c))^(3/2),x)","\frac{\left(-12 a b c \,d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a \,d^{2} x^{4}+3 b^{2} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-12 a b \,c^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+3 b^{2} c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+10 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b d \,x^{2}-4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a \,c^{2}+16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, b c +10 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{16 \sqrt{a \,d^{2}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, d^{2}}"," ",0,"1/16*(4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^4*a*d^2-12*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a*b*c*d^2+3*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*b^2*d^2+10*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^2*b*d-12*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a*b*c^2*d-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*c^2+3*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*b^2*c*d+16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*b*c+10*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*b*c)/d^2*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2)^(1/2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","B"
333,1,336,78,0.046000," ","int(x*(a+b/(d*x^2+c))^(3/2),x)","-\frac{\left(-3 a b \,d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-3 a b c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a d \,x^{2}-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a c +4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, b \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, d}"," ",0,"-1/4*(-3*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a*b*d^2-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*d*x^2-3*a*b*c*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*c+4*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*b)/d*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*d^2)^(1/2)","B"
334,1,652,108,0.061000," ","int((a+b/(d*x^2+c))^(3/2)/x,x)","\frac{\left(a^{2} c^{2} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+a^{2} c^{3} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-\sqrt{a \,d^{2}}\, \sqrt{a \,c^{2}+b c}\, a c d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-\sqrt{a \,d^{2}}\, \sqrt{a \,c^{2}+b c}\, b d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-\sqrt{a \,d^{2}}\, \sqrt{a \,c^{2}+b c}\, a \,c^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-\sqrt{a \,d^{2}}\, \sqrt{a \,c^{2}+b c}\, b c \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, b c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{2 \sqrt{a \,d^{2}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, c^{2}}"," ",0,"1/2*(ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a^2*c^2*d^2-(a*d^2)^(1/2)*(a*c^2+b*c)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*a*c*d+ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a^2*c^3*d-(a*d^2)^(1/2)*(a*c^2+b*c)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*b*d-(a*d^2)^(1/2)*(a*c^2+b*c)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*a*c^2-(a*d^2)^(1/2)*(a*c^2+b*c)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*b*c+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*b*c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2)^(1/2)/c^2/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","B"
335,1,820,118,0.071000," ","int((a+b/(d*x^2+c))^(3/2)/x^3,x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(-3 a b \,c^{2} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a \,d^{3} x^{6}-3 b^{2} c \,d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-3 a b \,c^{3} d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a c \,d^{2} x^{4}-3 b^{2} c^{2} d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, b \,d^{2} x^{4}-4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a \,c^{2} d \,x^{2}+4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,c^{2}+b c}\, b c d \,x^{2}-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, b c d \,x^{2}+2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,c^{2}+b c}\, d \,x^{2}+2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,c^{2}+b c}\, c \right)}{4 \sqrt{a \,c^{2}+b c}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, c^{3} x^{2}}"," ",0,"-1/4*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^6*a*d^3-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a*b*c^2*d^2-6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^4*a*c*d^2-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*b^2*c*d^2-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^4*b*d^2-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*a*b*c^3*d-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^2*a*c^2*d-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*b^2*c^2*d+4*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*c^2+b*c)^(1/2)*x^2*b*c*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(1/2)*x^2*d-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^2*b*c*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(1/2)*c)/(a*c^2+b*c)^(1/2)/x^2/c^3/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","B"
336,1,1653,183,0.078000," ","int((a+b/(d*x^2+c))^(3/2)/x^5,x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(-12 a^{3} b \,c^{5} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-39 a^{2} b^{2} c^{4} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-12 a^{3} b \,c^{6} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-42 a \,b^{3} c^{3} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-39 a^{2} b^{2} c^{5} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-15 b^{4} c^{2} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-12 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c \,d^{4} x^{8}-42 a \,b^{3} c^{4} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-18 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b \,d^{4} x^{8}-15 b^{4} c^{3} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-32 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c^{2} d^{3} x^{6}-62 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b c \,d^{3} x^{6}-20 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c^{3} d^{2} x^{4}-18 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b^{2} d^{3} x^{6}+16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b \,c^{2} d^{2} x^{4}-44 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b \,c^{2} d^{2} x^{4}+16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b^{2} c \,d^{2} x^{4}-18 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b^{2} c \,d^{2} x^{4}+12 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a c \,d^{2} x^{4}+18 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b \,d^{2} x^{4}+8 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a \,c^{2} d \,x^{2}+14 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b c d \,x^{2}-4 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a \,c^{3}-4 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b \,c^{2}\right)}{16 \left(a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a c +b \right) \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, c^{4} x^{4}}"," ",0,"1/16*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(-12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^8*a^2*c*d^4-12*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^3*b*c^5*d^3-18*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^8*a*b*d^4-39*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^2*b^2*c^4*d^3-32*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^6*a^2*c^2*d^3-42*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a*b^3*c^3*d^3-12*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a^3*b*c^6*d^2-62*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^6*a*b*c*d^3-15*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*b^4*c^2*d^3-39*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a^2*b^2*c^5*d^2-18*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^6*b^2*d^3-20*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^4*a^2*c^3*d^2-42*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a*b^3*c^4*d^2+16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*c^2+b*c)^(3/2)*x^4*a*b*c^2*d^2+12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^4*a*c*d^2-44*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^4*a*b*c^2*d^2-15*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*b^4*c^3*d^2+16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*c^2+b*c)^(3/2)*x^4*b^2*c*d^2+18*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^4*b*d^2-18*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^4*b^2*c*d^2+8*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^2*a*c^2*d+14*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^2*b*c*d-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*a*c^3-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*b*c^2)/(a*c^2+b*c)^(3/2)/x^4/(a*c+b)/c^4/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","B"
337,1,2605,266,0.085000," ","int((a+b/(d*x^2+c))^(3/2)/x^7,x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(-72 a^{5} b \,c^{8} d^{4} x^{8} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-396 a^{4} b^{2} c^{7} d^{4} x^{8} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-72 a^{5} b \,c^{9} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-861 a^{3} b^{3} c^{6} d^{4} x^{8} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-396 a^{4} b^{2} c^{8} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-927 a^{2} b^{4} c^{5} d^{4} x^{8} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-861 a^{3} b^{3} c^{7} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-495 a \,b^{5} c^{4} d^{4} x^{8} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-927 a^{2} b^{4} c^{6} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-105 b^{6} c^{3} d^{4} x^{8} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-495 a \,b^{5} c^{5} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-96 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{3} c^{2} d^{5} x^{10}-105 b^{6} c^{4} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-276 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} b c \,d^{5} x^{10}-240 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{3} c^{3} d^{4} x^{8}-174 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a \,b^{2} d^{5} x^{10}-816 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} b \,c^{2} d^{4} x^{8}-144 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{3} c^{4} d^{3} x^{6}-738 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a \,b^{2} c \,d^{4} x^{8}-540 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} b \,c^{3} d^{3} x^{6}+96 \left(a \,c^{2}+b c \right)^{\frac{5}{2}} \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} b \,c^{3} d^{3} x^{6}-174 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{3} d^{4} x^{8}-564 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a \,b^{2} c^{2} d^{3} x^{6}+192 \left(a \,c^{2}+b c \right)^{\frac{5}{2}} \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a \,b^{2} c^{2} d^{3} x^{6}+96 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} c^{2} d^{3} x^{6}-174 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{3} c \,d^{3} x^{6}+96 \left(a \,c^{2}+b c \right)^{\frac{5}{2}} \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{3} c \,d^{3} x^{6}+276 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a b c \,d^{3} x^{6}+48 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} c^{3} d^{2} x^{4}+174 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{2} d^{3} x^{6}+168 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a b \,c^{2} d^{2} x^{4}-32 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} c^{4} d \,x^{2}+114 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{2} c \,d^{2} x^{4}-76 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a b \,c^{3} d \,x^{2}+16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a^{2} c^{5}-44 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{2} c^{2} d \,x^{2}+32 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} a b \,c^{4}+16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{5}{2}} b^{2} c^{3}\right)}{96 \left(a \,c^{2}+b c \right)^{\frac{5}{2}} \left(a c +b \right)^{2} \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, c^{5} x^{6}}"," ",0,"-1/96*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(-738*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^8*a*b^2*c*d^4-540*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^6*a^2*b*c^3*d^3+96*(a*c^2+b*c)^(5/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^6*a^2*b*c^3*d^3+276*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^6*a*b*c*d^3-564*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^6*a*b^2*c^2*d^3+192*(a*c^2+b*c)^(5/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^6*a*b^2*c^2*d^3+168*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^4*a*b*c^2*d^2-76*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^2*a*b*c^3*d-276*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^10*a^2*b*c*d^5-816*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^8*a^2*b*c^2*d^4-144*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^6*a^3*c^4*d^3-105*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^8*b^6*c^3*d^4-174*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^8*b^3*d^4-105*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*b^6*c^4*d^3+174*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^6*b^2*d^3+32*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*a*b*c^4-927*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^2*b^4*c^6*d^3+96*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^6*a^2*c^2*d^3-495*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a*b^5*c^5*d^3+48*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^4*a^2*c^3*d^2-174*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^6*b^3*c*d^3+96*(a*c^2+b*c)^(5/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^6*b^3*c*d^3+114*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^4*b^2*c*d^2-32*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^2*a^2*c^4*d-44*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*x^2*b^2*c^2*d-72*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^8*a^5*b*c^8*d^4-96*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^10*a^3*c^2*d^5-396*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^8*a^4*b^2*c^7*d^4-861*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^8*a^3*b^3*c^6*d^4-72*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^5*b*c^9*d^3-174*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^10*a*b^2*d^5-240*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(5/2)*x^8*a^3*c^3*d^4-927*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^8*a^2*b^4*c^5*d^4-396*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^4*b^2*c^8*d^3-495*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^8*a*b^5*c^4*d^4-861*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^3*b^3*c^7*d^3+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*a^2*c^5+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(5/2)*b^2*c^3)/(a*c^2+b*c)^(5/2)/x^6/(a*c+b)^2/c^5/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","B"
338,1,1098,441,0.055000," ","int(x^4*(a+b/(d*x^2+c))^(3/2),x)","\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} d^{3} x^{7}+\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c \,d^{2} x^{5}+3 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,d^{2} x^{5}-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{2} d \,x^{3}+5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b c d \,x^{3}+4 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b c d \,x^{3}-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{3} x +\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+2 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} d \,x^{3}+5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b \,c^{2} x +\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{2} x -14 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+8 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{2} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} c x +2 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c x +\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-8 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a d \,x^{2}+a c +b \right) d^{2}}"," ",0,"1/5*((-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^7*a^2*d^3+(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^5*a^2*c*d^2+3*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^5*a*b*d^2-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^3*a^2*c^2*d+5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^3*a*b*c*d+4*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^3*a*b*c*d+((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c^3+2*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^3*b^2*d-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x*a^2*c^3+8*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c^2-14*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c^2+5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*a*b*c^2+(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x*a*b*c^2-8*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*c+((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*c+5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*b^2*c+2*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x*b^2*c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/d^2/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/(a*d*x^2+a*c+b)","B"
339,1,820,371,0.038000," ","int(x^2*(a+b/(d*x^2+c))^(3/2),x)","\frac{\left(\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} d^{2} x^{5}+2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} c d \,x^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a b d \,x^{3}-3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b d \,x^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{2} x -\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a b c x -3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b c x +7 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-5 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} x +3 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a d \,x^{2}+a c +b \right) d}"," ",0,"1/3*(((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^5*a^2*d^2+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^3*a^2*c*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^3*a*b*d-((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a^2*c^2-3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^3*a*b*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*a^2*c^2-5*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*b*c+7*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*b*c+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*a*b*c+3*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b^2-3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*a*b*c-3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*b^2)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/d/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/(a*d*x^2+a*c+b)","B"
340,1,515,310,0.030000," ","int((a+b/(d*x^2+c))^(3/2),x)","\frac{\left(\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b d \,x^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b c x -\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} x \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a d \,x^{2}+a c +b \right) c}"," ",0,"(((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a^2*c^2+(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*b*d*x^3+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*b*c-((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*b*c+(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*b*c*x+(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*b^2*x)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/c/(a*d*x^2+a*c+b)","A"
341,1,873,360,0.037000," ","int((a+b/(d*x^2+c))^(3/2)/x^2,x)","-\frac{\left(\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} c \,d^{2} x^{4}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a b \,d^{2} x^{4}+\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b \,d^{2} x^{4}+2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{2} d \,x^{2}-\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{2} d x \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+3 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a b c d \,x^{2}+\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b c d \,x^{2}-2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d x \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d x \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} d \,x^{2}+\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} d \,x^{2}+2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a b \,c^{2}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a d \,x^{2}+a c +b \right) c^{2} x}"," ",0,"-(((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*a^2*c*d^2+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*a*b*d^2-((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x*a^2*c^2*d+(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*a*b*d^2+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*a^2*c^2*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x*a*b*c*d-2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x*a*b*c*d+3*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*a*b*c*d+(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*a*b*c*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*b^2*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a^2*c^3+(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*b^2*d+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*b*c^2+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*b^2*c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/x/c^2/(a*d*x^2+a*c+b)","B"
342,1,1039,424,0.040000," ","int((a+b/(d*x^2+c))^(3/2)/x^4,x)","\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c \,d^{3} x^{6}+3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b \,d^{3} x^{6}+5 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,d^{3} x^{6}+\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{2} d^{2} x^{4}-\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{2} d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b c \,d^{2} x^{4}+10 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b c \,d^{2} x^{4}-8 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \,d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \,d^{2} x^{3} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{3} d \,x^{2}+3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} d^{2} x^{4}+5 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} d^{2} x^{4}+3 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{2} d \,x^{2}-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{4}+4 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c d \,x^{2}-2 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{3}-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c^{2}\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a d \,x^{2}+a c +b \right) c^{3} x^{3}}"," ",0,"1/3*((-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^6*a^2*c*d^3+3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^6*a*b*d^3+5*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^6*a*b*d^3-((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a^2*c^2*d^2+(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^4*a^2*c^2*d^2+4*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a*b*c*d^2-8*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a*b*c*d^2+3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*a*b*c*d^2+10*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^4*a*b*c*d^2+3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*b^2*d^2+5*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^4*b^2*d^2-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^2*a^2*c^3*d+3*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^2*a*b*c^2*d+4*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*x^2*b^2*c*d-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c^4-2*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c^3-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*c^2)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/x^3/c^3/(a*d*x^2+a*c+b)","B"
343,1,1666,526,0.044000," ","int((a+b/(d*x^2+c))^(3/2)/x^6,x)","-\frac{\left(\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{3} c^{2} d^{4} x^{8}+5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} b c \,d^{4} x^{8}+11 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} b c \,d^{4} x^{8}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{3} c^{3} d^{3} x^{6}-\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} c^{3} d^{3} x^{5} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} d^{4} x^{8}+11 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} d^{4} x^{8}+5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} b \,c^{2} d^{3} x^{6}+19 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} b \,c^{2} d^{3} x^{6}-16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{3} x^{5} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+7 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{3} x^{5} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+10 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c \,d^{3} x^{6}+30 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c \,d^{3} x^{6}-16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c \,d^{3} x^{5} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+8 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c \,d^{3} x^{5} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+5 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} b \,c^{3} d^{2} x^{4}+5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b^{3} d^{3} x^{6}+11 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b^{3} d^{3} x^{6}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{3} c^{5} d \,x^{2}+13 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c^{2} d^{2} x^{4}+8 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b^{3} c \,d^{2} x^{4}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{3} c^{6}-3 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c^{3} d \,x^{2}+3 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a^{2} b \,c^{5}-2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b^{3} c^{2} d \,x^{2}+3 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,b^{2} c^{4}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b^{3} c^{3}\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{5 \left(a c +b \right) \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a d \,x^{2}+a c +b \right) c^{4} x^{5}}"," ",0,"-1/5*(7*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a^2*b*c^2*d^3-16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a^2*b*c^2*d^3+8*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a*b^2*c*d^3-16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a*b^2*c*d^3+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a^3*c^6+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*b^3*c^3+5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^8*a*b^2*d^4+5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^6*b^3*d^3+11*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^6*b^3*d^3+3*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a^2*b*c^5+3*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*b^2*c^4+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^8*a^3*c^2*d^4+11*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^8*a*b^2*d^4+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^6*a^3*c^3*d^3+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*a^3*c^5*d+8*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*b^3*c*d^2+5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^8*a^2*b*c*d^4+5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^6*a^2*b*c^2*d^3+10*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^6*a*b^2*c*d^3+11*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^8*a^2*b*c*d^4+19*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^6*a^2*b*c^2*d^3+30*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^6*a*b^2*c*d^3+5*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*a^2*b*c^3*d^2+13*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*a*b^2*c^2*d^2-3*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*a*b^2*c^3*d-2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*b^3*c^2*d-((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^5*a^3*c^3*d^3)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*c+b)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/x^5/c^4/(a*d*x^2+a*c+b)","B"
344,1,533,205,0.052000," ","int(x^5/(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-24 a^{2} b \,c^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-48 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{2} c d \,x^{2}-36 a \,b^{2} c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-36 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b d \,x^{2}-15 b^{3} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+36 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b c +30 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b^{2}+16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,d^{2}}\, a \right)}{96 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a^{3} d^{3}}"," ",0,"1/96*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)/a^3/d^3*(-48*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a^2*c*d*x^2-36*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*b*d*x^2-24*a^2*b*c^2*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))-36*a*b^2*c*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*d^2)^(1/2)*a+36*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*b*c-15*b^3*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+30*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*b^2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*d^2)^(1/2)","B"
345,1,354,132,0.038000," ","int(x^3/(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(4 a b c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a d \,x^{2}+3 b^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a c -6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b \right)}{16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a^{2} d^{2}}"," ",0,"1/16*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)/d^2*(4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*d*x^2+4*a*b*c*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*c+3*b^2*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))-6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*b)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/a^2/(a*d^2)^(1/2)","B"
346,1,184,60,0.027000," ","int(x/(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-b d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\right)}{4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a d}"," ",0,"1/4*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(-b*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/a/d/(a*d^2)^(1/2)","B"
347,1,312,80,0.042000," ","int(1/x/(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(a c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+b d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-\sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)\right)}{2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right) \sqrt{a \,d^{2}}}"," ",0,"1/2*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(a*c*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+b*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))-(a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2))/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*c+b)/(a*d^2)^(1/2)","B"
348,1,452,92,0.043000," ","int(1/x^3/(a+b/(d*x^2+c))^(1/2),x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(a b \,c^{2} d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a \,d^{2} x^{4}+b^{2} c d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a c d \,x^{2}-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, b d \,x^{2}+2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,c^{2}+b c}\right)}{4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right)^{2} \sqrt{a \,c^{2}+b c}\, c \,x^{2}}"," ",0,"-1/4*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(-2*a*d^2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*x^4*(a*c^2+b*c)^(1/2)+ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*a*b*c^2*d-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*a*c*d*x^2*(a*c^2+b*c)^(1/2)+ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*b^2*c*d-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*b*d*x^2*(a*c^2+b*c)^(1/2)+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(1/2))/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*c+b)^2/c/x^2/(a*c^2+b*c)^(1/2)","B"
349,1,922,157,0.054000," ","int(1/x^5/(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(4 a^{3} b \,c^{5} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+9 a^{2} b^{2} c^{4} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+6 a \,b^{3} c^{3} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+b^{4} c^{2} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-12 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c \,d^{3} x^{6}-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b \,d^{3} x^{6}-20 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c^{2} d^{2} x^{4}-12 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b c \,d^{2} x^{4}-2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b^{2} d^{2} x^{4}+12 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a c d \,x^{2}+2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b d \,x^{2}-4 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a \,c^{2}-4 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b c \right)}{16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right)^{3} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} c^{2} x^{4}}"," ",0,"1/16*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(-12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*a^2*c*d^3*x^6+4*a^3*b*c^5*d^2*x^4*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*a*b*d^3*x^6+9*a^2*b^2*c^4*d^2*x^4*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)-20*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*a^2*c^2*d^2*x^4+6*a*b^3*c^3*d^2*x^4*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)-12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*a*b*c*d^2*x^4+b^4*c^2*d^2*x^4*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*b^2*d^2*x^4+12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*a*c*d*x^2+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*b*d*x^2-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*a*c^2-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*b*c)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*c+b)^3/c^2/x^4/(a*c^2+b*c)^(3/2)","B"
350,1,665,481,0.035000," ","int(x^4/(a+b/(d*x^2+c))^(1/2),x)","\frac{\left(3 \sqrt{-\frac{a d}{a c +b}}\, a^{2} d^{3} x^{7}+3 \sqrt{-\frac{a d}{a c +b}}\, a^{2} c \,d^{2} x^{5}-\sqrt{-\frac{a d}{a c +b}}\, a b \,d^{2} x^{5}-3 \sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{2} d \,x^{3}-8 \sqrt{-\frac{a d}{a c +b}}\, a b c d \,x^{3}-3 \sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{3} x +3 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-4 \sqrt{-\frac{a d}{a c +b}}\, b^{2} d \,x^{3}-7 \sqrt{-\frac{a d}{a c +b}}\, a b \,c^{2} x +13 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-6 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-4 \sqrt{-\frac{a d}{a c +b}}\, b^{2} c x +8 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-4 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{15 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} d^{2}}"," ",0,"1/15*(3*(-1/(a*c+b)*a*d)^(1/2)*a^2*d^3*x^7+3*(-1/(a*c+b)*a*d)^(1/2)*a^2*c*d^2*x^5-(-1/(a*c+b)*a*d)^(1/2)*a*b*d^2*x^5-3*(-1/(a*c+b)*a*d)^(1/2)*a^2*c^2*d*x^3-8*(-1/(a*c+b)*a*d)^(1/2)*a*b*c*d*x^3+3*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a^2*c^3-4*(-1/(a*c+b)*a*d)^(1/2)*b^2*d*x^3-3*(-1/(a*c+b)*a*d)^(1/2)*a^2*c^3*x-6*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*b*c^2+13*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*b*c^2-7*(-1/(a*c+b)*a*d)^(1/2)*a*b*c^2*x-4*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b^2*c+8*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b^2*c-4*(-1/(a*c+b)*a*d)^(1/2)*b^2*c*x)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/d^2/a^2/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
351,1,409,396,0.024000," ","int(x^2/(a+b/(d*x^2+c))^(1/2),x)","\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, a \,d^{2} x^{5}+2 \sqrt{-\frac{a d}{a c +b}}\, a c d \,x^{3}+\sqrt{-\frac{a d}{a c +b}}\, b d \,x^{3}+\sqrt{-\frac{a d}{a c +b}}\, a \,c^{2} x -\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{-\frac{a d}{a c +b}}\, b c x -2 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a d}"," ",0,"1/3*((-1/(a*c+b)*a*d)^(1/2)*a*d^2*x^5+2*(-1/(a*c+b)*a*d)^(1/2)*a*c*d*x^3+(-1/(a*c+b)*a*d)^(1/2)*b*d*x^3-((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*c^2+(-1/(a*c+b)*a*d)^(1/2)*a*c^2*x+((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b*c-2*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b*c+(-1/(a*c+b)*a*d)^(1/2)*b*c*x)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/d/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/a/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
352,1,164,338,0.019000," ","int(1/(a+b/(d*x^2+c))^(1/2),x)","\frac{\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)}{\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}}"," ",0,"EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)/c)^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*c*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
353,1,345,396,0.028000," ","int(1/x^2/(a+b/(d*x^2+c))^(1/2),x)","-\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, a \,d^{2} x^{4}+2 \sqrt{-\frac{a d}{a c +b}}\, a c d \,x^{2}-\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d x \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{-\frac{a d}{a c +b}}\, b d \,x^{2}-\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b d x \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{-\frac{a d}{a c +b}}\, a \,c^{2}+\sqrt{-\frac{a d}{a c +b}}\, b c \right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a c +b \right) \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, x}"," ",0,"-((-1/(a*c+b)*a*d)^(1/2)*a*d^2*x^4-a*d*c*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*x*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))+2*(-1/(a*c+b)*a*d)^(1/2)*a*c*d*x^2-((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x*b*d+(-1/(a*c+b)*a*d)^(1/2)*b*d*x^2+(-1/(a*c+b)*a*d)^(1/2)*a*c^2+(-1/(a*c+b)*a*d)^(1/2)*b*c)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/x/(a*c+b)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
354,1,596,473,0.030000," ","int(1/x^4/(a+b/(d*x^2+c))^(1/2),x)","\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, a^{2} c \,d^{3} x^{6}-\sqrt{-\frac{a d}{a c +b}}\, a b \,d^{3} x^{6}+\sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{2} d^{2} x^{4}-\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{2} d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-2 \sqrt{-\frac{a d}{a c +b}}\, a b c \,d^{2} x^{4}+\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \,d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-2 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \,d^{2} x^{3} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-\sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{3} d \,x^{2}-\sqrt{-\frac{a d}{a c +b}}\, b^{2} d^{2} x^{4}-3 \sqrt{-\frac{a d}{a c +b}}\, a b \,c^{2} d \,x^{2}-\sqrt{-\frac{a d}{a c +b}}\, a^{2} c^{4}-2 \sqrt{-\frac{a d}{a c +b}}\, b^{2} c d \,x^{2}-2 \sqrt{-\frac{a d}{a c +b}}\, a b \,c^{3}-\sqrt{-\frac{a d}{a c +b}}\, b^{2} c^{2}\right) \left(d \,x^{2}+c \right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a c +b \right)^{2} \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, c \,x^{3}}"," ",0,"1/3*((-1/(a*c+b)*a*d)^(1/2)*a^2*c*d^3*x^6-(-1/(a*c+b)*a*d)^(1/2)*a*b*d^3*x^6-((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a^2*c^2*d^2+(-1/(a*c+b)*a*d)^(1/2)*a^2*c^2*d^2*x^4-2*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a*b*c*d^2+((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a*b*c*d^2-2*(-1/(a*c+b)*a*d)^(1/2)*a*b*c*d^2*x^4-(-1/(a*c+b)*a*d)^(1/2)*b^2*d^2*x^4-(-1/(a*c+b)*a*d)^(1/2)*a^2*c^3*d*x^2-3*(-1/(a*c+b)*a*d)^(1/2)*x^2*a*b*c^2*d-2*(-1/(a*c+b)*a*d)^(1/2)*b^2*c*d*x^2-(-1/(a*c+b)*a*d)^(1/2)*a^2*c^4-2*(-1/(a*c+b)*a*d)^(1/2)*a*b*c^3-(-1/(a*c+b)*a*d)^(1/2)*b^2*c^2)*(d*x^2+c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/c/x^3/(a*c+b)^2/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)","A"
355,1,1240,288,0.073000," ","int(x^5/(a+b/(d*x^2+c))^(3/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-72 a^{3} b \,c^{2} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-48 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{3} c \,d^{2} x^{4}-180 a^{2} b^{2} c \,d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-72 a^{3} b \,c^{3} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-60 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{2} b \,d^{2} x^{4}-105 a \,b^{3} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-48 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{3} c^{2} d \,x^{2}-252 a^{2} b^{2} c^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-285 a \,b^{3} c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+54 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a \,b^{2} d \,x^{2}-105 b^{4} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+96 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a^{2} b \,c^{2}+108 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{2} b \,c^{2}+16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,d^{2}}\, a^{2} d \,x^{2}+192 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a \,b^{2} c +222 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a \,b^{2} c +16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,d^{2}}\, a^{2} c +96 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, b^{3}+114 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b^{3}+16 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,d^{2}}\, a b \right)}{96 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, \left(a d \,x^{2}+a c +b \right) a^{4} d^{3}}"," ",0,"1/96*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)/a^4/d^3*(-48*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^4*a^3*c*d^2-60*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^4*a^2*b*d^2-72*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a^3*b*c^2*d^2-48*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^2*a^3*c^2*d-180*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a^2*b^2*c*d^2+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*d^2)^(1/2)*x^2*a^2*d-105*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a*b^3*d^2-72*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a^3*b*c^3*d+54*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^2*a*b^2*d-252*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a^2*b^2*c^2*d+96*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*a^2*b*c^2+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*d^2)^(1/2)*a^2*c+108*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a^2*b*c^2-285*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a*b^3*c*d+192*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*a*b^2*c+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*d^2)^(1/2)*a*b+222*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*b^2*c-105*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*b^4*d+96*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*b^3+114*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*b^3)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*d^2)^(1/2)/(a*d*x^2+a*c+b)","B"
356,1,783,169,0.063000," ","int(x^3/(a+b/(d*x^2+c))^(3/2),x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-12 a^{2} b c \,d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{2} d^{2} x^{4}-15 a \,b^{2} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-12 a^{2} b \,c^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-27 a \,b^{2} c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+10 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b d \,x^{2}-15 b^{3} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a^{2} c^{2}+16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a b c +18 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a b c +16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, b^{2}+14 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b^{2}\right)}{16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, \left(a d \,x^{2}+a c +b \right) a^{3} d^{2}}"," ",0,"-1/16*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)/a^3/d^2*(-4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*x^4*a^2*d^2-12*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a^2*b*c*d^2-15*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a*b^2*d^2+10*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*b*d*x^2-12*a^2*b*c^2*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a^2*c^2-27*a*b^2*c*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*a*b*c+18*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*b*c-15*b^3*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*b^2+14*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*b^2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*d^2)^(1/2)/(a*d*x^2+a*c+b)","B"
357,1,478,84,0.047000," ","int(x/(a+b/(d*x^2+c))^(3/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-3 a b \,d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-3 a b c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a d \,x^{2}-3 b^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, a c +4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, b +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}\, b \right)}{4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, \left(a d \,x^{2}+a c +b \right) a^{2} d}"," ",0,"1/4*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)/a^2/d*(-3*a*b*d^2*x^2*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*d*x^2-3*a*b*c*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))-3*b^2*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*a*c+4*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*b+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2)*b)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*d^2)^(1/2)/(a*d*x^2+a*c+b)","B"
358,1,1015,116,0.059000," ","int(1/x/(a+b/(d*x^2+c))^(3/2),x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-a^{3} c^{2} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-2 a^{2} b c \,d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-a^{3} c^{3} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-a \,b^{2} d^{2} x^{2} \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)-3 a^{2} b \,c^{2} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+\sqrt{a \,d^{2}}\, \sqrt{a \,c^{2}+b c}\, a^{2} c d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-3 a \,b^{2} c d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+\sqrt{a \,d^{2}}\, \sqrt{a \,c^{2}+b c}\, a^{2} c^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-b^{3} d \ln \left(\frac{2 a \,d^{2} x^{2}+2 a c d +b d +2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,d^{2}}}{2 \sqrt{a \,d^{2}}}\right)+\sqrt{a \,d^{2}}\, \sqrt{a \,c^{2}+b c}\, a b c \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, a b c +2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,d^{2}}\, b^{2}\right)}{2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right)^{2} \sqrt{a \,d^{2}}\, \left(a d \,x^{2}+a c +b \right) a}"," ",0,"-1/2*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)/a*(-ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*x^2*a^3*c^2*d^2-2*a^2*b*c*d^2*x^2*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+(a*d^2)^(1/2)*(a*c^2+b*c)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*a^2*c*d-a*b^2*d^2*x^2*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))-ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))*a^3*c^3*d-3*a^2*b*c^2*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+(a*d^2)^(1/2)*(a*c^2+b*c)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*a^2*c^2-3*a*b^2*c*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+(a*d^2)^(1/2)*(a*c^2+b*c)^(1/2)*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*a*b*c+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*a*b*c-b^3*d*ln(1/2*(2*a*d^2*x^2+2*a*c*d+b*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*d^2)^(1/2))/(a*d^2)^(1/2))+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*d^2)^(1/2)*b^2)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*c+b)^2/(a*d^2)^(1/2)/(a*d*x^2+a*c+b)","B"
359,1,1088,129,0.068000," ","int(1/x^3/(a+b/(d*x^2+c))^(3/2),x)","\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-3 a^{2} b \,c^{2} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a^{2} d^{3} x^{6}-3 a \,b^{2} c \,d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-3 a^{2} b \,c^{3} d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a^{2} c \,d^{2} x^{4}-6 a \,b^{2} c^{2} d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a b \,d^{2} x^{4}-3 b^{3} c d \,x^{2} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+4 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a^{2} c^{2} d \,x^{2}+4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,c^{2}+b c}\, a b c d \,x^{2}+6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, a b c d \,x^{2}+4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{a \,c^{2}+b c}\, b^{2} d \,x^{2}+2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{a \,c^{2}+b c}\, b^{2} d \,x^{2}-2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,c^{2}+b c}\, a d \,x^{2}-2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,c^{2}+b c}\, a c -2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \sqrt{a \,c^{2}+b c}\, b \right)}{4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right)^{3} \left(a d \,x^{2}+a c +b \right) \sqrt{a \,c^{2}+b c}\, x^{2}}"," ",0,"1/4*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^6*a^2*d^3-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a^2*b*c^2*d^2+6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^4*a^2*c*d^2-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a*b^2*c*d^2+4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^4*a*b*d^2-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*a^2*b*c^3*d+4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^2*a^2*c^2*d-6*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*a*b^2*c^2*d+4*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*c^2+b*c)^(1/2)*x^2*a*b*c*d-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(1/2)*x^2*a*d+6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^2*a*b*c*d-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^2*b^3*c*d+4*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*c^2+b*c)^(1/2)*x^2*b^2*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(1/2)*x^2*b^2*d-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(1/2)*a*c-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(1/2)*b)/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*c+b)^3/(a*d*x^2+a*c+b)/x^2/(a*c^2+b*c)^(1/2)","B"
360,1,1947,190,0.081000," ","int(1/x^5/(a+b/(d*x^2+c))^(3/2),x)","-\frac{\sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}\, \left(d \,x^{2}+c \right) \left(-12 a^{4} b \,c^{5} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-21 a^{3} b^{2} c^{4} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-12 a^{4} b \,c^{6} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-6 a^{2} b^{3} c^{3} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-33 a^{3} b^{2} c^{5} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+3 a \,b^{4} c^{2} d^{3} x^{6} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+12 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{3} c \,d^{4} x^{8}-27 a^{2} b^{3} c^{4} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)-6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} b \,d^{4} x^{8}-3 a \,b^{4} c^{3} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+32 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{3} c^{2} d^{3} x^{6}+3 b^{5} c^{2} d^{2} x^{4} \ln \left(\frac{2 a c d \,x^{2}+b d \,x^{2}+2 a \,c^{2}+2 b c +2 \sqrt{a \,c^{2}+b c}\, \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}}{x^{2}}\right)+2 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} b c \,d^{3} x^{6}+20 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{3} c^{3} d^{2} x^{4}-12 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a \,b^{2} d^{3} x^{6}+16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} b \,c^{2} d^{2} x^{4}+16 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} b \,c^{2} d^{2} x^{4}+16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a \,b^{2} c \,d^{2} x^{4}-10 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a \,b^{2} c \,d^{2} x^{4}-12 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c \,d^{2} x^{4}-6 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b^{3} d^{2} x^{4}+6 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b \,d^{2} x^{4}-8 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c^{2} d \,x^{2}-2 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b c d \,x^{2}+4 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a^{2} c^{3}+6 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b^{2} d \,x^{2}+8 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} a b \,c^{2}+4 \left(a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} b^{2} c \right)}{16 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \left(a c +b \right)^{4} \left(a \,c^{2}+b c \right)^{\frac{3}{2}} \left(a d \,x^{2}+a c +b \right) c \,x^{4}}"," ",0,"-1/16*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)*(d*x^2+c)*(-33*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a^3*b^2*c^5*d^2+16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*c^2+b*c)^(3/2)*x^4*a^2*b*c^2*d^2+16*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^4*a^2*b*c^2*d^2+16*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(a*c^2+b*c)^(3/2)*x^4*a*b^2*c*d^2-10*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^4*a*b^2*c*d^2-2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^2*a*b*c*d+2*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^6*a^2*b*c*d^3+3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*b^5*c^2*d^2-6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^4*b^3*d^2+6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^2*b^2*d+8*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*a*b*c^2-3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a*b^4*c^3*d^2+6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^4*a*b*d^2-8*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^2*a^2*c^2*d+12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^8*a^3*c*d^4-12*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^4*b*c^5*d^3-6*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^8*a^2*b*d^4-21*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^3*b^2*c^4*d^3+32*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^6*a^3*c^2*d^3-6*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a^2*b^3*c^3*d^3-12*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a^4*b*c^6*d^2+3*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^6*a*b^4*c^2*d^3+4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*a^2*c^3+4*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*b^2*c-12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^6*a*b^2*d^3+20*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(a*c^2+b*c)^(3/2)*x^4*a^3*c^3*d^2-27*ln((2*a*c*d*x^2+b*d*x^2+2*a*c^2+2*b*c+2*(a*c^2+b*c)^(1/2)*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2))/x^2)*x^4*a^2*b^3*c^4*d^2-12*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(3/2)*(a*c^2+b*c)^(3/2)*x^4*a^2*c*d^2)/c/((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)/(a*c+b)^4/x^4/(a*c^2+b*c)^(3/2)/(a*d*x^2+a*c+b)","B"
361,1,1158,518,0.056000," ","int(x^4/(a+b/(d*x^2+c))^(3/2),x)","\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} d^{3} x^{7}+\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c \,d^{2} x^{5}-2 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,d^{2} x^{5}-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{2} d \,x^{3}-6 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b c d \,x^{3}-5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b c d \,x^{3}-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{3} x +\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-3 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} d \,x^{3}-5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} d \,x^{3}-4 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{2} x -5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b \,c^{2} x +16 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-7 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{2} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-3 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c x -5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b^{2} c x +16 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-8 \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{5 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a d \,x^{2}+a c +b \right) a^{3} d^{2}}"," ",0,"1/5*((-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*d^3*x^7+(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c*d^2*x^5-2*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*d^2*x^5-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c^2*d*x^3-6*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c*d*x^3+((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c^3-5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*b*c*d*x^3-3*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*d*x^3-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c^3*x-7*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c^2+16*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c^2-5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^3*b^2*d-4*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c^2*x-8*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*c+16*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*c-5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*b*c^2*x-3*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*c*x-5*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*b^2*c*x)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/d^2/a^3/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/(a*d*x^2+a*c+b)","B"
362,1,667,449,0.039000," ","int(x^2/(a+b/(d*x^2+c))^(3/2),x)","\frac{\left(\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,d^{2} x^{5}+2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a c d \,x^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b d \,x^{3}+3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b d \,x^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,c^{2} x -\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b c x +3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b c x -8 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+4 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a d \,x^{2}+a c +b \right) a^{2} d}"," ",0,"1/3*(((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^5*a*d^2+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^3*a*c*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^3*b*d-((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*c^2+3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^3*b*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*a*c^2+4*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b*c-8*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b*c+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*b*c+3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x*b*c)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/a^2/d/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/(a*d*x^2+a*c+b)","A"
363,1,466,406,0.033000," ","int(1/(a+b/(d*x^2+c))^(3/2),x)","-\frac{\left(\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b d \,x^{3}-\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,c^{2} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b c x -2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a c +b \right) \left(a d \,x^{2}+a c +b \right) a}"," ",0,"-((a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*b*d*x^3-((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*a*c^2+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b*c-2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*b*c+(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*b*c*x)/a*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/(a*c+b)/(a*d*x^2+a*c+b)","A"
364,1,685,458,0.040000," ","int(1/x^2/(a+b/(d*x^2+c))^(3/2),x)","-\frac{\left(\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a c \,d^{2} x^{4}-\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b \,d^{2} x^{4}+2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,c^{2} d \,x^{2}-\sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a \,c^{2} d x \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b c d \,x^{2}-\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, b c d \,x^{2}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c d x \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-2 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b c d x \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, a \,c^{3}+\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{-\frac{a d}{a c +b}}\, b \,c^{2}\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{\sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a c +b \right)^{2} \left(a d \,x^{2}+a c +b \right) x}"," ",0,"-(((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*a*c*d^2-a*c^2*d*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)-(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^4*b*d^2+2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*a*c^2*d-2*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x*b*c*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x*b*c*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*b*c*d-(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*x^2*b*c*d+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*c^3+((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*b*c^2)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/x/(a*c+b)^2/(a*d*x^2+a*c+b)","A"
365,1,1082,526,0.042000," ","int(1/x^4/(a+b/(d*x^2+c))^(3/2),x)","\frac{\left(\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c \,d^{3} x^{6}-4 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,d^{3} x^{6}-3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b \,d^{3} x^{6}+\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{2} d^{2} x^{4}-\sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c^{2} d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-8 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b c \,d^{2} x^{4}-3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, a b c \,d^{2} x^{4}+7 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \,d^{2} x^{3} \EllipticE \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-5 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c \,d^{2} x^{3} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{3} d \,x^{2}-4 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} d^{2} x^{4}+3 \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, \sqrt{\frac{a d \,x^{2}+a c +b}{a c +b}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} d^{2} x^{3} \EllipticF \left(\sqrt{-\frac{a d}{a c +b}}\, x , \sqrt{\frac{a c +b}{a c}}\right)-6 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{2} d \,x^{2}-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a^{2} c^{4}-5 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c d \,x^{2}-2 \sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, a b \,c^{3}-\sqrt{-\frac{a d}{a c +b}}\, \sqrt{\left(d \,x^{2}+c \right) \left(a d \,x^{2}+a c +b \right)}\, b^{2} c^{2}\right) \sqrt{\frac{a d \,x^{2}+a c +b}{d \,x^{2}+c}}}{3 \sqrt{a \,d^{2} x^{4}+2 a c d \,x^{2}+b d \,x^{2}+a \,c^{2}+b c}\, \sqrt{-\frac{a d}{a c +b}}\, \left(a c +b \right)^{3} \left(a d \,x^{2}+a c +b \right) x^{3}}"," ",0,"1/3*((-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c*d^3*x^6-4*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*d^3*x^6-((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a^2*c^2*d^2-3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*b*d^3*x^6+(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c^2*d^2*x^4-5*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a*b*c*d^2+7*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*a*b*c*d^2-8*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c*d^2*x^4+3*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*((a*d*x^2+a*c+b)/(a*c+b))^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/(a*c+b)*a*d)^(1/2)*x,((a*c+b)/a/c)^(1/2))*x^3*b^2*d^2-3*(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)*(-1/(a*c+b)*a*d)^(1/2)*a*b*c*d^2*x^4-4*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*d^2*x^4-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c^3*d*x^2-6*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c^2*d*x^2-5*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*c*d*x^2-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a^2*c^4-2*(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*a*b*c^3-(-1/(a*c+b)*a*d)^(1/2)*((d*x^2+c)*(a*d*x^2+a*c+b))^(1/2)*b^2*c^2)*((a*d*x^2+a*c+b)/(d*x^2+c))^(1/2)/(a*d^2*x^4+2*a*c*d*x^2+b*d*x^2+a*c^2+b*c)^(1/2)/(-1/(a*c+b)*a*d)^(1/2)/x^3/(a*c+b)^3/(a*d*x^2+a*c+b)","B"
366,1,64,55,0.072000," ","int((a*x^23)^(1/2)/(x^5+1)^(1/2),x)","\frac{\left(2 x^{5}-3\right) \sqrt{x^{5}+1}\, \sqrt{a \,x^{23}}}{20 x^{9}}+\frac{3 \sqrt{a \,x^{23}}\, \sqrt{\left(x^{5}+1\right) a x}\, \arcsinh \left(x^{\frac{5}{2}}\right)}{20 \sqrt{x^{5}+1}\, \sqrt{a}\, x^{12}}"," ",0,"1/20/x^9*(2*x^5-3)*(x^5+1)^(1/2)*(a*x^23)^(1/2)+3/20/a^(1/2)*arcsinh(x^(5/2))*(a*x^23)^(1/2)/x^12*(a*x*(x^5+1))^(1/2)/(x^5+1)^(1/2)","A"
367,1,57,36,0.061000," ","int((a*x^13)^(1/2)/(x^5+1)^(1/2),x)","\frac{\sqrt{a \,x^{13}}\, \sqrt{x^{5}+1}}{5 x^{4}}-\frac{\sqrt{a \,x^{13}}\, \sqrt{\left(x^{5}+1\right) a x}\, \arcsinh \left(x^{\frac{5}{2}}\right)}{5 \sqrt{x^{5}+1}\, \sqrt{a}\, x^{7}}"," ",0,"1/5*(a*x^13)^(1/2)*(x^5+1)^(1/2)/x^4-1/5/a^(1/2)*arcsinh(x^(5/2))*(a*x^13)^(1/2)/x^7*((x^5+1)*a*x)^(1/2)/(x^5+1)^(1/2)","A"
368,1,17,16,0.051000," ","int((a*x^3)^(1/2)/(x^5+1)^(1/2),x)","\frac{2 \sqrt{a \,x^{3}}\, \arcsinh \left(x^{\frac{5}{2}}\right)}{5 x^{\frac{3}{2}}}"," ",0,"2/5*arcsinh(x^(5/2))*(a*x^3)^(1/2)/x^(3/2)","A"
369,1,37,17,0.005000," ","int((a/x^7)^(1/2)/(x^5+1)^(1/2),x)","-\frac{2 \left(x +1\right) \left(x^{4}-x^{3}+x^{2}-x +1\right) \sqrt{\frac{a}{x^{7}}}\, x}{5 \sqrt{x^{5}+1}}"," ",0,"-2/5*x*(x+1)*(x^4-x^3+x^2-x+1)*(a/x^7)^(1/2)/(x^5+1)^(1/2)","B"
370,1,44,37,0.004000," ","int((a/x^17)^(1/2)/(x^5+1)^(1/2),x)","\frac{2 \left(x +1\right) \left(x^{4}-x^{3}+x^{2}-x +1\right) \left(2 x^{5}-1\right) \sqrt{\frac{a}{x^{17}}}\, x}{15 \sqrt{x^{5}+1}}"," ",0,"2/15*x*(x+1)*(x^4-x^3+x^2-x+1)*(2*x^5-1)*(a/x^17)^(1/2)/(x^5+1)^(1/2)","A"
371,1,28,29,0.013000," ","int((a*x^6)^(1/2)/x/(-x^4+1),x)","-\frac{\sqrt{a \,x^{6}}\, \left(2 \arctan \left(x \right)+\ln \left(x -1\right)-\ln \left(x +1\right)\right)}{4 x^{3}}"," ",0,"-1/4*(a*x^6)^(1/2)*(ln(x-1)-ln(x+1)+2*arctan(x))/x^3","A"
372,1,28,29,0.012000," ","int((a*x^6)^(1/2)/(-x^5+x),x)","-\frac{\sqrt{a \,x^{6}}\, \left(2 \arctan \left(x \right)+\ln \left(x -1\right)-\ln \left(x +1\right)\right)}{4 x^{3}}"," ",0,"-1/4*(a*x^6)^(1/2)*(2*arctan(x)+ln(x-1)-ln(x+1))/x^3","A"
373,1,38,57,0.012000," ","int((a*x^6)^(3/2)/x/(-x^4+1),x)","-\frac{\left(a \,x^{6}\right)^{\frac{3}{2}} \left(4 x^{5}+20 x -10 \arctan \left(x \right)+5 \ln \left(x -1\right)-5 \ln \left(x +1\right)\right)}{20 x^{9}}"," ",0,"-1/20*(a*x^6)^(3/2)*(4*x^5+5*ln(x-1)-5*ln(x+1)-10*arctan(x)+20*x)/x^9","A"
374,1,37,37,0.008000," ","int(1/(-x^4+1)-(a*x^6)^(1/2)/x/(-x^4+1),x)","\frac{\arctanh \left(x \right)}{2}+\frac{\arctan \left(x \right)}{2}+\frac{\sqrt{a \,x^{6}}\, \left(2 \arctan \left(x \right)+\ln \left(x -1\right)-\ln \left(x +1\right)\right)}{4 x^{3}}"," ",0,"1/2*arctanh(x)+1/2*arctan(x)+1/4*(a*x^6)^(1/2)*(2*arctan(x)+ln(x-1)-ln(x+1))/x^3","A"
375,1,37,37,0.008000," ","int(1/(-x^4+1)-(a*x^6)^(1/2)/(-x^5+x),x)","\frac{\arctanh \left(x \right)}{2}+\frac{\arctan \left(x \right)}{2}+\frac{\sqrt{a \,x^{6}}\, \left(2 \arctan \left(x \right)+\ln \left(x -1\right)-\ln \left(x +1\right)\right)}{4 x^{3}}"," ",0,"1/2*arctanh(x)+1/2*arctan(x)+1/4*(a*x^6)^(1/2)*(2*arctan(x)+ln(x-1)-ln(x+1))/x^3","A"
376,1,43,32,0.015000," ","int((a*x^3)^(1/2)/(-x^3+x),x)","\frac{\sqrt{a \,x^{3}}\, \left(\arctanh \left(\frac{\sqrt{a x}}{\sqrt{a}}\right)-\arctan \left(\frac{\sqrt{a x}}{\sqrt{a}}\right)\right) \sqrt{a}}{\sqrt{a x}\, x}"," ",0,"(a*x^3)^(1/2)*a^(1/2)*(arctanh((a*x)^(1/2)/a^(1/2))-arctan((a*x)^(1/2)/a^(1/2)))/x/(a*x)^(1/2)","A"
377,1,27,34,0.008000," ","int((a*x^4)^(1/2)/(x^2+1)^(1/2),x)","\frac{\sqrt{a \,x^{4}}\, \left(\sqrt{x^{2}+1}\, x -\arcsinh \left(x \right)\right)}{2 x^{2}}"," ",0,"1/2*(a*x^4)^(1/2)*(x*(x^2+1)^(1/2)-arcsinh(x))/x^2","A"
378,1,76,88,0.034000," ","int((a*x^3)^(1/2)/(x^2+1)^(1/2),x)","-\frac{\sqrt{a \,x^{3}}\, \left(-2 x^{3}-2 x +i \sqrt{-i \left(x +i\right)}\, \sqrt{-i \left(-x +i\right)}\, \sqrt{i x}\, \sqrt{2}\, \EllipticF \left(\sqrt{-i \left(x +i\right)}, \frac{\sqrt{2}}{2}\right)\right)}{3 \sqrt{x^{2}+1}\, x^{2}}"," ",0,"-1/3*(a*x^3)^(1/2)/x^2/(x^2+1)^(1/2)*(I*(-I*(x+I))^(1/2)*(-I*(-x+I))^(1/2)*(I*x)^(1/2)*EllipticF((-I*(x+I))^(1/2),1/2*2^(1/2))*2^(1/2)-2*x^3-2*x)","C"
379,1,19,18,0.003000," ","int((a*x^2)^(1/2)/(x^2+1)^(1/2),x)","\frac{\sqrt{a \,x^{2}}\, \sqrt{x^{2}+1}}{x}"," ",0,"(a*x^2)^(1/2)*(x^2+1)^(1/2)/x","A"
380,1,81,177,0.028000," ","int((a*x)^(1/2)/(x^2+1)^(1/2),x)","\frac{\sqrt{a x}\, \sqrt{-i \left(x +i\right)}\, \sqrt{2}\, \sqrt{-i \left(-x +i\right)}\, \sqrt{i x}\, \left(2 \EllipticE \left(\sqrt{-i \left(x +i\right)}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{-i \left(x +i\right)}, \frac{\sqrt{2}}{2}\right)\right)}{\sqrt{x^{2}+1}\, x}"," ",0,"(a*x)^(1/2)/(x^2+1)^(1/2)*(-I*(x+I))^(1/2)*2^(1/2)*(-I*(-x+I))^(1/2)*(I*x)^(1/2)*(2*EllipticE((-I*(x+I))^(1/2),1/2*2^(1/2))-EllipticF((-I*(x+I))^(1/2),1/2*2^(1/2)))/x","C"
381,1,62,67,0.038000," ","int((a/x)^(1/2)/(x^2+1)^(1/2),x)","\frac{i \sqrt{\frac{a}{x}}\, \sqrt{-i \left(x +i\right)}\, \sqrt{2}\, \sqrt{-i \left(-x +i\right)}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(x +i\right)}, \frac{\sqrt{2}}{2}\right)}{\sqrt{x^{2}+1}}"," ",0,"I*(a/x)^(1/2)/(x^2+1)^(1/2)*(-I*(x+I))^(1/2)*2^(1/2)*(-I*(-x+I))^(1/2)*(I*x)^(1/2)*EllipticF((-I*(x+I))^(1/2),1/2*2^(1/2))","C"
382,1,19,18,0.008000," ","int((a/x^2)^(1/2)/(x^2+1)^(1/2),x)","-\sqrt{\frac{a}{x^{2}}}\, x \arctanh \left(\frac{1}{\sqrt{x^{2}+1}}\right)"," ",0,"-(a/x^2)^(1/2)*x*arctanh(1/(x^2+1)^(1/2))","A"
383,1,116,177,0.043000," ","int((a/x^3)^(1/2)/(x^2+1)^(1/2),x)","\frac{\sqrt{\frac{a}{x^{3}}}\, \left(-2 x^{2}+2 \sqrt{-i \left(x +i\right)}\, \sqrt{2}\, \sqrt{-i \left(-x +i\right)}\, \sqrt{i x}\, \EllipticE \left(\sqrt{-i \left(x +i\right)}, \frac{\sqrt{2}}{2}\right)-\sqrt{-i \left(x +i\right)}\, \sqrt{2}\, \sqrt{-i \left(-x +i\right)}\, \sqrt{i x}\, \EllipticF \left(\sqrt{-i \left(x +i\right)}, \frac{\sqrt{2}}{2}\right)-2\right) x}{\sqrt{x^{2}+1}}"," ",0,"(a/x^3)^(1/2)*x*(2*(-I*(x+I))^(1/2)*2^(1/2)*(-I*(-x+I))^(1/2)*(I*x)^(1/2)*EllipticE((-I*(x+I))^(1/2),1/2*2^(1/2))-(-I*(x+I))^(1/2)*2^(1/2)*(-I*(-x+I))^(1/2)*(I*x)^(1/2)*EllipticF((-I*(x+I))^(1/2),1/2*2^(1/2))-2*x^2-2)/(x^2+1)^(1/2)","C"
384,1,18,17,0.004000," ","int((a/x^4)^(1/2)/(x^2+1)^(1/2),x)","-\sqrt{\frac{a}{x^{4}}}\, \sqrt{x^{2}+1}\, x"," ",0,"-x*(a/x^4)^(1/2)*(x^2+1)^(1/2)","A"
385,1,31,19,0.006000," ","int((a*x^4)^(1/2)/(x^3+1)^(1/2),x)","\frac{2 \left(x +1\right) \left(x^{2}-x +1\right) \sqrt{a \,x^{4}}}{3 \sqrt{x^{3}+1}\, x^{2}}"," ",0,"2/3*(x+1)*(x^2-x+1)/x^2*(a*x^4)^(1/2)/(x^3+1)^(1/2)","A"
386,1,1521,354,0.275000," ","int((a*x^3)^(1/2)/(x^3+1)^(1/2),x)","-\frac{2 \sqrt{a \,x^{3}}\, \sqrt{x^{3}+1}\, \left(-i \sqrt{3}\, x^{3}-3 x^{3}+i \sqrt{3}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x^{2} \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+3 \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x^{2} \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-2 \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x^{2} \EllipticF \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+i \sqrt{3}\, x^{2}+3 x^{2}+2 i \sqrt{3}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+6 \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-4 \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x \EllipticF \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-i \sqrt{3}\, x -3 x +i \sqrt{3}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+3 \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-2 \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \EllipticF \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)\right) a}{\sqrt{\left(x^{3}+1\right) a x}\, \left(3+i \sqrt{3}\right) \sqrt{-\left(x +1\right) \left(2 x +i \sqrt{3}-1\right) \left(-2 x +i \sqrt{3}+1\right) a x}\, x}"," ",0,"-2*(a*x^3)^(1/2)/x*(x^3+1)^(1/2)*a*(I*3^(1/2)*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x^2+2*I*3^(1/2)*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x+I*3^(1/2)*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))-2*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticF(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x^2+3*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x^2-I*3^(1/2)*x^3-4*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticF(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x+6*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x+I*3^(1/2)*x^2-2*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticF(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))+3*((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2)*((I*3^(1/2)+2*x-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((I*3^(1/2)-2*x+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))*x/(1+I*3^(1/2))/(x+1))^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))-I*3^(1/2)*x-3*x^3+3*x^2-3*x)/(x*(x^3+1)*a)^(1/2)/(3+I*3^(1/2))/(-a*x*(x+1)*(I*3^(1/2)+2*x-1)*(I*3^(1/2)-2*x+1))^(1/2)","C"
387,1,270,212,0.065000," ","int((a*x^2)^(1/2)/(x^3+1)^(1/2),x)","\frac{\sqrt{a \,x^{2}}\, \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}{3+i \sqrt{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}}{3+i \sqrt{3}}}\right)+3 \EllipticE \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{3+i \sqrt{3}}}\right)-i \sqrt{3}\, \EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{3+i \sqrt{3}}}\right)-\EllipticF \left(\sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}, \sqrt{-\frac{-3+i \sqrt{3}}{3+i \sqrt{3}}}\right)\right)}{2 \sqrt{x^{3}+1}\, x}"," ",0,"1/2*(a*x^2)^(1/2)*(-3+I*3^(1/2))*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(3+I*3^(1/2)))^(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))/(3+I*3^(1/2)))^(1/2))*3^(1/2)-I*EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(3+I*3^(1/2)))^(1/2))*3^(1/2)+3*EllipticE((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(3+I*3^(1/2)))^(1/2))-EllipticF((-2*(x+1)/(-3+I*3^(1/2)))^(1/2),(-(-3+I*3^(1/2))/(3+I*3^(1/2)))^(1/2)))/x/(x^3+1)^(1/2)","A"
388,1,321,15,0.137000," ","int((a*x)^(1/2)/(x^3+1)^(1/2),x)","-\frac{4 \sqrt{a x}\, \sqrt{x^{3}+1}\, \left(1+i \sqrt{3}\right) \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \left(x +1\right)^{2} \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \left(\EllipticF \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-\EllipticPi \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \frac{1+i \sqrt{3}}{3+i \sqrt{3}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)\right) a}{\sqrt{\left(x^{3}+1\right) a x}\, \left(3+i \sqrt{3}\right) \sqrt{-\left(x +1\right) \left(2 x +i \sqrt{3}-1\right) \left(-2 x +i \sqrt{3}+1\right) a x}}"," ",0,"-4*(a*x)^(1/2)*(x^3+1)^(1/2)*a*(1+I*3^(1/2))*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*(x+1)^2*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*(EllipticF(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))-EllipticPi(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),(1+I*3^(1/2))/(3+I*3^(1/2)),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2)))/((x^3+1)*a*x)^(1/2)/(3+I*3^(1/2))/(-(x+1)*(2*x+I*3^(1/2)-1)*(-2*x+I*3^(1/2)+1)*a*x)^(1/2)","C"
389,1,232,154,0.176000," ","int((a/x)^(1/2)/(x^3+1)^(1/2),x)","\frac{4 \sqrt{\frac{a}{x}}\, \sqrt{x^{3}+1}\, \left(1+i \sqrt{3}\right) \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \left(x +1\right)^{2} \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x \EllipticF \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)}{\sqrt{\left(x^{3}+1\right) x}\, \left(3+i \sqrt{3}\right) \sqrt{-\left(x +1\right) \left(2 x +i \sqrt{3}-1\right) \left(-2 x +i \sqrt{3}+1\right) x}}"," ",0,"4*(a/x)^(1/2)*x*(x^3+1)^(1/2)*(1+I*3^(1/2))*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*(x+1)^2*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticF(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))/((x^3+1)*x)^(1/2)/(3+I*3^(1/2))/(-x*(x+1)*(2*x+I*3^(1/2)-1)*(-2*x+I*3^(1/2)+1))^(1/2)","C"
390,1,19,18,0.008000," ","int((a/x^2)^(1/2)/(x^3+1)^(1/2),x)","-\frac{2 \sqrt{\frac{a}{x^{2}}}\, x \arctanh \left(\sqrt{x^{3}+1}\right)}{3}"," ",0,"-2/3*x*arctanh((x^3+1)^(1/2))*(a/x^2)^(1/2)","A"
391,1,1784,372,0.139000," ","int((a/x^3)^(1/2)/(x^3+1)^(1/2),x)","-\frac{2 \sqrt{\frac{a}{x^{3}}}\, \left(-2 i \sqrt{3}\, \sqrt{\left(x^{3}+1\right) x}\, x^{3}+i \sqrt{3}\, \sqrt{-\left(x +1\right) \left(2 x +i \sqrt{3}-1\right) \left(-2 x +i \sqrt{3}+1\right) x}\, x^{3}-6 \sqrt{\left(x^{3}+1\right) x}\, x^{3}+3 \sqrt{-\left(x +1\right) \left(2 x +i \sqrt{3}-1\right) \left(-2 x +i \sqrt{3}+1\right) x}\, x^{3}+6 \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x^{2} \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+2 i \sqrt{3}\, \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x^{2} \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-4 \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x^{2} \EllipticF \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+2 i \sqrt{3}\, \sqrt{\left(x^{3}+1\right) x}\, x^{2}+6 \sqrt{\left(x^{3}+1\right) x}\, x^{2}+4 i \sqrt{3}\, \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+12 \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-8 \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, x \EllipticF \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-2 i \sqrt{3}\, \sqrt{\left(x^{3}+1\right) x}\, x -6 \sqrt{\left(x^{3}+1\right) x}\, x +2 i \sqrt{3}\, \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+6 \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \EllipticE \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)-4 \sqrt{\left(x^{3}+1\right) x}\, \sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \sqrt{\frac{2 x +i \sqrt{3}-1}{\left(i \sqrt{3}-1\right) \left(x +1\right)}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}\, \EllipticF \left(\sqrt{\frac{\left(3+i \sqrt{3}\right) x}{\left(1+i \sqrt{3}\right) \left(x +1\right)}}, \sqrt{\frac{\left(-3+i \sqrt{3}\right) \left(1+i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(3+i \sqrt{3}\right)}}\right)+i \sqrt{3}\, \sqrt{-\left(x +1\right) \left(2 x +i \sqrt{3}-1\right) \left(-2 x +i \sqrt{3}+1\right) x}+3 \sqrt{-\left(x +1\right) \left(2 x +i \sqrt{3}-1\right) \left(-2 x +i \sqrt{3}+1\right) x}\right) x}{\sqrt{x^{3}+1}\, \left(3+i \sqrt{3}\right) \sqrt{-\left(x +1\right) \left(2 x +i \sqrt{3}-1\right) \left(-2 x +i \sqrt{3}+1\right) x}}"," ",0,"-2*(a/x^3)^(1/2)*x/(x^3+1)^(1/2)*(-2*I*3^(1/2)*((x^3+1)*x)^(1/2)*x-2*I*3^(1/2)*((x^3+1)*x)^(1/2)*x^3+I*3^(1/2)*(-(x+1)*(2*x+I*3^(1/2)-1)*(-2*x+I*3^(1/2)+1)*x)^(1/2)-4*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticF(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x^2+6*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x^2+I*3^(1/2)*(-(x+1)*(2*x+I*3^(1/2)-1)*(-2*x+I*3^(1/2)+1)*x)^(1/2)*x^3+4*I*3^(1/2)*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x-8*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticF(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x+12*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x+2*I*3^(1/2)*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))-4*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticF(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))+6*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))+2*I*3^(1/2)*((x^3+1)*x)^(1/2)*((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2)*((2*x+I*3^(1/2)-1)/(I*3^(1/2)-1)/(x+1))^(1/2)*((-2*x+I*3^(1/2)+1)/(1+I*3^(1/2))/(x+1))^(1/2)*EllipticE(((3+I*3^(1/2))/(1+I*3^(1/2))/(x+1)*x)^(1/2),((-3+I*3^(1/2))*(1+I*3^(1/2))/(I*3^(1/2)-1)/(3+I*3^(1/2)))^(1/2))*x^2-6*((x^3+1)*x)^(1/2)*x^3+3*(-(x+1)*(2*x+I*3^(1/2)-1)*(-2*x+I*3^(1/2)+1)*x)^(1/2)*x^3+2*I*3^(1/2)*((x^3+1)*x)^(1/2)*x^2+6*((x^3+1)*x)^(1/2)*x^2-6*((x^3+1)*x)^(1/2)*x+3*(-(x+1)*(2*x+I*3^(1/2)-1)*(-2*x+I*3^(1/2)+1)*x)^(1/2))/(3+I*3^(1/2))/(-(x+1)*(2*x+I*3^(1/2)-1)*(-2*x+I*3^(1/2)+1)*x)^(1/2)","C"
392,1,353,228,0.073000," ","int((a/x^4)^(1/2)/(x^3+1)^(1/2),x)","\frac{\sqrt{\frac{a}{x^{4}}}\, \left(-2 x^{3}-6 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{3+i \sqrt{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}}{3+i \sqrt{3}}}\right)+i \sqrt{3}\, \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{3+i \sqrt{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}}{3+i \sqrt{3}}}\right)+3 \sqrt{-\frac{2 \left(x +1\right)}{-3+i \sqrt{3}}}\, \sqrt{\frac{-2 x +i \sqrt{3}+1}{3+i \sqrt{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}}{3+i \sqrt{3}}}\right)-2\right) x}{2 \sqrt{x^{3}+1}}"," ",0,"1/2*(a/x^4)^(1/2)*x*(I*3^(1/2)*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(3+I*3^(1/2)))^(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))/(3+I*3^(1/2)))^(1/2))*x-6*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(3+I*3^(1/2)))^(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))/(3+I*3^(1/2)))^(1/2))*x+3*(-2*(x+1)/(-3+I*3^(1/2)))^(1/2)*((-2*x+I*3^(1/2)+1)/(3+I*3^(1/2)))^(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))/(3+I*3^(1/2)))^(1/2))*x-2*x^3-2)/(x^3+1)^(1/2)","A"
393,0,0,35,0.097000," ","int((a*x^(2*n))^(1/2)/(1+x^n)^(1/2),x)","\int \frac{\sqrt{a \,x^{2 n}}}{\sqrt{x^{n}+1}}\, dx"," ",0,"int((a*x^(2*n))^(1/2)/(1+x^n)^(1/2),x)","F"
394,1,35,34,0.079000," ","int((a*x^n)^(1/2)/(x^n+1)^(1/2),x)","\frac{2 \sqrt{a \,x^{n}}\, x \hypergeom \left(\left[\frac{1}{2}, \frac{1}{n}+\frac{1}{2}\right], \left[\frac{1}{n}+\frac{3}{2}\right], -x^{n}\right)}{n +2}"," ",0,"2*x*hypergeom([1/2,1/2+1/n],[3/2+1/n],-x^n)*(a*x^n)^(1/2)/(n+2)","A"
395,1,37,36,0.092000," ","int((a*x^(1/2*n))^(1/2)/(x^n+1)^(1/2),x)","\frac{4 \sqrt{a \,x^{\frac{n}{2}}}\, x \hypergeom \left(\left[\frac{1}{2}, \frac{1}{n}+\frac{1}{4}\right], \left[\frac{1}{n}+\frac{5}{4}\right], -x^{n}\right)}{n +4}"," ",0,"4*x*hypergeom([1/2,1/4+1/n],[5/4+1/n],-x^n)*(a*x^(1/2*n))^(1/2)/(4+n)","A"
396,1,30,30,0.046000," ","int((a*x^(2*n))^(1/2)/(x^n+1)^(1/2)+2*(a*x^(2*n))^(1/2)/(n+2)/(x^n)/(x^n+1)^(1/2),x)","\frac{2 \sqrt{x^{n}+1}\, \sqrt{a \,x^{2 n}}\, x \,x^{-n}}{n +2}"," ",0,"2*x*(x^n+1)^(1/2)/(n+2)*(a*(x^n)^2)^(1/2)/(x^n)","A"
397,1,191,97,0.066000," ","int((a*x)^(1/2)/(e*x+d)^(1/2)/(f*x+e)^(1/2),x)","-\frac{2 \left(d f \EllipticE \left(\sqrt{\frac{e x +d}{d}}, \sqrt{\frac{d f}{d f -e^{2}}}\right)-e^{2} \EllipticE \left(\sqrt{\frac{e x +d}{d}}, \sqrt{\frac{d f}{d f -e^{2}}}\right)+e^{2} \EllipticF \left(\sqrt{\frac{e x +d}{d}}, \sqrt{\frac{d f}{d f -e^{2}}}\right)\right) \sqrt{-\frac{e x}{d}}\, \sqrt{-\frac{\left(f x +e \right) e}{d f -e^{2}}}\, \sqrt{\frac{e x +d}{d}}\, \sqrt{f x +e}\, \sqrt{e x +d}\, \sqrt{a x}\, d}{\left(e f \,x^{2}+d f x +e^{2} x +d e \right) e^{2} f x}"," ",0,"-2*(e^2*EllipticF(((e*x+d)/d)^(1/2),(d*f/(d*f-e^2))^(1/2))+EllipticE(((e*x+d)/d)^(1/2),(d*f/(d*f-e^2))^(1/2))*d*f-EllipticE(((e*x+d)/d)^(1/2),(d*f/(d*f-e^2))^(1/2))*e^2)*(-e*x/d)^(1/2)*(-(f*x+e)*e/(d*f-e^2))^(1/2)*((e*x+d)/d)^(1/2)*d*(f*x+e)^(1/2)*(e*x+d)^(1/2)*(a*x)^(1/2)/f/e^2/x/(e*f*x^2+d*f*x+e^2*x+d*e)","A"
398,1,17,16,0.002000," ","int((a*x^m)^r,x)","\frac{x \left(a \,x^{m}\right)^{r}}{m r +1}"," ",0,"x*(a*x^m)^r/(m*r+1)","A"
399,1,27,26,0.002000," ","int((a*x^m)^r*(b*x^n)^s,x)","\frac{x \left(a \,x^{m}\right)^{r} \left(b \,x^{n}\right)^{s}}{m r +n s +1}"," ",0,"x*(a*x^m)^r*(b*x^n)^s/(m*r+n*s+1)","A"
400,1,37,36,0.003000," ","int((a*x^m)^r*(b*x^n)^s*(c*x^p)^t,x)","\frac{x \left(a \,x^{m}\right)^{r} \left(b \,x^{n}\right)^{s} \left(c \,x^{p}\right)^{t}}{m r +n s +p t +1}"," ",0,"x*(a*x^m)^r*(b*x^n)^s*(c*x^p)^t/(m*r+n*s+p*t+1)","A"
401,1,90,123,0.005000," ","int(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x)","\frac{\frac{2 \left(b x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{4 \left(b x +a \right)^{\frac{5}{2}} a}{5}+\frac{2 \left(b x +a \right)^{\frac{7}{2}}}{7}}{\left(a -c \right) b^{3}}-\frac{2 \left(\frac{\left(b x +c \right)^{\frac{3}{2}} c^{2}}{3}-\frac{2 \left(b x +c \right)^{\frac{5}{2}} c}{5}+\frac{\left(b x +c \right)^{\frac{7}{2}}}{7}\right)}{\left(a -c \right) b^{3}}"," ",0,"2/(a-c)/b^3*(1/7*(b*x+a)^(7/2)-2/5*(b*x+a)^(5/2)*a+1/3*a^2*(b*x+a)^(3/2))-2/(a-c)/b^3*(1/7*(b*x+c)^(7/2)-2/5*(b*x+c)^(5/2)*c+1/3*c^2*(b*x+c)^(3/2))","A"
402,1,66,79,0.005000," ","int(x/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x)","\frac{-\frac{2 \left(b x +a \right)^{\frac{3}{2}} a}{3}+\frac{2 \left(b x +a \right)^{\frac{5}{2}}}{5}}{\left(a -c \right) b^{2}}-\frac{2 \left(-\frac{\left(b x +c \right)^{\frac{3}{2}} c}{3}+\frac{\left(b x +c \right)^{\frac{5}{2}}}{5}\right)}{\left(a -c \right) b^{2}}"," ",0,"2/(a-c)/b^2*(1/5*(b*x+a)^(5/2)-1/3*a*(b*x+a)^(3/2))-2/(a-c)/b^2*(1/5*(b*x+c)^(5/2)-1/3*(b*x+c)^(3/2)*c)","A"
403,1,40,39,0.003000," ","int(1/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x)","\frac{2 \left(b x +a \right)^{\frac{3}{2}}}{3 \left(a -c \right) b}-\frac{2 \left(b x +c \right)^{\frac{3}{2}}}{3 \left(a -c \right) b}"," ",0,"2/3*(b*x+a)^(3/2)/b/(a-c)-2/3*(b*x+c)^(3/2)/b/(a-c)","A"
404,1,73,81,0.006000," ","int(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x)","\frac{-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+2 \sqrt{b x +a}}{a -c}-\frac{-2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{b x +c}}{\sqrt{c}}\right)+2 \sqrt{b x +c}}{a -c}"," ",0,"1/(a-c)*(2*(b*x+a)^(1/2)-2*a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))-1/(a-c)*(2*(b*x+c)^(1/2)-2*c^(1/2)*arctanh((b*x+c)^(1/2)/c^(1/2)))","A"
405,1,88,87,0.016000," ","int(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2)),x)","\frac{2 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b x +a}}{2 b x}\right) b}{a -c}-\frac{2 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +c}}{\sqrt{c}}\right)}{2 \sqrt{c}}-\frac{\sqrt{b x +c}}{2 b x}\right) b}{a -c}"," ",0,"2/(a-c)*b*(-1/2*(b*x+a)^(1/2)/b/x-1/2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2))-2/(a-c)*b*(-1/2*(b*x+c)^(1/2)/b/x-1/2/c^(1/2)*arctanh((b*x+c)^(1/2)/c^(1/2)))","A"
406,1,604,194,0.023000," ","int(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x)","\frac{b \,x^{4}}{2 \left(a -c \right)^{2}}+\frac{a \,x^{3}}{3 \left(a -c \right)^{2}}+\frac{c \,x^{3}}{3 \left(a -c \right)^{2}}-\frac{\sqrt{b x +a}\, \sqrt{b x +c}\, \left(96 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, b^{3} x^{3} \mathrm{csgn}\left(b \right)+16 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a \,b^{2} x^{2} \mathrm{csgn}\left(b \right)+16 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, b^{2} c \,x^{2} \mathrm{csgn}\left(b \right)-15 a^{4} \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)+12 a^{3} c \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)-20 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a^{2} b x \,\mathrm{csgn}\left(b \right)+6 a^{2} c^{2} \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)+8 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a b c x \,\mathrm{csgn}\left(b \right)+12 a \,c^{3} \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)-20 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, b \,c^{2} x \,\mathrm{csgn}\left(b \right)-15 c^{4} \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)+30 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a^{3} \mathrm{csgn}\left(b \right)-14 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a^{2} c \,\mathrm{csgn}\left(b \right)-14 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a \,c^{2} \mathrm{csgn}\left(b \right)+30 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, c^{3} \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{192 \left(a -c \right)^{2} \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, b^{3}}"," ",0,"1/3*x^3/(a-c)^2*a+1/3*x^3/(a-c)^2*c+1/2*b*x^4/(a-c)^2-1/192/(a-c)^2*(b*x+a)^(1/2)*(b*x+c)^(1/2)*(96*csgn(b)*x^3*b^3*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)+16*csgn(b)*x^2*a*b^2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)+16*csgn(b)*x^2*b^2*c*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)-20*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*x*a^2*b+8*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*x*a*b*c-20*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*x*b*c^2+30*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*a^3-14*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*a^2*c-14*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*a*c^2+30*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*c^3-15*ln(1/2*(2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)+2*b*x+a+c)*csgn(b))*a^4+12*ln(1/2*(2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)+2*b*x+a+c)*csgn(b))*a^3*c+6*ln(1/2*(2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)+2*b*x+a+c)*csgn(b))*a^2*c^2+12*ln(1/2*(2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)+2*b*x+a+c)*csgn(b))*a*c^3-15*ln(1/2*(2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)+2*b*x+a+c)*csgn(b))*c^4)*csgn(b)/b^3/(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)","C"
407,1,431,137,0.016000," ","int(x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x)","\frac{2 b \,x^{3}}{3 \left(a -c \right)^{2}}+\frac{a \,x^{2}}{2 \left(a -c \right)^{2}}+\frac{c \,x^{2}}{2 \left(a -c \right)^{2}}-\frac{\sqrt{b x +a}\, \sqrt{b x +c}\, \left(16 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, b^{2} x^{2} \mathrm{csgn}\left(b \right)+3 a^{3} \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)-3 a^{2} c \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)+4 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a b x \,\mathrm{csgn}\left(b \right)-3 a \,c^{2} \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)+4 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, b c x \,\mathrm{csgn}\left(b \right)+3 c^{3} \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)-6 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a^{2} \mathrm{csgn}\left(b \right)+4 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, a c \,\mathrm{csgn}\left(b \right)-6 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, c^{2} \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{24 \left(a -c \right)^{2} \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, b^{2}}"," ",0,"1/2*x^2/(a-c)^2*a+1/2*x^2/(a-c)^2*c+2/3*b*x^3/(a-c)^2-1/24/(a-c)^2*(b*x+a)^(1/2)*(b*x+c)^(1/2)*(16*csgn(b)*x^2*b^2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)+4*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*x*a*b+4*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*x*b*c-6*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*a^2+4*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*a*c-6*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b)*c^2+3*ln(1/2*(2*b*x+a+c+2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b))*csgn(b))*a^3-3*ln(1/2*(2*b*x+a+c+2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b))*csgn(b))*a^2*c-3*ln(1/2*(2*b*x+a+c+2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b))*csgn(b))*a*c^2+3*ln(1/2*(2*b*x+a+c+2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b))*csgn(b))*c^3)*csgn(b)/b^2/(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)","C"
408,1,377,51,0.009000," ","int(1/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x)","\frac{\sqrt{\left(b x +a \right) \left(b x +c \right)}\, a^{2} \ln \left(\frac{b^{2} x +\frac{1}{2} a b +\frac{1}{2} b c}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+a c +\left(a b +b c \right) x}\right)}{4 \left(a -c \right)^{2} \sqrt{b x +c}\, \sqrt{b x +a}\, \sqrt{b^{2}}}-\frac{\sqrt{\left(b x +a \right) \left(b x +c \right)}\, a c \ln \left(\frac{b^{2} x +\frac{1}{2} a b +\frac{1}{2} b c}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+a c +\left(a b +b c \right) x}\right)}{2 \left(a -c \right)^{2} \sqrt{b x +c}\, \sqrt{b x +a}\, \sqrt{b^{2}}}+\frac{b \,x^{2}}{\left(a -c \right)^{2}}+\frac{\sqrt{\left(b x +a \right) \left(b x +c \right)}\, c^{2} \ln \left(\frac{b^{2} x +\frac{1}{2} a b +\frac{1}{2} b c}{\sqrt{b^{2}}}+\sqrt{b^{2} x^{2}+a c +\left(a b +b c \right) x}\right)}{4 \left(a -c \right)^{2} \sqrt{b x +c}\, \sqrt{b x +a}\, \sqrt{b^{2}}}+\frac{a x}{\left(a -c \right)^{2}}+\frac{c x}{\left(a -c \right)^{2}}-\frac{\sqrt{b x +c}\, \sqrt{b x +a}\, a}{2 \left(a -c \right)^{2} b}+\frac{\sqrt{b x +c}\, \sqrt{b x +a}\, c}{2 \left(a -c \right)^{2} b}-\frac{\sqrt{b x +a}\, \left(b x +c \right)^{\frac{3}{2}}}{\left(a -c \right)^{2} b}"," ",0,"x/(a-c)^2*a+x/(a-c)^2*c+b*x^2/(a-c)^2-1/(a-c)^2/b*(b*x+a)^(1/2)*(b*x+c)^(3/2)-1/2/(a-c)^2/b*(b*x+c)^(1/2)*(b*x+a)^(1/2)*a+1/2/(a-c)^2/b*(b*x+c)^(1/2)*(b*x+a)^(1/2)*c+1/4/(a-c)^2*((b*x+a)*(b*x+c))^(1/2)/(b*x+c)^(1/2)/(b*x+a)^(1/2)*ln((1/2*a*b+1/2*b*c+x*b^2)/(b^2)^(1/2)+(b^2*x^2+(a*b+b*c)*x+a*c)^(1/2))/(b^2)^(1/2)*a^2-1/2/(a-c)^2*((b*x+a)*(b*x+c))^(1/2)/(b*x+c)^(1/2)/(b*x+a)^(1/2)*ln((1/2*a*b+1/2*b*c+x*b^2)/(b^2)^(1/2)+(b^2*x^2+(a*b+b*c)*x+a*c)^(1/2))/(b^2)^(1/2)*a*c+1/4/(a-c)^2*((b*x+a)*(b*x+c))^(1/2)/(b*x+c)^(1/2)/(b*x+a)^(1/2)*ln((1/2*a*b+1/2*b*c+x*b^2)/(b^2)^(1/2)+(b^2*x^2+(a*b+b*c)*x+a*c)^(1/2))/(b^2)^(1/2)*c^2","B"
409,1,258,113,0.020000," ","int(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x)","\frac{a \ln \left(x \right)}{\left(a -c \right)^{2}}+\frac{2 b x}{\left(a -c \right)^{2}}+\frac{c \ln \left(x \right)}{\left(a -c \right)^{2}}+\frac{\sqrt{b x +a}\, \sqrt{b x +c}\, \left(2 a c \,\mathrm{csgn}\left(b \right) \ln \left(\frac{a b x +b c x +2 a c +2 \sqrt{a c}\, \sqrt{b^{2} x^{2}+a b x +b c x +a c}}{x}\right)-\sqrt{a c}\, a \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)-\sqrt{a c}\, c \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)-2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \sqrt{a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{\left(a -c \right)^{2} \sqrt{a c}\, \sqrt{b^{2} x^{2}+a b x +b c x +a c}}"," ",0,"1/(a-c)^2*a*ln(x)+1/(a-c)^2*c*ln(x)+2*b*x/(a-c)^2+1/(a-c)^2*(b*x+a)^(1/2)*(b*x+c)^(1/2)*(2*csgn(b)*ln((a*b*x+b*c*x+2*(a*c)^(1/2)*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)+2*a*c)/x)*a*c-2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*(a*c)^(1/2)*csgn(b)-(a*c)^(1/2)*ln(1/2*(2*b*x+a+c+2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b))*csgn(b))*a-(a*c)^(1/2)*ln(1/2*(2*b*x+a+c+2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b))*csgn(b))*c)*csgn(b)/(a*c)^(1/2)/(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)","C"
410,1,274,124,0.017000," ","int(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^2,x)","\frac{2 b \ln \left(x \right)}{\left(a -c \right)^{2}}-\frac{a}{\left(a -c \right)^{2} x}-\frac{c}{\left(a -c \right)^{2} x}+\frac{\sqrt{b x +a}\, \sqrt{b x +c}\, \left(a b x \,\mathrm{csgn}\left(b \right) \ln \left(\frac{a b x +b c x +2 a c +2 \sqrt{a c}\, \sqrt{b^{2} x^{2}+a b x +b c x +a c}}{x}\right)+b c x \,\mathrm{csgn}\left(b \right) \ln \left(\frac{a b x +b c x +2 a c +2 \sqrt{a c}\, \sqrt{b^{2} x^{2}+a b x +b c x +a c}}{x}\right)-2 \sqrt{a c}\, b x \ln \left(\frac{\left(2 b x +a +c +2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{2}\right)+2 \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \sqrt{a c}\, \mathrm{csgn}\left(b \right)\right) \mathrm{csgn}\left(b \right)}{\left(a -c \right)^{2} \sqrt{b^{2} x^{2}+a b x +b c x +a c}\, \sqrt{a c}\, x}"," ",0,"-1/x/(a-c)^2*a-1/x/(a-c)^2*c+2*b*ln(x)/(a-c)^2+1/(a-c)^2*(b*x+a)^(1/2)*(b*x+c)^(1/2)*(csgn(b)*ln((a*b*x+b*c*x+2*a*c+2*(a*c)^(1/2)*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2))/x)*x*a*b+csgn(b)*ln((a*b*x+b*c*x+2*a*c+2*(a*c)^(1/2)*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2))/x)*x*b*c-2*ln(1/2*(2*b*x+a+c+2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*csgn(b))*csgn(b))*x*b*(a*c)^(1/2)+2*(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)*(a*c)^(1/2)*csgn(b))*csgn(b)/(b^2*x^2+a*b*x+b*c*x+a*c)^(1/2)/x/(a*c)^(1/2)","C"
411,1,294,319,0.006000," ","int(x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x)","\frac{2 \left(\frac{\left(b x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{2 \left(b x +a \right)^{\frac{5}{2}} a}{5}+\frac{\left(b x +a \right)^{\frac{7}{2}}}{7}\right) a}{\left(a -c \right)^{3} b^{3}}-\frac{6 \left(\frac{\left(b x +c \right)^{\frac{3}{2}} c^{2}}{3}-\frac{2 \left(b x +c \right)^{\frac{5}{2}} c}{5}+\frac{\left(b x +c \right)^{\frac{7}{2}}}{7}\right) a}{\left(a -c \right)^{3} b^{3}}+\frac{6 \left(\frac{\left(b x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{2 \left(b x +a \right)^{\frac{5}{2}} a}{5}+\frac{\left(b x +a \right)^{\frac{7}{2}}}{7}\right) c}{\left(a -c \right)^{3} b^{3}}-\frac{2 \left(\frac{\left(b x +c \right)^{\frac{3}{2}} c^{2}}{3}-\frac{2 \left(b x +c \right)^{\frac{5}{2}} c}{5}+\frac{\left(b x +c \right)^{\frac{7}{2}}}{7}\right) c}{\left(a -c \right)^{3} b^{3}}+\frac{-\frac{8 \left(b x +a \right)^{\frac{3}{2}} a^{3}}{3}+\frac{24 \left(b x +a \right)^{\frac{5}{2}} a^{2}}{5}-\frac{24 \left(b x +a \right)^{\frac{7}{2}} a}{7}+\frac{8 \left(b x +a \right)^{\frac{9}{2}}}{9}}{\left(a -c \right)^{3} b^{3}}-\frac{8 \left(-\frac{\left(b x +c \right)^{\frac{3}{2}} c^{3}}{3}+\frac{3 \left(b x +c \right)^{\frac{5}{2}} c^{2}}{5}-\frac{3 \left(b x +c \right)^{\frac{7}{2}} c}{7}+\frac{\left(b x +c \right)^{\frac{9}{2}}}{9}\right)}{\left(a -c \right)^{3} b^{3}}"," ",0,"2/(a-c)^3*a/b^3*(1/3*(b*x+a)^(3/2)*a^2-2/5*(b*x+a)^(5/2)*a+1/7*(b*x+a)^(7/2))+6/(a-c)^3*c/b^3*(1/3*(b*x+a)^(3/2)*a^2-2/5*(b*x+a)^(5/2)*a+1/7*(b*x+a)^(7/2))-6/(a-c)^3*a/b^3*(1/3*(b*x+c)^(3/2)*c^2-2/5*(b*x+c)^(5/2)*c+1/7*(b*x+c)^(7/2))-2/(a-c)^3*c/b^3*(1/3*(b*x+c)^(3/2)*c^2-2/5*(b*x+c)^(5/2)*c+1/7*(b*x+c)^(7/2))+8/(a-c)^3/b^3*(1/9*(b*x+a)^(9/2)-3/7*a*(b*x+a)^(7/2)+3/5*a^2*(b*x+a)^(5/2)-1/3*a^3*(b*x+a)^(3/2))-8/(a-c)^3/b^3*(1/9*(b*x+c)^(9/2)-3/7*c*(b*x+c)^(7/2)+3/5*c^2*(b*x+c)^(5/2)-1/3*c^3*(b*x+c)^(3/2))","A"
412,1,222,221,0.004000," ","int(x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x)","\frac{2 \left(-\frac{\left(b x +a \right)^{\frac{3}{2}} a}{3}+\frac{\left(b x +a \right)^{\frac{5}{2}}}{5}\right) a}{\left(a -c \right)^{3} b^{2}}-\frac{6 \left(-\frac{\left(b x +c \right)^{\frac{3}{2}} c}{3}+\frac{\left(b x +c \right)^{\frac{5}{2}}}{5}\right) a}{\left(a -c \right)^{3} b^{2}}+\frac{6 \left(-\frac{\left(b x +a \right)^{\frac{3}{2}} a}{3}+\frac{\left(b x +a \right)^{\frac{5}{2}}}{5}\right) c}{\left(a -c \right)^{3} b^{2}}-\frac{2 \left(-\frac{\left(b x +c \right)^{\frac{3}{2}} c}{3}+\frac{\left(b x +c \right)^{\frac{5}{2}}}{5}\right) c}{\left(a -c \right)^{3} b^{2}}+\frac{\frac{8 \left(b x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{16 \left(b x +a \right)^{\frac{5}{2}} a}{5}+\frac{8 \left(b x +a \right)^{\frac{7}{2}}}{7}}{\left(a -c \right)^{3} b^{2}}-\frac{8 \left(\frac{\left(b x +c \right)^{\frac{3}{2}} c^{2}}{3}-\frac{2 \left(b x +c \right)^{\frac{5}{2}} c}{5}+\frac{\left(b x +c \right)^{\frac{7}{2}}}{7}\right)}{\left(a -c \right)^{3} b^{2}}"," ",0,"2/(a-c)^3*a/b^2*(-1/3*(b*x+a)^(3/2)*a+1/5*(b*x+a)^(5/2))+6/(a-c)^3*c/b^2*(-1/3*(b*x+a)^(3/2)*a+1/5*(b*x+a)^(5/2))-6/(a-c)^3*a/b^2*(-1/3*(b*x+c)^(3/2)*c+1/5*(b*x+c)^(5/2))-2/(a-c)^3*c/b^2*(-1/3*(b*x+c)^(3/2)*c+1/5*(b*x+c)^(5/2))+8/(a-c)^3/b^2*(1/3*(b*x+a)^(3/2)*a^2-2/5*(b*x+a)^(5/2)*a+1/7*(b*x+a)^(7/2))-8/(a-c)^3/b^2*(1/3*(b*x+c)^(3/2)*c^2-2/5*(b*x+c)^(5/2)*c+1/7*(b*x+c)^(7/2))","A"
413,1,146,52,0.006000," ","int(1/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x)","\frac{2 \left(b x +a \right)^{\frac{3}{2}} a}{3 \left(a -c \right)^{3} b}-\frac{2 \left(b x +c \right)^{\frac{3}{2}} a}{\left(a -c \right)^{3} b}+\frac{2 \left(b x +a \right)^{\frac{3}{2}} c}{\left(a -c \right)^{3} b}-\frac{2 \left(b x +c \right)^{\frac{3}{2}} c}{3 \left(a -c \right)^{3} b}+\frac{-\frac{8 \left(b x +a \right)^{\frac{3}{2}} a}{3}+\frac{8 \left(b x +a \right)^{\frac{5}{2}}}{5}}{\left(a -c \right)^{3} b}-\frac{8 \left(-\frac{\left(b x +c \right)^{\frac{3}{2}} c}{3}+\frac{\left(b x +c \right)^{\frac{5}{2}}}{5}\right)}{\left(a -c \right)^{3} b}"," ",0,"2/3*a*(b*x+a)^(3/2)/b/(a-c)^3+2/(a-c)^3*c*(b*x+a)^(3/2)/b-2/(a-c)^3*a*(b*x+c)^(3/2)/b-2/3*c*(b*x+c)^(3/2)/b/(a-c)^3+8/(a-c)^3/b*(-1/3*(b*x+a)^(3/2)*a+1/5*(b*x+a)^(5/2))-8/(a-c)^3/b*(-1/3*(b*x+c)^(3/2)*c+1/5*(b*x+c)^(5/2))","B"
414,1,181,133,0.006000," ","int(1/x/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x)","\frac{\left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+2 \sqrt{b x +a}\right) a}{\left(a -c \right)^{3}}-\frac{3 \left(-2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{b x +c}}{\sqrt{c}}\right)+2 \sqrt{b x +c}\right) a}{\left(a -c \right)^{3}}+\frac{3 \left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+2 \sqrt{b x +a}\right) c}{\left(a -c \right)^{3}}-\frac{\left(-2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{b x +c}}{\sqrt{c}}\right)+2 \sqrt{b x +c}\right) c}{\left(a -c \right)^{3}}+\frac{8 \left(b x +a \right)^{\frac{3}{2}}}{3 \left(a -c \right)^{3}}-\frac{8 \left(b x +c \right)^{\frac{3}{2}}}{3 \left(a -c \right)^{3}}"," ",0,"1/(a-c)^3*a*(2*(b*x+a)^(1/2)-2*a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))+8/3*(b*x+a)^(3/2)/(a-c)^3-8/3*(b*x+c)^(3/2)/(a-c)^3+3/(a-c)^3*c*(2*(b*x+a)^(1/2)-2*a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))-3/(a-c)^3*a*(2*(b*x+c)^(1/2)-2*c^(1/2)*arctanh((b*x+c)^(1/2)/c^(1/2)))-1/(a-c)^3*c*(2*(b*x+c)^(1/2)-2*c^(1/2)*arctanh((b*x+c)^(1/2)/c^(1/2)))","A"
415,1,252,142,0.018000," ","int(1/x^2/((b*x+a)^(1/2)+(b*x+c)^(1/2))^3,x)","\frac{2 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b x +a}}{2 b x}\right) a b}{\left(a -c \right)^{3}}-\frac{6 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +c}}{\sqrt{c}}\right)}{2 \sqrt{c}}-\frac{\sqrt{b x +c}}{2 b x}\right) a b}{\left(a -c \right)^{3}}+\frac{6 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b x +a}}{2 b x}\right) b c}{\left(a -c \right)^{3}}-\frac{2 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +c}}{\sqrt{c}}\right)}{2 \sqrt{c}}-\frac{\sqrt{b x +c}}{2 b x}\right) b c}{\left(a -c \right)^{3}}+\frac{4 \left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+2 \sqrt{b x +a}\right) b}{\left(a -c \right)^{3}}-\frac{4 \left(-2 \sqrt{c}\, \arctanh \left(\frac{\sqrt{b x +c}}{\sqrt{c}}\right)+2 \sqrt{b x +c}\right) b}{\left(a -c \right)^{3}}"," ",0,"2/(a-c)^3*a*b*(-1/2*(b*x+a)^(1/2)/b/x-1/2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2))+6/(a-c)^3*c*b*(-1/2*(b*x+a)^(1/2)/b/x-1/2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2))-6/(a-c)^3*a*b*(-1/2*(b*x+c)^(1/2)/b/x-1/2/c^(1/2)*arctanh((b*x+c)^(1/2)/c^(1/2)))-2/(a-c)^3*c*b*(-1/2*(b*x+c)^(1/2)/b/x-1/2/c^(1/2)*arctanh((b*x+c)^(1/2)/c^(1/2)))+4/(a-c)^3*b*(2*(b*x+a)^(1/2)-2*a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))-4/(a-c)^3*b*(2*(b*x+c)^(1/2)-2*c^(1/2)*arctanh((b*x+c)^(1/2)/c^(1/2)))","A"
416,1,14,13,0.003000," ","int(1/(x^(1/2)+(x+1)^(1/2)),x)","-\frac{2 x^{\frac{3}{2}}}{3}+\frac{2 \left(x +1\right)^{\frac{3}{2}}}{3}"," ",0,"-2/3*x^(3/2)+2/3*(x+1)^(3/2)","A"
417,1,14,13,0.003000," ","int(1/((x-1)^(1/2)+x^(1/2)),x)","\frac{2 x^{\frac{3}{2}}}{3}-\frac{2 \left(x -1\right)^{\frac{3}{2}}}{3}"," ",0,"-2/3*(x-1)^(3/2)+2/3*x^(3/2)","A"
418,1,16,15,0.003000," ","int(1/((x-1)^(1/2)+(x+1)^(1/2)),x)","-\frac{\left(x -1\right)^{\frac{3}{2}}}{3}+\frac{\left(x +1\right)^{\frac{3}{2}}}{3}"," ",0,"-1/3*(x-1)^(3/2)+1/3*(x+1)^(3/2)","A"
419,1,33,28,0.006000," ","int(x^3*((1-x)^(1/2)+(x+1)^(1/2))^2,x)","\frac{x^{4}}{2}+\frac{2 \sqrt{x +1}\, \sqrt{-x +1}\, \left(x^{2}-1\right) \left(3 x^{2}+2\right)}{15}"," ",0,"1/2*x^4+2/15*(x+1)^(1/2)*(1-x)^(1/2)*(x^2-1)*(3*x^2+2)","A"
420,1,59,36,0.008000," ","int(x^2*((-x+1)^(1/2)+(x+1)^(1/2))^2,x)","\frac{2 x^{3}}{3}+\frac{\sqrt{x +1}\, \sqrt{-x +1}\, \left(2 \sqrt{-x^{2}+1}\, x^{3}-\sqrt{-x^{2}+1}\, x +\arcsin \left(x \right)\right)}{4 \sqrt{-x^{2}+1}}"," ",0,"2/3*x^3+1/4*(x+1)^(1/2)*(-x+1)^(1/2)*(2*x^3*(-x^2+1)^(1/2)-x*(-x^2+1)^(1/2)+arcsin(x))/(-x^2+1)^(1/2)","A"
421,1,24,15,0.003000," ","int(x*((-x+1)^(1/2)+(x+1)^(1/2))^2,x)","x^{2}+\frac{2 \sqrt{x +1}\, \sqrt{-x +1}\, \left(x^{2}-1\right)}{3}"," ",0,"x^2+2/3*(x+1)^(1/2)*(-x+1)^(1/2)*(x^2-1)","A"
422,1,58,17,0.006000," ","int(((-x+1)^(1/2)+(x+1)^(1/2))^2,x)","2 x +\frac{\sqrt{\left(x +1\right) \left(-x +1\right)}\, \arcsin \left(x \right)}{\sqrt{-x +1}\, \sqrt{x +1}}-\sqrt{x +1}\, \left(-x +1\right)^{\frac{3}{2}}+\sqrt{-x +1}\, \sqrt{x +1}"," ",0,"2*x-(x+1)^(1/2)*(-x+1)^(3/2)+(-x+1)^(1/2)*(x+1)^(1/2)+((x+1)*(-x+1))^(1/2)/(-x+1)^(1/2)/(x+1)^(1/2)*arcsin(x)","B"
423,1,51,28,0.010000," ","int(((-x+1)^(1/2)+(x+1)^(1/2))^2/x,x)","2 \ln \left(x \right)+\frac{2 \sqrt{x +1}\, \sqrt{-x +1}\, \left(-\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)+\sqrt{-x^{2}+1}\right)}{\sqrt{-x^{2}+1}}"," ",0,"2*ln(x)+2*(x+1)^(1/2)*(-x+1)^(1/2)/(-x^2+1)^(1/2)*((-x^2+1)^(1/2)-arctanh(1/(-x^2+1)^(1/2)))","A"
424,1,50,24,0.015000," ","int(((-x+1)^(1/2)+(x+1)^(1/2))^2/x^2,x)","-\frac{2}{x}+\frac{2 \left(-x \arcsin \left(x \right)-\sqrt{-x^{2}+1}\right) \sqrt{x +1}\, \sqrt{-x +1}}{\sqrt{-x^{2}+1}\, x}"," ",0,"-2/x+2*(-arcsin(x)*x-(-x^2+1)^(1/2))*(x+1)^(1/2)*(-x+1)^(1/2)/x/(-x^2+1)^(1/2)","B"
425,1,58,30,0.017000," ","int(((-x+1)^(1/2)+(x+1)^(1/2))^2/x^3,x)","-\frac{1}{x^{2}}+\frac{\sqrt{x +1}\, \sqrt{-x +1}\, \left(x^{2} \arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)-\sqrt{-x^{2}+1}\right)}{\sqrt{-x^{2}+1}\, x^{2}}"," ",0,"-1/x^2+(x+1)^(1/2)*(-x+1)^(1/2)*(arctanh(1/(-x^2+1)^(1/2))*x^2-(-x^2+1)^(1/2))/x^2/(-x^2+1)^(1/2)","A"
426,1,90,123,0.004000," ","int(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x)","\frac{\frac{2 \left(b x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{4 \left(b x +a \right)^{\frac{5}{2}} a}{5}+\frac{2 \left(b x +a \right)^{\frac{7}{2}}}{7}}{\left(b -c \right) b^{3}}-\frac{2 \left(\frac{\left(c x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{2 \left(c x +a \right)^{\frac{5}{2}} a}{5}+\frac{\left(c x +a \right)^{\frac{7}{2}}}{7}\right)}{\left(b -c \right) c^{3}}"," ",0,"2/(b-c)/b^3*(1/3*(b*x+a)^(3/2)*a^2-2/5*(b*x+a)^(5/2)*a+1/7*(b*x+a)^(7/2))-2/(b-c)/c^3*(1/7*(c*x+a)^(7/2)-2/5*(c*x+a)^(5/2)*a+1/3*a^2*(c*x+a)^(3/2))","A"
427,1,66,79,0.005000," ","int(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x)","\frac{-\frac{2 \left(b x +a \right)^{\frac{3}{2}} a}{3}+\frac{2 \left(b x +a \right)^{\frac{5}{2}}}{5}}{\left(b -c \right) b^{2}}-\frac{2 \left(-\frac{\left(c x +a \right)^{\frac{3}{2}} a}{3}+\frac{\left(c x +a \right)^{\frac{5}{2}}}{5}\right)}{\left(b -c \right) c^{2}}"," ",0,"2/(b-c)/b^2*(-1/3*(b*x+a)^(3/2)*a+1/5*(b*x+a)^(5/2))-2/(b-c)/c^2*(1/5*(c*x+a)^(5/2)-1/3*a*(c*x+a)^(3/2))","A"
428,1,40,39,0.004000," ","int(x/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x)","\frac{2 \left(b x +a \right)^{\frac{3}{2}}}{3 \left(b -c \right) b}-\frac{2 \left(c x +a \right)^{\frac{3}{2}}}{3 \left(b -c \right) c}"," ",0,"2/3*(b*x+a)^(3/2)/b/(b-c)-2/3*(c*x+a)^(3/2)/(b-c)/c","A"
429,1,73,81,0.006000," ","int(1/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x)","\frac{-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+2 \sqrt{b x +a}}{b -c}-\frac{-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)+2 \sqrt{c x +a}}{b -c}"," ",0,"1/(b-c)*(2*(b*x+a)^(1/2)-2*a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))-1/(b-c)*(2*(c*x+a)^(1/2)-2*a^(1/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))","A"
430,1,88,87,0.010000," ","int(1/x/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x)","\frac{2 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b x +a}}{2 b x}\right) b}{b -c}-\frac{2 \left(-\frac{\arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{c x +a}}{2 c x}\right) c}{b -c}"," ",0,"2/(b-c)*b*(-1/2*(b*x+a)^(1/2)/b/x-1/2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2))-2/(b-c)*c*(-1/2*(c*x+a)^(1/2)/x/c-1/2/a^(1/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))","A"
431,1,120,139,0.013000," ","int(1/x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2)),x)","\frac{2 \left(\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{8 a^{\frac{3}{2}}}+\frac{-\frac{\left(b x +a \right)^{\frac{3}{2}}}{8 a}-\frac{\sqrt{b x +a}}{8}}{b^{2} x^{2}}\right) b^{2}}{b -c}-\frac{2 \left(\frac{\arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)}{8 a^{\frac{3}{2}}}+\frac{-\frac{\left(c x +a \right)^{\frac{3}{2}}}{8 a}-\frac{\sqrt{c x +a}}{8}}{c^{2} x^{2}}\right) c^{2}}{b -c}"," ",0,"2/(b-c)*b^2*((-1/8/a*(b*x+a)^(3/2)-1/8*(b*x+a)^(1/2))/b^2/x^2+1/8/a^(3/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))-2/(b-c)*c^2*((-1/8/a*(c*x+a)^(3/2)-1/8*(c*x+a)^(1/2))/x^2/c^2+1/8/a^(3/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))","A"
432,1,517,161,0.021000," ","int(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x)","\frac{b \,x^{3}}{3 \left(b -c \right)^{2}}+\frac{c \,x^{3}}{3 \left(b -c \right)^{2}}+\frac{a \,x^{2}}{\left(b -c \right)^{2}}-\frac{\sqrt{b x +a}\, \sqrt{c x +a}\, \left(3 a^{3} b^{3} \ln \left(\frac{2 b c x +a b +a c +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}}{2 \sqrt{b c}}\right)-3 a^{3} b^{2} c \ln \left(\frac{2 b c x +a b +a c +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}}{2 \sqrt{b c}}\right)-3 a^{3} b \,c^{2} \ln \left(\frac{2 b c x +a b +a c +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}}{2 \sqrt{b c}}\right)+3 a^{3} c^{3} \ln \left(\frac{2 b c x +a b +a c +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}}{2 \sqrt{b c}}\right)+16 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, b^{2} c^{2} x^{2}+4 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, a \,b^{2} c x +4 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, a b \,c^{2} x -6 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, a^{2} b^{2}+4 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, a^{2} b c -6 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, a^{2} c^{2}\right)}{24 \left(b -c \right)^{2} \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, b^{2} c^{2}}"," ",0,"1/3*x^3/(b-c)^2*b+1/3*x^3/(b-c)^2*c+a*x^2/(b-c)^2-1/24/(b-c)^2*(b*x+a)^(1/2)*(c*x+a)^(1/2)*(16*x^2*b^2*c^2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)+3*ln(1/2*(2*b*c*x+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)+a*b+a*c)/(b*c)^(1/2))*a^3*b^3-3*ln(1/2*(2*b*c*x+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)+a*b+a*c)/(b*c)^(1/2))*a^3*b^2*c-3*ln(1/2*(2*b*c*x+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)+a*b+a*c)/(b*c)^(1/2))*a^3*b*c^2+3*ln(1/2*(2*b*c*x+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)+a*b+a*c)/(b*c)^(1/2))*a^3*c^3+4*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)*x*a*b^2*c+4*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)*x*a*b*c^2-6*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)*a^2*b^2+4*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)*a^2*b*c-6*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)*a^2*c^2)/(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)/b^2/c^2/(b*c)^(1/2)","B"
433,1,385,116,0.008000," ","int(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x)","\frac{\sqrt{\left(b x +a \right) \left(c x +a \right)}\, a^{2} b \ln \left(\frac{b c x +\frac{1}{2} a b +\frac{1}{2} a c}{\sqrt{b c}}+\sqrt{b c \,x^{2}+a^{2}+\left(a b +a c \right) x}\right)}{4 \left(b -c \right)^{2} \sqrt{c x +a}\, \sqrt{b x +a}\, \sqrt{b c}\, c}+\frac{\sqrt{\left(b x +a \right) \left(c x +a \right)}\, a^{2} c \ln \left(\frac{b c x +\frac{1}{2} a b +\frac{1}{2} a c}{\sqrt{b c}}+\sqrt{b c \,x^{2}+a^{2}+\left(a b +a c \right) x}\right)}{4 \left(b -c \right)^{2} \sqrt{c x +a}\, \sqrt{b x +a}\, \sqrt{b c}\, b}-\frac{\sqrt{\left(b x +a \right) \left(c x +a \right)}\, a^{2} \ln \left(\frac{b c x +\frac{1}{2} a b +\frac{1}{2} a c}{\sqrt{b c}}+\sqrt{b c \,x^{2}+a^{2}+\left(a b +a c \right) x}\right)}{2 \left(b -c \right)^{2} \sqrt{c x +a}\, \sqrt{b x +a}\, \sqrt{b c}}+\frac{b \,x^{2}}{2 \left(b -c \right)^{2}}+\frac{c \,x^{2}}{2 \left(b -c \right)^{2}}+\frac{2 a x}{\left(b -c \right)^{2}}-\frac{\sqrt{c x +a}\, \sqrt{b x +a}\, a}{2 \left(b -c \right)^{2} b}+\frac{\sqrt{c x +a}\, \sqrt{b x +a}\, a}{2 \left(b -c \right)^{2} c}-\frac{\sqrt{b x +a}\, \left(c x +a \right)^{\frac{3}{2}}}{\left(b -c \right)^{2} c}"," ",0,"1/2*x^2/(b-c)^2*b+1/2*x^2/(b-c)^2*c+2*a*x/(b-c)^2-1/(b-c)^2/c*(b*x+a)^(1/2)*(c*x+a)^(3/2)+1/2/(b-c)^2/c*(c*x+a)^(1/2)*(b*x+a)^(1/2)*a-1/2/(b-c)^2/b*(c*x+a)^(1/2)*(b*x+a)^(1/2)*a+1/4/(b-c)^2/c*((b*x+a)*(c*x+a))^(1/2)/(c*x+a)^(1/2)/(b*x+a)^(1/2)*ln((1/2*a*b+1/2*a*c+b*c*x)/(b*c)^(1/2)+(b*c*x^2+(a*b+a*c)*x+a^2)^(1/2))/(b*c)^(1/2)*a^2*b-1/2/(b-c)^2*((b*x+a)*(c*x+a))^(1/2)/(c*x+a)^(1/2)/(b*x+a)^(1/2)*ln((1/2*a*b+1/2*a*c+b*c*x)/(b*c)^(1/2)+(b*c*x^2+(a*b+a*c)*x+a^2)^(1/2))/(b*c)^(1/2)*a^2+1/4/(b-c)^2*c/b*((b*x+a)*(c*x+a))^(1/2)/(c*x+a)^(1/2)/(b*x+a)^(1/2)*ln((1/2*a*b+1/2*a*c+b*c*x)/(b*c)^(1/2)+(b*c*x^2+(a*b+a*c)*x+a^2)^(1/2))/(b*c)^(1/2)*a^2","B"
434,1,266,115,0.021000," ","int(x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x)","\frac{2 a \ln \left(x \right)}{\left(b -c \right)^{2}}+\frac{b x}{\left(b -c \right)^{2}}+\frac{c x}{\left(b -c \right)^{2}}-\frac{\sqrt{b x +a}\, \sqrt{c x +a}\, \left(a b \,\mathrm{csgn}\left(a \right) \ln \left(\frac{2 b c x +a b +a c +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}}{2 \sqrt{b c}}\right)+a c \,\mathrm{csgn}\left(a \right) \ln \left(\frac{2 b c x +a b +a c +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}}{2 \sqrt{b c}}\right)-2 \sqrt{b c}\, a \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)+2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, \mathrm{csgn}\left(a \right)\right) \mathrm{csgn}\left(a \right)}{\left(b -c \right)^{2} \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}}"," ",0,"x/(b-c)^2*b+x/(b-c)^2*c+2*a*ln(x)/(b-c)^2-1/(b-c)^2*(b*x+a)^(1/2)*(c*x+a)^(1/2)*(csgn(a)*ln(1/2*(2*b*c*x+a*b+a*c+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2))/(b*c)^(1/2))*a*b+csgn(a)*ln(1/2*(2*b*c*x+a*b+a*c+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2))/(b*c)^(1/2))*a*c+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)*(b*c)^(1/2)-2*ln(a*(2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)+b*x+c*x+2*a)/x)*(b*c)^(1/2)*a)*csgn(a)/(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)/(b*c)^(1/2)","C"
435,1,272,118,0.017000," ","int(1/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x)","\frac{b \ln \left(x \right)}{\left(b -c \right)^{2}}+\frac{c \ln \left(x \right)}{\left(b -c \right)^{2}}-\frac{2 a}{\left(b -c \right)^{2} x}-\frac{\sqrt{b x +a}\, \sqrt{c x +a}\, \left(2 b c x \,\mathrm{csgn}\left(a \right) \ln \left(\frac{2 b c x +a b +a c +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}}{2 \sqrt{b c}}\right)-\sqrt{b c}\, b x \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)-\sqrt{b c}\, c x \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)-2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, \mathrm{csgn}\left(a \right)\right) \mathrm{csgn}\left(a \right)}{\left(b -c \right)^{2} \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \sqrt{b c}\, x}"," ",0,"1/(b-c)^2*b*ln(x)+1/(b-c)^2*c*ln(x)-2*a/(b-c)^2/x-1/(b-c)^2*(b*x+a)^(1/2)*(c*x+a)^(1/2)*(2*csgn(a)*ln(1/2*(2*b*c*x+a*b+a*c+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2))/(b*c)^(1/2))*x*b*c-ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x*b*(b*c)^(1/2)-ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x*c*(b*c)^(1/2)-2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*(b*c)^(1/2)*csgn(a))*csgn(a)/(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)/x/(b*c)^(1/2)","C"
436,1,313,110,0.014000," ","int(1/x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x)","-\frac{b}{\left(b -c \right)^{2} x}-\frac{c}{\left(b -c \right)^{2} x}-\frac{a}{\left(b -c \right)^{2} x^{2}}+\frac{\sqrt{b x +a}\, \sqrt{c x +a}\, \left(-b^{2} x^{2} \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)+2 b c \,x^{2} \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)-c^{2} x^{2} \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)+2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, b x \,\mathrm{csgn}\left(a \right)+2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, c x \,\mathrm{csgn}\left(a \right)+4 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, a \,\mathrm{csgn}\left(a \right)\right) \mathrm{csgn}\left(a \right)}{4 \left(b -c \right)^{2} \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, a \,x^{2}}"," ",0,"-1/x/(b-c)^2*b-1/x/(b-c)^2*c-a/(b-c)^2/x^2+1/4/(b-c)^2*(b*x+a)^(1/2)*(c*x+a)^(1/2)/a*(-ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x^2*b^2+2*ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x^2*b*c-ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x^2*c^2+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)*x*b+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)*x*c+4*csgn(a)*a*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2))*csgn(a)/(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)/x^2","C"
437,1,457,150,0.018000," ","int(1/x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^2,x)","-\frac{b}{2 \left(b -c \right)^{2} x^{2}}-\frac{c}{2 \left(b -c \right)^{2} x^{2}}-\frac{2 a}{3 \left(b -c \right)^{2} x^{3}}-\frac{\sqrt{b x +a}\, \sqrt{c x +a}\, \left(-3 b^{3} x^{3} \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)+3 b^{2} c \,x^{3} \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)+3 b \,c^{2} x^{3} \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)-3 c^{3} x^{3} \ln \left(\frac{\left(b x +c x +2 a +2 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, \mathrm{csgn}\left(a \right)\right) a}{x}\right)+6 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, b^{2} x^{2} \mathrm{csgn}\left(a \right)-4 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, b c \,x^{2} \mathrm{csgn}\left(a \right)+6 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, c^{2} x^{2} \mathrm{csgn}\left(a \right)-4 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, a b x \,\mathrm{csgn}\left(a \right)-4 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, a c x \,\mathrm{csgn}\left(a \right)-16 \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, a^{2} \mathrm{csgn}\left(a \right)\right) \mathrm{csgn}\left(a \right)}{24 \left(b -c \right)^{2} \sqrt{b c \,x^{2}+a b x +a c x +a^{2}}\, a^{2} x^{3}}"," ",0,"-1/2/x^2/(b-c)^2*b-1/2/x^2/(b-c)^2*c-2/3*a/(b-c)^2/x^3-1/24/(b-c)^2*(b*x+a)^(1/2)*(c*x+a)^(1/2)/a^2*(-3*ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x^3*b^3+3*ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x^3*b^2*c+3*ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x^3*b*c^2-3*ln((b*x+c*x+2*a+2*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a))*a/x)*x^3*c^3+6*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)*x^2*b^2-4*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)*x^2*b*c+6*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)*x^2*c^2-4*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)*a*x*b-4*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*csgn(a)*a*x*c-16*(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)*a^2*csgn(a))*csgn(a)/(b*c*x^2+a*b*x+a*c*x+a^2)^(1/2)/x^3","C"
438,1,246,237,0.006000," ","int(x^4/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x)","\frac{8 \left(-\frac{\left(b x +a \right)^{\frac{3}{2}} a}{3}+\frac{\left(b x +a \right)^{\frac{5}{2}}}{5}\right) a}{\left(b -c \right)^{3} b^{2}}-\frac{8 \left(-\frac{\left(c x +a \right)^{\frac{3}{2}} a}{3}+\frac{\left(c x +a \right)^{\frac{5}{2}}}{5}\right) a}{\left(b -c \right)^{3} c^{2}}-\frac{6 \left(\frac{\left(c x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{2 \left(c x +a \right)^{\frac{5}{2}} a}{5}+\frac{\left(c x +a \right)^{\frac{7}{2}}}{7}\right) b}{\left(b -c \right)^{3} c^{3}}+\frac{\frac{2 \left(b x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{4 \left(b x +a \right)^{\frac{5}{2}} a}{5}+\frac{2 \left(b x +a \right)^{\frac{7}{2}}}{7}}{\left(b -c \right)^{3} b^{2}}+\frac{6 \left(\frac{\left(b x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{2 \left(b x +a \right)^{\frac{5}{2}} a}{5}+\frac{\left(b x +a \right)^{\frac{7}{2}}}{7}\right) c}{\left(b -c \right)^{3} b^{3}}-\frac{2 \left(\frac{\left(c x +a \right)^{\frac{3}{2}} a^{2}}{3}-\frac{2 \left(c x +a \right)^{\frac{5}{2}} a}{5}+\frac{\left(c x +a \right)^{\frac{7}{2}}}{7}\right)}{\left(b -c \right)^{3} c^{2}}"," ",0,"2/(b-c)^3/b^2*(1/3*(b*x+a)^(3/2)*a^2-2/5*(b*x+a)^(5/2)*a+1/7*(b*x+a)^(7/2))+8/(b-c)^3*a/b^2*(-1/3*(b*x+a)^(3/2)*a+1/5*(b*x+a)^(5/2))-8/(b-c)^3*a/c^2*(-1/3*(c*x+a)^(3/2)*a+1/5*(c*x+a)^(5/2))+6/(b-c)^3*c/b^3*(1/3*(b*x+a)^(3/2)*a^2-2/5*(b*x+a)^(5/2)*a+1/7*(b*x+a)^(7/2))-6/(b-c)^3*b/c^3*(1/7*(c*x+a)^(7/2)-2/5*(c*x+a)^(5/2)*a+1/3*(c*x+a)^(3/2)*a^2)-2/(b-c)^3/c^2*(1/7*(c*x+a)^(7/2)-2/5*(c*x+a)^(5/2)*a+1/3*(c*x+a)^(3/2)*a^2)","A"
439,1,172,139,0.004000," ","int(x^3/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x)","\frac{8 \left(b x +a \right)^{\frac{3}{2}} a}{3 \left(b -c \right)^{3} b}-\frac{8 \left(c x +a \right)^{\frac{3}{2}} a}{3 \left(b -c \right)^{3} c}-\frac{6 \left(-\frac{\left(c x +a \right)^{\frac{3}{2}} a}{3}+\frac{\left(c x +a \right)^{\frac{5}{2}}}{5}\right) b}{\left(b -c \right)^{3} c^{2}}+\frac{-\frac{2 \left(b x +a \right)^{\frac{3}{2}} a}{3}+\frac{2 \left(b x +a \right)^{\frac{5}{2}}}{5}}{\left(b -c \right)^{3} b}+\frac{6 \left(-\frac{\left(b x +a \right)^{\frac{3}{2}} a}{3}+\frac{\left(b x +a \right)^{\frac{5}{2}}}{5}\right) c}{\left(b -c \right)^{3} b^{2}}-\frac{2 \left(-\frac{\left(c x +a \right)^{\frac{3}{2}} a}{3}+\frac{\left(c x +a \right)^{\frac{5}{2}}}{5}\right)}{\left(b -c \right)^{3} c}"," ",0,"2/(b-c)^3/b*(-1/3*(b*x+a)^(3/2)*a+1/5*(b*x+a)^(5/2))+8/3*a*(b*x+a)^(3/2)/b/(b-c)^3-8/3*a*(c*x+a)^(3/2)/(b-c)^3/c+6/(b-c)^3*c/b^2*(-1/3*(b*x+a)^(3/2)*a+1/5*(b*x+a)^(5/2))-6/(b-c)^3*b/c^2*(-1/3*(c*x+a)^(3/2)*a+1/5*(c*x+a)^(5/2))-2/(b-c)^3/c*(-1/3*(c*x+a)^(3/2)*a+1/5*(c*x+a)^(5/2))","A"
440,1,148,131,0.005000," ","int(x^2/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x)","\frac{4 \left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+2 \sqrt{b x +a}\right) a}{\left(b -c \right)^{3}}-\frac{4 \left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)+2 \sqrt{c x +a}\right) a}{\left(b -c \right)^{3}}-\frac{2 \left(c x +a \right)^{\frac{3}{2}} b}{\left(b -c \right)^{3} c}+\frac{2 \left(b x +a \right)^{\frac{3}{2}} c}{\left(b -c \right)^{3} b}+\frac{2 \left(b x +a \right)^{\frac{3}{2}}}{3 \left(b -c \right)^{3}}-\frac{2 \left(c x +a \right)^{\frac{3}{2}}}{3 \left(b -c \right)^{3}}"," ",0,"2/3/(b-c)^3*(b*x+a)^(3/2)+2/(b-c)^3*c*(b*x+a)^(3/2)/b-2/(b-c)^3*b*(c*x+a)^(3/2)/c-2/3/(b-c)^3*(c*x+a)^(3/2)+4/(b-c)^3*a*(2*(b*x+a)^(1/2)-2*a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))-4/(b-c)^3*a*(2*(c*x+a)^(1/2)-2*a^(1/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))","A"
441,1,237,137,0.014000," ","int(x/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x)","\frac{8 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b x +a}}{2 b x}\right) a b}{\left(b -c \right)^{3}}-\frac{8 \left(-\frac{\arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{c x +a}}{2 c x}\right) a c}{\left(b -c \right)^{3}}+\frac{\left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+2 \sqrt{b x +a}\right) b}{\left(b -c \right)^{3}}-\frac{3 \left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)+2 \sqrt{c x +a}\right) b}{\left(b -c \right)^{3}}+\frac{3 \left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)+2 \sqrt{b x +a}\right) c}{\left(b -c \right)^{3}}-\frac{\left(-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)+2 \sqrt{c x +a}\right) c}{\left(b -c \right)^{3}}"," ",0,"1/(b-c)^3*b*(2*(b*x+a)^(1/2)-2*a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))+8/(b-c)^3*a*b*(-1/2*(b*x+a)^(1/2)/b/x-1/2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2))-8/(b-c)^3*a*c*(-1/2*(c*x+a)^(1/2)/c/x-1/2/a^(1/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))+3/(b-c)^3*c*(2*(b*x+a)^(1/2)-2*a^(1/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))-3/(b-c)^3*b*(2*(c*x+a)^(1/2)-2*a^(1/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))-1/(b-c)^3*c*(2*(c*x+a)^(1/2)-2*a^(1/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))","A"
442,1,300,144,0.018000," ","int(1/((b*x+a)^(1/2)+(c*x+a)^(1/2))^3,x)","\frac{8 \left(\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{8 a^{\frac{3}{2}}}+\frac{-\frac{\left(b x +a \right)^{\frac{3}{2}}}{8 a}-\frac{\sqrt{b x +a}}{8}}{b^{2} x^{2}}\right) a \,b^{2}}{\left(b -c \right)^{3}}-\frac{8 \left(\frac{\arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)}{8 a^{\frac{3}{2}}}+\frac{-\frac{\left(c x +a \right)^{\frac{3}{2}}}{8 a}-\frac{\sqrt{c x +a}}{8}}{c^{2} x^{2}}\right) a \,c^{2}}{\left(b -c \right)^{3}}+\frac{2 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b x +a}}{2 b x}\right) b^{2}}{\left(b -c \right)^{3}}+\frac{6 \left(-\frac{\arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b x +a}}{2 b x}\right) b c}{\left(b -c \right)^{3}}-\frac{6 \left(-\frac{\arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{c x +a}}{2 c x}\right) b c}{\left(b -c \right)^{3}}-\frac{2 \left(-\frac{\arctanh \left(\frac{\sqrt{c x +a}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{\sqrt{c x +a}}{2 c x}\right) c^{2}}{\left(b -c \right)^{3}}"," ",0,"2/(b-c)^3*b^2*(-1/2*(b*x+a)^(1/2)/b/x-1/2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2))+8/(b-c)^3*a*b^2*((-1/8*(b*x+a)^(3/2)/a-1/8*(b*x+a)^(1/2))/b^2/x^2+1/8/a^(3/2)*arctanh((b*x+a)^(1/2)/a^(1/2)))-8/(b-c)^3*a*c^2*((-1/8*(c*x+a)^(3/2)/a-1/8*(c*x+a)^(1/2))/x^2/c^2+1/8/a^(3/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))+6/(b-c)^3*c*b*(-1/2*(b*x+a)^(1/2)/b/x-1/2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2))-6/(b-c)^3*b*c*(-1/2*(c*x+a)^(1/2)/c/x-1/2/a^(1/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))-2/(b-c)^3*c^2*(-1/2*(c*x+a)^(1/2)/c/x-1/2/a^(1/2)*arctanh((c*x+a)^(1/2)/a^(1/2)))","B"
443,1,63,23,0.005000," ","int((-x+1)^(1/2)*((-x+1)^(1/2)+(x+1)^(1/2)),x)","-\frac{x^{2}}{2}+x +\frac{\sqrt{\left(x +1\right) \left(-x +1\right)}\, \arcsin \left(x \right)}{2 \sqrt{-x +1}\, \sqrt{x +1}}-\frac{\sqrt{x +1}\, \left(-x +1\right)^{\frac{3}{2}}}{2}+\frac{\sqrt{-x +1}\, \sqrt{x +1}}{2}"," ",0,"x-1/2*x^2-1/2*(x+1)^(1/2)*(-x+1)^(3/2)+1/2*(-x+1)^(1/2)*(x+1)^(1/2)+1/2*((x+1)*(-x+1))^(1/2)/(-x+1)^(1/2)/(x+1)^(1/2)*arcsin(x)","B"
444,1,33,28,0.006000," ","int(x^3*(-(-x+1)^(1/2)-(x+1)^(1/2))*((-x+1)^(1/2)+(x+1)^(1/2)),x)","-\frac{x^{4}}{2}-\frac{2 \sqrt{x +1}\, \sqrt{-x +1}\, \left(x^{2}-1\right) \left(3 x^{2}+2\right)}{15}"," ",0,"-1/2*x^4-2/15*(x+1)^(1/2)*(-x+1)^(1/2)*(x^2-1)*(3*x^2+2)","A"
445,1,59,36,0.004000," ","int(x^2*(-(-x+1)^(1/2)-(x+1)^(1/2))*((-x+1)^(1/2)+(x+1)^(1/2)),x)","-\frac{2 x^{3}}{3}-\frac{\sqrt{x +1}\, \sqrt{-x +1}\, \left(2 \sqrt{-x^{2}+1}\, x^{3}-\sqrt{-x^{2}+1}\, x +\arcsin \left(x \right)\right)}{4 \sqrt{-x^{2}+1}}"," ",0,"-2/3*x^3-1/4*(x+1)^(1/2)*(-x+1)^(1/2)*(2*(-x^2+1)^(1/2)*x^3-(-x^2+1)^(1/2)*x+arcsin(x))/(-x^2+1)^(1/2)","A"
446,1,26,17,0.003000," ","int(x*(-(-x+1)^(1/2)-(x+1)^(1/2))*((-x+1)^(1/2)+(x+1)^(1/2)),x)","-x^{2}-\frac{2 \sqrt{x +1}\, \sqrt{-x +1}\, \left(x^{2}-1\right)}{3}"," ",0,"-x^2-2/3*(x+1)^(1/2)*(-x+1)^(1/2)*(x^2-1)","A"
447,1,59,20,0.005000," ","int((-(-x+1)^(1/2)-(x+1)^(1/2))*((-x+1)^(1/2)+(x+1)^(1/2)),x)","-2 x -\frac{\sqrt{\left(x +1\right) \left(-x +1\right)}\, \arcsin \left(x \right)}{\sqrt{-x +1}\, \sqrt{x +1}}+\sqrt{x +1}\, \left(-x +1\right)^{\frac{3}{2}}-\sqrt{-x +1}\, \sqrt{x +1}"," ",0,"-2*x+(x+1)^(1/2)*(-x+1)^(3/2)-(-x+1)^(1/2)*(x+1)^(1/2)-((x+1)*(-x+1))^(1/2)/(-x+1)^(1/2)/(x+1)^(1/2)*arcsin(x)","B"
448,1,51,28,0.007000," ","int((-(-x+1)^(1/2)-(x+1)^(1/2))*((-x+1)^(1/2)+(x+1)^(1/2))/x,x)","-2 \ln \left(x \right)-\frac{2 \sqrt{x +1}\, \sqrt{-x +1}\, \left(-\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)+\sqrt{-x^{2}+1}\right)}{\sqrt{-x^{2}+1}}"," ",0,"-2*ln(x)-2*(x+1)^(1/2)*(-x+1)^(1/2)/(-x^2+1)^(1/2)*((-x^2+1)^(1/2)-arctanh(1/(-x^2+1)^(1/2)))","A"
449,1,50,24,0.013000," ","int((-(-x+1)^(1/2)-(x+1)^(1/2))*((-x+1)^(1/2)+(x+1)^(1/2))/x^2,x)","\frac{2}{x}-\frac{2 \left(-x \arcsin \left(x \right)-\sqrt{-x^{2}+1}\right) \sqrt{x +1}\, \sqrt{-x +1}}{\sqrt{-x^{2}+1}\, x}"," ",0,"2/x-2*(-arcsin(x)*x-(-x^2+1)^(1/2))*(x+1)^(1/2)*(-x+1)^(1/2)/x/(-x^2+1)^(1/2)","B"
450,1,57,29,0.015000," ","int((-(-x+1)^(1/2)-(x+1)^(1/2))*((-x+1)^(1/2)+(x+1)^(1/2))/x^3,x)","\frac{1}{x^{2}}-\frac{\sqrt{x +1}\, \sqrt{-x +1}\, \left(x^{2} \arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)-\sqrt{-x^{2}+1}\right)}{\sqrt{-x^{2}+1}\, x^{2}}"," ",0,"1/x^2-(x+1)^(1/2)*(-x+1)^(1/2)*(arctanh(1/(-x^2+1)^(1/2))*x^2-(-x^2+1)^(1/2))/x^2/(-x^2+1)^(1/2)","A"
451,1,48,24,0.007000," ","int(((-x+1)^(1/2)+(x+1)^(1/2))/(-(-x+1)^(1/2)+(x+1)^(1/2)),x)","\ln \left(x \right)+\frac{\sqrt{x +1}\, \sqrt{-x +1}\, \left(-\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)+\sqrt{-x^{2}+1}\right)}{\sqrt{-x^{2}+1}}"," ",0,"ln(x)+(x+1)^(1/2)*(-x+1)^(1/2)/(-x^2+1)^(1/2)*((-x^2+1)^(1/2)-arctanh(1/(-x^2+1)^(1/2)))","A"
452,1,62,23,0.007000," ","int((-(x-1)^(1/2)+(x+1)^(1/2))/((x-1)^(1/2)+(x+1)^(1/2)),x)","\frac{x^{2}}{2}+\frac{\sqrt{\left(x -1\right) \left(x +1\right)}\, \ln \left(x +\sqrt{x^{2}-1}\right)}{2 \sqrt{x +1}\, \sqrt{x -1}}-\frac{\sqrt{x -1}\, \left(x +1\right)^{\frac{3}{2}}}{2}+\frac{\sqrt{x -1}\, \sqrt{x +1}}{2}"," ",0,"-1/2*(x-1)^(1/2)*(x+1)^(3/2)+1/2*(x-1)^(1/2)*(x+1)^(1/2)+1/2*((x-1)*(x+1))^(1/2)/(x+1)^(1/2)/(x-1)^(1/2)*ln(x+(x^2-1)^(1/2))+1/2*x^2","B"
453,0,0,113,0.014000," ","int((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^n,x)","\int \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{n}\, dx"," ",0,"int((d+e*x+f*(a+e^2*x^2/f^2)^(1/2))^n,x)","F"
454,1,175,157,0.013000," ","int((e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^3,x)","e^{3} x^{4}+\frac{3 a e \,f^{2} x^{2}}{2}+2 d \,e^{2} x^{3}+\frac{3 a \,d^{2} f \ln \left(\frac{e^{2} x}{\sqrt{\frac{e^{2}}{f^{2}}}\, f^{2}}+\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{2 \sqrt{\frac{e^{2}}{f^{2}}}}+3 a d \,f^{2} x +\frac{3 d^{2} e \,x^{2}}{2}+d^{3} x +\frac{3 \sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, d^{2} f x}{2}+\left(\frac{e^{2} x^{2}}{f^{2}}+a \right)^{\frac{3}{2}} f^{3} x +\frac{d^{4}}{4 e}+\frac{2 \left(\frac{e^{2} x^{2}+a \,f^{2}}{f^{2}}\right)^{\frac{3}{2}} d \,f^{3}}{e}"," ",0,"f^3*x*(e^2/f^2*x^2+a)^(3/2)+e^3*x^4+2*d*e^2*x^3+3/2*f^2*a*e*x^2+3*f^2*a*d*x+2*d/e*f^3*((e^2*x^2+a*f^2)/f^2)^(3/2)+3/2*f*d^2*x*(e^2/f^2*x^2+a)^(1/2)+3/2*f*d^2*a*ln(e^2*x/f^2/(e^2/f^2)^(1/2)+(e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)+3/2*e*x^2*d^2+d^3*x+1/4/e*d^4","A"
455,1,126,122,0.007000," ","int((e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^2,x)","\frac{2 e^{2} x^{3}}{3}+\frac{a d f \ln \left(\frac{e^{2} x}{\sqrt{\frac{e^{2}}{f^{2}}}\, f^{2}}+\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{\sqrt{\frac{e^{2}}{f^{2}}}}+a \,f^{2} x +d e \,x^{2}+d^{2} x +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, d f x +\frac{d^{3}}{3 e}+\frac{2 \left(\frac{e^{2} x^{2}+a \,f^{2}}{f^{2}}\right)^{\frac{3}{2}} f^{3}}{3 e}"," ",0,"f^2*a*x+2/3*e^2*x^3+2/3/e*f^3*((e^2*x^2+a*f^2)/f^2)^(3/2)+f*d*x*(e^2/f^2*x^2+a)^(1/2)+f*d*a*ln(1/(e^2/f^2)^(1/2)*e^2/f^2*x+(e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)+e*x^2*d+x*d^2+1/3/e*d^3","A"
456,1,75,58,0.004000," ","int(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f,x)","\frac{a f \ln \left(\frac{e^{2} x}{\sqrt{\frac{e^{2}}{f^{2}}}\, f^{2}}+\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{2 \sqrt{\frac{e^{2}}{f^{2}}}}+\frac{e \,x^{2}}{2}+d x +\frac{\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, f x}{2}"," ",0,"d*x+1/2*e*x^2+1/2*f*x*(e^2/f^2*x^2+a)^(1/2)+1/2*f*a*ln(1/(e^2/f^2)^(1/2)*e^2/f^2*x+(e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)","A"
457,1,1325,105,0.039000," ","int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f),x)","\frac{a^{2} f^{3} \ln \left(\frac{\frac{\left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{2 d^{2} f^{2}}+\frac{\sqrt{\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}\, \sqrt{\frac{4 \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right)^{2} e^{2}}{f^{2}}+\frac{4 \left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}}{2}}{x +\frac{-a \,f^{2}+d^{2}}{2 d e}}\right)}{4 \sqrt{\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}\, d^{3} e}+\frac{a f \ln \left(\frac{\frac{\left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{2 d^{2} f^{2}}+\frac{\sqrt{\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}\, \sqrt{\frac{4 \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right)^{2} e^{2}}{f^{2}}+\frac{4 \left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}}{2}}{x +\frac{-a \,f^{2}+d^{2}}{2 d e}}\right)}{2 \sqrt{\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}\, d e}+\frac{a \,f^{2} \ln \left(-a \,f^{2}+2 d e x +d^{2}\right)}{4 d^{2} e}-\frac{a f \ln \left(\frac{\frac{\left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e^{2}}{f^{2}}+\frac{\left(a \,f^{2}-d^{2}\right) e}{2 d \,f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{\frac{\left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right)^{2} e^{2}}{f^{2}}+\frac{\left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{4 d^{2} f^{2}}}\right)}{4 \sqrt{\frac{e^{2}}{f^{2}}}\, d^{2}}+\frac{d \ln \left(\frac{\frac{\left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{2 d^{2} f^{2}}+\frac{\sqrt{\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}\, \sqrt{\frac{4 \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right)^{2} e^{2}}{f^{2}}+\frac{4 \left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}}{2}}{x +\frac{-a \,f^{2}+d^{2}}{2 d e}}\right)}{4 \sqrt{\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}\, e f}+\frac{x}{2 d}-\frac{\ln \left(-a \,f^{2}+2 d e x +d^{2}\right)}{4 e}+\frac{\ln \left(a \,f^{2}-2 d e x -d^{2}\right)}{2 e}+\frac{\ln \left(\frac{\frac{\left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e^{2}}{f^{2}}+\frac{\left(a \,f^{2}-d^{2}\right) e}{2 d \,f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{\frac{\left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right)^{2} e^{2}}{f^{2}}+\frac{\left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{4 d^{2} f^{2}}}\right)}{4 \sqrt{\frac{e^{2}}{f^{2}}}\, f}-\frac{\sqrt{\frac{4 \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right)^{2} e^{2}}{f^{2}}+\frac{4 \left(a \,f^{2}-d^{2}\right) \left(x +\frac{-a \,f^{2}+d^{2}}{2 d e}\right) e}{d \,f^{2}}+\frac{a^{2} f^{4}+2 a \,f^{2} d^{2}+d^{4}}{d^{2} f^{2}}}\, f}{4 d e}"," ",0,"-1/4*f/d/e*(4*e^2*(x+1/2*(-a*f^2+d^2)/d/e)^2/f^2+4*e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2)-1/4*f/d^2*ln((1/2*e*(a*f^2-d^2)/f^2/d+e^2/f^2*(x+1/2*(-a*f^2+d^2)/d/e))/(e^2/f^2)^(1/2)+(e^2*(x+1/2*(-a*f^2+d^2)/d/e)^2/f^2+e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2))/(e^2/f^2)^(1/2)*a+1/4/f*ln((1/2*e*(a*f^2-d^2)/f^2/d+e^2/f^2*(x+1/2*(-a*f^2+d^2)/d/e))/(e^2/f^2)^(1/2)+(e^2*(x+1/2*(-a*f^2+d^2)/d/e)^2/f^2+e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2))/(e^2/f^2)^(1/2)+1/4*f^3/d^3/e/((a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2)*ln((1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2+e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2)*(4*e^2*(x+1/2*(-a*f^2+d^2)/d/e)^2/f^2+4*e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))*a^2+1/2*f/d/e/((a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2)*ln((1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2+e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2)*(4*e^2*(x+1/2*(-a*f^2+d^2)/d/e)^2/f^2+4*e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))*a+1/4/f*d/e/((a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2)*ln((1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2+e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2)*(4*e^2*(x+1/2*(-a*f^2+d^2)/d/e)^2/f^2+4*e*(a*f^2-d^2)/f^2/d*(x+1/2*(-a*f^2+d^2)/d/e)+(a^2*f^4+2*a*d^2*f^2+d^4)/f^2/d^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))+1/2*ln(a*f^2-2*d*e*x-d^2)/e+1/2/d*x+1/4/d^2/e*ln(-a*f^2+2*d*e*x+d^2)*a*f^2-1/4/e*ln(-a*f^2+2*d*e*x+d^2)","B"
458,1,4136,140,0.038000," ","int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^2,x)","\text{output too large to display}"," ",0,"1/2/d^2*x-1/4*f/e/d^2*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)+1/4/f/d*ln(((x+1/2*(-a*f^2+d^2)/d/e)*e^2/f^2+1/2*(a*f^2-d^2)/d*e/f^2)/(e^2/f^2)^(1/2)+((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(e^2/f^2)^(1/2)+1/4/f/e/((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*ln(((a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))+1/2/e/d^3*ln(-a*f^2+2*d*e*x+d^2)*a*f^2-1/2*a*f^2/(-a*f^2+2*d*e*x+d^2)/d/e+1/4*d^2*f/e/(a^2*f^4+2*a*d^2*f^2+d^4)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)-1/4*d^3/f/(a^2*f^4+2*a*d^2*f^2+d^4)*ln(((x+1/2*(-a*f^2+d^2)/d/e)*e^2/f^2+1/2*(a*f^2-d^2)/d*e/f^2)/(e^2/f^2)^(1/2)+((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(e^2/f^2)^(1/2)-d*f/(a^2*f^4+2*a*d^2*f^2+d^4)*((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*x-1/4/e/d^3/(-a*f^2+2*d*e*x+d^2)*a^2*f^4-1/4*f/d^3*ln(((x+1/2*(-a*f^2+d^2)/d/e)*e^2/f^2+1/2*(a*f^2-d^2)/d*e/f^2)/(e^2/f^2)^(1/2)+((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(e^2/f^2)^(1/2)*a-1/4*d/(-a*f^2+2*d*e*x+d^2)/e+d*f^3/e^2/(a^2*f^4+2*a*d^2*f^2+d^4)/(x-1/2/e/d*a*f^2+1/2*d/e)*((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(3/2)-3/4/d*f^3/(a^2*f^4+2*a*d^2*f^2+d^4)*ln(((x+1/2*(-a*f^2+d^2)/d/e)*e^2/f^2+1/2*(a*f^2-d^2)/d*e/f^2)/(e^2/f^2)^(1/2)+((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(e^2/f^2)^(1/2)*a^2-3/4*d*f/(a^2*f^4+2*a*d^2*f^2+d^4)*ln(((x+1/2*(-a*f^2+d^2)/d/e)*e^2/f^2+1/2*(a*f^2-d^2)/d*e/f^2)/(e^2/f^2)^(1/2)+((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(e^2/f^2)^(1/2)*a-1/4*d^4/f/e/(a^2*f^4+2*a*d^2*f^2+d^4)/((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*ln(((a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))+1/4*f^3/e/d^4/((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*ln(((a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))*a^2+1/2*f/e/d^2/((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*ln(((a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))*a-1/4*f^5/e/d^2/(a^2*f^4+2*a*d^2*f^2+d^4)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*a^2-1/4*f^5/d^3/(a^2*f^4+2*a*d^2*f^2+d^4)*ln(((x+1/2*(-a*f^2+d^2)/d/e)*e^2/f^2+1/2*(a*f^2-d^2)/d*e/f^2)/(e^2/f^2)^(1/2)+((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(e^2/f^2)^(1/2)*a^3-f^3/d/(a^2*f^4+2*a*d^2*f^2+d^4)*((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*x*a+f^5/e^2/d/(a^2*f^4+2*a*d^2*f^2+d^4)/(x-1/2/e/d*a*f^2+1/2*d/e)*((x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/4*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(3/2)*a+1/4*f^7/e/d^4/(a^2*f^4+2*a*d^2*f^2+d^4)/((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*ln(((a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))*a^4+1/2/d^2*f^5/e/(a^2*f^4+2*a*d^2*f^2+d^4)/((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*ln(((a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))*a^3-1/2*d^2*f/e/(a^2*f^4+2*a*d^2*f^2+d^4)/((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*ln(((a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+1/2*(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2+1/2*((a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2)*(4*(x+1/2*(-a*f^2+d^2)/d/e)^2*e^2/f^2+4*(a*f^2-d^2)*(x+1/2*(-a*f^2+d^2)/d/e)/d*e/f^2+(a^2*f^4+2*a*d^2*f^2+d^4)/d^2/f^2)^(1/2))/(x+1/2*(-a*f^2+d^2)/d/e))*a","B"
459,1,9721,176,0.052000," ","int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
460,0,0,191,0.050000," ","int((e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(5/2),x)","\int \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{\frac{5}{2}}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(5/2),x)","F"
461,0,0,155,0.021000," ","int((e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(3/2),x)","\int \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{\frac{3}{2}}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(3/2),x)","F"
462,0,0,123,0.011000," ","int((e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(1/2),x)","\int \sqrt{e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, f}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(1/2),x)","F"
463,0,0,125,0.020000," ","int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(1/2),x)","\int \frac{1}{\sqrt{e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, f}}\, dx"," ",0,"int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(1/2),x)","F"
464,0,0,136,0.013000," ","int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(3/2),x)","\int \frac{1}{\left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(3/2),x)","F"
465,0,0,172,0.015000," ","int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(5/2),x)","\int \frac{1}{\left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(e*x+d+(e^2/f^2*x^2+a)^(1/2)*f)^(5/2),x)","F"
466,0,0,31,0.079000," ","int((x-(x^2-4)^(1/2))^(1/2),x)","\int \sqrt{x -\sqrt{x^{2}-4}}\, dx"," ",0,"int((x-(x^2-4)^(1/2))^(1/2),x)","F"
467,0,0,59,0.045000," ","int((a*x+b*(c+a^2*x^2/b^2)^(1/2))^(1/2),x)","\int \sqrt{a x +\sqrt{\frac{a^{2} x^{2}}{b^{2}}+c}\, b}\, dx"," ",0,"int((a*x+b*(c+a^2*x^2/b^2)^(1/2))^(1/2),x)","F"
468,1,60,35,0.039000," ","int((1+(-x^2+1)^(1/2))^(1/2),x)","\frac{i \left(\frac{32 i \sqrt{\pi}\, \sqrt{2}\, x^{3} \cos \left(\frac{3 \arcsin \left(x \right)}{2}\right)}{3}-\frac{8 i \sqrt{\pi}\, \sqrt{2}\, \left(-\frac{4}{3} x^{4}+\frac{2}{3} x^{2}+\frac{2}{3}\right) \sin \left(\frac{3 \arcsin \left(x \right)}{2}\right)}{\sqrt{-x^{2}+1}}\right)}{8 \sqrt{\pi}}"," ",0,"1/8*I/Pi^(1/2)*(32/3*I*Pi^(1/2)*2^(1/2)*x^3*cos(3/2*arcsin(x))-8*I*Pi^(1/2)*2^(1/2)*(-4/3*x^4+2/3*x^2+2/3)*sin(3/2*arcsin(x))/(-x^2+1)^(1/2))","C"
469,1,55,31,0.028000," ","int((1+(x^2+1)^(1/2))^(1/2),x)","-\frac{-\frac{32 \sqrt{\pi}\, \sqrt{2}\, x^{3} \cosh \left(\frac{3 \arcsinh \left(x \right)}{2}\right)}{3}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, \left(-\frac{4}{3} x^{4}-\frac{2}{3} x^{2}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(x \right)}{2}\right)}{\sqrt{x^{2}+1}}}{8 \sqrt{\pi}}"," ",0,"-1/8/Pi^(1/2)*(-32/3*Pi^(1/2)*2^(1/2)*x^3*cosh(3/2*arcsinh(x))-8*Pi^(1/2)*2^(1/2)*(-4/3*x^4-2/3*x^2+2/3)*sinh(3/2*arcsinh(x))/(x^2+1)^(1/2))","C"
470,1,64,31,0.025000," ","int((5+(x^2+25)^(1/2))^(1/2),x)","-\frac{5 \sqrt{5}\, \left(-\frac{32 \sqrt{\pi}\, \sqrt{2}\, x^{3} \cosh \left(\frac{3 \arcsinh \left(\frac{x}{5}\right)}{2}\right)}{375}-\frac{8 \sqrt{\pi}\, \sqrt{2}\, \left(-\frac{4}{1875} x^{4}-\frac{2}{75} x^{2}+\frac{2}{3}\right) \sinh \left(\frac{3 \arcsinh \left(\frac{x}{5}\right)}{2}\right)}{\sqrt{\frac{x^{2}}{25}+1}}\right)}{8 \sqrt{\pi}}"," ",0,"-5/8*5^(1/2)/Pi^(1/2)*(-32/375*Pi^(1/2)*2^(1/2)*x^3*cosh(3/2*arcsinh(1/5*x))-8*Pi^(1/2)*2^(1/2)*(-4/1875*x^4-2/75*x^2+2/3)*sinh(3/2*arcsinh(1/5*x))/(1/25*x^2+1)^(1/2))","C"
471,0,0,56,0.044000," ","int((a+b*(a^2/b^2+c*x^2)^(1/2))^(1/2),x)","\int \sqrt{a +\sqrt{c \,x^{2}+\frac{a^{2}}{b^{2}}}\, b}\, dx"," ",0,"int((a+b*(a^2/b^2+c*x^2)^(1/2))^(1/2),x)","F"
472,0,0,158,0.019000," ","int((d+e*x+f*(a+b*x+e^2/f^2*x^2)^(1/2))^n,x)","\int \left(e x +d +\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{n}\, dx"," ",0,"int((d+e*x+f*(a+b*x+e^2/f^2*x^2)^(1/2))^n,x)","F"
473,1,685,283,0.015000," ","int((e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^3,x)","-\frac{3 b^{4} f^{7} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{32 \sqrt{\frac{e^{2}}{f^{2}}}\, e^{4}}+\frac{3 a \,b^{2} f^{5} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{8 \sqrt{\frac{e^{2}}{f^{2}}}\, e^{2}}+\frac{3 b^{3} d \,f^{5} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{8 \sqrt{\frac{e^{2}}{f^{2}}}\, e^{3}}+b e \,f^{2} x^{3}+e^{3} x^{4}-\frac{3 a b d \,f^{3} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{2 \sqrt{\frac{e^{2}}{f^{2}}}\, e}+\frac{3 a e \,f^{2} x^{2}}{2}+\frac{3 \sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b^{3} f^{7}}{16 e^{4}}-\frac{3 b^{2} d^{2} f^{3} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{8 \sqrt{\frac{e^{2}}{f^{2}}}\, e^{2}}+\frac{3 \sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b^{2} f^{5} x}{8 e^{2}}+\frac{3 b d \,f^{2} x^{2}}{2}+2 d \,e^{2} x^{3}+\frac{3 a \,d^{2} f \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{2 \sqrt{\frac{e^{2}}{f^{2}}}}+3 a d \,f^{2} x -\frac{3 \sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b^{2} d \,f^{5}}{4 e^{3}}-\frac{3 \sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b d \,f^{3} x}{2 e}+\frac{3 d^{2} e \,x^{2}}{2}+\frac{3 \sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b \,d^{2} f^{3}}{4 e^{2}}-\frac{\left(b x +\frac{e^{2} x^{2}}{f^{2}}+a \right)^{\frac{3}{2}} b \,f^{5}}{2 e^{2}}+d^{3} x +\frac{3 \sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, d^{2} f x}{2}+\left(b x +\frac{e^{2} x^{2}}{f^{2}}+a \right)^{\frac{3}{2}} f^{3} x +\frac{d^{4}}{4 e}+\frac{2 \left(b x +\frac{e^{2} x^{2}}{f^{2}}+a \right)^{\frac{3}{2}} d \,f^{3}}{e}"," ",0,"3/2*d^2*e*x^2+d^3*x+e^3*x^4-3/2*d/e*f^3*b*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*a+1/4*d^4/e+2*d/e*f^3*(b*x+e^2/f^2*x^2+a)^(3/2)+3/2*f*d^2*(b*x+e^2/f^2*x^2+a)^(1/2)*x+3/8*f^5/e^2*a*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*b^2-1/2*f^5/e^2*(b*x+e^2/f^2*x^2+a)^(3/2)*b+3/16*f^7/e^4*b^3*(b*x+e^2/f^2*x^2+a)^(1/2)+f^2*x^3*b*e+3/2*f^2*x^2*b*d+2*d*e^2*x^3+3/2*a*e*f^2*x^2+3*a*d*f^2*x+f^3*(b*x+e^2/f^2*x^2+a)^(3/2)*x-3/4*d/e^3*f^5*b^2*(b*x+e^2/f^2*x^2+a)^(1/2)+3/4*d^2/e^2*f^3*(b*x+e^2/f^2*x^2+a)^(1/2)*b+3/2*f*d^2*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*a-3/2*d/e*f^3*b*(b*x+e^2/f^2*x^2+a)^(1/2)*x+3/8*d/e^3*f^5*b^3*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)-3/8*d^2/e^2*f^3*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*b^2+3/8*f^5/e^2*b^2*(b*x+e^2/f^2*x^2+a)^(1/2)*x-3/32*f^7/e^4*b^4*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)","B"
474,1,409,221,0.009000," ","int((e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^2,x)","\frac{b^{3} f^{5} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{8 \sqrt{\frac{e^{2}}{f^{2}}}\, e^{3}}-\frac{a b \,f^{3} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{2 \sqrt{\frac{e^{2}}{f^{2}}}\, e}-\frac{b^{2} d \,f^{3} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{4 \sqrt{\frac{e^{2}}{f^{2}}}\, e^{2}}+\frac{b \,f^{2} x^{2}}{2}+\frac{2 e^{2} x^{3}}{3}+\frac{a d f \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{\sqrt{\frac{e^{2}}{f^{2}}}}+a \,f^{2} x -\frac{\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b^{2} f^{5}}{4 e^{3}}-\frac{\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b \,f^{3} x}{2 e}+d e \,x^{2}+\frac{\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b d \,f^{3}}{2 e^{2}}+d^{2} x +\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, d f x +\frac{d^{3}}{3 e}+\frac{2 \left(b x +\frac{e^{2} x^{2}}{f^{2}}+a \right)^{\frac{3}{2}} f^{3}}{3 e}"," ",0,"a*f^2*x+1/2*f^2*b*x^2+2/3*e^2*x^3+2/3*(b*x+e^2/f^2*x^2+a)^(3/2)/e*f^3-1/2/e*f^3*b*(b*x+e^2/f^2*x^2+a)^(1/2)*x-1/4/e^3*f^5*b^2*(b*x+e^2/f^2*x^2+a)^(1/2)-1/2/e*f^3*b*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*a+1/8/e^3*f^5*b^3*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)+f*d*(b*x+e^2/f^2*x^2+a)^(1/2)*x+1/2*d/e^2*f^3*(b*x+e^2/f^2*x^2+a)^(1/2)*b+f*d*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*a-1/4*d/e^2*f^3*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*b^2+d*e*x^2+d^2*x+1/3*d^3/e","A"
475,1,173,106,0.006000," ","int(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f,x)","-\frac{b^{2} f^{3} \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{8 \sqrt{\frac{e^{2}}{f^{2}}}\, e^{2}}+\frac{a f \ln \left(\frac{\frac{b}{2}+\frac{e^{2} x}{f^{2}}}{\sqrt{\frac{e^{2}}{f^{2}}}}+\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\right)}{2 \sqrt{\frac{e^{2}}{f^{2}}}}+\frac{e \,x^{2}}{2}+\frac{\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, b \,f^{3}}{4 e^{2}}+d x +\frac{\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, f x}{2}"," ",0,"d*x+1/2*e*x^2+1/2*f*(b*x+e^2/f^2*x^2+a)^(1/2)*x+1/4/e^2*f^3*(b*x+e^2/f^2*x^2+a)^(1/2)*b+1/2*f*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*a-1/8/e^2*f^3*ln((1/2*b+e^2/f^2*x)/(e^2/f^2)^(1/2)+(b*x+e^2/f^2*x^2+a)^(1/2))/(e^2/f^2)^(1/2)*b^2","A"
476,1,4918,205,0.065000," ","int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f),x)","\text{output too large to display}"," ",0,"f/(b*f^2-2*d*e)*(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)+1/2*f^3/(b*f^2-2*d*e)^2*ln((-1/2*(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)+e^2/f^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e)))/(e^2/f^2)^(1/2)+(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(e^2/f^2)^(1/2)*b^2-f/(b*f^2-2*d*e)^2*ln((-1/2*(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)+e^2/f^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e)))/(e^2/f^2)^(1/2)+(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(e^2/f^2)^(1/2)*a*e^2-f/(b*f^2-2*d*e)^2*ln((-1/2*(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)+e^2/f^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e)))/(e^2/f^2)^(1/2)+(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(e^2/f^2)^(1/2)*b*d*e+1/f/(b*f^2-2*d*e)^2*ln((-1/2*(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)+e^2/f^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e)))/(e^2/f^2)^(1/2)+(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(e^2/f^2)^(1/2)*d^2*e^2-f^3/(b*f^2-2*d*e)^3/((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*ln((2*(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+2*((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(x+(a*f^2-d^2)/(b*f^2-2*d*e)))*a^2*e^2+2*f^3/(b*f^2-2*d*e)^3/((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*ln((2*(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+2*((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(x+(a*f^2-d^2)/(b*f^2-2*d*e)))*a*b*d*e-f^3/(b*f^2-2*d*e)^3/((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*ln((2*(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+2*((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(x+(a*f^2-d^2)/(b*f^2-2*d*e)))*b^2*d^2-2*f/(b*f^2-2*d*e)^3/((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*ln((2*(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+2*((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(x+(a*f^2-d^2)/(b*f^2-2*d*e)))*a*d^2*e^2+2*f/(b*f^2-2*d*e)^3/((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*ln((2*(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+2*((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(x+(a*f^2-d^2)/(b*f^2-2*d*e)))*b*d^3*e-1/f/(b*f^2-2*d*e)^3/((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*ln((2*(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+2*((a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2)*(e^2*(x+(a*f^2-d^2)/(b*f^2-2*d*e))^2/f^2-(-b^2*f^4+2*a*e^2*f^2+2*b*d*e*f^2-2*d^2*e^2)/f^2/(b*f^2-2*d*e)*(x+(a*f^2-d^2)/(b*f^2-2*d*e))+(a^2*e^2*f^4-2*a*b*d*e*f^4+b^2*d^2*f^4+2*a*d^2*e^2*f^2-2*b*d^3*e*f^2+d^4*e^2)/f^2/(b*f^2-2*d*e)^2)^(1/2))/(x+(a*f^2-d^2)/(b*f^2-2*d*e)))*d^4*e^2-d*ln((b*f^2-2*d*e)*x+a*f^2-d^2)/(b*f^2-2*d*e)-e/(b*f^2-2*d*e)*x+e/(b*f^2-2*d*e)^2*ln(b*f^2*x+a*f^2-2*d*e*x-d^2)*a*f^2-e/(b*f^2-2*d*e)^2*ln(b*f^2*x+a*f^2-2*d*e*x-d^2)*d^2","B"
477,1,58067,258,0.052000," ","int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
478,1,295147,320,0.164000," ","int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
479,0,0,326,0.054000," ","int((e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(5/2),x)","\int \left(e x +d +\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{\frac{5}{2}}\, dx"," ",0,"int((e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(5/2),x)","F"
480,0,0,264,0.022000," ","int((e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(3/2),x)","\int \left(e x +d +\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{\frac{3}{2}}\, dx"," ",0,"int((e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(3/2),x)","F"
481,0,0,201,0.012000," ","int((e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(1/2),x)","\int \sqrt{e x +d +\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, f}\, dx"," ",0,"int((e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(1/2),x)","F"
482,0,0,214,0.021000," ","int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(1/2),x)","\int \frac{1}{\sqrt{e x +d +\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, f}}\, dx"," ",0,"int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(1/2),x)","F"
483,0,0,243,0.014000," ","int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(3/2),x)","\int \frac{1}{\left(e x +d +\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(3/2),x)","F"
484,0,0,303,0.015000," ","int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(5/2),x)","\int \frac{1}{\left(e x +d +\sqrt{b x +\frac{e^{2} x^{2}}{f^{2}}+a}\, f \right)^{\frac{5}{2}}}\, dx"," ",0,"int(1/(e*x+d+(b*x+e^2/f^2*x^2+a)^(1/2)*f)^(5/2),x)","F"
485,1,216,140,0.086000," ","int((x^2+a)^2*(x+(x^2+a)^(1/2))^n,x)","\frac{a 2^{n +1} x^{n +3} \hypergeom \left(\left[-\frac{n}{2}, -\frac{n}{2}+\frac{1}{2}, -\frac{n}{2}-\frac{3}{2}\right], \left[-n +1, -\frac{n}{2}-\frac{1}{2}\right], -\frac{a}{x^{2}}\right)}{n +3}+\frac{2^{n} x^{n +5} \hypergeom \left(\left[-\frac{n}{2}, -\frac{n}{2}-\frac{5}{2}, -\frac{n}{2}+\frac{1}{2}\right], \left[-n +1, -\frac{n}{2}-\frac{3}{2}\right], -\frac{a}{x^{2}}\right)}{n +5}+\frac{\left(\frac{8 \sqrt{\pi}\, \left(n +\frac{a n}{x^{2}}-1\right) a^{-\frac{n}{2}-\frac{1}{2}} x^{n +1} \left(\sqrt{\frac{a}{x^{2}}+1}+1\right)^{n -1}}{\left(n +1\right) \left(2 n -2\right) n}+\frac{4 \sqrt{\pi}\, \sqrt{\frac{a}{x^{2}}+1}\, a^{-\frac{n}{2}-\frac{1}{2}} x^{n +1} \left(\sqrt{\frac{a}{x^{2}}+1}+1\right)^{n -1}}{\left(n +1\right) n}\right) n \,a^{\frac{n}{2}+\frac{5}{2}}}{4 \sqrt{\pi}}"," ",0,"2^n/(5+n)*x^(5+n)*hypergeom([-1/2*n,-1/2*n-5/2,1/2-1/2*n],[1-n,-3/2-1/2*n],-a/x^2)+2^(n+1)*a/(3+n)*x^(3+n)*hypergeom([-1/2*n,1/2-1/2*n,-3/2-1/2*n],[1-n,-1/2-1/2*n],-a/x^2)+1/4*a^(5/2+1/2*n)/Pi^(1/2)*n*(8*Pi^(1/2)/(n+1)/n*x^(n+1)*a^(-1/2-1/2*n)*(a/x^2*n+n-1)/(2*n-2)*((1+a/x^2)^(1/2)+1)^(n-1)+4*Pi^(1/2)/(n+1)/n*x^(n+1)*a^(-1/2-1/2*n)*(1+a/x^2)^(1/2)*((1+a/x^2)^(1/2)+1)^(n-1))","C"
486,1,167,92,0.020000," ","int((x^2+a)*(x+(x^2+a)^(1/2))^n,x)","\frac{2^{n} x^{n +3} \hypergeom \left(\left[-\frac{n}{2}, -\frac{n}{2}+\frac{1}{2}, -\frac{n}{2}-\frac{3}{2}\right], \left[-n +1, -\frac{n}{2}-\frac{1}{2}\right], -\frac{a}{x^{2}}\right)}{n +3}+\frac{\left(\frac{8 \sqrt{\pi}\, \left(n +\frac{a n}{x^{2}}-1\right) a^{-\frac{n}{2}-\frac{1}{2}} x^{n +1} \left(\sqrt{\frac{a}{x^{2}}+1}+1\right)^{n -1}}{\left(n +1\right) \left(2 n -2\right) n}+\frac{4 \sqrt{\pi}\, \sqrt{\frac{a}{x^{2}}+1}\, a^{-\frac{n}{2}-\frac{1}{2}} x^{n +1} \left(\sqrt{\frac{a}{x^{2}}+1}+1\right)^{n -1}}{\left(n +1\right) n}\right) n \,a^{\frac{n}{2}+\frac{3}{2}}}{4 \sqrt{\pi}}"," ",0,"2^n/(n+3)*x^(n+3)*hypergeom([-1/2*n,-1/2*n+1/2,-1/2*n-3/2],[-n+1,-1/2*n-1/2],-a/x^2)+1/4*a^(3/2+1/2*n)/Pi^(1/2)*n*(8*Pi^(1/2)/(n+1)*(n+a*n/x^2-1)/(2*n-2)/n*a^(-1/2*n-1/2)*x^(n+1)*((a/x^2+1)^(1/2)+1)^(n-1)+4*Pi^(1/2)/(n+1)*(a/x^2+1)^(1/2)/n*a^(-1/2*n-1/2)*x^(n+1)*((a/x^2+1)^(1/2)+1)^(n-1))","C"
487,1,120,44,0.017000," ","int((x+(x^2+a)^(1/2))^n,x)","\frac{\left(\frac{8 \sqrt{\pi}\, \left(n +\frac{a n}{x^{2}}-1\right) a^{-\frac{n}{2}-\frac{1}{2}} x^{n +1} \left(\sqrt{\frac{a}{x^{2}}+1}+1\right)^{n -1}}{\left(n +1\right) \left(2 n -2\right) n}+\frac{4 \sqrt{\pi}\, \sqrt{\frac{a}{x^{2}}+1}\, a^{-\frac{n}{2}-\frac{1}{2}} x^{n +1} \left(\sqrt{\frac{a}{x^{2}}+1}+1\right)^{n -1}}{\left(n +1\right) n}\right) n \,a^{\frac{n}{2}+\frac{1}{2}}}{4 \sqrt{\pi}}"," ",0,"1/4*a^(1/2+1/2*n)/Pi^(1/2)*n*(8*Pi^(1/2)/(n+1)*(n+a*n/x^2-1)/(2*n-2)/n*a^(-1/2*n-1/2)*x^(n+1)*((a/x^2+1)^(1/2)+1)^(n-1)+4*Pi^(1/2)/(n+1)*(a/x^2+1)^(1/2)/n*a^(-1/2*n-1/2)*x^(n+1)*((a/x^2+1)^(1/2)+1)^(n-1))","B"
488,0,0,53,0.057000," ","int((x+(x^2+a)^(1/2))^n/(x^2+a),x)","\int \frac{\left(x +\sqrt{x^{2}+a}\right)^{n}}{x^{2}+a}\, dx"," ",0,"int((x+(x^2+a)^(1/2))^n/(x^2+a),x)","F"
489,0,0,53,0.048000," ","int((x+(x^2+a)^(1/2))^n/(x^2+a)^2,x)","\int \frac{\left(x +\sqrt{x^{2}+a}\right)^{n}}{\left(x^{2}+a \right)^{2}}\, dx"," ",0,"int((x+(x^2+a)^(1/2))^n/(x^2+a)^2,x)","F"
490,0,0,152,0.056000," ","int((x^2+a)^2*(x-(x^2+a)^(1/2))^n,x)","\int \left(x^{2}+a \right)^{2} \left(x -\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x^2+a)^2*(x-(x^2+a)^(1/2))^n,x)","F"
491,0,0,100,0.049000," ","int((x^2+a)*(x-(x^2+a)^(1/2))^n,x)","\int \left(x^{2}+a \right) \left(x -\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x^2+a)*(x-(x^2+a)^(1/2))^n,x)","F"
492,0,0,48,0.049000," ","int((x-(x^2+a)^(1/2))^n,x)","\int \left(x -\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x-(x^2+a)^(1/2))^n,x)","F"
493,0,0,57,0.057000," ","int((x-(x^2+a)^(1/2))^n/(x^2+a),x)","\int \frac{\left(x -\sqrt{x^{2}+a}\right)^{n}}{x^{2}+a}\, dx"," ",0,"int((x-(x^2+a)^(1/2))^n/(x^2+a),x)","F"
494,0,0,57,0.058000," ","int((x-(x^2+a)^(1/2))^n/(x^2+a)^2,x)","\int \frac{\left(x -\sqrt{x^{2}+a}\right)^{n}}{\left(x^{2}+a \right)^{2}}\, dx"," ",0,"int((x-(x^2+a)^(1/2))^n/(x^2+a)^2,x)","F"
495,0,0,159,0.052000," ","int((x^2+a)^(5/2)*(x+(x^2+a)^(1/2))^n,x)","\int \left(x^{2}+a \right)^{\frac{5}{2}} \left(x +\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x^2+a)^(5/2)*(x+(x^2+a)^(1/2))^n,x)","F"
496,0,0,111,0.051000," ","int((x^2+a)^(3/2)*(x+(x^2+a)^(1/2))^n,x)","\int \left(x^{2}+a \right)^{\frac{3}{2}} \left(x +\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x^2+a)^(3/2)*(x+(x^2+a)^(1/2))^n,x)","F"
497,0,0,63,0.052000," ","int((x^2+a)^(1/2)*(x+(x^2+a)^(1/2))^n,x)","\int \sqrt{x^{2}+a}\, \left(x +\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x^2+a)^(1/2)*(x+(x^2+a)^(1/2))^n,x)","F"
498,0,0,15,0.050000," ","int((x+(x^2+a)^(1/2))^n/(x^2+a)^(1/2),x)","\int \frac{\left(x +\sqrt{x^{2}+a}\right)^{n}}{\sqrt{x^{2}+a}}\, dx"," ",0,"int((x+(x^2+a)^(1/2))^n/(x^2+a)^(1/2),x)","F"
499,0,0,53,0.048000," ","int((x+(x^2+a)^(1/2))^n/(x^2+a)^(3/2),x)","\int \frac{\left(x +\sqrt{x^{2}+a}\right)^{n}}{\left(x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((x+(x^2+a)^(1/2))^n/(x^2+a)^(3/2),x)","F"
500,0,0,53,0.052000," ","int((x+(x^2+a)^(1/2))^n/(x^2+a)^(5/2),x)","\int \frac{\left(x +\sqrt{x^{2}+a}\right)^{n}}{\left(x^{2}+a \right)^{\frac{5}{2}}}\, dx"," ",0,"int((x+(x^2+a)^(1/2))^n/(x^2+a)^(5/2),x)","F"
501,0,0,173,0.060000," ","int((x^2+a)^(5/2)*(x-(x^2+a)^(1/2))^n,x)","\int \left(x^{2}+a \right)^{\frac{5}{2}} \left(x -\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x^2+a)^(5/2)*(x-(x^2+a)^(1/2))^n,x)","F"
502,0,0,121,0.059000," ","int((x^2+a)^(3/2)*(x-(x^2+a)^(1/2))^n,x)","\int \left(x^{2}+a \right)^{\frac{3}{2}} \left(x -\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x^2+a)^(3/2)*(x-(x^2+a)^(1/2))^n,x)","F"
503,0,0,69,0.061000," ","int((x^2+a)^(1/2)*(x-(x^2+a)^(1/2))^n,x)","\int \sqrt{x^{2}+a}\, \left(x -\sqrt{x^{2}+a}\right)^{n}\, dx"," ",0,"int((x^2+a)^(1/2)*(x-(x^2+a)^(1/2))^n,x)","F"
504,0,0,18,0.059000," ","int((x-(x^2+a)^(1/2))^n/(x^2+a)^(1/2),x)","\int \frac{\left(x -\sqrt{x^{2}+a}\right)^{n}}{\sqrt{x^{2}+a}}\, dx"," ",0,"int((x-(x^2+a)^(1/2))^n/(x^2+a)^(1/2),x)","F"
505,0,0,57,0.058000," ","int((x-(x^2+a)^(1/2))^n/(x^2+a)^(3/2),x)","\int \frac{\left(x -\sqrt{x^{2}+a}\right)^{n}}{\left(x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((x-(x^2+a)^(1/2))^n/(x^2+a)^(3/2),x)","F"
506,0,0,57,0.060000," ","int((x-(x^2+a)^(1/2))^n/(x^2+a)^(5/2),x)","\int \frac{\left(x -\sqrt{x^{2}+a}\right)^{n}}{\left(x^{2}+a \right)^{\frac{5}{2}}}\, dx"," ",0,"int((x-(x^2+a)^(1/2))^n/(x^2+a)^(5/2),x)","F"
507,0,0,341,0.112000," ","int((a+2*d*e*x/f^2+e^2/f^2*x^2)^2*(d+e*x+f*(a+2*d*e*x/f^2+e^2/f^2*x^2)^(1/2))^n,x)","\int \left(\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}\right)^{2} \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}\, dx"," ",0,"int((a+2*d*e*x/f^2+e^2/f^2*x^2)^2*(d+e*x+f*(a+2*d*e*x/f^2+e^2/f^2*x^2)^(1/2))^n,x)","F"
508,0,0,223,0.011000," ","int((e^2/f^2*x^2+a+2*d*e/f^2*x)*(e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","\int \left(\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}\right) \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}\, dx"," ",0,"int((e^2/f^2*x^2+a+2*d*e/f^2*x)*(e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","F"
509,0,0,99,0.010000," ","int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","\int \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","F"
510,0,0,116,0.153000," ","int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x),x)","\int \frac{\left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}}{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x),x)","F"
511,0,0,116,0.109000," ","int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x)^2,x)","\int \frac{\left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}}{\left(\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}\right)^{2}}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x)^2,x)","F"
512,0,0,99,0.010000," ","int((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n,x)","\int \left(e x +d +\sqrt{\frac{a \,f^{2}+\left(e x +2 d \right) e x}{f^{2}}}\, f \right)^{n}\, dx"," ",0,"int((d+e*x+f*((a*f^2+e*x*(e*x+2*d))/f^2)^(1/2))^n,x)","F"
513,0,0,116,0.116000," ","int((e*x+d+((a*f^2+(e*x+2*d)*e*x)/f^2)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x),x)","\int \frac{\left(e x +d +\sqrt{\frac{a \,f^{2}+\left(e x +2 d \right) e x}{f^{2}}}\, f \right)^{n}}{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, dx"," ",0,"int((e*x+d+((a*f^2+(e*x+2*d)*e*x)/f^2)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x),x)","F"
514,0,0,277,0.109000," ","int((e^2/f^2*x^2+a+2*d*e/f^2*x)^(3/2)*(e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","\int \left(\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}\right)^{\frac{3}{2}} \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}\, dx"," ",0,"int((e^2/f^2*x^2+a+2*d*e/f^2*x)^(3/2)*(e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","F"
515,0,0,159,0.109000," ","int((e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*(e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","\int \sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}\, dx"," ",0,"int((e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*(e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","F"
516,0,0,39,0.107000," ","int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2),x)","\int \frac{\left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}}{\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2),x)","F"
517,0,0,116,0.115000," ","int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x)^(3/2),x)","\int \frac{\left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}}{\left(\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*x^2+a+2*d*e/f^2*x)^(3/2),x)","F"
518,0,0,39,0.108000," ","int((e*x+d+((a*f^2+(e*x+2*d)*e*x)/f^2)^(1/2)*f)^n/((a*f^2+(e*x+2*d)*e*x)/f^2)^(1/2),x)","\int \frac{\left(e x +d +\sqrt{\frac{a \,f^{2}+\left(e x +2 d \right) e x}{f^{2}}}\, f \right)^{n}}{\sqrt{\frac{a \,f^{2}+\left(e x +2 d \right) e x}{f^{2}}}}\, dx"," ",0,"int((e*x+d+((a*f^2+(e*x+2*d)*e*x)/f^2)^(1/2)*f)^n/((a*f^2+(e*x+2*d)*e*x)/f^2)^(1/2),x)","F"
519,0,0,303,0.110000," ","int((a*g+2*d*e*g*x/f^2+e^2*g*x^2/f^2)^(1/2)*(e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","\int \sqrt{\frac{e^{2} g \,x^{2}}{f^{2}}+a g +\frac{2 d e g x}{f^{2}}}\, \left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}\, dx"," ",0,"int((a*g+2*d*e*g*x/f^2+e^2*g*x^2/f^2)^(1/2)*(e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n,x)","F"
520,0,0,87,0.107000," ","int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*g*x^2+a*g+2*d*e/f^2*g*x)^(1/2),x)","\int \frac{\left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}}{\sqrt{\frac{e^{2} g \,x^{2}}{f^{2}}+a g +\frac{2 d e g x}{f^{2}}}}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*g*x^2+a*g+2*d*e/f^2*g*x)^(1/2),x)","F"
521,0,0,167,0.106000," ","int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*g*x^2+a*g+2*d*e/f^2*g*x)^(3/2),x)","\int \frac{\left(e x +d +\sqrt{\frac{e^{2} x^{2}}{f^{2}}+a +\frac{2 d e x}{f^{2}}}\, f \right)^{n}}{\left(\frac{e^{2} g \,x^{2}}{f^{2}}+a g +\frac{2 d e g x}{f^{2}}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((e*x+d+(e^2/f^2*x^2+a+2*d*e/f^2*x)^(1/2)*f)^n/(e^2/f^2*g*x^2+a*g+2*d*e/f^2*g*x)^(3/2),x)","F"
522,0,0,87,0.107000," ","int((e*x+d+((a*f^2+(e*x+2*d)*e*x)/f^2)^(1/2)*f)^n/((a*f^2*g+e*g*x*(e*x+2*d))/f^2)^(1/2),x)","\int \frac{\left(e x +d +\sqrt{\frac{a \,f^{2}+\left(e x +2 d \right) e x}{f^{2}}}\, f \right)^{n}}{\sqrt{\frac{a \,f^{2} g +\left(e x +2 d \right) e g x}{f^{2}}}}\, dx"," ",0,"int((e*x+d+((a*f^2+(e*x+2*d)*e*x)/f^2)^(1/2)*f)^n/((a*f^2*g+e*g*x*(e*x+2*d))/f^2)^(1/2),x)","F"
523,1,353,164,0.077000," ","int(1/(b*x+a)/(d*x^2+c)^(1/2)/(f*x^2+e)^(1/2),x)","\frac{\left(-\sqrt{-\frac{d}{c}}\, \sqrt{d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e}\, a \arctanh \left(\frac{2 a^{2} d f \,x^{2}+b^{2} c f \,x^{2}+b^{2} d e \,x^{2}+a^{2} c f +a^{2} d e +2 b^{2} c e}{2 \sqrt{\frac{a^{4} d f +a^{2} b^{2} c f +a^{2} b^{2} d e +b^{4} c e}{b^{4}}}\, \sqrt{d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e}\, b^{2}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{f \,x^{2}+e}{e}}\, \sqrt{\frac{a^{4} d f +a^{2} b^{2} c f +a^{2} b^{2} d e +b^{4} c e}{b^{4}}}\, b \EllipticPi \left(\sqrt{-\frac{d}{c}}\, x , -\frac{b^{2} c}{a^{2} d}, \frac{\sqrt{-\frac{f}{e}}}{\sqrt{-\frac{d}{c}}}\right)\right) \sqrt{f \,x^{2}+e}\, \sqrt{d \,x^{2}+c}}{2 \sqrt{\frac{a^{4} d f +a^{2} b^{2} c f +a^{2} b^{2} d e +b^{4} c e}{b^{4}}}\, \sqrt{-\frac{d}{c}}\, \left(d f \,x^{4}+c f \,x^{2}+d e \,x^{2}+c e \right) a b}"," ",0,"1/2*(2*b*((d*x^2+c)/c)^(1/2)*((f*x^2+e)/e)^(1/2)*EllipticPi(x*(-1/c*d)^(1/2),-b^2*c/a^2/d,(-f/e)^(1/2)/(-1/c*d)^(1/2))*((a^4*d*f+a^2*b^2*c*f+a^2*b^2*d*e+b^4*c*e)/b^4)^(1/2)-arctanh(1/2*(2*a^2*d*f*x^2+b^2*c*f*x^2+b^2*d*e*x^2+a^2*c*f+a^2*d*e+2*b^2*c*e)/b^2/((a^4*d*f+a^2*b^2*c*f+a^2*b^2*d*e+b^4*c*e)/b^4)^(1/2)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)^(1/2))*(-1/c*d)^(1/2)*a*(d*f*x^4+c*f*x^2+d*e*x^2+c*e)^(1/2))*(f*x^2+e)^(1/2)*(d*x^2+c)^(1/2)/b/a/((a^4*d*f+a^2*b^2*c*f+a^2*b^2*d*e+b^4*c*e)/b^4)^(1/2)/(-1/c*d)^(1/2)/(d*f*x^4+c*f*x^2+d*e*x^2+c*e)","B"
524,1,394,61,0.053000," ","int((-2*f*x^2+e)/(4*f^2*x^4+4*d*f*x^2+4*e*f*x^2+e^2),x)","-\frac{\sqrt{2}\, d f \arctanh \left(\frac{\sqrt{2}\, f x}{\sqrt{-d f -e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}\right)}{4 \sqrt{\left(d +2 e \right) d \,f^{2}}\, \sqrt{-d f -e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}-\frac{\sqrt{2}\, d f \arctan \left(\frac{\sqrt{2}\, f x}{\sqrt{d f +e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}\right)}{4 \sqrt{\left(d +2 e \right) d \,f^{2}}\, \sqrt{d f +e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}-\frac{\sqrt{2}\, e f \arctanh \left(\frac{\sqrt{2}\, f x}{\sqrt{-d f -e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}\right)}{2 \sqrt{\left(d +2 e \right) d \,f^{2}}\, \sqrt{-d f -e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}-\frac{\sqrt{2}\, e f \arctan \left(\frac{\sqrt{2}\, f x}{\sqrt{d f +e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}\right)}{2 \sqrt{\left(d +2 e \right) d \,f^{2}}\, \sqrt{d f +e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, f x}{\sqrt{-d f -e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}\right)}{4 \sqrt{-d f -e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, f x}{\sqrt{d f +e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}\right)}{4 \sqrt{d f +e f +\sqrt{\left(d +2 e \right) d \,f^{2}}}}"," ",0,"-1/4*f/(d*f^2*(d+2*e))^(1/2)*2^(1/2)/(d*f+f*e+(d*f^2*(d+2*e))^(1/2))^(1/2)*arctan(f*x*2^(1/2)/(d*f+f*e+(d*f^2*(d+2*e))^(1/2))^(1/2))*d-1/2*f/(d*f^2*(d+2*e))^(1/2)*2^(1/2)/(d*f+f*e+(d*f^2*(d+2*e))^(1/2))^(1/2)*arctan(f*x*2^(1/2)/(d*f+f*e+(d*f^2*(d+2*e))^(1/2))^(1/2))*e-1/4*2^(1/2)/(d*f+f*e+(d*f^2*(d+2*e))^(1/2))^(1/2)*arctan(f*x*2^(1/2)/(d*f+f*e+(d*f^2*(d+2*e))^(1/2))^(1/2))-1/4*f/(d*f^2*(d+2*e))^(1/2)*2^(1/2)/(-d*f-f*e+(d*f^2*(d+2*e))^(1/2))^(1/2)*arctanh(f*x*2^(1/2)/(-d*f-f*e+(d*f^2*(d+2*e))^(1/2))^(1/2))*d-1/2*f/(d*f^2*(d+2*e))^(1/2)*2^(1/2)/(-d*f-f*e+(d*f^2*(d+2*e))^(1/2))^(1/2)*arctanh(f*x*2^(1/2)/(-d*f-f*e+(d*f^2*(d+2*e))^(1/2))^(1/2))*e+1/4*2^(1/2)/(-d*f-f*e+(d*f^2*(d+2*e))^(1/2))^(1/2)*arctanh(f*x*2^(1/2)/(-d*f-f*e+(d*f^2*(d+2*e))^(1/2))^(1/2))","B"
525,1,394,53,0.054000," ","int((-2*f*x^2+e)/(4*f^2*x^4-4*d*f*x^2+4*e*f*x^2+e^2),x)","\frac{\sqrt{2}\, d f \arctanh \left(\frac{\sqrt{2}\, f x}{\sqrt{d f -e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}\right)}{4 \sqrt{\left(d -2 e \right) d \,f^{2}}\, \sqrt{d f -e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}+\frac{\sqrt{2}\, d f \arctan \left(\frac{\sqrt{2}\, f x}{\sqrt{-d f +e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}\right)}{4 \sqrt{\left(d -2 e \right) d \,f^{2}}\, \sqrt{-d f +e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}-\frac{\sqrt{2}\, e f \arctanh \left(\frac{\sqrt{2}\, f x}{\sqrt{d f -e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}\right)}{2 \sqrt{\left(d -2 e \right) d \,f^{2}}\, \sqrt{d f -e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}-\frac{\sqrt{2}\, e f \arctan \left(\frac{\sqrt{2}\, f x}{\sqrt{-d f +e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}\right)}{2 \sqrt{\left(d -2 e \right) d \,f^{2}}\, \sqrt{-d f +e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}+\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, f x}{\sqrt{d f -e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}\right)}{4 \sqrt{d f -e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, f x}{\sqrt{-d f +e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}\right)}{4 \sqrt{-d f +e f +\sqrt{\left(d -2 e \right) d \,f^{2}}}}"," ",0,"1/4*f/(d*f^2*(d-2*e))^(1/2)*2^(1/2)/(d*f-e*f+(d*f^2*(d-2*e))^(1/2))^(1/2)*arctanh(f*x*2^(1/2)/(d*f-e*f+(d*f^2*(d-2*e))^(1/2))^(1/2))*d-1/2*f/(d*f^2*(d-2*e))^(1/2)*2^(1/2)/(d*f-e*f+(d*f^2*(d-2*e))^(1/2))^(1/2)*arctanh(f*x*2^(1/2)/(d*f-e*f+(d*f^2*(d-2*e))^(1/2))^(1/2))*e+1/4*2^(1/2)/(d*f-e*f+(d*f^2*(d-2*e))^(1/2))^(1/2)*arctanh(f*x*2^(1/2)/(d*f-e*f+(d*f^2*(d-2*e))^(1/2))^(1/2))+1/4*f/(d*f^2*(d-2*e))^(1/2)*2^(1/2)/(-d*f+e*f+(d*f^2*(d-2*e))^(1/2))^(1/2)*arctan(f*x*2^(1/2)/(-d*f+e*f+(d*f^2*(d-2*e))^(1/2))^(1/2))*d-1/2*f/(d*f^2*(d-2*e))^(1/2)*2^(1/2)/(-d*f+e*f+(d*f^2*(d-2*e))^(1/2))^(1/2)*arctan(f*x*2^(1/2)/(-d*f+e*f+(d*f^2*(d-2*e))^(1/2))^(1/2))*e-1/4*2^(1/2)/(-d*f+e*f+(d*f^2*(d-2*e))^(1/2))^(1/2)*arctan(f*x*2^(1/2)/(-d*f+e*f+(d*f^2*(d-2*e))^(1/2))^(1/2))","B"
526,1,70,28,0.010000," ","int((-4*f*x^3+e)/(4*f^2*x^6+4*e*f*x^3+4*d*f*x^2+e^2),x)","\frac{\left(-4 \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}+4 d f \,\textit{\_Z}^{2}+e^{2}\right)^{3} f +e \right) \ln \left(-\RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}+4 d f \,\textit{\_Z}^{2}+e^{2}\right)+x \right)}{4 f \left(6 f \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}+4 d f \,\textit{\_Z}^{2}+e^{2}\right)^{5}+3 e \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}+4 d f \,\textit{\_Z}^{2}+e^{2}\right)^{2}+2 d \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}+4 d f \,\textit{\_Z}^{2}+e^{2}\right)\right)}"," ",0,"1/4/f*sum((-4*_R^3*f+e)/(6*_R^5*f+3*_R^2*e+2*_R*d)*ln(-_R+x),_R=RootOf(4*_Z^6*f^2+4*_Z^3*e*f+4*_Z^2*d*f+e^2))","C"
527,1,70,28,0.010000," ","int((-4*f*x^3+e)/(4*f^2*x^6+4*e*f*x^3-4*d*f*x^2+e^2),x)","\frac{\left(-4 \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}-4 d f \,\textit{\_Z}^{2}+e^{2}\right)^{3} f +e \right) \ln \left(-\RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}-4 d f \,\textit{\_Z}^{2}+e^{2}\right)+x \right)}{4 f \left(6 f \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}-4 d f \,\textit{\_Z}^{2}+e^{2}\right)^{5}+3 e \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}-4 d f \,\textit{\_Z}^{2}+e^{2}\right)^{2}-2 d \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 e f \,\textit{\_Z}^{3}-4 d f \,\textit{\_Z}^{2}+e^{2}\right)\right)}"," ",0,"1/4/f*sum((-4*_R^3*f+e)/(6*_R^5*f+3*_R^2*e-2*_R*d)*ln(-_R+x),_R=RootOf(4*_Z^6*f^2+4*_Z^3*e*f-4*_Z^2*d*f+e^2))","C"
528,1,78,28,0.069000," ","int((e-2*f*(n-1)*x^n)/(e^2+4*d*f*x^2+4*e*f*x^n+4*f^2*x^(2*n)),x)","\frac{\ln \left(x^{n}+\frac{-2 d f x +\sqrt{-d f}\, e}{2 \sqrt{-d f}\, f}\right)}{4 \sqrt{-d f}}-\frac{\ln \left(x^{n}+\frac{2 d f x +\sqrt{-d f}\, e}{2 \sqrt{-d f}\, f}\right)}{4 \sqrt{-d f}}"," ",0,"-1/4/(-d*f)^(1/2)*ln(x^n+1/2*(2*d*f*x+e*(-d*f)^(1/2))/(-d*f)^(1/2)/f)+1/4/(-d*f)^(1/2)*ln(x^n+1/2*(-2*d*f*x+e*(-d*f)^(1/2))/(-d*f)^(1/2)/f)","B"
529,1,72,28,0.068000," ","int((e-2*f*(n-1)*x^n)/(e^2-4*d*f*x^2+4*e*f*x^n+4*f^2*x^(2*n)),x)","-\frac{\ln \left(x^{n}+\frac{-2 d f x +\sqrt{d f}\, e}{2 \sqrt{d f}\, f}\right)}{4 \sqrt{d f}}+\frac{\ln \left(x^{n}+\frac{2 d f x +\sqrt{d f}\, e}{2 \sqrt{d f}\, f}\right)}{4 \sqrt{d f}}"," ",0,"1/4/(d*f)^(1/2)*ln(x^n+1/2*(2*d*f*x+e*(d*f)^(1/2))/(d*f)^(1/2)/f)-1/4/(d*f)^(1/2)*ln(x^n+1/2*(-2*d*f*x+e*(d*f)^(1/2))/(d*f)^(1/2)/f)","B"
530,1,42,32,0.005000," ","int(x/(4*d*f*x^4+4*f^2*x^4+4*e*f*x^2+e^2),x)","\frac{\arctan \left(\frac{4 e f +2 \left(4 d f +4 f^{2}\right) x^{2}}{4 \sqrt{d f}\, e}\right)}{4 \sqrt{d f}\, e}"," ",0,"1/4/(d*f)^(1/2)/e*arctan(1/4*(2*(4*d*f+4*f^2)*x^2+4*e*f)/(d*f)^(1/2)/e)","A"
531,1,42,34,0.003000," ","int(x/(-4*d*f*x^4+4*f^2*x^4+4*e*f*x^2+e^2),x)","\frac{\arctanh \left(\frac{-4 e f +2 \left(4 d f -4 f^{2}\right) x^{2}}{4 \sqrt{d f}\, e}\right)}{4 \sqrt{d f}\, e}"," ",0,"1/4/(d*f)^(1/2)/e*arctanh(1/4*(2*(4*d*f-4*f^2)*x^2-4*e*f)/(d*f)^(1/2)/e)","A"
532,1,74,30,0.152000," ","int(x^2*(2*f*x^2+3*e)/(4*d*f*x^6+4*f^2*x^4+4*e*f*x^2+e^2),x)","\frac{\left(2 \RootOf \left(4 d f \,\textit{\_Z}^{6}+4 f^{2} \textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{2}+e^{2}\right)^{4} f +3 \RootOf \left(4 d f \,\textit{\_Z}^{6}+4 f^{2} \textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{2}+e^{2}\right)^{2} e \right) \ln \left(-\RootOf \left(4 d f \,\textit{\_Z}^{6}+4 f^{2} \textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{2}+e^{2}\right)+x \right)}{8 f \left(3 d \RootOf \left(4 d f \,\textit{\_Z}^{6}+4 f^{2} \textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{2}+e^{2}\right)^{5}+2 f \RootOf \left(4 d f \,\textit{\_Z}^{6}+4 f^{2} \textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{2}+e^{2}\right)^{3}+e \RootOf \left(4 d f \,\textit{\_Z}^{6}+4 f^{2} \textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{2}+e^{2}\right)\right)}"," ",0,"1/8/f*sum((2*_R^4*f+3*_R^2*e)/(3*_R^5*d+2*_R^3*f+_R*e)*ln(-_R+x),_R=RootOf(4*_Z^6*d*f+4*_Z^4*f^2+4*_Z^2*e*f+e^2))","C"
533,1,77,30,0.141000," ","int(x^2*(2*f*x^2+3*e)/(-4*d*f*x^6+4*f^2*x^4+4*e*f*x^2+e^2),x)","-\frac{\left(2 \RootOf \left(4 d f \,\textit{\_Z}^{6}-4 f^{2} \textit{\_Z}^{4}-4 e f \,\textit{\_Z}^{2}-e^{2}\right)^{4} f +3 \RootOf \left(4 d f \,\textit{\_Z}^{6}-4 f^{2} \textit{\_Z}^{4}-4 e f \,\textit{\_Z}^{2}-e^{2}\right)^{2} e \right) \ln \left(-\RootOf \left(4 d f \,\textit{\_Z}^{6}-4 f^{2} \textit{\_Z}^{4}-4 e f \,\textit{\_Z}^{2}-e^{2}\right)+x \right)}{8 f \left(3 d \RootOf \left(4 d f \,\textit{\_Z}^{6}-4 f^{2} \textit{\_Z}^{4}-4 e f \,\textit{\_Z}^{2}-e^{2}\right)^{5}-2 f \RootOf \left(4 d f \,\textit{\_Z}^{6}-4 f^{2} \textit{\_Z}^{4}-4 e f \,\textit{\_Z}^{2}-e^{2}\right)^{3}-e \RootOf \left(4 d f \,\textit{\_Z}^{6}-4 f^{2} \textit{\_Z}^{4}-4 e f \,\textit{\_Z}^{2}-e^{2}\right)\right)}"," ",0,"-1/8/f*sum((2*_R^4*f+3*_R^2*e)/(3*_R^5*d-2*_R^3*f-_R*e)*ln(-_R+x),_R=RootOf(4*_Z^6*d*f-4*_Z^4*f^2-4*_Z^2*e*f-e^2))","C"
534,1,78,32,0.088000," ","int(x^m*(e*(m+1)+2*f*(-1+m)*x^2)/(e^2+4*e*f*x^2+4*f^2*x^4+4*d*f*x^(2+2*m)),x)","\frac{\ln \left(x^{m}-\frac{\left(2 f \,x^{2}+e \right) \sqrt{-d f}}{2 d f x}\right)}{4 \sqrt{-d f}}-\frac{\ln \left(x^{m}+\frac{\left(2 f \,x^{2}+e \right) \sqrt{-d f}}{2 d f x}\right)}{4 \sqrt{-d f}}"," ",0,"-1/4/(-d*f)^(1/2)*ln(x^m+1/2*(2*f*x^2+e)*(-d*f)^(1/2)/d/f/x)+1/4/(-d*f)^(1/2)*ln(x^m-1/2*(2*f*x^2+e)*(-d*f)^(1/2)/d/f/x)","B"
535,1,74,32,0.088000," ","int(x^m*(e*(m+1)+2*f*(-1+m)*x^2)/(e^2+4*e*f*x^2+4*f^2*x^4-4*d*f*x^(2+2*m)),x)","-\frac{\ln \left(x^{m}-\frac{\left(2 f \,x^{2}+e \right) \sqrt{d f}}{2 d f x}\right)}{4 \sqrt{d f}}+\frac{\ln \left(x^{m}+\frac{\left(2 f \,x^{2}+e \right) \sqrt{d f}}{2 d f x}\right)}{4 \sqrt{d f}}"," ",0,"1/4/(d*f)^(1/2)*ln(x^m+1/2*(2*f*x^2+e)*(d*f)^(1/2)/d/f/x)-1/4/(d*f)^(1/2)*ln(x^m-1/2*(2*f*x^2+e)*(d*f)^(1/2)/d/f/x)","B"
536,1,74,30,0.010000," ","int(x*(-2*f*x^3+2*e)/(4*f^2*x^6+4*d*f*x^4+4*e*f*x^3+e^2),x)","-\frac{\left(\RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)^{4} f -\RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right) e \right) \ln \left(-\RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)+x \right)}{2 f \left(6 f \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)^{5}+4 d \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)^{3}+3 e \RootOf \left(4 f^{2} \textit{\_Z}^{6}+4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)^{2}\right)}"," ",0,"-1/2/f*sum((_R^4*f-_R*e)/(6*_R^5*f+4*_R^3*d+3*_R^2*e)*ln(-_R+x),_R=RootOf(4*_Z^6*f^2+4*_Z^4*d*f+4*_Z^3*e*f+e^2))","C"
537,1,74,30,0.011000," ","int(x*(-2*f*x^3+2*e)/(4*f^2*x^6-4*d*f*x^4+4*e*f*x^3+e^2),x)","-\frac{\left(\RootOf \left(4 f^{2} \textit{\_Z}^{6}-4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)^{4} f -\RootOf \left(4 f^{2} \textit{\_Z}^{6}-4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right) e \right) \ln \left(-\RootOf \left(4 f^{2} \textit{\_Z}^{6}-4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)+x \right)}{2 f \left(6 f \RootOf \left(4 f^{2} \textit{\_Z}^{6}-4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)^{5}-4 d \RootOf \left(4 f^{2} \textit{\_Z}^{6}-4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)^{3}+3 e \RootOf \left(4 f^{2} \textit{\_Z}^{6}-4 d f \,\textit{\_Z}^{4}+4 e f \,\textit{\_Z}^{3}+e^{2}\right)^{2}\right)}"," ",0,"-1/2/f*sum((_R^4*f-_R*e)/(6*_R^5*f-4*_R^3*d+3*_R^2*e)*ln(-_R+x),_R=RootOf(4*_Z^6*f^2-4*_Z^4*d*f+4*_Z^3*e*f+e^2))","C"
538,1,42,32,0.004000," ","int(x^2/(4*d*f*x^6+4*f^2*x^6+4*e*f*x^3+e^2),x)","\frac{\arctan \left(\frac{2 \left(4 d f +4 f^{2}\right) x^{3}+4 e f}{4 \sqrt{d f}\, e}\right)}{6 \sqrt{d f}\, e}"," ",0,"1/6/(d*f)^(1/2)/e*arctan(1/4*(2*(4*d*f+4*f^2)*x^3+4*e*f)/(d*f)^(1/2)/e)","A"
539,1,42,34,0.005000," ","int(x^2/(-4*d*f*x^6+4*f^2*x^6+4*e*f*x^3+e^2),x)","\frac{\arctanh \left(\frac{2 \left(4 d f -4 f^{2}\right) x^{3}-4 e f}{4 \sqrt{d f}\, e}\right)}{6 \sqrt{d f}\, e}"," ",0,"1/6/(d*f)^(1/2)/e*arctanh(1/4*(2*(4*d*f-4*f^2)*x^3-4*e*f)/(d*f)^(1/2)/e)","A"
540,1,78,32,0.052000," ","int(x^m*(e*(m+1)+2*f*(-2+m)*x^3)/(e^2+4*e*f*x^3+4*f^2*x^6+4*d*f*x^(2+2*m)),x)","\frac{\ln \left(x^{m}-\frac{\left(2 f \,x^{3}+e \right) \sqrt{-d f}}{2 d f x}\right)}{4 \sqrt{-d f}}-\frac{\ln \left(x^{m}+\frac{\left(2 f \,x^{3}+e \right) \sqrt{-d f}}{2 d f x}\right)}{4 \sqrt{-d f}}"," ",0,"-1/4/(-d*f)^(1/2)*ln(x^m+1/2*(2*f*x^3+e)*(-d*f)^(1/2)/d/f/x)+1/4/(-d*f)^(1/2)*ln(x^m-1/2*(2*f*x^3+e)*(-d*f)^(1/2)/d/f/x)","B"
541,1,74,32,0.055000," ","int(x^m*(e*(m+1)+2*f*(-2+m)*x^3)/(e^2+4*e*f*x^3+4*f^2*x^6-4*d*f*x^(2+2*m)),x)","-\frac{\ln \left(x^{m}-\frac{\left(2 f \,x^{3}+e \right) \sqrt{d f}}{2 d f x}\right)}{4 \sqrt{d f}}+\frac{\ln \left(x^{m}+\frac{\left(2 f \,x^{3}+e \right) \sqrt{d f}}{2 d f x}\right)}{4 \sqrt{d f}}"," ",0,"1/4/(d*f)^(1/2)*ln(x^m+1/2*(2*f*x^3+e)*(d*f)^(1/2)/d/f/x)-1/4/(d*f)^(1/2)*ln(x^m-1/2*(2*f*x^3+e)*(d*f)^(1/2)/d/f/x)","B"
542,1,84,32,0.089000," ","int(x^m*(e*(m+1)+2*f*(1+m-n)*x^n)/(e^2+4*d*f*x^(2+2*m)+4*e*f*x^n+4*f^2*x^(2*n)),x)","\frac{\ln \left(x^{n}+\frac{-2 d f x \,x^{m}+\sqrt{-d f}\, e}{2 \sqrt{-d f}\, f}\right)}{4 \sqrt{-d f}}-\frac{\ln \left(x^{n}+\frac{2 d f x \,x^{m}+\sqrt{-d f}\, e}{2 \sqrt{-d f}\, f}\right)}{4 \sqrt{-d f}}"," ",0,"-1/4/(-d*f)^(1/2)*ln(x^n+1/2*(2*d*f*x*x^m+(-d*f)^(1/2)*e)/(-d*f)^(1/2)/f)+1/4/(-d*f)^(1/2)*ln(x^n+1/2*(-2*d*f*x*x^m+(-d*f)^(1/2)*e)/(-d*f)^(1/2)/f)","B"
543,1,78,32,0.084000," ","int(x^m*(e*(m+1)+2*f*(1+m-n)*x^n)/(e^2-4*d*f*x^(2+2*m)+4*e*f*x^n+4*f^2*x^(2*n)),x)","-\frac{\ln \left(x^{n}+\frac{-2 d f x \,x^{m}+\sqrt{d f}\, e}{2 \sqrt{d f}\, f}\right)}{4 \sqrt{d f}}+\frac{\ln \left(x^{n}+\frac{2 d f x \,x^{m}+\sqrt{d f}\, e}{2 \sqrt{d f}\, f}\right)}{4 \sqrt{d f}}"," ",0,"1/4/(d*f)^(1/2)*ln(x^n+1/2*(2*d*f*x*x^m+(d*f)^(1/2)*e)/(d*f)^(1/2)/f)-1/4/(d*f)^(1/2)*ln(x^n+1/2*(-2*d*f*x*x^m+(d*f)^(1/2)*e)/(d*f)^(1/2)/f)","B"
544,1,4947,122,0.092000," ","int(x^5/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x)","\text{output too large to display}"," ",0,"-a/c^3/b^3*d^2*ln(b*c^2*x^2+a*c^2-d^2)-1/3*d*(b*x^2+a)^(3/2)/b^3/c^2-1/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*a*d^3+1/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^2*d^5/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))*a+1/2/b^3/c^5*d^4*ln(b*c^2*x^2+a*c^2-d^2)-1/2*a/c/b^2*x^2+1/2*a^2/c/b^3*ln(b*c^2*x^2+a*c^2-d^2)+1/2/b^2/c^3*d^2*x^2-1/2/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))*a^2-1/2/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^4*d^7/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))-1/2*d/b^2*c^2*a^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(b*(x+(-a*b)^(1/2)/b)^2-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)-1/2*d/b^2*c^2*a^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(b*(x-(-a*b)^(1/2)/b)^2+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)+1/2*d/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*c^2*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*a^2-1/2*d/b^(5/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln((-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*a^2-1/2/b^(5/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^4*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln((-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*d^5-1/2/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))*a^2-1/2/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^4*d^7/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))+1/2*d/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*c^2*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*a^2+1/2*d/b^(5/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*a^2+1/2/b^(5/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^4*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*d^5+1/4/b/c*x^4+1/2*d/b^(5/2)*c^2*a^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-a*b)^(1/2)*ln((b*(x+(-a*b)^(1/2)/b)-(-a*b)^(1/2))/b^(1/2)+(b*(x+(-a*b)^(1/2)/b)^2-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))-1/2*d/b^(5/2)*c^2*a^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-a*b)^(1/2)*ln((b*(x-(-a*b)^(1/2)/b)+(-a*b)^(1/2))/b^(1/2)+(b*(x-(-a*b)^(1/2)/b)^2+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))+1/b^(5/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^2*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln((-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*a*d^3+1/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^2*d^5/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))*a-1/b^(5/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^2*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*a*d^3+1/2/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^2*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*d^5-1/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*a*d^3+1/2/b^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/c^2*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*d^5","B"
545,1,3410,63,0.040000," ","int(x^3/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x)","\text{output too large to display}"," ",0,"-1/2*d*c^2*a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b*(b*(x+(-a*b)^(1/2)/b)^2-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)+1/2*d*c^2*a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b^(3/2)*(-a*b)^(1/2)*ln((b*(x+(-a*b)^(1/2)/b)-(-a*b)^(1/2))/b^(1/2)+(b*(x+(-a*b)^(1/2)/b)^2-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))-1/2*d*c^2*a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b*(b*(x-(-a*b)^(1/2)/b)^2+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)-1/2*d*c^2*a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b^(3/2)*(-a*b)^(1/2)*ln((b*(x-(-a*b)^(1/2)/b)+(-a*b)^(1/2))/b^(1/2)+(b*(x-(-a*b)^(1/2)/b)^2+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))+1/2*d/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*a*c^2-1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*d^3-1/2*d/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b^(3/2)*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln((-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*a+1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b^(3/2)*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*ln((-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*d^3-1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))*a+1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b/c^2*d^5/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))+1/2*d/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*a*c^2-1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)*d^3+1/2*d/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b^(3/2)*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*a-1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b^(3/2)*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*ln(((-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))*d^3-1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))*a+1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/b/c^2*d^5/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))-1/2*a/c/b^2*ln(b*c^2*x^2+a*c^2-d^2)+1/2*x^2/b/c+1/2/b^2/c^3*d^2*ln(b*c^2*x^2+a*c^2-d^2)","B"
546,1,1931,21,0.037000," ","int(x/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x)","\frac{d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{\frac{d^{2}}{c^{2}}}}+\frac{d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{\frac{d^{2}}{c^{2}}}}+\frac{\sqrt{-a b}\, c^{2} d \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) b +\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{b}}-\frac{\sqrt{-a b}\, c^{2} d \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b -\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{b}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\, c^{2} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\, c^{2} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, c^{2} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, c^{2} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, d \ln \left(\frac{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{b}}-\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, d \ln \left(\frac{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{b}}+\frac{\ln \left(b \,c^{2} x^{2}+a \,c^{2}-d^{2}\right)}{2 b c}"," ",0,"1/2*d*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*(b*(x+(-a*b)^(1/2)/b)^2-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)-1/2*d*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*(-a*b)^(1/2)*ln((b*(x+(-a*b)^(1/2)/b)-(-a*b)^(1/2))/b^(1/2)+(b*(x+(-a*b)^(1/2)/b)^2-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))/b^(1/2)+1/2*d*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*(b*(x-(-a*b)^(1/2)/b)^2+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)+1/2*d*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*(-a*b)^(1/2)*ln((b*(x-(-a*b)^(1/2)/b)+(-a*b)^(1/2))/b^(1/2)+(b*(x-(-a*b)^(1/2)/b)^2+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))/b^(1/2)-1/2*d*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)+1/2*d/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln((-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/b^(1/2)+1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))-1/2*d*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2)-1/2*d/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((-(a*c^2-d^2)*b*c^2)^(1/2)/c^2+b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))/b^(1/2)+(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/b^(1/2)+1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+2*(1/c^2*d^2)^(1/2)*(b*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)+1/c^2*d^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))+1/2/b/c*ln(b*c^2*x^2+a*c^2-d^2)","B"
547,1,2175,80,0.042000," ","int(1/x/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x)","\frac{b \,c^{2} d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{\frac{d^{2}}{c^{2}}}}+\frac{b \,c^{2} d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{\frac{d^{2}}{c^{2}}}}-\frac{\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, b \,c^{4} d}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, b \,c^{4} d}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \sqrt{b}\, c^{2} d \ln \left(\frac{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \sqrt{b}\, c^{2} d \ln \left(\frac{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\sqrt{-a b}\, \sqrt{b}\, c^{2} d \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) b +\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a}-\frac{\sqrt{-a b}\, \sqrt{b}\, c^{2} d \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b -\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a}-\frac{a \,c^{3} \ln \left(b \,c^{2} x^{2}+a \,c^{2}-d^{2}\right)}{2 \left(a \,c^{2}-d^{2}\right) d^{2}}+\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\, b \,c^{2} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\, b \,c^{2} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a}+\frac{c \ln \left(x \right)}{a \,c^{2}-d^{2}}+\frac{d \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(a \,c^{2}-d^{2}\right) \sqrt{a}}-\frac{\sqrt{b \,x^{2}+a}\, d}{\left(a \,c^{2}-d^{2}\right) a}+\frac{c \ln \left(b \,c^{2} x^{2}+a \,c^{2}-d^{2}\right)}{2 d^{2}}"," ",0,"-1/2*a*c^3/(a*c^2-d^2)/d^2*ln(b*c^2*x^2+a*c^2-d^2)+c*ln(x)/(a*c^2-d^2)+1/2*c/d^2*ln(b*c^2*x^2+a*c^2-d^2)+1/2*d*b*c^2/a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)-1/2*d*b^(1/2)*c^2/a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*b-(-a*b)^(1/2))/b^(1/2)+((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))+1/2*d*b*c^2/a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)+1/2*d*b^(1/2)*c^2/a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*b+(-a*b)^(1/2))/b^(1/2)+((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))-1/2*d*b*c^4/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)+1/2*d*b^(1/2)*c^2/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))+1/2*b*c^2/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))+d/a^(1/2)/(a*c^2-d^2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-d/a/(a*c^2-d^2)*(b*x^2+a)^(1/2)-1/2*d*b*c^4/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)-1/2*d*b^(1/2)*c^2/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b+(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))+1/2*b*c^2/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))","B"
548,1,2459,137,0.054000," ","int(1/x^3/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x)","-\frac{b^{2} c^{4} d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right)^{2} \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{\frac{d^{2}}{c^{2}}}}-\frac{b^{2} c^{4} d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right)^{2} \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{\frac{d^{2}}{c^{2}}}}+\frac{\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, b^{2} c^{6} d}{2 \left(a \,c^{2}-d^{2}\right)^{2} \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, b^{2} c^{6} d}{2 \left(a \,c^{2}-d^{2}\right)^{2} \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, b^{\frac{3}{2}} c^{4} d \ln \left(\frac{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right)^{2} \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, b^{\frac{3}{2}} c^{4} d \ln \left(\frac{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right)^{2} \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{a b \,c^{5} \ln \left(b \,c^{2} x^{2}+a \,c^{2}-d^{2}\right)}{2 \left(a \,c^{2}-d^{2}\right)^{2} d^{2}}-\frac{2 b \,c^{3} \ln \left(x \right)}{\left(a \,c^{2}-d^{2}\right)^{2}}-\frac{2 b \,c^{2} d \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(a \,c^{2}-d^{2}\right)^{2} \sqrt{a}}+\frac{b c \,d^{2} \ln \left(x \right)}{\left(a \,c^{2}-d^{2}\right)^{2} a}+\frac{b \,d^{3} \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\left(a \,c^{2}-d^{2}\right)^{2} a^{\frac{3}{2}}}-\frac{\sqrt{-a b}\, b^{\frac{3}{2}} c^{2} d \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) b +\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a^{2}}+\frac{\sqrt{-a b}\, b^{\frac{3}{2}} c^{2} d \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b -\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a^{2}}+\frac{2 \sqrt{b \,x^{2}+a}\, b \,c^{2} d}{\left(a \,c^{2}-d^{2}\right)^{2} a}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\, b^{2} c^{2} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\, b^{2} c^{2} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a^{2}}-\frac{b \,c^{3} \ln \left(b \,c^{2} x^{2}+a \,c^{2}-d^{2}\right)}{2 \left(a \,c^{2}-d^{2}\right) d^{2}}+\frac{b c \ln \left(x \right)}{\left(a \,c^{2}-d^{2}\right) a}-\frac{\sqrt{b \,x^{2}+a}\, b \,d^{3}}{\left(a \,c^{2}-d^{2}\right)^{2} a^{2}}+\frac{b d \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 \left(a \,c^{2}-d^{2}\right) a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{2}+a}\, b d}{2 \left(a \,c^{2}-d^{2}\right) a^{2}}-\frac{c}{2 \left(a \,c^{2}-d^{2}\right) x^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} d}{2 \left(a \,c^{2}-d^{2}\right) a^{2} x^{2}}"," ",0,"1/2*a*c^5*b/(a*c^2-d^2)^2/d^2*ln(b*c^2*x^2+a*c^2-d^2)-1/2*c/(a*c^2-d^2)/x^2-2*b*c^3*ln(x)/(a*c^2-d^2)^2+1/a*c*b/(a*c^2-d^2)^2*ln(x)*d^2-1/2*b*c^3/(a*c^2-d^2)/d^2*ln(b*c^2*x^2+a*c^2-d^2)+b*c/a/(a*c^2-d^2)*ln(x)-1/2*d*b^2*c^2/a^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)+1/2*d*b^(3/2)*c^2/a^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*b-(-a*b)^(1/2))/b^(1/2)+((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))-1/2*d*b^2*c^2/a^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)-1/2*d*b^(3/2)*c^2/a^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*b+(-a*b)^(1/2))/b^(1/2)+((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))+1/2*d/a^2/(a*c^2-d^2)/x^2*(b*x^2+a)^(3/2)+1/2*d/a^(3/2)/(a*c^2-d^2)*b*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)-1/2*d/a^2/(a*c^2-d^2)*b*(b*x^2+a)^(1/2)+1/2*d*b^2*c^6/(a*c^2-d^2)^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)-1/2*d*b^(3/2)*c^4/(a*c^2-d^2)^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))-1/2*b^2*c^4/(a*c^2-d^2)^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))-2*d*b/a^(1/2)/(a*c^2-d^2)^2*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)*c^2+2*d*b/a/(a*c^2-d^2)^2*(b*x^2+a)^(1/2)*c^2+b/a^(3/2)/(a*c^2-d^2)^2*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)*d^3-b/a^2/(a*c^2-d^2)^2*(b*x^2+a)^(1/2)*d^3+1/2*d*b^2*c^6/(a*c^2-d^2)^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)+1/2*d*b^(3/2)*c^4/(a*c^2-d^2)^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*(-(a*c^2-d^2)*b*c^2)^(1/2)*ln(((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b+(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))-1/2*b^2*c^4/(a*c^2-d^2)^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))","B"
549,1,3485,123,0.044000," ","int(x^2/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x)","\text{output too large to display}"," ",0,"1/2*d*c^2*a/(-a*b)^(1/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)-1/2*d*c^2*a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x+(-a*b)^(1/2)/b)*b-(-a*b)^(1/2))/b^(1/2)+((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))/b^(1/2)-1/2*d*c^2*a/(-a*b)^(1/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)-1/2*d*c^2*a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x-(-a*b)^(1/2)/b)*b+(-a*b)^(1/2))/b^(1/2)+((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))/b^(1/2)-1/2*d*c^4/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)*a+1/2*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)*d^3+1/2*d*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/b^(1/2)*a-1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/b^(1/2)*d^3+1/2*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))*a-1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*d^5/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))+1/2*d*c^4/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)*a-1/2*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)*d^3+1/2*d*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b+(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/b^(1/2)*a-1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b+(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/b^(1/2)*d^3-1/2*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))*a+1/2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*d^5/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))-a/b/((a*c^2-d^2)*b)^(1/2)*arctan(x*b*c/((a*c^2-d^2)*b)^(1/2))+x/b/c+1/b/c^2*d^2/((a*c^2-d^2)*b)^(1/2)*arctan(x*b*c/((a*c^2-d^2)*b)^(1/2))","B"
550,1,1995,85,0.040000," ","int(1/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x)","\frac{b \,c^{2} d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \sqrt{\frac{d^{2}}{c^{2}}}}-\frac{b \,c^{2} d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \sqrt{\frac{d^{2}}{c^{2}}}}+\frac{\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, b \,c^{4} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}-\frac{\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, b \,c^{4} d}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}+\frac{\sqrt{b}\, c^{2} d \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) b +\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\sqrt{b}\, c^{2} d \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b -\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{\sqrt{b}\, c^{2} d \ln \left(\frac{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{\sqrt{b}\, c^{2} d \ln \left(\frac{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\, b \,c^{2} d}{2 \sqrt{-a b}\, \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\, b \,c^{2} d}{2 \sqrt{-a b}\, \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(-\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}+\frac{\arctan \left(\frac{b c x}{\sqrt{\left(a \,c^{2}-d^{2}\right) b}}\right)}{\sqrt{\left(a \,c^{2}-d^{2}\right) b}}"," ",0,"-1/2*d*b*c^2/(-a*b)^(1/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)+1/2*d*b^(1/2)*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x+(-a*b)^(1/2)/b)*b-(-a*b)^(1/2))/b^(1/2)+((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))+1/2*d*b*c^2/(-a*b)^(1/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)+1/2*d*b^(1/2)*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x-(-a*b)^(1/2)/b)*b+(-a*b)^(1/2))/b^(1/2)+((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))+1/2*d*b*c^4/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)-1/2*d*b^(1/2)*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))-1/2*b*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))-1/2*d*b*c^4/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)-1/2*d*b^(1/2)*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b+(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))+1/2*b*c^2/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))+1/((a*c^2-d^2)*b)^(1/2)*arctan(x*b*c/((a*c^2-d^2)*b)^(1/2))","B"
551,1,2289,140,0.048000," ","int(1/x^2/(a*c+b*c*x^2+d*(b*x^2+a)^(1/2)),x)","\frac{b^{2} c^{4} d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \sqrt{\frac{d^{2}}{c^{2}}}}-\frac{b^{2} c^{4} d^{3} \ln \left(\frac{\frac{2 d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}+2 \sqrt{\frac{d^{2}}{c^{2}}}\, \sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}}{x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \sqrt{\frac{d^{2}}{c^{2}}}}+\frac{\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, b^{2} c^{6} d}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}-\frac{\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\, b^{2} c^{6} d}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}-\frac{b^{\frac{3}{2}} c^{4} d \ln \left(\frac{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}-\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{b^{\frac{3}{2}} c^{4} d \ln \left(\frac{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right) b +\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{c^{2}}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)^{2} b +\frac{d^{2}}{c^{2}}+\frac{2 \sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\, \left(x -\frac{\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}}{b \,c^{2}}\right)}{c^{2}}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right)}-\frac{a b \,c^{4} \arctan \left(\frac{b c x}{\sqrt{\left(a \,c^{2}-d^{2}\right) b}}\right)}{\left(a \,c^{2}-d^{2}\right) \sqrt{\left(a \,c^{2}-d^{2}\right) b}\, d^{2}}+\frac{b^{\frac{3}{2}} c^{2} d \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) b +\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a}+\frac{b^{\frac{3}{2}} c^{2} d \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b -\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\, b^{2} c^{2} d}{2 \sqrt{-a b}\, \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a}+\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\, b^{2} c^{2} d}{2 \sqrt{-a b}\, \left(\sqrt{-a b}\, c^{2}+\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) \left(\sqrt{-a b}\, c^{2}-\sqrt{-\left(a \,c^{2}-d^{2}\right) b \,c^{2}}\right) a}+\frac{b \,c^{2} \arctan \left(\frac{b c x}{\sqrt{\left(a \,c^{2}-d^{2}\right) b}}\right)}{\sqrt{\left(a \,c^{2}-d^{2}\right) b}\, d^{2}}-\frac{\sqrt{b}\, d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\left(a \,c^{2}-d^{2}\right) a}-\frac{\sqrt{b \,x^{2}+a}\, b d x}{\left(a \,c^{2}-d^{2}\right) a^{2}}-\frac{c}{\left(a \,c^{2}-d^{2}\right) x}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} d}{\left(a \,c^{2}-d^{2}\right) a^{2} x}"," ",0,"b*c^2/d^2/((a*c^2-d^2)*b)^(1/2)*arctan(1/((a*c^2-d^2)*b)^(1/2)*b*c*x)-c/(a*c^2-d^2)/x-a*c^4/(a*c^2-d^2)*b/d^2/((a*c^2-d^2)*b)^(1/2)*arctan(1/((a*c^2-d^2)*b)^(1/2)*b*c*x)-1/2*d*b^2*c^2/a/(-a*b)^(1/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)+1/2*d*b^(3/2)*c^2/a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x+(-a*b)^(1/2)/b)*b-(-a*b)^(1/2))/b^(1/2)+((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))+d/a^2/(a*c^2-d^2)/x*(b*x^2+a)^(3/2)-d/a^2/(a*c^2-d^2)*b*x*(b*x^2+a)^(1/2)-d/a/(a*c^2-d^2)*b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*d*b^2*c^2/a/(-a*b)^(1/2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)+1/2*d*b^(3/2)*c^2/a/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x-(-a*b)^(1/2)/b)*b+(-a*b)^(1/2))/b^(1/2)+((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))+1/2*d*b^2*c^6/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)-1/2*d*b^(3/2)*c^4/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b-(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))-1/2*b^2*c^4/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2-2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x+(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))-1/2*d*b^2*c^6/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2)-1/2*d*b^(3/2)*c^4/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))*ln(((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)*b+(-(a*c^2-d^2)*b*c^2)^(1/2)/c^2)/b^(1/2)+((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))+1/2*b^2*c^4/(a*c^2-d^2)/((-a*b)^(1/2)*c^2+(-(a*c^2-d^2)*b*c^2)^(1/2))/((-a*b)^(1/2)*c^2-(-(a*c^2-d^2)*b*c^2)^(1/2))/(-(a*c^2-d^2)*b*c^2)^(1/2)*d^3/(1/c^2*d^2)^(1/2)*ln((2/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2+2*(1/c^2*d^2)^(1/2)*((x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)^2*b+1/c^2*d^2+2*(-(a*c^2-d^2)*b*c^2)^(1/2)*(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2)/c^2)^(1/2))/(x-(-(a*c^2-d^2)*b*c^2)^(1/2)/b/c^2))","B"
552,1,1473,124,0.182000," ","int(x^8/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","\frac{x^{6}}{6 b c}-\frac{a \,x^{3}}{3 b^{2} c}+\frac{d^{2} x^{3}}{3 b^{2} c^{3}}+\frac{a^{2} \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 b^{3} c}-\frac{2 a \,d^{2} \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 b^{3} c^{3}}-\frac{i a^{2} \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{5} d \sqrt{b \,x^{3}+a}}+\frac{4 \sqrt{b \,x^{3}+a}\, a d}{3 b^{3} c^{2}}+\frac{d^{4} \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 b^{3} c^{5}}+\frac{2 i a d \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{5} c^{2} \sqrt{b \,x^{3}+a}}-\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} d}{9 b^{3} c^{2}}-\frac{2 \sqrt{b \,x^{3}+a}\, d^{3}}{3 b^{3} c^{4}}-\frac{i d^{3} \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{5} c^{4} \sqrt{b \,x^{3}+a}}"," ",0,"-2/9*d*(b*x^3+a)^(3/2)/b^3/c^2+4/3*d/b^3/c^2*(b*x^3+a)^(1/2)*a-2/3/b^3/c^4*d^3*(b*x^3+a)^(1/2)-1/3*I/b^5/d*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*b*(2*x+1/b*((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(b*(x-1/b*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*b*(2*x+1/b*((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(b*x^3+a)^(1/2)*(I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)+2*_alpha^2*b^2-(-a*b^2)^(1/3)*_alpha*b-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/b*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(-a*b^2)^(1/3))*3^(1/2)*b/(-a*b^2)^(1/3))^(1/2),-1/2/b*c^2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*a*b-3*(-a*b^2)^(2/3)*_alpha-3*a*b)/d^2,(I*3^(1/2)/b*(-a*b^2)^(1/3)/(-3/2/b*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/b*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))*a^2+2/3*I*d/b^5/c^2*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*b*(2*x+1/b*((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(b*(x-1/b*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*b*(2*x+1/b*((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(b*x^3+a)^(1/2)*(I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)+2*_alpha^2*b^2-(-a*b^2)^(1/3)*_alpha*b-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/b*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(-a*b^2)^(1/3))*3^(1/2)*b/(-a*b^2)^(1/3))^(1/2),-1/2/b*c^2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*a*b-3*(-a*b^2)^(2/3)*_alpha-3*a*b)/d^2,(I*3^(1/2)/b*(-a*b^2)^(1/3)/(-3/2/b*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/b*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))*a-1/3*I/b^5/c^4*d^3*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*b*(2*x+1/b*((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)*(b*(x-1/b*(-a*b^2)^(1/3))/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))^(1/2)*(-1/2*I*b*(2*x+1/b*((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3)))/(-a*b^2)^(1/3))^(1/2)/(b*x^3+a)^(1/2)*(I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)+2*_alpha^2*b^2-(-a*b^2)^(1/3)*_alpha*b-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2/b*(-a*b^2)^(1/3)-1/2*I*3^(1/2)/b*(-a*b^2)^(1/3))*3^(1/2)*b/(-a*b^2)^(1/3))^(1/2),-1/2/b*c^2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha+I*3^(1/2)*a*b-3*(-a*b^2)^(2/3)*_alpha-3*a*b)/d^2,(I*3^(1/2)/b*(-a*b^2)^(1/3)/(-3/2/b*(-a*b^2)^(1/3)+1/2*I*3^(1/2)/b*(-a*b^2)^(1/3)))^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))-1/3*a/c/b^2*x^3+1/3*a^2/c/b^3*ln(b*c^2*x^3+a*c^2-d^2)-2/3*a/c^3/b^3*d^2*ln(b*c^2*x^3+a*c^2-d^2)+1/6/b/c*x^6+1/3/b^2/c^3*x^3*d^2+1/3/b^3/c^5*d^4*ln(b*c^2*x^3+a*c^2-d^2)","C"
553,1,943,63,0.026000," ","int(x^5/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","\frac{x^{3}}{3 b c}-\frac{a \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 b^{2} c}+\frac{d^{2} \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 b^{2} c^{3}}+\frac{i a \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{4} d \sqrt{b \,x^{3}+a}}-\frac{2 \sqrt{b \,x^{3}+a}\, d}{3 b^{2} c^{2}}-\frac{i d \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{4} c^{2} \sqrt{b \,x^{3}+a}}"," ",0,"-2/3*d*(b*x^3+a)^(1/2)/b^2/c^2+1/3*I/b^4/d*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))*a-1/3*I*d/b^4/c^2*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))-1/3*a/c/b^2*ln(b*c^2*x^3+a*c^2-d^2)+1/3*x^3/b/c+1/3/b^2/c^3*d^2*ln(b*c^2*x^3+a*c^2-d^2)","C"
554,1,455,22,0.027000," ","int(x^2/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","\frac{\ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 b c}-\frac{i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{3} d \sqrt{b \,x^{3}+a}}"," ",0,"-1/3*I/d/b^3*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))+1/3/b/c*ln(b*c^2*x^3+a*c^2-d^2)","C"
555,1,636,81,0.059000," ","int(1/x/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","-\frac{a \,c^{3} \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 \left(a \,c^{2}-d^{2}\right) d^{2}}+\frac{c \ln \left(x \right)}{a \,c^{2}-d^{2}}+\frac{2 d \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \left(a \,c^{2}-d^{2}\right) \sqrt{a}}+\frac{2 \sqrt{b \,x^{3}+a}\, c^{2}}{3 \left(a \,c^{2}-d^{2}\right) d}-\frac{2 \sqrt{b \,x^{3}+a}\, d}{3 \left(a \,c^{2}-d^{2}\right) a}+\frac{i c^{2} \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \left(a \,c^{2}-d^{2}\right) b^{2} d \sqrt{b \,x^{3}+a}}+\frac{c \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 d^{2}}-\frac{2 \sqrt{b \,x^{3}+a}}{3 a d}"," ",0,"1/(a*c^2-d^2)*c*ln(x)-1/3*a*c^3/(a*c^2-d^2)/d^2*ln(b*c^2*x^3+a*c^2-d^2)+1/3*c/d^2*ln(b*c^2*x^3+a*c^2-d^2)-2/3/a/d*(b*x^3+a)^(1/2)-2/3*d/a/(a*c^2-d^2)*(b*x^3+a)^(1/2)+2/3*d*arctanh((b*x^3+a)^(1/2)/a^(1/2))/(a*c^2-d^2)/a^(1/2)+2/3*c^2/(a*c^2-d^2)/d*(b*x^3+a)^(1/2)+1/3*I/b^2*c^2/(a*c^2-d^2)/d*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))","C"
556,1,863,138,0.073000," ","int(1/x^4/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","\frac{a b \,c^{5} \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 \left(a \,c^{2}-d^{2}\right)^{2} d^{2}}-\frac{2 b \,c^{3} \ln \left(x \right)}{\left(a \,c^{2}-d^{2}\right)^{2}}-\frac{4 b \,c^{2} d \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \left(a \,c^{2}-d^{2}\right)^{2} \sqrt{a}}+\frac{b c \,d^{2} \ln \left(x \right)}{\left(a \,c^{2}-d^{2}\right)^{2} a}-\frac{2 \sqrt{b \,x^{3}+a}\, b \,c^{4}}{3 \left(a \,c^{2}-d^{2}\right)^{2} d}+\frac{2 b \,d^{3} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \left(a \,c^{2}-d^{2}\right)^{2} a^{\frac{3}{2}}}+\frac{4 \sqrt{b \,x^{3}+a}\, b \,c^{2} d}{3 \left(a \,c^{2}-d^{2}\right)^{2} a}-\frac{b \,c^{3} \ln \left(b \,c^{2} x^{3}+a \,c^{2}-d^{2}\right)}{3 \left(a \,c^{2}-d^{2}\right) d^{2}}-\frac{i c^{4} \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \left(a \,c^{2}-d^{2}\right)^{2} b d \sqrt{b \,x^{3}+a}}+\frac{b c \ln \left(x \right)}{\left(a \,c^{2}-d^{2}\right) a}-\frac{2 \sqrt{b \,x^{3}+a}\, b \,d^{3}}{3 \left(a \,c^{2}-d^{2}\right)^{2} a^{2}}+\frac{b d \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \left(a \,c^{2}-d^{2}\right) a^{\frac{3}{2}}}+\frac{2 \sqrt{b \,x^{3}+a}\, b}{3 a^{2} d}-\frac{c}{3 \left(a \,c^{2}-d^{2}\right) x^{3}}+\frac{\sqrt{b \,x^{3}+a}\, d}{3 \left(a \,c^{2}-d^{2}\right) a \,x^{3}}"," ",0,"-1/3*c/(a*c^2-d^2)/x^3-2/(a*c^2-d^2)^2*b*c^3*ln(x)+1/(a*c^2-d^2)^2/a*b*c*d^2*ln(x)+1/3*a*c^5*b/(a*c^2-d^2)^2/d^2*ln(b*c^2*x^3+a*c^2-d^2)+1/(a*c^2-d^2)/a*b*c*ln(x)-1/3*b*c^3/(a*c^2-d^2)/d^2*ln(b*c^2*x^3+a*c^2-d^2)+2/3*b/d/a^2*(b*x^3+a)^(1/2)+1/3*d/a/(a*c^2-d^2)*(b*x^3+a)^(1/2)/x^3+1/3*d/a^(3/2)/(a*c^2-d^2)*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))+4/3*d*b/a/(a*c^2-d^2)^2*(b*x^3+a)^(1/2)*c^2-2/3*b/a^2/(a*c^2-d^2)^2*(b*x^3+a)^(1/2)*d^3-4/3*d*b/a^(1/2)/(a*c^2-d^2)^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))*c^2+2/3*b/a^(3/2)/(a*c^2-d^2)^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))*d^3-2/3*b*c^4/(a*c^2-d^2)^2/d*(b*x^3+a)^(1/2)-1/3*I/b*c^4/(a*c^2-d^2)^2/d*2^(1/2)*sum((-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))","C"
557,1,1544,251,0.076000," ","int(x^3/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","-\frac{\sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b^{2} c}-\frac{a \ln \left(x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b^{2} c}+\frac{a \ln \left(x^{2}-\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b^{2} c}+\frac{x}{b c}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b^{2} c^{2}}+\frac{\sqrt{3}\, d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b^{2} c^{3}}+\frac{d^{2} \ln \left(x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b^{2} c^{3}}-\frac{d^{2} \ln \left(x^{2}-\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b^{2} c^{3}}+\frac{i a \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{4} d \sqrt{b \,x^{3}+a}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2}}-\frac{i d \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{4} c^{2} \sqrt{b \,x^{3}+a}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2}}"," ",0,"2/3*I*d/b^2/c^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)*b/(-a*b^2)^(1/3))^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+1/3*I/b^4/d*2^(1/2)*sum(1/_alpha^2*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))*a-1/3*I*d/b^4/c^2*2^(1/2)*sum(1/_alpha^2*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))-1/3*a/c/b^2/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x+((a*c^2-d^2)/b/c^2)^(1/3))+1/6*a/c/b^2/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x^2-((a*c^2-d^2)/b/c^2)^(1/3)*x+((a*c^2-d^2)/b/c^2)^(2/3))-1/3*a/c/b^2/((a*c^2-d^2)/b/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/((a*c^2-d^2)/b/c^2)^(1/3)*x-1))+x/b/c+1/3/b^2/c^3*d^2/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x+((a*c^2-d^2)/b/c^2)^(1/3))-1/6/b^2/c^3*d^2/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x^2-((a*c^2-d^2)/b/c^2)^(1/3)*x+((a*c^2-d^2)/b/c^2)^(2/3))+1/3/b^2/c^3*d^2/((a*c^2-d^2)/b/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/((a*c^2-d^2)/b/c^2)^(1/3)*x-1))","C"
558,1,619,243,0.080000," ","int(x/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} b c}-\frac{\ln \left(x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} b c}+\frac{\ln \left(x^{2}-\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} b c}-\frac{i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{3} d \sqrt{b \,x^{3}+a}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)}"," ",0,"-1/3*I/d/b^3*2^(1/2)*sum(1/_alpha*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))-1/3/b/c/((a*c^2-d^2)/b/c^2)^(1/3)*ln(x+((a*c^2-d^2)/b/c^2)^(1/3))+1/6/b/c/((a*c^2-d^2)/b/c^2)^(1/3)*ln(x^2-((a*c^2-d^2)/b/c^2)^(1/3)*x+((a*c^2-d^2)/b/c^2)^(2/3))+1/3/b/c*3^(1/2)/((a*c^2-d^2)/b/c^2)^(1/3)*arctan(1/3*3^(1/2)*(2/((a*c^2-d^2)/b/c^2)^(1/3)*x-1))","C"
559,1,619,241,0.028000," ","int(1/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b c}+\frac{\ln \left(x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b c}-\frac{\ln \left(x^{2}-\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} b c}-\frac{i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 b^{3} d \sqrt{b \,x^{3}+a}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2}}"," ",0,"-1/3*I/d/b^3*2^(1/2)*sum(1/_alpha^2*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))+1/3/b/c/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x+((a*c^2-d^2)/b/c^2)^(1/3))-1/6/b/c/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x^2-((a*c^2-d^2)/b/c^2)^(1/3)*x+((a*c^2-d^2)/b/c^2)^(2/3))+1/3/b/c/((a*c^2-d^2)/b/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/((a*c^2-d^2)/b/c^2)^(1/3)*x-1))","C"
560,1,3560,261,0.066000," ","int(1/x^2/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","\text{output too large to display}"," ",0,"-1/(a*c^2-d^2)*c/x+1/3*a*c^3/(a*c^2-d^2)/d^2/((a*c^2-d^2)/b/c^2)^(1/3)*ln(x+((a*c^2-d^2)/b/c^2)^(1/3))-1/6*a*c^3/(a*c^2-d^2)/d^2/((a*c^2-d^2)/b/c^2)^(1/3)*ln(x^2-((a*c^2-d^2)/b/c^2)^(1/3)*x+((a*c^2-d^2)/b/c^2)^(2/3))-1/3*a*c^3/(a*c^2-d^2)/d^2*3^(1/2)/((a*c^2-d^2)/b/c^2)^(1/3)*arctan(1/3*3^(1/2)*(2/((a*c^2-d^2)/b/c^2)^(1/3)*x-1))-1/3*c/d^2/((a*c^2-d^2)/b/c^2)^(1/3)*ln(x+((a*c^2-d^2)/b/c^2)^(1/3))+1/6*c/d^2/((a*c^2-d^2)/b/c^2)^(1/3)*ln(x^2-((a*c^2-d^2)/b/c^2)^(1/3)*x+((a*c^2-d^2)/b/c^2)^(2/3))+1/3*c/d^2*3^(1/2)/((a*c^2-d^2)/b/c^2)^(1/3)*arctan(1/3*3^(1/2)*(2/((a*c^2-d^2)/b/c^2)^(1/3)*x-1))-2/3*I/b*c^2/(a*c^2-d^2)/d*3^(1/2)*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-1/a/d*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))/b+2/3*I/a/d*3^(1/2)*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+d/a/(a*c^2-d^2)*(b*x^3+a)^(1/2)/x-3/2*I*d/a/(a*c^2-d^2)*3^(1/2)*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))/b-3/2*d/a/(a*c^2-d^2)*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))/b+I*d/a/(a*c^2-d^2)*3^(1/2)*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+I/b*c^2/(a*c^2-d^2)/d*3^(1/2)*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+1/b*c^2/(a*c^2-d^2)/d*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+1/3*I/b^2*c^2/(a*c^2-d^2)/d*2^(1/2)*sum(1/_alpha*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))-I/a/d*3^(1/2)*(-a*b^2)^(2/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))/b","C"
561,1,1789,262,0.063000," ","int(1/x^3/(a*c+b*c*x^3+d*(b*x^3+a)^(1/2)),x)","-\frac{\sqrt{3}\, a \,c^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a \,c^{2}-d^{2}\right) \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} d^{2}}-\frac{a \,c^{3} \ln \left(x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}\right)}{3 \left(a \,c^{2}-d^{2}\right) \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} d^{2}}+\frac{a \,c^{3} \ln \left(x^{2}-\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}}\right)}{6 \left(a \,c^{2}-d^{2}\right) \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} d^{2}}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, c^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \left(a \,c^{2}-d^{2}\right) \sqrt{b \,x^{3}+a}\, d}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{2 \left(a \,c^{2}-d^{2}\right) \sqrt{b \,x^{3}+a}\, a}+\frac{i c^{2} \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}-i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{\left(x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{-3 \left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{-\frac{i \left(2 x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}+i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}\right) b}{2 \left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(2 \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b^{2}+i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -\left(-a \,b^{2}\right)^{\frac{1}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right) b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}-\left(-a \,b^{2}\right)^{\frac{2}{3}}\right) \EllipticPi \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, -\frac{\left(2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2} b +i \sqrt{3}\, a b -3 a b -i \left(-a \,b^{2}\right)^{\frac{2}{3}} \sqrt{3}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)-3 \left(-a \,b^{2}\right)^{\frac{2}{3}} \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)\right) c^{2}}{2 b \,d^{2}}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \left(a \,c^{2}-d^{2}\right) b^{2} d \sqrt{b \,x^{3}+a}\, \RootOf \left(b \,c^{2} \textit{\_Z}^{3}+a \,c^{2}-d^{2}\right)^{2}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} d^{2}}+\frac{c \ln \left(x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} d^{2}}-\frac{c \ln \left(x^{2}-\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{1}{3}} x +\left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a \,c^{2}-d^{2}}{b \,c^{2}}\right)^{\frac{2}{3}} d^{2}}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, a d}-\frac{c}{2 \left(a \,c^{2}-d^{2}\right) x^{2}}+\frac{\sqrt{b \,x^{3}+a}\, d}{2 \left(a \,c^{2}-d^{2}\right) a \,x^{2}}"," ",0,"1/3*c/d^2/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x+((a*c^2-d^2)/b/c^2)^(1/3))-1/6*c/d^2/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x^2-((a*c^2-d^2)/b/c^2)^(1/3)*x+((a*c^2-d^2)/b/c^2)^(2/3))+1/3*c/d^2/((a*c^2-d^2)/b/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/((a*c^2-d^2)/b/c^2)^(1/3)*x-1))-1/2/(a*c^2-d^2)*c/x^2-1/3*a*c^3/(a*c^2-d^2)/d^2/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x+((a*c^2-d^2)/b/c^2)^(1/3))+1/6*a*c^3/(a*c^2-d^2)/d^2/((a*c^2-d^2)/b/c^2)^(2/3)*ln(x^2-((a*c^2-d^2)/b/c^2)^(1/3)*x+((a*c^2-d^2)/b/c^2)^(2/3))-1/3*a*c^3/(a*c^2-d^2)/d^2/((a*c^2-d^2)/b/c^2)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/((a*c^2-d^2)/b/c^2)^(1/3)*x-1))+2/3*I/a/d*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+1/2*d/a/(a*c^2-d^2)/x^2*(b*x^3+a)^(1/2)+1/2*I*d/a/(a*c^2-d^2)*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I/(a*c^2-d^2)*c^2/d*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+1/3*I/(a*c^2-d^2)/b^2*c^2/d*2^(1/2)*sum(1/_alpha^2*(-a*b^2)^(1/3)*(1/2*I*(2*x+((-a*b^2)^(1/3)-I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3*(-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))*b)^(1/2)*(-1/2*I*(2*x+((-a*b^2)^(1/3)+I*3^(1/2)*(-a*b^2)^(1/3))/b)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*(2*_alpha^2*b^2+I*(-a*b^2)^(1/3)*3^(1/2)*_alpha*b-(-a*b^2)^(1/3)*_alpha*b-I*(-a*b^2)^(2/3)*3^(1/2)-(-a*b^2)^(2/3))*EllipticPi(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),-1/2*(2*I*(-a*b^2)^(1/3)*3^(1/2)*_alpha^2*b+I*3^(1/2)*a*b-3*a*b-I*(-a*b^2)^(2/3)*3^(1/2)*_alpha-3*(-a*b^2)^(2/3)*_alpha)/b*c^2/d^2,(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)),_alpha=RootOf(_Z^3*b*c^2+a*c^2-d^2))","C"
562,0,0,131,0.019000," ","int(1/(a*c+b*c*x^n+d*(a+b*x^n)^(1/2)),x)","\int \frac{1}{b c \,x^{n}+a c +\sqrt{b \,x^{n}+a}\, d}\, dx"," ",0,"int(1/(a*c+b*c*x^n+d*(a+b*x^n)^(1/2)),x)","F"
563,0,0,163,0.023000," ","int(x^m/(b*c*x^n+a*c+(b*x^n+a)^(1/2)*d),x)","\int \frac{x^{m}}{b c \,x^{n}+a c +\sqrt{b \,x^{n}+a}\, d}\, dx"," ",0,"int(x^m/(b*c*x^n+a*c+(b*x^n+a)^(1/2)*d),x)","F"
564,0,0,25,0.024000," ","int(x^(n-1)/(b*c*x^n+a*c+(b*x^n+a)^(1/2)*d),x)","\int \frac{x^{n -1}}{b c \,x^{n}+a c +\sqrt{b \,x^{n}+a}\, d}\, dx"," ",0,"int(x^(n-1)/(b*c*x^n+a*c+(b*x^n+a)^(1/2)*d),x)","F"
565,1,7,6,0.005000," ","int(1/(4*x^(3/2)+x^(1/2)),x)","\arctan \left(2 \sqrt{x}\right)"," ",0,"arctan(2*x^(1/2))","A"
566,1,10,9,0.007000," ","int(1/(-x^(5/2)+x^(1/2)),x)","\arctanh \left(\sqrt{x}\right)+\arctan \left(\sqrt{x}\right)"," ",0,"arctan(x^(1/2))+arctanh(x^(1/2))","A"
567,1,20,21,0.014000," ","int(1/(-x^(1/4)+x^(1/2)),x)","4 \ln \left(x^{\frac{1}{4}}-1\right)+2 \sqrt{x}+4 x^{\frac{1}{4}}"," ",0,"2*x^(1/2)+4*x^(1/4)+4*ln(x^(1/4)-1)","A"
568,1,92,24,0.030000," ","int(1/(x^(1/3)+x^(1/2)),x)","-\ln \left(x -1\right)+\ln \left(\sqrt{x}-1\right)-\ln \left(\sqrt{x}+1\right)-2 \ln \left(x^{\frac{1}{6}}+1\right)-2 \ln \left(x^{\frac{1}{3}}-1\right)+2 \ln \left(x^{\frac{1}{6}}-1\right)+\ln \left(x^{\frac{1}{3}}-x^{\frac{1}{6}}+1\right)-\ln \left(x^{\frac{1}{3}}+x^{\frac{1}{6}}+1\right)+\ln \left(x^{\frac{2}{3}}+x^{\frac{1}{3}}+1\right)+2 \sqrt{x}-3 x^{\frac{1}{3}}+6 x^{\frac{1}{6}}"," ",0,"2*ln(x^(1/6)-1)-ln(x^(1/3)+x^(1/6)+1)+ln(1-x^(1/6)+x^(1/3))-2*ln(1+x^(1/6))+2*x^(1/2)+ln(-1+x^(1/2))-ln(1+x^(1/2))+6*x^(1/6)-ln(x-1)-2*ln(x^(1/3)-1)+ln(x^(2/3)+x^(1/3)+1)-3*x^(1/3)","B"
569,1,20,19,0.013000," ","int(1/(x^(1/4)+x^(1/2)),x)","4 \ln \left(x^{\frac{1}{4}}+1\right)+2 \sqrt{x}-4 x^{\frac{1}{4}}"," ",0,"-4*x^(1/4)+4*ln(1+x^(1/4))+2*x^(1/2)","A"
570,1,15,16,0.002000," ","int(1/(-x^(1/3)+x^(2/3)),x)","3 \ln \left(x^{\frac{1}{3}}-1\right)+3 x^{\frac{1}{3}}"," ",0,"3*x^(1/3)+3*ln(x^(1/3)-1)","A"
571,1,46,45,0.010000," ","int(1/(1/x^(1/4)+x^(1/2)),x)","-\frac{4 \sqrt{3}\, \arctan \left(\frac{\left(2 x^{\frac{1}{4}}-1\right) \sqrt{3}}{3}\right)}{3}+\frac{4 \ln \left(x^{\frac{1}{4}}+1\right)}{3}-\frac{2 \ln \left(\sqrt{x}-x^{\frac{1}{4}}+1\right)}{3}+2 \sqrt{x}"," ",0,"2*x^(1/2)-2/3*ln(1-x^(1/4)+x^(1/2))-4/3*3^(1/2)*arctan(1/3*(2*x^(1/4)-1)*3^(1/2))+4/3*ln(x^(1/4)+1)","A"
572,1,173,49,0.122000," ","int(1/(x^(1/4)+x^(1/3)),x)","\ln \left(x -1\right)+\ln \left(\sqrt{x}-1\right)-\ln \left(\sqrt{x}+1\right)+2 \ln \left(x^{\frac{1}{4}}+1\right)-2 \ln \left(x^{\frac{1}{6}}+1\right)+4 \ln \left(x^{\frac{1}{12}}+1\right)+2 \ln \left(x^{\frac{1}{3}}-1\right)-2 \ln \left(x^{\frac{1}{4}}-1\right)+2 \ln \left(x^{\frac{1}{6}}-1\right)-4 \ln \left(x^{\frac{1}{12}}-1\right)+\ln \left(x^{\frac{1}{3}}-x^{\frac{1}{6}}+1\right)-2 \ln \left(x^{\frac{1}{6}}-x^{\frac{1}{12}}+1\right)-\ln \left(x^{\frac{1}{3}}+x^{\frac{1}{6}}+1\right)+2 \ln \left(x^{\frac{1}{6}}+x^{\frac{1}{12}}+1\right)-\ln \left(x^{\frac{2}{3}}+x^{\frac{1}{3}}+1\right)+\frac{3 x^{\frac{2}{3}}}{2}-\frac{12 x^{\frac{7}{12}}}{7}+2 \sqrt{x}-\frac{12 x^{\frac{5}{12}}}{5}+3 x^{\frac{1}{3}}-4 x^{\frac{1}{4}}+6 x^{\frac{1}{6}}-12 x^{\frac{1}{12}}"," ",0,"ln(x-1)-2*ln(x^(1/6)+1)+ln(x^(1/3)-x^(1/6)+1)+2*ln(x^(1/6)-1)-ln(x^(1/3)+x^(1/6)+1)+ln(x^(1/2)-1)-ln(x^(1/2)+1)-12/7*x^(7/12)-12/5*x^(5/12)-12*x^(1/12)-2*ln(x^(1/4)-1)+2*ln(x^(1/4)+1)+6*x^(1/6)+3/2*x^(2/3)+3*x^(1/3)+2*x^(1/2)-4*x^(1/4)-2*ln(1-x^(1/12)+x^(1/6))-ln(x^(2/3)+x^(1/3)+1)+4*ln(1+x^(1/12))+2*ln(x^(1/3)-1)-4*ln(x^(1/12)-1)+2*ln(x^(1/6)+x^(1/12)+1)","B"
573,1,83,82,0.004000," ","int(1/(1/x^(1/3)+1/x^(1/4)),x)","\frac{4 x^{\frac{5}{4}}}{5}-\frac{6 x^{\frac{7}{6}}}{7}+\frac{12 x^{\frac{13}{12}}}{13}-x -12 \ln \left(x^{\frac{1}{12}}+1\right)+\frac{12 x^{\frac{11}{12}}}{11}-\frac{6 x^{\frac{5}{6}}}{5}+\frac{4 x^{\frac{3}{4}}}{3}-\frac{3 x^{\frac{2}{3}}}{2}+\frac{12 x^{\frac{7}{12}}}{7}-2 \sqrt{x}+\frac{12 x^{\frac{5}{12}}}{5}-3 x^{\frac{1}{3}}+4 x^{\frac{1}{4}}-6 x^{\frac{1}{6}}+12 x^{\frac{1}{12}}"," ",0,"12*x^(1/12)-6*x^(1/6)+4*x^(1/4)-3*x^(1/3)+12/5*x^(5/12)+12/7*x^(7/12)-3/2*x^(2/3)+4/3*x^(3/4)-6/5*x^(5/6)+12/11*x^(11/12)-x+12/13*x^(13/12)-6/7*x^(7/6)+4/5*x^(5/4)-12*ln(x^(1/12)+1)-2*x^(1/2)","A"
574,1,175,136,0.045000," ","int(1/(-1/x^(1/3)+x^(1/2)),x)","\frac{12 \sqrt{5}\, \arctan \left(\frac{4 x^{\frac{1}{6}}+1-\sqrt{5}}{\sqrt{10+2 \sqrt{5}}}\right)}{5 \sqrt{10+2 \sqrt{5}}}-\frac{12 \sqrt{5}\, \arctan \left(\frac{4 x^{\frac{1}{6}}+1+\sqrt{5}}{\sqrt{10-2 \sqrt{5}}}\right)}{5 \sqrt{10-2 \sqrt{5}}}+\frac{6 \ln \left(x^{\frac{1}{6}}-1\right)}{5}-\frac{3 \sqrt{5}\, \ln \left(2 x^{\frac{1}{3}}+x^{\frac{1}{6}}-\sqrt{5}\, x^{\frac{1}{6}}+2\right)}{10}-\frac{3 \ln \left(2 x^{\frac{1}{3}}+x^{\frac{1}{6}}-\sqrt{5}\, x^{\frac{1}{6}}+2\right)}{10}+\frac{3 \sqrt{5}\, \ln \left(2 x^{\frac{1}{3}}+x^{\frac{1}{6}}+\sqrt{5}\, x^{\frac{1}{6}}+2\right)}{10}-\frac{3 \ln \left(2 x^{\frac{1}{3}}+x^{\frac{1}{6}}+\sqrt{5}\, x^{\frac{1}{6}}+2\right)}{10}+2 \sqrt{x}"," ",0,"2*x^(1/2)+6/5*ln(x^(1/6)-1)+3/10*ln(2+x^(1/6)+2*x^(1/3)+x^(1/6)*5^(1/2))*5^(1/2)-3/10*ln(2+x^(1/6)+2*x^(1/3)+x^(1/6)*5^(1/2))-12/5/(10-2*5^(1/2))^(1/2)*arctan((1+4*x^(1/6)+5^(1/2))/(10-2*5^(1/2))^(1/2))*5^(1/2)-3/10*ln(2+x^(1/6)+2*x^(1/3)-x^(1/6)*5^(1/2))*5^(1/2)-3/10*ln(2+x^(1/6)+2*x^(1/3)-x^(1/6)*5^(1/2))+12/5/(10+2*5^(1/2))^(1/2)*arctan((1+4*x^(1/6)-5^(1/2))/(10+2*5^(1/2))^(1/2))*5^(1/2)","A"
575,1,7,6,0.003000," ","int(x^(1/2)/(x^2+x),x)","2 \arctan \left(\sqrt{x}\right)"," ",0,"2*arctan(x^(1/2))","A"
576,1,16,15,0.003000," ","int(x/(x+4*x^(1/2)),x)","x +32 \ln \left(\sqrt{x}+4\right)-8 \sqrt{x}"," ",0,"x+32*ln(4+x^(1/2))-8*x^(1/2)","A"
577,1,71,73,0.005000," ","int(x^(1/2)/(x^(1/3)+x),x)","-\frac{3 \sqrt{2}\, \arctan \left(\sqrt{2}\, x^{\frac{1}{6}}-1\right)}{2}-\frac{3 \sqrt{2}\, \arctan \left(\sqrt{2}\, x^{\frac{1}{6}}+1\right)}{2}-\frac{3 \sqrt{2}\, \ln \left(\frac{x^{\frac{1}{3}}-\sqrt{2}\, x^{\frac{1}{6}}+1}{x^{\frac{1}{3}}+\sqrt{2}\, x^{\frac{1}{6}}+1}\right)}{4}+2 \sqrt{x}"," ",0,"2*x^(1/2)-3/2*arctan(1+x^(1/6)*2^(1/2))*2^(1/2)-3/2*arctan(-1+x^(1/6)*2^(1/2))*2^(1/2)-3/4*2^(1/2)*ln((1+x^(1/3)-x^(1/6)*2^(1/2))/(1+x^(1/3)+x^(1/6)*2^(1/2)))","A"
578,1,61,55,0.010000," ","int(x^(1/3)/(x^(1/4)+x^(1/2)),x)","4 \sqrt{3}\, \arctan \left(\frac{\left(2 x^{\frac{1}{12}}-1\right) \sqrt{3}}{3}\right)+4 \ln \left(x^{\frac{1}{12}}+1\right)-2 \ln \left(x^{\frac{1}{6}}-x^{\frac{1}{12}}+1\right)+\frac{6 x^{\frac{5}{6}}}{5}-\frac{12 x^{\frac{7}{12}}}{7}+3 x^{\frac{1}{3}}-12 x^{\frac{1}{12}}"," ",0,"6/5*x^(5/6)-12/7*x^(7/12)+3*x^(1/3)-12*x^(1/12)-2*ln(x^(1/6)-x^(1/12)+1)+4*3^(1/2)*arctan(1/3*(2*x^(1/12)-1)*3^(1/2))+4*ln(x^(1/12)+1)","A"
579,1,76,75,0.004000," ","int(x^(1/2)/(x^(1/4)+x^(1/3)),x)","\frac{6 x^{\frac{7}{6}}}{7}-\frac{12 x^{\frac{13}{12}}}{13}+x +12 \ln \left(x^{\frac{1}{12}}+1\right)-\frac{12 x^{\frac{11}{12}}}{11}+\frac{6 x^{\frac{5}{6}}}{5}-\frac{4 x^{\frac{3}{4}}}{3}+\frac{3 x^{\frac{2}{3}}}{2}-\frac{12 x^{\frac{7}{12}}}{7}+2 \sqrt{x}-\frac{12 x^{\frac{5}{12}}}{5}+3 x^{\frac{1}{3}}-4 x^{\frac{1}{4}}+6 x^{\frac{1}{6}}-12 x^{\frac{1}{12}}"," ",0,"-12*x^(1/12)+6*x^(1/6)-4*x^(1/4)+3*x^(1/3)-12/5*x^(5/12)-12/7*x^(7/12)+3/2*x^(2/3)-4/3*x^(3/4)+6/5*x^(5/6)-12/11*x^(11/12)+x-12/13*x^(13/12)+6/7*x^(7/6)+12*ln(x^(1/12)+1)+2*x^(1/2)","A"
580,1,242,137,0.030000," ","int(x^(1/2)/(-1/x^(1/3)+x^(1/2)),x)","x -\frac{6 \arctan \left(\frac{4 x^{\frac{1}{6}}+1-\sqrt{5}}{\sqrt{10+2 \sqrt{5}}}\right)}{\sqrt{10+2 \sqrt{5}}}-\frac{6 \sqrt{5}\, \arctan \left(\frac{4 x^{\frac{1}{6}}+1-\sqrt{5}}{\sqrt{10+2 \sqrt{5}}}\right)}{5 \sqrt{10+2 \sqrt{5}}}-\frac{6 \arctan \left(\frac{4 x^{\frac{1}{6}}+1+\sqrt{5}}{\sqrt{10-2 \sqrt{5}}}\right)}{\sqrt{10-2 \sqrt{5}}}+\frac{6 \sqrt{5}\, \arctan \left(\frac{4 x^{\frac{1}{6}}+1+\sqrt{5}}{\sqrt{10-2 \sqrt{5}}}\right)}{5 \sqrt{10-2 \sqrt{5}}}+\frac{6 \ln \left(x^{\frac{1}{6}}-1\right)}{5}+\frac{3 \sqrt{5}\, \ln \left(2 x^{\frac{1}{3}}+x^{\frac{1}{6}}-\sqrt{5}\, x^{\frac{1}{6}}+2\right)}{10}-\frac{3 \ln \left(2 x^{\frac{1}{3}}+x^{\frac{1}{6}}-\sqrt{5}\, x^{\frac{1}{6}}+2\right)}{10}-\frac{3 \sqrt{5}\, \ln \left(2 x^{\frac{1}{3}}+x^{\frac{1}{6}}+\sqrt{5}\, x^{\frac{1}{6}}+2\right)}{10}-\frac{3 \ln \left(2 x^{\frac{1}{3}}+x^{\frac{1}{6}}+\sqrt{5}\, x^{\frac{1}{6}}+2\right)}{10}+6 x^{\frac{1}{6}}"," ",0,"x+6*x^(1/6)+6/5*ln(x^(1/6)-1)-3/10*5^(1/2)*ln(2*x^(1/3)+x^(1/6)+5^(1/2)*x^(1/6)+2)-3/10*ln(2*x^(1/3)+x^(1/6)+5^(1/2)*x^(1/6)+2)-6/(10-2*5^(1/2))^(1/2)*arctan((4*x^(1/6)+1+5^(1/2))/(10-2*5^(1/2))^(1/2))+6/5/(10-2*5^(1/2))^(1/2)*5^(1/2)*arctan((4*x^(1/6)+1+5^(1/2))/(10-2*5^(1/2))^(1/2))+3/10*5^(1/2)*ln(2*x^(1/3)+x^(1/6)-5^(1/2)*x^(1/6)+2)-3/10*ln(2*x^(1/3)+x^(1/6)-5^(1/2)*x^(1/6)+2)-6/(10+2*5^(1/2))^(1/2)*arctan((4*x^(1/6)+1-5^(1/2))/(10+2*5^(1/2))^(1/2))-6/5/(10+2*5^(1/2))^(1/2)*5^(1/2)*arctan((4*x^(1/6)+1-5^(1/2))/(10+2*5^(1/2))^(1/2))","A"
581,1,36,32,0.006000," ","int(x^m*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x)","\frac{2 \sqrt{-\frac{-b x +a}{x}}\, x^{m +1}}{\left(2 m +1\right) \sqrt{-b x +a}}"," ",0,"2*x^(m+1)/(1+2*m)*(-(-b*x+a)/x)^(1/2)/(-b*x+a)^(1/2)","A"
582,1,27,23,0.004000," ","int(x^2*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x)","\frac{2 \sqrt{-\frac{-b x +a}{x}}\, x^{3}}{5 \sqrt{-b x +a}}"," ",0,"2/5*x^3*(-(-b*x+a)/x)^(1/2)/(-b*x+a)^(1/2)","A"
583,1,27,23,0.001000," ","int(x*(b-a/x)^(1/2)/(-b*x+a)^(1/2),x)","\frac{2 \sqrt{-\frac{-b x +a}{x}}\, x^{2}}{3 \sqrt{-b x +a}}"," ",0,"2/3*x^2*(-(-b*x+a)/x)^(1/2)/(-b*x+a)^(1/2)","A"
584,1,25,21,0.004000," ","int((b-a/x)^(1/2)/(-b*x+a)^(1/2),x)","\frac{2 \sqrt{-\frac{-b x +a}{x}}\, x}{\sqrt{-b x +a}}"," ",0,"2*x*(-(-b*x+a)/x)^(1/2)/(-b*x+a)^(1/2)","A"
585,1,24,20,0.003000," ","int((b-a/x)^(1/2)/x/(-b*x+a)^(1/2),x)","-\frac{2 \sqrt{-\frac{-b x +a}{x}}}{\sqrt{-b x +a}}"," ",0,"-2*(-(-b*x+a)/x)^(1/2)/(-b*x+a)^(1/2)","A"
586,1,27,23,0.001000," ","int((b-a/x)^(1/2)/x^2/(-b*x+a)^(1/2),x)","-\frac{2 \sqrt{-\frac{-b x +a}{x}}}{3 \sqrt{-b x +a}\, x}"," ",0,"-2/3*(-(-b*x+a)/x)^(1/2)/x/(-b*x+a)^(1/2)","A"
587,0,0,80,0.106000," ","int((a+b/x)^m*(d*x+c)^n,x)","\int \left(a +\frac{b}{x}\right)^{m} \left(d x +c \right)^{n}\, dx"," ",0,"int((a+b/x)^m*(d*x+c)^n,x)","F"
588,0,0,134,0.049000," ","int((a+b/x)^m*(d*x+c)^2,x)","\int \left(d x +c \right)^{2} \left(a +\frac{b}{x}\right)^{m}\, dx"," ",0,"int((a+b/x)^m*(d*x+c)^2,x)","F"
589,0,0,77,0.023000," ","int((a+b/x)^m*(d*x+c),x)","\int \left(d x +c \right) \left(a +\frac{b}{x}\right)^{m}\, dx"," ",0,"int((a+b/x)^m*(d*x+c),x)","F"
590,0,0,42,0.016000," ","int((a+b/x)^m,x)","\int \left(a +\frac{b}{x}\right)^{m}\, dx"," ",0,"int((a+b/x)^m,x)","F"
591,0,0,105,0.060000," ","int((a+b/x)^m/(d*x+c),x)","\int \frac{\left(a +\frac{b}{x}\right)^{m}}{d x +c}\, dx"," ",0,"int((a+b/x)^m/(d*x+c),x)","F"
592,0,0,58,0.056000," ","int((a+b/x)^m/(d*x+c)^2,x)","\int \frac{\left(a +\frac{b}{x}\right)^{m}}{\left(d x +c \right)^{2}}\, dx"," ",0,"int((a+b/x)^m/(d*x+c)^2,x)","F"
593,0,0,110,0.067000," ","int((a+b/x)^m/(d*x+c)^3,x)","\int \frac{\left(a +\frac{b}{x}\right)^{m}}{\left(d x +c \right)^{3}}\, dx"," ",0,"int((a+b/x)^m/(d*x+c)^3,x)","F"
594,0,0,181,0.105000," ","int((a+b/x)^m/(d*x+c)^4,x)","\int \frac{\left(a +\frac{b}{x}\right)^{m}}{\left(d x +c \right)^{4}}\, dx"," ",0,"int((a+b/x)^m/(d*x+c)^4,x)","F"
595,1,35,29,0.005000," ","int(x^m*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x)","\frac{\sqrt{-\frac{-b \,x^{2}+a}{x^{2}}}\, x^{m +1}}{\sqrt{-b \,x^{2}+a}\, m}"," ",0,"x^(m+1)/m*(-(-b*x^2+a)/x^2)^(1/2)/(-b*x^2+a)^(1/2)","A"
596,1,31,25,0.004000," ","int(x^2*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x)","\frac{\sqrt{-\frac{-b \,x^{2}+a}{x^{2}}}\, x^{3}}{2 \sqrt{-b \,x^{2}+a}}"," ",0,"1/2*x^3*(-(-b*x^2+a)/x^2)^(1/2)/(-b*x^2+a)^(1/2)","A"
597,1,42,24,0.014000," ","int(x*(b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x)","-\frac{\sqrt{\frac{b \,x^{2}-a}{x^{2}}}\, \sqrt{-b \,x^{2}+a}\, x^{2}}{b \,x^{2}-a}"," ",0,"-((b*x^2-a)/x^2)^(1/2)*x^2/(b*x^2-a)*(-b*x^2+a)^(1/2)","A"
598,1,42,24,0.014000," ","int((b-a/x^2)^(1/2)/(-b*x^2+a)^(1/2),x)","-\frac{\sqrt{\frac{b \,x^{2}-a}{x^{2}}}\, \sqrt{-b \,x^{2}+a}\, x \ln \left(x \right)}{b \,x^{2}-a}"," ",0,"-((b*x^2-a)/x^2)^(1/2)*x/(b*x^2-a)*(-b*x^2+a)^(1/2)*ln(x)","A"
599,1,28,22,0.006000," ","int((b-a/x^2)^(1/2)/x/(-b*x^2+a)^(1/2),x)","-\frac{\sqrt{-\frac{-b \,x^{2}+a}{x^{2}}}}{\sqrt{-b \,x^{2}+a}}"," ",0,"-(-(-b*x^2+a)/x^2)^(1/2)/(-b*x^2+a)^(1/2)","A"
600,1,31,25,0.005000," ","int((b-a/x^2)^(1/2)/x^2/(-b*x^2+a)^(1/2),x)","-\frac{\sqrt{-\frac{-b \,x^{2}+a}{x^{2}}}}{2 \sqrt{-b \,x^{2}+a}\, x}"," ",0,"-1/2*(-(-b*x^2+a)/x^2)^(1/2)/x/(-b*x^2+a)^(1/2)","A"
601,1,1145,330,0.123000," ","int((d*x+c)^(3/2)/(a+b/x^2)^(1/2),x)","\frac{\frac{2 a^{2} d^{4} x^{4}}{5}+\frac{6 a^{2} c \,d^{3} x^{3}}{5}+\frac{4 a^{2} c^{2} d^{2} x^{2}}{5}+\frac{2 a b \,d^{4} x^{2}}{5}-\frac{2 \sqrt{\frac{\left(-a x +\sqrt{-a b}\right) d}{a c +\sqrt{-a b}\, d}}\, \sqrt{\frac{\left(a x +\sqrt{-a b}\right) d}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}\, a^{2} c^{4} \EllipticE \left(\sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}, \sqrt{-\frac{-a c +\sqrt{-a b}\, d}{a c +\sqrt{-a b}\, d}}\right)}{5}+\frac{4 \sqrt{\frac{\left(-a x +\sqrt{-a b}\right) d}{a c +\sqrt{-a b}\, d}}\, \sqrt{\frac{\left(a x +\sqrt{-a b}\right) d}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}\, a b \,c^{2} d^{2} \EllipticE \left(\sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}, \sqrt{-\frac{-a c +\sqrt{-a b}\, d}{a c +\sqrt{-a b}\, d}}\right)}{5}-\frac{6 \sqrt{\frac{\left(-a x +\sqrt{-a b}\right) d}{a c +\sqrt{-a b}\, d}}\, \sqrt{\frac{\left(a x +\sqrt{-a b}\right) d}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}\, a b \,c^{2} d^{2} \EllipticF \left(\sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}, \sqrt{-\frac{-a c +\sqrt{-a b}\, d}{a c +\sqrt{-a b}\, d}}\right)}{5}+\frac{6 a b c \,d^{3} x}{5}+\frac{6 \sqrt{\frac{\left(-a x +\sqrt{-a b}\right) d}{a c +\sqrt{-a b}\, d}}\, \sqrt{\frac{\left(a x +\sqrt{-a b}\right) d}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}\, b^{2} d^{4} \EllipticE \left(\sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}, \sqrt{-\frac{-a c +\sqrt{-a b}\, d}{a c +\sqrt{-a b}\, d}}\right)}{5}-\frac{6 \sqrt{\frac{\left(-a x +\sqrt{-a b}\right) d}{a c +\sqrt{-a b}\, d}}\, \sqrt{\frac{\left(a x +\sqrt{-a b}\right) d}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}\, b^{2} d^{4} \EllipticF \left(\sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}, \sqrt{-\frac{-a c +\sqrt{-a b}\, d}{a c +\sqrt{-a b}\, d}}\right)}{5}+\frac{4 a b \,c^{2} d^{2}}{5}+\frac{2 \sqrt{\frac{\left(-a x +\sqrt{-a b}\right) d}{a c +\sqrt{-a b}\, d}}\, \sqrt{\frac{\left(a x +\sqrt{-a b}\right) d}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-a b}\, a \,c^{3} d \EllipticF \left(\sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}, \sqrt{-\frac{-a c +\sqrt{-a b}\, d}{a c +\sqrt{-a b}\, d}}\right)}{5}+\frac{2 \sqrt{\frac{\left(-a x +\sqrt{-a b}\right) d}{a c +\sqrt{-a b}\, d}}\, \sqrt{\frac{\left(a x +\sqrt{-a b}\right) d}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}\, \sqrt{-a b}\, b c \,d^{3} \EllipticF \left(\sqrt{-\frac{\left(d x +c \right) a}{-a c +\sqrt{-a b}\, d}}, \sqrt{-\frac{-a c +\sqrt{-a b}\, d}{a c +\sqrt{-a b}\, d}}\right)}{5}}{\sqrt{d x +c}\, \sqrt{\frac{a \,x^{2}+b}{x^{2}}}\, a^{2} d^{2} x}"," ",0,"2/5*(((-a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d+a*c))^(1/2)*((a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d-a*c))^(1/2)*EllipticF((-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2),(-((-a*b)^(1/2)*d-a*c)/((-a*b)^(1/2)*d+a*c))^(1/2))*(-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2)*(-a*b)^(1/2)*a*c^3*d+((-a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d+a*c))^(1/2)*((a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d-a*c))^(1/2)*EllipticF((-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2),(-((-a*b)^(1/2)*d-a*c)/((-a*b)^(1/2)*d+a*c))^(1/2))*(-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2)*(-a*b)^(1/2)*b*c*d^3-3*((-a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d+a*c))^(1/2)*((a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d-a*c))^(1/2)*EllipticF((-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2),(-((-a*b)^(1/2)*d-a*c)/((-a*b)^(1/2)*d+a*c))^(1/2))*(-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2)*a*b*c^2*d^2-3*((-a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d+a*c))^(1/2)*((a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d-a*c))^(1/2)*EllipticF((-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2),(-((-a*b)^(1/2)*d-a*c)/((-a*b)^(1/2)*d+a*c))^(1/2))*(-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2)*b^2*d^4-((-a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d+a*c))^(1/2)*((a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d-a*c))^(1/2)*EllipticE((-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2),(-((-a*b)^(1/2)*d-a*c)/((-a*b)^(1/2)*d+a*c))^(1/2))*(-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2)*a^2*c^4+2*((-a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d+a*c))^(1/2)*((a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d-a*c))^(1/2)*EllipticE((-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2),(-((-a*b)^(1/2)*d-a*c)/((-a*b)^(1/2)*d+a*c))^(1/2))*(-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2)*a*b*c^2*d^2+3*((-a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d+a*c))^(1/2)*((a*x+(-a*b)^(1/2))*d/((-a*b)^(1/2)*d-a*c))^(1/2)*EllipticE((-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2),(-((-a*b)^(1/2)*d-a*c)/((-a*b)^(1/2)*d+a*c))^(1/2))*(-(d*x+c)*a/((-a*b)^(1/2)*d-a*c))^(1/2)*b^2*d^4+x^4*a^2*d^4+3*x^3*a^2*c*d^3+2*x^2*a^2*c^2*d^2+x^2*a*b*d^4+3*x*a*b*c*d^3+2*a*b*c^2*d^2)/(d*x+c)^(1/2)/d^2/a^2/x/((a*x^2+b)/x^2)^(1/2)","B"
602,1,18,11,0.007000," ","int((x^3-1)/(x^4-4*x)^(2/3),x)","\frac{3 \left(x^{3}-4\right) x}{4 \left(x^{4}-4 x \right)^{\frac{2}{3}}}"," ",0,"3/4*x*(x^3-4)/(x^4-4*x)^(2/3)","A"
603,1,20,13,0.004000," ","int((-x^2+2)*(-x^3+6*x)^(1/4),x)","-\frac{4 \left(-x^{3}+6 x \right)^{\frac{1}{4}} \left(x^{2}-6\right) x}{15}"," ",0,"-4/15*(-x^3+6*x)^(1/4)*x*(x^2-6)","A"
604,1,18,11,0.006000," ","int((x^4+1)*(x^5+5*x)^(1/2),x)","\frac{2 \left(x^{4}+5\right) \sqrt{x^{5}+5 x}\, x}{15}"," ",0,"2/15*x*(x^4+5)*(x^5+5*x)^(1/2)","A"
605,1,18,11,0.005000," ","int((5*x^4+2)*(x^5+2*x)^(1/2),x)","\frac{2 \left(x^{4}+2\right) \sqrt{x^{5}+2 x}\, x}{3}"," ",0,"2/3*x*(x^4+2)*(x^5+2*x)^(1/2)","A"
606,1,21,11,0.003000," ","int((3*x^2+x)/(2*x^3+x^2)^(1/2),x)","\frac{\left(2 x +1\right) x^{2}}{\sqrt{2 x^{3}+x^{2}}}"," ",0,"x^2*(2*x+1)/(2*x^3+x^2)^(1/2)","A"
607,1,34,32,0.003000," ","int((2+(1-5*x)^(1/3))/(3+(1-5*x)^(1/3)),x)","x +\frac{27 \ln \left(3+\left(-5 x +1\right)^{\frac{1}{3}}\right)}{5}-\frac{1}{5}+\frac{3 \left(-5 x +1\right)^{\frac{2}{3}}}{10}-\frac{9 \left(-5 x +1\right)^{\frac{1}{3}}}{5}"," ",0,"-1/5+x+3/10*(1-5*x)^(2/3)-9/5*(1-5*x)^(1/3)+27/5*ln(3+(1-5*x)^(1/3))","A"
608,1,16,17,0.003000," ","int((x^(1/2)+1)/(x^(1/2)-1),x)","x +4 \ln \left(\sqrt{x}-1\right)+4 \sqrt{x}"," ",0,"x+4*x^(1/2)+4*ln(x^(1/2)-1)","A"
609,1,27,25,0.006000," ","int((1-(3*x+2)^(1/2))/(1+(3*x+2)^(1/2)),x)","-x -\frac{4 \ln \left(1+\sqrt{3 x +2}\right)}{3}+\frac{4 \sqrt{3 x +2}}{3}-\frac{2}{3}"," ",0,"4/3*(3*x+2)^(1/2)-x-2/3-4/3*ln(1+(3*x+2)^(1/2))","A"
610,1,35,29,0.004000," ","int((-1+(b*x+a)^(1/2))/(1+(b*x+a)^(1/2)),x)","x +\frac{a}{b}+\frac{4 \ln \left(1+\sqrt{b x +a}\right)}{b}-\frac{4 \sqrt{b x +a}}{b}"," ",0,"-4*(b*x+a)^(1/2)/b+x+a/b+4*ln(1+(b*x+a)^(1/2))/b","A"
611,1,13,10,0.017000," ","int((a+b*n*x^(n-1))/(a*x+b*x^n),x)","\ln \left(a x +b \,{\mathrm e}^{n \ln \left(x \right)}\right)"," ",0,"ln(a*x+b*exp(n*ln(x)))","A"
612,1,13,17,0.027000," ","int((a+b*n*x^(n-1))/(x^n)/(b+a*x^(-n+1)),x)","\ln \left(a x +b \,{\mathrm e}^{n \ln \left(x \right)}\right)"," ",0,"ln(a*x+b*exp(n*ln(x)))","A"
613,1,38,37,0.031000," ","int(x*(c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(2*a*d+(a*e*n+b*d*m+3*a*e+3*b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+4*a*f+4*b*e+4*c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+5*a*g+5*b*f+5*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+6*b*g+6*c*f)*x^4+c*g*(7+2*m+3*n)*x^5),x)","x^{2} \left(c \,x^{2}+b x +a \right)^{m +1} \left(g \,x^{3}+f \,x^{2}+e x +d \right)^{n +1}"," ",0,"x^2*(c*x^2+b*x+a)^(m+1)*(g*x^3+f*x^2+e*x+d)^(n+1)","A"
614,1,36,35,0.030000," ","int((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(a*d+(a*e*n+b*d*m+2*a*e+2*b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+3*a*f+3*b*e+3*c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+4*a*g+4*b*f+4*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+5*b*g+5*c*f)*x^4+c*g*(6+2*m+3*n)*x^5),x)","x \left(c \,x^{2}+b x +a \right)^{m +1} \left(g \,x^{3}+f \,x^{2}+e x +d \right)^{n +1}"," ",0,"x*(c*x^2+b*x+a)^(m+1)*(g*x^3+f*x^2+e*x+d)^(n+1)","A"
615,1,35,34,0.031000," ","int((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(b*d+a*e+b*d*m+a*e*n+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+2*a*f+2*b*e+2*c*d)*x+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+3*a*g+3*b*f+3*c*e)*x^2+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+4*b*g+4*c*f)*x^3+c*g*(5+2*m+3*n)*x^4),x)","\left(c \,x^{2}+b x +a \right)^{m +1} \left(g \,x^{3}+f \,x^{2}+e x +d \right)^{n +1}"," ",0,"(c*x^2+b*x+a)^(m+1)*(g*x^3+f*x^2+e*x+d)^(n+1)","A"
616,1,38,37,0.033000," ","int((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(-a*d+(a*e*n+b*d*m)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m+a*f+b*e+c*d)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+2*a*g+2*b*f+2*c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+3*b*g+3*c*f)*x^4+c*g*(4+2*m+3*n)*x^5)/x^2,x)","\frac{\left(c \,x^{2}+b x +a \right)^{m +1} \left(g \,x^{3}+f \,x^{2}+e x +d \right)^{n +1}}{x}"," ",0,"(c*x^2+b*x+a)^(m+1)*(g*x^3+f*x^2+e*x+d)^(n+1)/x","A"
617,1,38,37,0.032000," ","int((c*x^2+b*x+a)^m*(g*x^3+f*x^2+e*x+d)^n*(-2*a*d+(a*e*n+b*d*m-a*e-b*d)*x+(2*a*f*n+b*e*m+b*e*n+2*c*d*m)*x^2+(3*a*g*n+b*f*m+2*b*f*n+2*c*e*m+c*e*n+a*g+b*f+c*e)*x^3+(b*g*m+3*b*g*n+2*c*f*m+2*c*f*n+2*b*g+2*c*f)*x^4+c*g*(3+2*m+3*n)*x^5)/x^3,x)","\frac{\left(c \,x^{2}+b x +a \right)^{m +1} \left(g \,x^{3}+f \,x^{2}+e x +d \right)^{n +1}}{x^{2}}"," ",0,"(c*x^2+b*x+a)^(m+1)*(g*x^3+f*x^2+e*x+d)^(n+1)/x^2","A"
618,1,78,163,0.003000," ","int(x^3*(a+b*(d*x+c)^(1/2))^2,x)","\frac{a^{2} x^{4}}{4}+\left(\frac{1}{5} d \,x^{5}+\frac{1}{4} c \,x^{4}\right) b^{2}+\frac{4 \left(-\frac{\left(d x +c \right)^{\frac{3}{2}} c^{3}}{3}+\frac{3 \left(d x +c \right)^{\frac{5}{2}} c^{2}}{5}-\frac{3 \left(d x +c \right)^{\frac{7}{2}} c}{7}+\frac{\left(d x +c \right)^{\frac{9}{2}}}{9}\right) a b}{d^{4}}"," ",0,"b^2*(1/5*d*x^5+1/4*c*x^4)+4*a*b/d^4*(1/9*(d*x+c)^(9/2)-3/7*c*(d*x+c)^(7/2)+3/5*c^2*(d*x+c)^(5/2)-1/3*c^3*(d*x+c)^(3/2))+1/4*a^2*x^4","A"
619,1,66,120,0.004000," ","int(x^2*(a+b*(d*x+c)^(1/2))^2,x)","\frac{a^{2} x^{3}}{3}+\left(\frac{1}{4} d \,x^{4}+\frac{1}{3} c \,x^{3}\right) b^{2}+\frac{4 \left(\frac{\left(d x +c \right)^{\frac{3}{2}} c^{2}}{3}-\frac{2 \left(d x +c \right)^{\frac{5}{2}} c}{5}+\frac{\left(d x +c \right)^{\frac{7}{2}}}{7}\right) a b}{d^{3}}"," ",0,"b^2*(1/4*x^4*d+1/3*c*x^3)+4*a*b/d^3*(1/7*(d*x+c)^(7/2)-2/5*(d*x+c)^(5/2)*c+1/3*c^2*(d*x+c)^(3/2))+1/3*a^2*x^3","A"
620,1,54,77,0.003000," ","int(x*(a+b*(d*x+c)^(1/2))^2,x)","\frac{a^{2} x^{2}}{2}+\left(\frac{1}{3} d \,x^{3}+\frac{1}{2} c \,x^{2}\right) b^{2}+\frac{4 \left(-\frac{\left(d x +c \right)^{\frac{3}{2}} c}{3}+\frac{\left(d x +c \right)^{\frac{5}{2}}}{5}\right) a b}{d^{2}}"," ",0,"b^2*(1/3*d*x^3+1/2*c*x^2)+4*a*b/d^2*(1/5*(d*x+c)^(5/2)-1/3*(d*x+c)^(3/2)*c)+1/2*a^2*x^2","A"
621,1,35,35,0.001000," ","int((a+b*(d*x+c)^(1/2))^2,x)","a^{2} x +\left(\frac{1}{2} d \,x^{2}+c x \right) b^{2}+\frac{4 \left(d x +c \right)^{\frac{3}{2}} a b}{3 d}"," ",0,"b^2*(1/2*d*x^2+c*x)+4/3*a*b*(d*x+c)^(3/2)/d+a^2*x","A"
622,1,51,49,0.006000," ","int((a+b*(d*x+c)^(1/2))^2/x,x)","b^{2} c \ln \left(x \right)+b^{2} d x -4 a b \sqrt{c}\, \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)+a^{2} \ln \left(x \right)+4 \sqrt{d x +c}\, a b"," ",0,"ln(x)*b^2*c+b^2*d*x-4*a*b*arctanh((d*x+c)^(1/2)/c^(1/2))*c^(1/2)+4*a*b*(d*x+c)^(1/2)+a^2*ln(x)","A"
623,1,60,46,0.015000," ","int((a+b*(d*x+c)^(1/2))^2/x^2,x)","b^{2} d \ln \left(x \right)-\frac{2 a b d \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{\sqrt{c}}-\frac{b^{2} c}{x}-\frac{a^{2}}{x}-\frac{2 \sqrt{d x +c}\, a b}{x}"," ",0,"-b^2*c/x+b^2*d*ln(x)-2*a*b/x*(d*x+c)^(1/2)-2*a*b*d*arctanh((d*x+c)^(1/2)/c^(1/2))/c^(1/2)-a^2/x","A"
624,1,81,64,0.016000," ","int((a+b*(d*x+c)^(1/2))^2/x^3,x)","4 \left(\frac{\arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{8 c^{\frac{3}{2}}}+\frac{-\frac{\left(d x +c \right)^{\frac{3}{2}}}{8 c}-\frac{\sqrt{d x +c}}{8}}{d^{2} x^{2}}\right) a b \,d^{2}+\left(-\frac{d}{x}-\frac{c}{2 x^{2}}\right) b^{2}-\frac{a^{2}}{2 x^{2}}"," ",0,"b^2*(-d/x-1/2*c/x^2)+4*a*b*d^2*((-1/8/c*(d*x+c)^(3/2)-1/8*(d*x+c)^(1/2))/x^2/d^2+1/8/c^(3/2)*arctanh((d*x+c)^(1/2)/c^(1/2)))-1/2*a^2/x^2","A"
625,1,383,278,0.006000," ","int(x^3*(a+b*(d*x+c)^(1/2))^(1/2),x)","\frac{-\frac{28 \left(a +\sqrt{d x +c}\, b \right)^{\frac{15}{2}} a}{15}-\frac{4 \left(-b^{2} c +a^{2}\right)^{3} \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} a}{3}+\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{17}{2}}}{17}+\frac{4 \left(-3 b^{2} c +21 a^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{13}{2}}}{13}+\frac{4 \left(-8 \left(-b^{2} c +a^{2}\right) a -2 \left(-2 b^{2} c +6 a^{2}\right) a -\left(-3 b^{2} c +15 a^{2}\right) a \right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{11}{2}}}{11}+\frac{4 \left(8 \left(-b^{2} c +a^{2}\right) a^{2}-\left(-8 \left(-b^{2} c +a^{2}\right) a -2 \left(-2 b^{2} c +6 a^{2}\right) a \right) a +\left(-b^{2} c +a^{2}\right) \left(-2 b^{2} c +6 a^{2}\right)+\left(-b^{2} c +a^{2}\right)^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{9}{2}}}{9}+\frac{4 \left(-6 \left(-b^{2} c +a^{2}\right)^{2} a -\left(8 \left(-b^{2} c +a^{2}\right) a^{2}+\left(-b^{2} c +a^{2}\right) \left(-2 b^{2} c +6 a^{2}\right)+\left(-b^{2} c +a^{2}\right)^{2}\right) a \right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{7}{2}}}{7}+\frac{4 \left(6 \left(-b^{2} c +a^{2}\right)^{2} a^{2}+\left(-b^{2} c +a^{2}\right)^{3}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}}}{5}}{b^{8} d^{4}}"," ",0,"4/d^4/b^8*(1/17*(a+b*(d*x+c)^(1/2))^(17/2)-7/15*a*(a+b*(d*x+c)^(1/2))^(15/2)+1/13*(-3*b^2*c+21*a^2)*(a+b*(d*x+c)^(1/2))^(13/2)+1/11*(-8*(-b^2*c+a^2)*a-2*a*(-2*b^2*c+6*a^2)-(-3*b^2*c+15*a^2)*a)*(a+b*(d*x+c)^(1/2))^(11/2)+1/9*((-b^2*c+a^2)*(-2*b^2*c+6*a^2)+8*a^2*(-b^2*c+a^2)+(-b^2*c+a^2)^2-(-8*(-b^2*c+a^2)*a-2*a*(-2*b^2*c+6*a^2))*a)*(a+b*(d*x+c)^(1/2))^(9/2)+1/7*(-6*(-b^2*c+a^2)^2*a-((-b^2*c+a^2)*(-2*b^2*c+6*a^2)+8*a^2*(-b^2*c+a^2)+(-b^2*c+a^2)^2)*a)*(a+b*(d*x+c)^(1/2))^(7/2)+1/5*((-b^2*c+a^2)^3+6*(-b^2*c+a^2)^2*a^2)*(a+b*(d*x+c)^(1/2))^(5/2)-1/3*(-b^2*c+a^2)^3*a*(a+b*(d*x+c)^(1/2))^(3/2))","A"
626,1,183,188,0.003000," ","int(x^2*(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{-\frac{20 \left(a +\sqrt{d x +c}\, b \right)^{\frac{11}{2}} a}{11}-\frac{4 \left(-b^{2} c +a^{2}\right)^{2} \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} a}{3}+\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{13}{2}}}{13}+\frac{4 \left(-2 b^{2} c +10 a^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{9}{2}}}{9}+\frac{4 \left(-4 \left(-b^{2} c +a^{2}\right) a -\left(-2 b^{2} c +6 a^{2}\right) a \right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{7}{2}}}{7}+\frac{4 \left(4 \left(-b^{2} c +a^{2}\right) a^{2}+\left(-b^{2} c +a^{2}\right)^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}}}{5}}{b^{6} d^{3}}"," ",0,"4/d^3/b^6*(1/13*(a+(d*x+c)^(1/2)*b)^(13/2)-5/11*a*(a+(d*x+c)^(1/2)*b)^(11/2)+1/9*(-2*b^2*c+10*a^2)*(a+(d*x+c)^(1/2)*b)^(9/2)+1/7*(-4*(-b^2*c+a^2)*a-(-2*b^2*c+6*a^2)*a)*(a+(d*x+c)^(1/2)*b)^(7/2)+1/5*((-b^2*c+a^2)^2+4*(-b^2*c+a^2)*a^2)*(a+(d*x+c)^(1/2)*b)^(5/2)-1/3*(-b^2*c+a^2)^2*a*(a+(d*x+c)^(1/2)*b)^(3/2))","A"
627,1,94,109,0.004000," ","int(x*(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{-\frac{12 \left(a +\sqrt{d x +c}\, b \right)^{\frac{7}{2}} a}{7}-\frac{4 \left(-b^{2} c +a^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} a}{3}+\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{9}{2}}}{9}+\frac{4 \left(-b^{2} c +3 a^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}}}{5}}{b^{4} d^{2}}"," ",0,"4/d^2/b^4*(1/9*(a+(d*x+c)^(1/2)*b)^(9/2)-3/7*a*(a+(d*x+c)^(1/2)*b)^(7/2)+1/5*(-b^2*c+3*a^2)*(a+(d*x+c)^(1/2)*b)^(5/2)-1/3*(-b^2*c+a^2)*a*(a+(d*x+c)^(1/2)*b)^(3/2))","A"
628,1,41,44,0.003000," ","int((a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{-\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} a}{3}+\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}}}{5}}{b^{2} d}"," ",0,"4/d/b^2*(1/5*(a+(d*x+c)^(1/2)*b)^(5/2)-1/3*a*(a+(d*x+c)^(1/2)*b)^(3/2))","A"
629,1,221,88,0.037000," ","int((a+(d*x+c)^(1/2)*b)^(1/2)/x,x)","\frac{2 b^{2} c \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{\sqrt{b^{2} c}\, \sqrt{-a -\sqrt{b^{2} c}}}-\frac{2 b^{2} c \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{\sqrt{b^{2} c}\, \sqrt{-a +\sqrt{b^{2} c}}}+\frac{2 a \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{\sqrt{-a -\sqrt{b^{2} c}}}+\frac{2 a \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{\sqrt{-a +\sqrt{b^{2} c}}}+4 \sqrt{a +\sqrt{d x +c}\, b}"," ",0,"4*(a+(d*x+c)^(1/2)*b)^(1/2)+2/(b^2*c)^(1/2)/(-(b^2*c)^(1/2)-a)^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-(b^2*c)^(1/2)-a)^(1/2))*b^2*c+2/(-(b^2*c)^(1/2)-a)^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-(b^2*c)^(1/2)-a)^(1/2))*a-2/(b^2*c)^(1/2)/((b^2*c)^(1/2)-a)^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/((b^2*c)^(1/2)-a)^(1/2))*b^2*c+2/((b^2*c)^(1/2)-a)^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/((b^2*c)^(1/2)-a)^(1/2))*a","B"
630,1,151,101,0.026000," ","int((a+(d*x+c)^(1/2)*b)^(1/2)/x^2,x)","\frac{b^{2} d \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{2 \sqrt{b^{2} c}\, \sqrt{-a -\sqrt{b^{2} c}}}-\frac{b^{2} d \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{2 \sqrt{b^{2} c}\, \sqrt{-a +\sqrt{b^{2} c}}}-\frac{\sqrt{a +\sqrt{d x +c}\, b}\, b^{2} d}{-b^{2} c +\left(d x +c \right) b^{2}}"," ",0,"-d*b^2*(a+(d*x+c)^(1/2)*b)^(1/2)/((d*x+c)*b^2-b^2*c)+1/2*d*b^2/(b^2*c)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2))-1/2*d*b^2/(b^2*c)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2))","A"
631,1,784,174,0.037000," ","int((a+(d*x+c)^(1/2)*b)^(1/2)/x^3,x)","-\frac{\left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} a \,b^{4} d^{2}}{8 \left(-b^{2} c +\left(d x +c \right) b^{2}\right)^{2} \left(-b^{2} c +a^{2}\right)}+\frac{3 b^{4} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{16 \left(-b^{2} c +a^{2}\right) \sqrt{b^{2} c}\, \sqrt{-a -\sqrt{b^{2} c}}}-\frac{3 b^{4} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{16 \left(-b^{2} c +a^{2}\right) \sqrt{b^{2} c}\, \sqrt{-a +\sqrt{b^{2} c}}}-\frac{3 \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} a^{3} b^{2} d^{2}}{8 \left(-b^{2} c +\left(d x +c \right) b^{2}\right)^{2} \left(-b^{2} c +a^{2}\right) c}-\frac{a^{2} b^{2} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{8 \left(-b^{2} c +a^{2}\right) \sqrt{b^{2} c}\, \sqrt{-a -\sqrt{b^{2} c}}\, c}+\frac{a^{2} b^{2} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{8 \left(-b^{2} c +a^{2}\right) \sqrt{b^{2} c}\, \sqrt{-a +\sqrt{b^{2} c}}\, c}+\frac{\left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}} b^{4} d^{2}}{8 \left(-b^{2} c +\left(d x +c \right) b^{2}\right)^{2} \left(-b^{2} c +a^{2}\right)}-\frac{3 \sqrt{a +\sqrt{d x +c}\, b}\, b^{4} d^{2}}{8 \left(-b^{2} c +\left(d x +c \right) b^{2}\right)^{2}}+\frac{3 \left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}} a^{2} b^{2} d^{2}}{8 \left(-b^{2} c +\left(d x +c \right) b^{2}\right)^{2} \left(-b^{2} c +a^{2}\right) c}+\frac{\sqrt{a +\sqrt{d x +c}\, b}\, a^{2} b^{2} d^{2}}{8 \left(-b^{2} c +\left(d x +c \right) b^{2}\right)^{2} c}-\frac{a \,b^{2} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{16 \left(-b^{2} c +a^{2}\right) \sqrt{-a -\sqrt{b^{2} c}}\, c}-\frac{a \,b^{2} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{16 \left(-b^{2} c +a^{2}\right) \sqrt{-a +\sqrt{b^{2} c}}\, c}-\frac{\left(a +\sqrt{d x +c}\, b \right)^{\frac{7}{2}} a \,b^{2} d^{2}}{8 \left(-b^{2} c +\left(d x +c \right) b^{2}\right)^{2} \left(-b^{2} c +a^{2}\right) c}"," ",0,"-1/8*b^2*d^2/(-b^2*c+(d*x+c)*b^2)^2*a/c/(-b^2*c+a^2)*(a+(d*x+c)^(1/2)*b)^(7/2)+1/8*b^4*d^2/(-b^2*c+(d*x+c)*b^2)^2/(-b^2*c+a^2)*(a+(d*x+c)^(1/2)*b)^(5/2)+3/8*b^2*d^2/(-b^2*c+(d*x+c)*b^2)^2/c/(-b^2*c+a^2)*(a+(d*x+c)^(1/2)*b)^(5/2)*a^2-1/8*b^4*d^2/(-b^2*c+(d*x+c)*b^2)^2*a/(-b^2*c+a^2)*(a+(d*x+c)^(1/2)*b)^(3/2)-3/8*b^2*d^2/(-b^2*c+(d*x+c)*b^2)^2*a^3/c/(-b^2*c+a^2)*(a+(d*x+c)^(1/2)*b)^(3/2)-3/8*b^4*d^2/(-b^2*c+(d*x+c)*b^2)^2*(a+(d*x+c)^(1/2)*b)^(1/2)+1/8*b^2*d^2/(-b^2*c+(d*x+c)*b^2)^2/c*(a+(d*x+c)^(1/2)*b)^(1/2)*a^2+3/16*b^4*d^2/(-b^2*c+a^2)/(b^2*c)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2))-1/16*b^2*d^2/c/(-b^2*c+a^2)/(-a-(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2))*a-1/8*b^2*d^2/c/(-b^2*c+a^2)/(b^2*c)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2))*a^2-3/16*b^4*d^2/(-b^2*c+a^2)/(b^2*c)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2))-1/16*b^2*d^2/c/(-b^2*c+a^2)/(-a+(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2))*a+1/8*b^2*d^2/c/(-b^2*c+a^2)/(b^2*c)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2))*a^2","B"
632,1,394,210,0.007000," ","int(x^3/(a+(d*x+c)^(1/2)*b),x)","-\frac{a \,x^{3}}{3 b^{2} d}+\frac{a c \,x^{2}}{2 b^{2} d^{2}}-\frac{a^{3} x^{2}}{2 b^{4} d^{2}}+\frac{2 a \,c^{3} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{2} d^{4}}-\frac{a \,c^{2} x}{b^{2} d^{3}}-\frac{6 a^{3} c^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{4} d^{4}}+\frac{2 a^{3} c x}{b^{4} d^{3}}-\frac{11 a \,c^{3}}{6 b^{2} d^{4}}-\frac{2 \sqrt{d x +c}\, c^{3}}{b \,d^{4}}+\frac{6 a^{5} c \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{6} d^{4}}-\frac{a^{5} x}{b^{6} d^{3}}+\frac{5 a^{3} c^{2}}{2 b^{4} d^{4}}+\frac{6 \sqrt{d x +c}\, a^{2} c^{2}}{b^{3} d^{4}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} c^{2}}{b \,d^{4}}-\frac{2 a^{7} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{8} d^{4}}-\frac{a^{5} c}{b^{6} d^{4}}-\frac{6 \sqrt{d x +c}\, a^{4} c}{b^{5} d^{4}}-\frac{2 \left(d x +c \right)^{\frac{3}{2}} a^{2} c}{b^{3} d^{4}}-\frac{6 \left(d x +c \right)^{\frac{5}{2}} c}{5 b \,d^{4}}+\frac{2 \sqrt{d x +c}\, a^{6}}{b^{7} d^{4}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} a^{4}}{3 b^{5} d^{4}}+\frac{2 \left(d x +c \right)^{\frac{5}{2}} a^{2}}{5 b^{3} d^{4}}+\frac{2 \left(d x +c \right)^{\frac{7}{2}}}{7 b \,d^{4}}"," ",0,"-11/6/d^4/b^2*a*c^3-6/5/d^4/b*(d*x+c)^(5/2)*c+2/5/d^4/b^3*(d*x+c)^(5/2)*a^2+2/d^4/b*(d*x+c)^(3/2)*c^2-2/d^4/b*(d*x+c)^(1/2)*c^3+2/3/d^4/b^5*(d*x+c)^(3/2)*a^4+2/7*(d*x+c)^(7/2)/b/d^4+2/d^4/b^7*(d*x+c)^(1/2)*a^6-1/d^3/b^6*x*a^5-1/2/d^2/b^4*x^2*a^3+6/d^4/b^3*(d*x+c)^(1/2)*a^2*c^2-6/d^4/b^5*(d*x+c)^(1/2)*a^4*c-1/3/d/b^2*x^3*a-2/d^4/b^3*(d*x+c)^(3/2)*a^2*c+1/2/d^2/b^2*x^2*a*c-1/d^3/b^2*x*a*c^2+2/d^3/b^4*x*a^3*c-1/d^4/b^6*a^5*c+5/2/d^4/b^4*a^3*c^2+2/d^4*a/b^2*ln(a+(d*x+c)^(1/2)*b)*c^3-6/d^4*a^3/b^4*ln(a+(d*x+c)^(1/2)*b)*c^2+6/d^4*a^5/b^6*ln(a+(d*x+c)^(1/2)*b)*c-2/d^4*a^7/b^8*ln(a+(d*x+c)^(1/2)*b)","A"
633,1,235,137,0.006000," ","int(x^2/(a+(d*x+c)^(1/2)*b),x)","-\frac{a \,x^{2}}{2 b^{2} d}-\frac{2 a \,c^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{2} d^{3}}+\frac{a c x}{b^{2} d^{2}}+\frac{4 a^{3} c \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{4} d^{3}}-\frac{a^{3} x}{b^{4} d^{2}}+\frac{3 a \,c^{2}}{2 b^{2} d^{3}}+\frac{2 \sqrt{d x +c}\, c^{2}}{b \,d^{3}}-\frac{2 a^{5} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{6} d^{3}}-\frac{a^{3} c}{b^{4} d^{3}}-\frac{4 \sqrt{d x +c}\, a^{2} c}{b^{3} d^{3}}-\frac{4 \left(d x +c \right)^{\frac{3}{2}} c}{3 b \,d^{3}}+\frac{2 \sqrt{d x +c}\, a^{4}}{b^{5} d^{3}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}} a^{2}}{3 b^{3} d^{3}}+\frac{2 \left(d x +c \right)^{\frac{5}{2}}}{5 b \,d^{3}}"," ",0,"2/5*(d*x+c)^(5/2)/b/d^3-1/2/d/b^2*x^2*a+1/d^2/b^2*x*a*c+3/2/d^3/b^2*a*c^2-4/3/d^3/b*(d*x+c)^(3/2)*c+2/3/d^3/b^3*(d*x+c)^(3/2)*a^2+2/d^3/b*(d*x+c)^(1/2)*c^2-1/d^2/b^4*x*a^3-1/d^3/b^4*a^3*c-4/d^3/b^3*(d*x+c)^(1/2)*a^2*c+2/d^3/b^5*(d*x+c)^(1/2)*a^4-2/d^3*a/b^2*ln(a+(d*x+c)^(1/2)*b)*c^2+4/d^3*a^3/b^4*ln(a+(d*x+c)^(1/2)*b)*c-2/d^3*a^5/b^6*ln(a+(d*x+c)^(1/2)*b)","A"
634,1,116,82,0.004000," ","int(x/(a+(d*x+c)^(1/2)*b),x)","\frac{2 a c \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{2} d^{2}}-\frac{a x}{b^{2} d}-\frac{2 a^{3} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{4} d^{2}}-\frac{a c}{b^{2} d^{2}}-\frac{2 \sqrt{d x +c}\, c}{b \,d^{2}}+\frac{2 \sqrt{d x +c}\, a^{2}}{b^{3} d^{2}}+\frac{2 \left(d x +c \right)^{\frac{3}{2}}}{3 b \,d^{2}}"," ",0,"2/3*(d*x+c)^(3/2)/b/d^2-a*x/b^2/d-1/d^2/b^2*a*c-2/d^2/b*(d*x+c)^(1/2)*c+2/d^2/b^3*(d*x+c)^(1/2)*a^2+2/d^2*a/b^2*ln(a+(d*x+c)^(1/2)*b)*c-2/d^2*a^3/b^4*ln(a+(d*x+c)^(1/2)*b)","A"
635,1,87,37,0.010000," ","int(1/(a+(d*x+c)^(1/2)*b),x)","\frac{a \ln \left(-a +\sqrt{d x +c}\, b \right)}{b^{2} d}-\frac{a \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{2} d}-\frac{a \ln \left(b^{2} d x +b^{2} c -a^{2}\right)}{b^{2} d}+\frac{2 \sqrt{d x +c}}{b d}"," ",0,"2*(d*x+c)^(1/2)/b/d+1/b^2/d*a*ln(-a+(d*x+c)^(1/2)*b)-a*ln(a+(d*x+c)^(1/2)*b)/b^2/d-a*ln(b^2*d*x+b^2*c-a^2)/b^2/d","B"
636,1,77,74,0.010000," ","int(1/x/(a+(d*x+c)^(1/2)*b),x)","\frac{2 b \sqrt{c}\, \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{-b^{2} c +a^{2}}+\frac{a \ln \left(d x \right)}{-b^{2} c +a^{2}}-\frac{2 a \ln \left(a +\sqrt{d x +c}\, b \right)}{-b^{2} c +a^{2}}"," ",0,"1/(-b^2*c+a^2)*a*ln(d*x)+2*b*arctanh((d*x+c)^(1/2)/c^(1/2))*c^(1/2)/(-b^2*c+a^2)-2*a*ln(a+(d*x+c)^(1/2)*b)/(-b^2*c+a^2)","A"
637,1,216,120,0.016000," ","int(1/x^2/(a+(d*x+c)^(1/2)*b),x)","\frac{b^{3} \sqrt{c}\, d \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{\left(-b^{2} c +a^{2}\right)^{2}}+\frac{a \,b^{2} d \ln \left(d x \right)}{\left(-b^{2} c +a^{2}\right)^{2}}-\frac{2 a \,b^{2} d \ln \left(a +\sqrt{d x +c}\, b \right)}{\left(-b^{2} c +a^{2}\right)^{2}}+\frac{a^{2} b d \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{\left(-b^{2} c +a^{2}\right)^{2} \sqrt{c}}+\frac{a \,b^{2} c}{\left(-b^{2} c +a^{2}\right)^{2} x}-\frac{\sqrt{d x +c}\, b^{3} c}{\left(-b^{2} c +a^{2}\right)^{2} x}-\frac{a^{3}}{\left(-b^{2} c +a^{2}\right)^{2} x}+\frac{\sqrt{d x +c}\, a^{2} b}{\left(-b^{2} c +a^{2}\right)^{2} x}"," ",0,"-1/(-b^2*c+a^2)^2/x*(d*x+c)^(1/2)*b^3*c+1/(-b^2*c+a^2)^2/x*(d*x+c)^(1/2)*b*a^2+1/(-b^2*c+a^2)^2/x*a*b^2*c-1/(-b^2*c+a^2)^2/x*a^3+d/(-b^2*c+a^2)^2*a*b^2*ln(d*x)+d/(-b^2*c+a^2)^2*c^(1/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*b^3+d/(-b^2*c+a^2)^2*b/c^(1/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*a^2-2*a*b^2*d*ln(a+(d*x+c)^(1/2)*b)/(-b^2*c+a^2)^2","A"
638,1,459,187,0.018000," ","int(1/x^3/(a+(d*x+c)^(1/2)*b),x)","\frac{3 b^{5} \sqrt{c}\, d^{2} \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{4 \left(-b^{2} c +a^{2}\right)^{3}}+\frac{a \,b^{4} d^{2} \ln \left(d x \right)}{\left(-b^{2} c +a^{2}\right)^{3}}-\frac{2 a \,b^{4} d^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{\left(-b^{2} c +a^{2}\right)^{3}}+\frac{3 a^{2} b^{3} d^{2} \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{2 \left(-b^{2} c +a^{2}\right)^{3} \sqrt{c}}-\frac{a^{4} b \,d^{2} \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{4 \left(-b^{2} c +a^{2}\right)^{3} c^{\frac{3}{2}}}+\frac{a \,b^{4} c d}{\left(-b^{2} c +a^{2}\right)^{3} x}-\frac{a^{3} b^{2} d}{\left(-b^{2} c +a^{2}\right)^{3} x}-\frac{a \,b^{4} c^{2}}{2 \left(-b^{2} c +a^{2}\right)^{3} x^{2}}+\frac{5 \sqrt{d x +c}\, b^{5} c^{2}}{4 \left(-b^{2} c +a^{2}\right)^{3} x^{2}}+\frac{a^{3} b^{2} c}{\left(-b^{2} c +a^{2}\right)^{3} x^{2}}-\frac{3 \sqrt{d x +c}\, a^{2} b^{3} c}{2 \left(-b^{2} c +a^{2}\right)^{3} x^{2}}-\frac{3 \left(d x +c \right)^{\frac{3}{2}} b^{5} c}{4 \left(-b^{2} c +a^{2}\right)^{3} x^{2}}-\frac{a^{5}}{2 \left(-b^{2} c +a^{2}\right)^{3} x^{2}}+\frac{\sqrt{d x +c}\, a^{4} b}{4 \left(-b^{2} c +a^{2}\right)^{3} x^{2}}+\frac{\left(d x +c \right)^{\frac{3}{2}} a^{2} b^{3}}{2 \left(-b^{2} c +a^{2}\right)^{3} x^{2}}+\frac{\left(d x +c \right)^{\frac{3}{2}} a^{4} b}{4 \left(-b^{2} c +a^{2}\right)^{3} c \,x^{2}}"," ",0,"-3/4/(-b^2*c+a^2)^3/x^2*b^5*c*(d*x+c)^(3/2)+1/2/(-b^2*c+a^2)^3/x^2*b^3*(d*x+c)^(3/2)*a^2+1/4/(-b^2*c+a^2)^3/x^2*b/c*(d*x+c)^(3/2)*a^4+d/(-b^2*c+a^2)^3/x*a*b^4*c-1/2/(-b^2*c+a^2)^3/x^2*b^4*a*c^2-d/(-b^2*c+a^2)^3/x*a^3*b^2+1/(-b^2*c+a^2)^3/x^2*b^2*a^3*c-3/2/(-b^2*c+a^2)^3/x^2*(d*x+c)^(1/2)*a^2*b^3*c+1/4/(-b^2*c+a^2)^3/x^2*(d*x+c)^(1/2)*b*a^4+5/4/(-b^2*c+a^2)^3/x^2*(d*x+c)^(1/2)*c^2*b^5-1/2/(-b^2*c+a^2)^3/x^2*a^5+d^2/(-b^2*c+a^2)^3*b^4*a*ln(d*x)+3/4*d^2/(-b^2*c+a^2)^3*b^5*c^(1/2)*arctanh((d*x+c)^(1/2)/c^(1/2))+3/2*d^2/(-b^2*c+a^2)^3*b^3/c^(1/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*a^2-1/4*d^2/(-b^2*c+a^2)^3*b/c^(3/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*a^4-2*a*b^4*d^2*ln(a+(d*x+c)^(1/2)*b)/(-b^2*c+a^2)^3","B"
639,1,416,222,0.013000," ","int(x^3/(a+(d*x+c)^(1/2)*b)^2,x)","\frac{x^{3}}{3 b^{2} d}-\frac{c \,x^{2}}{2 b^{2} d^{2}}+\frac{3 a^{2} x^{2}}{2 b^{4} d^{2}}-\frac{2 a \,c^{3}}{\left(a +\sqrt{d x +c}\, b \right) b^{2} d^{4}}-\frac{2 c^{3} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{2} d^{4}}+\frac{c^{2} x}{b^{2} d^{3}}+\frac{6 a^{3} c^{2}}{\left(a +\sqrt{d x +c}\, b \right) b^{4} d^{4}}+\frac{18 a^{2} c^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{4} d^{4}}-\frac{6 a^{2} c x}{b^{4} d^{3}}+\frac{11 c^{3}}{6 b^{2} d^{4}}-\frac{6 a^{5} c}{\left(a +\sqrt{d x +c}\, b \right) b^{6} d^{4}}-\frac{30 a^{4} c \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{6} d^{4}}+\frac{5 a^{4} x}{b^{6} d^{3}}-\frac{15 a^{2} c^{2}}{2 b^{4} d^{4}}-\frac{12 \sqrt{d x +c}\, a \,c^{2}}{b^{3} d^{4}}+\frac{2 a^{7}}{\left(a +\sqrt{d x +c}\, b \right) b^{8} d^{4}}+\frac{14 a^{6} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{8} d^{4}}+\frac{5 a^{4} c}{b^{6} d^{4}}+\frac{24 \sqrt{d x +c}\, a^{3} c}{b^{5} d^{4}}+\frac{4 \left(d x +c \right)^{\frac{3}{2}} a c}{b^{3} d^{4}}-\frac{12 \sqrt{d x +c}\, a^{5}}{b^{7} d^{4}}-\frac{8 \left(d x +c \right)^{\frac{3}{2}} a^{3}}{3 b^{5} d^{4}}-\frac{4 \left(d x +c \right)^{\frac{5}{2}} a}{5 b^{3} d^{4}}"," ",0,"1/3/d/b^2*x^3-1/2/d^2/b^2*x^2*c+1/d^3/b^2*x*c^2+11/6/d^4/b^2*c^3-4/5*a*(d*x+c)^(5/2)/b^3/d^4+3/2/d^2/b^4*x^2*a^2-6/d^3/b^4*x*a^2*c-15/2/d^4/b^4*a^2*c^2+4/d^4/b^3*(d*x+c)^(3/2)*a*c-8/3/d^4/b^5*(d*x+c)^(3/2)*a^3-12/d^4/b^3*a*c^2*(d*x+c)^(1/2)+5/d^3/b^6*x*a^4+5/d^4/b^6*a^4*c+24/d^4/b^5*a^3*c*(d*x+c)^(1/2)-12/d^4/b^7*a^5*(d*x+c)^(1/2)-2/d^4*a/b^2/(a+(d*x+c)^(1/2)*b)*c^3+6/d^4*a^3/b^4/(a+(d*x+c)^(1/2)*b)*c^2-6/d^4*a^5/b^6/(a+(d*x+c)^(1/2)*b)*c+2/d^4*a^7/b^8/(a+(d*x+c)^(1/2)*b)-2/d^4/b^2*ln(a+(d*x+c)^(1/2)*b)*c^3+18/d^4/b^4*ln(a+(d*x+c)^(1/2)*b)*a^2*c^2-30/d^4/b^6*ln(a+(d*x+c)^(1/2)*b)*a^4*c+14/d^4/b^8*ln(a+(d*x+c)^(1/2)*b)*a^6","A"
640,1,253,154,0.013000," ","int(x^2/(a+(d*x+c)^(1/2)*b)^2,x)","\frac{x^{2}}{2 b^{2} d}+\frac{2 a \,c^{2}}{\left(a +\sqrt{d x +c}\, b \right) b^{2} d^{3}}+\frac{2 c^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{2} d^{3}}-\frac{c x}{b^{2} d^{2}}-\frac{4 a^{3} c}{\left(a +\sqrt{d x +c}\, b \right) b^{4} d^{3}}-\frac{12 a^{2} c \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{4} d^{3}}+\frac{3 a^{2} x}{b^{4} d^{2}}-\frac{3 c^{2}}{2 b^{2} d^{3}}+\frac{2 a^{5}}{\left(a +\sqrt{d x +c}\, b \right) b^{6} d^{3}}+\frac{10 a^{4} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{6} d^{3}}+\frac{3 a^{2} c}{b^{4} d^{3}}+\frac{8 \sqrt{d x +c}\, a c}{b^{3} d^{3}}-\frac{8 \sqrt{d x +c}\, a^{3}}{b^{5} d^{3}}-\frac{4 \left(d x +c \right)^{\frac{3}{2}} a}{3 b^{3} d^{3}}"," ",0,"1/2/d/b^2*x^2-1/d^2/b^2*x*c-3/2/d^3/b^2*c^2-4/3*a*(d*x+c)^(3/2)/b^3/d^3+3/d^2/b^4*x*a^2+3/d^3/b^4*a^2*c+8/d^3/b^3*a*c*(d*x+c)^(1/2)-8/d^3/b^5*a^3*(d*x+c)^(1/2)+2/d^3*a/b^2/(a+(d*x+c)^(1/2)*b)*c^2-4/d^3*a^3/b^4/(a+(d*x+c)^(1/2)*b)*c+2/d^3*a^5/b^6/(a+(d*x+c)^(1/2)*b)+2/d^3/b^2*ln(a+(d*x+c)^(1/2)*b)*c^2-12/d^3/b^4*ln(a+(d*x+c)^(1/2)*b)*a^2*c+10/d^3/b^6*ln(a+(d*x+c)^(1/2)*b)*a^4","A"
641,1,125,89,0.010000," ","int(x/(a+(d*x+c)^(1/2)*b)^2,x)","-\frac{2 a c}{\left(a +\sqrt{d x +c}\, b \right) b^{2} d^{2}}-\frac{2 c \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{2} d^{2}}+\frac{x}{b^{2} d}+\frac{2 a^{3}}{\left(a +\sqrt{d x +c}\, b \right) b^{4} d^{2}}+\frac{6 a^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{b^{4} d^{2}}+\frac{c}{b^{2} d^{2}}-\frac{4 \sqrt{d x +c}\, a}{b^{3} d^{2}}"," ",0,"x/b^2/d+1/d^2/b^2*c-4*a*(d*x+c)^(1/2)/b^3/d^2-2/d^2*a/b^2/(a+(d*x+c)^(1/2)*b)*c+2/d^2*a^3/b^4/(a+(d*x+c)^(1/2)*b)-2/d^2/b^2*ln(a+(d*x+c)^(1/2)*b)*c+6/d^2/b^4*ln(a+(d*x+c)^(1/2)*b)*a^2","A"
642,1,142,43,0.020000," ","int(1/(a+(d*x+c)^(1/2)*b)^2,x)","-\frac{2 a^{2}}{\left(b^{2} d x +b^{2} c -a^{2}\right) b^{2} d}+\frac{a}{\left(-a +\sqrt{d x +c}\, b \right) b^{2} d}+\frac{a}{\left(a +\sqrt{d x +c}\, b \right) b^{2} d}-\frac{\ln \left(-a +\sqrt{d x +c}\, b \right)}{b^{2} d}+\frac{\ln \left(a +\sqrt{d x +c}\, b \right)}{b^{2} d}+\frac{\ln \left(b^{2} d x +b^{2} c -a^{2}\right)}{b^{2} d}"," ",0,"-2*a^2/(b^2*d*x+b^2*c-a^2)/b^2/d+ln(b^2*d*x+b^2*c-a^2)/b^2/d+a/b^2/d/(-a+(d*x+c)^(1/2)*b)-1/b^2/d*ln(-a+(d*x+c)^(1/2)*b)+a/b^2/d/(a+(d*x+c)^(1/2)*b)+ln(a+(d*x+c)^(1/2)*b)/b^2/d","B"
643,1,161,119,0.014000," ","int(1/x/(a+(d*x+c)^(1/2)*b)^2,x)","\frac{b^{2} c \ln \left(d x \right)}{\left(-b^{2} c +a^{2}\right)^{2}}-\frac{2 b^{2} c \ln \left(a +\sqrt{d x +c}\, b \right)}{\left(-b^{2} c +a^{2}\right)^{2}}+\frac{4 a b \sqrt{c}\, \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{\left(-b^{2} c +a^{2}\right)^{2}}+\frac{a^{2} \ln \left(d x \right)}{\left(-b^{2} c +a^{2}\right)^{2}}-\frac{2 a^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{\left(-b^{2} c +a^{2}\right)^{2}}+\frac{2 a}{\left(-b^{2} c +a^{2}\right) \left(a +\sqrt{d x +c}\, b \right)}"," ",0,"1/(-b^2*c+a^2)^2*ln(d*x)*b^2*c+1/(-b^2*c+a^2)^2*ln(d*x)*a^2+4*a*b*arctanh((d*x+c)^(1/2)/c^(1/2))*c^(1/2)/(-b^2*c+a^2)^2+2*a/(-b^2*c+a^2)/(a+(d*x+c)^(1/2)*b)-2/(-b^2*c+a^2)^2*ln(a+(d*x+c)^(1/2)*b)*b^2*c-2/(-b^2*c+a^2)^2*ln(a+(d*x+c)^(1/2)*b)*a^2","A"
644,1,312,188,0.018000," ","int(1/x^2/(a+(d*x+c)^(1/2)*b)^2,x)","\frac{b^{4} c d \ln \left(d x \right)}{\left(-b^{2} c +a^{2}\right)^{3}}-\frac{2 b^{4} c d \ln \left(a +\sqrt{d x +c}\, b \right)}{\left(-b^{2} c +a^{2}\right)^{3}}+\frac{6 a \,b^{3} \sqrt{c}\, d \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{\left(-b^{2} c +a^{2}\right)^{3}}+\frac{3 a^{2} b^{2} d \ln \left(d x \right)}{\left(-b^{2} c +a^{2}\right)^{3}}-\frac{6 a^{2} b^{2} d \ln \left(a +\sqrt{d x +c}\, b \right)}{\left(-b^{2} c +a^{2}\right)^{3}}+\frac{2 a^{3} b d \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{\left(-b^{2} c +a^{2}\right)^{3} \sqrt{c}}+\frac{b^{4} c^{2}}{\left(-b^{2} c +a^{2}\right)^{3} x}-\frac{2 \sqrt{d x +c}\, a \,b^{3} c}{\left(-b^{2} c +a^{2}\right)^{3} x}+\frac{2 a \,b^{2} d}{\left(-b^{2} c +a^{2}\right)^{2} \left(a +\sqrt{d x +c}\, b \right)}-\frac{a^{4}}{\left(-b^{2} c +a^{2}\right)^{3} x}+\frac{2 \sqrt{d x +c}\, a^{3} b}{\left(-b^{2} c +a^{2}\right)^{3} x}"," ",0,"-2/(-b^2*c+a^2)^3/x*(d*x+c)^(1/2)*a*b^3*c+2/(-b^2*c+a^2)^3/x*(d*x+c)^(1/2)*a^3*b+1/(-b^2*c+a^2)^3/x*b^4*c^2-1/(-b^2*c+a^2)^3/x*a^4+d/(-b^2*c+a^2)^3*ln(d*x)*b^4*c+3*d/(-b^2*c+a^2)^3*ln(d*x)*b^2*a^2+6*d/(-b^2*c+a^2)^3*c^(1/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*a*b^3+2*d/(-b^2*c+a^2)^3*b/c^(1/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*a^3+2*a*b^2*d/(-b^2*c+a^2)^2/(a+(d*x+c)^(1/2)*b)-2*d*b^4/(-b^2*c+a^2)^3*ln(a+(d*x+c)^(1/2)*b)*c-6*d*b^2/(-b^2*c+a^2)^3*ln(a+(d*x+c)^(1/2)*b)*a^2","A"
645,1,610,281,0.023000," ","int(1/x^3/(a+(d*x+c)^(1/2)*b)^2,x)","\frac{b^{6} c \,d^{2} \ln \left(d x \right)}{\left(-b^{2} c +a^{2}\right)^{4}}-\frac{2 b^{6} c \,d^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{\left(-b^{2} c +a^{2}\right)^{4}}+\frac{15 a \,b^{5} \sqrt{c}\, d^{2} \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{2 \left(-b^{2} c +a^{2}\right)^{4}}+\frac{5 a^{2} b^{4} d^{2} \ln \left(d x \right)}{\left(-b^{2} c +a^{2}\right)^{4}}-\frac{10 a^{2} b^{4} d^{2} \ln \left(a +\sqrt{d x +c}\, b \right)}{\left(-b^{2} c +a^{2}\right)^{4}}+\frac{5 a^{3} b^{3} d^{2} \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{\left(-b^{2} c +a^{2}\right)^{4} \sqrt{c}}+\frac{b^{6} c^{2} d}{\left(-b^{2} c +a^{2}\right)^{4} x}-\frac{a^{5} b \,d^{2} \arctanh \left(\frac{\sqrt{d x +c}}{\sqrt{c}}\right)}{2 \left(-b^{2} c +a^{2}\right)^{4} c^{\frac{3}{2}}}+\frac{2 a^{2} b^{4} c d}{\left(-b^{2} c +a^{2}\right)^{4} x}+\frac{2 a \,b^{4} d^{2}}{\left(-b^{2} c +a^{2}\right)^{3} \left(a +\sqrt{d x +c}\, b \right)}-\frac{b^{6} c^{3}}{2 \left(-b^{2} c +a^{2}\right)^{4} x^{2}}-\frac{3 a^{4} b^{2} d}{\left(-b^{2} c +a^{2}\right)^{4} x}+\frac{a^{2} b^{4} c^{2}}{2 \left(-b^{2} c +a^{2}\right)^{4} x^{2}}+\frac{9 \sqrt{d x +c}\, a \,b^{5} c^{2}}{2 \left(-b^{2} c +a^{2}\right)^{4} x^{2}}+\frac{a^{4} b^{2} c}{2 \left(-b^{2} c +a^{2}\right)^{4} x^{2}}-\frac{5 \sqrt{d x +c}\, a^{3} b^{3} c}{\left(-b^{2} c +a^{2}\right)^{4} x^{2}}-\frac{7 \left(d x +c \right)^{\frac{3}{2}} a \,b^{5} c}{2 \left(-b^{2} c +a^{2}\right)^{4} x^{2}}-\frac{a^{6}}{2 \left(-b^{2} c +a^{2}\right)^{4} x^{2}}+\frac{\sqrt{d x +c}\, a^{5} b}{2 \left(-b^{2} c +a^{2}\right)^{4} x^{2}}+\frac{3 \left(d x +c \right)^{\frac{3}{2}} a^{3} b^{3}}{\left(-b^{2} c +a^{2}\right)^{4} x^{2}}+\frac{\left(d x +c \right)^{\frac{3}{2}} a^{5} b}{2 \left(-b^{2} c +a^{2}\right)^{4} c \,x^{2}}"," ",0,"-7/2/(-b^2*c+a^2)^4/x^2*a*b^5*c*(d*x+c)^(3/2)+3/(-b^2*c+a^2)^4/x^2*a^3*b^3*(d*x+c)^(3/2)+1/2/(-b^2*c+a^2)^4/x^2*a^5*b/c*(d*x+c)^(3/2)+d/(-b^2*c+a^2)^4/x*b^6*c^2-1/2/(-b^2*c+a^2)^4/x^2*c^3*b^6+2*d/(-b^2*c+a^2)^4/x*a^2*b^4*c+1/2/(-b^2*c+a^2)^4/x^2*b^4*a^2*c^2-3*d/(-b^2*c+a^2)^4/x*a^4*b^2+1/2/(-b^2*c+a^2)^4/x^2*b^2*a^4*c+9/2/(-b^2*c+a^2)^4/x^2*(d*x+c)^(1/2)*a*b^5*c^2-5/(-b^2*c+a^2)^4/x^2*(d*x+c)^(1/2)*b^3*a^3*c+1/2/(-b^2*c+a^2)^4/x^2*(d*x+c)^(1/2)*b*a^5-1/2/(-b^2*c+a^2)^4/x^2*a^6+d^2/(-b^2*c+a^2)^4*b^6*c*ln(d*x)+5*d^2/(-b^2*c+a^2)^4*b^4*ln(d*x)*a^2+15/2*d^2/(-b^2*c+a^2)^4*b^5*c^(1/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*a+5*d^2/(-b^2*c+a^2)^4*b^3/c^(1/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*a^3-1/2*d^2/(-b^2*c+a^2)^4*b/c^(3/2)*arctanh((d*x+c)^(1/2)/c^(1/2))*a^5+2*d^2*b^4/(-b^2*c+a^2)^3*a/(a+(d*x+c)^(1/2)*b)-2*d^2*b^6/(-b^2*c+a^2)^4*ln(a+(d*x+c)^(1/2)*b)*c-10*d^2*b^4/(-b^2*c+a^2)^4*ln(a+(d*x+c)^(1/2)*b)*a^2","B"
646,1,383,278,0.003000," ","int(x^3/(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{-\frac{28 \left(a +\sqrt{d x +c}\, b \right)^{\frac{13}{2}} a}{13}-4 \left(-b^{2} c +a^{2}\right)^{3} \sqrt{a +\sqrt{d x +c}\, b}\, a +\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{15}{2}}}{15}+\frac{4 \left(-3 b^{2} c +21 a^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{11}{2}}}{11}+\frac{4 \left(-8 \left(-b^{2} c +a^{2}\right) a -2 \left(-2 b^{2} c +6 a^{2}\right) a -\left(-3 b^{2} c +15 a^{2}\right) a \right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{9}{2}}}{9}+\frac{4 \left(8 \left(-b^{2} c +a^{2}\right) a^{2}-\left(-8 \left(-b^{2} c +a^{2}\right) a -2 \left(-2 b^{2} c +6 a^{2}\right) a \right) a +\left(-b^{2} c +a^{2}\right) \left(-2 b^{2} c +6 a^{2}\right)+\left(-b^{2} c +a^{2}\right)^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{7}{2}}}{7}+\frac{4 \left(-6 \left(-b^{2} c +a^{2}\right)^{2} a -\left(8 \left(-b^{2} c +a^{2}\right) a^{2}+\left(-b^{2} c +a^{2}\right) \left(-2 b^{2} c +6 a^{2}\right)+\left(-b^{2} c +a^{2}\right)^{2}\right) a \right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}}}{5}+\frac{4 \left(6 \left(-b^{2} c +a^{2}\right)^{2} a^{2}+\left(-b^{2} c +a^{2}\right)^{3}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}}}{3}}{b^{8} d^{4}}"," ",0,"4/d^4/b^8*(1/15*(a+(d*x+c)^(1/2)*b)^(15/2)-7/13*a*(a+(d*x+c)^(1/2)*b)^(13/2)+1/11*(-3*b^2*c+21*a^2)*(a+(d*x+c)^(1/2)*b)^(11/2)+1/9*(-8*(-b^2*c+a^2)*a-2*(-2*b^2*c+6*a^2)*a-(-3*b^2*c+15*a^2)*a)*(a+(d*x+c)^(1/2)*b)^(9/2)+1/7*(8*(-b^2*c+a^2)*a^2-(-8*(-b^2*c+a^2)*a-2*(-2*b^2*c+6*a^2)*a)*a+(-b^2*c+a^2)*(-2*b^2*c+6*a^2)+(-b^2*c+a^2)^2)*(a+(d*x+c)^(1/2)*b)^(7/2)+1/5*(-6*(-b^2*c+a^2)^2*a-(8*(-b^2*c+a^2)*a^2+(-b^2*c+a^2)*(-2*b^2*c+6*a^2)+(-b^2*c+a^2)^2)*a)*(a+(d*x+c)^(1/2)*b)^(5/2)+1/3*(6*(-b^2*c+a^2)^2*a^2+(-b^2*c+a^2)^3)*(a+(d*x+c)^(1/2)*b)^(3/2)-(-b^2*c+a^2)^3*a*(a+(d*x+c)^(1/2)*b)^(1/2))","A"
647,1,183,188,0.003000," ","int(x^2/(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{-\frac{20 \left(a +\sqrt{d x +c}\, b \right)^{\frac{9}{2}} a}{9}-4 \left(-b^{2} c +a^{2}\right)^{2} \sqrt{a +\sqrt{d x +c}\, b}\, a +\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{11}{2}}}{11}+\frac{4 \left(-2 b^{2} c +10 a^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{7}{2}}}{7}+\frac{4 \left(-4 \left(-b^{2} c +a^{2}\right) a -\left(-2 b^{2} c +6 a^{2}\right) a \right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}}}{5}+\frac{4 \left(4 \left(-b^{2} c +a^{2}\right) a^{2}+\left(-b^{2} c +a^{2}\right)^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}}}{3}}{b^{6} d^{3}}"," ",0,"4/d^3/b^6*(1/11*(a+(d*x+c)^(1/2)*b)^(11/2)-5/9*a*(a+(d*x+c)^(1/2)*b)^(9/2)+1/7*(-2*b^2*c+10*a^2)*(a+(d*x+c)^(1/2)*b)^(7/2)+1/5*(-4*(-b^2*c+a^2)*a-(-2*b^2*c+6*a^2)*a)*(a+(d*x+c)^(1/2)*b)^(5/2)+1/3*(4*(-b^2*c+a^2)*a^2+(-b^2*c+a^2)^2)*(a+(d*x+c)^(1/2)*b)^(3/2)-(-b^2*c+a^2)^2*a*(a+(d*x+c)^(1/2)*b)^(1/2))","A"
648,1,94,109,0.004000," ","int(x/(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{-\frac{12 \left(a +\sqrt{d x +c}\, b \right)^{\frac{5}{2}} a}{5}-4 \left(-b^{2} c +a^{2}\right) \sqrt{a +\sqrt{d x +c}\, b}\, a +\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{7}{2}}}{7}+\frac{4 \left(-b^{2} c +3 a^{2}\right) \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}}}{3}}{b^{4} d^{2}}"," ",0,"4/d^2/b^4*(1/7*(a+(d*x+c)^(1/2)*b)^(7/2)-3/5*(a+(d*x+c)^(1/2)*b)^(5/2)*a+1/3*(-b^2*c+3*a^2)*(a+(d*x+c)^(1/2)*b)^(3/2)-(-b^2*c+a^2)*a*(a+(d*x+c)^(1/2)*b)^(1/2))","A"
649,1,41,44,0.006000," ","int(1/(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{-4 \sqrt{a +\sqrt{d x +c}\, b}\, a +\frac{4 \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}}}{3}}{b^{2} d}"," ",0,"4/d/b^2*(1/3*(a+(d*x+c)^(1/2)*b)^(3/2)-a*(a+(d*x+c)^(1/2)*b)^(1/2))","A"
650,1,92,73,0.018000," ","int(1/x/(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{2 \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{\sqrt{-a -\sqrt{b^{2} c}}}+\frac{2 \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{\sqrt{-a +\sqrt{b^{2} c}}}"," ",0,"2/(-a-(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2))+2/(-a+(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2))","A"
651,1,265,125,0.027000," ","int(1/x^2/(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{2 \sqrt{b^{2} c}\, d \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{\left(-4 a -4 \sqrt{b^{2} c}\right) \sqrt{-a -\sqrt{b^{2} c}}\, c}-\frac{2 \sqrt{b^{2} c}\, d \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{\left(-4 a +4 \sqrt{b^{2} c}\right) \sqrt{-a +\sqrt{b^{2} c}}\, c}-\frac{2 \sqrt{b^{2} c}\, \sqrt{a +\sqrt{d x +c}\, b}\, d}{\left(-4 a -4 \sqrt{b^{2} c}\right) \left(-\sqrt{d x +c}\, b +\sqrt{b^{2} c}\right) c}-\frac{2 \sqrt{b^{2} c}\, \sqrt{a +\sqrt{d x +c}\, b}\, d}{\left(-4 a +4 \sqrt{b^{2} c}\right) \left(\sqrt{d x +c}\, b +\sqrt{b^{2} c}\right) c}"," ",0,"-2*d*(b^2*c)^(1/2)/c*(a+(d*x+c)^(1/2)*b)^(1/2)/(-4*(b^2*c)^(1/2)-4*a)/(-(d*x+c)^(1/2)*b+(b^2*c)^(1/2))+2*d*(b^2*c)^(1/2)/c/(-4*(b^2*c)^(1/2)-4*a)/(-a-(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2))-2*d*(b^2*c)^(1/2)/c*(a+(d*x+c)^(1/2)*b)^(1/2)/(4*(b^2*c)^(1/2)-4*a)/((d*x+c)^(1/2)*b+(b^2*c)^(1/2))-2*d*(b^2*c)^(1/2)/c/(4*(b^2*c)^(1/2)-4*a)/(-a+(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2))","B"
652,1,840,209,0.102000," ","int(1/x^3/(a+(d*x+c)^(1/2)*b)^(1/2),x)","\frac{a \,b^{2} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{8 \sqrt{b^{2} c}\, \left(b^{2} c +a^{2}+2 \sqrt{b^{2} c}\, a \right) \sqrt{-a -\sqrt{b^{2} c}}\, c}+\frac{a \,b^{2} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{8 \sqrt{b^{2} c}\, \left(-b^{2} c -a^{2}+2 \sqrt{b^{2} c}\, a \right) \sqrt{-a +\sqrt{b^{2} c}}\, c}+\frac{\left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} a \,b^{2} d^{2}}{8 \sqrt{b^{2} c}\, \left(\sqrt{d x +c}\, b -\sqrt{b^{2} c}\right)^{2} \left(b^{2} c +a^{2}+2 \sqrt{b^{2} c}\, a \right) c}-\frac{\sqrt{a +\sqrt{d x +c}\, b}\, a \,b^{2} d^{2}}{8 \sqrt{b^{2} c}\, \left(\sqrt{d x +c}\, b -\sqrt{b^{2} c}\right)^{2} \left(a +\sqrt{b^{2} c}\right) c}-\frac{\left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} a \,b^{2} d^{2}}{8 \sqrt{b^{2} c}\, \left(\sqrt{d x +c}\, b +\sqrt{b^{2} c}\right)^{2} \left(b^{2} c +a^{2}-2 \sqrt{b^{2} c}\, a \right) c}+\frac{\sqrt{a +\sqrt{d x +c}\, b}\, a \,b^{2} d^{2}}{8 \sqrt{b^{2} c}\, \left(\sqrt{d x +c}\, b +\sqrt{b^{2} c}\right)^{2} \left(a -\sqrt{b^{2} c}\right) c}+\frac{5 b^{2} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a -\sqrt{b^{2} c}}}\right)}{16 \left(b^{2} c +a^{2}+2 \sqrt{b^{2} c}\, a \right) \sqrt{-a -\sqrt{b^{2} c}}\, c}-\frac{5 b^{2} d^{2} \arctan \left(\frac{\sqrt{a +\sqrt{d x +c}\, b}}{\sqrt{-a +\sqrt{b^{2} c}}}\right)}{16 \left(-b^{2} c -a^{2}+2 \sqrt{b^{2} c}\, a \right) \sqrt{-a +\sqrt{b^{2} c}}\, c}+\frac{5 \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} b^{2} d^{2}}{16 \left(\sqrt{d x +c}\, b -\sqrt{b^{2} c}\right)^{2} \left(b^{2} c +a^{2}+2 \sqrt{b^{2} c}\, a \right) c}-\frac{7 \sqrt{a +\sqrt{d x +c}\, b}\, b^{2} d^{2}}{16 \left(\sqrt{d x +c}\, b -\sqrt{b^{2} c}\right)^{2} \left(a +\sqrt{b^{2} c}\right) c}+\frac{5 \left(a +\sqrt{d x +c}\, b \right)^{\frac{3}{2}} b^{2} d^{2}}{16 \left(\sqrt{d x +c}\, b +\sqrt{b^{2} c}\right)^{2} \left(b^{2} c +a^{2}-2 \sqrt{b^{2} c}\, a \right) c}-\frac{7 \sqrt{a +\sqrt{d x +c}\, b}\, b^{2} d^{2}}{16 \left(\sqrt{d x +c}\, b +\sqrt{b^{2} c}\right)^{2} \left(a -\sqrt{b^{2} c}\right) c}"," ",0,"5/16*b^2*d^2/c/((d*x+c)^(1/2)*b-(b^2*c)^(1/2))^2/(b^2*c+2*a*(b^2*c)^(1/2)+a^2)*(a+(d*x+c)^(1/2)*b)^(3/2)+1/8*b^2*d^2/c/(b^2*c)^(1/2)/((d*x+c)^(1/2)*b-(b^2*c)^(1/2))^2/(b^2*c+2*a*(b^2*c)^(1/2)+a^2)*(a+(d*x+c)^(1/2)*b)^(3/2)*a-7/16*b^2*d^2/c/((d*x+c)^(1/2)*b-(b^2*c)^(1/2))^2/((b^2*c)^(1/2)+a)*(a+(d*x+c)^(1/2)*b)^(1/2)-1/8*b^2*d^2/c/(b^2*c)^(1/2)/((d*x+c)^(1/2)*b-(b^2*c)^(1/2))^2/((b^2*c)^(1/2)+a)*(a+(d*x+c)^(1/2)*b)^(1/2)*a+5/16*b^2*d^2/c/(b^2*c+2*a*(b^2*c)^(1/2)+a^2)/(-a-(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2))+1/8*b^2*d^2/c/(b^2*c)^(1/2)/(b^2*c+2*a*(b^2*c)^(1/2)+a^2)/(-a-(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a-(b^2*c)^(1/2))^(1/2))*a+5/16*b^2*d^2/c/((d*x+c)^(1/2)*b+(b^2*c)^(1/2))^2/(b^2*c-2*a*(b^2*c)^(1/2)+a^2)*(a+(d*x+c)^(1/2)*b)^(3/2)-1/8*b^2*d^2/c/(b^2*c)^(1/2)/((d*x+c)^(1/2)*b+(b^2*c)^(1/2))^2/(b^2*c-2*a*(b^2*c)^(1/2)+a^2)*(a+(d*x+c)^(1/2)*b)^(3/2)*a+1/8*b^2*d^2/c/(b^2*c)^(1/2)/((d*x+c)^(1/2)*b+(b^2*c)^(1/2))^2/(-(b^2*c)^(1/2)+a)*(a+(d*x+c)^(1/2)*b)^(1/2)*a-7/16*b^2*d^2/c/((d*x+c)^(1/2)*b+(b^2*c)^(1/2))^2/(-(b^2*c)^(1/2)+a)*(a+(d*x+c)^(1/2)*b)^(1/2)-5/16*b^2*d^2/c/(-b^2*c+2*a*(b^2*c)^(1/2)-a^2)/(-a+(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2))+1/8*b^2*d^2/c/(b^2*c)^(1/2)/(-b^2*c+2*a*(b^2*c)^(1/2)-a^2)/(-a+(b^2*c)^(1/2))^(1/2)*arctan((a+(d*x+c)^(1/2)*b)^(1/2)/(-a+(b^2*c)^(1/2))^(1/2))*a","B"
653,0,0,334,0.007000," ","int(x^3*(a+(d*x+c)^(1/2)*b)^p,x)","\int x^{3} \left(a +\sqrt{d x +c}\, b \right)^{p}\, dx"," ",0,"int(x^3*(a+(d*x+c)^(1/2)*b)^p,x)","F"
654,0,0,230,0.005000," ","int(x^2*(a+(d*x+c)^(1/2)*b)^p,x)","\int x^{2} \left(a +\sqrt{d x +c}\, b \right)^{p}\, dx"," ",0,"int(x^2*(a+(d*x+c)^(1/2)*b)^p,x)","F"
655,0,0,137,0.005000," ","int(x*(a+(d*x+c)^(1/2)*b)^p,x)","\int x \left(a +\sqrt{d x +c}\, b \right)^{p}\, dx"," ",0,"int(x*(a+(d*x+c)^(1/2)*b)^p,x)","F"
656,0,0,58,0.006000," ","int((a+(d*x+c)^(1/2)*b)^p,x)","\int \left(a +\sqrt{d x +c}\, b \right)^{p}\, dx"," ",0,"int((a+(d*x+c)^(1/2)*b)^p,x)","F"
657,0,0,127,0.005000," ","int((a+(d*x+c)^(1/2)*b)^p/x,x)","\int \frac{\left(a +\sqrt{d x +c}\, b \right)^{p}}{x}\, dx"," ",0,"int((a+(d*x+c)^(1/2)*b)^p/x,x)","F"
658,1,70,77,0.008000," ","int((a+b*(c*x)^n)^(5/2)/x,x)","\frac{-2 a^{\frac{5}{2}} \arctanh \left(\frac{\sqrt{b \left(c x \right)^{n}+a}}{\sqrt{a}}\right)+2 \sqrt{b \left(c x \right)^{n}+a}\, a^{2}+\frac{2 \left(b \left(c x \right)^{n}+a \right)^{\frac{3}{2}} a}{3}+\frac{2 \left(b \left(c x \right)^{n}+a \right)^{\frac{5}{2}}}{5}}{n}"," ",0,"1/n*(2/5*(a+b*(c*x)^n)^(5/2)+2/3*a*(a+b*(c*x)^n)^(3/2)+2*(a+b*(c*x)^n)^(1/2)*a^2-2*a^(5/2)*arctanh((a+b*(c*x)^n)^(1/2)/a^(1/2)))","A"
659,1,54,58,0.003000," ","int((b*(c*x)^n+a)^(3/2)/x,x)","\frac{-2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \left(c x \right)^{n}+a}}{\sqrt{a}}\right)+2 \sqrt{b \left(c x \right)^{n}+a}\, a +\frac{2 \left(b \left(c x \right)^{n}+a \right)^{\frac{3}{2}}}{3}}{n}"," ",0,"1/n*(2/3*(b*(c*x)^n+a)^(3/2)+2*a*(b*(c*x)^n+a)^(1/2)-2*a^(3/2)*arctanh((b*(c*x)^n+a)^(1/2)/a^(1/2)))","A"
660,1,40,41,0.003000," ","int((b*(c*x)^n+a)^(1/2)/x,x)","\frac{-2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \left(c x \right)^{n}+a}}{\sqrt{a}}\right)+2 \sqrt{b \left(c x \right)^{n}+a}}{n}"," ",0,"1/n*(2*(b*(c*x)^n+a)^(1/2)-2*a^(1/2)*arctanh((b*(c*x)^n+a)^(1/2)/a^(1/2)))","A"
661,1,25,24,0.006000," ","int(1/x/(b*(c*x)^n+a)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{b \left(c x \right)^{n}+a}}{\sqrt{a}}\right)}{\sqrt{a}\, n}"," ",0,"-2*arctanh((b*(c*x)^n+a)^(1/2)/a^(1/2))/n/a^(1/2)","A"
662,1,43,44,0.008000," ","int(1/x/(b*(c*x)^n+a)^(3/2),x)","\frac{-\frac{2 \arctanh \left(\frac{\sqrt{b \left(c x \right)^{n}+a}}{\sqrt{a}}\right)}{a^{\frac{3}{2}}}+\frac{2}{\sqrt{b \left(c x \right)^{n}+a}\, a}}{n}"," ",0,"1/n*(2/a/(b*(c*x)^n+a)^(1/2)-2/a^(3/2)*arctanh((b*(c*x)^n+a)^(1/2)/a^(1/2)))","A"
663,1,59,63,0.011000," ","int(1/x/(b*(c*x)^n+a)^(5/2),x)","\frac{\frac{2}{3 \left(b \left(c x \right)^{n}+a \right)^{\frac{3}{2}} a}-\frac{2 \arctanh \left(\frac{\sqrt{b \left(c x \right)^{n}+a}}{\sqrt{a}}\right)}{a^{\frac{5}{2}}}+\frac{2}{\sqrt{b \left(c x \right)^{n}+a}\, a^{2}}}{n}"," ",0,"1/n*(-2/a^(5/2)*arctanh((b*(c*x)^n+a)^(1/2)/a^(1/2))+2/a^2/(b*(c*x)^n+a)^(1/2)+2/3/a/(b*(c*x)^n+a)^(3/2))","A"
664,1,86,85,0.010000," ","int((-a+b*(c*x)^n)^(5/2)/x,x)","-\frac{2 a^{\frac{5}{2}} \arctan \left(\frac{\sqrt{b \left(c x \right)^{n}-a}}{\sqrt{a}}\right)}{n}+\frac{2 \sqrt{b \left(c x \right)^{n}-a}\, a^{2}}{n}-\frac{2 \left(b \left(c x \right)^{n}-a \right)^{\frac{3}{2}} a}{3 n}+\frac{2 \left(b \left(c x \right)^{n}-a \right)^{\frac{5}{2}}}{5 n}"," ",0,"-2/3*a*(-a+b*(c*x)^n)^(3/2)/n+2/5*(-a+b*(c*x)^n)^(5/2)/n-2*a^(5/2)*arctan((-a+b*(c*x)^n)^(1/2)/a^(1/2))/n+2*a^2*(-a+b*(c*x)^n)^(1/2)/n","A"
665,1,65,64,0.007000," ","int((b*(c*x)^n-a)^(3/2)/x,x)","\frac{2 a^{\frac{3}{2}} \arctan \left(\frac{\sqrt{b \left(c x \right)^{n}-a}}{\sqrt{a}}\right)}{n}-\frac{2 \sqrt{b \left(c x \right)^{n}-a}\, a}{n}+\frac{2 \left(b \left(c x \right)^{n}-a \right)^{\frac{3}{2}}}{3 n}"," ",0,"2/3*(b*(c*x)^n-a)^(3/2)/n+2*a^(3/2)*arctan((b*(c*x)^n-a)^(1/2)/a^(1/2))/n-2*a*(b*(c*x)^n-a)^(1/2)/n","A"
666,1,46,45,0.005000," ","int((b*(c*x)^n-a)^(1/2)/x,x)","-\frac{2 \sqrt{a}\, \arctan \left(\frac{\sqrt{b \left(c x \right)^{n}-a}}{\sqrt{a}}\right)}{n}+\frac{2 \sqrt{b \left(c x \right)^{n}-a}}{n}"," ",0,"-2*arctan((b*(c*x)^n-a)^(1/2)/a^(1/2))*a^(1/2)/n+2*(b*(c*x)^n-a)^(1/2)/n","A"
667,1,27,26,0.007000," ","int(1/x/(b*(c*x)^n-a)^(1/2),x)","\frac{2 \arctan \left(\frac{\sqrt{b \left(c x \right)^{n}-a}}{\sqrt{a}}\right)}{\sqrt{a}\, n}"," ",0,"2*arctan((b*(c*x)^n-a)^(1/2)/a^(1/2))/n/a^(1/2)","A"
668,1,49,48,0.011000," ","int(1/x/(b*(c*x)^n-a)^(3/2),x)","-\frac{2 \arctan \left(\frac{\sqrt{b \left(c x \right)^{n}-a}}{\sqrt{a}}\right)}{a^{\frac{3}{2}} n}-\frac{2}{\sqrt{b \left(c x \right)^{n}-a}\, a n}"," ",0,"-2*arctan((b*(c*x)^n-a)^(1/2)/a^(1/2))/a^(3/2)/n-2/a/n/(b*(c*x)^n-a)^(1/2)","A"
669,1,70,69,0.010000," ","int(1/x/(b*(c*x)^n-a)^(5/2),x)","-\frac{2}{3 \left(b \left(c x \right)^{n}-a \right)^{\frac{3}{2}} a n}+\frac{2 \arctan \left(\frac{\sqrt{b \left(c x \right)^{n}-a}}{\sqrt{a}}\right)}{a^{\frac{5}{2}} n}+\frac{2}{\sqrt{b \left(c x \right)^{n}-a}\, a^{2} n}"," ",0,"-2/3/a/n/(b*(c*x)^n-a)^(3/2)+2*arctan((b*(c*x)^n-a)^(1/2)/a^(1/2))/a^(5/2)/n+2/a^2/n/(b*(c*x)^n-a)^(1/2)","A"
670,1,18,17,0.004000," ","int(1/x/(b*x+a)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{b x +a}}{\sqrt{a}}\right)}{\sqrt{a}}"," ",0,"-2*arctanh((b*x+a)^(1/2)/a^(1/2))/a^(1/2)","A"
671,1,25,24,0.007000," ","int(1/x/(a+b*(c*x)^m)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{b \left(c x \right)^{m}+a}}{\sqrt{a}}\right)}{\sqrt{a}\, m}"," ",0,"-2*arctanh((a+b*(c*x)^m)^(1/2)/a^(1/2))/m/a^(1/2)","A"
672,1,32,31,0.012000," ","int(1/x/(a+b*(c*(d*x)^m)^n)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{b \left(c \left(d x \right)^{m}\right)^{n}+a}}{\sqrt{a}}\right)}{\sqrt{a}\, m n}"," ",0,"-2*arctanh((a+b*(c*(d*x)^m)^n)^(1/2)/a^(1/2))/m/n/a^(1/2)","A"
673,1,39,38,0.019000," ","int(1/x/(a+b*(c*(d*(e*x)^m)^n)^p)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{b \left(c \left(d \left(e x \right)^{m}\right)^{n}\right)^{p}+a}}{\sqrt{a}}\right)}{\sqrt{a}\, m n p}"," ",0,"-2*arctanh((a+b*(c*(d*(e*x)^m)^n)^p)^(1/2)/a^(1/2))/m/n/p/a^(1/2)","A"
674,1,46,45,0.024000," ","int(1/x/(a+b*(c*(d*(e*(f*x)^m)^n)^p)^q)^(1/2),x)","-\frac{2 \arctanh \left(\frac{\sqrt{b \left(c \left(d \left(e \left(f x \right)^{m}\right)^{n}\right)^{p}\right)^{q}+a}}{\sqrt{a}}\right)}{\sqrt{a}\, m n p q}"," ",0,"-2*arctanh((a+b*(c*(d*(e*(f*x)^m)^n)^p)^q)^(1/2)/a^(1/2))/m/n/p/q/a^(1/2)","A"
675,1,83,56,0.019000," ","int((x^2-1)^3*(-1+1/x^2)^(1/2)/x,x)","\frac{\sqrt{-\frac{x^{2}-1}{x^{2}}}\, \left(-8 \left(-x^{2}+1\right)^{\frac{3}{2}} x^{4}+30 \left(-x^{2}+1\right)^{\frac{3}{2}} x^{2}+105 \sqrt{-x^{2}+1}\, x^{2}+105 x \arcsin \left(x \right)+48 \left(-x^{2}+1\right)^{\frac{3}{2}}\right)}{48 \sqrt{-x^{2}+1}}"," ",0,"1/48*(-(x^2-1)/x^2)^(1/2)*(-8*x^4*(-x^2+1)^(3/2)+30*x^2*(-x^2+1)^(3/2)+48*(-x^2+1)^(3/2)+105*x^2*(-x^2+1)^(1/2)+105*arcsin(x)*x)/(-x^2+1)^(1/2)","A"
676,1,69,44,0.014000," ","int((x^2-1)^2*(-1+1/x^2)^(1/2)/x,x)","-\frac{\sqrt{-\frac{x^{2}-1}{x^{2}}}\, \left(2 \left(-x^{2}+1\right)^{\frac{3}{2}} x^{2}+15 \sqrt{-x^{2}+1}\, x^{2}+15 x \arcsin \left(x \right)+8 \left(-x^{2}+1\right)^{\frac{3}{2}}\right)}{8 \sqrt{-x^{2}+1}}"," ",0,"-1/8*(-(x^2-1)/x^2)^(1/2)*(2*(-x^2+1)^(3/2)*x^2+8*(-x^2+1)^(3/2)+15*(-x^2+1)^(1/2)*x^2+15*x*arcsin(x))/(-x^2+1)^(1/2)","A"
677,1,55,32,0.013000," ","int((x^2-1)*(-1+1/x^2)^(1/2)/x,x)","\frac{\sqrt{-\frac{x^{2}-1}{x^{2}}}\, \left(3 \sqrt{-x^{2}+1}\, x^{2}+3 x \arcsin \left(x \right)+2 \left(-x^{2}+1\right)^{\frac{3}{2}}\right)}{2 \sqrt{-x^{2}+1}}"," ",0,"1/2*(-(x^2-1)/x^2)^(1/2)*(2*(-x^2+1)^(3/2)+3*(-x^2+1)^(1/2)*x^2+3*x*arcsin(x))/(-x^2+1)^(1/2)","A"
678,1,13,7,0.005000," ","int((-1+1/x^2)^(1/2)/x/(x^2-1),x)","\sqrt{-\frac{x^{2}-1}{x^{2}}}"," ",0,"(-(x^2-1)/x^2)^(1/2)","A"
679,1,29,17,0.007000," ","int((-1+1/x^2)^(1/2)/x/(x^2-1)^2,x)","-\frac{\left(2 x^{2}-1\right) \sqrt{-\frac{x^{2}-1}{x^{2}}}}{x^{2}-1}"," ",0,"-(2*x^2-1)*(-(x^2-1)/x^2)^(1/2)/(x^2-1)","A"
680,1,34,26,0.005000," ","int((-1+1/x^2)^(1/2)/x/(x^2-1)^3,x)","\frac{\left(8 x^{4}-12 x^{2}+3\right) \sqrt{-\frac{x^{2}-1}{x^{2}}}}{3 \left(x^{2}-1\right)^{2}}"," ",0,"1/3*(8*x^4-12*x^2+3)*(-(x^2-1)/x^2)^(1/2)/(x^2-1)^2","A"
681,1,23,7,0.006000," ","int(x*(1+1/x^2)^(1/2)/(x^2+1)^2,x)","\frac{\sqrt{\frac{x^{2}+1}{x^{2}}}\, x^{2}}{x^{2}+1}"," ",0,"1/(x^2+1)*x^2*((x^2+1)/x^2)^(1/2)","B"
682,1,12,7,0.004000," ","int(1/x/(x^2+1)/(1+1/x^2)^(1/2),x)","\frac{1}{\sqrt{\frac{x^{2}+1}{x^{2}}}}"," ",0,"1/((x^2+1)/x^2)^(1/2)","A"
683,1,1059,16,0.056000," ","int(x/(a+b*x^2+(b*x^2+a)^(1/2)),x)","-\frac{\arctanh \left(\frac{2+2 \sqrt{-\left(a -1\right) b}\, \left(x -\frac{\sqrt{-\left(a -1\right) b}}{b}\right)}{2 \sqrt{\left(x -\frac{\sqrt{-\left(a -1\right) b}}{b}\right)^{2} b +2 \sqrt{-\left(a -1\right) b}\, \left(x -\frac{\sqrt{-\left(a -1\right) b}}{b}\right)+1}}\right)}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right)}-\frac{\arctanh \left(\frac{2-2 \sqrt{-\left(a -1\right) b}\, \left(x +\frac{\sqrt{-\left(a -1\right) b}}{b}\right)}{2 \sqrt{\left(x +\frac{\sqrt{-\left(a -1\right) b}}{b}\right)^{2} b -2 \sqrt{-\left(a -1\right) b}\, \left(x +\frac{\sqrt{-\left(a -1\right) b}}{b}\right)+1}}\right)}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right)}-\frac{\sqrt{-a b}\, \ln \left(\frac{\left(x -\frac{\sqrt{-a b}}{b}\right) b +\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \sqrt{b}}+\frac{\sqrt{-a b}\, \ln \left(\frac{\left(x +\frac{\sqrt{-a b}}{b}\right) b -\sqrt{-a b}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}\right)}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \sqrt{b}}+\frac{\sqrt{-\left(a -1\right) b}\, \ln \left(\frac{\left(x -\frac{\sqrt{-\left(a -1\right) b}}{b}\right) b +\sqrt{-\left(a -1\right) b}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-\left(a -1\right) b}}{b}\right)^{2} b +2 \sqrt{-\left(a -1\right) b}\, \left(x -\frac{\sqrt{-\left(a -1\right) b}}{b}\right)+1}\right)}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \sqrt{b}}-\frac{\sqrt{-\left(a -1\right) b}\, \ln \left(\frac{\left(x +\frac{\sqrt{-\left(a -1\right) b}}{b}\right) b -\sqrt{-\left(a -1\right) b}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-\left(a -1\right) b}}{b}\right)^{2} b -2 \sqrt{-\left(a -1\right) b}\, \left(x +\frac{\sqrt{-\left(a -1\right) b}}{b}\right)+1}\right)}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \sqrt{b}}+\frac{\ln \left(b \,x^{2}+a -1\right)}{2 b}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} b -2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right)}}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right)}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} b +2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right)}}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right)}+\frac{\sqrt{\left(x +\frac{\sqrt{-\left(a -1\right) b}}{b}\right)^{2} b -2 \sqrt{-\left(a -1\right) b}\, \left(x +\frac{\sqrt{-\left(a -1\right) b}}{b}\right)+1}}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right)}+\frac{\sqrt{\left(x -\frac{\sqrt{-\left(a -1\right) b}}{b}\right)^{2} b +2 \sqrt{-\left(a -1\right) b}\, \left(x -\frac{\sqrt{-\left(a -1\right) b}}{b}\right)+1}}{2 \left(\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right) \left(-\sqrt{-\left(a -1\right) b}+\sqrt{-a b}\right)}"," ",0,"-1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2)+1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*(-a*b)^(1/2)*ln(((x+(-a*b)^(1/2)/b)*b-(-a*b)^(1/2))/b^(1/2)+((x+(-a*b)^(1/2)/b)^2*b-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b))^(1/2))/b^(1/2)-1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2)-1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*(-a*b)^(1/2)*ln(((x-(-a*b)^(1/2)/b)*b+(-a*b)^(1/2))/b^(1/2)+((x-(-a*b)^(1/2)/b)^2*b+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b))^(1/2))/b^(1/2)+1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*(b*(x+(-(a-1)*b)^(1/2)/b)^2-2*(-(a-1)*b)^(1/2)*(x+(-(a-1)*b)^(1/2)/b)+1)^(1/2)-1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*(-(a-1)*b)^(1/2)*ln((b*(x+(-(a-1)*b)^(1/2)/b)-(-(a-1)*b)^(1/2))/b^(1/2)+(b*(x+(-(a-1)*b)^(1/2)/b)^2-2*(-(a-1)*b)^(1/2)*(x+(-(a-1)*b)^(1/2)/b)+1)^(1/2))/b^(1/2)-1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*arctanh(1/2*(2-2*(-(a-1)*b)^(1/2)*(x+(-(a-1)*b)^(1/2)/b))/(b*(x+(-(a-1)*b)^(1/2)/b)^2-2*(-(a-1)*b)^(1/2)*(x+(-(a-1)*b)^(1/2)/b)+1)^(1/2))+1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*(b*(x-(-(a-1)*b)^(1/2)/b)^2+2*(-(a-1)*b)^(1/2)*(x-(-(a-1)*b)^(1/2)/b)+1)^(1/2)+1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*(-(a-1)*b)^(1/2)*ln((b*(x-(-(a-1)*b)^(1/2)/b)+(-(a-1)*b)^(1/2))/b^(1/2)+(b*(x-(-(a-1)*b)^(1/2)/b)^2+2*(-(a-1)*b)^(1/2)*(x-(-(a-1)*b)^(1/2)/b)+1)^(1/2))/b^(1/2)-1/2/((-(a-1)*b)^(1/2)+(-a*b)^(1/2))/(-(-(a-1)*b)^(1/2)+(-a*b)^(1/2))*arctanh(1/2*(2+2*(-(a-1)*b)^(1/2)*(x-(-(a-1)*b)^(1/2)/b))/(b*(x-(-(a-1)*b)^(1/2)/b)^2+2*(-(a-1)*b)^(1/2)*(x-(-(a-1)*b)^(1/2)/b)+1)^(1/2))+1/2/b*ln(b*x^2+a-1)","B"
684,1,70,12,0.046000," ","int(x/(x^2-(x^2)^(1/3)),x)","\frac{\ln \left(\left(x^{2}\right)^{\frac{1}{3}}-1\right)}{2}+\frac{\ln \left(\left(x^{2}\right)^{\frac{1}{3}}+1\right)}{2}-\frac{\ln \left(\left(x^{2}\right)^{\frac{2}{3}}-\left(x^{2}\right)^{\frac{1}{3}}+1\right)}{4}-\frac{\ln \left(\left(x^{2}\right)^{\frac{2}{3}}+\left(x^{2}\right)^{\frac{1}{3}}+1\right)}{4}+\frac{\ln \left(x^{2}-1\right)}{4}+\frac{\ln \left(x^{2}+1\right)}{4}"," ",0,"1/4*ln(x^2-1)+1/4*ln(x^2+1)+1/2*ln((x^2)^(1/3)-1)-1/4*ln((x^2)^(2/3)+(x^2)^(1/3)+1)-1/4*ln((x^2)^(2/3)-(x^2)^(1/3)+1)+1/2*ln((x^2)^(1/3)+1)","B"
685,1,27,36,0.007000," ","int(x*(x^2+1)^3*(x^4+2*x^2+2)^(1/2),x)","\frac{\left(x^{4}+2 x^{2}+2\right)^{\frac{3}{2}} \left(3 x^{4}+6 x^{2}+1\right)}{30}"," ",0,"1/30*(x^4+2*x^2+2)^(3/2)*(3*x^4+6*x^2+1)","A"
686,1,58,89,0.013000," ","int(x^5*(x^9+1)^2*(-x^3+1)^(1/2),x)","\frac{2 \sqrt{-x^{3}+1}\, \left(45045 x^{21}+42042 x^{18}+38808 x^{15}+174510 x^{12}+155120 x^{9}+132960 x^{6}+259521 x^{3}+173014\right) \left(x -1\right) \left(x^{2}+x +1\right)}{2297295}"," ",0,"2/2297295*(-x^3+1)^(1/2)*(45045*x^21+42042*x^18+38808*x^15+174510*x^12+155120*x^9+132960*x^6+259521*x^3+173014)*(x-1)*(x^2+x+1)","A"
687,1,42,42,0.028000," ","int(x/(b*x^2+a)^(3/2)+x/(x^2+1)/(b*x^2+a)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{b \,x^{2}+a}}{\sqrt{-a +b}}\right)}{\sqrt{-a +b}}-\frac{1}{\sqrt{b \,x^{2}+a}\, b}"," ",0,"-1/b/(b*x^2+a)^(1/2)+1/(b-a)^(1/2)*arctan((b*x^2+a)^(1/2)/(b-a)^(1/2))","A"
688,1,133,42,0.023000," ","int(x*(b*x^2+x^2+a+1)/(x^2+1)/(b*x^2+a)^(3/2),x)","\frac{a \arctan \left(\frac{\sqrt{b \,x^{2}+a}}{\sqrt{-a +b}}\right)}{\left(a -b \right) \sqrt{-a +b}}-\frac{b \arctan \left(\frac{\sqrt{b \,x^{2}+a}}{\sqrt{-a +b}}\right)}{\left(a -b \right) \sqrt{-a +b}}+\frac{a}{\left(a -b \right) \sqrt{b \,x^{2}+a}}-\frac{b}{\left(a -b \right) \sqrt{b \,x^{2}+a}}-\frac{1}{\sqrt{b \,x^{2}+a}\, b}-\frac{1}{\sqrt{b \,x^{2}+a}}"," ",0,"-1/(b*x^2+a)^(1/2)-1/(b*x^2+a)^(1/2)/b-b/(-b+a)/(b*x^2+a)^(1/2)-b/(-b+a)/(-a+b)^(1/2)*arctan((b*x^2+a)^(1/2)/(-a+b)^(1/2))+a/(-b+a)/(b*x^2+a)^(1/2)+a/(-b+a)/(-a+b)^(1/2)*arctan((b*x^2+a)^(1/2)/(-a+b)^(1/2))","B"
689,1,56,56,0.023000," ","int(x/(b*x^2+a)^(5/2)+x/(b*x^2+a)^(3/2)+x/(x^2+1)/(b*x^2+a)^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{b \,x^{2}+a}}{\sqrt{-a +b}}\right)}{\sqrt{-a +b}}-\frac{1}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{1}{\sqrt{b \,x^{2}+a}\, b}"," ",0,"-1/3/b/(b*x^2+a)^(3/2)-1/(b*x^2+a)^(1/2)/b+1/(-a+b)^(1/2)*arctan((b*x^2+a)^(1/2)/(-a+b)^(1/2))","A"
690,1,314,56,0.027000," ","int(x*(b^2*x^4+b*x^4+2*a*b*x^2+a*x^2+b*x^2+a^2+x^2+a+1)/(x^2+1)/(b*x^2+a)^(5/2),x)","\frac{a^{2} \arctan \left(\frac{\sqrt{b \,x^{2}+a}}{\sqrt{-a +b}}\right)}{\left(a -b \right)^{2} \sqrt{-a +b}}-\frac{2 a b \arctan \left(\frac{\sqrt{b \,x^{2}+a}}{\sqrt{-a +b}}\right)}{\left(a -b \right)^{2} \sqrt{-a +b}}+\frac{b^{2} \arctan \left(\frac{\sqrt{b \,x^{2}+a}}{\sqrt{-a +b}}\right)}{\left(a -b \right)^{2} \sqrt{-a +b}}-\frac{b \,x^{2}}{\left(b \,x^{2}+a \right)^{\frac{3}{2}}}+\frac{a^{2}}{\left(a -b \right)^{2} \sqrt{b \,x^{2}+a}}+\frac{a^{2}}{3 \left(a -b \right) \left(b \,x^{2}+a \right)^{\frac{3}{2}}}-\frac{2 a b}{\left(a -b \right)^{2} \sqrt{b \,x^{2}+a}}-\frac{2 a b}{3 \left(a -b \right) \left(b \,x^{2}+a \right)^{\frac{3}{2}}}+\frac{b^{2}}{\left(a -b \right)^{2} \sqrt{b \,x^{2}+a}}+\frac{b^{2}}{3 \left(a -b \right) \left(b \,x^{2}+a \right)^{\frac{3}{2}}}-\frac{x^{2}}{\left(b \,x^{2}+a \right)^{\frac{3}{2}}}-\frac{4 a}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}}}+\frac{b}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}}}-\frac{a}{\left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{1}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}"," ",0,"-x^2*b/(b*x^2+a)^(3/2)-x^2/(b*x^2+a)^(3/2)-4/3*a/(b*x^2+a)^(3/2)-a/b/(b*x^2+a)^(3/2)+1/3*b/(b*x^2+a)^(3/2)-1/3/(b*x^2+a)^(3/2)/b+1/(a-b)^2/(b*x^2+a)^(1/2)*a^2-2/(a-b)^2/(b*x^2+a)^(1/2)*a*b+1/(a-b)^2/(b*x^2+a)^(1/2)*b^2+1/(a-b)^2/(-a+b)^(1/2)*arctan((b*x^2+a)^(1/2)/(-a+b)^(1/2))*a^2-2/(a-b)^2/(-a+b)^(1/2)*arctan((b*x^2+a)^(1/2)/(-a+b)^(1/2))*a*b+1/(a-b)^2/(-a+b)^(1/2)*arctan((b*x^2+a)^(1/2)/(-a+b)^(1/2))*b^2+1/3/(a-b)/(b*x^2+a)^(3/2)*a^2-2/3/(a-b)/(b*x^2+a)^(3/2)*a*b+1/3/(a-b)/(b*x^2+a)^(3/2)*b^2","B"
691,1,44,24,0.012000," ","int(1/(x+x^(1/2))^(1/2),x)","-\frac{\sqrt{x +\sqrt{x}}\, \left(\ln \left(\sqrt{x}+\frac{1}{2}+\sqrt{x +\sqrt{x}}\right)-2 \sqrt{x +\sqrt{x}}\right)}{\sqrt{\left(\sqrt{x}+1\right) \sqrt{x}}}"," ",0,"-(x+x^(1/2))^(1/2)*(-2*(x+x^(1/2))^(1/2)+ln(x^(1/2)+1/2+(x+x^(1/2))^(1/2)))/(x^(1/2)*(x^(1/2)+1))^(1/2)","A"
692,1,42,46,0.005000," ","int((x+x^(1/2))^(1/2),x)","\frac{\ln \left(\sqrt{x}+\frac{1}{2}+\sqrt{x +\sqrt{x}}\right)}{8}+\frac{2 \left(x +\sqrt{x}\right)^{\frac{3}{2}}}{3}-\frac{\left(2 \sqrt{x}+1\right) \sqrt{x +\sqrt{x}}}{4}"," ",0,"2/3*(x+x^(1/2))^(3/2)-1/4*(1+2*x^(1/2))*(x+x^(1/2))^(1/2)+1/8*ln(x^(1/2)+1/2+(x+x^(1/2))^(1/2))","A"
693,1,14,13,0.002000," ","int((-x)^(1/2)*(x+(-x)^(1/2)),x)","-\frac{x^{2}}{2}+\frac{2 \left(-x \right)^{\frac{5}{2}}}{5}"," ",0,"2/5*(-x)^(5/2)-1/2*x^2","A"
694,1,52,42,0.005000," ","int((5+x^(1/4))/(-6+x),x)","-2 \,6^{\frac{1}{4}} \arctan \left(\frac{6^{\frac{3}{4}} x^{\frac{1}{4}}}{6}\right)-6^{\frac{1}{4}} \ln \left(\frac{x^{\frac{1}{4}}+6^{\frac{1}{4}}}{x^{\frac{1}{4}}-6^{\frac{1}{4}}}\right)+5 \ln \left(x -6\right)+4 x^{\frac{1}{4}}"," ",0,"4*x^(1/4)-2*6^(1/4)*arctan(1/6*x^(1/4)*6^(3/4))-6^(1/4)*ln((x^(1/4)+6^(1/4))/(x^(1/4)-6^(1/4)))+5*ln(-6+x)","A"
695,1,18,12,0.013000," ","int(1/(4-x+(4-x)^(1/2)),x)","-2 \arctanh \left(\sqrt{-x +4}\right)-\ln \left(x -3\right)"," ",0,"-ln(x-3)-2*arctanh((4-x)^(1/2))","A"
696,1,91,45,0.009000," ","int(1/(1+x-(x+2)^(1/2)),x)","-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x +1\right) \sqrt{5}}{5}\right)}{5}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{x +2}-1\right) \sqrt{5}}{5}\right)}{5}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{x +2}+1\right) \sqrt{5}}{5}\right)}{5}+\frac{\ln \left(x +1-\sqrt{x +2}\right)}{2}-\frac{\ln \left(x +1+\sqrt{x +2}\right)}{2}+\frac{\ln \left(x^{2}+x -1\right)}{2}"," ",0,"-1/5*5^(1/2)*arctanh(1/5*(2*x+1)*5^(1/2))+1/2*ln(x^2+x-1)-1/2*ln(1+x+(x+2)^(1/2))-1/5*5^(1/2)*arctanh(1/5*(2*(x+2)^(1/2)+1)*5^(1/2))+1/2*ln(1+x-(x+2)^(1/2))-1/5*5^(1/2)*arctanh(1/5*(2*(x+2)^(1/2)-1)*5^(1/2))","A"
697,1,93,30,0.013000," ","int(1/(4+x+(x+1)^(1/2)),x)","-\frac{\sqrt{11}\, \arctan \left(\frac{\left(1+2 \sqrt{x +1}\right) \sqrt{11}}{11}\right)}{11}+\frac{\sqrt{11}\, \arctan \left(\frac{\left(2 x +7\right) \sqrt{11}}{11}\right)}{11}-\frac{\sqrt{11}\, \arctan \left(\frac{\left(2 \sqrt{x +1}-1\right) \sqrt{11}}{11}\right)}{11}+\frac{\ln \left(x +4+\sqrt{x +1}\right)}{2}-\frac{\ln \left(x +4-\sqrt{x +1}\right)}{2}+\frac{\ln \left(x^{2}+7 x +15\right)}{2}"," ",0,"-1/2*ln(x+4-(x+1)^(1/2))-1/11*11^(1/2)*arctan(1/11*(2*(x+1)^(1/2)-1)*11^(1/2))+1/2*ln(4+x+(x+1)^(1/2))-1/11*arctan(1/11*(1+2*(x+1)^(1/2))*11^(1/2))*11^(1/2)+1/11*11^(1/2)*arctan(1/11*(2*x+7)*11^(1/2))+1/2*ln(x^2+7*x+15)","B"
698,1,91,45,0.007000," ","int(1/(x-(x+1)^(1/2)),x)","-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x -1\right) \sqrt{5}}{5}\right)}{5}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(1+2 \sqrt{x +1}\right) \sqrt{5}}{5}\right)}{5}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{x +1}-1\right) \sqrt{5}}{5}\right)}{5}+\frac{\ln \left(x -\sqrt{x +1}\right)}{2}-\frac{\ln \left(x +\sqrt{x +1}\right)}{2}+\frac{\ln \left(x^{2}-x -1\right)}{2}"," ",0,"1/2*ln(x^2-x-1)-1/5*5^(1/2)*arctanh(1/5*(2*x-1)*5^(1/2))-1/2*ln(x+(x+1)^(1/2))-1/5*5^(1/2)*arctanh(1/5*(1+2*(x+1)^(1/2))*5^(1/2))+1/2*ln(x-(x+1)^(1/2))-1/5*5^(1/2)*arctanh(1/5*(2*(x+1)^(1/2)-1)*5^(1/2))","A"
699,1,54,23,0.016000," ","int(1/(x-(x+2)^(1/2)),x)","\frac{2 \ln \left(x -2\right)}{3}+\frac{2 \ln \left(-2+\sqrt{x +2}\right)}{3}+\frac{\ln \left(x +1\right)}{3}+\frac{\ln \left(1+\sqrt{x +2}\right)}{3}-\frac{\ln \left(\sqrt{x +2}-1\right)}{3}-\frac{2 \ln \left(\sqrt{x +2}+2\right)}{3}"," ",0,"2/3*ln(x-2)+1/3*ln(x+1)-1/3*ln((x+2)^(1/2)-1)+2/3*ln(-2+(x+2)^(1/2))-2/3*ln((x+2)^(1/2)+2)+1/3*ln(1+(x+2)^(1/2))","B"
700,1,101,49,0.007000," ","int(1/(x-(-x+1)^(1/2)),x)","\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x +1\right) \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{-x +1}-1\right) \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 \sqrt{-x +1}+1\right) \sqrt{5}}{5}\right)}{5}-\frac{\ln \left(-x -\sqrt{-x +1}\right)}{2}+\frac{\ln \left(-x +\sqrt{-x +1}\right)}{2}+\frac{\ln \left(x^{2}+x -1\right)}{2}"," ",0,"1/2*ln(x^2+x-1)+1/5*5^(1/2)*arctanh(1/5*(2*x+1)*5^(1/2))+1/2*ln(-x+(-x+1)^(1/2))+1/5*5^(1/2)*arctanh(1/5*(2*(-x+1)^(1/2)+1)*5^(1/2))-1/2*ln(-x-(-x+1)^(1/2))+1/5*5^(1/2)*arctanh(1/5*(2*(-x+1)^(1/2)-1)*5^(1/2))","B"
701,1,42,43,0.007000," ","int((1+x+x^(1/2))^(1/2),x)","-\frac{3 \arcsinh \left(\frac{2 \sqrt{3}\, \left(\sqrt{x}+\frac{1}{2}\right)}{3}\right)}{8}+\frac{2 \left(x +\sqrt{x}+1\right)^{\frac{3}{2}}}{3}-\frac{\left(2 \sqrt{x}+1\right) \sqrt{x +\sqrt{x}+1}}{4}"," ",0,"2/3*(1+x+x^(1/2))^(3/2)-1/4*(2*x^(1/2)+1)*(1+x+x^(1/2))^(1/2)-3/8*arcsinh(2/3*3^(1/2)*(x^(1/2)+1/2))","A"
702,1,55,53,0.007000," ","int((1+x+(x+1)^(1/2))^(1/2),x)","\frac{\ln \left(\sqrt{x +1}+\frac{1}{2}+\sqrt{x +1+\sqrt{x +1}}\right)}{8}+\frac{2 \left(x +1+\sqrt{x +1}\right)^{\frac{3}{2}}}{3}-\frac{\left(1+2 \sqrt{x +1}\right) \sqrt{x +1+\sqrt{x +1}}}{4}"," ",0,"2/3*(1+x+(x+1)^(1/2))^(3/2)-1/4*(1+2*(x+1)^(1/2))*(1+x+(x+1)^(1/2))^(1/2)+1/8*ln((x+1)^(1/2)+1/2+(1+x+(x+1)^(1/2))^(1/2))","A"
703,1,48,49,0.007000," ","int((x+(x-1)^(1/2))^(1/2),x)","-\frac{3 \arcsinh \left(\frac{2 \sqrt{3}\, \left(\sqrt{x -1}+\frac{1}{2}\right)}{3}\right)}{8}+\frac{2 \left(x +\sqrt{x -1}\right)^{\frac{3}{2}}}{3}-\frac{\left(1+2 \sqrt{x -1}\right) \sqrt{x +\sqrt{x -1}}}{4}"," ",0,"2/3*(x+(x-1)^(1/2))^(3/2)-1/4*(1+2*(x-1)^(1/2))*(x+(x-1)^(1/2))^(1/2)-3/8*arcsinh(2/3*3^(1/2)*((x-1)^(1/2)+1/2))","A"
704,1,60,61,0.007000," ","int((2*x+(2*x-1)^(1/2))^(1/2),x)","-\frac{3 \arcsinh \left(\frac{2 \sqrt{3}\, \left(\sqrt{2 x -1}+\frac{1}{2}\right)}{3}\right)}{16}+\frac{\left(2 x +\sqrt{2 x -1}\right)^{\frac{3}{2}}}{3}-\frac{\left(1+2 \sqrt{2 x -1}\right) \sqrt{2 x +\sqrt{2 x -1}}}{8}"," ",0,"1/3*(2*x+(2*x-1)^(1/2))^(3/2)-1/8*(1+2*(2*x-1)^(1/2))*(2*x+(2*x-1)^(1/2))^(1/2)-3/16*arcsinh(2/3*3^(1/2)*((2*x-1)^(1/2)+1/2))","A"
705,1,67,74,0.010000," ","int((3*x+(-7+8*x)^(1/2))^(1/2),x)","-\frac{47 \sqrt{6}\, \arcsinh \left(\frac{3 \sqrt{47}\, \left(\sqrt{8 x -7}+\frac{4}{3}\right)}{47}\right)}{216}+\frac{\left(48 x +16 \sqrt{8 x -7}\right)^{\frac{3}{2}}}{288}-\frac{\left(12 \sqrt{8 x -7}+16\right) \sqrt{48 x +16 \sqrt{8 x -7}}}{288}"," ",0,"1/288*(48*x+16*(-7+8*x)^(1/2))^(3/2)-1/288*(12*(-7+8*x)^(1/2)+16)*(48*x+16*(-7+8*x)^(1/2))^(1/2)-47/216*6^(1/2)*arcsinh(3/47*47^(1/2)*((-7+8*x)^(1/2)+4/3))","A"
706,1,32,35,0.010000," ","int(1/(x+(x+1)^(1/2))^(1/2),x)","-\ln \left(\sqrt{x +1}+\frac{1}{2}+\sqrt{x +\sqrt{x +1}}\right)+2 \sqrt{x +\sqrt{x +1}}"," ",0,"2*(x+(x+1)^(1/2))^(1/2)-ln((x+1)^(1/2)+1/2+(x+(x+1)^(1/2))^(1/2))","A"
707,1,52,51,0.007000," ","int((x+1)/(4+x+(-9+6*x)^(1/2)),x)","x +4 \sqrt{6}\, \arctan \left(\frac{\left(2 \sqrt{6 x -9}+6\right) \sqrt{6}}{24}\right)+3 \ln \left(6 x +24+6 \sqrt{6 x -9}\right)-2 \sqrt{6 x -9}-\frac{3}{2}"," ",0,"-2*(-9+6*x)^(1/2)-3/2+x+3*ln(24+6*x+6*(-9+6*x)^(1/2))+4*6^(1/2)*arctan(1/24*(2*(-9+6*x)^(1/2)+6)*6^(1/2))","A"
708,1,54,53,0.005000," ","int((12-x)/(4+x+(6*x-9)^(1/2)),x)","-x -\frac{21 \sqrt{6}\, \arctan \left(\frac{\left(2 \sqrt{6 x -9}+6\right) \sqrt{6}}{24}\right)}{2}+10 \ln \left(6 x +24+6 \sqrt{6 x -9}\right)+2 \sqrt{6 x -9}+\frac{3}{2}"," ",0,"2*(6*x-9)^(1/2)+3/2-x+10*ln(6*x+24+6*(6*x-9)^(1/2))-21/2*6^(1/2)*arctan(1/24*(2*(6*x-9)^(1/2)+6)*6^(1/2))","A"
709,1,97,36,0.010000," ","int((x^3-1)/(x^2+1)/x^(1/2),x)","\frac{2 x^{\frac{3}{2}}}{3}-\sqrt{2}\, \arctan \left(\sqrt{2}\, \sqrt{x}-1\right)-\sqrt{2}\, \arctan \left(\sqrt{2}\, \sqrt{x}+1\right)-\frac{\sqrt{2}\, \ln \left(\frac{x -\sqrt{2}\, \sqrt{x}+1}{x +\sqrt{2}\, \sqrt{x}+1}\right)}{4}-\frac{\sqrt{2}\, \ln \left(\frac{x +\sqrt{2}\, \sqrt{x}+1}{x -\sqrt{2}\, \sqrt{x}+1}\right)}{4}"," ",0,"2/3*x^(3/2)-arctan(1+2^(1/2)*x^(1/2))*2^(1/2)-arctan(-1+2^(1/2)*x^(1/2))*2^(1/2)-1/4*2^(1/2)*ln((x+2^(1/2)*x^(1/2)+1)/(x-2^(1/2)*x^(1/2)+1))-1/4*2^(1/2)*ln((x-2^(1/2)*x^(1/2)+1)/(x+2^(1/2)*x^(1/2)+1))","B"
710,1,14,17,0.008000," ","int(1/2/(x-1)^(1/2)/(x-(x-1)^(1/2))^(1/2),x)","\arcsinh \left(\frac{2 \sqrt{3}\, \left(\sqrt{x -1}-\frac{1}{2}\right)}{3}\right)"," ",0,"arcsinh(2/3*3^(1/2)*((x-1)^(1/2)-1/2))","A"
711,1,34,31,0.008000," ","int((1+x^(7/2))/(-x^2+1),x)","-\frac{2 x^{\frac{5}{2}}}{5}+\arctanh \left(x \right)+\arctan \left(\sqrt{x}\right)-\frac{\ln \left(\sqrt{x}-1\right)}{2}+\frac{\ln \left(\sqrt{x}+1\right)}{2}-2 \sqrt{x}"," ",0,"-2/5*x^(5/2)-2*x^(1/2)-1/2*ln(x^(1/2)-1)+1/2*ln(x^(1/2)+1)+arctan(x^(1/2))+arctanh(x)","A"
712,1,90,88,0.005000," ","int((4+2*x)/((2*x-1)^(1/3)+(2*x-1)^(1/2)),x)","-x -18 \ln \left(1+\left(2 x -1\right)^{\frac{1}{6}}\right)+\frac{\left(2 x -1\right)^{\frac{3}{2}}}{3}-\frac{3 \left(2 x -1\right)^{\frac{4}{3}}}{8}+\frac{3 \left(2 x -1\right)^{\frac{7}{6}}}{7}+\frac{1}{2}+\frac{3 \left(2 x -1\right)^{\frac{5}{6}}}{5}-\frac{3 \left(2 x -1\right)^{\frac{2}{3}}}{4}+6 \sqrt{2 x -1}-9 \left(2 x -1\right)^{\frac{1}{3}}+18 \left(2 x -1\right)^{\frac{1}{6}}"," ",0,"1/3*(2*x-1)^(3/2)-3/8*(2*x-1)^(4/3)+3/7*(2*x-1)^(7/6)-x+1/2+3/5*(2*x-1)^(5/6)-3/4*(2*x-1)^(2/3)+6*(2*x-1)^(1/2)-9*(2*x-1)^(1/3)+18*(2*x-1)^(1/6)-18*ln(1+(2*x-1)^(1/6))","A"
713,1,54,53,0.011000," ","int(1/(2+(x^(1/2)+1)^(1/2))^(1/2),x)","\frac{88 \left(2+\sqrt{\sqrt{x}+1}\right)^{\frac{3}{2}}}{3}-\frac{48 \left(2+\sqrt{\sqrt{x}+1}\right)^{\frac{5}{2}}}{5}+\frac{8 \left(2+\sqrt{\sqrt{x}+1}\right)^{\frac{7}{2}}}{7}-48 \sqrt{2+\sqrt{\sqrt{x}+1}}"," ",0,"88/3*(2+(x^(1/2)+1)^(1/2))^(3/2)-48/5*(2+(x^(1/2)+1)^(1/2))^(5/2)+8/7*(2+(x^(1/2)+1)^(1/2))^(7/2)-48*(2+(x^(1/2)+1)^(1/2))^(1/2)","A"
714,1,41,40,0.010000," ","int((2+(x^(1/2)+4)^(1/2))^(1/2),x)","\frac{64 \left(2+\sqrt{\sqrt{x}+4}\right)^{\frac{5}{2}}}{5}-\frac{48 \left(2+\sqrt{\sqrt{x}+4}\right)^{\frac{7}{2}}}{7}+\frac{8 \left(2+\sqrt{\sqrt{x}+4}\right)^{\frac{9}{2}}}{9}"," ",0,"64/5*(2+(x^(1/2)+4)^(1/2))^(5/2)-48/7*(2+(x^(1/2)+4)^(1/2))^(7/2)+8/9*(2+(x^(1/2)+4)^(1/2))^(9/2)","A"
715,1,59,58,0.013000," ","int((2-(4+(-9+5*x)^(1/2))^(1/2))^(1/2),x)","\frac{64 \left(2-\sqrt{4+\sqrt{5 x -9}}\right)^{\frac{5}{2}}}{25}-\frac{48 \left(2-\sqrt{4+\sqrt{5 x -9}}\right)^{\frac{7}{2}}}{35}+\frac{8 \left(2-\sqrt{4+\sqrt{5 x -9}}\right)^{\frac{9}{2}}}{45}"," ",0,"64/25*(2-(4+(-9+5*x)^(1/2))^(1/2))^(5/2)-48/35*(2-(4+(-9+5*x)^(1/2))^(1/2))^(7/2)+8/45*(2-(4+(-9+5*x)^(1/2))^(1/2))^(9/2)","A"
716,1,54,53,0.006000," ","int(1/(2+(x^(1/2)+1)^(1/2))^(1/2),x)","\frac{88 \left(2+\sqrt{\sqrt{x}+1}\right)^{\frac{3}{2}}}{3}-\frac{48 \left(2+\sqrt{\sqrt{x}+1}\right)^{\frac{5}{2}}}{5}+\frac{8 \left(2+\sqrt{\sqrt{x}+1}\right)^{\frac{7}{2}}}{7}-48 \sqrt{2+\sqrt{\sqrt{x}+1}}"," ",0,"88/3*(2+(x^(1/2)+1)^(1/2))^(3/2)-48/5*(2+(x^(1/2)+1)^(1/2))^(5/2)+8/7*(2+(x^(1/2)+1)^(1/2))^(7/2)-48*(2+(x^(1/2)+1)^(1/2))^(1/2)","A"
717,1,121,120,0.014000," ","int((1+(1+(x^(1/2)+1)^(1/2))^(1/2))^(1/2),x)","-\frac{32 \left(1+\sqrt{1+\sqrt{\sqrt{x}+1}}\right)^{\frac{5}{2}}}{5}+\frac{48 \left(1+\sqrt{1+\sqrt{\sqrt{x}+1}}\right)^{\frac{7}{2}}}{7}+\frac{112 \left(1+\sqrt{1+\sqrt{\sqrt{x}+1}}\right)^{\frac{9}{2}}}{9}-\frac{320 \left(1+\sqrt{1+\sqrt{\sqrt{x}+1}}\right)^{\frac{11}{2}}}{11}+\frac{288 \left(1+\sqrt{1+\sqrt{\sqrt{x}+1}}\right)^{\frac{13}{2}}}{13}-\frac{112 \left(1+\sqrt{1+\sqrt{\sqrt{x}+1}}\right)^{\frac{15}{2}}}{15}+\frac{16 \left(1+\sqrt{1+\sqrt{\sqrt{x}+1}}\right)^{\frac{17}{2}}}{17}"," ",0,"-32/5*(1+(1+(x^(1/2)+1)^(1/2))^(1/2))^(5/2)+48/7*(1+(1+(x^(1/2)+1)^(1/2))^(1/2))^(7/2)+112/9*(1+(1+(x^(1/2)+1)^(1/2))^(1/2))^(9/2)-320/11*(1+(1+(x^(1/2)+1)^(1/2))^(1/2))^(11/2)+288/13*(1+(1+(x^(1/2)+1)^(1/2))^(1/2))^(13/2)-112/15*(1+(1+(x^(1/2)+1)^(1/2))^(1/2))^(15/2)+16/17*(1+(1+(x^(1/2)+1)^(1/2))^(1/2))^(17/2)","A"
718,1,154,153,0.020000," ","int((2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(1/2),x)","-\frac{16 \left(2+\sqrt{3+\sqrt{2 \sqrt{x}-1}}\right)^{\frac{3}{2}}}{3}+\frac{136 \left(2+\sqrt{3+\sqrt{2 \sqrt{x}-1}}\right)^{\frac{5}{2}}}{5}-\frac{480 \left(2+\sqrt{3+\sqrt{2 \sqrt{x}-1}}\right)^{\frac{7}{2}}}{7}+\frac{304 \left(2+\sqrt{3+\sqrt{2 \sqrt{x}-1}}\right)^{\frac{9}{2}}}{3}-\frac{760 \left(2+\sqrt{3+\sqrt{2 \sqrt{x}-1}}\right)^{\frac{11}{2}}}{11}+\frac{300 \left(2+\sqrt{3+\sqrt{2 \sqrt{x}-1}}\right)^{\frac{13}{2}}}{13}-\frac{56 \left(2+\sqrt{3+\sqrt{2 \sqrt{x}-1}}\right)^{\frac{15}{2}}}{15}+\frac{4 \left(2+\sqrt{3+\sqrt{2 \sqrt{x}-1}}\right)^{\frac{17}{2}}}{17}"," ",0,"-16/3*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(3/2)+136/5*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(5/2)-480/7*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(7/2)+304/3*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(9/2)-760/11*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(11/2)+300/13*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(13/2)-56/15*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(15/2)+4/17*(2+(3+(-1+2*x^(1/2))^(1/2))^(1/2))^(17/2)","A"
719,1,107,106,0.013000," ","int(x*(1+(1+(x-1)^(1/2))^(1/2))^(1/2),x)","\frac{16 \left(1+\sqrt{1+\sqrt{x -1}}\right)^{\frac{5}{2}}}{5}-\frac{24 \left(1+\sqrt{1+\sqrt{x -1}}\right)^{\frac{7}{2}}}{7}+8 \left(1+\sqrt{1+\sqrt{x -1}}\right)^{\frac{9}{2}}-\frac{160 \left(1+\sqrt{1+\sqrt{x -1}}\right)^{\frac{11}{2}}}{11}+\frac{144 \left(1+\sqrt{1+\sqrt{x -1}}\right)^{\frac{13}{2}}}{13}-\frac{56 \left(1+\sqrt{1+\sqrt{x -1}}\right)^{\frac{15}{2}}}{15}+\frac{8 \left(1+\sqrt{1+\sqrt{x -1}}\right)^{\frac{17}{2}}}{17}"," ",0,"16/5*(1+(1+(x-1)^(1/2))^(1/2))^(5/2)-24/7*(1+(1+(x-1)^(1/2))^(1/2))^(7/2)+8*(1+(1+(x-1)^(1/2))^(1/2))^(9/2)-160/11*(1+(1+(x-1)^(1/2))^(1/2))^(11/2)+144/13*(1+(1+(x-1)^(1/2))^(1/2))^(13/2)-56/15*(1+(1+(x-1)^(1/2))^(1/2))^(15/2)+8/17*(1+(1+(x-1)^(1/2))^(1/2))^(17/2)","A"
720,1,16,17,0.005000," ","int(1/(x-1)^(1/2)/(x-(x-1)^(1/2))^(1/2),x)","2 \arcsinh \left(\frac{2 \sqrt{3}\, \left(\sqrt{x -1}-\frac{1}{2}\right)}{3}\right)"," ",0,"2*arcsinh(2/3*3^(1/2)*((x-1)^(1/2)-1/2))","A"
721,1,38,35,0.010000," ","int(1/(1+x+(2*x-1)^(1/2))^(1/2),x)","-\sqrt{2}\, \arcsinh \left(\frac{\left(1+\sqrt{2 x -1}\right) \sqrt{2}}{2}\right)+\sqrt{4 x +4+4 \sqrt{2 x -1}}"," ",0,"(4*x+4+4*(2*x-1)^(1/2))^(1/2)-arcsinh(1/2*(1+(2*x-1)^(1/2))*2^(1/2))*2^(1/2)","A"
722,1,80,50,0.004000," ","int((p*x+q)/(a*x+b)^(1/2)/(f+(a*x+b)^(1/2)),x)","\frac{2 f^{2} p \ln \left(f +\sqrt{a x +b}\right)}{a^{2}}+\frac{p x}{a}+\frac{2 q \ln \left(f +\sqrt{a x +b}\right)}{a}-\frac{2 b p \ln \left(f +\sqrt{a x +b}\right)}{a^{2}}+\frac{b p}{a^{2}}-\frac{2 \sqrt{a x +b}\, f p}{a^{2}}"," ",0,"p*x/a+1/a^2*b*p-2*f*p*(a*x+b)^(1/2)/a^2+2/a^2*ln(f+(a*x+b)^(1/2))*f^2*p+2/a*ln(f+(a*x+b)^(1/2))*q-2/a^2*ln(f+(a*x+b)^(1/2))*b*p","A"
723,1,50,51,0.006000," ","int((1-x-x^(1/2))^(1/2),x)","-\frac{5 \arcsin \left(\frac{2 \sqrt{5}\, \left(\sqrt{x}+\frac{1}{2}\right)}{5}\right)}{8}-\frac{2 \left(-x -\sqrt{x}+1\right)^{\frac{3}{2}}}{3}+\frac{\left(-2 \sqrt{x}-1\right) \sqrt{-x -\sqrt{x}+1}}{4}"," ",0,"-2/3*(1-x-x^(1/2))^(3/2)+1/4*(-2*x^(1/2)-1)*(1-x-x^(1/2))^(1/2)-5/8*arcsin(2/5*5^(1/2)*(x^(1/2)+1/2))","A"
724,1,16,15,0.002000," ","int((9+x+6*x^(1/2))/(x+4*x^(1/2)),x)","x +2 \ln \left(\sqrt{x}+4\right)+4 \sqrt{x}"," ",0,"x+2*ln(x^(1/2)+4)+4*x^(1/2)","A"
725,1,50,49,0.005000," ","int((6-8*x^(7/2))/(5-9*x^(1/2)),x)","\frac{2 x^{4}}{9}+\frac{80 x^{\frac{7}{2}}}{567}+\frac{200 x^{3}}{2187}+\frac{400 x^{\frac{5}{2}}}{6561}+\frac{2500 x^{2}}{59049}+\frac{50000 x^{\frac{3}{2}}}{1594323}+\frac{125000 x}{4782969}-\frac{280728140 \ln \left(9 \sqrt{x}-5\right)}{387420489}-\frac{56145628 \sqrt{x}}{43046721}"," ",0,"2/9*x^4+80/567*x^(7/2)+200/2187*x^3+400/6561*x^(5/2)+2500/59049*x^2+50000/1594323*x^(3/2)+125000/4782969*x-56145628/43046721*x^(1/2)-280728140/387420489*ln(-5+9*x^(1/2))","A"
726,1,443,58,0.049000," ","int((x^3+1)*(x+1)^(1/2)/(x^2+1),x)","\frac{\left(2+2 \sqrt{2}\right) \sqrt{2}\, \arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}-\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{2 \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{\left(2+2 \sqrt{2}\right) \sqrt{2}\, \arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{2 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 \sqrt{x +1}+\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{\sqrt{-2+2 \sqrt{2}}}+\frac{2 \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}}\, \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)}{2}-\frac{\sqrt{2+2 \sqrt{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)}{2}+\frac{2 \left(x +1\right)^{\frac{5}{2}}}{5}-\frac{2 \left(x +1\right)^{\frac{3}{2}}}{3}-2 \sqrt{x +1}"," ",0,"2/5*(x+1)^(5/2)-2/3*(x+1)^(3/2)-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)*2^(1/2)+1/2*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*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+2*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))*(2+2*2^(1/2))+2/(-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)+1/4*ln(1+x+2^(1/2)-(x+1)^(1/2)*(2+2*2^(1/2))^(1/2))*(2+2*2^(1/2))^(1/2)*2^(1/2)-1/2*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*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+2*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))*(2+2*2^(1/2))+2/(-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)","B"
727,1,130,65,0.017000," ","int((-1+x-x^(1/2))^(1/2)/(x-1)/x^(1/2),x)","\arctanh \left(\frac{-3 \sqrt{x}-1}{2 \sqrt{-3 \sqrt{x}+\left(\sqrt{x}+1\right)^{2}-2}}\right)-\arctan \left(\frac{\sqrt{x}-3}{2 \sqrt{\sqrt{x}+\left(\sqrt{x}-1\right)^{2}-2}}\right)+\frac{3 \ln \left(\sqrt{x}-\frac{1}{2}+\sqrt{-3 \sqrt{x}+\left(\sqrt{x}+1\right)^{2}-2}\right)}{2}+\frac{\ln \left(\sqrt{x}-\frac{1}{2}+\sqrt{\sqrt{x}+\left(\sqrt{x}-1\right)^{2}-2}\right)}{2}+\sqrt{\sqrt{x}+\left(\sqrt{x}-1\right)^{2}-2}-\sqrt{-3 \sqrt{x}+\left(\sqrt{x}+1\right)^{2}-2}"," ",0,"((x^(1/2)-1)^2+x^(1/2)-2)^(1/2)+1/2*ln(x^(1/2)-1/2+((x^(1/2)-1)^2+x^(1/2)-2)^(1/2))-arctan(1/2*(x^(1/2)-3)/((x^(1/2)-1)^2+x^(1/2)-2)^(1/2))-((x^(1/2)+1)^2-3*x^(1/2)-2)^(1/2)+3/2*ln(-1/2+x^(1/2)+((x^(1/2)+1)^2-3*x^(1/2)-2)^(1/2))+arctanh(1/2*(-1-3*x^(1/2))/((x^(1/2)+1)^2-3*x^(1/2)-2)^(1/2))","A"
728,1,68,45,0.019000," ","int((1+2*(x+1)^(1/2))/x/(x+1)^(1/2)/(x+(x+1)^(1/2))^(1/2),x)","-3 \arctanh \left(\frac{3 \sqrt{x +1}-1}{2 \sqrt{\left(\sqrt{x +1}-1\right)^{2}+3 \sqrt{x +1}-2}}\right)+\arctan \left(\frac{-\sqrt{x +1}-3}{2 \sqrt{\left(1+\sqrt{x +1}\right)^{2}-\sqrt{x +1}-2}}\right)"," ",0,"-3*arctanh(1/2*(3*(x+1)^(1/2)-1)/(((x+1)^(1/2)-1)^2+3*(x+1)^(1/2)-2)^(1/2))+arctan(1/2*(-(x+1)^(1/2)-3)/((1+(x+1)^(1/2))^2-(x+1)^(1/2)-2)^(1/2))","A"
729,1,28,6,0.005000," ","int(1/x^(1/2)/(x+1)^(1/2),x)","\frac{\sqrt{\left(x +1\right) x}\, \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{\sqrt{x +1}\, \sqrt{x}}"," ",0,"(x*(x+1))^(1/2)/x^(1/2)/(x+1)^(1/2)*ln(x+1/2+(x^2+x)^(1/2))","B"
730,1,32,6,0.016000," ","int((x/(x+1))^(1/2)/x,x)","\frac{\sqrt{\frac{x}{x +1}}\, \left(x +1\right) \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{\sqrt{\left(x +1\right) x}}"," ",0,"(x/(x+1))^(1/2)*(x+1)/((x+1)*x)^(1/2)*ln(x+1/2+(x^2+x)^(1/2))","B"
731,1,39,16,0.004000," ","int(x^(1/2)/(x+1)^(1/2),x)","\sqrt{x +1}\, \sqrt{x}-\frac{\sqrt{\left(x +1\right) x}\, \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{2 \sqrt{x +1}\, \sqrt{x}}"," ",0,"x^(1/2)*(x+1)^(1/2)-1/2*((x+1)*x)^(1/2)/(x+1)^(1/2)/x^(1/2)*ln(x+1/2+(x^2+x)^(1/2))","B"
732,1,45,16,0.007000," ","int((1/(x+1)*x)^(1/2),x)","\frac{\sqrt{\frac{x}{x +1}}\, \left(x +1\right) \left(-\ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)+2 \sqrt{x^{2}+x}\right)}{2 \sqrt{\left(x +1\right) x}}"," ",0,"1/2*(1/(x+1)*x)^(1/2)*(x+1)*(2*(x^2+x)^(1/2)-ln(x+1/2+(x^2+x)^(1/2)))/((x+1)*x)^(1/2)","B"
733,1,43,28,0.017000," ","int((x-1)^(1/2)/x^2/(x+1)^(1/2),x)","\frac{\left(-x \arctan \left(\frac{1}{\sqrt{x^{2}-1}}\right)-\sqrt{x^{2}-1}\right) \sqrt{x -1}\, \sqrt{x +1}}{\sqrt{x^{2}-1}\, x}"," ",0,"(-arctan(1/(x^2-1)^(1/2))*x-(x^2-1)^(1/2))*(x-1)^(1/2)*(x+1)^(1/2)/x/(x^2-1)^(1/2)","A"
734,1,59,28,0.019000," ","int(((x-1)/(x+1))^(1/2)/x^2,x)","\frac{\sqrt{\frac{x -1}{x +1}}\, \left(x +1\right) \left(-\sqrt{x^{2}-1}\, x^{2}-x \arctan \left(\frac{1}{\sqrt{x^{2}-1}}\right)+\left(x^{2}-1\right)^{\frac{3}{2}}\right)}{\sqrt{\left(x -1\right) \left(x +1\right)}\, x}"," ",0,"((x-1)/(x+1))^(1/2)*(x+1)*((x^2-1)^(3/2)-x^2*(x^2-1)^(1/2)-x*arctan(1/(x^2-1)^(1/2)))/((x-1)*(x+1))^(1/2)/x","B"
735,1,76,49,0.013000," ","int(x^3*(x-1)^(1/2)/(x+1)^(1/2),x)","\frac{\sqrt{x -1}\, \sqrt{x +1}\, \left(6 \sqrt{x^{2}-1}\, x^{3}-8 \sqrt{x^{2}-1}\, x^{2}+9 \sqrt{x^{2}-1}\, x +9 \ln \left(x +\sqrt{x^{2}-1}\right)-16 \sqrt{x^{2}-1}\right)}{24 \sqrt{x^{2}-1}}"," ",0,"1/24*(x-1)^(1/2)*(x+1)^(1/2)*(6*x^3*(x^2-1)^(1/2)-8*(x^2-1)^(1/2)*x^2+9*x*(x^2-1)^(1/2)+9*ln(x+(x^2-1)^(1/2))-16*(x^2-1)^(1/2))/(x^2-1)^(1/2)","A"
736,1,79,49,0.012000," ","int(x^3*((x-1)/(x+1))^(1/2),x)","\frac{\sqrt{\frac{x -1}{x +1}}\, \left(x +1\right) \left(6 \left(x^{2}-1\right)^{\frac{3}{2}} x +15 \sqrt{x^{2}-1}\, x +9 \ln \left(x +\sqrt{x^{2}-1}\right)-8 \left(\left(x -1\right) \left(x +1\right)\right)^{\frac{3}{2}}-24 \sqrt{x^{2}-1}\right)}{24 \sqrt{\left(x -1\right) \left(x +1\right)}}"," ",0,"1/24*((x-1)/(x+1))^(1/2)*(x+1)*(6*x*(x^2-1)^(3/2)-8*((x-1)*(x+1))^(3/2)+15*(x^2-1)^(1/2)*x-24*(x^2-1)^(1/2)+9*ln(x+(x^2-1)^(1/2)))/((x-1)*(x+1))^(1/2)","A"
737,1,33,13,0.016000," ","int((-1/(x+1)*x)^(1/2)/x,x)","\frac{\sqrt{-\frac{x}{x +1}}\, \left(x +1\right) \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)}{\sqrt{\left(x +1\right) x}}"," ",0,"(-1/(x+1)*x)^(1/2)*(x+1)/((x+1)*x)^(1/2)*ln(x+1/2+(x^2+x)^(1/2))","B"
738,1,30,16,0.015000," ","int(((-x+1)/(x+1))^(1/2)/(x-1),x)","-\frac{\sqrt{-\frac{x -1}{x +1}}\, \left(x +1\right) \arcsin \left(x \right)}{\sqrt{-\left(x -1\right) \left(x +1\right)}}"," ",0,"-(-(x-1)/(x+1))^(1/2)*(x+1)/(-(x-1)*(x+1))^(1/2)*arcsin(x)","A"
739,1,85,22,0.033000," ","int(((b*x+a)/(-b*x+c))^(1/2)/(b*x+a),x)","-\frac{\left(b x -c \right) \sqrt{-\frac{b x +a}{b x -c}}\, \arctan \left(\frac{\sqrt{b^{2}}\, \left(2 b x +a -c \right)}{2 \sqrt{-\left(b x +a \right) \left(b x -c \right)}\, b}\right)}{\sqrt{b^{2}}\, \sqrt{-\left(b x +a \right) \left(b x -c \right)}}"," ",0,"-arctan(1/2*(b^2)^(1/2)/b*(2*b*x+a-c)/(-(b*x+a)*(b*x-c))^(1/2))*(b*x-c)*(-(b*x+a)/(b*x-c))^(1/2)/(b^2)^(1/2)/(-(b*x+a)*(b*x-c))^(1/2)","B"
740,1,80,31,0.026000," ","int(((b*x+a)/(d*x+c))^(1/2)/(b*x+a),x)","\frac{\left(d x +c \right) \sqrt{\frac{b x +a}{d x +c}}\, \ln \left(\frac{2 b d x +a d +b c +2 \sqrt{\left(b x +a \right) \left(d x +c \right)}\, \sqrt{b d}}{2 \sqrt{b d}}\right)}{\sqrt{\left(b x +a \right) \left(d x +c \right)}\, \sqrt{b d}}"," ",0,"ln(1/2*(2*b*d*x+2*((b*x+a)*(d*x+c))^(1/2)*(b*d)^(1/2)+a*d+b*c)/(b*d)^(1/2))*(d*x+c)*((b*x+a)/(d*x+c))^(1/2)/((b*x+a)*(d*x+c))^(1/2)/(b*d)^(1/2)","B"
741,1,46,28,0.007000," ","int((-1/(x+1)*x)^(1/2),x)","\frac{\sqrt{-\frac{x}{x +1}}\, \left(x +1\right) \left(-\ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)+2 \sqrt{x^{2}+x}\right)}{2 \sqrt{\left(x +1\right) x}}"," ",0,"1/2*(-1/(x+1)*x)^(1/2)*(x+1)*(-ln(x+1/2+(x^2+x)^(1/2))+2*(x^2+x)^(1/2))/((x+1)*x)^(1/2)","A"
742,1,39,34,0.008000," ","int(((-x+1)/(x+1))^(1/2),x)","\frac{\sqrt{-\frac{x -1}{x +1}}\, \left(x +1\right) \left(\arcsin \left(x \right)+\sqrt{-x^{2}+1}\right)}{\sqrt{-\left(x -1\right) \left(x +1\right)}}"," ",0,"(-(x-1)/(x+1))^(1/2)*(x+1)/(-(x-1)*(x+1))^(1/2)*((-x^2+1)^(1/2)+arcsin(x))","A"
743,1,64,38,0.017000," ","int(((a+x)/(a-x))^(1/2),x)","-\frac{\sqrt{-\frac{a +x}{-a +x}}\, \left(-a +x \right) \left(a \arctan \left(\frac{x}{\sqrt{a^{2}-x^{2}}}\right)-\sqrt{a^{2}-x^{2}}\right)}{\sqrt{-\left(a +x \right) \left(-a +x \right)}}"," ",0,"-(-(a+x)/(-a+x))^(1/2)*(-a+x)*(a*arctan(x/(a^2-x^2)^(1/2))-(a^2-x^2)^(1/2))/(-(a+x)*(-a+x))^(1/2)","A"
744,1,60,35,0.013000," ","int(((-a+x)/(a+x))^(1/2),x)","-\frac{\sqrt{\frac{-a +x}{a +x}}\, \left(a +x \right) \left(a \ln \left(x +\sqrt{-a^{2}+x^{2}}\right)-\sqrt{-a^{2}+x^{2}}\right)}{\sqrt{\left(a +x \right) \left(-a +x \right)}}"," ",0,"-((-a+x)/(a+x))^(1/2)*(a+x)*(a*ln(x+(-a^2+x^2)^(1/2))-(-a^2+x^2)^(1/2))/((a+x)*(-a+x))^(1/2)","A"
745,1,152,64,0.010000," ","int(((b*x+a)/(d*x+c))^(1/2),x)","\frac{\sqrt{\frac{b x +a}{d x +c}}\, \left(d x +c \right) \left(a d \ln \left(\frac{2 b d x +a d +b c +2 \sqrt{\left(b x +a \right) \left(d x +c \right)}\, \sqrt{b d}}{2 \sqrt{b d}}\right)-b c \ln \left(\frac{2 b d x +a d +b c +2 \sqrt{\left(b x +a \right) \left(d x +c \right)}\, \sqrt{b d}}{2 \sqrt{b d}}\right)+2 \sqrt{\left(b x +a \right) \left(d x +c \right)}\, \sqrt{b d}\right)}{2 \sqrt{\left(b x +a \right) \left(d x +c \right)}\, \sqrt{b d}\, d}"," ",0,"1/2*((b*x+a)/(d*x+c))^(1/2)*(d*x+c)*(ln(1/2*(2*b*d*x+a*d+b*c+2*((b*x+a)*(d*x+c))^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*a*d-ln(1/2*(2*b*d*x+a*d+b*c+2*((b*x+a)*(d*x+c))^(1/2)*(b*d)^(1/2))/(b*d)^(1/2))*b*c+2*((b*x+a)*(d*x+c))^(1/2)*(b*d)^(1/2))/((b*x+a)*(d*x+c))^(1/2)/d/(b*d)^(1/2)","B"
746,1,76,31,0.013000," ","int(((x-1)/(5+3*x))^(1/2),x)","-\frac{\sqrt{\frac{x -1}{3 x +5}}\, \left(3 x +5\right) \left(4 \sqrt{3}\, \ln \left(\sqrt{3}\, x +\frac{\sqrt{3}}{3}+\sqrt{3 x^{2}+2 x -5}\right)-3 \sqrt{3 x^{2}+2 x -5}\right)}{9 \sqrt{\left(3 x +5\right) \left(x -1\right)}}"," ",0,"-1/9*((x-1)/(5+3*x))^(1/2)*(5+3*x)*(4*ln(3^(1/2)*x+1/3*3^(1/2)+(3*x^2+2*x-5)^(1/2))*3^(1/2)-3*(3*x^2+2*x-5)^(1/2))/((5+3*x)*(x-1))^(1/2)","B"
747,1,103,38,0.025000," ","int(((-1+5*x)/(1+7*x))^(1/2)/x^2,x)","\frac{\sqrt{\frac{5 x -1}{7 x +1}}\, \left(7 x +1\right) \left(-35 \sqrt{35 x^{2}-2 x -1}\, x^{2}-6 x \arctan \left(\frac{x +1}{\sqrt{35 x^{2}-2 x -1}}\right)+2 \sqrt{35 x^{2}-2 x -1}\, x +\left(35 x^{2}-2 x -1\right)^{\frac{3}{2}}\right)}{\sqrt{\left(5 x -1\right) \left(7 x +1\right)}\, x}"," ",0,"((-1+5*x)/(1+7*x))^(1/2)*(1+7*x)*((35*x^2-2*x-1)^(3/2)-35*(35*x^2-2*x-1)^(1/2)*x^2+2*(35*x^2-2*x-1)^(1/2)*x-6*arctan((x+1)/(35*x^2-2*x-1)^(1/2))*x)/((-1+5*x)*(1+7*x))^(1/2)/x","B"
748,1,17,18,0.004000," ","int(x/(x+1)/((-x+1)/(x+1))^(1/2),x)","\frac{x -1}{\sqrt{-\frac{x -1}{x +1}}}"," ",0,"(x-1)/(-(x-1)/(x+1))^(1/2)","A"
749,1,17,16,0.003000," ","int(x/(x+1)/(-1+2/(x+1))^(1/2),x)","\frac{x -1}{\sqrt{-\frac{x -1}{x +1}}}"," ",0,"(x-1)/(-(x-1)/(x+1))^(1/2)","A"
750,1,81,40,0.023000," ","int(x/(x+1)/((x+2)/(x+3))^(1/2),x)","\frac{\left(x +2\right) \left(2 \sqrt{2}\, \arctanh \left(\frac{\left(3 x +7\right) \sqrt{2}}{4 \sqrt{x^{2}+5 x +6}}\right)-\ln \left(x +\frac{5}{2}+\sqrt{x^{2}+5 x +6}\right)+2 \sqrt{x^{2}+5 x +6}\right)}{2 \sqrt{\frac{x +2}{x +3}}\, \sqrt{\left(x +3\right) \left(x +2\right)}}"," ",0,"1/2*(x+2)*(2*2^(1/2)*arctanh(1/4*(7+3*x)*2^(1/2)/(x^2+5*x+6)^(1/2))+2*(x^2+5*x+6)^(1/2)-ln(x+5/2+(x^2+5*x+6)^(1/2)))/((x+2)/(x+3))^(1/2)/((x+3)*(x+2))^(1/2)","A"
751,1,18,9,0.006000," ","int((1+1/x)^(1/2)/(x+1)^2,x)","\frac{2 \sqrt{\frac{x +1}{x}}\, x}{x +1}"," ",0,"2/(x+1)*x*((x+1)/x)^(1/2)","A"
752,1,40,22,0.023000," ","int((1+1/x)^(1/2)/(-x^2+1)^(1/2),x)","\frac{\sqrt{\frac{x +1}{x}}\, \sqrt{-x^{2}+1}\, x \arcsin \left(2 x -1\right)}{\left(x +1\right) \sqrt{-\left(x -1\right) x}}"," ",0,"((x+1)/x)^(1/2)*x*(-x^2+1)^(1/2)/(x+1)/(-(x-1)*x)^(1/2)*arcsin(2*x-1)","A"
753,1,551,138,0.072000," ","int(1/(x+(-x^2-2*x+3)^(1/2)),x)","\frac{\sqrt{7}\, \arctanh \left(\frac{4-\sqrt{7}+\left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)}{\left(-\frac{1}{2}+\frac{\sqrt{7}}{2}\right) \sqrt{-4 \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+8-2 \sqrt{7}}}\right)}{-\frac{7}{2}+\frac{7 \sqrt{7}}{2}}-\frac{\arctanh \left(\frac{4-\sqrt{7}+\left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)}{\left(-\frac{1}{2}+\frac{\sqrt{7}}{2}\right) \sqrt{-4 \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+8-2 \sqrt{7}}}\right)}{4 \left(-\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}-\frac{\sqrt{7}\, \arctanh \left(\frac{4+\sqrt{7}+\left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}{\left(\frac{1}{2}+\frac{\sqrt{7}}{2}\right) \sqrt{-4 \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+8+2 \sqrt{7}}}\right)}{7 \left(\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}-\frac{\arctanh \left(\frac{4+\sqrt{7}+\left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}{\left(\frac{1}{2}+\frac{\sqrt{7}}{2}\right) \sqrt{-4 \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+8+2 \sqrt{7}}}\right)}{4 \left(\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}+\frac{\sqrt{7}\, \arctanh \left(\frac{\left(4 x +2\right) \sqrt{7}}{14}\right)}{14}+\frac{\sqrt{7}\, \arcsin \left(\frac{x +1}{\sqrt{2-\frac{\sqrt{7}}{2}+\frac{\left(-1-\sqrt{7}\right)^{2}}{4}}}\right)}{28}+\frac{\arcsin \left(\frac{x +1}{\sqrt{2-\frac{\sqrt{7}}{2}+\frac{\left(-1-\sqrt{7}\right)^{2}}{4}}}\right)}{4}-\frac{\sqrt{7}\, \arcsin \left(\frac{x +1}{\sqrt{2+\frac{\sqrt{7}}{2}+\frac{\left(-1+\sqrt{7}\right)^{2}}{4}}}\right)}{28}+\frac{\arcsin \left(\frac{x +1}{\sqrt{2+\frac{\sqrt{7}}{2}+\frac{\left(-1+\sqrt{7}\right)^{2}}{4}}}\right)}{4}+\frac{\ln \left(2 x^{2}+2 x -3\right)}{4}+\frac{\sqrt{7}\, \sqrt{-4 \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+8+2 \sqrt{7}}}{28}-\frac{\sqrt{7}\, \sqrt{-4 \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+8-2 \sqrt{7}}}{28}"," ",0,"1/28*7^(1/2)*(-4*(x+1/2+1/2*7^(1/2))^2+4*(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+8+2*7^(1/2))^(1/2)-1/28*arcsin(1/(2+1/2*7^(1/2)+1/4*(-1+7^(1/2))^2)^(1/2)*(x+1))*7^(1/2)+1/4*arcsin(1/(2+1/2*7^(1/2)+1/4*(-1+7^(1/2))^2)^(1/2)*(x+1))-1/7/(1/2+1/2*7^(1/2))*arctanh((4+7^(1/2)+(-1+7^(1/2))*(x+1/2+1/2*7^(1/2)))/(1/2+1/2*7^(1/2))/(-4*(x+1/2+1/2*7^(1/2))^2+4*(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+8+2*7^(1/2))^(1/2))*7^(1/2)-1/4/(1/2+1/2*7^(1/2))*arctanh((4+7^(1/2)+(-1+7^(1/2))*(x+1/2+1/2*7^(1/2)))/(1/2+1/2*7^(1/2))/(-4*(x+1/2+1/2*7^(1/2))^2+4*(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+8+2*7^(1/2))^(1/2))-1/28*7^(1/2)*(-4*(x+1/2-1/2*7^(1/2))^2+4*(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+8-2*7^(1/2))^(1/2)+1/28*arcsin(1/(2-1/2*7^(1/2)+1/4*(-1-7^(1/2))^2)^(1/2)*(x+1))*7^(1/2)+1/4*arcsin(1/(2-1/2*7^(1/2)+1/4*(-1-7^(1/2))^2)^(1/2)*(x+1))+1/7/(-1/2+1/2*7^(1/2))*arctanh((4-7^(1/2)+(-1-7^(1/2))*(x+1/2-1/2*7^(1/2)))/(-1/2+1/2*7^(1/2))/(-4*(x+1/2-1/2*7^(1/2))^2+4*(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+8-2*7^(1/2))^(1/2))*7^(1/2)-1/4/(-1/2+1/2*7^(1/2))*arctanh((4-7^(1/2)+(-1-7^(1/2))*(x+1/2-1/2*7^(1/2)))/(-1/2+1/2*7^(1/2))/(-4*(x+1/2-1/2*7^(1/2))^2+4*(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+8-2*7^(1/2))^(1/2))+1/4*ln(2*x^2+2*x-3)+1/14*7^(1/2)*arctanh(1/14*(4*x+2)*7^(1/2))","B"
754,1,1066,139,0.049000," ","int(1/(x+(-x^2-2*x+3)^(1/2))^2,x)","\frac{4 \sqrt{7}\, \arctanh \left(\frac{\left(4 x +2\right) \sqrt{7}}{14}\right)}{49}-\frac{3 \left(4 x +2\right)}{28 \left(2 x^{2}+2 x -3\right)}+\frac{-2 x +6}{28 x^{2}+28 x -42}-2 \left(-\frac{1}{14}-\frac{\sqrt{7}}{14}\right) \left(-\frac{\left(-\left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+\left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+2+\frac{\sqrt{7}}{2}\right)^{\frac{3}{2}}}{4 \left(2+\frac{\sqrt{7}}{2}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}+\frac{\left(-1+\sqrt{7}\right) \left(-\frac{\left(2+\frac{\sqrt{7}}{2}\right) \arctanh \left(\frac{4+\sqrt{7}+\left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}{\left(\frac{1}{2}+\frac{\sqrt{7}}{2}\right) \sqrt{-4 \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+8+2 \sqrt{7}}}\right)}{\frac{1}{2}+\frac{\sqrt{7}}{2}}+\frac{\left(-1+\sqrt{7}\right) \arcsin \left(\frac{x +1}{\sqrt{2+\frac{\sqrt{7}}{2}+\frac{\left(-1+\sqrt{7}\right)^{2}}{4}}}\right)}{2}+\frac{\sqrt{-4 \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+8+2 \sqrt{7}}}{2}\right)}{16+4 \sqrt{7}}-\frac{-\frac{\left(-8-2 \sqrt{7}-\left(-1+\sqrt{7}\right)^{2}\right) \arcsin \left(\frac{x +1}{\sqrt{2+\frac{\sqrt{7}}{2}+\frac{\left(-1+\sqrt{7}\right)^{2}}{4}}}\right)}{8}-\frac{\left(-2 x -2\right) \sqrt{-\left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+\left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+2+\frac{\sqrt{7}}{2}}}{4}}{2 \left(2+\frac{\sqrt{7}}{2}\right)}\right)+\frac{\sqrt{7}\, \left(-\frac{\left(2+\frac{\sqrt{7}}{2}\right) \arctanh \left(\frac{4+\sqrt{7}+\left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}{\left(\frac{1}{2}+\frac{\sqrt{7}}{2}\right) \sqrt{-4 \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+8+2 \sqrt{7}}}\right)}{2 \left(\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}+\frac{\left(-1+\sqrt{7}\right) \arcsin \left(\frac{x +1}{\sqrt{2+\frac{\sqrt{7}}{2}+\frac{\left(-1+\sqrt{7}\right)^{2}}{4}}}\right)}{4}+\frac{\sqrt{-4 \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1+\sqrt{7}\right) \left(x +\frac{1}{2}+\frac{\sqrt{7}}{2}\right)+8+2 \sqrt{7}}}{4}\right)}{49}-\frac{\sqrt{7}\, \left(-\frac{\left(2-\frac{\sqrt{7}}{2}\right) \arctanh \left(\frac{4-\sqrt{7}+\left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)}{\left(-\frac{1}{2}+\frac{\sqrt{7}}{2}\right) \sqrt{-4 \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+8-2 \sqrt{7}}}\right)}{2 \left(-\frac{1}{2}+\frac{\sqrt{7}}{2}\right)}+\frac{\left(-1-\sqrt{7}\right) \arcsin \left(\frac{x +1}{\sqrt{2-\frac{\sqrt{7}}{2}+\frac{\left(-1-\sqrt{7}\right)^{2}}{4}}}\right)}{4}+\frac{\sqrt{-4 \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+8-2 \sqrt{7}}}{4}\right)}{49}-2 \left(-\frac{1}{14}+\frac{\sqrt{7}}{14}\right) \left(-\frac{\left(-\left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+\left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+2-\frac{\sqrt{7}}{2}\right)^{\frac{3}{2}}}{4 \left(2-\frac{\sqrt{7}}{2}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)}+\frac{\left(-1-\sqrt{7}\right) \left(-\frac{\left(2-\frac{\sqrt{7}}{2}\right) \arctanh \left(\frac{4-\sqrt{7}+\left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)}{\left(-\frac{1}{2}+\frac{\sqrt{7}}{2}\right) \sqrt{-4 \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+8-2 \sqrt{7}}}\right)}{-\frac{1}{2}+\frac{\sqrt{7}}{2}}+\frac{\left(-1-\sqrt{7}\right) \arcsin \left(\frac{x +1}{\sqrt{2-\frac{\sqrt{7}}{2}+\frac{\left(-1-\sqrt{7}\right)^{2}}{4}}}\right)}{2}+\frac{\sqrt{-4 \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+4 \left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+8-2 \sqrt{7}}}{2}\right)}{16-4 \sqrt{7}}-\frac{-\frac{\left(-8+2 \sqrt{7}-\left(-1-\sqrt{7}\right)^{2}\right) \arcsin \left(\frac{x +1}{\sqrt{2-\frac{\sqrt{7}}{2}+\frac{\left(-1-\sqrt{7}\right)^{2}}{4}}}\right)}{8}-\frac{\left(-2 x -2\right) \sqrt{-\left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)^{2}+\left(-1-\sqrt{7}\right) \left(x +\frac{1}{2}-\frac{\sqrt{7}}{2}\right)+2-\frac{\sqrt{7}}{2}}}{4}}{2 \left(2-\frac{\sqrt{7}}{2}\right)}\right)"," ",0,"-3/28*(4*x+2)/(2*x^2+2*x-3)+4/49*7^(1/2)*arctanh(1/14*(4*x+2)*7^(1/2))+1/14*(-2*x+6)/(2*x^2+2*x-3)-2*(-1/14-1/14*7^(1/2))*(-1/4/(2+1/2*7^(1/2))/(x+1/2+1/2*7^(1/2))*(-(x+1/2+1/2*7^(1/2))^2+(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+2+1/2*7^(1/2))^(3/2)+1/8*(-1+7^(1/2))/(2+1/2*7^(1/2))*(1/2*(-4*(x+1/2+1/2*7^(1/2))^2+4*(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+8+2*7^(1/2))^(1/2)+1/2*(-1+7^(1/2))*arcsin(1/(2+1/2*7^(1/2)+1/4*(-1+7^(1/2))^2)^(1/2)*(x+1))-(2+1/2*7^(1/2))/(1/2+1/2*7^(1/2))*arctanh((4+7^(1/2)+(-1+7^(1/2))*(x+1/2+1/2*7^(1/2)))/(1/2+1/2*7^(1/2))/(-4*(x+1/2+1/2*7^(1/2))^2+4*(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+8+2*7^(1/2))^(1/2)))-1/2/(2+1/2*7^(1/2))*(-1/4*(-2*x-2)*(-(x+1/2+1/2*7^(1/2))^2+(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+2+1/2*7^(1/2))^(1/2)-1/8*(-8-2*7^(1/2)-(-1+7^(1/2))^2)*arcsin(1/(2+1/2*7^(1/2)+1/4*(-1+7^(1/2))^2)^(1/2)*(x+1))))+1/49*7^(1/2)*(1/4*(-4*(x+1/2+1/2*7^(1/2))^2+4*(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+8+2*7^(1/2))^(1/2)+1/4*(-1+7^(1/2))*arcsin(1/(2+1/2*7^(1/2)+1/4*(-1+7^(1/2))^2)^(1/2)*(x+1))-1/2*(2+1/2*7^(1/2))/(1/2+1/2*7^(1/2))*arctanh((4+7^(1/2)+(-1+7^(1/2))*(x+1/2+1/2*7^(1/2)))/(1/2+1/2*7^(1/2))/(-4*(x+1/2+1/2*7^(1/2))^2+4*(-1+7^(1/2))*(x+1/2+1/2*7^(1/2))+8+2*7^(1/2))^(1/2)))-1/49*7^(1/2)*(1/4*(-4*(x+1/2-1/2*7^(1/2))^2+4*(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+8-2*7^(1/2))^(1/2)+1/4*(-1-7^(1/2))*arcsin(1/(2-1/2*7^(1/2)+1/4*(-1-7^(1/2))^2)^(1/2)*(x+1))-1/2*(2-1/2*7^(1/2))/(-1/2+1/2*7^(1/2))*arctanh((4-7^(1/2)+(-1-7^(1/2))*(x+1/2-1/2*7^(1/2)))/(-1/2+1/2*7^(1/2))/(-4*(x+1/2-1/2*7^(1/2))^2+4*(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+8-2*7^(1/2))^(1/2)))-2*(-1/14+1/14*7^(1/2))*(-1/4/(2-1/2*7^(1/2))/(x+1/2-1/2*7^(1/2))*(-(x+1/2-1/2*7^(1/2))^2+(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+2-1/2*7^(1/2))^(3/2)+1/8*(-1-7^(1/2))/(2-1/2*7^(1/2))*(1/2*(-4*(x+1/2-1/2*7^(1/2))^2+4*(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+8-2*7^(1/2))^(1/2)+1/2*(-1-7^(1/2))*arcsin(1/(2-1/2*7^(1/2)+1/4*(-1-7^(1/2))^2)^(1/2)*(x+1))-(2-1/2*7^(1/2))/(-1/2+1/2*7^(1/2))*arctanh((4-7^(1/2)+(-1-7^(1/2))*(x+1/2-1/2*7^(1/2)))/(-1/2+1/2*7^(1/2))/(-4*(x+1/2-1/2*7^(1/2))^2+4*(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+8-2*7^(1/2))^(1/2)))-1/2/(2-1/2*7^(1/2))*(-1/4*(-2*x-2)*(-(x+1/2-1/2*7^(1/2))^2+(-1-7^(1/2))*(x+1/2-1/2*7^(1/2))+2-1/2*7^(1/2))^(1/2)-1/8*(-8+2*7^(1/2)-(-1-7^(1/2))^2)*arcsin(1/(2-1/2*7^(1/2)+1/4*(-1-7^(1/2))^2)^(1/2)*(x+1))))","B"
755,1,5984,248,0.067000," ","int(1/(x+(-x^2-2*x+3)^(1/2))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
756,1,71,57,0.006000," ","int(1/(x+(x^2-2*x-3)^(1/2)),x)","\frac{x}{2}+\frac{3 \arctanh \left(\frac{-\frac{10 x}{3}-2}{\sqrt{-20 x +4 \left(x +\frac{3}{2}\right)^{2}-21}}\right)}{4}-\frac{3 \ln \left(2 x +3\right)}{4}+\frac{5 \ln \left(x -1+\sqrt{-5 x +\left(x +\frac{3}{2}\right)^{2}-\frac{21}{4}}\right)}{4}-\frac{\sqrt{-20 x +4 \left(x +\frac{3}{2}\right)^{2}-21}}{4}"," ",0,"-1/4*(4*(x+3/2)^2-20*x-21)^(1/2)+5/4*ln(-1+x+((x+3/2)^2-5*x-21/4)^(1/2))+3/4*arctanh(2/3*(-3-5*x)/(4*(x+3/2)^2-20*x-21)^(1/2))+1/2*x-3/4*ln(2*x+3)","A"
757,1,118,73,0.021000," ","int(1/(x+(x^2-2*x-3)^(1/2))^2,x)","\frac{x}{2}+2 \arctanh \left(\frac{-\frac{10 x}{3}-2}{\sqrt{-20 x +4 \left(x +\frac{3}{2}\right)^{2}-21}}\right)-2 \ln \left(2 x +3\right)+2 \ln \left(x -1+\sqrt{-5 x +\left(x +\frac{3}{2}\right)^{2}-\frac{21}{4}}\right)-\frac{9}{4 \left(2 x +3\right)}-\frac{2 \sqrt{-20 x +4 \left(x +\frac{3}{2}\right)^{2}-21}}{3}-\frac{\left(-5 x +\left(x +\frac{3}{2}\right)^{2}-\frac{21}{4}\right)^{\frac{3}{2}}}{3 \left(x +\frac{3}{2}\right)}+\frac{\left(2 x -2\right) \sqrt{-5 x +\left(x +\frac{3}{2}\right)^{2}-\frac{21}{4}}}{6}"," ",0,"-2*ln(2*x+3)+1/2*x-9/4/(2*x+3)-2/3*(-20*x+4*(x+3/2)^2-21)^(1/2)+2*ln(x-1+(-5*x+(x+3/2)^2-21/4)^(1/2))+2*arctanh(2/3*(-5*x-3)/(-20*x+4*(x+3/2)^2-21)^(1/2))-1/3/(x+3/2)*(-5*x+(x+3/2)^2-21/4)^(3/2)+1/6*(2*x-2)*(-5*x+(x+3/2)^2-21/4)^(1/2)","A"
758,1,146,89,0.027000," ","int(1/(x+(x^2-2*x-3)^(1/2))^3,x)","\frac{x}{2}+3 \arctanh \left(\frac{-\frac{10 x}{3}-2}{\sqrt{-20 x +4 \left(x +\frac{3}{2}\right)^{2}-21}}\right)-3 \ln \left(2 x +3\right)+3 \ln \left(x -1+\sqrt{-5 x +\left(x +\frac{3}{2}\right)^{2}-\frac{21}{4}}\right)-\frac{9}{2 x +3}+\frac{27}{8 \left(2 x +3\right)^{2}}-\frac{\left(-5 x +\left(x +\frac{3}{2}\right)^{2}-\frac{21}{4}\right)^{\frac{3}{2}}}{2 \left(x +\frac{3}{2}\right)}-\sqrt{-20 x +4 \left(x +\frac{3}{2}\right)^{2}-21}+\frac{\left(2 x -2\right) \sqrt{-5 x +\left(x +\frac{3}{2}\right)^{2}-\frac{21}{4}}}{4}+\frac{\left(-5 x +\left(x +\frac{3}{2}\right)^{2}-\frac{21}{4}\right)^{\frac{3}{2}}}{4 \left(x +\frac{3}{2}\right)^{2}}"," ",0,"-9/(2*x+3)-3*ln(2*x+3)+1/2*x+27/8/(2*x+3)^2-1/2/(x+3/2)*(-5*x+(x+3/2)^2-21/4)^(3/2)-(-20*x+4*(x+3/2)^2-21)^(1/2)+3*arctanh(2/3*(-5*x-3)/(-20*x+4*(x+3/2)^2-21)^(1/2))+1/4*(2*x-2)*(-5*x+(x+3/2)^2-21/4)^(1/2)+3*ln(x-1+(-5*x+(x+3/2)^2-21/4)^(1/2))+1/4/(x+3/2)^2*(-5*x+(x+3/2)^2-21/4)^(3/2)","A"
759,1,370,85,0.031000," ","int(1/(x+(-x^2-4*x-3)^(1/2)),x)","\frac{\arcsin \left(x +2\right)}{2}-\frac{\sqrt{2}\, \arctan \left(\frac{\left(4 x +4\right) \sqrt{2}}{4}\right)}{2}+\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)}{3 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}+\frac{\ln \left(2 x^{2}+4 x +3\right)}{4}-\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(-\arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{12 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}-\frac{\sqrt{3}\, \sqrt{4}\, \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \left(\arctanh \left(\frac{3 x}{\left(-x -\frac{3}{2}\right) \sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}}\right)+\sqrt{2}\, \arctan \left(\frac{\sqrt{\frac{3 x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-12}\, \sqrt{2}}{6}\right)\right)}{6 \sqrt{\frac{\frac{x^{2}}{\left(-x -\frac{3}{2}\right)^{2}}-4}{\left(\frac{x}{-x -\frac{3}{2}}+1\right)^{2}}}\, \left(\frac{x}{-x -\frac{3}{2}}+1\right)}"," ",0,"1/2*arcsin(x+2)-1/12*3^(1/2)*4^(1/2)*(3*x^2/(-3/2-x)^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3*x^2/(-3/2-x)^2-12)^(1/2)*2^(1/2))-arctanh(3*x/(-3/2-x)/(3*x^2/(-3/2-x)^2-12)^(1/2)))/((x^2/(-3/2-x)^2-4)/(x/(-3/2-x)+1)^2)^(1/2)/(x/(-3/2-x)+1)+1/3*3^(1/2)*4^(1/2)/((x^2/(-3/2-x)^2-4)/(x/(-3/2-x)+1)^2)^(1/2)/(x/(-3/2-x)+1)*(3*x^2/(-3/2-x)^2-12)^(1/2)*2^(1/2)*arctan(1/6*(3*x^2/(-3/2-x)^2-12)^(1/2)*2^(1/2))-1/6*3^(1/2)*4^(1/2)*(3*x^2/(-3/2-x)^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3*x^2/(-3/2-x)^2-12)^(1/2)*2^(1/2))+arctanh(3*x/(-3/2-x)/(3*x^2/(-3/2-x)^2-12)^(1/2)))/((x^2/(-3/2-x)^2-4)/(x/(-3/2-x)+1)^2)^(1/2)/(x/(-3/2-x)+1)+1/4*ln(2*x^2+4*x+3)-1/2*2^(1/2)*arctan(1/4*(4+4*x)*2^(1/2))","B"
760,1,2407,73,0.089000," ","int(1/(x+(-x^2-4*x-3)^(1/2))^2,x)","\text{Expression too large to display}"," ",0,"-3/8*(4*x+4)/(2*x^2+4*x+3)+1/4*2^(1/2)*arctan(1/4*(4*x+4)*2^(1/2))-1/2*(-4*x-6)/(2*x^2+4*x+3)+1/72*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))*x^2/(-x-3/2)^2-8*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x)*x^2/(-x-3/2)^2+2*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))-6*(3/(-x-3/2)^2*x^2-12)^(1/2)-16*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)/(1/(-x-3/2)^2*x^2+2)+1/36*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(7*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))+4*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/(1/(-x-3/2)*x+1)/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)-2/9*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(3*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))*x^6/(-x-3/2)^6+2*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)-1/(-x-3/2)^2*x^2+4)/(1/(-x-3/2)^2*x^2-4))*x^6/(-x-3/2)^6-2*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)^2*x^2-4))*x^6/(-x-3/2)^6+4*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x)*x^6/(-x-3/2)^6+(3/(-x-3/2)^2*x^2-12)^(1/2)*x^5/(-x-3/2)^5-(3/(-x-3/2)^2*x^2-12)^(3/2)*x^2/(-x-3/2)^2+(3/(-x-3/2)^2*x^2-12)^(1/2)*x^4/(-x-3/2)^4-36*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))*x^2/(-x-3/2)^2-2*(3/(-x-3/2)^2*x^2-12)^(1/2)*x^3/(-x-3/2)^3-8*(3/(-x-3/2)^2*x^2-12)^(1/2)*x^2/(-x-3/2)^2-24*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)-1/(-x-3/2)^2*x^2+4)/(1/(-x-3/2)^2*x^2-4))*x^2/(-x-3/2)^2+24*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)^2*x^2-4))*x^2/(-x-3/2)^2-48*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x)*x^2/(-x-3/2)^2-48*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))-8*(3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+16*(3/(-x-3/2)^2*x^2-12)^(1/2)-32*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)-1/(-x-3/2)^2*x^2+4)/(1/(-x-3/2)^2*x^2-4))+32*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)^2*x^2-4))-64*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)/(1/(-x-3/2)^2*x^2+2)/((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)-1/(-x-3/2)^2*x^2+4)/((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+1/(-x-3/2)^2*x^2-4)-2/9*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))+arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)+1/18*3^(1/2)*4^(1/2)*(3/(-x-3/2)^2*x^2-12)^(1/2)*(11*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))*x^6/(-x-3/2)^6+8*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)-1/(-x-3/2)^2*x^2+4)/(1/(-x-3/2)^2*x^2-4))*x^6/(-x-3/2)^6-8*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)^2*x^2-4))*x^6/(-x-3/2)^6+24*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x)*x^6/(-x-3/2)^6+4*(3/(-x-3/2)^2*x^2-12)^(1/2)*x^5/(-x-3/2)^5-(3/(-x-3/2)^2*x^2-12)^(3/2)*x^2/(-x-3/2)^2+(3/(-x-3/2)^2*x^2-12)^(1/2)*x^4/(-x-3/2)^4-132*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))*x^2/(-x-3/2)^2-8*(3/(-x-3/2)^2*x^2-12)^(1/2)*x^3/(-x-3/2)^3-8*(3/(-x-3/2)^2*x^2-12)^(1/2)*x^2/(-x-3/2)^2-96*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)-1/(-x-3/2)^2*x^2+4)/(1/(-x-3/2)^2*x^2-4))*x^2/(-x-3/2)^2+96*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)^2*x^2-4))*x^2/(-x-3/2)^2-288*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x)*x^2/(-x-3/2)^2-176*2^(1/2)*arctan(1/6*(3/(-x-3/2)^2*x^2-12)^(1/2)*2^(1/2))-32*(3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+16*(3/(-x-3/2)^2*x^2-12)^(1/2)-128*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)-1/(-x-3/2)^2*x^2+4)/(1/(-x-3/2)^2*x^2-4))+128*ln(((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)^2*x^2-4))-384*arctanh(3/(-x-3/2)/(3/(-x-3/2)^2*x^2-12)^(1/2)*x))/((1/(-x-3/2)^2*x^2-4)/(1/(-x-3/2)*x+1)^2)^(1/2)/(1/(-x-3/2)*x+1)/(1/(-x-3/2)^2*x^2+2)/((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)-1/(-x-3/2)^2*x^2+4)/((3/(-x-3/2)^2*x^2-12)^(1/2)*x/(-x-3/2)+1/(-x-3/2)^2*x^2-4)","B"
761,1,14529,120,0.278000," ","int(1/(x+(-x^2-4*x-3)^(1/2))^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
762,1,51,38,0.009000," ","int(x^3*(x+1)^3*(2*x+1)*(-x^4-2*x^3-x^2+1)^(1/2),x)","\frac{\left(x^{2}+x +1\right) \left(x^{2}+x -1\right) \left(3 x^{4}+6 x^{3}+3 x^{2}+2\right) \sqrt{-x^{4}-2 x^{3}-x^{2}+1}}{15}"," ",0,"1/15*(x^2+x+1)*(x^2+x-1)*(3*x^4+6*x^3+3*x^2+2)*(-x^4-2*x^3-x^2+1)^(1/2)","A"
763,1,51,38,0.007000," ","int((2*x+1)*(x^2+x)^3*(1-(x^2+x)^2)^(1/2),x)","\frac{\left(x^{2}+x +1\right) \left(x^{2}+x -1\right) \left(3 x^{4}+6 x^{3}+3 x^{2}+2\right) \sqrt{-x^{4}-2 x^{3}-x^{2}+1}}{15}"," ",0,"1/15*(x^2+x+1)*(x^2+x-1)*(3*x^4+6*x^3+3*x^2+2)*(-x^4-2*x^3-x^2+1)^(1/2)","A"
764,1,1050,86,0.147000," ","int((-x^4+4*x^3-8*x^2+8*x)^(3/2),x)","-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x^{5}}{7}+\frac{5 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x^{4}}{7}-\frac{66 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x^{3}}{35}+\frac{14 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x^{2}}{5}-\frac{32 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x}{35}+\frac{32 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{7 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{4 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}}{7}+\frac{64 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}-1}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)\right)}{5 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{16 \left(\left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x +2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(\frac{\left(i \sqrt{3}-1\right) \EllipticE \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2}+\frac{\left(6+2 i \sqrt{3}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2 i \sqrt{3}-2}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{-1-i \sqrt{3}}{1-i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{i \sqrt{3}-1}\right)\right)}{5 \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"-1/7*x^5*(-x^4+4*x^3-8*x^2+8*x)^(1/2)+5/7*x^4*(-x^4+4*x^3-8*x^2+8*x)^(1/2)-66/35*x^3*(-x^4+4*x^3-8*x^2+8*x)^(1/2)+14/5*x^2*(-x^4+4*x^3-8*x^2+8*x)^(1/2)-32/35*x*(-x^4+4*x^3-8*x^2+8*x)^(1/2)-4/7*(-x^4+4*x^3-8*x^2+8*x)^(1/2)+32/7*(-1-I*3^(1/2))*((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-x*(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2)))^(1/2)*EllipticF(((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+64/5*(-1-I*3^(1/2))*((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-x*(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2)))^(1/2)*(2*EllipticF(((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-2*EllipticPi(((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2),(1+I*3^(1/2))/(I*3^(1/2)-1),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2)))-16/5*(x*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))+2*(-1-I*3^(1/2))*((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)*(1/2*(6+2*I*3^(1/2))/(I*3^(1/2)-1)*EllipticF(((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/2*(I*3^(1/2)-1)*EllipticE(((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-4/(I*3^(1/2)-1)*EllipticPi(((I*3^(1/2)-1)*x/(1+I*3^(1/2))/(x-2))^(1/2),(-1-I*3^(1/2))/(1-I*3^(1/2)),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))))/(-x*(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2)))^(1/2)","B"
765,1,946,54,0.075000," ","int((-x^4+4*x^3-8*x^2+8*x)^(1/2),x)","\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x}{3}+\frac{8 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{3 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}}{3}+\frac{8 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}-1}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)\right)}{3 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{2 \left(\left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x +2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(\frac{\left(i \sqrt{3}-1\right) \EllipticE \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2}+\frac{\left(6+2 i \sqrt{3}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2 i \sqrt{3}-2}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{-1-i \sqrt{3}}{1-i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{i \sqrt{3}-1}\right)\right)}{3 \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"1/3*(-x^4+4*x^3-8*x^2+8*x)^(1/2)*x-1/3*(-x^4+4*x^3-8*x^2+8*x)^(1/2)+8/3*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+8/3*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*(2*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-2*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(1+I*3^(1/2))/(I*3^(1/2)-1),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2)))-2/3*((x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x+2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)*(1/2*(6+2*I*3^(1/2))/(I*3^(1/2)-1)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/2*(I*3^(1/2)-1)*EllipticE(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-4/(I*3^(1/2)-1)*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(-1-I*3^(1/2))/(1-I*3^(1/2)),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))))/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)","B"
766,1,200,15,0.074000," ","int(1/(-x^4+4*x^3-8*x^2+8*x)^(1/2),x)","\frac{2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{\left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))","B"
767,1,963,61,0.072000," ","int(1/(-x^4+4*x^3-8*x^2+8*x)^(3/2),x)","\frac{2 \left(\frac{x^{2}}{192}+\frac{1}{24}\right) x}{\sqrt{-\left(x^{3}-4 x^{2}+8 x -8\right) x}}+\frac{\left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{6 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{-x^{3}+4 x^{2}-8 x +8}{32 \sqrt{\left(-x^{3}+4 x^{2}-8 x +8\right) x}}+\frac{\left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}-1}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)\right)}{6 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{\left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x +2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(\frac{\left(i \sqrt{3}-1\right) \EllipticE \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2}+\frac{\left(6+2 i \sqrt{3}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2 i \sqrt{3}-2}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{-1-i \sqrt{3}}{1-i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{i \sqrt{3}-1}\right)}{24 \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"2*x*(1/24+1/192*x^2)/(-x*(x^3-4*x^2+8*x-8))^(1/2)-1/32*(-x^3+4*x^2-8*x+8)/(x*(-x^3+4*x^2-8*x+8))^(1/2)+1/6*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/6*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*(2*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-2*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(1+I*3^(1/2))/(I*3^(1/2)-1),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2)))-1/24*((x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x+2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)*(1/2*(6+2*I*3^(1/2))/(I*3^(1/2)-1)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/2*(I*3^(1/2)-1)*EllipticE(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-4/(I*3^(1/2)-1)*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(-1-I*3^(1/2))/(1-I*3^(1/2)),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))))/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)","B"
768,1,1039,93,0.076000," ","int(1/(-x^4+4*x^3-8*x^2+8*x)^(5/2),x)","\frac{2 \left(\frac{5}{1728} x^{2}-\frac{19}{4608} x +\frac{53}{3456}\right) x}{\sqrt{-\left(x^{3}-4 x^{2}+8 x -8\right) x}}+\frac{5 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{216 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}}{768 x^{2}}-\frac{-x^{3}+4 x^{2}-8 x +8}{96 \sqrt{\left(-x^{3}+4 x^{2}-8 x +8\right) x}}+\frac{\left(\frac{1}{288} x^{2}-\frac{1}{96} x +\frac{1}{36}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}}{\left(x^{3}-4 x^{2}+8 x -8\right)^{2}}+\frac{7 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}-1}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)\right)}{108 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{7 \left(\left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x +2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(\frac{\left(i \sqrt{3}-1\right) \EllipticE \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2}+\frac{\left(6+2 i \sqrt{3}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2 i \sqrt{3}-2}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{-1-i \sqrt{3}}{1-i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{i \sqrt{3}-1}\right)\right)}{432 \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"-1/768*(-x^4+4*x^3-8*x^2+8*x)^(1/2)/x^2-1/96*(-x^3+4*x^2-8*x+8)/((-x^3+4*x^2-8*x+8)*x)^(1/2)+(1/36+1/288*x^2-1/96*x)*(-x^4+4*x^3-8*x^2+8*x)^(1/2)/(x^3-4*x^2+8*x-8)^2+2*x*(53/3456+5/1728*x^2-19/4608*x)/(-(x^3-4*x^2+8*x-8)*x)^(1/2)+5/216*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+7/108*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*(2*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-2*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(1+I*3^(1/2))/(I*3^(1/2)-1),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2)))-7/432*((x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x+2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)*(1/2*(6+2*I*3^(1/2))/(I*3^(1/2)-1)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/2*(I*3^(1/2)-1)*EllipticE(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-4/(I*3^(1/2)-1)*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(-1-I*3^(1/2))/(1-I*3^(1/2)),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))))/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)","B"
769,1,1050,86,0.073000," ","int(((2-x)*x*(x^2-2*x+4))^(3/2),x)","-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x^{5}}{7}+\frac{5 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x^{4}}{7}-\frac{66 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x^{3}}{35}+\frac{14 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x^{2}}{5}-\frac{32 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x}{35}+\frac{32 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{7 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{4 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}}{7}+\frac{64 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}-1}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)\right)}{5 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{16 \left(\left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x +2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(\frac{\left(i \sqrt{3}-1\right) \EllipticE \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2}+\frac{\left(6+2 i \sqrt{3}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2 i \sqrt{3}-2}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{-1-i \sqrt{3}}{1-i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{i \sqrt{3}-1}\right)\right)}{5 \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"-1/7*(-x^4+4*x^3-8*x^2+8*x)^(1/2)*x^5+5/7*(-x^4+4*x^3-8*x^2+8*x)^(1/2)*x^4-66/35*(-x^4+4*x^3-8*x^2+8*x)^(1/2)*x^3+14/5*(-x^4+4*x^3-8*x^2+8*x)^(1/2)*x^2-32/35*(-x^4+4*x^3-8*x^2+8*x)^(1/2)*x-4/7*(-x^4+4*x^3-8*x^2+8*x)^(1/2)+32/7*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+64/5*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*(2*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-2*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(1+I*3^(1/2))/(I*3^(1/2)-1),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2)))-16/5*((x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x+2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)*(1/2*(6+2*I*3^(1/2))/(I*3^(1/2)-1)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/2*(I*3^(1/2)-1)*EllipticE(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-4/(I*3^(1/2)-1)*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(-1-I*3^(1/2))/(1-I*3^(1/2)),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))))/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)","B"
770,1,946,54,0.078000," ","int(((2-x)*x*(x^2-2*x+4))^(1/2),x)","\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}\, x}{3}+\frac{8 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{3 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}}{3}+\frac{8 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}-1}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)\right)}{3 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{2 \left(\left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x +2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(\frac{\left(i \sqrt{3}-1\right) \EllipticE \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2}+\frac{\left(6+2 i \sqrt{3}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2 i \sqrt{3}-2}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{-1-i \sqrt{3}}{1-i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{i \sqrt{3}-1}\right)\right)}{3 \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"1/3*(-x^4+4*x^3-8*x^2+8*x)^(1/2)*x-1/3*(-x^4+4*x^3-8*x^2+8*x)^(1/2)+8/3*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+8/3*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*(2*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-2*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(1+I*3^(1/2))/(I*3^(1/2)-1),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2)))-2/3*((x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x+2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)*(1/2*(6+2*I*3^(1/2))/(I*3^(1/2)-1)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/2*(I*3^(1/2)-1)*EllipticE(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-4/(I*3^(1/2)-1)*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(-1-I*3^(1/2))/(1-I*3^(1/2)),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))))/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)","B"
771,1,200,15,0.073000," ","int(1/((2-x)*x*(x^2-2*x+4))^(1/2),x)","\frac{2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{\left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))","B"
772,1,963,61,0.075000," ","int(1/((2-x)*x*(x^2-2*x+4))^(3/2),x)","\frac{2 \left(\frac{x^{2}}{192}+\frac{1}{24}\right) x}{\sqrt{-\left(x^{3}-4 x^{2}+8 x -8\right) x}}+\frac{\left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{6 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{-x^{3}+4 x^{2}-8 x +8}{32 \sqrt{\left(-x^{3}+4 x^{2}-8 x +8\right) x}}+\frac{\left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}-1}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)\right)}{6 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{\left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x +2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(\frac{\left(i \sqrt{3}-1\right) \EllipticE \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2}+\frac{\left(6+2 i \sqrt{3}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2 i \sqrt{3}-2}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{-1-i \sqrt{3}}{1-i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{i \sqrt{3}-1}\right)}{24 \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"2*(1/192*x^2+1/24)/(-(x^3-4*x^2+8*x-8)*x)^(1/2)*x-1/32*(-x^3+4*x^2-8*x+8)/((-x^3+4*x^2-8*x+8)*x)^(1/2)+1/6*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/6*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*(2*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-2*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(1+I*3^(1/2))/(I*3^(1/2)-1),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2)))-1/24*((x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x+2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)*(1/2*(6+2*I*3^(1/2))/(I*3^(1/2)-1)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/2*(I*3^(1/2)-1)*EllipticE(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-4/(I*3^(1/2)-1)*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(-1-I*3^(1/2))/(1-I*3^(1/2)),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))))/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)","B"
773,1,1039,93,0.074000," ","int(1/((2-x)*x*(x^2-2*x+4))^(5/2),x)","\frac{2 \left(\frac{5}{1728} x^{2}-\frac{19}{4608} x +\frac{53}{3456}\right) x}{\sqrt{-\left(x^{3}-4 x^{2}+8 x -8\right) x}}+\frac{5 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{216 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}}{768 x^{2}}-\frac{-x^{3}+4 x^{2}-8 x +8}{96 \sqrt{\left(-x^{3}+4 x^{2}-8 x +8\right) x}}+\frac{\left(\frac{1}{288} x^{2}-\frac{1}{96} x +\frac{1}{36}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+8 x}}{\left(x^{3}-4 x^{2}+8 x -8\right)^{2}}+\frac{7 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(2 \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)-2 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{1+i \sqrt{3}}{i \sqrt{3}-1}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)\right)}{108 \left(i \sqrt{3}-1\right) \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}-\frac{7 \left(\left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x +2 \left(-1-i \sqrt{3}\right) \sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(x -2\right)^{2} \sqrt{\frac{x -1+i \sqrt{3}}{\left(1-i \sqrt{3}\right) \left(x -2\right)}}\, \sqrt{\frac{x -1-i \sqrt{3}}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}\, \left(\frac{\left(i \sqrt{3}-1\right) \EllipticE \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2}+\frac{\left(6+2 i \sqrt{3}\right) \EllipticF \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{2 i \sqrt{3}-2}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(i \sqrt{3}-1\right) x}{\left(1+i \sqrt{3}\right) \left(x -2\right)}}, \frac{-1-i \sqrt{3}}{1-i \sqrt{3}}, \sqrt{\frac{\left(1+i \sqrt{3}\right) \left(-1-i \sqrt{3}\right)}{\left(i \sqrt{3}-1\right) \left(1-i \sqrt{3}\right)}}\right)}{i \sqrt{3}-1}\right)\right)}{432 \sqrt{-\left(x -2\right) \left(x -1+i \sqrt{3}\right) \left(x -1-i \sqrt{3}\right) x}}"," ",0,"-1/768*(-x^4+4*x^3-8*x^2+8*x)^(1/2)/x^2-1/96*(-x^3+4*x^2-8*x+8)/((-x^3+4*x^2-8*x+8)*x)^(1/2)+(1/288*x^2-1/96*x+1/36)*(-x^4+4*x^3-8*x^2+8*x)^(1/2)/(x^3-4*x^2+8*x-8)^2+2*(5/1728*x^2-19/4608*x+53/3456)/(-(x^3-4*x^2+8*x-8)*x)^(1/2)*x+5/216*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+7/108*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)/(I*3^(1/2)-1)/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)*(2*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-2*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(1+I*3^(1/2))/(I*3^(1/2)-1),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2)))-7/432*((x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x+2*(-1-I*3^(1/2))*((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2)*(x-2)^2*((x-1+I*3^(1/2))/(1-I*3^(1/2))/(x-2))^(1/2)*((x-1-I*3^(1/2))/(1+I*3^(1/2))/(x-2))^(1/2)*(1/2*(6+2*I*3^(1/2))/(I*3^(1/2)-1)*EllipticF(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))+1/2*(I*3^(1/2)-1)*EllipticE(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))-4/(I*3^(1/2)-1)*EllipticPi(((I*3^(1/2)-1)/(1+I*3^(1/2))/(x-2)*x)^(1/2),(-1-I*3^(1/2))/(1-I*3^(1/2)),((1+I*3^(1/2))*(-1-I*3^(1/2))/(I*3^(1/2)-1)/(1-I*3^(1/2)))^(1/2))))/(-(x-2)*(x-1+I*3^(1/2))*(x-1-I*3^(1/2))*x)^(1/2)","B"
774,1,5229,772,0.199000," ","int((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
775,1,4890,668,0.066000," ","int((d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(1/2),x)","\text{output too large to display}"," ",0,"1/3*x*(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(1/2)+1/3*c/d*(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(1/2)+16/3*a*c*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)^2*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(d^2*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*EllipticF(((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2),((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2))-8/3*c^3/d*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)^2*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(d^2*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d*EllipticF(((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2),((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2))+((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*EllipticPi(((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2),(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d),((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)))-2/3*c^2*((x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)+((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)^2*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d^2*(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d^2*(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d^2*(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))^2/d^2)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*EllipticF(((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2),((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2))+((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*EllipticE(((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2),((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2))/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)+4*c/d/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*EllipticPi(((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2),((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d),((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2))))/(d^2*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)","B"
776,1,1056,259,0.066000," ","int(1/(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(1/2),x)","\frac{2 \left(\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}+\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right) \sqrt{\frac{\left(-\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}+\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x -\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right)}{\left(-\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x +\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right)}}\, \left(x +\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right)^{2} \sqrt{\frac{\left(-\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x -\frac{-c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right)}{\left(\frac{-c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x +\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right)}}\, \sqrt{\frac{\left(-\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x +\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right)}{\left(-\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x +\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}+\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x -\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right)}{\left(-\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x +\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right)}}, \sqrt{\frac{\left(-\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right) \left(\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}+\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right)}{\left(\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right) \left(-\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}+\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right)}}\right)}{\left(-\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}+\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(-\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}-\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \sqrt{\left(x -\frac{-c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x +\frac{c +\sqrt{c^{2}+2 \sqrt{-a c}\, d}}{d}\right) \left(x -\frac{-c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right) \left(x +\frac{c +\sqrt{c^{2}-2 \sqrt{-a c}\, d}}{d}\right) d^{2}}}"," ",0,"2*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)^2*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(d^2*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2)*EllipticF(((-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*(x-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(x+(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2),((-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)*((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/((-c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d-(-c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d)/(-(c+(2*d*(-a*c)^(1/2)+c^2)^(1/2))/d+(c+(-2*d*(-a*c)^(1/2)+c^2)^(1/2))/d))^(1/2))","B"
777,1,5024,720,0.081000," ","int(1/(d^2*x^4+4*c*d*x^3+4*c^2*x^2+4*a*c)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
778,1,7887,715,0.267000," ","int((8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
779,1,1704,273,0.062000," ","int(1/(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(1/2),x)","\frac{\left(\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}+\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \sqrt{\frac{\left(-\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}+\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x -\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}{\left(-\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x +\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}}\, \left(x +\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)^{2} \sqrt{\frac{\left(-\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x -\frac{-d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}{\left(\frac{-d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x +\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}}\, \sqrt{\frac{\left(-\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x +\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}{\left(-\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x +\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}}\, \sqrt{2}\, \EllipticF \left(\sqrt{\frac{\left(-\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}+\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x -\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}{\left(-\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x +\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}}, \sqrt{\frac{\left(-\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}+\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}{\left(\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(-\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}+\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right)}}\right)}{2 \left(-\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}+\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(-\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}-\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \sqrt{\left(x -\frac{-d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x +\frac{d e +\sqrt{3 d^{2} e^{2}+2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x -\frac{-d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) \left(x +\frac{d e +\sqrt{3 d^{2} e^{2}-2 \sqrt{-64 a \,e^{3}+d^{4}}\, e^{2}}}{4 e^{2}}\right) e^{3}}}"," ",0,"1/2*(1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2+1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*((-1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*(x-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(-1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(x+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2))^(1/2)*(x+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)^2*((-1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*(x-1/4*(-d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(1/4*(-d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(x+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2))^(1/2)*((-1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*(x+1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(-1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(x+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2))^(1/2)/(-1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(-1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*2^(1/2)/(e^3*(x-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*(x+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*(x-1/4*(-d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*(x+1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2))^(1/2)*EllipticF(((-1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*(x-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(-1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(x+1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2))^(1/2),((-1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)*(1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2+1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(1/4*(-d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2-1/4*(-d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2)/(-1/4*(d*e+(3*e^2*d^2+2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2+1/4*(d*e+(3*e^2*d^2-2*(-64*a*e^3+d^4)^(1/2)*e^2)^(1/2))/e^2))^(1/2))","B"
780,1,8103,804,0.080000," ","int(1/(8*e^3*x^4+8*d*e^2*x^3-d^3*x+8*a*e^2)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
781,1,2655,506,0.076000," ","int((-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x)","-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{5}}{7}+\frac{5 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{4}}{7}-\frac{66 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{3}}{35}+\frac{14 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{2}}{5}+\left(\frac{3 a}{7}-\frac{32}{35}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x -\frac{\left(a^{2}-\left(\frac{3 a}{7}-\frac{32}{35}\right) a +\frac{12 a}{7}+\frac{16}{7}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\left(-\frac{3 a}{7}-\frac{4}{7}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}-\frac{\left(\frac{64 a}{35}+\frac{32}{5}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\left(-\frac{32 a}{35}-\frac{16}{5}\right) \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{\sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"-1/7*x^5*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+5/7*x^4*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-66/35*x^3*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+14/5*x^2*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+(3/7*a-32/35)*x*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+(-3/7*a-4/7)*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(a^2-(3/7*a-32/35)*a+12/7*a+16/7)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-(64/35*a+32/5)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))+(-32/35*a-16/5)*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
782,1,2519,455,0.029000," ","int((-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x)","\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x}{3}-\frac{\left(\frac{2 a}{3}+\frac{4}{3}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}{3}-\frac{4 \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{3 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{2 \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{3 \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"1/3*x*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-1/3*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(2/3*a+4/3)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-4/3*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))-2/3*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
783,1,530,182,0.029000," ","int(1/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x)","-\frac{\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"-((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))","B"
784,1,2601,495,0.032000," ","int(1/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x)","-\frac{\left(\frac{a +5}{a^{2}+7 a +12}-\frac{a +8}{2 \left(a^{2}+7 a +12\right)}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\frac{2 x^{3}}{4 a^{2}+28 a +48}-\frac{3 x^{2}}{2 \left(a^{2}+7 a +12\right)}+\frac{2 \left(a +8\right) x}{4 a^{2}+28 a +48}-\frac{a +6}{2 \left(a^{2}+7 a +12\right)}}{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}-\frac{\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(a^{2}+7 a +12\right) \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)}{2 \left(a^{2}+7 a +12\right) \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"2*(1/4/(a^2+7*a+12)*x^3-3/4/(a^2+7*a+12)*x^2+1/4*(a+8)/(a^2+7*a+12)*x-1/4*(a+6)/(a^2+7*a+12))/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-((a+5)/(a^2+7*a+12)-1/2*(a+8)/(a^2+7*a+12))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/(a^2+7*a+12)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))-1/2/(a^2+7*a+12)*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
785,1,2757,571,0.040000," ","int(1/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x)","-\frac{\left(\frac{5 a^{2}+47 a +104}{6 \left(a^{2}+7 a +12\right)^{2}}-\frac{5 a^{2}+71 a +188}{12 \left(a^{2}+7 a +12\right)^{2}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\left(\frac{x^{3}}{6 a^{2}+42 a +72}-\frac{x^{2}}{2 \left(a^{2}+7 a +12\right)}+\frac{\left(a +8\right) x}{6 a^{2}+42 a +72}-\frac{a +6}{6 \left(a^{2}+7 a +12\right)}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}{\left(x^{4}-4 x^{3}+8 x^{2}-a -8 x \right)^{2}}+\frac{\frac{\left(2 a +7\right) x^{3}}{3 \left(a^{2}+7 a +12\right)^{2}}-\frac{\left(2 a +7\right) x^{2}}{\left(a^{2}+7 a +12\right)^{2}}+\frac{\left(5 a^{2}+71 a +188\right) x}{12 \left(a^{2}+7 a +12\right)^{2}}-\frac{5 a^{2}+55 a +132}{12 \left(a^{2}+7 a +12\right)^{2}}}{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}-\frac{2 \left(2 a +7\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{3 \left(a^{2}+7 a +12\right)^{2} \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{\left(2 a +7\right) \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{3 \left(a^{2}+7 a +12\right)^{2} \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"(1/6/(a^2+7*a+12)*x^3-1/2/(a^2+7*a+12)*x^2+1/6*(a+8)/(a^2+7*a+12)*x-1/6*(a+6)/(a^2+7*a+12))*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)/(x^4-4*x^3+8*x^2-a-8*x)^2+2*(1/6*(2*a+7)/(a^2+7*a+12)^2*x^3-1/2*(2*a+7)/(a^2+7*a+12)^2*x^2+1/24*(5*a^2+71*a+188)/(a^2+7*a+12)^2*x-1/24*(5*a^2+55*a+132)/(a^2+7*a+12)^2)/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(1/6*(5*a^2+47*a+104)/(a^2+7*a+12)^2-1/12*(5*a^2+71*a+188)/(a^2+7*a+12)^2)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-2/3*(2*a+7)/(a^2+7*a+12)^2*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))-1/3*(2*a+7)/(a^2+7*a+12)^2*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
786,1,2694,600,0.031000," ","int(x*(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x)","-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{6}}{8}+\frac{17 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{5}}{28}-\frac{43 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{4}}{28}+\frac{74 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{3}}{35}+\left(\frac{5 a}{16}-\frac{9}{20}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{2}+\left(-\frac{11 a}{56}-\frac{29}{70}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x -\frac{\left(-\left(-\frac{11 a}{56}-\frac{29}{70}\right) a -\frac{11 a}{14}-\frac{26}{7}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\left(\frac{11 a}{56}+\frac{13}{14}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}-\frac{\left(a^{2}-2 \left(\frac{5 a}{16}-\frac{9}{20}\right) a +\frac{55 a}{14}+\frac{62}{5}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\left(-\frac{32 a}{35}-\frac{16}{5}\right) \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{\sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"-1/8*x^6*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+17/28*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^5-43/28*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^4+74/35*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^3+(5/16*a-9/20)*x^2*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+(-11/56*a-29/70)*x*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+(11/56*a+13/14)*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(-(-11/56*a-29/70)*a-11/14*a-26/7)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-(a^2-2*(5/16*a-9/20)*a+55/14*a+62/5)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))+(-32/35*a-16/5)*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
787,1,2551,516,0.029000," ","int((-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x,x)","\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{2}}{4}-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x}{6}-\frac{\left(\frac{a}{6}-\frac{2}{3}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}{6}-\frac{\left(\frac{a}{2}+\frac{10}{3}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{2 \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{3 \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"1/4*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^2-1/6*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x+1/6*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(1/6*a-2/3)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-(1/2*a+10/3)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))-2/3*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
788,1,788,213,0.028000," ","int(x/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x)","-\frac{\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"-((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))","B"
789,1,2616,528,0.033000," ","int(x/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x)","-\frac{\left(\frac{2}{a^{2}+7 a +12}+\frac{a -2}{2 a^{2}+14 a +24}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\frac{2 a \,x^{2}}{4 a^{2}+28 a +48}+\frac{2 x^{3}}{4 a^{2}+28 a +48}+\frac{2 a}{4 a^{2}+28 a +48}-\frac{\left(a -2\right) x}{2 \left(a^{2}+7 a +12\right)}}{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}-\frac{\left(-\frac{a}{a^{2}+7 a +12}+\frac{a +1}{a^{2}+7 a +12}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)}{2 \left(a^{2}+7 a +12\right) \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"2*(1/4/(a^2+7*a+12)*x^3+1/4*a/(a^2+7*a+12)*x^2-1/4*(a-2)/(a^2+7*a+12)*x+1/4/(a^2+7*a+12)*a)/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(2/(a^2+7*a+12)+1/2*(a-2)/(a^2+7*a+12))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-((1+a)/(a^2+7*a+12)-1/(a^2+7*a+12)*a)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))-1/2/(a^2+7*a+12)*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
790,1,2777,637,0.043000," ","int(x/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x)","-\frac{\left(\frac{a^{2}+23 a +68}{6 \left(a^{2}+7 a +12\right)^{2}}+\frac{3 a^{2}-23 a -116}{12 \left(a^{2}+7 a +12\right)^{2}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\left(\frac{a \,x^{2}}{6 a^{2}+42 a +72}+\frac{x^{3}}{6 a^{2}+42 a +72}+\frac{a}{6 a^{2}+42 a +72}-\frac{\left(a -2\right) x}{6 \left(a^{2}+7 a +12\right)}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}{\left(x^{4}-4 x^{3}+8 x^{2}-a -8 x \right)^{2}}+\frac{\frac{\left(2 a +7\right) x^{3}}{3 \left(a^{2}+7 a +12\right)^{2}}+\frac{\left(a^{2}-12\right) x^{2}}{3 \left(a^{2}+7 a +12\right)^{2}}-\frac{\left(3 a^{2}-23 a -116\right) x}{12 \left(a^{2}+7 a +12\right)^{2}}+\frac{3 a^{2}-7 a -60}{12 \left(a^{2}+7 a +12\right)^{2}}}{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}-\frac{\left(\frac{-\frac{10}{3}+\frac{4}{3} a +\frac{2}{3} a^{2}}{\left(a^{2}+7 a +12\right)^{2}}-\frac{2 \left(a^{2}-12\right)}{3 \left(a^{2}+7 a +12\right)^{2}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{\left(2 a +7\right) \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{3 \left(a^{2}+7 a +12\right)^{2} \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"(1/6/(a^2+7*a+12)*x^3+1/6/(a^2+7*a+12)*a*x^2-1/6*(a-2)/(a^2+7*a+12)*x+1/6/(a^2+7*a+12)*a)*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)/(x^4-4*x^3+8*x^2-a-8*x)^2+2*(1/6*(2*a+7)/(a^2+7*a+12)^2*x^3+1/6*(a^2-12)/(a^2+7*a+12)^2*x^2-1/24*(3*a^2-23*a-116)/(a^2+7*a+12)^2*x+1/24*(3*a^2-7*a-60)/(a^2+7*a+12)^2)/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(1/6*(a^2+23*a+68)/(a^2+7*a+12)^2+1/12*(3*a^2-23*a-116)/(a^2+7*a+12)^2)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-(2/3*(a^2+2*a-5)/(a^2+7*a+12)^2-2/3*(a^2-12)/(a^2+7*a+12)^2)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))-1/3*(2*a+7)/(a^2+7*a+12)^2*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
791,1,2733,624,0.030000," ","int(x^2*(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x)","-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{7}}{9}+\frac{19 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{6}}{36}-\frac{163 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{5}}{126}+\frac{71 \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{4}}{42}+\left(\frac{11 a}{45}-\frac{16}{63}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{3}+\left(-\frac{13 a}{120}-\frac{5}{18}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{2}+\left(\frac{9 a}{140}+\frac{23}{63}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x -\frac{\left(-\left(\frac{9 a}{140}+\frac{23}{63}\right) a -\frac{107 a}{63}-\frac{404}{63}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\left(\frac{107 a}{252}+\frac{101}{63}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}-\frac{\left(-2 \left(-\frac{13 a}{120}-\frac{5}{18}\right) a +\frac{827 a}{315}+\frac{76}{9}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\left(a^{2}-3 \left(\frac{11 a}{45}-\frac{16}{63}\right) a +\frac{68 a}{105}+\frac{16}{9}\right) \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{\sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"-1/9*x^7*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+19/36*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^6-163/126*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^5+71/42*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^4+(11/45*a-16/63)*x^3*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+(-13/120*a-5/18)*x^2*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+(9/140*a+23/63)*x*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)+(107/252*a+101/63)*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(-(9/140*a+23/63)*a-107/63*a-404/63)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-(-2*(-13/120*a-5/18)*a+827/315*a+76/9)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))+(a^2-3*(11/45*a-16/63)*a+68/105*a+16/9)*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
792,1,2582,535,0.031000," ","int((-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^2,x)","\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{3}}{5}-\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x^{2}}{10}+\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}\, x}{15}-\frac{\left(-\frac{a}{15}-\frac{4}{3}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}{3}-\frac{\left(\frac{a}{5}+\frac{28}{15}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\left(\frac{2 a}{5}+\frac{16}{15}\right) \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{\sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"1/5*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^3-1/10*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x^2+1/15*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)*x+1/3*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(-1/15*a-4/3)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-(1/5*a+28/15)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))+(2/5*a+16/15)*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
793,1,1147,454,0.031000," ","int(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2),x)","\frac{\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)}{\sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
794,1,2607,331,0.034000," ","int(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(3/2),x)","-\frac{\left(\frac{2}{a^{2}+7 a +12}-\frac{a +8}{2 \left(a^{2}+7 a +12\right)}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\frac{2 x^{3}}{4 a +12}-\frac{\left(a +6\right) x^{2}}{2 \left(a^{2}+7 a +12\right)}+\frac{2 a}{4 a^{2}+28 a +48}+\frac{2 \left(a +8\right) x}{4 a^{2}+28 a +48}}{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}-\frac{\left(-\frac{2}{a^{2}+7 a +12}+\frac{a +6}{a^{2}+7 a +12}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)}{2 \left(a +3\right) \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"2*(1/4/(a+3)*x^3-1/4*(a+6)/(a^2+7*a+12)*x^2+1/4*(a+8)/(a^2+7*a+12)*x+1/4/(a^2+7*a+12)*a)/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(2/(a^2+7*a+12)-1/2*(a+8)/(a^2+7*a+12))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-(-2/(a^2+7*a+12)+(a+6)/(a^2+7*a+12))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))-1/2/(a+3)*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
795,1,2780,628,0.043000," ","int(x^2/(-x^4+4*x^3-8*x^2+a+8*x)^(5/2),x)","-\frac{\left(-\frac{a^{2}-9 a -44}{6 \left(a^{2}+7 a +12\right)^{2}}-\frac{9 a +32}{3 \left(a^{2}+7 a +12\right)^{2}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}+\frac{\left(\frac{x^{3}}{6 a +18}-\frac{\left(a +6\right) x^{2}}{6 \left(a^{2}+7 a +12\right)}+\frac{a}{6 a^{2}+42 a +72}+\frac{\left(a +8\right) x}{6 a^{2}+42 a +72}\right) \sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}{\left(x^{4}-4 x^{3}+8 x^{2}-a -8 x \right)^{2}}+\frac{\frac{\left(3 a +13\right) x^{3}}{12 \left(a +3\right) \left(a^{2}+7 a +12\right)}-\frac{\left(a^{2}+27 a +84\right) x^{2}}{12 \left(a^{2}+7 a +12\right)^{2}}+\frac{\left(9 a +32\right) x}{3 \left(a^{2}+7 a +12\right)^{2}}+\frac{3 a^{2}+7 a -12}{6 \left(a^{2}+7 a +12\right)^{2}}}{\sqrt{-x^{4}+4 x^{3}-8 x^{2}+a +8 x}}-\frac{\left(\frac{a^{2}-a -16}{3 \left(a^{2}+7 a +12\right)^{2}}+\frac{a^{2}+27 a +84}{6 \left(a^{2}+7 a +12\right)^{2}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)+2 \sqrt{-1+\sqrt{a +4}}\, \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}\, \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}-\frac{\left(3 a +13\right) \left(\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)+\left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)^{2} \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1-\sqrt{-1-\sqrt{a +4}}\right)}{\left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \sqrt{-\frac{2 \sqrt{-1+\sqrt{a +4}}\, \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}\, \left(-\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \EllipticE \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \sqrt{-1+\sqrt{a +4}}}-\frac{\left(\left(1-\sqrt{-1+\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)-\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1+\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1-\sqrt{a +4}}\right) \left(1-\sqrt{-1+\sqrt{a +4}}\right)+\left(1-\sqrt{-1+\sqrt{a +4}}\right)^{2}\right) \EllipticF \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{2 \left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \sqrt{-1+\sqrt{a +4}}}-\frac{4 \EllipticPi \left(\sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right)}}, \frac{\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}{\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}}, \sqrt{\frac{\left(-\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right)}{\left(-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}\right) \left(\sqrt{-1-\sqrt{a +4}}-\sqrt{-1+\sqrt{a +4}}\right)}}\right)}{-\sqrt{-1-\sqrt{a +4}}+\sqrt{-1+\sqrt{a +4}}}\right)\right)}{12 \left(a +3\right) \left(a^{2}+7 a +12\right) \sqrt{-\left(x -1-\sqrt{-1+\sqrt{a +4}}\right) \left(x -1+\sqrt{-1+\sqrt{a +4}}\right) \left(x -1-\sqrt{-1-\sqrt{a +4}}\right) \left(x -1+\sqrt{-1-\sqrt{a +4}}\right)}}"," ",0,"(1/6/(a+3)*x^3-1/6*(a+6)/(a^2+7*a+12)*x^2+1/6*(a+8)/(a^2+7*a+12)*x+1/6/(a^2+7*a+12)*a)*(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)/(x^4-4*x^3+8*x^2-a-8*x)^2+2*(1/24*(13+3*a)/(a+3)/(a^2+7*a+12)*x^3-1/24*(a^2+27*a+84)/(a^2+7*a+12)^2*x^2+1/6*(9*a+32)/(a^2+7*a+12)^2*x+1/12*(3*a^2+7*a-12)/(a^2+7*a+12)^2)/(-x^4+4*x^3-8*x^2+a+8*x)^(1/2)-(-1/6*(a^2-9*a-44)/(a^2+7*a+12)^2-1/3*(9*a+32)/(a^2+7*a+12)^2)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-(1/3*(a^2-a-16)/(a^2+7*a+12)^2+1/6*(a^2+27*a+84)/(a^2+7*a+12)^2)*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)*((1-(-1+(a+4)^(1/2))^(1/2))*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))+2*(-1+(a+4)^(1/2))^(1/2)*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2)))-1/12*(13+3*a)/(a+3)/(a^2+7*a+12)*((x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2))+((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(x-1+(-1+(a+4)^(1/2))^(1/2))^2*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1-(-1-(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-2*(-1+(a+4)^(1/2))^(1/2)*(x-1+(-1-(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2)*(-1/2*((1-(-1+(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))-(1-(-1-(a+4)^(1/2))^(1/2))*(1+(-1+(a+4)^(1/2))^(1/2))+(1-(-1-(a+4)^(1/2))^(1/2))*(1-(-1+(a+4)^(1/2))^(1/2))+(1-(-1+(a+4)^(1/2))^(1/2))^2)/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-1+(a+4)^(1/2))^(1/2)*EllipticF(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))-1/2*(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticE(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))/(-1+(a+4)^(1/2))^(1/2)-4/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*EllipticPi(((-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))/(x-1+(-1+(a+4)^(1/2))^(1/2)))^(1/2),((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)),((-(-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2))*((-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/(-(-1-(a+4)^(1/2))^(1/2)+(-1+(a+4)^(1/2))^(1/2))/((-1-(a+4)^(1/2))^(1/2)-(-1+(a+4)^(1/2))^(1/2)))^(1/2))))/(-(x-1-(-1+(a+4)^(1/2))^(1/2))*(x-1+(-1+(a+4)^(1/2))^(1/2))*(x-1-(-1-(a+4)^(1/2))^(1/2))*(x-1+(-1-(a+4)^(1/2))^(1/2)))^(1/2)","B"
796,1,965,155,1.130000," ","int(1/(8*x^4-x^3+8*x+8)^(1/2),x)","\frac{\left(\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right) \sqrt{\frac{\left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)\right)}{\left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right)}}\, \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right)^{2} \sqrt{\frac{\left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =3\right)\right)}{\left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =3\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right)}}\, \sqrt{\frac{\left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right)}{\left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right)}}\, \sqrt{2}\, \EllipticF \left(\sqrt{\frac{\left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)\right)}{\left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right)}}, \sqrt{\frac{\left(\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =3\right)\right) \left(\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right)}{\left(\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =3\right)\right) \left(\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right)}}\right)}{2 \left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(-\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right) \sqrt{\left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =1\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =2\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =3\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-\textit{\_Z}^{3}+8 \textit{\_Z} +8, \mathit{index} =4\right)\right)}}"," ",0,"1/2*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))^2*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*2^(1/2)/((x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2)*EllipticF(((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2),((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2))","C"
797,1,4426,465,0.118000," ","int(1/(8*x^4-x^3+8*x+8)^(3/2),x)","\text{output too large to display}"," ",0,"-16*(-17/10962-57/12992*x+191/58464*x^2-7/3132*x^3)/(8*x^4-x^3+8*x+8)^(1/2)+421/12528*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))^2*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*2^(1/2)/((x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2)*EllipticF(((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2),((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2))+7/6264*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))^2*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*2^(1/2)/((x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2)*(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)*EllipticF(((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2),((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2))+(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*EllipticPi(((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2),(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)),((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2)))-7/783*((x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4))+(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))^2*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2)*((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)*RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1)*RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)*RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)^2)/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*EllipticF(((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2),((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2))+(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*EllipticE(((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2),((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))-1/8/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*EllipticPi(((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)))^(1/2),(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)),((RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3)+RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))/(RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2)-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2))))*2^(1/2)/((x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=1))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=2))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=3))*(x-RootOf(8*_Z^4-_Z^3+8*_Z+8,index=4)))^(1/2)","C"
798,1,961,130,0.849000," ","int(1/(4*x^4+4*x^2+4*x+1)^(1/2),x)","\frac{\left(\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \sqrt{\frac{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)\right)}{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right)}}\, \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right)^{2} \sqrt{\frac{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =3\right)\right)}{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right)}}\, \sqrt{\frac{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right)}{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right)}}\, \EllipticF \left(\sqrt{\frac{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)\right)}{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right)}}, \sqrt{\frac{\left(\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \left(\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right)}{\left(\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \left(\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right)}}\right)}{\left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right) \left(-\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)+\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right) \sqrt{\left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =1\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =2\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =3\right)\right) \left(x -\RootOf \left(4 \textit{\_Z}^{4}+4 \textit{\_Z}^{2}+4 \textit{\_Z} +1, \mathit{index} =4\right)\right)}}"," ",0,"(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))^2*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/((x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)))^(1/2)*EllipticF(((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2),((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)))^(1/2))","C"
799,1,2564,397,0.110000," ","int(1/(4*x^4+4*x^2+4*x+1)^(3/2),x)","\text{Expression too large to display}"," ",0,"-8*(-9/20*x^3+1/5*x^2-21/40*x-19/80)/(4*x^4+4*x^2+4*x+1)^(1/2)+3/5*(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))^2*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/((x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)))^(1/2)*EllipticF(((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2),((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)))^(1/2))-9/5*((x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))+(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))^2*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2)*((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)*RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)*RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)+RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)*RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)+RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)^2)/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*EllipticF(((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2),((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)))^(1/2))+(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*EllipticE(((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))/(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)))^(1/2),((RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)))^(1/2))/(RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2)-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))))/((x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=1))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=2))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=3))*(x-RootOf(4*_Z^4+4*_Z^2+4*_Z+1,index=4)))^(1/2)","C"
800,1,1180,152,1.681000," ","int(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(1/2),x)","\frac{\left(\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right) \sqrt{\frac{\left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)\right)}{\left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right)}}\, \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right)^{2} \sqrt{\frac{\left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =3\right)\right)}{\left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =3\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right)}}\, \sqrt{\frac{\left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right)}{\left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right)}}\, \sqrt{2}\, \EllipticF \left(\sqrt{\frac{\left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)\right)}{\left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right)}}, \sqrt{\frac{\left(\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =3\right)\right) \left(\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right)}{\left(\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =3\right)\right) \left(\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right)}}\right)}{2 \left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right) \left(-\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)+\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right) \sqrt{\left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =1\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =2\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =3\right)\right) \left(x -\RootOf \left(8 \textit{\_Z}^{4}-15 \textit{\_Z}^{3}+8 \textit{\_Z}^{2}+24 \textit{\_Z} +8, \mathit{index} =4\right)\right)}}"," ",0,"1/2*(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4))*((RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2))*(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))/(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))/(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)))^(1/2)*(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2))^2*((RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))*(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=3))/(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=3)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))/(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)))^(1/2)*((RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))*(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4))/(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))/(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)))^(1/2)/(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2))/(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))*2^(1/2)/((x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))*(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2))*(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=3))*(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4)))^(1/2)*EllipticF(((RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2))*(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))/(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))/(x-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)))^(1/2),((RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=3))*(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4))/(-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=3)+RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=1))/(RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=2)-RootOf(8*_Z^4-15*_Z^3+8*_Z^2+24*_Z+8,index=4)))^(1/2))","C"
801,1,5421,470,0.118000," ","int(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
802,1,5477,605,0.137000," ","int(1/(8*x^4-15*x^3+8*x^2+24*x+8)^(5/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
803,1,1182,156,0.495000," ","int(1/(3*x^4+15*x^3-44*x^2-6*x+9)^(1/2),x)","\frac{2 \left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right) \sqrt{\frac{\left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)\right) \left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right)}{\left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right) \left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right)}}\, \left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right)^{2} \sqrt{-\frac{\left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =3\right)\right) \left(-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)+\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right)}{\left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =3\right)\right) \left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right)}}\, \sqrt{-\frac{\left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right) \left(-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)+\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right)}{\left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right) \left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right)}}\, \sqrt{3}\, \EllipticF \left(\sqrt{\frac{\left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)\right) \left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right)}{\left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right) \left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right)}}, \sqrt{\frac{\left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =3\right)\right) \left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right)}{\left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =3\right)\right) \left(\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right)}}\right)}{3 \left(-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)+\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right) \left(-\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)+\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right) \sqrt{\left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =1\right)\right) \left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =2\right)\right) \left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =3\right)\right) \left(x -\RootOf \left(3 \textit{\_Z}^{4}+15 \textit{\_Z}^{3}-44 \textit{\_Z}^{2}-6 \textit{\_Z} +9, \mathit{index} =4\right)\right)}}"," ",0,"2/3*(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))*((x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))/(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))/(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2))*(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2)))^(1/2)*(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2))^2*(-(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=3))/(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=3)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))/(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2))*(RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2)-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1)))^(1/2)*(-(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4))/(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))/(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2))*(RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2)-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1)))^(1/2)/(RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2))/(RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2)-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))*3^(1/2)/((x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))*(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2))*(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=3))*(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)))^(1/2)*EllipticF(((x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))/(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))/(x-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2))*(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2)))^(1/2),((RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2)-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=3))*(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))/(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=3)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=1))/(-RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=4)+RootOf(3*_Z^4+15*_Z^3-44*_Z^2-6*_Z+9,index=2)))^(1/2))","C"
804,1,5427,480,0.071000," ","int(1/(3*x^4+15*x^3-44*x^2-6*x+9)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
805,1,76,44,0.021000," ","int((2*(3-x)^(1/2)+3/(x+1)^(1/2))^2/x,x)","-4 x +21 \ln \left(x \right)-9 \ln \left(x +1\right)+\frac{12 \sqrt{x +1}\, \sqrt{-x +3}\, \left(-\sqrt{3}\, \arctanh \left(\frac{\left(x +3\right) \sqrt{3}}{3 \sqrt{-x^{2}+2 x +3}}\right)-\arcsin \left(\frac{x}{2}-\frac{1}{2}\right)\right)}{\sqrt{-x^{2}+2 x +3}}"," ",0,"-4*x+21*ln(x)+12*(x+1)^(1/2)*(3-x)^(1/2)/(-x^2+2*x+3)^(1/2)*(-arcsin(-1/2+1/2*x)-3^(1/2)*arctanh(1/3*(x+3)*3^(1/2)/(-x^2+2*x+3)^(1/2)))-9*ln(x+1)","A"
806,1,56,53,0.007000," ","int((x^2+x-1)/(1+(x^2+1)^(1/2)),x)","-x -\frac{\sqrt{x^{2}+1}\, x}{2}-\frac{\arcsinh \left(x \right)}{2}-\arctanh \left(\frac{1}{\sqrt{x^{2}+1}}\right)-\ln \left(x \right)-\frac{1}{x}+\frac{\left(x^{2}+1\right)^{\frac{3}{2}}}{x}+\sqrt{x^{2}+1}"," ",0,"-x-1/x-1/2*(x^2+1)^(1/2)*x-1/2*arcsinh(x)+(x^2+1)^(1/2)-arctanh(1/(x^2+1)^(1/2))-ln(x)+1/x*(x^2+1)^(3/2)","A"
807,1,58,46,0.006000," ","int((x^2+x-1)/(1+x+(x^2+1)^(1/2)),x)","\frac{x^{3}}{6}+\frac{x^{2}}{2}-\frac{\sqrt{x^{2}+1}\, x}{4}-\frac{\arcsinh \left(x \right)}{4}-\frac{\arctanh \left(\frac{1}{\sqrt{x^{2}+1}}\right)}{2}-\frac{\ln \left(x \right)}{2}+\frac{\sqrt{x^{2}+1}}{2}-\frac{\left(x^{2}+1\right)^{\frac{3}{2}}}{6}"," ",0,"1/2*x^2-1/2*ln(x)+1/6*x^3-1/4*(x^2+1)^(1/2)*x-1/4*arcsinh(x)+1/2*(x^2+1)^(1/2)-1/2*arctanh(1/(x^2+1)^(1/2))-1/6*(x^2+1)^(3/2)","A"
808,1,13,12,0.003000," ","int((x+2*(x-1)^(1/2))/x/(x-1)^(1/2),x)","2 \ln \left(x \right)+2 \sqrt{x -1}"," ",0,"2*ln(x)+2*(x-1)^(1/2)","A"
809,1,46,43,0.001000," ","int((a+b*x^(2/3)+c*x^(1/2))^2,x)","\frac{3 b^{2} x^{\frac{7}{3}}}{7}+\frac{c^{2} x^{2}}{2}+\frac{6 a b \,x^{\frac{5}{3}}}{5}+a^{2} x +2 \left(\frac{6 b \,x^{\frac{13}{6}}}{13}+\frac{2 a \,x^{\frac{3}{2}}}{3}\right) c"," ",0,"1/2*c^2*x^2+2*c*(6/13*b*x^(13/6)+2/3*a*x^(3/2))+a^2*x+3/7*b^2*x^(7/3)+6/5*a*b*x^(5/3)","A"
810,1,86,84,0.003000," ","int((a+b*x^(2/3)+c*x^(1/2))^3,x)","\frac{b^{3} x^{3}}{3}+\frac{2 c^{3} x^{\frac{5}{2}}}{5}+\frac{9 a \,b^{2} x^{\frac{7}{3}}}{7}+\frac{9 a^{2} b \,x^{\frac{5}{3}}}{5}+a^{3} x +3 \left(\frac{3 b \,x^{\frac{8}{3}}}{8}+\frac{a \,x^{2}}{2}\right) c^{2}+3 \left(\frac{6 b^{2} x^{\frac{17}{6}}}{17}+\frac{12 a b \,x^{\frac{13}{6}}}{13}+\frac{2 a^{2} x^{\frac{3}{2}}}{3}\right) c"," ",0,"2/5*c^3*x^(5/2)+3*c^2*(3/8*b*x^(8/3)+1/2*a*x^2)+3*c*(6/17*b^2*x^(17/6)+12/13*a*b*x^(13/6)+2/3*a^2*x^(3/2))+a^3*x+1/3*b^3*x^3+9/5*a^2*b*x^(5/3)+9/7*a*b^2*x^(7/3)","A"
811,1,102,50,0.024000," ","int((x^2-1)/x^3/(a-b+b/x^2)^(1/2),x)","\frac{\sqrt{a \,x^{2}-b \,x^{2}+b}\, \left(b x \ln \left(\sqrt{a -b}\, x +\sqrt{a \,x^{2}-b \,x^{2}+b}\right)+\sqrt{a \,x^{2}-b \,x^{2}+b}\, \sqrt{a -b}\right)}{\sqrt{\frac{a \,x^{2}-b \,x^{2}+b}{x^{2}}}\, \sqrt{a -b}\, b \,x^{2}}"," ",0,"(a*x^2-b*x^2+b)^(1/2)*(ln((a-b)^(1/2)*x+(a*x^2-b*x^2+b)^(1/2))*b*x+(a*x^2-b*x^2+b)^(1/2)*(a-b)^(1/2))/((a*x^2-b*x^2+b)/x^2)^(1/2)/x^2/(a-b)^(1/2)/b","B"
812,1,102,50,0.017000," ","int((x^2-1)/x^3/(a+b*(-1+1/x^2))^(1/2),x)","\frac{\sqrt{a \,x^{2}-b \,x^{2}+b}\, \left(b x \ln \left(\sqrt{a -b}\, x +\sqrt{a \,x^{2}-b \,x^{2}+b}\right)+\sqrt{a \,x^{2}-b \,x^{2}+b}\, \sqrt{a -b}\right)}{\sqrt{\frac{a \,x^{2}-b \,x^{2}+b}{x^{2}}}\, \sqrt{a -b}\, b \,x^{2}}"," ",0,"(a*x^2-b*x^2+b)^(1/2)*(b*x*ln((a-b)^(1/2)*x+(a*x^2-b*x^2+b)^(1/2))+(a*x^2-b*x^2+b)^(1/2)*(a-b)^(1/2))/((a*x^2-b*x^2+b)/x^2)^(1/2)/(a-b)^(1/2)/b/x^2","B"
813,1,39,38,0.023000," ","int((x+1)/(x^2+4)/(x^2+9)^(1/2),x)","-\frac{\sqrt{5}\, \arctanh \left(\frac{\sqrt{x^{2}+9}\, \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctan \left(\frac{\sqrt{5}\, x}{2 \sqrt{x^{2}+9}}\right)}{10}"," ",0,"1/10*arctan(1/2*x*5^(1/2)/(x^2+9)^(1/2))*5^(1/2)-1/5*arctanh(1/5*(x^2+9)^(1/2)*5^(1/2))*5^(1/2)","A"
814,1,18,17,0.002000," ","int(x*(1+(-x^2+1)^(1/2)),x)","\frac{x^{2}}{2}-\frac{\left(-x^{2}+1\right)^{\frac{3}{2}}}{3}"," ",0,"1/2*x^2-1/3*(-x^2+1)^(3/2)","A"
815,1,26,17,0.003000," ","int(x*(1+(-x+1)^(1/2)*(x+1)^(1/2)),x)","\frac{x^{2}}{2}+\frac{\sqrt{x +1}\, \sqrt{-x +1}\, \left(x^{2}-1\right)}{3}"," ",0,"1/3*(x+1)^(1/2)*(-x+1)^(1/2)*(x^2-1)+1/2*x^2","A"
816,1,58,25,0.014000," ","int(x*(1+1/(x+2)^(1/2)/(x+3)^(1/2)),x)","\frac{x^{2}}{2}-\frac{\sqrt{x +2}\, \sqrt{x +3}\, \left(5 \ln \left(x +\frac{5}{2}+\sqrt{x^{2}+5 x +6}\right)-2 \sqrt{x^{2}+5 x +6}\right)}{2 \sqrt{x^{2}+5 x +6}}"," ",0,"-1/2*(x+2)^(1/2)*(x+3)^(1/2)*(-2*(x^2+5*x+6)^(1/2)+5*ln(x+5/2+(x^2+5*x+6)^(1/2)))/(x^2+5*x+6)^(1/2)+1/2*x^2","B"
817,1,35,33,0.009000," ","int((x-(x^6)^(1/2))/x/(-x^4+1),x)","\frac{\arctanh \left(x \right)}{2}+\frac{\arctan \left(x \right)}{2}+\frac{\sqrt{x^{6}}\, \left(2 \arctan \left(x \right)+\ln \left(x -1\right)-\ln \left(x +1\right)\right)}{4 x^{3}}"," ",0,"1/4*(x^6)^(1/2)*(ln(x-1)-ln(x+1)+2*arctan(x))/x^3+1/2*arctanh(x)+1/2*arctan(x)","A"
818,1,35,33,0.008000," ","int((1-(x^6)^(1/2)/x)/(-x^4+1),x)","\frac{\arctanh \left(x \right)}{2}+\frac{\arctan \left(x \right)}{2}+\frac{\sqrt{x^{6}}\, \left(2 \arctan \left(x \right)+\ln \left(x -1\right)-\ln \left(x +1\right)\right)}{4 x^{3}}"," ",0,"1/4*(x^6)^(1/2)*(2*arctan(x)+ln(x-1)-ln(x+1))/x^3+1/2*arctanh(x)+1/2*arctan(x)","A"
819,1,35,33,0.010000," ","int((x-(x^6)^(1/2))/(-x^5+x),x)","\frac{\arctanh \left(x \right)}{2}+\frac{\arctan \left(x \right)}{2}+\frac{\sqrt{x^{6}}\, \left(2 \arctan \left(x \right)+\ln \left(x -1\right)-\ln \left(x +1\right)\right)}{4 x^{3}}"," ",0,"1/4*(x^6)^(1/2)*(2*arctan(x)+ln(x-1)-ln(x+1))/x^3+1/2*arctanh(x)+1/2*arctan(x)","A"
820,1,27,33,0.008000," ","int(x/(x+(x^6)^(1/2)),x)","\frac{\arctan \left(\sqrt{\frac{\sqrt{x^{6}}}{x^{3}}}\, x \right)}{\sqrt{\frac{\sqrt{x^{6}}}{x^{3}}}}"," ",0,"1/((x^6)^(1/2)/x^3)^(1/2)*arctan(((x^6)^(1/2)/x^3)^(1/2)*x)","A"
821,1,41,36,0.010000," ","int((x^(1/2)-(x^3)^(1/2))/(-x^3+x),x)","\arctanh \left(\sqrt{x}\right)+\arctan \left(\sqrt{x}\right)+\frac{\sqrt{x^{3}}\, \left(2 \arctan \left(\sqrt{x}\right)+\ln \left(\sqrt{x}-1\right)-\ln \left(\sqrt{x}+1\right)\right)}{2 x^{\frac{3}{2}}}"," ",0,"arctanh(x^(1/2))+arctan(x^(1/2))+1/2*(x^3)^(1/2)*(ln(x^(1/2)-1)-ln(x^(1/2)+1)+2*arctan(x^(1/2)))/x^(3/2)","A"
822,1,30,36,0.009000," ","int(1/(x^(1/2)+(x^3)^(1/2)),x)","\frac{2 \arctan \left(\sqrt{\frac{\sqrt{x^{3}}}{x^{\frac{3}{2}}}}\, \sqrt{x}\right)}{\sqrt{\frac{\sqrt{x^{3}}}{x^{\frac{3}{2}}}}}"," ",0,"2/((x^3)^(1/2)/x^(3/2))^(1/2)*arctan(x^(1/2)*((x^3)^(1/2)/x^(3/2))^(1/2))","A"
823,1,40,52,0.012000," ","int(1/((x-1)^(1/2)+((x-1)^3)^(1/2)),x)","\frac{2 \arctan \left(\sqrt{\frac{\sqrt{\left(x -1\right)^{3}}}{\left(x -1\right)^{\frac{3}{2}}}}\, \sqrt{x -1}\right)}{\sqrt{\frac{\sqrt{\left(x -1\right)^{3}}}{\left(x -1\right)^{\frac{3}{2}}}}}"," ",0,"2/(((x-1)^3)^(1/2)/(x-1)^(3/2))^(1/2)*arctan((((x-1)^3)^(1/2)/(x-1)^(3/2))^(1/2)*(x-1)^(1/2))","A"
824,1,32,27,0.012000," ","int(-3/(4+5*x)^2+(-5-4*x)/(4+5*x)^2/(-x^2+1)^(1/2),x)","\frac{\sqrt{\frac{8 x}{5}-\left(x +\frac{4}{5}\right)^{2}+\frac{41}{25}}}{5 x +4}+\frac{3}{5 \left(5 x +4\right)}"," ",0,"1/5/(x+4/5)*(-(x+4/5)^2+8/5*x+41/25)^(1/2)+3/5/(4+5*x)","A"
825,1,32,27,0.010000," ","int((-5-4*x-3*(-x^2+1)^(1/2))/(5*x+4)^2/(-x^2+1)^(1/2),x)","\frac{\sqrt{\frac{8 x}{5}-\left(x +\frac{4}{5}\right)^{2}+\frac{41}{25}}}{5 x +4}+\frac{3}{5 \left(5 x +4\right)}"," ",0,"1/5/(x+4/5)*(8/5*x-(x+4/5)^2+41/25)^(1/2)+3/5/(5*x+4)","A"
826,1,81,27,0.035000," ","int(1/(-3*x^2+3+(-5-4*x)*(-x^2+1)^(1/2)),x)","\frac{5 \sqrt{\frac{8 x}{5}-\left(x +\frac{4}{5}\right)^{2}+\frac{41}{25}}\, x}{9}+\frac{3}{5 \left(5 x +4\right)}+\frac{\sqrt{-2 x -\left(x -1\right)^{2}+2}}{18}-\frac{\sqrt{2 x -\left(x +1\right)^{2}+2}}{2}+\frac{5 \left(\frac{8 x}{5}-\left(x +\frac{4}{5}\right)^{2}+\frac{41}{25}\right)^{\frac{3}{2}}}{9 \left(x +\frac{4}{5}\right)}"," ",0,"3/5/(5*x+4)+1/18*(-(x-1)^2-2*x+2)^(1/2)-1/2*(-(x+1)^2+2*x+2)^(1/2)+5/9/(x+4/5)*(8/5*x-(x+4/5)^2+41/25)^(3/2)+5/9*x*(8/5*x-(x+4/5)^2+41/25)^(1/2)","B"
827,1,81,27,0.036000," ","int(1/(3-3*x^2-5*(-x^2+1)^(1/2)-4*(-x^2+1)^(1/2)*x),x)","\frac{5 \sqrt{\frac{8 x}{5}-\left(x +\frac{4}{5}\right)^{2}+\frac{41}{25}}\, x}{9}+\frac{3}{5 \left(5 x +4\right)}+\frac{\sqrt{-2 x -\left(x -1\right)^{2}+2}}{18}-\frac{\sqrt{2 x -\left(x +1\right)^{2}+2}}{2}+\frac{5 \left(\frac{8 x}{5}-\left(x +\frac{4}{5}\right)^{2}+\frac{41}{25}\right)^{\frac{3}{2}}}{9 \left(x +\frac{4}{5}\right)}"," ",0,"5/9*(8/5*x-(x+4/5)^2+41/25)^(1/2)*x+3/5/(5*x+4)+1/18*(-2*x-(x-1)^2+2)^(1/2)-1/2*(2*x-(x+1)^2+2)^(1/2)+5/9/(x+4/5)*(8/5*x-(x+4/5)^2+41/25)^(3/2)","B"
828,1,32,27,0.013000," ","int((-1+(-x^2+1)^(1/2))/(2+x-2*(-x^2+1)^(1/2))^2/(-x^2+1)^(1/2),x)","\frac{\sqrt{\frac{8 x}{5}-\left(x +\frac{4}{5}\right)^{2}+\frac{41}{25}}}{5 x +4}+\frac{3}{5 \left(5 x +4\right)}"," ",0,"1/5/(x+4/5)*(8/5*x-(x+4/5)^2+41/25)^(1/2)+3/5/(5*x+4)","A"
829,1,73,43,0.018000," ","int((a+b*x^(n-1))/(c*x+d*x^n),x)","\frac{a n \ln \left(x \right)}{\left(n -1\right) c}-\frac{a \ln \left(c x +d \,{\mathrm e}^{n \ln \left(x \right)}\right)}{\left(n -1\right) c}-\frac{b \ln \left(x \right)}{\left(n -1\right) d}+\frac{b \ln \left(c x +d \,{\mathrm e}^{n \ln \left(x \right)}\right)}{\left(n -1\right) d}"," ",0,"1/c/(n-1)*ln(x)*a*n-1/d/(n-1)*ln(x)*b-1/c/(n-1)*ln(c*x+d*exp(n*ln(x)))*a+1/d/(n-1)*ln(c*x+d*exp(n*ln(x)))*b","A"
830,1,45,32,0.008000," ","int((2*x^2+1)^(1/2)/(1+(2*x^2+1)^(1/2)),x)","x -\sqrt{2 x^{2}+1}\, x -\frac{\sqrt{2}\, \arcsinh \left(\sqrt{2}\, x \right)}{2}-\frac{1}{2 x}+\frac{\left(2 x^{2}+1\right)^{\frac{3}{2}}}{2 x}"," ",0,"x-1/2/x+1/2/x*(2*x^2+1)^(3/2)-x*(2*x^2+1)^(1/2)-1/2*arcsinh(2^(1/2)*x)*2^(1/2)","A"
831,1,262,45,0.048000," ","int((4*x^2-1)^(1/2)/(x+(4*x^2-1)^(1/2)),x)","\frac{4 x}{3}-\frac{\sqrt{3}\, \arctanh \left(\sqrt{3}\, x \right)}{9}+\frac{\sqrt{3}\, \arctanh \left(\frac{3 \left(\frac{2}{3}+\frac{8 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}\right) \sqrt{3}}{2 \sqrt{36 \left(x -\frac{\sqrt{3}}{3}\right)^{2}+24 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}+3}}\right)}{18}+\frac{\sqrt{3}\, \arctanh \left(\frac{3 \left(\frac{2}{3}-\frac{8 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}\right) \sqrt{3}}{2 \sqrt{36 \left(x +\frac{\sqrt{3}}{3}\right)^{2}-24 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}+3}}\right)}{18}-\frac{\sqrt{3}\, \sqrt{4}\, \ln \left(\sqrt{4}\, x +\sqrt{4 \left(x -\frac{\sqrt{3}}{3}\right)^{2}+\frac{8 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{1}{3}}\right)}{18}+\frac{\sqrt{3}\, \sqrt{4}\, \ln \left(\sqrt{4}\, x +\sqrt{4 \left(x +\frac{\sqrt{3}}{3}\right)^{2}-\frac{8 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}}{3}+\frac{1}{3}}\right)}{18}-\frac{\sqrt{36 \left(x -\frac{\sqrt{3}}{3}\right)^{2}+24 \left(x -\frac{\sqrt{3}}{3}\right) \sqrt{3}+3}}{18}-\frac{\sqrt{36 \left(x +\frac{\sqrt{3}}{3}\right)^{2}-24 \left(x +\frac{\sqrt{3}}{3}\right) \sqrt{3}+3}}{18}"," ",0,"4/3*x-1/9*arctanh(3^(1/2)*x)*3^(1/2)-1/18*(36*(x-1/3*3^(1/2))^2+24*(x-1/3*3^(1/2))*3^(1/2)+3)^(1/2)-1/18*3^(1/2)*ln(x*4^(1/2)+(4*(x-1/3*3^(1/2))^2+8/3*(x-1/3*3^(1/2))*3^(1/2)+1/3)^(1/2))*4^(1/2)+1/18*3^(1/2)*arctanh(3/2*(2/3+8/3*(x-1/3*3^(1/2))*3^(1/2))*3^(1/2)/(36*(x-1/3*3^(1/2))^2+24*(x-1/3*3^(1/2))*3^(1/2)+3)^(1/2))-1/18*(36*(x+1/3*3^(1/2))^2-24*(x+1/3*3^(1/2))*3^(1/2)+3)^(1/2)+1/18*3^(1/2)*ln(x*4^(1/2)+(4*(x+1/3*3^(1/2))^2-8/3*(x+1/3*3^(1/2))*3^(1/2)+1/3)^(1/2))*4^(1/2)+1/18*3^(1/2)*arctanh(3/2*(2/3-8/3*(x+1/3*3^(1/2))*3^(1/2))*3^(1/2)/(36*(x+1/3*3^(1/2))^2-24*(x+1/3*3^(1/2))*3^(1/2)+3)^(1/2))","B"
832,1,1407,179,0.033000," ","int((c*x^2+b*x+a)/(e*x+d)^3/(x^2-1)^(1/2),x)","-\frac{3 a \,d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{2 d^{2}-2 e^{2}}{e^{2}}+2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}}{x +\frac{d}{e}}\right)}{2 \left(d^{2}-e^{2}\right)^{2} \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, e}+\frac{3 b \,d^{3} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{2 d^{2}-2 e^{2}}{e^{2}}+2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}}{x +\frac{d}{e}}\right)}{2 \left(d^{2}-e^{2}\right)^{2} \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, e^{2}}-\frac{3 c \,d^{4} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{2 d^{2}-2 e^{2}}{e^{2}}+2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}}{x +\frac{d}{e}}\right)}{2 \left(d^{2}-e^{2}\right)^{2} \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, e^{3}}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}\, a d}{2 \left(d^{2}-e^{2}\right)^{2} \left(x +\frac{d}{e}\right)}+\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}\, b \,d^{2}}{2 \left(d^{2}-e^{2}\right)^{2} \left(x +\frac{d}{e}\right) e}-\frac{3 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}\, c \,d^{3}}{2 \left(d^{2}-e^{2}\right)^{2} \left(x +\frac{d}{e}\right) e^{2}}+\frac{a \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{2 d^{2}-2 e^{2}}{e^{2}}+2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}}{x +\frac{d}{e}}\right)}{2 \left(d^{2}-e^{2}\right) \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, e}-\frac{3 b d \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{2 d^{2}-2 e^{2}}{e^{2}}+2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}}{x +\frac{d}{e}}\right)}{2 \left(d^{2}-e^{2}\right) \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, e^{2}}+\frac{5 c \,d^{2} \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{2 d^{2}-2 e^{2}}{e^{2}}+2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}}{x +\frac{d}{e}}\right)}{2 \left(d^{2}-e^{2}\right) \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, e^{3}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}\, a}{2 \left(d^{2}-e^{2}\right) \left(x +\frac{d}{e}\right)^{2} e}+\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}\, b d}{2 \left(d^{2}-e^{2}\right) \left(x +\frac{d}{e}\right)^{2} e^{2}}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}\, b}{\left(d^{2}-e^{2}\right) \left(x +\frac{d}{e}\right) e}-\frac{\sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}\, c \,d^{2}}{2 \left(d^{2}-e^{2}\right) \left(x +\frac{d}{e}\right)^{2} e^{3}}+\frac{2 \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}\, c d}{\left(d^{2}-e^{2}\right) \left(x +\frac{d}{e}\right) e^{2}}-\frac{c \ln \left(\frac{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{2 d^{2}-2 e^{2}}{e^{2}}+2 \sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, \sqrt{-\frac{2 \left(x +\frac{d}{e}\right) d}{e}+\frac{d^{2}-e^{2}}{e^{2}}+\left(x +\frac{d}{e}\right)^{2}}}{x +\frac{d}{e}}\right)}{\sqrt{\frac{d^{2}-e^{2}}{e^{2}}}\, e^{3}}"," ",0,"-1/2/e/(d^2-e^2)/(x+d/e)^2*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2)*a+1/2/e^2/(d^2-e^2)/(x+d/e)^2*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2)*b*d-1/2/e^3/(d^2-e^2)/(x+d/e)^2*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2)*c*d^2-3/2*d/(d^2-e^2)^2/(x+d/e)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2)*a+3/2/e*d^2/(d^2-e^2)^2/(x+d/e)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2)*b-3/2/e^2*d^3/(d^2-e^2)^2/(x+d/e)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2)*c-3/2/e*d^2/(d^2-e^2)^2/((d^2-e^2)/e^2)^(1/2)*ln((2*(d^2-e^2)/e^2-2*d/e*(x+d/e)+2*((d^2-e^2)/e^2)^(1/2)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2))/(x+d/e))*a+3/2/e^2*d^3/(d^2-e^2)^2/((d^2-e^2)/e^2)^(1/2)*ln((2*(d^2-e^2)/e^2-2*d/e*(x+d/e)+2*((d^2-e^2)/e^2)^(1/2)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2))/(x+d/e))*b-3/2/e^3*d^4/(d^2-e^2)^2/((d^2-e^2)/e^2)^(1/2)*ln((2*(d^2-e^2)/e^2-2*d/e*(x+d/e)+2*((d^2-e^2)/e^2)^(1/2)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2))/(x+d/e))*c+1/2/e/(d^2-e^2)/((d^2-e^2)/e^2)^(1/2)*ln((2*(d^2-e^2)/e^2-2*d/e*(x+d/e)+2*((d^2-e^2)/e^2)^(1/2)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2))/(x+d/e))*a-3/2/e^2/(d^2-e^2)/((d^2-e^2)/e^2)^(1/2)*ln((2*(d^2-e^2)/e^2-2*d/e*(x+d/e)+2*((d^2-e^2)/e^2)^(1/2)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2))/(x+d/e))*b*d+5/2/e^3/(d^2-e^2)/((d^2-e^2)/e^2)^(1/2)*ln((2*(d^2-e^2)/e^2-2*d/e*(x+d/e)+2*((d^2-e^2)/e^2)^(1/2)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2))/(x+d/e))*c*d^2-1/e/(d^2-e^2)/(x+d/e)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2)*b+2/e^2/(d^2-e^2)/(x+d/e)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2)*d*c-c/e^3/((d^2-e^2)/e^2)^(1/2)*ln((2*(d^2-e^2)/e^2-2*d/e*(x+d/e)+2*((d^2-e^2)/e^2)^(1/2)*((x+d/e)^2-2*d/e*(x+d/e)+(d^2-e^2)/e^2)^(1/2))/(x+d/e))","B"
833,1,29,20,0.032000," ","int((2*x^8+1)/x/(x^8+1)^(3/2),x)","\frac{\ln \left(\frac{\sqrt{x^{8}+1}-1}{\sqrt{x^{8}}}\right)}{4}-\frac{1}{4 \sqrt{x^{8}+1}}"," ",0,"-1/4/(x^8+1)^(1/2)+1/4*ln(((x^8+1)^(1/2)-1)/(x^8)^(1/2))","A"
834,1,29,20,0.034000," ","int((2*x^8+1)*(x^8+1)^(1/2)/(x^17+2*x^9+x),x)","\frac{\ln \left(\frac{\sqrt{x^{8}+1}-1}{\sqrt{x^{8}}}\right)}{4}-\frac{1}{4 \sqrt{x^{8}+1}}"," ",0,"1/4*ln(((x^8+1)^(1/2)-1)/(x^8)^(1/2))-1/4/(x^8+1)^(1/2)","A"
835,1,19,18,0.003000," ","int(1-9*x^2+x/(-9*x^2+1)^(1/2),x)","-3 x^{3}+x -\frac{\sqrt{-9 x^{2}+1}}{9}"," ",0,"x-3*x^3-1/9*(-9*x^2+1)^(1/2)","A"
836,1,19,18,0.004000," ","int((x+(-9*x^2+1)^(3/2))/(-9*x^2+1)^(1/2),x)","-3 x^{3}+x -\frac{\sqrt{-9 x^{2}+1}}{9}"," ",0,"-3*x^3+x-1/9*(-9*x^2+1)^(1/2)","A"
837,1,12,11,0.008000," ","int((x-3*x^(1/2))^(2/3)*(-3+2*x^(1/2))/x^(1/2),x)","\frac{6 \left(x -3 \sqrt{x}\right)^{\frac{5}{3}}}{5}"," ",0,"6/5*(x-3*x^(1/2))^(5/3)","A"
838,1,125,11,0.112000," ","int((9+2*x-9*x^(1/2))/(x-3*x^(1/2))^(1/3),x)","\frac{4 \,3^{\frac{2}{3}} \left(-\mathrm{signum}\left(\frac{\sqrt{x}}{3}-1\right)\right)^{\frac{1}{3}} x^{\frac{11}{6}} \hypergeom \left(\left[\frac{1}{3}, \frac{11}{3}\right], \left[\frac{14}{3}\right], \frac{\sqrt{x}}{3}\right)}{11 \mathrm{signum}\left(\frac{\sqrt{x}}{3}-1\right)^{\frac{1}{3}}}-\frac{9 \,3^{\frac{2}{3}} \left(-\mathrm{signum}\left(\frac{\sqrt{x}}{3}-1\right)\right)^{\frac{1}{3}} x^{\frac{4}{3}} \hypergeom \left(\left[\frac{1}{3}, \frac{8}{3}\right], \left[\frac{11}{3}\right], \frac{\sqrt{x}}{3}\right)}{4 \mathrm{signum}\left(\frac{\sqrt{x}}{3}-1\right)^{\frac{1}{3}}}+\frac{18 \,3^{\frac{2}{3}} \left(-\mathrm{signum}\left(\frac{\sqrt{x}}{3}-1\right)\right)^{\frac{1}{3}} x^{\frac{5}{6}} \hypergeom \left(\left[\frac{1}{3}, \frac{5}{3}\right], \left[\frac{8}{3}\right], \frac{\sqrt{x}}{3}\right)}{5 \mathrm{signum}\left(\frac{\sqrt{x}}{3}-1\right)^{\frac{1}{3}}}"," ",0,"18/5*3^(2/3)/signum(-1+1/3*x^(1/2))^(1/3)*(-signum(-1+1/3*x^(1/2)))^(1/3)*x^(5/6)*hypergeom([1/3,5/3],[8/3],1/3*x^(1/2))+4/11*3^(2/3)/signum(-1+1/3*x^(1/2))^(1/3)*(-signum(-1+1/3*x^(1/2)))^(1/3)*x^(11/6)*hypergeom([1/3,11/3],[14/3],1/3*x^(1/2))-9/4*3^(2/3)/signum(-1+1/3*x^(1/2))^(1/3)*(-signum(-1+1/3*x^(1/2)))^(1/3)*x^(4/3)*hypergeom([1/3,8/3],[11/3],1/3*x^(1/2))","C"
839,1,7,6,0.003000," ","int(1/(-9*x^2+4)^(1/2),x)","\frac{\arcsin \left(\frac{3 x}{2}\right)}{3}"," ",0,"1/3*arcsin(3/2*x)","A"
840,1,34,6,0.007000," ","int(1/(2-3*x)^(1/2)/(3*x+2)^(1/2),x)","\frac{\sqrt{\left(-3 x +2\right) \left(3 x +2\right)}\, \arcsin \left(\frac{3 x}{2}\right)}{3 \sqrt{-3 x +2}\, \sqrt{3 x +2}}"," ",0,"1/3*((2-3*x)*(3*x+2))^(1/2)/(2-3*x)^(1/2)/(3*x+2)^(1/2)*arcsin(3/2*x)","B"
841,1,7,6,0.009000," ","int(1/((-3*x+2)*(3*x+2))^(1/2),x)","\frac{\arcsin \left(\frac{3 x}{2}\right)}{3}"," ",0,"1/3*arcsin(3/2*x)","A"
842,1,7,6,0.004000," ","int(1/(-x^2-2*x+15)^(1/2),x)","\arcsin \left(\frac{x}{4}+\frac{1}{4}\right)"," ",0,"arcsin(1/4+1/4*x)","A"
843,1,31,6,0.006000," ","int(1/(-x+3)^(1/2)/(x+5)^(1/2),x)","\frac{\sqrt{\left(-x +3\right) \left(x +5\right)}\, \arcsin \left(\frac{x}{4}+\frac{1}{4}\right)}{\sqrt{-x +3}\, \sqrt{x +5}}"," ",0,"((-x+3)*(x+5))^(1/2)/(-x+3)^(1/2)/(x+5)^(1/2)*arcsin(1/4*x+1/4)","B"
844,1,7,6,0.008000," ","int(1/((-x+3)*(x+5))^(1/2),x)","\arcsin \left(\frac{x}{4}+\frac{1}{4}\right)"," ",0,"arcsin(1/4*x+1/4)","A"
845,1,5,4,0.004000," ","int(1/(-x^2-8*x-15)^(1/2),x)","\arcsin \left(x +4\right)"," ",0,"arcsin(x+4)","A"
846,1,29,4,0.007000," ","int(1/(-3-x)^(1/2)/(x+5)^(1/2),x)","\frac{\sqrt{\left(-x -3\right) \left(x +5\right)}\, \arcsin \left(x +4\right)}{\sqrt{-x -3}\, \sqrt{x +5}}"," ",0,"((-3-x)*(x+5))^(1/2)/(-3-x)^(1/2)/(x+5)^(1/2)*arcsin(x+4)","B"
847,1,5,4,0.007000," ","int(1/((-x-3)*(x+5))^(1/2),x)","\arcsin \left(x +4\right)"," ",0,"arcsin(x+4)","A"
848,1,8,7,0.002000," ","int(1-x^(1/2),x)","-\frac{2 x^{\frac{3}{2}}}{3}+x"," ",0,"x-2/3*x^(3/2)","A"
849,1,8,7,0.002000," ","int((-x+1)/(x^(1/2)+1),x)","-\frac{2 x^{\frac{3}{2}}}{3}+x"," ",0,"-2/3*x^(3/2)+x","A"
850,1,30,23,0.006000," ","int((1/(-x^2+1))^(1/2),x)","\sqrt{-\frac{1}{x^{2}-1}}\, \sqrt{x^{2}-1}\, \ln \left(x +\sqrt{x^{2}-1}\right)"," ",0,"(-1/(x^2-1))^(1/2)*(x^2-1)^(1/2)*ln(x+(x^2-1)^(1/2))","A"
851,1,30,23,0.007000," ","int(((x^2+1)/(-x^4+1))^(1/2),x)","\sqrt{-\frac{1}{x^{2}-1}}\, \sqrt{x^{2}-1}\, \ln \left(x +\sqrt{x^{2}-1}\right)"," ",0,"(-1/(x^2-1))^(1/2)*(x^2-1)^(1/2)*ln(x+(x^2-1)^(1/2))","A"
852,1,28,21,0.007000," ","int((1/(x^2-1))^(1/2),x)","\sqrt{\frac{1}{x^{2}-1}}\, \sqrt{x^{2}-1}\, \ln \left(x +\sqrt{x^{2}-1}\right)"," ",0,"(1/(x^2-1))^(1/2)*(x^2-1)^(1/2)*ln(x+(x^2-1)^(1/2))","A"
853,1,28,21,0.007000," ","int(((x^2+1)/(x^4-1))^(1/2),x)","\sqrt{\frac{1}{x^{2}-1}}\, \sqrt{x^{2}-1}\, \ln \left(x +\sqrt{x^{2}-1}\right)"," ",0,"(1/(x^2-1))^(1/2)*(x^2-1)^(1/2)*ln(x+(x^2-1)^(1/2))","A"
854,1,10,9,0.003000," ","int(1/(-x+1)^(1/2),x)","-2 \sqrt{-x +1}"," ",0,"-2*(-x+1)^(1/2)","A"
855,1,20,9,0.002000," ","int((x+1)^(1/2)/(-x^2+1)^(1/2),x)","\frac{2 \left(x -1\right) \sqrt{x +1}}{\sqrt{-x^{2}+1}}"," ",0,"2*(x-1)*(x+1)^(1/2)/(-x^2+1)^(1/2)","B"
856,1,8,7,0.003000," ","int(1/(x+1)^(1/2),x)","2 \sqrt{x +1}"," ",0,"2*(x+1)^(1/2)","A"
857,1,22,7,0.003000," ","int((-x+1)^(1/2)/(-x^2+1)^(1/2),x)","\frac{2 \left(x +1\right) \sqrt{-x +1}}{\sqrt{-x^{2}+1}}"," ",0,"2*(x+1)*(-x+1)^(1/2)/(-x^2+1)^(1/2)","B"
858,1,10,9,0.004000," ","int((-x+1)^(1/2),x)","-\frac{2 \left(-x +1\right)^{\frac{3}{2}}}{3}"," ",0,"-2/3*(-x+1)^(3/2)","A"
859,1,20,9,0.002000," ","int((-x^2+1)^(1/2)/(x+1)^(1/2),x)","\frac{2 \left(x -1\right) \sqrt{-x^{2}+1}}{3 \sqrt{x +1}}"," ",0,"2/3*(x-1)*(-x^2+1)^(1/2)/(x+1)^(1/2)","B"
860,1,8,7,0.003000," ","int((x+1)^(1/2),x)","\frac{2 \left(x +1\right)^{\frac{3}{2}}}{3}"," ",0,"2/3*(x+1)^(3/2)","A"
861,1,22,7,0.002000," ","int((-x^2+1)^(1/2)/(-x+1)^(1/2),x)","\frac{2 \left(x +1\right) \sqrt{-x^{2}+1}}{3 \sqrt{-x +1}}"," ",0,"2/3*(x+1)*(-x^2+1)^(1/2)/(-x+1)^(1/2)","B"
862,1,67,27,0.007000," ","int((3*x+2)^(1/2)/(x+1)^(1/2),x)","-\frac{\sqrt{\left(x +1\right) \left(3 x +2\right)}\, \sqrt{3}\, \ln \left(\frac{\left(3 x +\frac{5}{2}\right) \sqrt{3}}{3}+\sqrt{3 x^{2}+5 x +2}\right)}{6 \sqrt{3 x +2}\, \sqrt{x +1}}+\sqrt{x +1}\, \sqrt{3 x +2}"," ",0,"(x+1)^(1/2)*(3*x+2)^(1/2)-1/6*((x+1)*(3*x+2))^(1/2)/(3*x+2)^(1/2)/(x+1)^(1/2)*ln(1/3*(5/2+3*x)*3^(1/2)+(3*x^2+5*x+2)^(1/2))*3^(1/2)","B"
863,1,86,27,0.013000," ","int((-x+1)^(1/2)*(3*x+2)^(1/2)/(-x^2+1)^(1/2),x)","\frac{\sqrt{-x +1}\, \sqrt{3 x +2}\, \sqrt{-x^{2}+1}\, \left(\sqrt{3}\, \ln \left(\sqrt{3}\, x +\frac{5 \sqrt{3}}{6}+\sqrt{3 x^{2}+5 x +2}\right)-6 \sqrt{3 x^{2}+5 x +2}\right)}{6 \left(x -1\right) \sqrt{3 x^{2}+5 x +2}}"," ",0,"1/6*(-x+1)^(1/2)*(3*x+2)^(1/2)*(-x^2+1)^(1/2)*(ln(5/6*3^(1/2)+3^(1/2)*x+(3*x^2+5*x+2)^(1/2))*3^(1/2)-6*(3*x^2+5*x+2)^(1/2))/(x-1)/(3*x^2+5*x+2)^(1/2)","B"
864,1,70,35,0.018000," ","int((x+1)^(3/2)/(-x+1)^(3/2)/x,x)","\frac{\left(-x \arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)-x \arcsin \left(x \right)+\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)+\arcsin \left(x \right)-4 \sqrt{-x^{2}+1}\right) \sqrt{-x +1}\, \sqrt{x +1}}{\left(x -1\right) \sqrt{-x^{2}+1}}"," ",0,"(-arcsin(x)*x-arctanh(1/(-x^2+1)^(1/2))*x+arcsin(x)+arctanh(1/(-x^2+1)^(1/2))-4*(-x^2+1)^(1/2))*(-x+1)^(1/2)*(x+1)^(1/2)/(x-1)/(-x^2+1)^(1/2)","A"
865,1,41,31,0.010000," ","int((x+1)^3/x/(-x^2+1)^(3/2),x)","\frac{4 x}{\sqrt{-x^{2}+1}}-\arctanh \left(\frac{1}{\sqrt{-x^{2}+1}}\right)-\arcsin \left(x \right)+\frac{4}{\sqrt{-x^{2}+1}}"," ",0,"4*x/(-x^2+1)^(1/2)-arcsin(x)+4/(-x^2+1)^(1/2)-arctanh(1/(-x^2+1)^(1/2))","A"
866,1,134,43,0.041000," ","int((a*x+1)^(3/2)/x/(-a*x+1)^(3/2),x)","\frac{\left(-a x \arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(a \right)-a x \arctan \left(\frac{a x \,\mathrm{csgn}\left(a \right)}{\sqrt{-\left(a x +1\right) \left(a x -1\right)}}\right)+\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right) \mathrm{csgn}\left(a \right)+\arctan \left(\frac{a x \,\mathrm{csgn}\left(a \right)}{\sqrt{-\left(a x +1\right) \left(a x -1\right)}}\right)-4 \sqrt{-a^{2} x^{2}+1}\, \mathrm{csgn}\left(a \right)\right) \sqrt{-a x +1}\, \sqrt{a x +1}\, \mathrm{csgn}\left(a \right)}{\left(a x -1\right) \sqrt{-a^{2} x^{2}+1}}"," ",0,"(-arctanh(1/(-a^2*x^2+1)^(1/2))*csgn(a)*x*a-arctan(csgn(a)*a*x/(-(a*x+1)*(a*x-1))^(1/2))*x*a+arctanh(1/(-a^2*x^2+1)^(1/2))*csgn(a)-4*(-a^2*x^2+1)^(1/2)*csgn(a)+arctan(csgn(a)*a*x/(-(a*x+1)*(a*x-1))^(1/2)))*csgn(a)*(-a*x+1)^(1/2)*(a*x+1)^(1/2)/(a*x-1)/(-a^2*x^2+1)^(1/2)","C"
867,1,75,41,0.014000," ","int((a*x+1)^3/x/(-a^2*x^2+1)^(3/2),x)","\frac{4 a x}{\sqrt{-a^{2} x^{2}+1}}-\frac{a \arctan \left(\frac{\sqrt{a^{2}}\, x}{\sqrt{-a^{2} x^{2}+1}}\right)}{\sqrt{a^{2}}}-\arctanh \left(\frac{1}{\sqrt{-a^{2} x^{2}+1}}\right)+\frac{4}{\sqrt{-a^{2} x^{2}+1}}"," ",0,"4*a*x/(-a^2*x^2+1)^(1/2)-a/(a^2)^(1/2)*arctan((a^2)^(1/2)*x/(-a^2*x^2+1)^(1/2))+4/(-a^2*x^2+1)^(1/2)-arctanh(1/(-a^2*x^2+1)^(1/2))","A"
868,1,3,2,0.002000," ","int(1/(-x^2+1)^(1/2),x)","\arcsin \left(x \right)"," ",0,"arcsin(x)","A"
869,1,29,2,0.018000," ","int((x^2+1)^(1/2)/(-x^4+1)^(1/2),x)","\frac{\sqrt{-x^{4}+1}\, \arcsin \left(x \right)}{\sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}}"," ",0,"1/(x^2+1)^(1/2)*(-x^4+1)^(1/2)/(-x^2+1)^(1/2)*arcsin(x)","B"
870,1,3,2,0.004000," ","int(1/(x^2+1)^(1/2),x)","\arcsinh \left(x \right)"," ",0,"arcsinh(x)","A"
871,1,29,2,0.011000," ","int((-x^2+1)^(1/2)/(-x^4+1)^(1/2),x)","\frac{\sqrt{-x^{4}+1}\, \arcsinh \left(x \right)}{\sqrt{-x^{2}+1}\, \sqrt{x^{2}+1}}"," ",0,"1/(-x^2+1)^(1/2)/(x^2+1)^(1/2)*(-x^4+1)^(1/2)*arcsinh(x)","B"
872,1,18,17,0.004000," ","int((-x^2+1)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, x}{2}+\frac{\arcsin \left(x \right)}{2}"," ",0,"1/2*arcsin(x)+1/2*(-x^2+1)^(1/2)*x","A"
873,1,42,17,0.011000," ","int((-x^4+1)^(1/2)/(x^2+1)^(1/2),x)","\frac{\sqrt{-x^{4}+1}\, \left(\sqrt{-x^{2}+1}\, x +\arcsin \left(x \right)\right)}{2 \sqrt{x^{2}+1}\, \sqrt{-x^{2}+1}}"," ",0,"1/2*(-x^4+1)^(1/2)/(x^2+1)^(1/2)*((-x^2+1)^(1/2)*x+arcsin(x))/(-x^2+1)^(1/2)","B"
874,1,16,15,0.003000," ","int((x^2+1)^(1/2),x)","\frac{\sqrt{x^{2}+1}\, x}{2}+\frac{\arcsinh \left(x \right)}{2}"," ",0,"1/2*arcsinh(x)+1/2*(x^2+1)^(1/2)*x","A"
875,1,47,15,0.010000," ","int((-x^4+1)^(1/2)/(-x^2+1)^(1/2),x)","-\frac{\sqrt{-x^{4}+1}\, \sqrt{-x^{2}+1}\, \left(\sqrt{x^{2}+1}\, x +\arcsinh \left(x \right)\right)}{2 \left(x^{2}-1\right) \sqrt{x^{2}+1}}"," ",0,"-1/2*(-x^4+1)^(1/2)*(-x^2+1)^(1/2)*((x^2+1)^(1/2)*x+arcsinh(x))/(x^2-1)/(x^2+1)^(1/2)","B"
876,0,0,47,0.071000," ","int(((c*x^2+a+b)/d)^m,x)","\int \left(\frac{c \,x^{2}+a +b}{d}\right)^{m}\, dx"," ",0,"int(((c*x^2+a+b)/d)^m,x)","F"
877,1,21,20,0.004000," ","int(1/(x-(x^2+1)^(1/2)),x)","-\frac{x^{2}}{2}-\frac{\sqrt{x^{2}+1}\, x}{2}-\frac{\arcsinh \left(x \right)}{2}"," ",0,"-1/2*x^2-1/2*arcsinh(x)-1/2*(x^2+1)^(1/2)*x","A"
878,1,175,29,0.046000," ","int(1/(x-(-x^2+1)^(1/2)),x)","-\frac{\arctanh \left(\frac{\left(1-\left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}\right) \sqrt{2}}{\sqrt{-4 \left(x -\frac{\sqrt{2}}{2}\right)^{2}-4 \left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}\right)}{4}+\frac{\arctanh \left(\frac{\left(\left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+1\right) \sqrt{2}}{\sqrt{-4 \left(x +\frac{\sqrt{2}}{2}\right)^{2}+4 \left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}\right)}{4}-\frac{\arcsin \left(x \right)}{2}+\frac{\ln \left(2 x^{2}-1\right)}{4}-\frac{\sqrt{2}\, \sqrt{-4 \left(x +\frac{\sqrt{2}}{2}\right)^{2}+4 \left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}{8}+\frac{\sqrt{2}\, \sqrt{-4 \left(x -\frac{\sqrt{2}}{2}\right)^{2}-4 \left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}{8}"," ",0,"1/4*ln(2*x^2-1)-1/8*2^(1/2)*(-4*(x+1/2*2^(1/2))^2+4*(x+1/2*2^(1/2))*2^(1/2)+2)^(1/2)-1/2*arcsin(x)+1/4*arctanh(((x+1/2*2^(1/2))*2^(1/2)+1)*2^(1/2)/(-4*(x+1/2*2^(1/2))^2+4*(x+1/2*2^(1/2))*2^(1/2)+2)^(1/2))+1/8*2^(1/2)*(-4*(x-1/2*2^(1/2))^2-4*(x-1/2*2^(1/2))*2^(1/2)+2)^(1/2)-1/4*arctanh((1-(x-1/2*2^(1/2))*2^(1/2))*2^(1/2)/(-4*(x-1/2*2^(1/2))^2-4*(x-1/2*2^(1/2))*2^(1/2)+2)^(1/2))","B"
879,1,33,32,0.011000," ","int(1/(x-(2*x^2+1)^(1/2)),x)","-\sqrt{2}\, \arcsinh \left(\sqrt{2}\, x \right)+\arctanh \left(\frac{x}{\sqrt{2 x^{2}+1}}\right)-\frac{\ln \left(x^{2}+1\right)}{2}"," ",0,"arctanh(x/(2*x^2+1)^(1/2))-1/2*ln(x^2+1)-arcsinh(2^(1/2)*x)*2^(1/2)","A"
880,1,111,42,0.015000," ","int((2*x-x^3+x^2*(-x^2+2)^(1/2))/(2*x^2-2),x)","-\frac{x^{2}}{4}+\frac{\sqrt{-x^{2}+2}\, x}{4}-\frac{\arctanh \left(\frac{-2 x +4}{2 \sqrt{-2 x -\left(x -1\right)^{2}+3}}\right)}{4}+\frac{\arctanh \left(\frac{2 x +4}{2 \sqrt{2 x -\left(x +1\right)^{2}+3}}\right)}{4}+\frac{\ln \left(x -1\right)}{4}+\frac{\ln \left(x +1\right)}{4}+\frac{\sqrt{-2 x -\left(x -1\right)^{2}+3}}{4}-\frac{\sqrt{2 x -\left(x +1\right)^{2}+3}}{4}"," ",0,"1/4*x*(-x^2+2)^(1/2)+1/4*(-(x-1)^2-2*x+3)^(1/2)-1/4*arctanh(1/2*(4-2*x)/(-(x-1)^2-2*x+3)^(1/2))-1/4*(-(x+1)^2+2*x+3)^(1/2)+1/4*arctanh(1/2*(4+2*x)/(-(x+1)^2+2*x+3)^(1/2))-1/4*x^2+1/4*ln(x-1)+1/4*ln(x+1)","B"
881,1,111,46,0.017000," ","int(x*(-x^2+2)^(1/2)/(x-(-x^2+2)^(1/2)),x)","-\frac{x^{2}}{4}+\frac{\sqrt{-x^{2}+2}\, x}{4}-\frac{\arctanh \left(\frac{-2 x +4}{2 \sqrt{-2 x -\left(x -1\right)^{2}+3}}\right)}{4}+\frac{\arctanh \left(\frac{2 x +4}{2 \sqrt{2 x -\left(x +1\right)^{2}+3}}\right)}{4}+\frac{\ln \left(x -1\right)}{4}+\frac{\ln \left(x +1\right)}{4}+\frac{\sqrt{-2 x -\left(x -1\right)^{2}+3}}{4}-\frac{\sqrt{2 x -\left(x +1\right)^{2}+3}}{4}"," ",0,"1/4*(-x^2+2)^(1/2)*x+1/4*(-2*x-(x-1)^2+3)^(1/2)-1/4*arctanh(1/2*(-2*x+4)/(-2*x-(x-1)^2+3)^(1/2))-1/4*(2*x-(x+1)^2+3)^(1/2)+1/4*arctanh(1/2*(2*x+4)/(2*x-(x+1)^2+3)^(1/2))-1/4*x^2+1/4*ln(x-1)+1/4*ln(x+1)","B"
882,1,38,39,0.005000," ","int(x/(-x+(-x^2+2*x)^(1/2)),x)","-\frac{x}{2}+\frac{\arctanh \left(\frac{1}{\sqrt{-\left(x -1\right)^{2}+1}}\right)}{2}-\frac{\ln \left(x -1\right)}{2}-\frac{\sqrt{-\left(x -1\right)^{2}+1}}{2}"," ",0,"-1/2*x-1/2*ln(x-1)-1/2*(-(x-1)^2+1)^(1/2)+1/2*arctanh(1/(-(x-1)^2+1)^(1/2))","A"
883,1,38,39,0.006000," ","int((x+(-x^2+2*x)^(1/2))/(2-2*x),x)","-\frac{x}{2}+\frac{\arctanh \left(\frac{1}{\sqrt{-\left(x -1\right)^{2}+1}}\right)}{2}-\frac{\ln \left(x -1\right)}{2}-\frac{\sqrt{-\left(x -1\right)^{2}+1}}{2}"," ",0,"-1/2*x-1/2*ln(x-1)-1/2*(-(x-1)^2+1)^(1/2)+1/2*arctanh(1/(-(x-1)^2+1)^(1/2))","A"
884,1,51,39,0.011000," ","int((x+(2-x)^(1/2)*x^(1/2))/(2-2*x),x)","-\frac{x}{2}-\frac{\ln \left(x -1\right)}{2}-\frac{\sqrt{-x +2}\, \left(-\arctanh \left(\frac{1}{\sqrt{-\left(x -2\right) x}}\right)+\sqrt{-\left(x -2\right) x}\right) \sqrt{x}}{2 \sqrt{-\left(x -2\right) x}}"," ",0,"-1/2*(2-x)^(1/2)*x^(1/2)/(-x*(x-2))^(1/2)*((-x*(x-2))^(1/2)-arctanh(1/(-x*(x-2))^(1/2)))-1/2*x-1/2*ln(x-1)","A"
885,1,51,38,0.010000," ","int(x^(1/2)/((-x+2)^(1/2)-x^(1/2)),x)","-\frac{x}{2}-\frac{\ln \left(x -1\right)}{2}-\frac{\sqrt{-x +2}\, \left(-\arctanh \left(\frac{1}{\sqrt{-\left(x -2\right) x}}\right)+\sqrt{-\left(x -2\right) x}\right) \sqrt{x}}{2 \sqrt{-\left(x -2\right) x}}"," ",0,"-1/2*(-x+2)^(1/2)*x^(1/2)/(-(x-2)*x)^(1/2)*((-(x-2)*x)^(1/2)-arctanh(1/(-(x-2)*x)^(1/2)))-1/2*x-1/2*ln(x-1)","A"
886,1,20,23,0.003000," ","int(1/((x+1)*(x^2-1))^(2/3),x)","\frac{3 \left(x -1\right) \left(x +1\right)}{2 \left(\left(x +1\right) \left(x^{2}-1\right)\right)^{\frac{2}{3}}}"," ",0,"3/2*(x-1)*(x+1)/((x+1)*(x^2-1))^(2/3)","A"
887,1,13,12,0.007000," ","int((x^2-1)/(x^2+1)/(x*(x^2+1))^(1/2),x)","-\frac{2 x}{\sqrt{\left(x^{2}+1\right) x}}"," ",0,"-2*x/(x*(x^2+1))^(1/2)","A"
888,1,11,10,0.004000," ","int((x^2-1)/(x^2+1)/(x^3+x)^(1/2),x)","-\frac{2 x}{\sqrt{x^{3}+x}}"," ",0,"-2*x/(x^3+x)^(1/2)","A"
889,1,34,34,0.007000," ","int(((x^2-1)^2/x/(x^2+1))^(1/2)/(x^2+1),x)","-\frac{2 \sqrt{\frac{\left(x^{2}-1\right)^{2}}{\left(x^{2}+1\right) x}}\, x}{\left(x -1\right) \left(x +1\right)}"," ",0,"-2*x/(x-1)/(x+1)*((x^2-1)^2/x/(x^2+1))^(1/2)","A"
890,1,34,31,0.006000," ","int(((x^2-1)^2/(x^3+x))^(1/2)/(x^2+1),x)","-\frac{2 \sqrt{\frac{\left(x^{2}-1\right)^{2}}{\left(x^{2}+1\right) x}}\, x}{\left(x -1\right) \left(x +1\right)}"," ",0,"-2/(x-1)/(x+1)*((x^2-1)^2/(x^2+1)/x)^(1/2)*x","A"
891,1,117,54,0.053000," ","int(1/(a+b/x^2)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(a \,x^{2}+b \right) \sqrt{d \,x^{2}+c}\, \ln \left(\frac{2 a d \,x^{2}+a c +b d +2 \sqrt{a d \,x^{4}+a c \,x^{2}+b d \,x^{2}+b c}\, \sqrt{a d}}{2 \sqrt{a d}}\right)}{2 \sqrt{\frac{a \,x^{2}+b}{x^{2}}}\, \sqrt{a d}\, \sqrt{a d \,x^{4}+a c \,x^{2}+b d \,x^{2}+b c}\, x}"," ",0,"1/2/((a*x^2+b)/x^2)^(1/2)/x*(a*x^2+b)*ln(1/2*(2*a*d*x^2+2*(a*d*x^4+a*c*x^2+b*d*x^2+b*c)^(1/2)*(a*d)^(1/2)+a*c+b*d)/(a*d)^(1/2))*(d*x^2+c)^(1/2)/(a*d)^(1/2)/(a*d*x^4+a*c*x^2+b*d*x^2+b*c)^(1/2)","B"
892,1,63,65,0.032000," ","int((x^4-2*x^2)^(1/2)/(x^2-1)/(x^2+2),x)","-\frac{\sqrt{x^{4}-2 x^{2}}\, \left(\arctan \left(\frac{x -2}{\sqrt{x^{2}-2}}\right)-\arctan \left(\frac{x +2}{\sqrt{x^{2}-2}}\right)-4 \arctan \left(\frac{\sqrt{x^{2}-2}}{2}\right)\right)}{6 \sqrt{x^{2}-2}\, x}"," ",0,"-1/6*(x^4-2*x^2)^(1/2)*(arctan((x-2)/(x^2-2)^(1/2))-arctan((x+2)/(x^2-2)^(1/2))-4*arctan(1/2*(x^2-2)^(1/2)))/x/(x^2-2)^(1/2)","A"
893,1,63,41,0.026000," ","int((1-1/(x^2-1)^2)^(1/2)/(-x^2+2),x)","-\frac{\sqrt{\frac{\left(x^{2}-2\right) x^{2}}{\left(x^{2}-1\right)^{2}}}\, \left(x^{2}-1\right) \left(\arctan \left(\frac{x -2}{\sqrt{x^{2}-2}}\right)-\arctan \left(\frac{x +2}{\sqrt{x^{2}-2}}\right)\right)}{2 \sqrt{x^{2}-2}\, x}"," ",0,"-1/2*(x^2*(x^2-2)/(x^2-1)^2)^(1/2)*(x^2-1)*(arctan((x-2)/(x^2-2)^(1/2))-arctan((x+2)/(x^2-2)^(1/2)))/x/(x^2-2)^(1/2)","A"
894,1,75,99,0.028000," ","int(((x^4-2*x^2)/(x^2-1)^2)^(1/2)/(x^2+2),x)","-\frac{\sqrt{\frac{\left(x^{2}-2\right) x^{2}}{\left(x^{2}-1\right)^{2}}}\, \left(x^{2}-1\right) \left(\arctan \left(\frac{x -2}{\sqrt{x^{2}-2}}\right)-\arctan \left(\frac{x +2}{\sqrt{x^{2}-2}}\right)-4 \arctan \left(\frac{\sqrt{x^{2}-2}}{2}\right)\right)}{6 \sqrt{x^{2}-2}\, x}"," ",0,"-1/6*((x^2-2)/(x^2-1)^2*x^2)^(1/2)*(x^2-1)*(arctan((x-2)/(x^2-2)^(1/2))-arctan((x+2)/(x^2-2)^(1/2))-4*arctan(1/2*(x^2-2)^(1/2)))/x/(x^2-2)^(1/2)","A"
895,1,62,119,0.023000," ","int((1+2/(x^2+1)*x)^(5/2),x)","\frac{\left(\frac{x^{2}+2 x +1}{x^{2}+1}\right)^{\frac{5}{2}} \left(x^{2}+1\right) \left(3 x^{4}-8 x^{3}-18 x^{2}-12 x +15 \left(x^{2}+1\right)^{\frac{3}{2}} \arcsinh \left(x \right)-17\right)}{3 \left(x +1\right)^{5}}"," ",0,"1/3*((x^2+2*x+1)/(x^2+1))^(5/2)/(x+1)^5*(x^2+1)*(15*arcsinh(x)*(x^2+1)^(3/2)+3*x^4-8*x^3-18*x^2-12*x-17)","A"
896,1,49,82,0.016000," ","int((1+2/(x^2+1)*x)^(3/2),x)","\frac{\left(\frac{x^{2}+2 x +1}{x^{2}+1}\right)^{\frac{3}{2}} \left(x^{2}+1\right) \left(x^{2}-2 x +3 \sqrt{x^{2}+1}\, \arcsinh \left(x \right)-1\right)}{\left(x +1\right)^{3}}"," ",0,"((x^2+2*x+1)/(x^2+1))^(3/2)/(x+1)^3*(x^2+1)*(3*arcsinh(x)*(x^2+1)^(1/2)+x^2-2*x-1)","A"
897,1,42,55,0.010000," ","int((1+2/(x^2+1)*x)^(1/2),x)","\frac{\sqrt{\frac{x^{2}+2 x +1}{x^{2}+1}}\, \sqrt{x^{2}+1}\, \left(\arcsinh \left(x \right)+\sqrt{x^{2}+1}\right)}{x +1}"," ",0,"((x^2+2*x+1)/(x^2+1))^(1/2)/(x+1)*(x^2+1)^(1/2)*((x^2+1)^(1/2)+arcsinh(x))","A"
898,1,79,94,0.039000," ","int(1/(1+2/(x^2+1)*x)^(1/2),x)","\frac{x +1}{\sqrt{\frac{\left(x +1\right)^{2}}{x^{2}+1}}}+\frac{\left(-\arcsinh \left(x \right)-\sqrt{2}\, \arctanh \left(\frac{\left(-2 x +2\right) \sqrt{2}}{4 \sqrt{-2 x +\left(x +1\right)^{2}}}\right)\right) \left(x +1\right)}{\sqrt{\frac{\left(x +1\right)^{2}}{x^{2}+1}}\, \sqrt{x^{2}+1}}"," ",0,"1/((x+1)^2/(x^2+1))^(1/2)*(x+1)+(-arcsinh(x)-2^(1/2)*arctanh(1/4*(2-2*x)*2^(1/2)/((x+1)^2-2*x)^(1/2)))/((x+1)^2/(x^2+1))^(1/2)/(x^2+1)^(1/2)*(x+1)","A"
899,1,218,123,0.016000," ","int(1/(1+2/(x^2+1)*x)^(3/2),x)","\frac{\left(x +1\right) \left(-\left(x^{2}+1\right)^{\frac{3}{2}} x^{3}-6 \sqrt{x^{2}+1}\, x^{3}-24 x^{2} \arcsinh \left(x \right)+18 \sqrt{2}\, x^{2} \arctanh \left(\frac{\left(x -1\right) \sqrt{2}}{2 \sqrt{x^{2}+1}}\right)+\left(x^{2}+1\right)^{\frac{3}{2}} x^{2}+6 \sqrt{x^{2}+1}\, x^{2}-48 x \arcsinh \left(x \right)+36 \sqrt{2}\, x \arctanh \left(\frac{\left(x -1\right) \sqrt{2}}{2 \sqrt{x^{2}+1}}\right)+\left(x^{2}+1\right)^{\frac{5}{2}} x +5 \left(x^{2}+1\right)^{\frac{3}{2}} x +30 \sqrt{x^{2}+1}\, x -24 \arcsinh \left(x \right)+18 \sqrt{2}\, \arctanh \left(\frac{\left(x -1\right) \sqrt{2}}{2 \sqrt{x^{2}+1}}\right)-\left(x^{2}+1\right)^{\frac{5}{2}}+3 \left(x^{2}+1\right)^{\frac{3}{2}}+18 \sqrt{x^{2}+1}\right)}{8 \left(\frac{x^{2}+2 x +1}{x^{2}+1}\right)^{\frac{3}{2}} \left(x^{2}+1\right)^{\frac{3}{2}}}"," ",0,"1/8/((x^2+2*x+1)/(x^2+1))^(3/2)*(x+1)*((x^2+1)^(5/2)*x-(x^2+1)^(3/2)*x^3-(x^2+1)^(5/2)+(x^2+1)^(3/2)*x^2+18*2^(1/2)*arctanh(1/2*(x-1)*2^(1/2)/(x^2+1)^(1/2))*x^2+5*x*(x^2+1)^(3/2)-6*(x^2+1)^(1/2)*x^3+36*2^(1/2)*arctanh(1/2*(x-1)*2^(1/2)/(x^2+1)^(1/2))*x+3*(x^2+1)^(3/2)+6*(x^2+1)^(1/2)*x^2-24*arcsinh(x)*x^2+18*2^(1/2)*arctanh(1/2*(x-1)*2^(1/2)/(x^2+1)^(1/2))+30*(x^2+1)^(1/2)*x-48*arcsinh(x)*x+18*(x^2+1)^(1/2)-24*arcsinh(x))/(x^2+1)^(3/2)","A"
900,1,28,26,0.006000," ","int((1+2/(x^2+1)*x)^(1/2)/(x^2+1),x)","\frac{\left(x -1\right) \sqrt{\frac{x^{2}+2 x +1}{x^{2}+1}}}{x +1}"," ",0,"(x-1)/(x+1)*((x^2+2*x+1)/(x^2+1))^(1/2)","A"
901,0,0,14,0.068000," ","int(F(x)*(-x^2+x)^(1/2),x)","\int \sqrt{-x^{2}+x}\, F \left(x \right)\, dx"," ",0,"int(F(x)*(-x^2+x)^(1/2),x)","F"
902,0,0,14,0.066000," ","int(F(x)/(-x^2+x)^(1/2),x)","\int \frac{F \left(x \right)}{\sqrt{-x^{2}+x}}\, dx"," ",0,"int(F(x)/(-x^2+x)^(1/2),x)","F"
903,0,0,14,0.068000," ","int(F(x)*(-x+1)^(1/2)*x^(1/2),x)","\int \sqrt{-x +1}\, \sqrt{x}\, F \left(x \right)\, dx"," ",0,"int(F(x)*(-x+1)^(1/2)*x^(1/2),x)","F"
904,0,0,14,0.064000," ","int(F(x)/(-x+1)^(1/2)/x^(1/2),x)","\int \frac{F \left(x \right)}{\sqrt{-x +1}\, \sqrt{x}}\, dx"," ",0,"int(F(x)/(-x+1)^(1/2)/x^(1/2),x)","F"
905,0,0,10,0.020000," ","int(F((b*x+a)/x),x)","\int F \left(\frac{b x +a}{x}\right)\, dx"," ",0,"int(F((b*x+a)/x),x)","F"
906,0,0,10,0.019000," ","int(F((b*x^2+a)/x^2),x)","\int F \left(\frac{b \,x^{2}+a}{x^{2}}\right)\, dx"," ",0,"int(F((b*x^2+a)/x^2),x)","F"
907,0,0,12,0.015000," ","int(F(x/(b*x+a)),x)","\int F \left(\frac{x}{b x +a}\right)\, dx"," ",0,"int(F(x/(b*x+a)),x)","F"
908,0,0,16,0.010000," ","int(F(x^2/(b*x^2+a)),x)","\int F \left(\frac{x^{2}}{b \,x^{2}+a}\right)\, dx"," ",0,"int(F(x^2/(b*x^2+a)),x)","F"
909,0,0,14,0.018000," ","int(F(x^2/(b*x+a)^2),x)","\int F \left(\frac{x^{2}}{\left(b x +a \right)^{2}}\right)\, dx"," ",0,"int(F(x^2/(b*x+a)^2),x)","F"
910,0,0,16,0.016000," ","int(F(x^4/(b*x^2+a)^2),x)","\int F \left(\frac{x^{4}}{\left(b \,x^{2}+a \right)^{2}}\right)\, dx"," ",0,"int(F(x^4/(b*x^2+a)^2),x)","F"
911,-2,0,36,180.000000," ","int((b*x^2+(b^2*x^4+a)^(1/2))^(1/2)/(b^2*x^4+a)^(1/2),x)","\int \frac{\sqrt{b \,x^{2}+\sqrt{b^{2} x^{4}+a}}}{\sqrt{b^{2} x^{4}+a}}\, dx"," ",0,"int((b*x^2+(b^2*x^4+a)^(1/2))^(1/2)/(b^2*x^4+a)^(1/2),x)","F"
912,-2,0,37,180.000000," ","int((-b*x^2+(b^2*x^4+a)^(1/2))^(1/2)/(b^2*x^4+a)^(1/2),x)","\int \frac{\sqrt{-b \,x^{2}+\sqrt{b^{2} x^{4}+a}}}{\sqrt{b^{2} x^{4}+a}}\, dx"," ",0,"int((-b*x^2+(b^2*x^4+a)^(1/2))^(1/2)/(b^2*x^4+a)^(1/2),x)","F"
913,0,0,125,0.089000," ","int((2*x^2+(4*x^4+3)^(1/2))^(1/2)/(d*x+c)/(4*x^4+3)^(1/2),x)","\int \frac{\sqrt{2 x^{2}+\sqrt{4 x^{4}+3}}}{\left(d x +c \right) \sqrt{4 x^{4}+3}}\, dx"," ",0,"int((2*x^2+(4*x^4+3)^(1/2))^(1/2)/(d*x+c)/(4*x^4+3)^(1/2),x)","F"
914,0,0,208,0.073000," ","int((2*x^2+(4*x^4+3)^(1/2))^(1/2)/(d*x+c)^2/(4*x^4+3)^(1/2),x)","\int \frac{\sqrt{2 x^{2}+\sqrt{4 x^{4}+3}}}{\left(d x +c \right)^{2} \sqrt{4 x^{4}+3}}\, dx"," ",0,"int((2*x^2+(4*x^4+3)^(1/2))^(1/2)/(d*x+c)^2/(4*x^4+3)^(1/2),x)","F"
915,1,28,27,0.004000," ","int((x-4)/(1+x^(1/3))/x^(1/2),x)","\frac{6 x^{\frac{7}{6}}}{7}+30 \arctan \left(x^{\frac{1}{6}}\right)-\frac{6 x^{\frac{5}{6}}}{5}+2 \sqrt{x}-30 x^{\frac{1}{6}}"," ",0,"-30*x^(1/6)-6/5*x^(5/6)+6/7*x^(7/6)+30*arctan(x^(1/6))+2*x^(1/2)","A"
916,1,21,20,0.006000," ","int((x^(1/2)+1)/(x^(5/6)+x^(7/6)),x)","6 \arctan \left(x^{\frac{1}{6}}\right)-3 \ln \left(x^{\frac{1}{3}}+1\right)+3 x^{\frac{1}{3}}"," ",0,"3*x^(1/3)+6*arctan(x^(1/6))-3*ln(1+x^(1/3))","A"
917,1,48,30,0.015000," ","int((x^(1/2)+1)/(x^(1/3)+1)/x^(1/2),x)","-6 \arctan \left(x^{\frac{1}{6}}\right)+\ln \left(x +1\right)+2 \ln \left(x^{\frac{1}{3}}+1\right)-\ln \left(x^{\frac{2}{3}}-x^{\frac{1}{3}}+1\right)+\frac{3 x^{\frac{2}{3}}}{2}-3 x^{\frac{1}{3}}+6 x^{\frac{1}{6}}"," ",0,"ln(x+1)+3/2*x^(2/3)-ln(x^(2/3)-x^(1/3)+1)+2*ln(x^(1/3)+1)-3*x^(1/3)+6*x^(1/6)-6*arctan(x^(1/6))","A"
918,1,50,14,0.013000," ","int((2+b/x^2)^(1/2)/(2*x^2+b),x)","-\frac{\sqrt{\frac{2 x^{2}+b}{x^{2}}}\, x \ln \left(\frac{2 b +2 \sqrt{2 x^{2}+b}\, \sqrt{b}}{x}\right)}{\sqrt{2 x^{2}+b}\, \sqrt{b}}"," ",0,"-((2*x^2+b)/x^2)^(1/2)*x/(2*x^2+b)^(1/2)/b^(1/2)*ln(2*(b^(1/2)*(2*x^2+b)^(1/2)+b)/x)","B"
919,1,62,14,0.012000," ","int((2-b/x^2)^(1/2)/(2*x^2-b),x)","-\frac{\sqrt{\frac{2 x^{2}-b}{x^{2}}}\, x \ln \left(\frac{-2 b +2 \sqrt{-b}\, \sqrt{2 x^{2}-b}}{x}\right)}{\sqrt{2 x^{2}-b}\, \sqrt{-b}}"," ",0,"-((2*x^2-b)/x^2)^(1/2)*x/(2*x^2-b)^(1/2)/(-b)^(1/2)*ln(2*((-b)^(1/2)*(2*x^2-b)^(1/2)-b)/x)","B"
920,1,244,103,0.033000," ","int((a+c/x^2)^(1/2)/(e*x+d),x)","\frac{\sqrt{\frac{a \,x^{2}+c}{x^{2}}}\, \left(a \,d^{2} \ln \left(\frac{-2 a d x +2 c e +2 \sqrt{a \,x^{2}+c}\, \sqrt{\frac{a \,d^{2}+c \,e^{2}}{e^{2}}}\, e}{e x +d}\right)+c \,e^{2} \ln \left(\frac{-2 a d x +2 c e +2 \sqrt{a \,x^{2}+c}\, \sqrt{\frac{a \,d^{2}+c \,e^{2}}{e^{2}}}\, e}{e x +d}\right)+\sqrt{\frac{a \,d^{2}+c \,e^{2}}{e^{2}}}\, \sqrt{a}\, d e \ln \left(\frac{a x +\sqrt{a \,x^{2}+c}\, \sqrt{a}}{\sqrt{a}}\right)-\sqrt{\frac{a \,d^{2}+c \,e^{2}}{e^{2}}}\, \sqrt{c}\, e^{2} \ln \left(\frac{2 c +2 \sqrt{a \,x^{2}+c}\, \sqrt{c}}{x}\right)\right) x}{\sqrt{a \,x^{2}+c}\, \sqrt{\frac{a \,d^{2}+c \,e^{2}}{e^{2}}}\, d \,e^{2}}"," ",0,"((a*x^2+c)/x^2)^(1/2)*x*(a^(1/2)*d*ln(((a*x^2+c)^(1/2)*a^(1/2)+a*x)/a^(1/2))*e*((a*d^2+c*e^2)/e^2)^(1/2)-((a*d^2+c*e^2)/e^2)^(1/2)*c^(1/2)*ln(2*(c^(1/2)*(a*x^2+c)^(1/2)+c)/x)*e^2+ln(2*((a*x^2+c)^(1/2)*((a*d^2+c*e^2)/e^2)^(1/2)*e-a*x*d+c*e)/(e*x+d))*a*d^2+ln(2*((a*x^2+c)^(1/2)*((a*d^2+c*e^2)/e^2)^(1/2)*e-a*x*d+c*e)/(e*x+d))*c*e^2)/(a*x^2+c)^(1/2)/d/e^2/((a*d^2+c*e^2)/e^2)^(1/2)","B"
921,1,397,157,0.041000," ","int((a+c/x^2+b/x)^(1/2)/(e*x+d),x)","-\frac{\sqrt{\frac{a \,x^{2}+b x +c}{x^{2}}}\, \left(-a^{\frac{3}{2}} d^{2} \ln \left(\frac{-2 a d x +b e x -b d +2 c e +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{\frac{a \,d^{2}-b d e +c \,e^{2}}{e^{2}}}\, e}{e x +d}\right)+\sqrt{a}\, b d e \ln \left(\frac{-2 a d x +b e x -b d +2 c e +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{\frac{a \,d^{2}-b d e +c \,e^{2}}{e^{2}}}\, e}{e x +d}\right)-\sqrt{a}\, c \,e^{2} \ln \left(\frac{-2 a d x +b e x -b d +2 c e +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{\frac{a \,d^{2}-b d e +c \,e^{2}}{e^{2}}}\, e}{e x +d}\right)-\sqrt{\frac{a \,d^{2}-b d e +c \,e^{2}}{e^{2}}}\, a d e \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{a \,d^{2}-b d e +c \,e^{2}}{e^{2}}}\, \sqrt{a}\, \sqrt{c}\, e^{2} \ln \left(\frac{b x +2 c +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{c}}{x}\right)\right) x}{\sqrt{a \,x^{2}+b x +c}\, \sqrt{\frac{a \,d^{2}-b d e +c \,e^{2}}{e^{2}}}\, \sqrt{a}\, d \,e^{2}}"," ",0,"-((a*x^2+b*x+c)/x^2)^(1/2)*x*(((a*d^2-b*d*e+c*e^2)/e^2)^(1/2)*c^(1/2)*a^(1/2)*ln((2*c+b*x+2*c^(1/2)*(a*x^2+b*x+c)^(1/2))/x)*e^2-((a*d^2-b*d*e+c*e^2)/e^2)^(1/2)*ln(1/2*(2*(a*x^2+b*x+c)^(1/2)*a^(1/2)+2*a*x+b)/a^(1/2))*a*d*e-a^(3/2)*ln((2*(a*x^2+b*x+c)^(1/2)*((a*d^2-b*d*e+c*e^2)/e^2)^(1/2)*e-2*a*d*x+x*b*e-b*d+2*c*e)/(e*x+d))*d^2+a^(1/2)*ln((2*(a*x^2+b*x+c)^(1/2)*((a*d^2-b*d*e+c*e^2)/e^2)^(1/2)*e-2*a*d*x+x*b*e-b*d+2*c*e)/(e*x+d))*b*d*e-a^(1/2)*ln((2*(a*x^2+b*x+c)^(1/2)*((a*d^2-b*d*e+c*e^2)/e^2)^(1/2)*e-2*a*d*x+x*b*e-b*d+2*c*e)/(e*x+d))*c*e^2)/(a*x^2+b*x+c)^(1/2)/d/e^2/a^(1/2)/((a*d^2-b*d*e+c*e^2)/e^2)^(1/2)","B"
922,1,17,16,0.004000," ","int((x^(1/6)+(x^3)^(1/5))/x^(1/2),x)","\frac{3 x^{\frac{2}{3}}}{2}+\frac{10 \left(x^{3}\right)^{\frac{1}{5}} \sqrt{x}}{11}"," ",0,"3/2*x^(2/3)+10/11*(x^3)^(1/5)*x^(1/2)","A"
923,1,23,22,0.007000," ","int((x+2)/(-x^2+4*x)^(1/2),x)","4 \arcsin \left(\frac{x}{2}-1\right)-\sqrt{-x^{2}+4 x}"," ",0,"4*arcsin(1/2*x-1)-(-x^2+4*x)^(1/2)","A"
924,1,16,11,0.005000," ","int((x+3)/(x^2+6*x)^(1/3),x)","\frac{3 \left(x +6\right) x}{4 \left(x^{2}+6 x \right)^{\frac{1}{3}}}"," ",0,"3/4*x*(x+6)/(x^2+6*x)^(1/3)","A"
925,1,23,18,0.004000," ","int((x+4)/(-x^2+6*x)^(3/2),x)","-\frac{\left(x -6\right) \left(7 x -12\right) x}{9 \left(-x^{2}+6 x \right)^{\frac{3}{2}}}"," ",0,"-1/9*x*(x-6)*(-12+7*x)/(-x^2+6*x)^(3/2)","A"
926,1,13,10,0.006000," ","int(1/(x+1)/(x^2+2*x)^(1/2),x)","-\arctan \left(\frac{1}{\sqrt{\left(x +1\right)^{2}-1}}\right)"," ",0,"-arctan(1/((x+1)^2-1)^(1/2))","A"
927,1,15,10,0.007000," ","int(1/(2*x+1)/(x^2+x)^(1/2),x)","-\arctan \left(\frac{1}{\sqrt{4 \left(x +\frac{1}{2}\right)^{2}-1}}\right)"," ",0,"-arctan(1/(4*(x+1/2)^2-1)^(1/2))","A"
928,1,17,13,0.003000," ","int((x-1)/(-x^2+2*x)^(1/2),x)","\frac{\left(x -2\right) x}{\sqrt{-x^{2}+2 x}}"," ",0,"(x-2)*x/(-x^2+2*x)^(1/2)","A"
929,1,54,42,0.008000," ","int((-x^2+x)^(1/2)/(x+1),x)","\frac{3 \arcsin \left(2 x -1\right)}{2}-\sqrt{2}\, \arctan \left(\frac{\left(3 x -1\right) \sqrt{2}}{4 \sqrt{3 x -\left(x +1\right)^{2}+1}}\right)+\sqrt{3 x -\left(x +1\right)^{2}+1}"," ",0,"(-(x+1)^2+3*x+1)^(1/2)+3/2*arcsin(2*x-1)-2^(1/2)*arctan(1/4*(3*x-1)*2^(1/2)/(-(x+1)^2+3*x+1)^(1/2))","A"
930,1,342,37,0.102000," ","int((x^(1/4)+x)^(1/2),x)","\frac{2 \sqrt{x +x^{\frac{1}{4}}}\, x}{3}+\frac{\sqrt{x +x^{\frac{1}{4}}}\, x^{\frac{1}{4}}}{3}+\frac{\left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x^{\frac{1}{4}}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{\frac{1}{4}}+1\right)}}\, \left(x^{\frac{1}{4}}+1\right)^{2} \sqrt{-\frac{x^{\frac{1}{4}}-\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \left(x^{\frac{1}{4}}+1\right)}}\, \sqrt{-\frac{x^{\frac{1}{4}}-\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{\frac{1}{4}}+1\right)}}\, \left(-\EllipticF \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x^{\frac{1}{4}}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{\frac{1}{4}}+1\right)}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)+\EllipticPi \left(\sqrt{\frac{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) x^{\frac{1}{4}}}{\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{\frac{1}{4}}+1\right)}}, \frac{\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}, \sqrt{\frac{\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right)}{\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right)}}\right)\right)}{\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{\left(x^{\frac{1}{4}}+1\right) \left(x^{\frac{1}{4}}-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \left(x^{\frac{1}{4}}-\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) x^{\frac{1}{4}}}}"," ",0,"2/3*x*(x^(1/4)+x)^(1/2)+1/3*x^(1/4)*(x^(1/4)+x)^(1/2)+(-1/2-1/2*I*3^(1/2))*((3/2+1/2*I*3^(1/2))*x^(1/4)/(1/2+1/2*I*3^(1/2))/(x^(1/4)+1))^(1/2)*(x^(1/4)+1)^2*(-(x^(1/4)-1/2+1/2*I*3^(1/2))/(1/2-1/2*I*3^(1/2))/(x^(1/4)+1))^(1/2)*(-(x^(1/4)-1/2-1/2*I*3^(1/2))/(1/2+1/2*I*3^(1/2))/(x^(1/4)+1))^(1/2)/(3/2+1/2*I*3^(1/2))/(x^(1/4)*(x^(1/4)+1)*(x^(1/4)-1/2+1/2*I*3^(1/2))*(x^(1/4)-1/2-1/2*I*3^(1/2)))^(1/2)*(-EllipticF(((3/2+1/2*I*3^(1/2))*x^(1/4)/(1/2+1/2*I*3^(1/2))/(x^(1/4)+1))^(1/2),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+EllipticPi(((3/2+1/2*I*3^(1/2))*x^(1/4)/(1/2+1/2*I*3^(1/2))/(x^(1/4)+1))^(1/2),(1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)),((-3/2+1/2*I*3^(1/2))*(-1/2-1/2*I*3^(1/2))/(-1/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)))","C"
931,1,28,37,0.008000," ","int((x+x^(3/2))^(1/2),x)","\frac{4 \sqrt{x^{\frac{3}{2}}+x}\, \left(\sqrt{x}+1\right) \left(15 x -12 \sqrt{x}+8\right)}{105 \sqrt{x}}"," ",0,"4/105*(x+x^(3/2))^(1/2)*(x^(1/2)+1)*(15*x-12*x^(1/2)+8)/x^(1/2)","A"
932,1,38,58,0.003000," ","int(x*(x^(3/2)+x)^(1/2),x)","\frac{4 \sqrt{x^{\frac{3}{2}}+x}\, \left(\sqrt{x}+1\right) \left(315 x^{2}-280 x^{\frac{3}{2}}+240 x -192 \sqrt{x}+128\right)}{3465 \sqrt{x}}"," ",0,"4/3465*(x^(3/2)+x)^(1/2)*(x^(1/2)+1)*(315*x^2-280*x^(3/2)+240*x-192*x^(1/2)+128)/x^(1/2)","A"
933,1,20,14,0.007000," ","int((-x^2+1)*(1/(-x^2+2))^(1/2),x)","-\frac{\left(x^{2}-2\right) \sqrt{-\frac{1}{x^{2}-2}}\, x}{2}"," ",0,"-1/2*(x^2-2)*x*(-1/(x^2-2))^(1/2)","A"
934,1,81,92,0.007000," ","int((-x^4+x^3+x^2)^(1/2),x)","-\frac{\sqrt{-x^{4}+x^{3}+x^{2}}\, \left(-12 \sqrt{-x^{2}+x +1}\, x -15 \arcsin \left(\frac{\left(2 x -1\right) \sqrt{5}}{5}\right)+16 \left(-x^{2}+x +1\right)^{\frac{3}{2}}+6 \sqrt{-x^{2}+x +1}\right)}{48 \sqrt{-x^{2}+x +1}\, x}"," ",0,"-1/48*(-x^4+x^3+x^2)^(1/2)*(16*(-x^2+x+1)^(3/2)-12*x*(-x^2+x+1)^(1/2)+6*(-x^2+x+1)^(1/2)-15*arcsin(1/5*(2*x-1)*5^(1/2)))/x/(-x^2+x+1)^(1/2)","A"
935,1,24,23,0.005000," ","int(1/((a^2+x^2)^3)^(1/2),x)","\frac{\left(a^{2}+x^{2}\right) x}{\sqrt{\left(a^{2}+x^{2}\right)^{3}}\, a^{2}}"," ",0,"x*(a^2+x^2)/a^2/((a^2+x^2)^3)^(1/2)","A"
936,1,34,33,0.004000," ","int(x^(1/2)/(x+x^(1/2)+1),x)","-\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 \sqrt{x}+1\right) \sqrt{3}}{3}\right)}{3}-\ln \left(x +\sqrt{x}+1\right)+2 \sqrt{x}"," ",0,"-ln(x+x^(1/2)+1)-2/3*arctan(1/3*(2*x^(1/2)+1)*3^(1/2))*3^(1/2)+2*x^(1/2)","A"
937,1,26,25,0.004000," ","int(x/(x+x^(1/2)+1),x)","x +\frac{4 \sqrt{3}\, \arctan \left(\frac{\left(2 \sqrt{x}+1\right) \sqrt{3}}{3}\right)}{3}-2 \sqrt{x}"," ",0,"x+4/3*3^(1/2)*arctan(1/3*(2*x^(1/2)+1)*3^(1/2))-2*x^(1/2)","A"
938,1,53,52,0.003000," ","int(1/x^(1/2)/(x+x^(1/2)+1)^(7/2),x)","\frac{\frac{8 \sqrt{x}}{15}+\frac{4}{15}}{\left(x +\sqrt{x}+1\right)^{\frac{5}{2}}}+\frac{\frac{128 \sqrt{x}}{135}+\frac{64}{135}}{\left(x +\sqrt{x}+1\right)^{\frac{3}{2}}}+\frac{\frac{1024 \sqrt{x}}{405}+\frac{512}{405}}{\sqrt{x +\sqrt{x}+1}}"," ",0,"4/15*(2*x^(1/2)+1)/(x+x^(1/2)+1)^(5/2)+64/135*(2*x^(1/2)+1)/(x+x^(1/2)+1)^(3/2)+512/405*(2*x^(1/2)+1)/(x+x^(1/2)+1)^(1/2)","A"
939,1,53,40,0.004000," ","int((x-1)/(1+(x^2+1)^(1/2)),x)","-\sqrt{x^{2}+1}\, x -\arcsinh \left(x \right)-\arctanh \left(\frac{1}{\sqrt{x^{2}+1}}\right)-\ln \left(x \right)-\frac{1}{x}+\frac{\left(x^{2}+1\right)^{\frac{3}{2}}}{x}+\sqrt{x^{2}+1}"," ",0,"-1/x+(x^2+1)^(1/2)-arctanh(1/(x^2+1)^(1/2))-ln(x)+(x^2+1)^(3/2)/x-(x^2+1)^(1/2)*x-arcsinh(x)","A"
940,1,18,14,0.004000," ","int(1/(x+1)^(2/3)/(x^2-1)^(2/3),x)","\frac{3 \left(x -1\right) \left(x +1\right)^{\frac{1}{3}}}{2 \left(x^{2}-1\right)^{\frac{2}{3}}}"," ",0,"3/2*(x-1)*(x+1)^(1/3)/(x^2-1)^(2/3)","A"
941,1,35,27,0.007000," ","int((-x^6+1)^(2/3)+(-x^6+1)^(2/3)/x^6,x)","\frac{\left(-x^{6}+1\right)^{\frac{2}{3}} \left(x^{2}-x +1\right) \left(x^{2}+x +1\right) \left(x +1\right) \left(x -1\right)}{5 x^{5}}"," ",0,"1/5*(-x^6+1)^(2/3)*(x^2-x+1)*(x^2+x+1)*(x+1)/x^5*(x-1)","A"
942,0,0,13,0.092000," ","int(1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(b*x^n+a)^(3/2),x)","\int \frac{\left(2 a m +\left(2 m -n \right) b \,x^{n}\right) x^{m -1}}{2 \left(b \,x^{n}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/2*x^(-1+m)*(2*a*m+b*(2*m-n)*x^n)/(b*x^n+a)^(3/2),x)","F"
943,1,25,37,0.004000," ","int((-2*x^3+x)/(3*x+2)^(1/2),x)","-\frac{2 \left(270 x^{3}-216 x^{2}-123 x +164\right) \sqrt{3 x +2}}{2835}"," ",0,"-2/2835*(270*x^3-216*x^2-123*x+164)*(3*x+2)^(1/2)","A"
944,1,26,25,0.015000," ","int(1/((x+1)^(1/4)+(x+1)^(1/2)),x)","4 \ln \left(1+\left(x +1\right)^{\frac{1}{4}}\right)-4 \left(x +1\right)^{\frac{1}{4}}+2 \sqrt{x +1}"," ",0,"-4*(x+1)^(1/4)+4*ln(1+(x+1)^(1/4))+2*(x+1)^(1/2)","A"
945,1,14,9,0.004000," ","int((2*x+1)/(x^2+x)^(1/2),x)","\frac{2 \left(x +1\right) x}{\sqrt{x^{2}+x}}"," ",0,"2*(x+1)*x/(x^2+x)^(1/2)","A"
946,1,5,4,0.004000," ","int(1/2/(x+1)/x^(1/2),x)","\arctan \left(\sqrt{x}\right)"," ",0,"arctan(x^(1/2))","A"
947,1,17,16,0.002000," ","int(1/x/(-x^2+6*x)^(1/2),x)","\frac{x -6}{3 \sqrt{-x^{2}+6 x}}"," ",0,"1/3*(x-6)/(-x^2+6*x)^(1/2)","A"
948,1,12,11,0.002000," ","int((x^(1/2)+1)*x^(1/2),x)","\frac{x^{2}}{2}+\frac{2 x^{\frac{3}{2}}}{3}"," ",0,"2/3*x^(3/2)+1/2*x^2","A"
949,1,12,11,0.001000," ","int((1-x^(1/2))/x^(1/3),x)","-\frac{6 x^{\frac{7}{6}}}{7}+\frac{3 x^{\frac{2}{3}}}{2}"," ",0,"3/2*x^(2/3)-6/7*x^(7/6)","A"
950,1,28,27,0.004000," ","int(x^(1/2)/(x^(1/3)+1),x)","\frac{6 x^{\frac{7}{6}}}{7}+6 \arctan \left(x^{\frac{1}{6}}\right)-\frac{6 x^{\frac{5}{6}}}{5}+2 \sqrt{x}-6 x^{\frac{1}{6}}"," ",0,"-6*x^(1/6)-6/5*x^(5/6)+6/7*x^(7/6)+6*arctan(x^(1/6))+2*x^(1/2)","A"
951,1,64,50,0.010000," ","int((x^(1/2)+1)^(1/3)/x,x)","-2 \sqrt{3}\, \arctan \left(\frac{\left(1+2 \left(\sqrt{x}+1\right)^{\frac{1}{3}}\right) \sqrt{3}}{3}\right)+2 \ln \left(\left(\sqrt{x}+1\right)^{\frac{1}{3}}-1\right)-\ln \left(\left(\sqrt{x}+1\right)^{\frac{2}{3}}+\left(\sqrt{x}+1\right)^{\frac{1}{3}}+1\right)+6 \left(\sqrt{x}+1\right)^{\frac{1}{3}}"," ",0,"6*(x^(1/2)+1)^(1/3)+2*ln((x^(1/2)+1)^(1/3)-1)-ln((x^(1/2)+1)^(2/3)+(x^(1/2)+1)^(1/3)+1)-2*arctan(1/3*(1+2*(x^(1/2)+1)^(1/3))*3^(1/2))*3^(1/2)","A"
952,1,8,7,0.001000," ","int(1-x^(1/2),x)","-\frac{2 x^{\frac{3}{2}}}{3}+x"," ",0,"-2/3*x^(3/2)+x","A"
953,1,8,7,0.002000," ","int(1-x^(1/4),x)","-\frac{4 x^{\frac{5}{4}}}{5}+x"," ",0,"x-4/5*x^(5/4)","A"
954,1,44,7,0.013000," ","int((1-x^(1/2))/(x^(1/4)+1),x)","-\frac{4 x^{\frac{5}{4}}}{5}+x -\ln \left(x -1\right)-\ln \left(\sqrt{x}-1\right)+\ln \left(\sqrt{x}+1\right)+2 \ln \left(x^{\frac{1}{4}}+1\right)+2 \ln \left(x^{\frac{1}{4}}-1\right)"," ",0,"-4/5*x^(5/4)+x+2*ln(x^(1/4)+1)+2*ln(x^(1/4)-1)-ln(x-1)-ln(x^(1/2)-1)+ln(x^(1/2)+1)","C"
955,1,49,49,0.008000," ","int(1/((b*x+a)*(d*x+c))^(1/2),x)","\frac{\ln \left(\frac{b d x +\frac{1}{2} a d +\frac{1}{2} b c}{\sqrt{b d}}+\sqrt{b d \,x^{2}+a c +\left(a d +b c \right) x}\right)}{\sqrt{b d}}"," ",0,"ln((1/2*a*d+1/2*b*c+b*d*x)/(b*d)^(1/2)+(a*c+(a*d+b*c)*x+b*d*x^2)^(1/2))/(b*d)^(1/2)","A"
956,1,55,53,0.013000," ","int(1/((b*x+a)*(-d*x+c))^(1/2),x)","\frac{\arctan \left(\frac{\sqrt{b d}\, \left(x -\frac{-a d +b c}{2 b d}\right)}{\sqrt{-b d \,x^{2}+a c +\left(-a d +b c \right) x}}\right)}{\sqrt{b d}}"," ",0,"1/(b*d)^(1/2)*arctan((b*d)^(1/2)*(x-1/2*(-a*d+b*c)/b/d)/(a*c+(-a*d+b*c)*x-b*d*x^2)^(1/2))","A"
957,1,10,9,0.007000," ","int(1/(-x^2+1)/x^(1/2),x)","\arctanh \left(\sqrt{x}\right)+\arctan \left(\sqrt{x}\right)"," ",0,"arctan(x^(1/2))+arctanh(x^(1/2))","A"
958,1,10,9,0.006000," ","int(x^(1/2)/(-x^3+x),x)","\arctanh \left(\sqrt{x}\right)+\arctan \left(\sqrt{x}\right)"," ",0,"arctan(x^(1/2))+arctanh(x^(1/2))","A"
959,1,82,51,0.022000," ","int(x/(2+x^2-3^(1/2)+x*(1+3^(1/2))),x)","\frac{\arctanh \left(\frac{2 x +1+\sqrt{3}}{\sqrt{-4+6 \sqrt{3}}}\right)}{\sqrt{-4+6 \sqrt{3}}}+\frac{\sqrt{3}\, \arctanh \left(\frac{2 x +1+\sqrt{3}}{\sqrt{-4+6 \sqrt{3}}}\right)}{\sqrt{-4+6 \sqrt{3}}}+\frac{\ln \left(x^{2}+\sqrt{3}\, x +x -\sqrt{3}+2\right)}{2}"," ",0,"1/2*ln(3^(1/2)*x+x^2-3^(1/2)+x+2)+1/(-4+6*3^(1/2))^(1/2)*arctanh((1+2*x+3^(1/2))/(-4+6*3^(1/2))^(1/2))+1/(-4+6*3^(1/2))^(1/2)*arctanh((1+2*x+3^(1/2))/(-4+6*3^(1/2))^(1/2))*3^(1/2)","A"
960,1,23,29,0.003000," ","int((x^3+x^2)^(1/2),x)","\frac{2 \left(x +1\right) \left(3 x -2\right) \sqrt{x^{3}+x^{2}}}{15 x}"," ",0,"2/15*(x+1)*(3*x-2)*(x^3+x^2)^(1/2)/x","A"
961,1,13,10,0.004000," ","int(1/(x+1)/(x^2+2*x)^(1/2),x)","-\arctan \left(\frac{1}{\sqrt{\left(x +1\right)^{2}-1}}\right)"," ",0,"-arctan(1/((x+1)^2-1)^(1/2))","A"
962,1,67,68,0.007000," ","int(x^(1/2)*(-x-x^(1/2)+1)^(1/2),x)","\frac{45 \arcsin \left(\frac{2 \sqrt{5}\, \left(\sqrt{x}+\frac{1}{2}\right)}{5}\right)}{64}-\frac{\left(-x -\sqrt{x}+1\right)^{\frac{3}{2}} \sqrt{x}}{2}+\frac{5 \left(-x -\sqrt{x}+1\right)^{\frac{3}{2}}}{12}-\frac{9 \left(-2 \sqrt{x}-1\right) \sqrt{-x -\sqrt{x}+1}}{32}"," ",0,"-1/2*(-x-x^(1/2)+1)^(3/2)*x^(1/2)+5/12*(-x-x^(1/2)+1)^(3/2)-9/32*(-2*x^(1/2)-1)*(-x-x^(1/2)+1)^(1/2)+45/64*arcsin(2/5*5^(1/2)*(x^(1/2)+1/2))","A"
963,1,24,23,0.002000," ","int((1+(x-3)^(1/2))^(1/3),x)","-\frac{3 \left(1+\sqrt{x -3}\right)^{\frac{4}{3}}}{2}+\frac{6 \left(1+\sqrt{x -3}\right)^{\frac{7}{3}}}{7}"," ",0,"-3/2*(1+(x-3)^(1/2))^(4/3)+6/7*(1+(x-3)^(1/2))^(7/3)","A"
964,1,28,27,0.005000," ","int(1/(3+(2*x-1)^(1/2))^(1/2),x)","\frac{2 \left(3+\sqrt{2 x -1}\right)^{\frac{3}{2}}}{3}-6 \sqrt{3+\sqrt{2 x -1}}"," ",0,"2/3*(3+(2*x-1)^(1/2))^(3/2)-6*(3+(2*x-1)^(1/2))^(1/2)","A"
965,1,48,23,0.008000," ","int((-x+1)^(1/2)/(x^(1/2)+1),x)","-\frac{\sqrt{-x +1}\, \left(\arcsin \left(2 x -1\right)-2 \sqrt{-\left(x -1\right) x}\right) \sqrt{x}}{2 \sqrt{-\left(x -1\right) x}}-2 \sqrt{-x +1}"," ",0,"-1/2*(-x+1)^(1/2)*x^(1/2)*(-2*(-x*(x-1))^(1/2)+arcsin(2*x-1))/(-x*(x-1))^(1/2)-2*(-x+1)^(1/2)","B"
966,1,48,19,0.007000," ","int((-x+1)^(1/2)/(1-x^(1/2)),x)","\frac{\sqrt{-x +1}\, \left(\arcsin \left(2 x -1\right)-2 \sqrt{-\left(x -1\right) x}\right) \sqrt{x}}{2 \sqrt{-\left(x -1\right) x}}-2 \sqrt{-x +1}"," ",0,"-2*(-x+1)^(1/2)+1/2*(-x+1)^(1/2)*(arcsin(2*x-1)-2*(-(x-1)*x)^(1/2))/(-(x-1)*x)^(1/2)*x^(1/2)","B"
967,1,16,15,0.003000," ","int(x/(x-(x^2+1)^(1/2)),x)","-\frac{x^{3}}{3}-\frac{\left(x^{2}+1\right)^{\frac{3}{2}}}{3}"," ",0,"-1/3*x^3-1/3*(x^2+1)^(3/2)","A"
968,1,175,45,0.019000," ","int(x/(x-(-x^2+1)^(1/2)),x)","\frac{x}{2}-\frac{\sqrt{2}\, \arctanh \left(\sqrt{2}\, x \right)}{4}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(1-\left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}\right) \sqrt{2}}{\sqrt{-4 \left(x -\frac{\sqrt{2}}{2}\right)^{2}-4 \left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}\right)}{8}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(\left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+1\right) \sqrt{2}}{\sqrt{-4 \left(x +\frac{\sqrt{2}}{2}\right)^{2}+4 \left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}\right)}{8}+\frac{\sqrt{-4 \left(x +\frac{\sqrt{2}}{2}\right)^{2}+4 \left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}{8}+\frac{\sqrt{-4 \left(x -\frac{\sqrt{2}}{2}\right)^{2}-4 \left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}{8}"," ",0,"1/2*x-1/4*arctanh(2^(1/2)*x)*2^(1/2)+1/8*(-4*(x+1/2*2^(1/2))^2+4*(x+1/2*2^(1/2))*2^(1/2)+2)^(1/2)-1/8*2^(1/2)*arctanh(((x+1/2*2^(1/2))*2^(1/2)+1)*2^(1/2)/(-4*(x+1/2*2^(1/2))^2+4*(x+1/2*2^(1/2))*2^(1/2)+2)^(1/2))+1/8*(-4*(x-1/2*2^(1/2))^2-4*(x-1/2*2^(1/2))*2^(1/2)+2)^(1/2)-1/8*2^(1/2)*arctanh((1-(x-1/2*2^(1/2))*2^(1/2))*2^(1/2)/(-4*(x-1/2*2^(1/2))^2-4*(x-1/2*2^(1/2))*2^(1/2)+2)^(1/2))","B"
969,1,28,27,0.010000," ","int(x/(x-(2*x^2+1)^(1/2)),x)","-x +\arctan \left(x \right)+\arctan \left(\sqrt{2 x^{2}+1}\right)-\sqrt{2 x^{2}+1}"," ",0,"-x+arctan(x)+arctan((2*x^2+1)^(1/2))-(2*x^2+1)^(1/2)","A"
970,1,54,52,0.004000," ","int(x^(1/2)*(x+x^(1/2))^(1/2),x)","-\frac{5 \ln \left(\sqrt{x}+\frac{1}{2}+\sqrt{x +\sqrt{x}}\right)}{64}+\frac{\left(x +\sqrt{x}\right)^{\frac{3}{2}} \sqrt{x}}{2}-\frac{5 \left(x +\sqrt{x}\right)^{\frac{3}{2}}}{12}+\frac{5 \left(2 \sqrt{x}+1\right) \sqrt{x +\sqrt{x}}}{32}"," ",0,"1/2*x^(1/2)*(x+x^(1/2))^(3/2)-5/12*(x+x^(1/2))^(3/2)+5/32*(2*x^(1/2)+1)*(x+x^(1/2))^(1/2)-5/64*ln(x^(1/2)+1/2+(x+x^(1/2))^(1/2))","A"
971,1,56,55,0.011000," ","int((x^(1/3)+1)/(x^(1/2)+1),x)","2 \sqrt{3}\, \arctan \left(\frac{\left(2 x^{\frac{1}{6}}-1\right) \sqrt{3}}{3}\right)-4 \ln \left(x^{\frac{1}{6}}+1\right)-\ln \left(x^{\frac{1}{3}}-x^{\frac{1}{6}}+1\right)+\frac{6 x^{\frac{5}{6}}}{5}+2 \sqrt{x}-3 x^{\frac{1}{3}}"," ",0,"6/5*x^(5/6)+2*x^(1/2)-3*x^(1/3)-ln(x^(1/3)-x^(1/6)+1)+2*3^(1/2)*arctan(1/3*(2*x^(1/6)-1)*3^(1/2))-4*ln(x^(1/6)+1)","A"
972,1,81,80,0.011000," ","int((x^(1/3)+1)/(x^(1/4)+1),x)","\frac{12 x^{\frac{13}{12}}}{13}-4 \sqrt{3}\, \arctan \left(\frac{\left(2 x^{\frac{1}{12}}-1\right) \sqrt{3}}{3}\right)-8 \ln \left(x^{\frac{1}{12}}+1\right)-2 \ln \left(x^{\frac{1}{6}}-x^{\frac{1}{12}}+1\right)-\frac{6 x^{\frac{5}{6}}}{5}+\frac{4 x^{\frac{3}{4}}}{3}+\frac{12 x^{\frac{7}{12}}}{7}-2 \sqrt{x}-3 x^{\frac{1}{3}}+4 x^{\frac{1}{4}}+12 x^{\frac{1}{12}}"," ",0,"12/13*x^(13/12)-6/5*x^(5/6)+4/3*x^(3/4)+12/7*x^(7/12)-2*x^(1/2)-3*x^(1/3)+4*x^(1/4)+12*x^(1/12)-2*ln(x^(1/6)-x^(1/12)+1)-4*3^(1/2)*arctan(1/3*(2*x^(1/12)-1)*3^(1/2))-8*ln(x^(1/12)+1)","A"
973,1,51,4,0.016000," ","int(x^2/(-1+x^2+(-x^2+1)^(1/2)),x)","x +\arctanh \left(x \right)+\arcsin \left(x \right)+\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}-\frac{\sqrt{-2 x -\left(x -1\right)^{2}+2}}{2}+\frac{\sqrt{2 x -\left(x +1\right)^{2}+2}}{2}"," ",0,"x+1/2*ln(x-1)-1/2*ln(x+1)+arctanh(x)-1/2*(-(x-1)^2-2*x+2)^(1/2)+arcsin(x)+1/2*(-(x+1)^2+2*x+2)^(1/2)","B"
974,1,41,18,0.005000," ","int(((x+1)/x)^(1/2),x)","\frac{\sqrt{\frac{x +1}{x}}\, \left(\ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)+2 \sqrt{x^{2}+x}\right) x}{2 \sqrt{\left(x +1\right) x}}"," ",0,"1/2*((x+1)/x)^(1/2)*x*(2*(x^2+x)^(1/2)+ln(x+1/2+(x^2+x)^(1/2)))/((x+1)*x)^(1/2)","B"
975,1,40,20,0.006000," ","int(((-x+1)/x)^(1/2),x)","\frac{\sqrt{-\frac{x -1}{x}}\, \left(\arcsin \left(2 x -1\right)+2 \sqrt{-x^{2}+x}\right) x}{2 \sqrt{-\left(x -1\right) x}}"," ",0,"1/2*(-(x-1)/x)^(1/2)*x*(2*(-x^2+x)^(1/2)+arcsin(2*x-1))/(-(x-1)*x)^(1/2)","A"
976,1,45,18,0.007000," ","int(((x-1)/x)^(1/2),x)","-\frac{\sqrt{\frac{x -1}{x}}\, \left(\ln \left(x -\frac{1}{2}+\sqrt{x^{2}-x}\right)-2 \sqrt{x^{2}-x}\right) x}{2 \sqrt{\left(x -1\right) x}}"," ",0,"-1/2*((x-1)/x)^(1/2)*x*(-2*(x^2-x)^(1/2)+ln(x-1/2+(x^2-x)^(1/2)))/((x-1)*x)^(1/2)","B"
977,1,60,20,0.008000," ","int(((x+1)/x)^(1/2)/x,x)","-\frac{\sqrt{\frac{x +1}{x}}\, \left(-x^{2} \ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)-2 \sqrt{x^{2}+x}\, x^{2}+2 \left(x^{2}+x \right)^{\frac{3}{2}}\right)}{\sqrt{\left(x +1\right) x}\, x}"," ",0,"-((x+1)/x)^(1/2)/x*(2*(x^2+x)^(3/2)-2*(x^2+x)^(1/2)*x^2-ln(x+1/2+(x^2+x)^(1/2))*x^2)/((x+1)*x)^(1/2)","B"
978,1,43,16,0.008000," ","int((1/(x+1)*x)^(1/2),x)","-\frac{\sqrt{\frac{x}{x +1}}\, \left(x +1\right) \left(\ln \left(x +\frac{1}{2}+\sqrt{x^{2}+x}\right)-2 \sqrt{x^{2}+x}\right)}{2 \sqrt{\left(x +1\right) x}}"," ",0,"-1/2*(1/(x+1)*x)^(1/2)*(x+1)*(-2*(x^2+x)^(1/2)+ln(x+1/2+(x^2+x)^(1/2)))/((x+1)*x)^(1/2)","B"
979,1,44,27,0.007000," ","int(1/((-1-x)/x)^(1/2),x)","\frac{\left(x +1\right) \left(\arcsin \left(2 x +1\right)+2 \sqrt{-x^{2}-x}\right)}{2 \sqrt{-\frac{x +1}{x}}\, \sqrt{-\left(x +1\right) x}}"," ",0,"1/2*(x+1)*(2*(-x^2-x)^(1/2)+arcsin(2*x+1))/(-(x+1)/x)^(1/2)/(-(x+1)*x)^(1/2)","A"
980,1,28,27,0.008000," ","int(((-x+4)*x)^(1/2),x)","2 \arcsin \left(\frac{x}{2}-1\right)-\frac{\left(-2 x +4\right) \sqrt{-x^{2}+4 x}}{4}"," ",0,"-1/4*(-2*x+4)*(-x^2+4*x)^(1/2)+2*arcsin(1/2*x-1)","A"
981,1,7,6,0.006000," ","int(1/((-x+1)*x)^(1/2),x)","\arcsin \left(2 x -1\right)"," ",0,"arcsin(2*x-1)","A"
982,1,15,11,0.005000," ","int(x/(x*(x+2))^(3/2),x)","\frac{\left(x +2\right) x^{2}}{\left(\left(x +2\right) x \right)^{\frac{3}{2}}}"," ",0,"x^2*(x+2)/(x*(x+2))^(3/2)","A"
983,1,41,17,0.019000," ","int((1+1/x)^(1/2)/(-x^2+1),x)","\frac{\sqrt{\frac{x +1}{x}}\, \sqrt{2}\, x \arctanh \left(\frac{\left(3 x +1\right) \sqrt{2}}{4 \sqrt{x^{2}+x}}\right)}{2 \sqrt{\left(x +1\right) x}}"," ",0,"1/2*((x+1)/x)^(1/2)*x/((x+1)*x)^(1/2)*2^(1/2)*arctanh(1/4*(3*x+1)*2^(1/2)/(x^2+x)^(1/2))","B"
984,1,32,12,0.027000," ","int(1/(1-x^2+5^(1/2)+5^(1/2)*x^2),x)","\frac{4 \arctan \left(\frac{4 x}{2+2 \sqrt{5}}\right)}{\left(\sqrt{5}-1\right) \left(2+2 \sqrt{5}\right)}"," ",0,"4/(5^(1/2)-1)/(2+2*5^(1/2))*arctan(4*x/(2+2*5^(1/2)))","B"
985,1,29,22,0.004000," ","int(1/(b*x^2+a*x)^(1/2),x)","\frac{\ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{\sqrt{b}}"," ",0,"ln((1/2*a+b*x)/b^(1/2)+(b*x^2+a*x)^(1/2))/b^(1/2)","A"
986,1,29,22,0.007000," ","int(1/(x*(b*x+a))^(1/2),x)","\frac{\ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{\sqrt{b}}"," ",0,"1/b^(1/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
987,1,29,22,0.007000," ","int(1/((b+a/x)*x^2)^(1/2),x)","\frac{\ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{\sqrt{b}}"," ",0,"1/b^(1/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
988,1,29,22,0.006000," ","int(1/((a/x^2+b/x)*x^3)^(1/2),x)","\frac{\ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{\sqrt{b}}"," ",0,"1/b^(1/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
989,1,29,22,0.006000," ","int(1/((b*x^3+a*x^2)/x)^(1/2),x)","\frac{\ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{\sqrt{b}}"," ",0,"1/b^(1/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
990,1,29,22,0.007000," ","int(1/((b*x^4+a*x^3)/x^2)^(1/2),x)","\frac{\ln \left(\frac{b x +\frac{a}{2}}{\sqrt{b}}+\sqrt{b \,x^{2}+a x}\right)}{\sqrt{b}}"," ",0,"1/b^(1/2)*ln((b*x+1/2*a)/b^(1/2)+(b*x^2+a*x)^(1/2))","A"
991,1,37,30,0.006000," ","int(1/(b*c*x^2+a*c*x)^(1/2),x)","\frac{\ln \left(\frac{b c x +\frac{1}{2} a c}{\sqrt{b c}}+\sqrt{b c \,x^{2}+a c x}\right)}{\sqrt{b c}}"," ",0,"ln((1/2*a*c+b*c*x)/(b*c)^(1/2)+(b*c*x^2+a*c*x)^(1/2))/(b*c)^(1/2)","A"
992,1,37,30,0.009000," ","int(1/(c*(b*x^2+a*x))^(1/2),x)","\frac{\ln \left(\frac{b c x +\frac{1}{2} a c}{\sqrt{b c}}+\sqrt{b c \,x^{2}+a c x}\right)}{\sqrt{b c}}"," ",0,"1/(b*c)^(1/2)*ln((b*c*x+1/2*a*c)/(b*c)^(1/2)+(b*c*x^2+a*c*x)^(1/2))","A"
993,1,37,30,0.006000," ","int(1/(c*x*(b*x+a))^(1/2),x)","\frac{\ln \left(\frac{b c x +\frac{1}{2} a c}{\sqrt{b c}}+\sqrt{b c \,x^{2}+a c x}\right)}{\sqrt{b c}}"," ",0,"1/(b*c)^(1/2)*ln((b*c*x+1/2*a*c)/(b*c)^(1/2)+(b*c*x^2+a*c*x)^(1/2))","A"
994,1,37,30,0.006000," ","int(1/(c*(b+a/x)*x^2)^(1/2),x)","\frac{\ln \left(\frac{b c x +\frac{1}{2} a c}{\sqrt{b c}}+\sqrt{b c \,x^{2}+a c x}\right)}{\sqrt{b c}}"," ",0,"1/(b*c)^(1/2)*ln((b*c*x+1/2*a*c)/(b*c)^(1/2)+(b*c*x^2+a*c*x)^(1/2))","A"
995,0,0,49,0.024000," ","int((1-x^2+(x^2-1)^(1/2)*x)^(1/2),x)","\int \sqrt{-x^{2}+\sqrt{x^{2}-1}\, x +1}\, dx"," ",0,"int((1-x^2+(x^2-1)^(1/2)*x)^(1/2),x)","F"
996,0,0,46,0.089000," ","int((-x+(x+1)^(1/2)*x^(1/2))^(1/2)/(x+1)^(1/2),x)","\int \frac{\sqrt{-x +\sqrt{x +1}\, \sqrt{x}}}{\sqrt{x +1}}\, dx"," ",0,"int((-x+(x+1)^(1/2)*x^(1/2))^(1/2)/(x+1)^(1/2),x)","F"
997,1,438,58,0.199000," ","int((-x-2*(x^2+1)^(1/2))/(x+x^3+(x^2+1)^(1/2)),x)","-\frac{x}{2}+\frac{3 \sqrt{5}\, \arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{10 \sqrt{-2+\sqrt{5}}}-\frac{\arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{2 \sqrt{-2+\sqrt{5}}}+\frac{2 \sqrt{5}\, \sqrt{-2+\sqrt{5}}\, \arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{5}+\frac{\arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{2 \sqrt{2+\sqrt{5}}}+\frac{\sqrt{5}\, \arctanh \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{2 \sqrt{2+\sqrt{5}}}-\frac{\sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{\sqrt{-2+2 \sqrt{5}}}+\frac{\arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{\sqrt{-2+2 \sqrt{5}}}-\frac{\arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{2 \sqrt{-2+\sqrt{5}}}+\frac{\sqrt{5}\, \arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{-2+\sqrt{5}}}\right)}{2 \sqrt{-2+\sqrt{5}}}+\frac{3 \sqrt{5}\, \arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{10 \sqrt{2+\sqrt{5}}}+\frac{\arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{2 \sqrt{2+\sqrt{5}}}-\frac{2 \sqrt{2+\sqrt{5}}\, \sqrt{5}\, \arctan \left(\frac{-x +\sqrt{x^{2}+1}}{\sqrt{2+\sqrt{5}}}\right)}{5}-\frac{\sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{\sqrt{2+2 \sqrt{5}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{\sqrt{2+2 \sqrt{5}}}-\frac{\sqrt{x^{2}+1}}{2}+\frac{1}{-2 x +2 \sqrt{x^{2}+1}}"," ",0,"-5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2*x/(2+2*5^(1/2))^(1/2))-1/(2+2*5^(1/2))^(1/2)*arctan(2*x/(2+2*5^(1/2))^(1/2))-5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2*x/(-2+2*5^(1/2))^(1/2))+1/(-2+2*5^(1/2))^(1/2)*arctanh(2*x/(-2+2*5^(1/2))^(1/2))-1/2*(x^2+1)^(1/2)-1/2*x-1/2/(-2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))+1/2*5^(1/2)/(-2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))+1/2/(2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))+1/2*5^(1/2)/(2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))+1/2/((x^2+1)^(1/2)-x)+3/10*5^(1/2)/(-2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))-1/2/(-2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))+3/10*5^(1/2)/(2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))+1/2/(2+5^(1/2))^(1/2)*arctan(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))+2/5*5^(1/2)*(-2+5^(1/2))^(1/2)*arctanh(((x^2+1)^(1/2)-x)/(-2+5^(1/2))^(1/2))-2/5*(2+5^(1/2))^(1/2)*5^(1/2)*arctan(((x^2+1)^(1/2)-x)/(2+5^(1/2))^(1/2))","B"
998,1,753,94,0.106000," ","int((2*x+1)/(x^2+1)/(x^2+2*x+2)^(1/2),x)","-\frac{\sqrt{\frac{10 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}-\frac{2 \sqrt{5}\, \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+10+2 \sqrt{5}}\, \left(20 \sqrt{5}\, \arctanh \left(\frac{\sqrt{\frac{10 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}-\frac{2 \sqrt{5}\, \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+10+2 \sqrt{5}}}{\sqrt{-10+10 \sqrt{5}}}\right)-60 \arctanh \left(\frac{\sqrt{\frac{10 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}-\frac{2 \sqrt{5}\, \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+10+2 \sqrt{5}}}{\sqrt{-10+10 \sqrt{5}}}\right)+5 \sqrt{-10+10 \sqrt{5}}\, \sqrt{-22+10 \sqrt{5}}\, \arctan \left(\frac{\sqrt{-22+10 \sqrt{5}}\, \sqrt{\left(5-\sqrt{5}\right) \left(\frac{2 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+\sqrt{5}+3\right)}\, \left(\frac{11 \sqrt{5}\, \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+\frac{25 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+4 \sqrt{5}+10\right) \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right) \left(\sqrt{5}-5\right)}{80 \left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \left(\frac{\left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{4}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{4}}+\frac{3 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+1\right)}\right)+3 \sqrt{-10+10 \sqrt{5}}\, \sqrt{5}\, \sqrt{-22+10 \sqrt{5}}\, \arctan \left(\frac{\sqrt{-22+10 \sqrt{5}}\, \sqrt{\left(5-\sqrt{5}\right) \left(\frac{2 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+\sqrt{5}+3\right)}\, \left(\frac{11 \sqrt{5}\, \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+\frac{25 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+4 \sqrt{5}+10\right) \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right) \left(\sqrt{5}-5\right)}{80 \left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right) \left(\frac{\left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{4}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{4}}+\frac{3 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}+1\right)}\right)\right)}{2 \sqrt{-\frac{2 \left(\frac{\sqrt{5}\, \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}-\frac{5 \left(x -\frac{\sqrt{5}}{2}+\frac{1}{2}\right)^{2}}{\left(-x -\frac{\sqrt{5}}{2}-\frac{1}{2}\right)^{2}}-\sqrt{5}-5\right)}{\left(\frac{x -\frac{\sqrt{5}}{2}+\frac{1}{2}}{-x -\frac{\sqrt{5}}{2}-\frac{1}{2}}+1\right)^{2}}}\, \left(\frac{x -\frac{\sqrt{5}}{2}+\frac{1}{2}}{-x -\frac{\sqrt{5}}{2}-\frac{1}{2}}+1\right) \left(\sqrt{5}-5\right) \sqrt{-10+10 \sqrt{5}}}"," ",0,"-1/2*(10*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+10+2*5^(1/2))^(1/2)*(5*arctan(1/80*(-22+10*5^(1/2))^(1/2)*((5-5^(1/2))*(2*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+5^(1/2)+3))^(1/2)*(11*5^(1/2)*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+25*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+4*5^(1/2)+10)*(-1/2*5^(1/2)+1/2+x)/(-1/2*5^(1/2)-1/2-x)*(5^(1/2)-5)/((-1/2*5^(1/2)+1/2+x)^4/(-1/2*5^(1/2)-1/2-x)^4+3*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+1))*(-10+10*5^(1/2))^(1/2)*(-22+10*5^(1/2))^(1/2)+3*arctan(1/80*(-22+10*5^(1/2))^(1/2)*((5-5^(1/2))*(2*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+5^(1/2)+3))^(1/2)*(11*5^(1/2)*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+25*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+4*5^(1/2)+10)*(-1/2*5^(1/2)+1/2+x)/(-1/2*5^(1/2)-1/2-x)*(5^(1/2)-5)/((-1/2*5^(1/2)+1/2+x)^4/(-1/2*5^(1/2)-1/2-x)^4+3*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+1))*(-10+10*5^(1/2))^(1/2)*5^(1/2)*(-22+10*5^(1/2))^(1/2)+20*arctanh((10*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+10+2*5^(1/2))^(1/2)/(-10+10*5^(1/2))^(1/2))*5^(1/2)-60*arctanh((10*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2-2*5^(1/2)*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2+10+2*5^(1/2))^(1/2)/(-10+10*5^(1/2))^(1/2)))/(-2*(5^(1/2)*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2-5*(-1/2*5^(1/2)+1/2+x)^2/(-1/2*5^(1/2)-1/2-x)^2-5^(1/2)-5)/((-1/2*5^(1/2)+1/2+x)/(-1/2*5^(1/2)-1/2-x)+1)^2)^(1/2)/((-1/2*5^(1/2)+1/2+x)/(-1/2*5^(1/2)-1/2-x)+1)/(5^(1/2)-5)/(-10+10*5^(1/2))^(1/2)","B"
999,0,0,18,0.084000," ","int(1/(x^4+1)/(-x^2+(x^4+1)^(1/2))^(1/2),x)","\int \frac{1}{\left(x^{4}+1\right) \sqrt{-x^{2}+\sqrt{x^{4}+1}}}\, dx"," ",0,"int(1/(x^4+1)/(-x^2+(x^4+1)^(1/2))^(1/2),x)","F"
1000,0,0,32,0.090000," ","int(1/(b*x^4+a)/(c*x^2+d*(b*x^4+a)^(1/2))^(1/2),x)","\int \frac{1}{\left(b \,x^{4}+a \right) \sqrt{c \,x^{2}+\sqrt{b \,x^{4}+a}\, d}}\, dx"," ",0,"int(1/(b*x^4+a)/(c*x^2+d*(b*x^4+a)^(1/2))^(1/2),x)","F"
1001,0,0,33,0.083000," ","int(1/(b*x^4+a)/(-c*x^2+(b*x^4+a)^(1/2)*d)^(1/2),x)","\int \frac{1}{\left(b \,x^{4}+a \right) \sqrt{-c \,x^{2}+\sqrt{b \,x^{4}+a}\, d}}\, dx"," ",0,"int(1/(b*x^4+a)/(-c*x^2+(b*x^4+a)^(1/2)*d)^(1/2),x)","F"
1002,1,1528,195,0.425000," ","int(x/(b*d^4*x^4+4*b*c*d^3*x^3+6*b*c^2*d^2*x^2+4*b*c^3*d*x+b*c^4+a)^(1/2),x)","\frac{2 \left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \sqrt{\frac{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\, \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)^{2} \sqrt{\frac{\left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\, \sqrt{\frac{\left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\, \left(\left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \EllipticPi \left(\sqrt{\frac{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}, \frac{\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}}{\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}}, \sqrt{\frac{\left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\right)+\frac{\left(-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}\right) \EllipticF \left(\sqrt{\frac{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}, \sqrt{\frac{\left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\right)}{d}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \sqrt{\left(x -\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) b \,d^{4}}}"," ",0,"2*((1/b*(-a*b^3)^(1/4)-c)/d-(-I/b*(-a*b^3)^(1/4)-c)/d)*(((-I/b*(-a*b^3)^(1/4)-c)/d-(I/b*(-a*b^3)^(1/4)-c)/d)*(x-(1/b*(-a*b^3)^(1/4)-c)/d)/((-I/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)/(x-(I/b*(-a*b^3)^(1/4)-c)/d))^(1/2)*(x-(I/b*(-a*b^3)^(1/4)-c)/d)^2*(((I/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)*(x-(-1/b*(-a*b^3)^(1/4)-c)/d)/((-1/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)/(x-(I/b*(-a*b^3)^(1/4)-c)/d))^(1/2)*(((I/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)*(x-(-I/b*(-a*b^3)^(1/4)-c)/d)/((-I/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)/(x-(I/b*(-a*b^3)^(1/4)-c)/d))^(1/2)/((-I/b*(-a*b^3)^(1/4)-c)/d-(I/b*(-a*b^3)^(1/4)-c)/d)/((I/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)/(b*d^4*(x-(1/b*(-a*b^3)^(1/4)-c)/d)*(x-(I/b*(-a*b^3)^(1/4)-c)/d)*(x-(-1/b*(-a*b^3)^(1/4)-c)/d)*(x-(-I/b*(-a*b^3)^(1/4)-c)/d))^(1/2)*((I/b*(-a*b^3)^(1/4)-c)/d*EllipticF((((-I/b*(-a*b^3)^(1/4)-c)/d-(I/b*(-a*b^3)^(1/4)-c)/d)*(x-(1/b*(-a*b^3)^(1/4)-c)/d)/((-I/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)/(x-(I/b*(-a*b^3)^(1/4)-c)/d))^(1/2),(((I/b*(-a*b^3)^(1/4)-c)/d-(-1/b*(-a*b^3)^(1/4)-c)/d)*((1/b*(-a*b^3)^(1/4)-c)/d-(-I/b*(-a*b^3)^(1/4)-c)/d)/((1/b*(-a*b^3)^(1/4)-c)/d-(-1/b*(-a*b^3)^(1/4)-c)/d)/((I/b*(-a*b^3)^(1/4)-c)/d-(-I/b*(-a*b^3)^(1/4)-c)/d))^(1/2))+((1/b*(-a*b^3)^(1/4)-c)/d-(I/b*(-a*b^3)^(1/4)-c)/d)*EllipticPi((((-I/b*(-a*b^3)^(1/4)-c)/d-(I/b*(-a*b^3)^(1/4)-c)/d)*(x-(1/b*(-a*b^3)^(1/4)-c)/d)/((-I/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)/(x-(I/b*(-a*b^3)^(1/4)-c)/d))^(1/2),((-I/b*(-a*b^3)^(1/4)-c)/d-(1/b*(-a*b^3)^(1/4)-c)/d)/((-I/b*(-a*b^3)^(1/4)-c)/d-(I/b*(-a*b^3)^(1/4)-c)/d),(((I/b*(-a*b^3)^(1/4)-c)/d-(-1/b*(-a*b^3)^(1/4)-c)/d)*((1/b*(-a*b^3)^(1/4)-c)/d-(-I/b*(-a*b^3)^(1/4)-c)/d)/((1/b*(-a*b^3)^(1/4)-c)/d-(-1/b*(-a*b^3)^(1/4)-c)/d)/((I/b*(-a*b^3)^(1/4)-c)/d-(-I/b*(-a*b^3)^(1/4)-c)/d))^(1/2)))","C"
1003,1,1036,150,0.065000," ","int(1/(b*d^4*x^4+4*b*c*d^3*x^3+6*b*c^2*d^2*x^2+4*b*c^3*d*x+b*c^4+a)^(1/2),x)","\frac{2 \left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \sqrt{\frac{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\, \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)^{2} \sqrt{\frac{\left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\, \sqrt{\frac{\left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\, \EllipticF \left(\sqrt{\frac{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}, \sqrt{\frac{\left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}{\left(\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right)}}\right)}{\left(\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}-\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \sqrt{\left(x -\frac{-c +\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c +\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c -\frac{\left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) \left(x -\frac{-c -\frac{i \left(-a \,b^{3}\right)^{\frac{1}{4}}}{b}}{d}\right) b \,d^{4}}}"," ",0,"2*((-c+(-a*b^3)^(1/4)/b)/d-(-c-I*(-a*b^3)^(1/4)/b)/d)*(((-c-I*(-a*b^3)^(1/4)/b)/d-(-c+I*(-a*b^3)^(1/4)/b)/d)*(x-(-c+(-a*b^3)^(1/4)/b)/d)/((-c-I*(-a*b^3)^(1/4)/b)/d-(-c+(-a*b^3)^(1/4)/b)/d)/(x-(-c+I*(-a*b^3)^(1/4)/b)/d))^(1/2)*(x-(-c+I*(-a*b^3)^(1/4)/b)/d)^2*(((-c+I*(-a*b^3)^(1/4)/b)/d-(-c+(-a*b^3)^(1/4)/b)/d)*(x-(-c-(-a*b^3)^(1/4)/b)/d)/((-c-(-a*b^3)^(1/4)/b)/d-(-c+(-a*b^3)^(1/4)/b)/d)/(x-(-c+I*(-a*b^3)^(1/4)/b)/d))^(1/2)*(((-c+I*(-a*b^3)^(1/4)/b)/d-(-c+(-a*b^3)^(1/4)/b)/d)*(x-(-c-I*(-a*b^3)^(1/4)/b)/d)/((-c-I*(-a*b^3)^(1/4)/b)/d-(-c+(-a*b^3)^(1/4)/b)/d)/(x-(-c+I*(-a*b^3)^(1/4)/b)/d))^(1/2)/((-c-I*(-a*b^3)^(1/4)/b)/d-(-c+I*(-a*b^3)^(1/4)/b)/d)/((-c+I*(-a*b^3)^(1/4)/b)/d-(-c+(-a*b^3)^(1/4)/b)/d)/((x-(-c+(-a*b^3)^(1/4)/b)/d)*(x-(-c+I*(-a*b^3)^(1/4)/b)/d)*(x-(-c-(-a*b^3)^(1/4)/b)/d)*(x-(-c-I*(-a*b^3)^(1/4)/b)/d)*b*d^4)^(1/2)*EllipticF((((-c-I*(-a*b^3)^(1/4)/b)/d-(-c+I*(-a*b^3)^(1/4)/b)/d)*(x-(-c+(-a*b^3)^(1/4)/b)/d)/((-c-I*(-a*b^3)^(1/4)/b)/d-(-c+(-a*b^3)^(1/4)/b)/d)/(x-(-c+I*(-a*b^3)^(1/4)/b)/d))^(1/2),(((-c+I*(-a*b^3)^(1/4)/b)/d-(-c-(-a*b^3)^(1/4)/b)/d)*((-c+(-a*b^3)^(1/4)/b)/d-(-c-I*(-a*b^3)^(1/4)/b)/d)/((-c+(-a*b^3)^(1/4)/b)/d-(-c-(-a*b^3)^(1/4)/b)/d)/((-c+I*(-a*b^3)^(1/4)/b)/d-(-c-I*(-a*b^3)^(1/4)/b)/d))^(1/2))","C"
1004,1,514,44,0.093000," ","int((-c*x^4+a)/(c*d*x^4+a*e*x^2+a*d)/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{a \left(-\RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} e -2 d \right) \left(-\frac{\arctanh \left(\frac{2 \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} c \,x^{2}+b \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2}+b \,x^{2}+2 a}{2 \sqrt{\frac{\left(-a e +b d \right) \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2}}{d}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}\right)}{\sqrt{\frac{\left(-a e +b d \right) \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2}}{d}}}+\frac{\sqrt{2}\, \left(\RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} c d +a e \right) \sqrt{\frac{b \,x^{2}}{a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{a}+2}\, \sqrt{\frac{b \,x^{2}}{a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{a}+2}\, \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right) \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} b c d +\sqrt{-4 a c +b^{2}}\, \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} c d +a b e +\sqrt{-4 a c +b^{2}}\, a e}{2 a c d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, a d}\right)}{4 d \left(2 \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} c d +a e \right) \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d}"," ",0,"-1/4/d*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-1/4*a/d*sum((-_alpha^2*e-2*d)/_alpha/(2*_alpha^2*c*d+a*e)*(-1/(_alpha^2/d*(-a*e+b*d))^(1/2)*arctanh(1/2*(2*_alpha^2*c*x^2+_alpha^2*b+b*x^2+2*a)/(_alpha^2/d*(-a*e+b*d))^(1/2)/(c*x^4+b*x^2+a)^(1/2))+1/a/d*2^(1/2)*_alpha*(_alpha^2*c*d+a*e)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(2+b*x^2/a-1/a*x^2*(-4*a*c+b^2)^(1/2))^(1/2)*(2+b*x^2/a+1/a*x^2*(-4*a*c+b^2)^(1/2))^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(_alpha^2*(-4*a*c+b^2)^(1/2)*c*d+_alpha^2*b*c*d+(-4*a*c+b^2)^(1/2)*a*e+a*b*e)/a/d/c,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))),_alpha=RootOf(_Z^4*c*d+_Z^2*a*e+a*d))","C"
1005,1,517,43,0.076000," ","int((-c*x^4+a)/(c*d*x^4+a*e*x^2+a*d)/(c*x^4-b*x^2+a)^(1/2),x)","-\frac{a \left(-\RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} e -2 d \right) \left(-\frac{\arctanh \left(\frac{2 \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} c \,x^{2}-b \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2}-b \,x^{2}+2 a}{2 \sqrt{-\frac{\left(a e +b d \right) \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2}}{d}}\, \sqrt{c \,x^{4}-b \,x^{2}+a}}\right)}{\sqrt{-\frac{\left(a e +b d \right) \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2}}{d}}}+\frac{\sqrt{2}\, \left(\RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} c d +a e \right) \sqrt{-\frac{b \,x^{2}}{a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{a}+2}\, \sqrt{-\frac{b \,x^{2}}{a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{a}+2}\, \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right) \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{\RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} b c d -\sqrt{-4 a c +b^{2}}\, \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} c d +a b e -\sqrt{-4 a c +b^{2}}\, a e}{2 a c d}, \frac{\sqrt{-\frac{-b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}-b \,x^{2}+a}\, a d}\right)}{4 d \left(2 \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)^{2} c d +a e \right) \RootOf \left(c d \,\textit{\_Z}^{4}+a e \,\textit{\_Z}^{2}+a d \right)}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}-b \,x^{2}+a}\, d}"," ",0,"-1/4/d*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4-b*x^2+a)^(1/2)*EllipticF(1/2*x*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4-2*b*(-b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-1/4*a/d*sum((-_alpha^2*e-2*d)/_alpha/(2*_alpha^2*c*d+a*e)*(-1/(-_alpha^2*(a*e+b*d)/d)^(1/2)*arctanh(1/2*(2*_alpha^2*c*x^2-_alpha^2*b-b*x^2+2*a)/(-_alpha^2*(a*e+b*d)/d)^(1/2)/(c*x^4-b*x^2+a)^(1/2))+1/a/d*2^(1/2)*_alpha*(_alpha^2*c*d+a*e)/((b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(2-1/a*b*x^2-(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(2-1/a*b*x^2+(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(c*x^4-b*x^2+a)^(1/2)*EllipticPi(1/2*x*2^(1/2)*((b+(-4*a*c+b^2)^(1/2))/a)^(1/2),-1/2*(-(-4*a*c+b^2)^(1/2)*_alpha^2*c*d+_alpha^2*b*c*d-(-4*a*c+b^2)^(1/2)*a*e+a*b*e)/a/d/c,(-1/2*(-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))/a)^(1/2))),_alpha=RootOf(_Z^4*c*d+_Z^2*a*e+a*d))","C"
1006,1,69,66,0.032000," ","int(1/(x^3+8)/(x^2-2*x+5)^(1/2),x)","\frac{\arctanh \left(\sqrt{x^{2}-2 x +5}\right)}{12}-\frac{\sqrt{13}\, \arctanh \left(\frac{\left(-6 x +14\right) \sqrt{13}}{26 \sqrt{-6 x +\left(x +2\right)^{2}+1}}\right)}{156}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(2 x -2\right)}{6 \sqrt{x^{2}-2 x +5}}\right)}{12}"," ",0,"-1/156*13^(1/2)*arctanh(1/26*(14-6*x)*13^(1/2)/((x+2)^2-6*x+1)^(1/2))+1/12*arctanh((x^2-2*x+5)^(1/2))+1/12*3^(1/2)*arctan(1/6*3^(1/2)/(x^2-2*x+5)^(1/2)*(2*x-2))","A"
1007,1,23,16,0.004000," ","int((x^2/(x^2+1))^(1/2),x)","\frac{\left(x^{2}+1\right) \sqrt{\frac{x^{2}}{x^{2}+1}}}{x}"," ",0,"(x^2+1)/x*(x^2/(x^2+1))^(1/2)","A"
1008,0,0,32,0.030000," ","int((x^n/(x^n+1))^(1/2),x)","\int \sqrt{\frac{x^{n}}{x^{n}+1}}\, dx"," ",0,"int((x^n/(x^n+1))^(1/2),x)","F"
1009,1,242984,80,0.165000," ","int((-e*f*x^2+e*f)/(a*d*x^2+b*d*x+a*d)/(a*x^4+b*x^3+c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
1010,1,269221,80,0.164000," ","int((-e*f*x^2+e*f)/(-a*d*x^2+b*d*x-a*d)/(-a*x^4+b*x^3+c*x^2+b*x-a)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","C"
1011,0,0,38,0.089000," ","int((a*x^2+b*x*(-a/b^2+a^2/b^2*x^2)^(1/2))^(1/2)/x/(-a/b^2+a^2/b^2*x^2)^(1/2),x)","\int \frac{\sqrt{a \,x^{2}+\sqrt{\frac{a^{2} x^{2}}{b^{2}}-\frac{a}{b^{2}}}\, b x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}}-\frac{a}{b^{2}}}\, x}\, dx"," ",0,"int((a*x^2+b*x*(-a/b^2+a^2/b^2*x^2)^(1/2))^(1/2)/x/(-a/b^2+a^2/b^2*x^2)^(1/2),x)","F"
1012,0,0,38,0.089000," ","int((-a*x^2+b*x*(a/b^2+a^2/b^2*x^2)^(1/2))^(1/2)/x/(a/b^2+a^2/b^2*x^2)^(1/2),x)","\int \frac{\sqrt{-a \,x^{2}+\sqrt{\frac{a^{2} x^{2}}{b^{2}}+\frac{a}{b^{2}}}\, b x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+\frac{a}{b^{2}}}\, x}\, dx"," ",0,"int((-a*x^2+b*x*(a/b^2+a^2/b^2*x^2)^(1/2))^(1/2)/x/(a/b^2+a^2/b^2*x^2)^(1/2),x)","F"
1013,0,0,38,0.068000," ","int((x*(a*x+b*(a^2/b^2*x^2-a/b^2)^(1/2)))^(1/2)/x/(a^2/b^2*x^2-a/b^2)^(1/2),x)","\int \frac{\sqrt{\left(a x +\sqrt{\frac{a^{2} x^{2}}{b^{2}}-\frac{a}{b^{2}}}\, b \right) x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}}-\frac{a}{b^{2}}}\, x}\, dx"," ",0,"int((x*(a*x+b*(a^2/b^2*x^2-a/b^2)^(1/2)))^(1/2)/x/(a^2/b^2*x^2-a/b^2)^(1/2),x)","F"
1014,0,0,38,0.068000," ","int((x*((a^2/b^2*x^2+a/b^2)^(1/2)*b-a*x))^(1/2)/x/(a^2/b^2*x^2+a/b^2)^(1/2),x)","\int \frac{\sqrt{\left(-a x +\sqrt{\frac{a^{2} x^{2}}{b^{2}}+\frac{a}{b^{2}}}\, b \right) x}}{\sqrt{\frac{a^{2} x^{2}}{b^{2}}+\frac{a}{b^{2}}}\, x}\, dx"," ",0,"int((x*((a^2/b^2*x^2+a/b^2)^(1/2)*b-a*x))^(1/2)/x/(a^2/b^2*x^2+a/b^2)^(1/2),x)","F"
1015,1,147,15,0.056000," ","int((-(x-4)^(1/2)+x*(x-4)^(1/2)-4*(x-1)^(1/2)+x*(x-1)^(1/2))/(x^2-5*x+4)/(1+(x-4)^(1/2)+(x-1)^(1/2)),x)","\frac{7 \sqrt{x -4}\, \sqrt{x -1}\, \arctanh \left(\frac{5 x -17}{4 \sqrt{x^{2}-5 x +4}}\right)}{4 \sqrt{x^{2}-5 x +4}}+\frac{\ln \left(x -5\right)}{2}-\frac{\ln \left(-2+\sqrt{x -1}\right)}{2}+\frac{\ln \left(-1+\sqrt{x -4}\right)}{2}-\frac{\ln \left(1+\sqrt{x -4}\right)}{2}+\frac{\ln \left(\sqrt{x -1}+2\right)}{2}+\frac{\sqrt{x -4}\, \sqrt{x -1}\, \left(-5 \arctanh \left(\frac{5 x -17}{4 \sqrt{x^{2}-5 x +4}}\right)+2 \ln \left(x -\frac{5}{2}+\sqrt{x^{2}-5 x +4}\right)\right)}{4 \sqrt{x^{2}-5 x +4}}"," ",0,"1/2*ln(x-5)+1/2*ln(-1+(x-4)^(1/2))-1/2*ln(1+(x-4)^(1/2))-1/2*ln(-2+(x-1)^(1/2))+1/2*ln((x-1)^(1/2)+2)+7/4*(x-4)^(1/2)*(x-1)^(1/2)/(x^2-5*x+4)^(1/2)*arctanh(1/4*(-17+5*x)/(x^2-5*x+4)^(1/2))+1/4*(x-4)^(1/2)*(x-1)^(1/2)*(2*ln(-5/2+x+(x^2-5*x+4)^(1/2))-5*arctanh(1/4*(-17+5*x)/(x^2-5*x+4)^(1/2)))/(x^2-5*x+4)^(1/2)","B"
1016,1,2515,71,13.667000," ","int(1/x/(x^2+3*x+3)/(x^3+3*x^2+3*x+3)^(1/3),x)","\text{Expression too large to display}"," ",0,"RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*ln((114324537294*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)+4470714138*RootOf(_Z^3-9)+15589709631*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+609642837*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^2+97002637704*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3+291007913112*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2+291007913112*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x+3793333208*RootOf(_Z^3-9)*x^3+11379999624*RootOf(_Z^3-9)*x^2+11379999624*RootOf(_Z^3-9)*x+15322002984*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(2/3)*x+5196569877*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+203214279*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3+2837496903*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)+8512490709*(x^3+3*x^2+3*x+3)^(2/3)*x+8512490709*(x^3+3*x^2+3*x+3)^(2/3)+45966008952*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x^2+91932017904*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x+15322002984*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(2/3)+2837496903*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x^2+5674993806*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x+45966008952*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)+609642837*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x+15589709631*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x-36375989139*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2-1422499953*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3)/x/(x^2+3*x+3))-1/9*ln((-150700526433*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)-10851288846*RootOf(_Z^3-9)+15589709631*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+1122547122*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^2-91806067827*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-275418203481*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2-275418203481*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x-6610555274*RootOf(_Z^3-9)*x^3-19831665822*RootOf(_Z^3-9)*x^2-19831665822*RootOf(_Z^3-9)*x-15322002984*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(2/3)*x+5196569877*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+374182374*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3-2269837425*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)-6809512275*(x^3+3*x^2+3*x+3)^(2/3)*x-6809512275*(x^3+3*x^2+3*x+3)^(2/3)-45966008952*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x^2-91932017904*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x-15322002984*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(2/3)-2269837425*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x^2-4539674850*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x-45966008952*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)+1122547122*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x+15589709631*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x-36375989139*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2-2619276618*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3)/x/(x^2+3*x+3))*RootOf(_Z^3-9)-ln((-150700526433*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)-10851288846*RootOf(_Z^3-9)+15589709631*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^2+1122547122*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^2-91806067827*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^3-275418203481*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x^2-275418203481*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*x-6610555274*RootOf(_Z^3-9)*x^3-19831665822*RootOf(_Z^3-9)*x^2-19831665822*RootOf(_Z^3-9)*x-15322002984*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(2/3)*x+5196569877*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x^3+374182374*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x^3-2269837425*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)-6809512275*(x^3+3*x^2+3*x+3)^(2/3)*x-6809512275*(x^3+3*x^2+3*x+3)^(2/3)-45966008952*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x^2-91932017904*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)*x-15322002984*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(2/3)-2269837425*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x^2-4539674850*RootOf(_Z^3-9)^2*(x^3+3*x^2+3*x+3)^(1/3)*x-45966008952*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)*(x^3+3*x^2+3*x+3)^(1/3)+1122547122*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3*x+15589709631*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2*x-36375989139*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)^2*RootOf(_Z^3-9)^2-2619276618*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)*RootOf(_Z^3-9)^3)/x/(x^2+3*x+3))*RootOf(RootOf(_Z^3-9)^2+9*_Z*RootOf(_Z^3-9)+81*_Z^2)","C"
1017,1,1026,83,8.030000," ","int((-x^2+1)/(x^2-x+1)/(-x^3+1)^(2/3),x)","-\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(\frac{4 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}+2 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{4}-2 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)+3 x \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \left(-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{3}-2\right)-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)+2 \left(-x^{3}+1\right)^{\frac{2}{3}}}{x^{2}-x +1}\right)-\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{4 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}+2 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{4}-2 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)+3 x \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \left(-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-2 \left(-x^{3}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{3}-2\right)-2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)+2 \left(-x^{3}+1\right)^{\frac{2}{3}}}{x^{2}-x +1}\right)}{2}+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(-\frac{4 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}+2 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{4}+2 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-2 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-x \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 \left(-x^{3}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-4 \left(-x^{3}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-2 \left(-x^{3}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{3}-2\right)+2 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+4 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+2 \left(-x^{3}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)}{x^{2}-x +1}\right)}{2}"," ",0,"1/2*RootOf(_Z^3-2)*ln(-(2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x+2*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2+RootOf(_Z^3-2)^2*x^2+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2-RootOf(_Z^3-2)^2*x-2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-2*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*x-4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*(-x^3+1)^(1/3)*x+RootOf(_Z^3-2)^2+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+2*(-x^3+1)^(1/3)*RootOf(_Z^3-2)+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*(-x^3+1)^(1/3))/(x^2-x+1))-1/2*ln((2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x+2*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-RootOf(_Z^3-2)^2*x^2-2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2+3*RootOf(_Z^3-2)^2*x+6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-2*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*x-RootOf(_Z^3-2)^2-2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+2*(-x^3+1)^(1/3)*RootOf(_Z^3-2)+2*(-x^3+1)^(2/3))/(x^2-x+1))*RootOf(_Z^3-2)-ln((2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^4*x+4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^3*x+2*(-x^3+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-RootOf(_Z^3-2)^2*x^2-2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x^2+3*RootOf(_Z^3-2)^2*x+6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-2*(-x^3+1)^(1/3)*RootOf(_Z^3-2)*x-RootOf(_Z^3-2)^2-2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+2*(-x^3+1)^(1/3)*RootOf(_Z^3-2)+2*(-x^3+1)^(2/3))/(x^2-x+1))*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)","C"
1018,1,88,41,0.026000," ","int(x^2/(x^4+1)/(x^4-1)^(1/2),x)","-\frac{\arctan \left(-\frac{\sqrt{x^{4}-1}}{x}+1\right)}{8}+\frac{\arctan \left(\frac{\sqrt{x^{4}-1}}{x}+1\right)}{8}+\frac{\ln \left(\frac{\frac{\sqrt{x^{4}-1}}{x}+\frac{x^{4}-1}{2 x^{2}}+1}{-\frac{\sqrt{x^{4}-1}}{x}+\frac{x^{4}-1}{2 x^{2}}+1}\right)}{16}"," ",0,"1/8*arctan((x^4-1)^(1/2)/x+1)-1/8*arctan(-(x^4-1)^(1/2)/x+1)+1/16*ln((1/2*(x^4-1)/x^2+(x^4-1)^(1/2)/x+1)/(1/2*(x^4-1)/x^2-(x^4-1)^(1/2)/x+1))","B"
1019,1,555,66,0.086000," ","int((-c*x^4+a)/(c*d*x^2+a*e)/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d e}+\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d e}+\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 c d}{\left(-b +\sqrt{-4 a c +b^{2}}\right) e}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d e}"," ",0,"-1/4/d/e*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/d/e*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(1+1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*c*d/e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))+1/e/d*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(1+1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a*e/d,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))","C"
1020,1,2,1,0.001000," ","int(x+(-x^2+1)/(x+1),x)","x"," ",0,"x","A"
1021,1,234,89,0.042000," ","int(1/(1/x+(-x^2+1)^(1/2)),x)","-2 \arctan \left(\frac{-1+\sqrt{-x^{2}+1}}{x}\right)+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{3}-\frac{i \sqrt{3}\, \ln \left(\frac{\left(-1-i \sqrt{3}\right) \left(-1+\sqrt{-x^{2}+1}\right)}{x}+\frac{\left(-1+\sqrt{-x^{2}+1}\right)^{2}}{x^{2}}-1\right)}{6}-\frac{i \sqrt{3}\, \ln \left(\frac{\left(1-i \sqrt{3}\right) \left(-1+\sqrt{-x^{2}+1}\right)}{x}+\frac{\left(-1+\sqrt{-x^{2}+1}\right)^{2}}{x^{2}}-1\right)}{6}+\frac{i \sqrt{3}\, \ln \left(\frac{\left(1+i \sqrt{3}\right) \left(-1+\sqrt{-x^{2}+1}\right)}{x}+\frac{\left(-1+\sqrt{-x^{2}+1}\right)^{2}}{x^{2}}-1\right)}{6}+\frac{i \sqrt{3}\, \ln \left(\frac{\left(i \sqrt{3}-1\right) \left(-1+\sqrt{-x^{2}+1}\right)}{x}+\frac{\left(-1+\sqrt{-x^{2}+1}\right)^{2}}{x^{2}}-1\right)}{6}"," ",0,"1/6*I*3^(1/2)*ln((-1+(-x^2+1)^(1/2))^2/x^2+(1+I*3^(1/2))*(-1+(-x^2+1)^(1/2))/x-1)-1/6*I*3^(1/2)*ln((-1+(-x^2+1)^(1/2))^2/x^2+(1-I*3^(1/2))*(-1+(-x^2+1)^(1/2))/x-1)-2*arctan((-1+(-x^2+1)^(1/2))/x)+1/6*I*3^(1/2)*ln((-1+(-x^2+1)^(1/2))^2/x^2+(I*3^(1/2)-1)*(-1+(-x^2+1)^(1/2))/x-1)-1/6*I*3^(1/2)*ln((-1+(-x^2+1)^(1/2))^2/x^2+(-1-I*3^(1/2))*(-1+(-x^2+1)^(1/2))/x-1)+1/3*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))","C"
1022,1,234,89,0.064000," ","int(x*(-x^2+1)^(1/2)/(x-x^3+(-x^2+1)^(1/2)),x)","-2 \arctan \left(\frac{-1+\sqrt{-x^{2}+1}}{x}\right)+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{3}-\frac{i \sqrt{3}\, \ln \left(\frac{\left(-1-i \sqrt{3}\right) \left(-1+\sqrt{-x^{2}+1}\right)}{x}+\frac{\left(-1+\sqrt{-x^{2}+1}\right)^{2}}{x^{2}}-1\right)}{6}-\frac{i \sqrt{3}\, \ln \left(\frac{\left(1-i \sqrt{3}\right) \left(-1+\sqrt{-x^{2}+1}\right)}{x}+\frac{\left(-1+\sqrt{-x^{2}+1}\right)^{2}}{x^{2}}-1\right)}{6}+\frac{i \sqrt{3}\, \ln \left(\frac{\left(1+i \sqrt{3}\right) \left(-1+\sqrt{-x^{2}+1}\right)}{x}+\frac{\left(-1+\sqrt{-x^{2}+1}\right)^{2}}{x^{2}}-1\right)}{6}+\frac{i \sqrt{3}\, \ln \left(\frac{\left(i \sqrt{3}-1\right) \left(-1+\sqrt{-x^{2}+1}\right)}{x}+\frac{\left(-1+\sqrt{-x^{2}+1}\right)^{2}}{x^{2}}-1\right)}{6}"," ",0,"-2*arctan((-1+(-x^2+1)^(1/2))/x)+1/3*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))-1/6*I*3^(1/2)*ln((-1-I*3^(1/2))*(-1+(-x^2+1)^(1/2))/x+(-1+(-x^2+1)^(1/2))^2/x^2-1)-1/6*I*3^(1/2)*ln((1-I*3^(1/2))*(-1+(-x^2+1)^(1/2))/x+(-1+(-x^2+1)^(1/2))^2/x^2-1)+1/6*I*3^(1/2)*ln((1+I*3^(1/2))*(-1+(-x^2+1)^(1/2))/x+(-1+(-x^2+1)^(1/2))^2/x^2-1)+1/6*I*3^(1/2)*ln((I*3^(1/2)-1)*(-1+(-x^2+1)^(1/2))/x+(-1+(-x^2+1)^(1/2))^2/x^2-1)","C"
1023,1,32,34,0.003000," ","int((-x^4+1)^n/((x^3+x^2+x+1)^n),x)","\frac{\left(x -1\right) \left(-x^{4}+1\right)^{n} \left(x^{3}+x^{2}+x +1\right)^{-n}}{n +1}"," ",0,"(x-1)/(n+1)*(-x^4+1)^n/((x^3+x^2+x+1)^n)","A"
1024,1,1597,173,0.743000," ","int(x/(5308416*c^4*x^4+576000*b^2*c^2*x^2+576000*b^3*c*x-44375*b^4)^(1/2),x)","\text{Expression too large to display}"," ",0,"1/1152*(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c)*((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)^2*((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2)*((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(c^4*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c))^(1/2)*(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c*EllipticF(((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2),((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)*(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c))^(1/2))+(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)*EllipticPi(((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c)*(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(x-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c))^(1/2),(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c),((5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)*(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=1)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=3)*b/c)/(5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=2)*b/c-5/48*RootOf(_Z^4+10*_Z^2+96*_Z-71,index=4)*b/c))^(1/2)))","C"
1025,1,2992,96,1.123000," ","int((4*x+1)/(64*x^4+64*x^3+64*x^2+120*x+9)^(1/2),x)","\text{output too large to display}"," ",0,"1/4*(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4))*((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2)*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))^2*((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2)*((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2)/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/((x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)))^(1/2)*EllipticF(((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2),((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))*(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)))^(1/2))+(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4))*((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2)*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))^2*((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2)*((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2)/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/((x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)))^(1/2)*(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)*EllipticF(((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2),((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))*(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)))^(1/2))+(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))*EllipticPi(((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2))*(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(x-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)))^(1/2),(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)),((1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))*(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=1)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=3))/(1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=2)-1/2*RootOf(4*_Z^4+8*_Z^3+16*_Z^2+60*_Z+9,index=4)))^(1/2)))","C"