1,1,136,84,0.028000," ","int((a+b*x+b*f*x^2/e)/(f*x^2+e*x+d)^(1/2),x)","\frac{a \ln \left(\frac{f x +\frac{e}{2}}{\sqrt{f}}+\sqrt{f \,x^{2}+e x +d}\right)}{\sqrt{f}}-\frac{b d \ln \left(\frac{f x +\frac{e}{2}}{\sqrt{f}}+\sqrt{f \,x^{2}+e x +d}\right)}{2 e \sqrt{f}}-\frac{b e \ln \left(\frac{f x +\frac{e}{2}}{\sqrt{f}}+\sqrt{f \,x^{2}+e x +d}\right)}{8 f^{\frac{3}{2}}}+\frac{\sqrt{f \,x^{2}+e x +d}\, b x}{2 e}+\frac{\sqrt{f \,x^{2}+e x +d}\, b}{4 f}"," ",0,"1/2*b*x*(f*x^2+e*x+d)^(1/2)/e+1/4*b*(f*x^2+e*x+d)^(1/2)/f-1/8*e*b/f^(3/2)*ln((1/2*e+f*x)/f^(1/2)+(f*x^2+e*x+d)^(1/2))-1/2/e*b/f^(1/2)*d*ln((1/2*e+f*x)/f^(1/2)+(f*x^2+e*x+d)^(1/2))+a*ln((1/2*e+f*x)/f^(1/2)+(f*x^2+e*x+d)^(1/2))/f^(1/2)","A"
2,1,491,68,0.060000," ","int(1/(a+b*x+b*f*x^2/e)/(f*x^2+e*x+d)^(1/2),x)","-\frac{e \ln \left(\frac{-\frac{2 \left(a e -b d \right)}{b}+\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}+2 \sqrt{-\frac{a e -b d}{b}}\, \sqrt{\left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)^{2} f +\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}-\frac{a e -b d}{b}}}{x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}}\right)}{\sqrt{-\left(4 a f -b e \right) b e}\, \sqrt{-\frac{a e -b d}{b}}}+\frac{e \ln \left(\frac{-\frac{2 \left(a e -b d \right)}{b}-\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}+2 \sqrt{-\frac{a e -b d}{b}}\, \sqrt{\left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)^{2} f -\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}-\frac{a e -b d}{b}}}{x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}}\right)}{\sqrt{-\left(4 a f -b e \right) b e}\, \sqrt{-\frac{a e -b d}{b}}}"," ",0,"-e/(-b*e*(4*a*f-b*e))^(1/2)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f+(-b*e*(4*a*f-b*e))^(1/2)/b*(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x-1/2*(-b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))+e/(-b*e*(4*a*f-b*e))^(1/2)/(-1/b*(a*e-b*d))^(1/2)*ln((-2/b*(a*e-b*d)-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)+2*(-1/b*(a*e-b*d))^(1/2)*((x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)^2*f-(-b*e*(4*a*f-b*e))^(1/2)/b*(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f)-1/b*(a*e-b*d))^(1/2))/(x+1/2*(b*e+(-b*e*(4*a*f-b*e))^(1/2))/b/f))","B"
3,1,307,56,0.029000," ","int(1/(c*x^2+b*x+d)/(c*x^2+b*x+a)^(1/2),x)","-\frac{\ln \left(\frac{2 a -2 d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{\sqrt{b^{2}-4 c d}\, \sqrt{a -d}}+\frac{\ln \left(\frac{2 a -2 d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{\sqrt{b^{2}-4 c d}\, \sqrt{a -d}}"," ",0,"1/(b^2-4*c*d)^(1/2)/(a-d)^(1/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*((b^2-4*c*d)^(1/2)+b)/c)+2*(a-d)^(1/2)*((x+1/2*((b^2-4*c*d)^(1/2)+b)/c)^2*c-(b^2-4*c*d)^(1/2)*(x+1/2*((b^2-4*c*d)^(1/2)+b)/c)+a-d)^(1/2))/(x+1/2*((b^2-4*c*d)^(1/2)+b)/c))-1/(b^2-4*c*d)^(1/2)/(a-d)^(1/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*((x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+a-d)^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))","B"
4,1,829,117,0.033000," ","int(1/(c*x^2+b*x+d)^2/(c*x^2+b*x+a)^(1/2),x)","\frac{2 c \ln \left(\frac{2 a -2 d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{\left(b^{2}-4 c d \right)^{\frac{3}{2}} \sqrt{a -d}}-\frac{2 c \ln \left(\frac{2 a -2 d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{\left(b^{2}-4 c d \right)^{\frac{3}{2}} \sqrt{a -d}}+\frac{\ln \left(\frac{2 a -2 d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{2 \sqrt{b^{2}-4 c d}\, \left(a -d \right)^{\frac{3}{2}}}-\frac{\ln \left(\frac{2 a -2 d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{2 \sqrt{b^{2}-4 c d}\, \left(a -d \right)^{\frac{3}{2}}}-\frac{\sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{\left(b^{2}-4 c d \right) \left(a -d \right) \left(x +\frac{b}{2 c}-\frac{\sqrt{b^{2}-4 c d}}{2 c}\right)}-\frac{\sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{\left(b^{2}-4 c d \right) \left(a -d \right) \left(x +\frac{b}{2 c}+\frac{\sqrt{b^{2}-4 c d}}{2 c}\right)}"," ",0,"-2/(b^2-4*c*d)^(3/2)*c/(a-d)^(1/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))+2/(b^2-4*c*d)^(3/2)*c/(a-d)^(1/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))-1/(b^2-4*c*d)/(a-d)/(x-1/2/c*(b^2-4*c*d)^(1/2)+1/2/c*b)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)+1/2/(b^2-4*c*d)^(1/2)/(a-d)^(3/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))-1/(b^2-4*c*d)/(a-d)/(x+1/2/c*(b^2-4*c*d)^(1/2)+1/2/c*b)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)-1/2/(b^2-4*c*d)^(1/2)/(a-d)^(3/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))","B"
5,1,1884,204,0.032000," ","int(1/(c*x^2+b*x+d)^3/(c*x^2+b*x+a)^(1/2),x)","-\frac{3 b^{2} \ln \left(\frac{2 a -2 d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{8 \left(b^{2}-4 c d \right)^{\frac{3}{2}} \left(a -d \right)^{\frac{5}{2}}}+\frac{3 b^{2} \ln \left(\frac{2 a -2 d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{8 \left(b^{2}-4 c d \right)^{\frac{3}{2}} \left(a -d \right)^{\frac{5}{2}}}-\frac{6 c^{2} \ln \left(\frac{2 a -2 d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{\left(b^{2}-4 c d \right)^{\frac{5}{2}} \sqrt{a -d}}+\frac{6 c^{2} \ln \left(\frac{2 a -2 d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{\left(b^{2}-4 c d \right)^{\frac{5}{2}} \sqrt{a -d}}+\frac{3 c d \ln \left(\frac{2 a -2 d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{2 \left(b^{2}-4 c d \right)^{\frac{3}{2}} \left(a -d \right)^{\frac{5}{2}}}-\frac{3 c d \ln \left(\frac{2 a -2 d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{2 \left(b^{2}-4 c d \right)^{\frac{3}{2}} \left(a -d \right)^{\frac{5}{2}}}-\frac{c \ln \left(\frac{2 a -2 d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{\left(b^{2}-4 c d \right)^{\frac{3}{2}} \left(a -d \right)^{\frac{3}{2}}}+\frac{c \ln \left(\frac{2 a -2 d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)+2 \sqrt{a -d}\, \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}}\right)}{\left(b^{2}-4 c d \right)^{\frac{3}{2}} \left(a -d \right)^{\frac{3}{2}}}+\frac{3 \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}\, c}{\left(b^{2}-4 c d \right)^{2} \left(a -d \right) \left(x +\frac{b}{2 c}-\frac{\sqrt{b^{2}-4 c d}}{2 c}\right)}+\frac{3 \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}\, c}{\left(b^{2}-4 c d \right)^{2} \left(a -d \right) \left(x +\frac{b}{2 c}+\frac{\sqrt{b^{2}-4 c d}}{2 c}\right)}-\frac{\sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{2 \left(b^{2}-4 c d \right)^{\frac{3}{2}} \left(a -d \right) \left(x +\frac{b}{2 c}-\frac{\sqrt{b^{2}-4 c d}}{2 c}\right)^{2}}+\frac{3 \sqrt{a +\left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d +\sqrt{b^{2}-4 c d}\, \left(x -\frac{-b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{4 \left(b^{2}-4 c d \right) \left(a -d \right)^{2} \left(x +\frac{b}{2 c}-\frac{\sqrt{b^{2}-4 c d}}{2 c}\right)}+\frac{\sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{2 \left(b^{2}-4 c d \right)^{\frac{3}{2}} \left(a -d \right) \left(x +\frac{b}{2 c}+\frac{\sqrt{b^{2}-4 c d}}{2 c}\right)^{2}}+\frac{3 \sqrt{a +\left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)^{2} c -d -\sqrt{b^{2}-4 c d}\, \left(x +\frac{b +\sqrt{b^{2}-4 c d}}{2 c}\right)}}{4 \left(b^{2}-4 c d \right) \left(a -d \right)^{2} \left(x +\frac{b}{2 c}+\frac{\sqrt{b^{2}-4 c d}}{2 c}\right)}"," ",0,"-1/2/(b^2-4*c*d)^(3/2)/(a-d)/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)^2*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)+3/4/(b^2-4*c*d)/(a-d)^2/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)-3/8/(b^2-4*c*d)^(3/2)/(a-d)^(5/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))*b^2+3/2/(b^2-4*c*d)^(3/2)/(a-d)^(5/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))*c*d-1/(b^2-4*c*d)^(3/2)*c/(a-d)^(3/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))+1/2/(b^2-4*c*d)^(3/2)/(a-d)/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)^2*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)+3/4/(b^2-4*c*d)/(a-d)^2/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)+3/8/(b^2-4*c*d)^(3/2)/(a-d)^(5/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))*b^2-3/2/(b^2-4*c*d)^(3/2)/(a-d)^(5/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))*c*d+1/(b^2-4*c*d)^(3/2)*c/(a-d)^(3/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))+6*c^2/(b^2-4*c*d)^(5/2)/(a-d)^(1/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))-6*c^2/(b^2-4*c*d)^(5/2)/(a-d)^(1/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))+3/(b^2-4*c*d)^2*c/(a-d)/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)+3/(b^2-4*c*d)^2*c/(a-d)/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)","B"
6,1,3695,304,0.038000," ","int(1/(c*x^2+b*x+d)^4/(c*x^2+b*x+a)^(1/2),x)","\text{output too large to display}"," ",0,"5/2/(b^2-4*c*d)^2/(a-d)^3/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)*c*d+5/2/(b^2-4*c*d)^2/(a-d)^3/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)*c*d-3/4/(b^2-4*c*d)^(3/2)/(a-d)^(5/2)*c*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))-1/3/(b^2-4*c*d)^2/(a-d)/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)^3*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)-3/(b^2-4*c*d)^(5/2)*c^2/(a-d)^(3/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))-1/3/(b^2-4*c*d)^2/(a-d)/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)^3*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)+3/(b^2-4*c*d)^(5/2)*c^2/(a-d)^(3/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))+20*c^3/(b^2-4*c*d)^(7/2)/(a-d)^(1/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))-20*c^3/(b^2-4*c*d)^(7/2)/(a-d)^(1/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))-5/12/(b^2-4*c*d)^(3/2)/(a-d)^2/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)^2*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)-5/16/(b^2-4*c*d)^(3/2)/(a-d)^(7/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))*b^2+3/4/(b^2-4*c*d)^(3/2)/(a-d)^(5/2)*c*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))+5/12/(b^2-4*c*d)^(3/2)/(a-d)^2/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)^2*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)+5/16/(b^2-4*c*d)^(3/2)/(a-d)^(7/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))*b^2-5/8/(b^2-4*c*d)^2/(a-d)^3/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)*b^2-10/(b^2-4*c*d)^3*c^2/(a-d)/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)+2/(b^2-4*c*d)^(5/2)*c/(a-d)/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)^2*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)+3/2/(b^2-4*c*d)^(5/2)*c/(a-d)^(5/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))*b^2-6/(b^2-4*c*d)^(5/2)*c^2/(a-d)^(5/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))*d-2/(b^2-4*c*d)^(5/2)*c/(a-d)/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)^2*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)-7/3/(b^2-4*c*d)^2*c/(a-d)^2/(x+1/2*b/c+1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2)-3/2/(b^2-4*c*d)^(5/2)*c/(a-d)^(5/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))*b^2+6/(b^2-4*c*d)^(5/2)*c^2/(a-d)^(5/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))*d-10/(b^2-4*c*d)^3*c^2/(a-d)/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)-5/8/(b^2-4*c*d)^2/(a-d)^3/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)*b^2-7/3/(b^2-4*c*d)^2*c/(a-d)^2/(x+1/2*b/c-1/2*(b^2-4*c*d)^(1/2)/c)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2)+5/4/(b^2-4*c*d)^(3/2)/(a-d)^(7/2)*ln((2*a-2*d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x+1/2*(b+(b^2-4*c*d)^(1/2))/c)^2*c-d-(b^2-4*c*d)^(1/2)*(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x+1/2*(b+(b^2-4*c*d)^(1/2))/c))*c*d-5/4/(b^2-4*c*d)^(3/2)/(a-d)^(7/2)*ln((2*a-2*d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)+2*(a-d)^(1/2)*(a+(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c)^2*c-d+(b^2-4*c*d)^(1/2)*(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))^(1/2))/(x-1/2*(-b+(b^2-4*c*d)^(1/2))/c))*c*d","B"
7,1,1377,146,0.033000," ","int(1/(b*f*x^2+b*e*x+a*e)^2/(f*x^2+e*x+d)^(1/2),x)","-\frac{2 f \ln \left(\frac{-\frac{2 \left(a e -b d \right)}{b}+\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}+2 \sqrt{-\frac{a e -b d}{b}}\, \sqrt{\left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)^{2} f +\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}-\frac{a e -b d}{b}}}{x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}}\right)}{\left(4 a f -b e \right) \sqrt{-\left(4 a f -b e \right) b e}\, \sqrt{-\frac{a e -b d}{b}}\, e}+\frac{2 f \ln \left(\frac{-\frac{2 \left(a e -b d \right)}{b}-\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}+2 \sqrt{-\frac{a e -b d}{b}}\, \sqrt{\left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)^{2} f -\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}-\frac{a e -b d}{b}}}{x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}}\right)}{\left(4 a f -b e \right) \sqrt{-\left(4 a f -b e \right) b e}\, \sqrt{-\frac{a e -b d}{b}}\, e}+\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \ln \left(\frac{-\frac{2 \left(a e -b d \right)}{b}+\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}+2 \sqrt{-\frac{a e -b d}{b}}\, \sqrt{\left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)^{2} f +\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}-\frac{a e -b d}{b}}}{x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}}\right)}{2 \left(4 a f -b e \right) \left(a e -b d \right) \sqrt{-\frac{a e -b d}{b}}\, b e}-\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \ln \left(\frac{-\frac{2 \left(a e -b d \right)}{b}-\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}+2 \sqrt{-\frac{a e -b d}{b}}\, \sqrt{\left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)^{2} f -\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}-\frac{a e -b d}{b}}}{x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}}\right)}{2 \left(4 a f -b e \right) \left(a e -b d \right) \sqrt{-\frac{a e -b d}{b}}\, b e}-\frac{\sqrt{\left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)^{2} f +\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x -\frac{-b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}-\frac{a e -b d}{b}}}{\left(4 a f -b e \right) \left(a e -b d \right) \left(x +\frac{e}{2 f}-\frac{\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right) e}-\frac{\sqrt{\left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)^{2} f -\frac{\sqrt{-\left(4 a f -b e \right) b e}\, \left(x +\frac{b e +\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right)}{b}-\frac{a e -b d}{b}}}{\left(4 a f -b e \right) \left(a e -b d \right) \left(x +\frac{e}{2 f}+\frac{\sqrt{-\left(4 a f -b e \right) b e}}{2 b f}\right) e}"," ",0,"-2/(4*a*f-b*e)/e*f/(-(4*a*f-b*e)*b*e)^(1/2)/(-(a*e-b*d)/b)^(1/2)*ln((-2*(a*e-b*d)/b+(-(4*a*f-b*e)*b*e)^(1/2)*(x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b+2*(-(a*e-b*d)/b)^(1/2)*((x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)^2*f+(-(4*a*f-b*e)*b*e)^(1/2)*(x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b-(a*e-b*d)/b)^(1/2))/(x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f))-1/(4*a*f-b*e)/e/(a*e-b*d)/(x+1/2/f*e-1/2/b/f*(-(4*a*f-b*e)*b*e)^(1/2))*((x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)^2*f+(-(4*a*f-b*e)*b*e)^(1/2)*(x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b-(a*e-b*d)/b)^(1/2)+1/2/(4*a*f-b*e)/b/e*(-(4*a*f-b*e)*b*e)^(1/2)/(a*e-b*d)/(-(a*e-b*d)/b)^(1/2)*ln((-2*(a*e-b*d)/b+(-(4*a*f-b*e)*b*e)^(1/2)*(x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b+2*(-(a*e-b*d)/b)^(1/2)*((x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)^2*f+(-(4*a*f-b*e)*b*e)^(1/2)*(x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b-(a*e-b*d)/b)^(1/2))/(x-1/2*(-b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f))-1/(4*a*f-b*e)/e/(a*e-b*d)/(x+1/2/f*e+1/2/b/f*(-(4*a*f-b*e)*b*e)^(1/2))*((x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)^2*f-(-(4*a*f-b*e)*b*e)^(1/2)*(x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b-(a*e-b*d)/b)^(1/2)-1/2/(4*a*f-b*e)/b/e*(-(4*a*f-b*e)*b*e)^(1/2)/(a*e-b*d)/(-(a*e-b*d)/b)^(1/2)*ln((-2*(a*e-b*d)/b-(-(4*a*f-b*e)*b*e)^(1/2)*(x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b+2*(-(a*e-b*d)/b)^(1/2)*((x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)^2*f-(-(4*a*f-b*e)*b*e)^(1/2)*(x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b-(a*e-b*d)/b)^(1/2))/(x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f))+2/(4*a*f-b*e)/e*f/(-(4*a*f-b*e)*b*e)^(1/2)/(-(a*e-b*d)/b)^(1/2)*ln((-2*(a*e-b*d)/b-(-(4*a*f-b*e)*b*e)^(1/2)*(x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b+2*(-(a*e-b*d)/b)^(1/2)*((x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)^2*f-(-(4*a*f-b*e)*b*e)^(1/2)*(x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f)/b-(a*e-b*d)/b)^(1/2))/(x+1/2*(b*e+(-(4*a*f-b*e)*b*e)^(1/2))/b/f))","B"
8,1,27,24,0.022000," ","int(1/(x^2+2*x+4)/(x^2+2*x+5)^(1/2),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(2 x +2\right)}{6 \sqrt{x^{2}+2 x +5}}\right)}{3}"," ",0,"1/3*3^(1/2)*arctan(1/6*3^(1/2)/(x^2+2*x+5)^(1/2)*(2*x+2))","A"
9,0,0,125,0.253000," ","int((a+1/2*e*x+c*x^2)^p*(2*c*x^2+e*x+2*a)^q,x)","\int \left(c \,x^{2}+\frac{1}{2} e x +a \right)^{p} \left(2 c \,x^{2}+e x +2 a \right)^{q}\, dx"," ",0,"int((a+1/2*e*x+c*x^2)^p*(2*c*x^2+e*x+2*a)^q,x)","F"
10,0,0,180,0.302000," ","int((a+c*e*x/f+c*x^2)^p*(a*f/c+e*x+f*x^2)^q,x)","\int \left(c \,x^{2}+\frac{c e x}{f}+a \right)^{p} \left(f \,x^{2}+e x +\frac{a f}{c}\right)^{q}\, dx"," ",0,"int((a+c*e*x/f+c*x^2)^p*(a*f/c+e*x+f*x^2)^q,x)","F"
11,1,16,36,0.046000," ","int(((1+x)^2)^(1/2)/(x^2+1)^(1/2),x)","\left(\arcsinh \left(x \right)+\sqrt{x^{2}+1}\right) \mathrm{csgn}\left(x +1\right)"," ",0,"csgn(1+x)*(arcsinh(x)+(x^2+1)^(1/2))","C"
12,1,84,54,0.021000," ","int(1/(x^2-1)^2/(x^2+x-1)^(1/2),x)","\frac{5 \arctanh \left(\frac{3 x -1}{2 \sqrt{3 x +\left(x -1\right)^{2}-2}}\right)}{8}+\frac{\arctan \left(\frac{-x -3}{2 \sqrt{-x +\left(x +1\right)^{2}-2}}\right)}{8}+\frac{\sqrt{-x +\left(x +1\right)^{2}-2}}{4 x +4}-\frac{\sqrt{3 x +\left(x -1\right)^{2}-2}}{4 \left(x -1\right)}"," ",0,"1/4/(x+1)*((x+1)^2-2-x)^(1/2)+1/8*arctan(1/2*(-3-x)/((x+1)^2-2-x)^(1/2))+5/8*arctanh(1/2*(-1+3*x)/((x-1)^2+3*x-2)^(1/2))-1/4/(x-1)*((x-1)^2+3*x-2)^(1/2)","A"
13,1,661,1177,0.248000," ","int(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+d)^(1/2),x)","\frac{4 \left(b \,f^{2} x^{2}-4 c d f x +2 \sqrt{-d f}\, c f \,x^{2}+\sqrt{-4 a c +b^{2}}\, f^{2} x^{2}-b d f +2 \sqrt{-d f}\, b f x -2 \sqrt{-d f}\, c d -\sqrt{-4 a c +b^{2}}\, d f +2 \sqrt{-4 a c +b^{2}}\, \sqrt{-d f}\, f x \right) \sqrt{\frac{\sqrt{-d f}\, \left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) f}{\left(b f +2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(f x +\sqrt{-d f}\right)}}\, \sqrt{\frac{\sqrt{-d f}\, \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) f}{\left(-b f -2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(f x +\sqrt{-d f}\right)}}\, \sqrt{-\frac{\left(b f -2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(-f x +\sqrt{-d f}\right)}{\left(b f +2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(f x +\sqrt{-d f}\right)}}\, \sqrt{c \,x^{2}+b x +a}\, \sqrt{f \,x^{2}+d}\, \EllipticF \left(\sqrt{-\frac{\left(b f -2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(-f x +\sqrt{-d f}\right)}{\left(b f +2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(f x +\sqrt{-d f}\right)}}, \sqrt{\frac{\left(-b f +2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(b f +2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right)}{\left(-b f -2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(b f -2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right)}}\right)}{\sqrt{\frac{\left(-f x +\sqrt{-d f}\right) \left(f x +\sqrt{-d f}\right) \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) \left(2 c x +b +\sqrt{-4 a c +b^{2}}\right)}{c f}}\, \sqrt{-d f}\, \left(b f -2 \sqrt{-d f}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \sqrt{c f \,x^{4}+b f \,x^{3}+a f \,x^{2}+c d \,x^{2}+b d x +a d}}"," ",0,"4*(b*f^2*x^2+2*x^2*c*f*(-d*f)^(1/2)+x^2*f^2*(-4*a*c+b^2)^(1/2)+2*x*b*f*(-d*f)^(1/2)-4*c*x*f*d+2*x*f*(-4*a*c+b^2)^(1/2)*(-d*f)^(1/2)-b*d*f-2*c*d*(-d*f)^(1/2)-d*f*(-4*a*c+b^2)^(1/2))*EllipticF((-(f*(-4*a*c+b^2)^(1/2)-2*(-d*f)^(1/2)*c+b*f)*(-f*x+(-d*f)^(1/2))/(f*(-4*a*c+b^2)^(1/2)+2*(-d*f)^(1/2)*c+b*f)/(f*x+(-d*f)^(1/2)))^(1/2),((f*(-4*a*c+b^2)^(1/2)+2*(-d*f)^(1/2)*c-b*f)*(f*(-4*a*c+b^2)^(1/2)+2*(-d*f)^(1/2)*c+b*f)/(f*(-4*a*c+b^2)^(1/2)-2*(-d*f)^(1/2)*c-b*f)/(f*(-4*a*c+b^2)^(1/2)-2*(-d*f)^(1/2)*c+b*f))^(1/2))*((-d*f)^(1/2)*(b+2*c*x+(-4*a*c+b^2)^(1/2))*f/(f*(-4*a*c+b^2)^(1/2)+2*(-d*f)^(1/2)*c+b*f)/(f*x+(-d*f)^(1/2)))^(1/2)*((-d*f)^(1/2)*(-2*c*x+(-4*a*c+b^2)^(1/2)-b)*f/(f*(-4*a*c+b^2)^(1/2)-2*(-d*f)^(1/2)*c-b*f)/(f*x+(-d*f)^(1/2)))^(1/2)*(-(f*(-4*a*c+b^2)^(1/2)-2*(-d*f)^(1/2)*c+b*f)*(-f*x+(-d*f)^(1/2))/(f*(-4*a*c+b^2)^(1/2)+2*(-d*f)^(1/2)*c+b*f)/(f*x+(-d*f)^(1/2)))^(1/2)*(c*x^2+b*x+a)^(1/2)*(f*x^2+d)^(1/2)/(1/c/f*(-f*x+(-d*f)^(1/2))*(f*x+(-d*f)^(1/2))*(-2*c*x+(-4*a*c+b^2)^(1/2)-b)*(b+2*c*x+(-4*a*c+b^2)^(1/2)))^(1/2)/(-d*f)^(1/2)/(f*(-4*a*c+b^2)^(1/2)-2*(-d*f)^(1/2)*c+b*f)/(c*f*x^4+b*f*x^3+a*f*x^2+c*d*x^2+b*d*x+a*d)^(1/2)","A"
14,1,341,84,0.030000," ","int((-x^2-4*x-3)^(1/2)/(2*x^2+4*x+3),x)","-\frac{\arcsin \left(x +2\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{\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(2+x)+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)/(1+x/(-3/2-x))^2)^(1/2)/(1+x/(-3/2-x))-1/3*3^(1/2)*4^(1/2)/((x^2/(-3/2-x)^2-4)/(1+x/(-3/2-x))^2)^(1/2)/(1+x/(-3/2-x))*(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)/(1+x/(-3/2-x))^2)^(1/2)/(1+x/(-3/2-x))","B"
15,1,55,54,0.001000," ","int((2*x^2-x+3)*(5*x^2+3*x+2)^4,x)","\frac{1250}{11} x^{11}+\frac{475}{2} x^{10}+\frac{5075}{9} x^{9}+\frac{3415}{4} x^{8}+1176 x^{7}+\frac{2377}{2} x^{6}+\frac{5099}{5} x^{5}+656 x^{4}+\frac{1064}{3} x^{3}+136 x^{2}+48 x"," ",0,"48*x+136*x^2+1064/3*x^3+656*x^4+5099/5*x^5+2377/2*x^6+1176*x^7+3415/4*x^8+5075/9*x^9+475/2*x^10+1250/11*x^11","A"
16,1,45,44,0.001000," ","int((2*x^2-x+3)*(5*x^2+3*x+2)^3,x)","\frac{250}{9} x^{9}+\frac{325}{8} x^{8}+\frac{720}{7} x^{7}+134 x^{6}+\frac{876}{5} x^{5}+\frac{579}{4} x^{4}+\frac{322}{3} x^{3}+50 x^{2}+24 x"," ",0,"24*x+50*x^2+322/3*x^3+579/4*x^4+876/5*x^5+134*x^6+720/7*x^7+325/8*x^8+250/9*x^9","A"
17,1,35,34,0.001000," ","int((2*x^2-x+3)*(5*x^2+3*x+2)^2,x)","\frac{50}{7} x^{7}+\frac{35}{6} x^{6}+\frac{103}{5} x^{5}+\frac{85}{4} x^{4}+\frac{83}{3} x^{3}+16 x^{2}+12 x"," ",0,"12*x+16*x^2+83/3*x^3+85/4*x^4+103/5*x^5+35/6*x^6+50/7*x^7","A"
18,1,25,24,0.001000," ","int((2*x^2-x+3)*(5*x^2+3*x+2),x)","2 x^{5}+\frac{1}{4} x^{4}+\frac{16}{3} x^{3}+\frac{7}{2} x^{2}+6 x"," ",0,"6*x+7/2*x^2+16/3*x^3+1/4*x^4+2*x^5","A"
19,1,34,33,0.005000," ","int((2*x^2-x+3)/(5*x^2+3*x+2),x)","\frac{2 x}{5}+\frac{143 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{775}-\frac{11 \ln \left(5 x^{2}+3 x +2\right)}{50}"," ",0,"2/5*x-11/50*ln(5*x^2+3*x+2)+143/775*arctan(1/31*(3+10*x)*31^(1/2))*31^(1/2)","A"
20,1,34,36,0.005000," ","int((2*x^2-x+3)/(5*x^2+3*x+2)^2,x)","\frac{82 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{961}+\frac{\frac{143 x}{775}+\frac{77}{775}}{x^{2}+\frac{3}{5} x +\frac{2}{5}}"," ",0,"(143/775*x+77/775)/(x^2+3/5*x+2/5)+82/961*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
21,1,47,55,0.005000," ","int((2*x^2-x+3)/(5*x^2+3*x+2)^3,x)","\frac{1106 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{29791}+\frac{\frac{2765}{961} x^{3}+\frac{4977}{1922} x^{2}+\frac{2047}{961} x +\frac{1141}{1922}}{\left(5 x^{2}+3 x +2\right)^{2}}"," ",0,"25*(553/4805*x^3+4977/48050*x^2+2047/24025*x+1141/48050)/(5*x^2+3*x+2)^2+1106/29791*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
22,1,65,64,0.002000," ","int((2*x^2-x+3)^2*(5*x^2+3*x+2)^4,x)","\frac{2500}{13} x^{13}+\frac{875}{3} x^{12}+\frac{11525}{11} x^{11}+1571 x^{10}+\frac{24859}{9} x^{9}+3315 x^{8}+\frac{27763}{7} x^{7}+\frac{10771}{3} x^{6}+\frac{14801}{5} x^{5}+1838 x^{4}+\frac{3016}{3} x^{3}+384 x^{2}+144 x"," ",0,"144*x+384*x^2+3016/3*x^3+1838*x^4+14801/5*x^5+10771/3*x^6+27763/7*x^7+3315*x^8+24859/9*x^9+1571*x^10+11525/11*x^11+875/3*x^12+2500/13*x^13","A"
23,1,55,54,0.001000," ","int((2*x^2-x+3)^2*(5*x^2+3*x+2)^3,x)","\frac{500}{11} x^{11}+40 x^{10}+\frac{1865}{9} x^{9}+\frac{1863}{8} x^{8}+444 x^{7}+449 x^{6}+\frac{2693}{5} x^{5}+\frac{1615}{4} x^{4}+\frac{914}{3} x^{3}+138 x^{2}+72 x"," ",0,"72*x+138*x^2+914/3*x^3+1615/4*x^4+2693/5*x^5+449*x^6+444*x^7+1863/8*x^8+1865/9*x^9+40*x^10+500/11*x^11","A"
24,1,45,44,0.001000," ","int((2*x^2-x+3)^2*(5*x^2+3*x+2)^2,x)","\frac{100}{9} x^{9}+\frac{5}{2} x^{8}+\frac{321}{7} x^{7}+\frac{86}{3} x^{6}+78 x^{5}+59 x^{4}+\frac{241}{3} x^{3}+42 x^{2}+36 x"," ",0,"36*x+42*x^2+241/3*x^3+59*x^4+78*x^5+86/3*x^6+321/7*x^7+5/2*x^8+100/9*x^9","A"
25,1,35,34,0.001000," ","int((2*x^2-x+3)^2*(5*x^2+3*x+2),x)","\frac{20}{7} x^{7}-\frac{4}{3} x^{6}+\frac{61}{5} x^{5}+\frac{1}{4} x^{4}+\frac{53}{3} x^{3}+\frac{15}{2} x^{2}+18 x"," ",0,"18*x+15/2*x^2+53/3*x^3+1/4*x^4+61/5*x^5-4/3*x^6+20/7*x^7","A"
26,1,44,43,0.004000," ","int((2*x^2-x+3)^2/(5*x^2+3*x+2),x)","\frac{4 x^{3}}{15}-\frac{16 x^{2}}{25}+\frac{381 x}{125}+\frac{8349 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{19375}-\frac{1573 \ln \left(5 x^{2}+3 x +2\right)}{1250}"," ",0,"381/125*x-16/25*x^2+4/15*x^3-1573/1250*ln(5*x^2+3*x+2)+8349/19375*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
27,1,51,52,0.006000," ","int((2*x^2-x+3)^2/(5*x^2+3*x+2)^2,x)","\frac{4 x}{25}+\frac{41932 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{120125}-\frac{22 \ln \left(5 x^{2}+3 x +2\right)}{125}-\frac{11 \left(-\frac{759 x}{775}-\frac{671}{775}\right)}{25 \left(x^{2}+\frac{3}{5} x +\frac{2}{5}\right)}"," ",0,"4/25*x-11/25*(-759/775*x-671/775)/(x^2+3/5*x+2/5)-22/125*ln(5*x^2+3*x+2)+41932/120125*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
28,1,47,55,0.006000," ","int((2*x^2-x+3)^2/(5*x^2+3*x+2)^3,x)","\frac{4330 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{29791}+\frac{\frac{50281}{4805} x^{3}+\frac{494813}{48050} x^{2}+\frac{184382}{24025} x +\frac{123013}{48050}}{\left(5 x^{2}+3 x +2\right)^{2}}"," ",0,"25*(50281/120125*x^3+494813/1201250*x^2+184382/600625*x+123013/1201250)/(5*x^2+3*x+2)^2+4330/29791*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
29,1,57,74,0.007000," ","int((2*x^2-x+3)^2/(5*x^2+3*x+2)^4,x)","\frac{66752 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{923521}+\frac{\frac{834400}{29791} x^{5}+\frac{1251600}{29791} x^{4}+\frac{7163932}{148955} x^{3}+\frac{4260199}{148955} x^{2}+\frac{1891636}{148955} x +\frac{1259239}{446865}}{\left(5 x^{2}+3 x +2\right)^{3}}"," ",0,"125*(33376/148955*x^5+50064/148955*x^4+7163932/18619375*x^3+4260199/18619375*x^2+1891636/18619375*x+1259239/55858125)/(5*x^2+3*x+2)^3+66752/923521*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
30,1,75,74,0.000000," ","int((2*x^2-x+3)^3*(5*x^2+3*x+2)^4,x)","\frac{1000}{3} x^{15}+\frac{2250}{7} x^{14}+\frac{27050}{13} x^{13}+\frac{30395}{12} x^{12}+\frac{68583}{11} x^{11}+\frac{75311}{10} x^{10}+\frac{103583}{9} x^{9}+\frac{94881}{8} x^{8}+\frac{91349}{7} x^{7}+\frac{64529}{6} x^{6}+\frac{43083}{5} x^{5}+5144 x^{4}+2856 x^{3}+1080 x^{2}+432 x"," ",0,"432*x+1080*x^2+2856*x^3+5144*x^4+43083/5*x^5+64529/6*x^6+91349/7*x^7+94881/8*x^8+103583/9*x^9+75311/10*x^10+68583/11*x^11+30395/12*x^12+27050/13*x^13+2250/7*x^14+1000/3*x^15","A"
31,1,65,64,0.001000," ","int((2*x^2-x+3)^3*(5*x^2+3*x+2)^3,x)","\frac{1000}{13} x^{13}+25 x^{12}+\frac{4830}{11} x^{11}+\frac{3061}{10} x^{10}+\frac{3316}{3} x^{9}+\frac{7869}{8} x^{8}+\frac{12016}{7} x^{7}+\frac{2873}{2} x^{6}+\frac{8292}{5} x^{5}+\frac{4483}{4} x^{4}+870 x^{3}+378 x^{2}+216 x"," ",0,"216*x+378*x^2+870*x^3+4483/4*x^4+8292/5*x^5+2873/2*x^6+12016/7*x^7+7869/8*x^8+3316/3*x^9+3061/10*x^10+4830/11*x^11+25*x^12+1000/13*x^13","A"
32,1,55,54,0.002000," ","int((2*x^2-x+3)^3*(5*x^2+3*x+2)^2,x)","\frac{200}{11} x^{11}-6 x^{10}+\frac{922}{9} x^{9}+\frac{83}{8} x^{8}+\frac{1571}{7} x^{7}+\frac{299}{3} x^{6}+\frac{1416}{5} x^{5}+\frac{635}{4} x^{4}+237 x^{3}+108 x^{2}+108 x"," ",0,"108*x+108*x^2+237*x^3+635/4*x^4+1416/5*x^5+299/3*x^6+1571/7*x^7+83/8*x^8+922/9*x^9-6*x^10+200/11*x^11","A"
33,1,45,44,0.001000," ","int((2*x^2-x+3)^3*(5*x^2+3*x+2),x)","\frac{40}{9} x^{9}-\frac{9}{2} x^{8}+\frac{190}{7} x^{7}-\frac{83}{6} x^{6}+\frac{288}{5} x^{5}-5 x^{4}+60 x^{3}+\frac{27}{2} x^{2}+54 x"," ",0,"54*x+27/2*x^2+60*x^3-5*x^4+288/5*x^5-83/6*x^6+190/7*x^7-9/2*x^8+40/9*x^9","A"
34,1,54,53,0.004000," ","int((2*x^2-x+3)^3/(5*x^2+3*x+2),x)","\frac{8 x^{5}}{25}-\frac{21 x^{4}}{25}+\frac{1222 x^{3}}{375}-\frac{7451 x^{2}}{1250}+\frac{49508 x}{3125}+\frac{328757 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{484375}-\frac{158389 \ln \left(5 x^{2}+3 x +2\right)}{31250}"," ",0,"49508/3125*x-7451/1250*x^2+1222/375*x^3-21/25*x^4+8/25*x^5-158389/31250*ln(5*x^2+3*x+2)+328757/484375*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
35,1,61,62,0.008000," ","int((2*x^2-x+3)^3/(5*x^2+3*x+2)^2,x)","\frac{8 x^{3}}{75}-\frac{54 x^{2}}{125}+\frac{1466 x}{625}+\frac{3819607 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{3003125}-\frac{10769 \ln \left(5 x^{2}+3 x +2\right)}{6250}-\frac{121 \left(-\frac{2717 x}{775}-\frac{4873}{775}\right)}{625 \left(x^{2}+\frac{3}{5} x +\frac{2}{5}\right)}"," ",0,"8/75*x^3-54/125*x^2+1466/625*x-121/625*(-2717/775*x-4873/775)/(x^2+3/5*x+2/5)-10769/6250*ln(5*x^2+3*x+2)+3819607/3003125*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
36,1,63,71,0.009000," ","int((2*x^2-x+3)^3/(5*x^2+3*x+2)^3,x)","\frac{8 x}{125}+\frac{11341176 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{18619375}-\frac{66 \ln \left(5 x^{2}+3 x +2\right)}{625}-\frac{11 \left(-\frac{377124}{24025} x^{3}-\frac{866987}{48050} x^{2}-\frac{293711}{24025} x -\frac{232243}{48050}\right)}{5 \left(5 x^{2}+3 x +2\right)^{2}}"," ",0,"8/125*x-11/5*(-377124/24025*x^3-866987/48050*x^2-293711/24025*x-232243/48050)/(5*x^2+3*x+2)^2-66/625*ln(5*x^2+3*x+2)+11341176/18619375*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))","A"
37,1,64,63,0.006000," ","int((5*x^2+3*x+2)^4/(2*x^2-x+3),x)","\frac{625 x^{7}}{14}+\frac{3625 x^{6}}{24}+\frac{1855 x^{5}}{8}+\frac{6245 x^{4}}{64}-\frac{21229 x^{3}}{96}-\frac{28747 x^{2}}{128}+\frac{122691 x}{128}-\frac{1156639 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{5888}+\frac{307461 \ln \left(2 x^{2}-x +3\right)}{512}"," ",0,"625/14*x^7+3625/24*x^6+1855/8*x^5+6245/64*x^4-21229/96*x^3-28747/128*x^2+122691/128*x+307461/512*ln(2*x^2-x+3)-1156639/5888*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
38,1,54,53,0.004000," ","int((5*x^2+3*x+2)^3/(2*x^2-x+3),x)","\frac{25 x^{5}}{2}+\frac{575 x^{4}}{16}+\frac{965 x^{3}}{24}-\frac{829 x^{2}}{32}-\frac{4795 x}{32}+\frac{59895 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{1472}+\frac{1331 \ln \left(2 x^{2}-x +3\right)}{128}"," ",0,"25/2*x^5+575/16*x^4+965/24*x^3-829/32*x^2-4795/32*x+1331/128*ln(2*x^2-x+3)+59895/1472*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
39,1,44,43,0.004000," ","int((5*x^2+3*x+2)^2/(2*x^2-x+3),x)","\frac{25 x^{3}}{6}+\frac{85 x^{2}}{8}+\frac{51 x}{8}-\frac{847 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{368}-\frac{363 \ln \left(2 x^{2}-x +3\right)}{32}"," ",0,"25/6*x^3+85/8*x^2+51/8*x-363/32*ln(2*x^2-x+3)-847/368*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
40,1,34,33,0.004000," ","int((5*x^2+3*x+2)/(2*x^2-x+3),x)","\frac{5 x}{2}-\frac{33 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{92}+\frac{11 \ln \left(2 x^{2}-x +3\right)}{8}"," ",0,"5/2*x+11/8*ln(2*x^2-x+3)-33/92*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
41,1,60,59,0.006000," ","int(1/(2*x^2-x+3)/(5*x^2+3*x+2),x)","\frac{13 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{682}-\frac{3 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{506}-\frac{\ln \left(2 x^{2}-x +3\right)}{44}+\frac{\ln \left(5 x^{2}+3 x +2\right)}{44}"," ",0,"1/44*ln(5*x^2+3*x+2)+13/682*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))-1/44*ln(2*x^2-x+3)-3/506*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
42,1,77,78,0.007000," ","int(1/(2*x^2-x+3)/(5*x^2+3*x+2)^2,x)","\frac{2891 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{465124}-\frac{7 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{11132}+\frac{3 \ln \left(2 x^{2}-x +3\right)}{968}-\frac{3 \ln \left(5 x^{2}+3 x +2\right)}{968}-\frac{-\frac{286 x}{31}-\frac{88}{155}}{484 \left(x^{2}+\frac{3}{5} x +\frac{2}{5}\right)}"," ",0,"-1/484*(-286/31*x-88/155)/(x^2+3/5*x+2/5)-3/968*ln(5*x^2+3*x+2)+2891/465124*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))+3/968*ln(2*x^2-x+3)-7/11132*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
43,1,89,97,0.008000," ","int(1/(2*x^2-x+3)/(5*x^2+3*x+2)^3,x)","\frac{847793 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{317214568}+\frac{45 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{244904}-\frac{\ln \left(2 x^{2}-x +3\right)}{21296}+\frac{\ln \left(5 x^{2}+3 x +2\right)}{21296}+\frac{\frac{108025}{465124} x^{3}+\frac{52215}{232562} x^{2}+\frac{2026}{10571} x +\frac{8605}{232562}}{\left(5 x^{2}+3 x +2\right)^{2}}"," ",0,"25/10648*(95062/961*x^3+459492/4805*x^2+1961168/24025*x+75724/4805)/(5*x^2+3*x+2)^2+1/21296*ln(5*x^2+3*x+2)+847793/317214568*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))-1/21296*ln(2*x^2-x+3)+45/244904*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
44,1,71,72,0.010000," ","int((5*x^2+3*x+2)^4/(2*x^2-x+3)^2,x)","\frac{125 x^{5}}{4}+\frac{2125 x^{4}}{16}+\frac{9775 x^{3}}{48}-\frac{1185 x^{2}}{8}-\frac{89359 x}{64}+\frac{13292697 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{33856}-\frac{30613 \ln \left(2 x^{2}-x +3\right)}{128}-\frac{1331 \left(\frac{869 x}{92}+\frac{1111}{92}\right)}{64 \left(x^{2}-\frac{1}{2} x +\frac{3}{2}\right)}"," ",0,"125/4*x^5+2125/16*x^4+9775/48*x^3-1185/8*x^2-89359/64*x-1331/64*(869/92*x+1111/92)/(x^2-1/2*x+3/2)-30613/128*ln(2*x^2-x+3)+13292697/33856*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
45,1,61,62,0.008000," ","int((5*x^2+3*x+2)^3/(2*x^2-x+3)^2,x)","\frac{125 x^{3}}{12}+\frac{175 x^{2}}{4}+\frac{915 x}{16}-\frac{223971 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{8464}-\frac{2057 \ln \left(2 x^{2}-x +3\right)}{32}-\frac{121 \left(-\frac{495 x}{92}+\frac{187}{92}\right)}{16 \left(x^{2}-\frac{1}{2} x +\frac{3}{2}\right)}"," ",0,"125/12*x^3+175/4*x^2+915/16*x-121/16*(-495/92*x+187/92)/(x^2-1/2*x+3/2)-2057/32*ln(2*x^2-x+3)-223971/8464*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
46,1,51,52,0.007000," ","int((5*x^2+3*x+2)^2/(2*x^2-x+3)^2,x)","\frac{25 x}{4}-\frac{1859 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{2116}+\frac{55 \ln \left(2 x^{2}-x +3\right)}{8}+\frac{-\frac{847 x}{368}+\frac{2299}{368}}{x^{2}-\frac{1}{2} x +\frac{3}{2}}"," ",0,"25/4*x+11/4*(-77/92*x+209/92)/(x^2-1/2*x+3/2)+55/8*ln(2*x^2-x+3)-1859/2116*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
47,1,34,36,0.004000," ","int((5*x^2+3*x+2)/(2*x^2-x+3)^2,x)","\frac{82 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{529}+\frac{-\frac{33 x}{92}-\frac{55}{92}}{x^{2}-\frac{1}{2} x +\frac{3}{2}}"," ",0,"(-33/92*x-55/92)/(x^2-1/2*x+3/2)+82/529*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
48,1,77,78,0.007000," ","int(1/(2*x^2-x+3)^2/(5*x^2+3*x+2),x)","\frac{69 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{15004}-\frac{241 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{256036}-\frac{13 \ln \left(2 x^{2}-x +3\right)}{968}+\frac{13 \ln \left(5 x^{2}+3 x +2\right)}{968}-\frac{\frac{66 x}{23}-\frac{143}{23}}{484 \left(x^{2}-\frac{1}{2} x +\frac{3}{2}\right)}"," ",0,"13/968*ln(5*x^2+3*x+2)+69/15004*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))-1/484*(66/23*x-143/23)/(x^2-1/2*x+3/2)-13/968*ln(2*x^2-x+3)-241/256036*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
49,1,94,109,0.010000," ","int(1/(2*x^2-x+3)^2/(5*x^2+3*x+2)^2,x)","\frac{12643 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{5116364}-\frac{2769 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{2816396}+\frac{19 \ln \left(2 x^{2}-x +3\right)}{10648}-\frac{19 \ln \left(5 x^{2}+3 x +2\right)}{10648}-\frac{-\frac{759 x}{31}+\frac{1078}{155}}{5324 \left(x^{2}+\frac{3}{5} x +\frac{2}{5}\right)}+\frac{-\frac{77 x}{23}-\frac{341}{46}}{5324 x^{2}-2662 x +7986}"," ",0,"-1/5324*(-759/31*x+1078/155)/(x^2+3/5*x+2/5)-19/10648*ln(5*x^2+3*x+2)+12643/5116364*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))+1/5324*(-77/23*x-341/46)/(x^2-1/2*x+3/2)+19/10648*ln(2*x^2-x+3)-2769/2816396*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
50,1,106,128,0.011000," ","int(1/(2*x^2-x+3)^2/(5*x^2+3*x+2)^3,x)","\frac{4464079 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{6978720496}+\frac{25557 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{123921424}+\frac{97 \ln \left(2 x^{2}-x +3\right)}{468512}-\frac{97 \ln \left(5 x^{2}+3 x +2\right)}{468512}-\frac{25 \left(-\frac{723272}{961} x^{3}-\frac{3656422}{4805} x^{2}-\frac{14280728}{24025} x -\frac{2238016}{24025}\right)}{234256 \left(5 x^{2}+3 x +2\right)^{2}}+\frac{\frac{990 x}{23}-\frac{121}{23}}{234256 x^{2}-117128 x +351384}"," ",0,"-25/234256*(-723272/961*x^3-3656422/4805*x^2-14280728/24025*x-2238016/24025)/(5*x^2+3*x+2)^2-97/468512*ln(5*x^2+3*x+2)+4464079/6978720496*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))+1/234256*(990/23*x-121/23)/(x^2-1/2*x+3/2)+97/468512*ln(2*x^2-x+3)+25557/123921424*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
51,1,73,81,0.008000," ","int((5*x^2+3*x+2)^4/(2*x^2-x+3)^3,x)","\frac{625 x^{3}}{24}+\frac{4875 x^{2}}{32}+\frac{2725 x}{8}-\frac{63799791 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{389344}-\frac{13915 \ln \left(2 x^{2}-x +3\right)}{64}-\frac{121 \left(-\frac{210155}{4232} x^{3}+\frac{362791}{16928} x^{2}-\frac{561121}{8464} x +\frac{54263}{16928}\right)}{4 \left(2 x^{2}-x +3\right)^{2}}"," ",0,"625/24*x^3+4875/32*x^2+2725/8*x-121/4*(-210155/4232*x^3+362791/16928*x^2-561121/8464*x+54263/16928)/(2*x^2-x+3)^2-13915/64*ln(2*x^2-x+3)-63799791/389344*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
52,1,63,71,0.007000," ","int((5*x^2+3*x+2)^3/(2*x^2-x+3)^3,x)","\frac{125 x}{8}-\frac{165099 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{194672}+\frac{825 \ln \left(2 x^{2}-x +3\right)}{32}+\frac{-\frac{388047}{4232} x^{3}+\frac{3340447}{16928} x^{2}-\frac{1460833}{8464} x +\frac{3586319}{16928}}{\left(2 x^{2}-x +3\right)^{2}}"," ",0,"125/8*x+11/2*(-35277/2116*x^3+303677/8464*x^2-132803/4232*x+326029/8464)/(2*x^2-x+3)^2+825/32*ln(2*x^2-x+3)-165099/194672*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
53,1,47,55,0.006000," ","int((5*x^2+3*x+2)^2/(2*x^2-x+3)^3,x)","\frac{4330 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{12167}+\frac{-\frac{4565}{1058} x^{3}-\frac{44495}{4232} x^{2}-\frac{5159}{2116} x -\frac{53999}{4232}}{\left(2 x^{2}-x +3\right)^{2}}"," ",0,"4*(-4565/4232*x^3-44495/16928*x^2-5159/8464*x-53999/16928)/(2*x^2-x+3)^2+4330/12167*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
54,1,47,55,0.007000," ","int((5*x^2+3*x+2)/(2*x^2-x+3)^3,x)","\frac{262 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{12167}+\frac{\frac{262}{529} x^{3}-\frac{393}{1058} x^{2}+\frac{236}{529} x -\frac{829}{1058}}{\left(2 x^{2}-x +3\right)^{2}}"," ",0,"4*(131/1058*x^3-393/4232*x^2+59/529*x-829/4232)/(2*x^2-x+3)^2+262/12167*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
55,1,89,97,0.008000," ","int(1/(2*x^2-x+3)^3/(5*x^2+3*x+2),x)","\frac{247 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{330088}+\frac{53403 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{129554216}-\frac{119 \ln \left(2 x^{2}-x +3\right)}{21296}+\frac{119 \ln \left(5 x^{2}+3 x +2\right)}{21296}-\frac{\frac{8206}{529} x^{3}-\frac{43978}{529} x^{2}+\frac{81191}{1058} x -\frac{77902}{529}}{2662 \left(2 x^{2}-x +3\right)^{2}}"," ",0,"119/21296*ln(5*x^2+3*x+2)+247/330088*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))-1/2662*(8206/529*x^3-43978/529*x^2+81191/1058*x-77902/529)/(2*x^2-x+3)^2-119/21296*ln(2*x^2-x+3)+53403/129554216*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
56,1,106,140,0.011000," ","int(1/(2*x^2-x+3)^3/(5*x^2+3*x+2)^2,x)","\frac{246757 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{225120016}-\frac{2038497 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{2850192752}+\frac{181 \ln \left(2 x^{2}-x +3\right)}{468512}-\frac{181 \ln \left(5 x^{2}+3 x +2\right)}{468512}-\frac{-\frac{5434 x}{31}+\frac{32428}{155}}{234256 \left(x^{2}+\frac{3}{5} x +\frac{2}{5}\right)}+\frac{-\frac{128612}{529} x^{3}-\frac{14102}{529} x^{2}-\frac{173195}{529} x -\frac{321497}{1058}}{58564 \left(2 x^{2}-x +3\right)^{2}}"," ",0,"-1/234256*(-5434/31*x+32428/155)/(x^2+3/5*x+2/5)-181/468512*ln(5*x^2+3*x+2)+246757/225120016*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))+1/58564*(-128612/529*x^3-14102/529*x^2-173195/529*x-321497/1058)/(2*x^2-x+3)^2+181/468512*ln(2*x^2-x+3)-2038497/2850192752*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
57,1,118,159,0.013000," ","int(1/(2*x^2-x+3)^3/(5*x^2+3*x+2)^3,x)","\frac{2768835 \sqrt{31}\, \arctan \left(\frac{\left(10 x +3\right) \sqrt{31}}{31}\right)}{19191481364}+\frac{880575 \sqrt{23}\, \arctan \left(\frac{\left(4 x -1\right) \sqrt{23}}{23}\right)}{7838030068}+\frac{405 \ln \left(2 x^{2}-x +3\right)}{1288408}-\frac{405 \ln \left(5 x^{2}+3 x +2\right)}{1288408}-\frac{25 \left(-\frac{3013197}{961} x^{3}-\frac{14516062}{4805} x^{2}-\frac{51193868}{24025} x -\frac{5423968}{24025}\right)}{2576816 \left(5 x^{2}+3 x +2\right)^{2}}+\frac{\frac{302907}{529} x^{3}-\frac{368291}{529} x^{2}+\frac{2501587}{2116} x -\frac{665819}{1058}}{644204 \left(2 x^{2}-x +3\right)^{2}}"," ",0,"-25/2576816*(-3013197/961*x^3-14516062/4805*x^2-51193868/24025*x-5423968/24025)/(5*x^2+3*x+2)^2-405/1288408*ln(5*x^2+3*x+2)+2768835/19191481364*31^(1/2)*arctan(1/31*(10*x+3)*31^(1/2))+1/644204*(302907/529*x^3-368291/529*x^2+2501587/2116*x-665819/1058)/(2*x^2-x+3)^2+405/1288408*ln(2*x^2-x+3)+880575/7838030068*23^(1/2)*arctan(1/23*(4*x-1)*23^(1/2))","A"
58,1,166,167,0.031000," ","int((5*x^2+3*x+2)^4*(2*x^2-x+3)^(1/2),x)","\frac{125 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{7}}{4}+\frac{14125 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{6}}{144}+\frac{233225 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{5}}{1536}+\frac{4796405 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{4}}{43008}+\frac{8325631 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{3}}{1032192}-\frac{83948353 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{2}}{2293760}+\frac{804243809 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x}{36700160}+\frac{8267844569 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{268435456}+\frac{27185733541 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{440401920}+\frac{359471503 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{67108864}"," ",0,"125/4*x^7*(2*x^2-x+3)^(3/2)+27185733541/440401920*(2*x^2-x+3)^(3/2)+14125/144*x^6*(2*x^2-x+3)^(3/2)+233225/1536*x^5*(2*x^2-x+3)^(3/2)+4796405/43008*x^4*(2*x^2-x+3)^(3/2)+8325631/1032192*x^3*(2*x^2-x+3)^(3/2)-83948353/2293760*x^2*(2*x^2-x+3)^(3/2)+804243809/36700160*x*(2*x^2-x+3)^(3/2)+8267844569/268435456*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+359471503/67108864*(4*x-1)*(2*x^2-x+3)^(1/2)","A"
59,1,132,133,0.008000," ","int((5*x^2+3*x+2)^3*(2*x^2-x+3)^(1/2),x)","\frac{125 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{5}}{16}+\frac{8825 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{4}}{448}+\frac{247435 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{3}}{10752}+\frac{531681 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{2}}{71680}-\frac{9627393 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x}{1146880}+\frac{155620231 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{8388608}-\frac{22548119 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{4587520}+\frac{6766097 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{2097152}"," ",0,"-22548119/4587520*(2*x^2-x+3)^(3/2)+125/16*(2*x^2-x+3)^(3/2)*x^5+8825/448*(2*x^2-x+3)^(3/2)*x^4+247435/10752*(2*x^2-x+3)^(3/2)*x^3+531681/71680*(2*x^2-x+3)^(3/2)*x^2-9627393/1146880*(2*x^2-x+3)^(3/2)*x+155620231/8388608*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+6766097/2097152*(4*x-1)*(2*x^2-x+3)^(1/2)","A"
60,1,98,99,0.007000," ","int((5*x^2+3*x+2)^2*(2*x^2-x+3)^(1/2),x)","\frac{25 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{3}}{12}+\frac{63 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x^{2}}{16}+\frac{769 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x}{256}-\frac{284533 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{65536}-\frac{2107 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{3072}-\frac{12371 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{16384}"," ",0,"25/12*(2*x^2-x+3)^(3/2)*x^3+63/16*(2*x^2-x+3)^(3/2)*x^2+769/256*(2*x^2-x+3)^(3/2)*x-2107/3072*(2*x^2-x+3)^(3/2)-12371/16384*(4*x-1)*(2*x^2-x+3)^(1/2)-284533/65536*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","A"
61,1,64,65,0.006000," ","int((5*x^2+3*x+2)*(2*x^2-x+3)^(1/2),x)","\frac{5 \left(2 x^{2}-x +3\right)^{\frac{3}{2}} x}{8}+\frac{1863 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{2048}+\frac{73 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{96}+\frac{81 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{512}"," ",0,"5/8*(2*x^2-x+3)^(3/2)*x+73/96*(2*x^2-x+3)^(3/2)+81/512*(4*x-1)*(2*x^2-x+3)^(1/2)+1863/2048*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","A"
62,1,2065,125,0.149000," ","int((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2),x)","\frac{\sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{5}-\frac{\sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}\, \sqrt{2}\, \left(-274846 \sqrt{2}\, \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)-1543366 \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)+285 \sqrt{2}\, \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)+386 \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)\right)}{52855 \sqrt{\frac{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}{\left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right)^{2}}}\, \left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right) \left(8+3 \sqrt{2}\right) \sqrt{-8866+6820 \sqrt{2}}}+\frac{\sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}\, \sqrt{2}\, \left(401698 \sqrt{2}\, \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)-63426 \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)+151 \sqrt{2}\, \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)+218 \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)\right)}{21142 \sqrt{\frac{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}{\left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right)^{2}}}\, \left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right) \left(8+3 \sqrt{2}\right) \sqrt{-8866+6820 \sqrt{2}}}+\frac{3 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}\, \sqrt{2}\, \left(465124 \sqrt{2}\, \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)-866822 \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)+369 \sqrt{2}\, \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)+520 \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)\right)}{21142 \sqrt{\frac{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}{\left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right)^{2}}}\, \left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right) \left(8+3 \sqrt{2}\right) \sqrt{-8866+6820 \sqrt{2}}}"," ",0,"1/5*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))-1/52855*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(285*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+10368*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+22379*2^(1/2)+32016)/(23*(2^(1/2)-1+x)^4/(2^(1/2)+1-x)^4+82*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+23)*(2^(1/2)-1+x)/(2^(1/2)+1-x)*(8+3*2^(1/2)))*(-775687+549362*2^(1/2))^(1/2)+386*(-8866+6820*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+10368*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+22379*2^(1/2)+32016)/(23*(2^(1/2)-1+x)^4/(2^(1/2)+1-x)^4+82*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+23)*(2^(1/2)-1+x)/(2^(1/2)+1-x)*(8+3*2^(1/2)))*(-775687+549362*2^(1/2))^(1/2)-274846*arctanh(31/2*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-1543366*arctanh(31/2*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))/(1+(2^(1/2)-1+x)/(2^(1/2)+1-x))^2)^(1/2)/(1+(2^(1/2)-1+x)/(2^(1/2)+1-x))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)+1/21142*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(151*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+10368*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+22379*2^(1/2)+32016)/(23*(2^(1/2)-1+x)^4/(2^(1/2)+1-x)^4+82*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+23)*(2^(1/2)-1+x)/(2^(1/2)+1-x)*(8+3*2^(1/2)))*(-775687+549362*2^(1/2))^(1/2)+218*(-8866+6820*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+10368*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+22379*2^(1/2)+32016)/(23*(2^(1/2)-1+x)^4/(2^(1/2)+1-x)^4+82*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+23)*(2^(1/2)-1+x)/(2^(1/2)+1-x)*(8+3*2^(1/2)))*(-775687+549362*2^(1/2))^(1/2)+401698*arctanh(31/2*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-63426*arctanh(31/2*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))/(1+(2^(1/2)-1+x)/(2^(1/2)+1-x))^2)^(1/2)/(1+(2^(1/2)-1+x)/(2^(1/2)+1-x))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)+3/21142*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(369*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+10368*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+22379*2^(1/2)+32016)/(23*(2^(1/2)-1+x)^4/(2^(1/2)+1-x)^4+82*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+23)*(2^(1/2)-1+x)/(2^(1/2)+1-x)*(8+3*2^(1/2)))*(-775687+549362*2^(1/2))^(1/2)+520*(-8866+6820*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+10368*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+22379*2^(1/2)+32016)/(23*(2^(1/2)-1+x)^4/(2^(1/2)+1-x)^4+82*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+23)*(2^(1/2)-1+x)/(2^(1/2)+1-x)*(8+3*2^(1/2)))*(-775687+549362*2^(1/2))^(1/2)+465124*arctanh(31/2*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-866822*arctanh(31/2*(8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+3*2^(1/2)*(2^(1/2)-1+x)^2/(2^(1/2)+1-x)^2+8-3*2^(1/2))/(1+(2^(1/2)-1+x)/(2^(1/2)+1-x))^2)^(1/2)/(1+(2^(1/2)-1+x)/(2^(1/2)+1-x))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)","B"
63,1,16357,140,0.232000," ","int((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
64,1,44343,171,0.372000," ","int((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
65,1,185,186,0.035000," ","int((2*x^2-x+3)^(3/2)*(5*x^2+3*x+2)^4,x)","\frac{625 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{7}}{24}+\frac{7625 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{6}}{96}+\frac{95165 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{5}}{768}+\frac{941905 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{4}}{9216}+\frac{10444117 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{3}}{294912}-\frac{56422489 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{2}}{8257536}+\frac{48669967 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x}{22020096}+\frac{606427533063 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{8589934592}+\frac{2124689283 \left(2 x^{2}-x +3\right)^{\frac{5}{2}}}{146800640}+\frac{26366414481 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{2147483648}+\frac{382121949 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{134217728}"," ",0,"625/24*x^7*(2*x^2-x+3)^(5/2)+7625/96*x^6*(2*x^2-x+3)^(5/2)+2124689283/146800640*(2*x^2-x+3)^(5/2)+95165/768*x^5*(2*x^2-x+3)^(5/2)+941905/9216*x^4*(2*x^2-x+3)^(5/2)+10444117/294912*x^3*(2*x^2-x+3)^(5/2)-56422489/8257536*x^2*(2*x^2-x+3)^(5/2)+48669967/22020096*x*(2*x^2-x+3)^(5/2)+606427533063/8589934592*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+26366414481/2147483648*(4*x-1)*(2*x^2-x+3)^(1/2)+382121949/134217728*(4*x-1)*(2*x^2-x+3)^(3/2)","A"
66,1,151,152,0.007000," ","int((2*x^2-x+3)^(3/2)*(5*x^2+3*x+2)^3,x)","\frac{25 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{5}}{4}+\frac{725 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{4}}{48}+\frac{27785 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{3}}{1536}+\frac{384739 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{2}}{43008}-\frac{81685 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x}{114688}+\frac{1059790665 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{134217728}-\frac{4625907 \left(2 x^{2}-x +3\right)^{\frac{5}{2}}}{2293760}+\frac{46077855 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{33554432}+\frac{667795 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{2097152}"," ",0,"-4625907/2293760*(2*x^2-x+3)^(5/2)+25/4*(2*x^2-x+3)^(5/2)*x^5+725/48*(2*x^2-x+3)^(5/2)*x^4+27785/1536*(2*x^2-x+3)^(5/2)*x^3+384739/43008*(2*x^2-x+3)^(5/2)*x^2-81685/114688*(2*x^2-x+3)^(5/2)*x+1059790665/134217728*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+46077855/33554432*(4*x-1)*(2*x^2-x+3)^(1/2)+667795/2097152*(4*x-1)*(2*x^2-x+3)^(3/2)","A"
67,1,117,118,0.009000," ","int((2*x^2-x+3)^(3/2)*(5*x^2+3*x+2)^2,x)","\frac{25 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{3}}{16}+\frac{1235 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x^{2}}{448}+\frac{24499 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x}{10752}-\frac{12850997 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{4194304}+\frac{73861 \left(2 x^{2}-x +3\right)^{\frac{5}{2}}}{215040}-\frac{558739 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{1048576}-\frac{24293 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{196608}"," ",0,"73861/215040*(2*x^2-x+3)^(5/2)+25/16*(2*x^2-x+3)^(5/2)*x^3+1235/448*(2*x^2-x+3)^(5/2)*x^2+24499/10752*(2*x^2-x+3)^(5/2)*x-12850997/4194304*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))-558739/1048576*(4*x-1)*(2*x^2-x+3)^(1/2)-24293/196608*(4*x-1)*(2*x^2-x+3)^(3/2)","A"
68,1,83,84,0.006000," ","int((2*x^2-x+3)^(3/2)*(5*x^2+3*x+2),x)","\frac{5 \left(2 x^{2}-x +3\right)^{\frac{5}{2}} x}{12}+\frac{94691 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{32768}+\frac{107 \left(2 x^{2}-x +3\right)^{\frac{5}{2}}}{240}+\frac{179 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{1536}+\frac{4117 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{8192}"," ",0,"5/12*(2*x^2-x+3)^(5/2)*x+107/240*(2*x^2-x+3)^(5/2)+179/1536*(4*x-1)*(2*x^2-x+3)^(3/2)+4117/8192*(4*x-1)*(2*x^2-x+3)^(1/2)+94691/32768*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","A"
69,1,3460,144,0.053000," ","int((2*x^2-x+3)^(3/2)/(5*x^2+3*x+2),x)","\text{output too large to display}"," ",0,"1/5*x*(2*x^2-x+3)^(1/2)-49/100*(2*x^2-x+3)^(1/2)+2203/2000*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))-2/1321375*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(4245*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+6154*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+12325786*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-359414*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)-2/264275*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(2365*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+3338*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+3192442*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-5264358*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)-13/105710*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(285*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+386*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))-274846*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-1543366*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)+3/10571*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(151*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+218*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+401698*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-63426*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)+9/21142*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(369*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+520*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+465124*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-866822*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)","B"
70,1,28185,175,0.158000," ","int((2*x^2-x+3)^(3/2)/(5*x^2+3*x+2)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
71,1,81552,171,0.350000," ","int((2*x^2-x+3)^(3/2)/(5*x^2+3*x+2)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
72,1,204,205,0.040000," ","int((2*x^2-x+3)^(5/2)*(5*x^2+3*x+2)^4,x)","\frac{625 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{7}}{28}+\frac{13875 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{6}}{208}+\frac{1046225 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{5}}{9984}+\frac{3684995 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{4}}{39936}+\frac{23460839 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{3}}{532480}+\frac{122595067 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{2}}{19169280}+\frac{112244125 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x}{122683392}+\frac{14641852251147 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{137438953472}+\frac{25250178739 \left(2 x^{2}-x +3\right)^{\frac{7}{2}}}{5725224960}+\frac{636602271789 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{34359738368}+\frac{401135647 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{5}{2}}}{335544320}+\frac{9226119881 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{2147483648}"," ",0,"625/28*x^7*(2*x^2-x+3)^(7/2)+13875/208*x^6*(2*x^2-x+3)^(7/2)+25250178739/5725224960*(2*x^2-x+3)^(7/2)+1046225/9984*x^5*(2*x^2-x+3)^(7/2)+3684995/39936*x^4*(2*x^2-x+3)^(7/2)+23460839/532480*x^3*(2*x^2-x+3)^(7/2)+122595067/19169280*x^2*(2*x^2-x+3)^(7/2)+112244125/122683392*x*(2*x^2-x+3)^(7/2)+14641852251147/137438953472*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+636602271789/34359738368*(4*x-1)*(2*x^2-x+3)^(1/2)+401135647/335544320*(4*x-1)*(2*x^2-x+3)^(5/2)+9226119881/2147483648*(4*x-1)*(2*x^2-x+3)^(3/2)","A"
73,1,170,171,0.009000," ","int((2*x^2-x+3)^(5/2)*(5*x^2+3*x+2)^3,x)","\frac{125 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{5}}{24}+\frac{1175 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{4}}{96}+\frac{3823 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{3}}{256}+\frac{80483 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{2}}{9216}+\frac{509257 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x}{294912}+\frac{10569777075 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{4294967296}-\frac{1696165 \left(2 x^{2}-x +3\right)^{\frac{7}{2}}}{2752512}+\frac{459555525 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{1073741824}+\frac{57915 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{5}{2}}}{2097152}+\frac{6660225 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{67108864}"," ",0,"-1696165/2752512*(2*x^2-x+3)^(7/2)+125/24*(2*x^2-x+3)^(7/2)*x^5+1175/96*(2*x^2-x+3)^(7/2)*x^4+3823/256*(2*x^2-x+3)^(7/2)*x^3+80483/9216*(2*x^2-x+3)^(7/2)*x^2+509257/294912*(2*x^2-x+3)^(7/2)*x+10569777075/4294967296*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+459555525/1073741824*(4*x-1)*(2*x^2-x+3)^(1/2)+57915/2097152*(4*x-1)*(2*x^2-x+3)^(5/2)+6660225/67108864*(4*x-1)*(2*x^2-x+3)^(3/2)","A"
74,1,136,137,0.007000," ","int((2*x^2-x+3)^(5/2)*(5*x^2+3*x+2)^2,x)","\frac{5 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{3}}{4}+\frac{305 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x^{2}}{144}+\frac{8467 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x}{4608}+\frac{94111745 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{67108864}+\frac{23225 \left(2 x^{2}-x +3\right)^{\frac{7}{2}}}{43008}+\frac{4091815 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{16777216}+\frac{1547 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{5}{2}}}{98304}+\frac{177905 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{3145728}"," ",0,"23225/43008*(2*x^2-x+3)^(7/2)+5/4*(2*x^2-x+3)^(7/2)*x^3+305/144*(2*x^2-x+3)^(7/2)*x^2+8467/4608*(2*x^2-x+3)^(7/2)*x+94111745/67108864*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+4091815/16777216*(4*x-1)*(2*x^2-x+3)^(1/2)+1547/98304*(4*x-1)*(2*x^2-x+3)^(5/2)+177905/3145728*(4*x-1)*(2*x^2-x+3)^(3/2)","A"
75,1,102,103,0.006000," ","int((2*x^2-x+3)^(5/2)*(5*x^2+3*x+2),x)","\frac{5 \left(2 x^{2}-x +3\right)^{\frac{7}{2}} x}{16}+\frac{16851295 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{2097152}+\frac{141 \left(2 x^{2}-x +3\right)^{\frac{7}{2}}}{448}+\frac{277 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{5}{2}}}{3072}+\frac{31855 \left(4 x -1\right) \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}{98304}+\frac{732665 \left(4 x -1\right) \sqrt{2 x^{2}-x +3}}{524288}"," ",0,"5/16*(2*x^2-x+3)^(7/2)*x+141/448*(2*x^2-x+3)^(7/2)+277/3072*(4*x-1)*(2*x^2-x+3)^(5/2)+31855/98304*(4*x-1)*(2*x^2-x+3)^(3/2)+732665/524288*(4*x-1)*(2*x^2-x+3)^(1/2)+16851295/2097152*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","A"
76,1,4860,165,0.053000," ","int((2*x^2-x+3)^(5/2)/(5*x^2+3*x+2),x)","\text{output too large to display}"," 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/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+3338*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+3192442*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-5264358*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)-63/105710*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(285*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+386*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))-274846*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-1543366*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)+27/21142*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(151*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+218*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+401698*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-63426*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)+27/21142*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(369*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+520*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+465124*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-866822*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)","B"
77,1,40028,194,0.157000," ","int((2*x^2-x+3)^(5/2)/(5*x^2+3*x+2)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
78,1,119458,220,0.384000," ","int((2*x^2-x+3)^(5/2)/(5*x^2+3*x+2)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
79,1,147,148,0.019000," ","int((5*x^2+3*x+2)^4/(2*x^2-x+3)^(1/2),x)","\frac{625 \sqrt{2 x^{2}-x +3}\, x^{7}}{16}+\frac{57375 \sqrt{2 x^{2}-x +3}\, x^{6}}{448}+\frac{2116475 \sqrt{2 x^{2}-x +3}\, x^{5}}{10752}+\frac{686531 \sqrt{2 x^{2}-x +3}\, x^{4}}{6144}-\frac{19750457 \sqrt{2 x^{2}-x +3}\, x^{3}}{229376}-\frac{15428243 \sqrt{2 x^{2}-x +3}\, x^{2}}{131072}+\frac{1572007407 \sqrt{2 x^{2}-x +3}\, x}{7340032}-\frac{2899366573 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{16777216}+\frac{16493087661 \sqrt{2 x^{2}-x +3}}{29360128}"," ",0,"16493087661/29360128*(2*x^2-x+3)^(1/2)-2899366573/16777216*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+625/16*x^7*(2*x^2-x+3)^(1/2)+57375/448*x^6*(2*x^2-x+3)^(1/2)+2116475/10752*x^5*(2*x^2-x+3)^(1/2)+686531/6144*x^4*(2*x^2-x+3)^(1/2)-19750457/229376*x^3*(2*x^2-x+3)^(1/2)-15428243/131072*x^2*(2*x^2-x+3)^(1/2)+1572007407/7340032*x*(2*x^2-x+3)^(1/2)","A"
80,1,113,114,0.008000," ","int((5*x^2+3*x+2)^3/(2*x^2-x+3)^(1/2),x)","\frac{125 \sqrt{2 x^{2}-x +3}\, x^{5}}{12}+\frac{1355 \sqrt{2 x^{2}-x +3}\, x^{4}}{48}+\frac{8185 \sqrt{2 x^{2}-x +3}\, x^{3}}{256}-\frac{3387 \sqrt{2 x^{2}-x +3}\, x^{2}}{1024}-\frac{372783 \sqrt{2 x^{2}-x +3}\, x}{8192}+\frac{9267707 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{131072}-\frac{203373 \sqrt{2 x^{2}-x +3}}{32768}"," ",0,"-203373/32768*(2*x^2-x+3)^(1/2)+9267707/131072*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+125/12*(2*x^2-x+3)^(1/2)*x^5+1355/48*(2*x^2-x+3)^(1/2)*x^4+8185/256*(2*x^2-x+3)^(1/2)*x^3-3387/1024*(2*x^2-x+3)^(1/2)*x^2-372783/8192*(2*x^2-x+3)^(1/2)*x","A"
81,1,79,80,0.008000," ","int((5*x^2+3*x+2)^2/(2*x^2-x+3)^(1/2),x)","\frac{25 \sqrt{2 x^{2}-x +3}\, x^{3}}{8}+\frac{655 \sqrt{2 x^{2}-x +3}\, x^{2}}{96}+\frac{3443 \sqrt{2 x^{2}-x +3}\, x}{768}-\frac{30725 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{4096}-\frac{11373 \sqrt{2 x^{2}-x +3}}{1024}"," ",0,"25/8*(2*x^2-x+3)^(1/2)*x^3+655/96*(2*x^2-x+3)^(1/2)*x^2+3443/768*(2*x^2-x+3)^(1/2)*x-11373/1024*(2*x^2-x+3)^(1/2)-30725/4096*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","A"
82,1,45,46,0.006000," ","int((5*x^2+3*x+2)/(2*x^2-x+3)^(1/2),x)","\frac{5 \sqrt{2 x^{2}-x +3}\, x}{4}-\frac{17 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{64}+\frac{39 \sqrt{2 x^{2}-x +3}}{16}"," ",0,"5/4*(2*x^2-x+3)^(1/2)*x+39/16*(2*x^2-x+3)^(1/2)-17/64*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","A"
83,1,684,109,0.004000," ","int(1/(5*x^2+3*x+2)/(2*x^2-x+3)^(1/2),x)","\frac{\sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}\, \sqrt{2}\, \left(465124 \sqrt{2}\, \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)-866822 \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)+369 \sqrt{2}\, \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)+520 \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)\right)}{21142 \sqrt{\frac{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}{\left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right)^{2}}}\, \left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right) \left(8+3 \sqrt{2}\right) \sqrt{-8866+6820 \sqrt{2}}}"," ",0,"1/21142*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(369*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+520*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+465124*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-866822*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)","B"
84,1,5225,140,0.006000," ","int(1/(5*x^2+3*x+2)^2/(2*x^2-x+3)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
85,1,13040,171,0.007000," ","int(1/(5*x^2+3*x+2)^3/(2*x^2-x+3)^(1/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
86,1,166,133,0.029000," ","int((5*x^2+3*x+2)^4/(2*x^2-x+3)^(3/2),x)","\frac{625 x^{7}}{12 \sqrt{2 x^{2}-x +3}}+\frac{8825 x^{6}}{48 \sqrt{2 x^{2}-x +3}}+\frac{217675 x^{5}}{768 \sqrt{2 x^{2}-x +3}}+\frac{52235 x^{4}}{1024 \sqrt{2 x^{2}-x +3}}-\frac{4734827 x^{3}}{8192 \sqrt{2 x^{2}-x +3}}-\frac{18367831 x^{2}}{32768 \sqrt{2 x^{2}-x +3}}-\frac{310445587 x}{131072 \sqrt{2 x^{2}-x +3}}+\frac{310445587 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{262144}-\frac{1217267299}{524288 \sqrt{2 x^{2}-x +3}}+\frac{\frac{1234044515 x}{3014656}-\frac{1234044515}{12058624}}{\sqrt{2 x^{2}-x +3}}"," ",0,"-1217267299/524288/(2*x^2-x+3)^(1/2)+1234044515/12058624*(4*x-1)/(2*x^2-x+3)^(1/2)+310445587/262144*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+217675/768*x^5/(2*x^2-x+3)^(1/2)+52235/1024*x^4/(2*x^2-x+3)^(1/2)-4734827/8192*x^3/(2*x^2-x+3)^(1/2)+625/12*x^7/(2*x^2-x+3)^(1/2)+8825/48*x^6/(2*x^2-x+3)^(1/2)-18367831/32768*x^2/(2*x^2-x+3)^(1/2)-310445587/131072*x/(2*x^2-x+3)^(1/2)","A"
87,1,132,99,0.008000," ","int((5*x^2+3*x+2)^3/(2*x^2-x+3)^(3/2),x)","\frac{125 x^{5}}{8 \sqrt{2 x^{2}-x +3}}+\frac{1575 x^{4}}{32 \sqrt{2 x^{2}-x +3}}+\frac{14265 x^{3}}{256 \sqrt{2 x^{2}-x +3}}-\frac{125091 x^{2}}{1024 \sqrt{2 x^{2}-x +3}}+\frac{1168881 x}{4096 \sqrt{2 x^{2}-x +3}}-\frac{1168881 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{8192}-\frac{5130399}{16384 \sqrt{2 x^{2}-x +3}}+\frac{\frac{5392543 x}{94208}-\frac{5392543}{376832}}{\sqrt{2 x^{2}-x +3}}"," ",0,"-5130399/16384/(2*x^2-x+3)^(1/2)+5392543/376832*(4*x-1)/(2*x^2-x+3)^(1/2)-1168881/8192*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+125/8/(2*x^2-x+3)^(1/2)*x^5+1575/32/(2*x^2-x+3)^(1/2)*x^4+14265/256/(2*x^2-x+3)^(1/2)*x^3-125091/1024/(2*x^2-x+3)^(1/2)*x^2+1168881/4096/(2*x^2-x+3)^(1/2)*x","A"
88,1,98,65,0.008000," ","int((5*x^2+3*x+2)^2/(2*x^2-x+3)^(3/2),x)","\frac{25 x^{3}}{4 \sqrt{2 x^{2}-x +3}}+\frac{365 x^{2}}{16 \sqrt{2 x^{2}-x +3}}-\frac{223 x}{64 \sqrt{2 x^{2}-x +3}}+\frac{223 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{128}+\frac{15761}{256 \sqrt{2 x^{2}-x +3}}-\frac{13713 \left(4 x -1\right)}{5888 \sqrt{2 x^{2}-x +3}}"," ",0,"25/4/(2*x^2-x+3)^(1/2)*x^3+365/16/(2*x^2-x+3)^(1/2)*x^2-223/64/(2*x^2-x+3)^(1/2)*x+15761/256/(2*x^2-x+3)^(1/2)-13713/5888*(4*x-1)/(2*x^2-x+3)^(1/2)+223/128*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","A"
89,1,64,36,0.006000," ","int((5*x^2+3*x+2)/(2*x^2-x+3)^(3/2),x)","-\frac{5 x}{2 \sqrt{2 x^{2}-x +3}}+\frac{5 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{4}-\frac{17}{8 \sqrt{2 x^{2}-x +3}}+\frac{\frac{49 x}{46}-\frac{49}{184}}{\sqrt{2 x^{2}-x +3}}"," ",0,"-5/2/(2*x^2-x+3)^(1/2)*x-17/8/(2*x^2-x+3)^(1/2)+49/184*(4*x-1)/(2*x^2-x+3)^(1/2)+5/4*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","A"
90,1,718,128,0.034000," ","int(1/(2*x^2-x+3)^(3/2)/(5*x^2+3*x+2),x)","\frac{\sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}\, \sqrt{2}\, \left(1712502 \sqrt{2}\, \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)-6617446 \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)+2197 \sqrt{2}\, \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)+3070 \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)\right)}{465124 \sqrt{\frac{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}{\left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right)^{2}}}\, \left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right) \left(8+3 \sqrt{2}\right) \sqrt{-8866+6820 \sqrt{2}}}+\frac{1}{22 \sqrt{2 x^{2}-x +3}}-\frac{3 \left(4 x -1\right)}{506 \sqrt{2 x^{2}-x +3}}"," ",0,"1/465124*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(2197*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+3070*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+1712502*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-6617446*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)+1/22/(2*x^2-x+3)^(1/2)-3/506*(4*x-1)/(2*x^2-x+3)^(1/2)","B"
91,1,5942,159,0.099000," ","int(1/(2*x^2-x+3)^(3/2)/(5*x^2+3*x+2)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
92,1,18981,190,0.208000," ","int(1/(2*x^2-x+3)^(3/2)/(5*x^2+3*x+2)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
93,1,214,118,0.031000," ","int((5*x^2+3*x+2)^4/(2*x^2-x+3)^(5/2),x)","\frac{625 x^{7}}{8 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{30875 x^{6}}{96 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{138025 x^{5}}{256 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{799745 x^{4}}{1024 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{16955197 x^{3}}{12288 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{67488035 x^{2}}{16384 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{55167267 x}{131072 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{16955197 x}{8192 \sqrt{2 x^{2}-x +3}}-\frac{16955197 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{16384}+\frac{16955197}{32768 \sqrt{2 x^{2}-x +3}}-\frac{2149616639}{524288 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{\frac{992926033 x}{3250176}-\frac{992926033}{13000704}}{\sqrt{2 x^{2}-x +3}}+\frac{\frac{5141612725 x}{9043968}-\frac{5141612725}{36175872}}{\left(2 x^{2}-x +3\right)^{\frac{3}{2}}}"," ",0,"16955197/32768/(2*x^2-x+3)^(1/2)-2149616639/524288/(2*x^2-x+3)^(3/2)+992926033/13000704*(4*x-1)/(2*x^2-x+3)^(1/2)-16955197/16384*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))+5141612725/36175872*(4*x-1)/(2*x^2-x+3)^(3/2)+625/8*x^7/(2*x^2-x+3)^(3/2)+30875/96*x^6/(2*x^2-x+3)^(3/2)+138025/256*x^5/(2*x^2-x+3)^(3/2)-799745/1024*x^4/(2*x^2-x+3)^(3/2)+16955197/12288*x^3/(2*x^2-x+3)^(3/2)-67488035/16384*x^2/(2*x^2-x+3)^(3/2)+55167267/131072*x/(2*x^2-x+3)^(3/2)+16955197/8192/(2*x^2-x+3)^(1/2)*x","A"
94,1,180,84,0.008000," ","int((5*x^2+3*x+2)^3/(2*x^2-x+3)^(5/2),x)","\frac{125 x^{5}}{4 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{2675 x^{4}}{16 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{7495 x^{3}}{192 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{222809 x^{2}}{256 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{281177 x}{2048 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{7495 x}{128 \sqrt{2 x^{2}-x +3}}+\frac{7495 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{256}-\frac{7495}{512 \sqrt{2 x^{2}-x +3}}+\frac{20961031}{24576 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{3391139 \left(4 x -1\right)}{203136 \sqrt{2 x^{2}-x +3}}-\frac{14081711 \left(4 x -1\right)}{565248 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}"," ",0,"-7495/512/(2*x^2-x+3)^(1/2)+20961031/24576/(2*x^2-x+3)^(3/2)-3391139/203136*(4*x-1)/(2*x^2-x+3)^(1/2)+7495/256*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))-14081711/565248*(4*x-1)/(2*x^2-x+3)^(3/2)+125/4/(2*x^2-x+3)^(3/2)*x^5+2675/16/(2*x^2-x+3)^(3/2)*x^4-7495/192/(2*x^2-x+3)^(3/2)*x^3+222809/256/(2*x^2-x+3)^(3/2)*x^2-281177/2048/(2*x^2-x+3)^(3/2)*x-7495/128/(2*x^2-x+3)^(1/2)*x","B"
95,1,146,55,0.007000," ","int((5*x^2+3*x+2)^2/(2*x^2-x+3)^(5/2),x)","-\frac{25 x^{3}}{6 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{145 x^{2}}{8 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{319 x}{64 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{25 x}{4 \sqrt{2 x^{2}-x +3}}+\frac{25 \sqrt{2}\, \arcsinh \left(\frac{4 \sqrt{23}\, \left(x -\frac{1}{4}\right)}{23}\right)}{8}-\frac{15775}{768 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{\frac{8493 x}{1472}-\frac{8493}{5888}}{\left(2 x^{2}-x +3\right)^{\frac{3}{2}}}+\frac{\frac{2267 x}{529}-\frac{2267}{2116}}{\sqrt{2 x^{2}-x +3}}-\frac{25}{16 \sqrt{2 x^{2}-x +3}}"," ",0,"-25/6/(2*x^2-x+3)^(3/2)*x^3-145/8/(2*x^2-x+3)^(3/2)*x^2-319/64/(2*x^2-x+3)^(3/2)*x-15775/768/(2*x^2-x+3)^(3/2)+8493/5888*(4*x-1)/(2*x^2-x+3)^(3/2)+2267/2116*(4*x-1)/(2*x^2-x+3)^(1/2)-25/4/(2*x^2-x+3)^(1/2)*x-25/16/(2*x^2-x+3)^(1/2)+25/8*2^(1/2)*arcsinh(4/23*23^(1/2)*(x-1/4))","B"
96,1,30,39,0.005000," ","int((5*x^2+3*x+2)/(2*x^2-x+3)^(5/2),x)","\frac{\frac{568}{529} x^{3}-\frac{426}{529} x^{2}+\frac{670}{529} x -\frac{1904}{1587}}{\left(2 x^{2}-x +3\right)^{\frac{3}{2}}}"," ",0,"2/1587/(2*x^2-x+3)^(3/2)*(852*x^3-639*x^2+1005*x-952)","A"
97,1,751,147,0.039000," ","int(1/(2*x^2-x+3)^(5/2)/(5*x^2+3*x+2),x)","\frac{\sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}\, \sqrt{2}\, \left(-993674 \sqrt{2}\, \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)-42685698 \arctanh \left(\frac{31 \sqrt{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}}{2 \sqrt{-8866+6820 \sqrt{2}}}\right)+10111 \sqrt{2}\, \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)+13910 \sqrt{-8866+6820 \sqrt{2}}\, \sqrt{-775687+549362 \sqrt{2}}\, \arctan \left(\frac{\sqrt{-775687+549362 \sqrt{2}}\, \sqrt{-23 \left(8+3 \sqrt{2}\right) \left(-\frac{23 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+24 \sqrt{2}-41\right)}\, \left(\frac{6485 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{10368 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+22379 \sqrt{2}+32016\right) \left(x +\sqrt{2}-1\right) \left(8+3 \sqrt{2}\right)}{11692487 \left(\frac{23 \left(x +\sqrt{2}-1\right)^{4}}{\left(-x +\sqrt{2}+1\right)^{4}}+\frac{82 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+23\right) \left(-x +\sqrt{2}+1\right)}\right)\right)}{10232728 \sqrt{\frac{\frac{8 \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+\frac{3 \sqrt{2}\, \left(x +\sqrt{2}-1\right)^{2}}{\left(-x +\sqrt{2}+1\right)^{2}}+8-3 \sqrt{2}}{\left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right)^{2}}}\, \left(1+\frac{x +\sqrt{2}-1}{-x +\sqrt{2}+1}\right) \left(8+3 \sqrt{2}\right) \sqrt{-8866+6820 \sqrt{2}}}+\frac{13}{484 \sqrt{2 x^{2}-x +3}}-\frac{329 \left(4 x -1\right)}{256036 \sqrt{2 x^{2}-x +3}}+\frac{1}{66 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}-\frac{4 x -1}{506 \left(2 x^{2}-x +3\right)^{\frac{3}{2}}}"," ",0,"1/10232728*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)*2^(1/2)*(10111*2^(1/2)*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))+13910*(-8866+6820*2^(1/2))^(1/2)*(-775687+549362*2^(1/2))^(1/2)*arctan(1/11692487*(-775687+549362*2^(1/2))^(1/2)*(-23*(8+3*2^(1/2))*(-23*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+24*2^(1/2)-41))^(1/2)*(6485*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+10368*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+22379*2^(1/2)+32016)/(23*(x+2^(1/2)-1)^4/(-x+2^(1/2)+1)^4+82*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+23)*(x+2^(1/2)-1)/(-x+2^(1/2)+1)*(8+3*2^(1/2)))-993674*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2))*2^(1/2)-42685698*arctanh(31/2*(8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))^(1/2)/(-8866+6820*2^(1/2))^(1/2)))/((8*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+3*2^(1/2)*(x+2^(1/2)-1)^2/(-x+2^(1/2)+1)^2+8-3*2^(1/2))/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))^2)^(1/2)/(1+(x+2^(1/2)-1)/(-x+2^(1/2)+1))/(8+3*2^(1/2))/(-8866+6820*2^(1/2))^(1/2)+13/484/(2*x^2-x+3)^(1/2)-329/256036*(4*x-1)/(2*x^2-x+3)^(1/2)+1/66/(2*x^2-x+3)^(3/2)-1/506*(4*x-1)/(2*x^2-x+3)^(3/2)","B"
98,1,5975,178,0.104000," ","int(1/(2*x^2-x+3)^(5/2)/(5*x^2+3*x+2)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
99,1,19014,209,0.209000," ","int(1/(2*x^2-x+3)^(5/2)/(5*x^2+3*x+2)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
100,1,1429,406,0.023000," ","int((c*x^2+b*x+a)^(1/2)*(f*x^2+e*x+d)^2,x)","\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} f^{2} x^{3}}{6 c}+\frac{a^{3} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{15 a^{2} b^{2} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{7}{2}}}+\frac{3 a^{2} b e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{a^{2} d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{3}{2}}}-\frac{a^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}+\frac{35 a \,b^{4} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{9}{2}}}-\frac{5 a \,b^{3} e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{3 a \,b^{2} d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}+\frac{3 a \,b^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{a b d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{a \,d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}}-\frac{21 b^{6} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{11}{2}}}+\frac{7 b^{5} e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{9}{2}}}-\frac{5 b^{4} d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{7}{2}}}-\frac{5 b^{4} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}+\frac{b^{3} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}+\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} f^{2} x}{16 c^{2}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} f^{2} x}{32 c^{3}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b e f x}{8 c^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a d f x}{4 c}-\frac{\sqrt{c \,x^{2}+b x +a}\, a \,e^{2} x}{8 c}+\frac{21 \sqrt{c \,x^{2}+b x +a}\, b^{4} f^{2} x}{256 c^{4}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{3} e f x}{32 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} d f x}{16 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} e^{2} x}{32 c^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b d e x}{2 c}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,f^{2} x^{2}}{20 c^{2}}+\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} e f \,x^{2}}{5 c}+\frac{\sqrt{c \,x^{2}+b x +a}\, d^{2} x}{2}+\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} b \,f^{2}}{32 c^{3}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} f^{2}}{64 c^{4}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} e f}{16 c^{3}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a b d f}{8 c^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a b \,e^{2}}{16 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,f^{2} x}{8 c^{2}}+\frac{21 \sqrt{c \,x^{2}+b x +a}\, b^{5} f^{2}}{512 c^{5}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{4} e f}{64 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{3} d f}{32 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{3} e^{2}}{64 c^{3}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b^{2} d e}{4 c^{2}}+\frac{21 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} f^{2} x}{160 c^{3}}+\frac{\sqrt{c \,x^{2}+b x +a}\, b \,d^{2}}{4 c}-\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b e f x}{20 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d f x}{2 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} e^{2} x}{4 c}+\frac{49 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,f^{2}}{240 c^{3}}-\frac{4 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a e f}{15 c^{2}}-\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} f^{2}}{64 c^{4}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} e f}{24 c^{3}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b d f}{12 c^{2}}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,e^{2}}{24 c^{2}}+\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d e}{3 c}"," ",0,"1/6*f^2*x^3*(c*x^2+b*x+a)^(3/2)/c-7/32*f^2*b^2/c^3*a*x*(c*x^2+b*x+a)^(1/2)-7/20*e*f*b/c^2*x*(c*x^2+b*x+a)^(3/2)-7/32*e*f*b^3/c^3*x*(c*x^2+b*x+a)^(1/2)+2/3*d*e*(c*x^2+b*x+a)^(3/2)/c+1/4*d^2/c*(c*x^2+b*x+a)^(1/2)*b+1/2*d^2/c^(1/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/8*d^2/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2+1/4*x*(c*x^2+b*x+a)^(3/2)/c*e^2-5/24*b/c^2*(c*x^2+b*x+a)^(3/2)*e^2+5/64*b^3/c^3*(c*x^2+b*x+a)^(1/2)*e^2-5/128*b^4/c^(7/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2-1/8*a^2/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2+21/512*f^2*b^5/c^5*(c*x^2+b*x+a)^(1/2)-21/1024*f^2*b^6/c^(11/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/16*f^2*a^3/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-7/64*f^2*b^3/c^4*(c*x^2+b*x+a)^(3/2)+3/8*e*f*b/c^2*a*x*(c*x^2+b*x+a)^(1/2)-5/16*e*f*b^3/c^(7/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+3/16*e*f*b^2/c^3*a*(c*x^2+b*x+a)^(1/2)+3/8*e*f*b/c^(5/2)*a^2*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+5/16*b^2/c^2*x*(c*x^2+b*x+a)^(1/2)*d*f+3/8*b^2/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a*d*f-1/4*a/c*x*(c*x^2+b*x+a)^(1/2)*d*f-1/8*a/c^2*(c*x^2+b*x+a)^(1/2)*b*d*f-1/2*d*e*b/c*x*(c*x^2+b*x+a)^(1/2)-1/2*d*e*b/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/2*d^2*x*(c*x^2+b*x+a)^(1/2)+21/256*f^2*b^4/c^4*x*(c*x^2+b*x+a)^(1/2)-5/12*b/c^2*(c*x^2+b*x+a)^(3/2)*d*f+5/32*b^2/c^2*x*(c*x^2+b*x+a)^(1/2)*e^2+5/32*b^3/c^3*(c*x^2+b*x+a)^(1/2)*d*f+3/16*b^2/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a*e^2-5/64*b^4/c^(7/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f-1/8*a/c*x*(c*x^2+b*x+a)^(1/2)*e^2-1/16*a/c^2*(c*x^2+b*x+a)^(1/2)*b*e^2-1/4*a^2/c^(3/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f-1/4*d*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)+35/256*f^2*b^4/c^(9/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-7/64*f^2*b^3/c^4*a*(c*x^2+b*x+a)^(1/2)-15/64*f^2*b^2/c^(7/2)*a^2*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+49/240*f^2*b/c^3*a*(c*x^2+b*x+a)^(3/2)-1/8*f^2*a/c^2*x*(c*x^2+b*x+a)^(3/2)+1/16*f^2*a^2/c^2*x*(c*x^2+b*x+a)^(1/2)+1/32*f^2*a^2/c^3*(c*x^2+b*x+a)^(1/2)*b+2/5*e*f*x^2*(c*x^2+b*x+a)^(3/2)/c+7/24*e*f*b^2/c^3*(c*x^2+b*x+a)^(3/2)-7/64*e*f*b^4/c^4*(c*x^2+b*x+a)^(1/2)+7/128*e*f*b^5/c^(9/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-4/15*e*f*a/c^2*(c*x^2+b*x+a)^(3/2)-3/20*f^2*b/c^2*x^2*(c*x^2+b*x+a)^(3/2)+21/160*f^2*b^2/c^3*x*(c*x^2+b*x+a)^(3/2)+1/2*x*(c*x^2+b*x+a)^(3/2)/c*d*f+1/8*d*e*b^3/c^(5/2)*ln((1/2*b+c*x)/c^(1/2)+(c*x^2+b*x+a)^(1/2))","B"
101,1,453,153,0.007000," ","int((c*x^2+b*x+a)^(1/2)*(f*x^2+e*x+d),x)","-\frac{a^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}+\frac{3 a \,b^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{a b e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{3}{2}}}+\frac{a d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 \sqrt{c}}-\frac{5 b^{4} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}+\frac{b^{3} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{b^{2} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a f x}{8 c}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} f x}{32 c^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b e x}{4 c}+\frac{\sqrt{c \,x^{2}+b x +a}\, d x}{2}-\frac{\sqrt{c \,x^{2}+b x +a}\, a b f}{16 c^{2}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{3} f}{64 c^{3}}-\frac{\sqrt{c \,x^{2}+b x +a}\, b^{2} e}{8 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, b d}{4 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} f x}{4 c}-\frac{5 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b f}{24 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} e}{3 c}"," ",0,"1/4*f*x*(c*x^2+b*x+a)^(3/2)/c-5/24*f*b/c^2*(c*x^2+b*x+a)^(3/2)+5/32*f*b^2/c^2*(c*x^2+b*x+a)^(1/2)*x+5/64*f*b^3/c^3*(c*x^2+b*x+a)^(1/2)+3/16*f*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-5/128*f*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/8*f*a/c*(c*x^2+b*x+a)^(1/2)*x-1/16*f*a/c^2*(c*x^2+b*x+a)^(1/2)*b-1/8*f*a^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/3*e*(c*x^2+b*x+a)^(3/2)/c-1/4*e*b/c*(c*x^2+b*x+a)^(1/2)*x-1/8*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)-1/4*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/16*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/2*d*(c*x^2+b*x+a)^(1/2)*x+1/4*d/c*(c*x^2+b*x+a)^(1/2)*b+1/2*d/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-1/8*d/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2","B"
102,1,6019,376,0.052000," ","int((c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
103,1,22287,439,0.037000," ","int((c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
104,1,2458,530,0.025000," ","int((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)^2,x)","\frac{3 a^{4} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}-\frac{15 a^{3} b^{2} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}+\frac{3 a^{3} b e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{a^{3} d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}-\frac{a^{3} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{105 a^{2} b^{4} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{9}{2}}}-\frac{15 a^{2} b^{3} e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{7}{2}}}+\frac{9 a^{2} b^{2} d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{5}{2}}}+\frac{9 a^{2} b^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{5}{2}}}-\frac{3 a^{2} b d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{3}{2}}}+\frac{3 a^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 \sqrt{c}}-\frac{63 a \,b^{6} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2048 c^{\frac{11}{2}}}+\frac{21 a \,b^{5} e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{9}{2}}}-\frac{15 a \,b^{4} d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}-\frac{15 a \,b^{4} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{3 a \,b^{3} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{5}{2}}}-\frac{3 a \,b^{2} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{99 b^{8} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32768 c^{\frac{13}{2}}}-\frac{9 b^{7} e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{11}{2}}}+\frac{7 b^{6} d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{512 c^{\frac{9}{2}}}+\frac{7 b^{6} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{9}{2}}}-\frac{3 b^{5} d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{7}{2}}}+\frac{3 b^{4} d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{3} f^{2} x}{128 c^{2}}-\frac{57 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} f^{2} x}{512 c^{3}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{2} b e f x}{16 c^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} d f x}{8 c}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} e^{2} x}{16 c}+\frac{153 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} f^{2} x}{2048 c^{4}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} e f x}{16 c^{3}}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d f x}{4 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{2} e^{2} x}{8 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b d e x}{8 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,d^{2} x}{8}-\frac{99 \sqrt{c \,x^{2}+b x +a}\, b^{6} f^{2} x}{8192 c^{5}}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, b^{5} e f x}{256 c^{4}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{4} d f x}{128 c^{3}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{4} e^{2} x}{256 c^{3}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} d e x}{32 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{2} d^{2} x}{32 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} f^{2} x^{3}}{8 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{3} b \,f^{2}}{256 c^{3}}-\frac{57 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{3} f^{2}}{1024 c^{4}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a^{2} b^{2} e f}{32 c^{3}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} b d f}{16 c^{2}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} b \,e^{2}}{32 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} f^{2} x}{64 c^{2}}+\frac{153 \sqrt{c \,x^{2}+b x +a}\, a \,b^{5} f^{2}}{4096 c^{5}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{4} e f}{32 c^{4}}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{3} d f}{8 c^{3}}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{3} e^{2}}{16 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} d e}{16 c^{2}}-\frac{9 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} f^{2} x}{128 c^{3}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b \,d^{2}}{16 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b e f x}{8 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a d f x}{12 c}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,e^{2} x}{24 c}-\frac{99 \sqrt{c \,x^{2}+b x +a}\, b^{7} f^{2}}{16384 c^{6}}+\frac{9 \sqrt{c \,x^{2}+b x +a}\, b^{6} e f}{512 c^{5}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{5} d f}{256 c^{4}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{5} e^{2}}{512 c^{4}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{4} d e}{64 c^{3}}+\frac{33 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} f^{2} x}{1024 c^{4}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} d^{2}}{64 c^{2}}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} e f x}{32 c^{3}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d f x}{48 c^{2}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} e^{2} x}{96 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b d e x}{4 c}-\frac{11 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,f^{2} x^{2}}{112 c^{2}}+\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} e f \,x^{2}}{7 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d^{2} x}{4}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a^{2} b \,f^{2}}{128 c^{3}}-\frac{9 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{3} f^{2}}{256 c^{4}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a \,b^{2} e f}{16 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b d f}{24 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b \,e^{2}}{48 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a \,f^{2} x}{16 c^{2}}+\frac{33 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{5} f^{2}}{2048 c^{5}}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{4} e f}{64 c^{4}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} d f}{96 c^{3}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} e^{2}}{192 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} d e}{8 c^{2}}+\frac{33 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} f^{2} x}{448 c^{3}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b \,d^{2}}{8 c}-\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b e f x}{14 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d f x}{3 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} e^{2} x}{6 c}+\frac{93 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a b \,f^{2}}{1120 c^{3}}-\frac{4 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} a e f}{35 c^{2}}-\frac{33 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{3} f^{2}}{640 c^{4}}+\frac{3 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b^{2} e f}{20 c^{3}}-\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b d f}{30 c^{2}}-\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b \,e^{2}}{60 c^{2}}+\frac{2 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} d e}{5 c}"," ",0,"1/8*f^2*x^3*(c*x^2+b*x+a)^(5/2)/c+1/8*d^2/c*(c*x^2+b*x+a)^(3/2)*b+3/8*d^2*(c*x^2+b*x+a)^(1/2)*x*a-3/64*d^2/c^2*(c*x^2+b*x+a)^(1/2)*b^3+3/8*d^2/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+3/128*d^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4+2/5*d*e*(c*x^2+b*x+a)^(5/2)/c+1/6*x*(c*x^2+b*x+a)^(5/2)/c*e^2-7/60*b/c^2*(c*x^2+b*x+a)^(5/2)*e^2+7/192*b^3/c^3*(c*x^2+b*x+a)^(3/2)*e^2-7/512*b^5/c^4*(c*x^2+b*x+a)^(1/2)*e^2+7/1024*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2-1/16*a^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2+3/128*f^2*a^4/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+99/32768*f^2*b^8/c^(13/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-33/640*f^2*b^3/c^4*(c*x^2+b*x+a)^(5/2)+33/2048*f^2*b^5/c^5*(c*x^2+b*x+a)^(3/2)-99/16384*f^2*b^7/c^6*(c*x^2+b*x+a)^(1/2)-3/16*e*f*b^3/c^3*(c*x^2+b*x+a)^(1/2)*x*a+1/8*e*f*b/c^2*a*x*(c*x^2+b*x+a)^(3/2)+3/16*e*f*b/c^2*a^2*(c*x^2+b*x+a)^(1/2)*x+1/4*b^2/c^2*(c*x^2+b*x+a)^(1/2)*x*a*d*f-3/8*d*e*b/c*(c*x^2+b*x+a)^(1/2)*x*a+3/16*d*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+1/16*e*f*b^2/c^3*a*(c*x^2+b*x+a)^(3/2)+3/32*e*f*b^2/c^3*a^2*(c*x^2+b*x+a)^(1/2)-3/14*e*f*b/c^2*x*(c*x^2+b*x+a)^(5/2)-3/32*e*f*b^3/c^3*x*(c*x^2+b*x+a)^(3/2)+9/256*e*f*b^5/c^4*(c*x^2+b*x+a)^(1/2)*x-3/32*e*f*b^4/c^4*(c*x^2+b*x+a)^(1/2)*a-15/64*e*f*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+21/256*e*f*b^5/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a+3/16*e*f*b/c^(5/2)*a^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+7/48*b^2/c^2*x*(c*x^2+b*x+a)^(3/2)*d*f+1/8*b^2/c^2*(c*x^2+b*x+a)^(1/2)*x*a*e^2-7/128*b^4/c^3*(c*x^2+b*x+a)^(1/2)*x*d*f-57/512*f^2*b^2/c^3*a^2*(c*x^2+b*x+a)^(1/2)*x+153/2048*f^2*b^4/c^4*(c*x^2+b*x+a)^(1/2)*x*a-9/128*f^2*b^2/c^3*a*x*(c*x^2+b*x+a)^(3/2)+1/8*b^3/c^3*(c*x^2+b*x+a)^(1/2)*a*d*f+9/32*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2*d*f-15/128*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a*d*f-1/12*a/c*x*(c*x^2+b*x+a)^(3/2)*d*f-1/24*a/c^2*(c*x^2+b*x+a)^(3/2)*b*d*f-1/8*a^2/c*(c*x^2+b*x+a)^(1/2)*x*d*f-1/16*a^2/c^2*(c*x^2+b*x+a)^(1/2)*b*d*f-1/4*d*e*b/c*x*(c*x^2+b*x+a)^(3/2)+3/32*d*e*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x-3/16*d*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a-3/8*d*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+1/4*d^2*x*(c*x^2+b*x+a)^(3/2)+153/4096*f^2*b^5/c^5*(c*x^2+b*x+a)^(1/2)*a+93/1120*f^2*b/c^3*a*(c*x^2+b*x+a)^(5/2)-11/112*f^2*b/c^2*x^2*(c*x^2+b*x+a)^(5/2)+105/1024*f^2*b^4/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-1/8*a^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f-7/30*b/c^2*(c*x^2+b*x+a)^(5/2)*d*f+7/96*b^2/c^2*x*(c*x^2+b*x+a)^(3/2)*e^2+7/96*b^3/c^3*(c*x^2+b*x+a)^(3/2)*d*f-7/256*b^4/c^3*(c*x^2+b*x+a)^(1/2)*x*e^2+1/16*b^3/c^3*(c*x^2+b*x+a)^(1/2)*a*e^2-9/1024*e*f*b^7/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-4/35*e*f*a/c^2*(c*x^2+b*x+a)^(5/2)+3/20*e*f*b^2/c^3*(c*x^2+b*x+a)^(5/2)-3/64*e*f*b^4/c^4*(c*x^2+b*x+a)^(3/2)+9/512*e*f*b^6/c^5*(c*x^2+b*x+a)^(1/2)+2/7*e*f*x^2*(c*x^2+b*x+a)^(5/2)/c-9/256*f^2*b^3/c^4*a*(c*x^2+b*x+a)^(3/2)-57/1024*f^2*b^3/c^4*a^2*(c*x^2+b*x+a)^(1/2)+33/448*f^2*b^2/c^3*x*(c*x^2+b*x+a)^(5/2)-63/2048*f^2*b^6/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-15/128*f^2*b^2/c^(7/2)*a^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+1/64*f^2*a^2/c^2*x*(c*x^2+b*x+a)^(3/2)+1/128*f^2*a^2/c^3*(c*x^2+b*x+a)^(3/2)*b+3/128*f^2*a^3/c^2*(c*x^2+b*x+a)^(1/2)*x+3/256*f^2*a^3/c^3*(c*x^2+b*x+a)^(1/2)*b-1/16*f^2*a/c^2*x*(c*x^2+b*x+a)^(5/2)+33/1024*f^2*b^4/c^4*x*(c*x^2+b*x+a)^(3/2)-99/8192*f^2*b^6/c^5*(c*x^2+b*x+a)^(1/2)*x-15/256*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a*e^2+7/512*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f-1/24*a/c*x*(c*x^2+b*x+a)^(3/2)*e^2-1/48*a/c^2*(c*x^2+b*x+a)^(3/2)*b*e^2-1/16*a^2/c*(c*x^2+b*x+a)^(1/2)*x*e^2+1/3*x*(c*x^2+b*x+a)^(5/2)/c*d*f-1/8*d*e*b^2/c^2*(c*x^2+b*x+a)^(3/2)+3/64*d*e*b^4/c^3*(c*x^2+b*x+a)^(1/2)-3/128*d*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3/32*d^2/c*(c*x^2+b*x+a)^(1/2)*x*b^2+3/16*d^2/c*(c*x^2+b*x+a)^(1/2)*b*a-3/16*d^2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a-1/32*a^2/c^2*(c*x^2+b*x+a)^(1/2)*b*e^2-7/256*b^5/c^4*(c*x^2+b*x+a)^(1/2)*d*f+9/64*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2*e^2","B"
105,1,862,210,0.009000," ","int((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x)","-\frac{a^{3} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{9 a^{2} b^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{5}{2}}}-\frac{3 a^{2} b e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{3 a^{2} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 \sqrt{c}}-\frac{15 a \,b^{4} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{3 a \,b^{3} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{5}{2}}}-\frac{3 a \,b^{2} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{3}{2}}}+\frac{7 b^{6} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{9}{2}}}-\frac{3 b^{5} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{7}{2}}}+\frac{3 b^{4} d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{5}{2}}}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} f x}{16 c}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{2} f x}{8 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b e x}{16 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a d x}{8}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{4} f x}{256 c^{3}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} e x}{64 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{2} d x}{32 c}-\frac{\sqrt{c \,x^{2}+b x +a}\, a^{2} b f}{32 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, a \,b^{3} f}{16 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} e}{32 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, a b d}{16 c}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a f x}{24 c}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b^{5} f}{512 c^{4}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{4} e}{128 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b^{3} d}{64 c^{2}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} f x}{96 c^{2}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b e x}{8 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} d x}{4}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} a b f}{48 c^{2}}+\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{3} f}{192 c^{3}}-\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b^{2} e}{16 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} b d}{8 c}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} f x}{6 c}-\frac{7 \left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} b f}{60 c^{2}}+\frac{\left(c \,x^{2}+b x +a \right)^{\frac{5}{2}} e}{5 c}"," ",0,"1/8*f*b^2/c^2*(c*x^2+b*x+a)^(1/2)*x*a-3/16*e*b/c*(c*x^2+b*x+a)^(1/2)*x*a+1/4*d*(c*x^2+b*x+a)^(3/2)*x+1/5*e*(c*x^2+b*x+a)^(5/2)/c+1/6*f*x*(c*x^2+b*x+a)^(5/2)/c-3/32*d/c*(c*x^2+b*x+a)^(1/2)*x*b^2-3/16*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+3/128*d/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^4+1/8*d/c*(c*x^2+b*x+a)^(3/2)*b-1/16*e*b^2/c^2*(c*x^2+b*x+a)^(3/2)+3/128*e*b^4/c^3*(c*x^2+b*x+a)^(1/2)-3/256*e*b^5/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-7/60*f*b/c^2*(c*x^2+b*x+a)^(5/2)+7/192*f*b^3/c^3*(c*x^2+b*x+a)^(3/2)-7/512*f*b^5/c^4*(c*x^2+b*x+a)^(1/2)+7/1024*f*b^6/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/16*f*a^3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/8*d/c^(1/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2+3/8*d*(c*x^2+b*x+a)^(1/2)*x*a-3/64*d/c^2*(c*x^2+b*x+a)^(1/2)*b^3-1/24*f*a/c*(c*x^2+b*x+a)^(3/2)*x-1/48*f*a/c^2*(c*x^2+b*x+a)^(3/2)*b-1/16*f*a^2/c*(c*x^2+b*x+a)^(1/2)*x+7/96*f*b^2/c^2*(c*x^2+b*x+a)^(3/2)*x-7/256*f*b^4/c^3*(c*x^2+b*x+a)^(1/2)*x+1/16*f*b^3/c^3*(c*x^2+b*x+a)^(1/2)*a+9/64*f*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a^2-15/256*f*b^4/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a-3/16*d/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*b^2*a+3/16*d/c*(c*x^2+b*x+a)^(1/2)*b*a+3/64*e*b^3/c^2*(c*x^2+b*x+a)^(1/2)*x-3/32*e*b^2/c^2*(c*x^2+b*x+a)^(1/2)*a-1/8*e*b/c*(c*x^2+b*x+a)^(3/2)*x-1/32*f*a^2/c^2*(c*x^2+b*x+a)^(1/2)*b+3/32*e*b^3/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*a","B"
106,1,22523,618,0.029000," ","int((c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"result too large to display","B"
107,1,72576,640,0.039000," ","int((c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
108,1,178044,611,0.066000," ","int((c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
109,1,1930,683,0.028000," ","int((f*x^2+e*x+d)^3/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, f^{3} x^{5}}{6 c}-\frac{11 \sqrt{c \,x^{2}+b x +a}\, b \,f^{3} x^{4}}{60 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, e \,f^{2} x^{4}}{5 c}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, a \,f^{3} x^{3}}{24 c^{2}}+\frac{33 \sqrt{c \,x^{2}+b x +a}\, b^{2} f^{3} x^{3}}{160 c^{3}}-\frac{27 \sqrt{c \,x^{2}+b x +a}\, b e \,f^{2} x^{3}}{40 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, d \,f^{2} x^{3}}{4 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, e^{2} f \,x^{3}}{4 c}+\frac{39 \sqrt{c \,x^{2}+b x +a}\, a b \,f^{3} x^{2}}{80 c^{3}}-\frac{4 \sqrt{c \,x^{2}+b x +a}\, a e \,f^{2} x^{2}}{5 c^{2}}-\frac{77 \sqrt{c \,x^{2}+b x +a}\, b^{3} f^{3} x^{2}}{320 c^{4}}+\frac{63 \sqrt{c \,x^{2}+b x +a}\, b^{2} e \,f^{2} x^{2}}{80 c^{3}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b d \,f^{2} x^{2}}{8 c^{2}}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b \,e^{2} f \,x^{2}}{8 c^{2}}+\frac{2 \sqrt{c \,x^{2}+b x +a}\, d e f \,x^{2}}{c}+\frac{\sqrt{c \,x^{2}+b x +a}\, e^{3} x^{2}}{3 c}-\frac{5 a^{3} f^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{105 a^{2} b^{2} f^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{64 c^{\frac{9}{2}}}-\frac{45 a^{2} b e \,f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{9 a^{2} d \,f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}+\frac{9 a^{2} e^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{315 a \,b^{4} f^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{11}{2}}}+\frac{105 a \,b^{3} e \,f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{32 c^{\frac{9}{2}}}-\frac{45 a \,b^{2} d \,f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}-\frac{45 a \,b^{2} e^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{9 a b d e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{5}{2}}}+\frac{3 a b \,e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{5}{2}}}-\frac{3 a \,d^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}-\frac{3 a d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{231 b^{6} f^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{1024 c^{\frac{13}{2}}}-\frac{189 b^{5} e \,f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{256 c^{\frac{11}{2}}}+\frac{105 b^{4} d \,f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{9}{2}}}+\frac{105 b^{4} e^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{9}{2}}}-\frac{15 b^{3} d e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{7}{2}}}-\frac{5 b^{3} e^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{9 b^{2} d^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}+\frac{9 b^{2} d \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{3 b \,d^{2} e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{d^{3} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, a^{2} f^{3} x}{16 c^{3}}-\frac{147 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} f^{3} x}{160 c^{4}}+\frac{161 \sqrt{c \,x^{2}+b x +a}\, a b e \,f^{2} x}{80 c^{3}}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, a d \,f^{2} x}{8 c^{2}}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, a \,e^{2} f x}{8 c^{2}}+\frac{77 \sqrt{c \,x^{2}+b x +a}\, b^{4} f^{3} x}{256 c^{5}}-\frac{63 \sqrt{c \,x^{2}+b x +a}\, b^{3} e \,f^{2} x}{64 c^{4}}+\frac{35 \sqrt{c \,x^{2}+b x +a}\, b^{2} d \,f^{2} x}{32 c^{3}}+\frac{35 \sqrt{c \,x^{2}+b x +a}\, b^{2} e^{2} f x}{32 c^{3}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b d e f x}{2 c^{2}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b \,e^{3} x}{12 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, d^{2} f x}{2 c}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, d \,e^{2} x}{2 c}-\frac{231 \sqrt{c \,x^{2}+b x +a}\, a^{2} b \,f^{3}}{160 c^{4}}+\frac{8 \sqrt{c \,x^{2}+b x +a}\, a^{2} e \,f^{2}}{5 c^{3}}+\frac{119 \sqrt{c \,x^{2}+b x +a}\, a \,b^{3} f^{3}}{64 c^{5}}-\frac{147 \sqrt{c \,x^{2}+b x +a}\, a \,b^{2} e \,f^{2}}{32 c^{4}}+\frac{55 \sqrt{c \,x^{2}+b x +a}\, a b d \,f^{2}}{16 c^{3}}+\frac{55 \sqrt{c \,x^{2}+b x +a}\, a b \,e^{2} f}{16 c^{3}}-\frac{4 \sqrt{c \,x^{2}+b x +a}\, a d e f}{c^{2}}-\frac{2 \sqrt{c \,x^{2}+b x +a}\, a \,e^{3}}{3 c^{2}}-\frac{231 \sqrt{c \,x^{2}+b x +a}\, b^{5} f^{3}}{512 c^{6}}+\frac{189 \sqrt{c \,x^{2}+b x +a}\, b^{4} e \,f^{2}}{128 c^{5}}-\frac{105 \sqrt{c \,x^{2}+b x +a}\, b^{3} d \,f^{2}}{64 c^{4}}-\frac{105 \sqrt{c \,x^{2}+b x +a}\, b^{3} e^{2} f}{64 c^{4}}+\frac{15 \sqrt{c \,x^{2}+b x +a}\, b^{2} d e f}{4 c^{3}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} e^{3}}{8 c^{3}}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, b \,d^{2} f}{4 c^{2}}-\frac{9 \sqrt{c \,x^{2}+b x +a}\, b d \,e^{2}}{4 c^{2}}+\frac{3 \sqrt{c \,x^{2}+b x +a}\, d^{2} e}{c}"," ",0,"3*d^2*e/c*(c*x^2+b*x+a)^(1/2)+1/3*x^2/c*(c*x^2+b*x+a)^(1/2)*e^3+5/8*b^2/c^3*(c*x^2+b*x+a)^(1/2)*e^3-5/16*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^3-2/3*a/c^2*(c*x^2+b*x+a)^(1/2)*e^3-231/512*f^3*b^5/c^6*(c*x^2+b*x+a)^(1/2)+231/1024*f^3*b^6/c^(13/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-5/16*f^3*a^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+d^3*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)+161/80*e*f^2*b/c^3*a*x*(c*x^2+b*x+a)^(1/2)-5/2*b/c^2*x*(c*x^2+b*x+a)^(1/2)*d*e*f+9/2*b/c^(5/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*e*f-45/16*b^2/c^(7/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2*f+55/16*b/c^3*a*(c*x^2+b*x+a)^(1/2)*d*f^2+55/16*b/c^3*a*(c*x^2+b*x+a)^(1/2)*e^2*f-9/8*a/c^2*x*(c*x^2+b*x+a)^(1/2)*d*f^2-147/160*f^3*b^2/c^4*a*x*(c*x^2+b*x+a)^(1/2)+39/80*f^3*b/c^3*a*x^2*(c*x^2+b*x+a)^(1/2)-9/8*a/c^2*x*(c*x^2+b*x+a)^(1/2)*e^2*f+2*x^2/c*(c*x^2+b*x+a)^(1/2)*d*e*f+15/4*b^2/c^3*(c*x^2+b*x+a)^(1/2)*d*e*f-15/8*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*e*f-4*a/c^2*(c*x^2+b*x+a)^(1/2)*d*e*f-27/40*e*f^2*b/c^2*x^3*(c*x^2+b*x+a)^(1/2)+63/80*e*f^2*b^2/c^3*x^2*(c*x^2+b*x+a)^(1/2)-63/64*e*f^2*b^3/c^4*x*(c*x^2+b*x+a)^(1/2)+105/32*e*f^2*b^3/c^(9/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-147/32*e*f^2*b^2/c^4*a*(c*x^2+b*x+a)^(1/2)-45/16*e*f^2*b/c^(7/2)*a^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-4/5*e*f^2*a/c^2*x^2*(c*x^2+b*x+a)^(1/2)-7/8*b/c^2*x^2*(c*x^2+b*x+a)^(1/2)*d*f^2-7/8*b/c^2*x^2*(c*x^2+b*x+a)^(1/2)*e^2*f+35/32*b^2/c^3*x*(c*x^2+b*x+a)^(1/2)*d*f^2+35/32*b^2/c^3*x*(c*x^2+b*x+a)^(1/2)*e^2*f-45/16*b^2/c^(7/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f^2+1/6*f^3*x^5*(c*x^2+b*x+a)^(1/2)/c+9/8*a^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2*f-5/12*b/c^2*x*(c*x^2+b*x+a)^(1/2)*e^3+3/4*b/c^(5/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^3-105/64*b^3/c^4*(c*x^2+b*x+a)^(1/2)*e^2*f+105/128*b^4/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f^2+105/128*b^4/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2*f+9/8*a^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f^2+3/4*x^3/c*(c*x^2+b*x+a)^(1/2)*d*f^2+3/4*x^3/c*(c*x^2+b*x+a)^(1/2)*e^2*f-105/64*b^3/c^4*(c*x^2+b*x+a)^(1/2)*d*f^2+3/5*e*f^2*x^4/c*(c*x^2+b*x+a)^(1/2)+189/128*e*f^2*b^4/c^5*(c*x^2+b*x+a)^(1/2)-189/256*e*f^2*b^5/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+8/5*e*f^2*a^2/c^3*(c*x^2+b*x+a)^(1/2)-315/256*f^3*b^4/c^(11/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+119/64*f^3*b^3/c^5*a*(c*x^2+b*x+a)^(1/2)+105/64*f^3*b^2/c^(9/2)*a^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-231/160*f^3*b/c^4*a^2*(c*x^2+b*x+a)^(1/2)-5/24*f^3*a/c^2*x^3*(c*x^2+b*x+a)^(1/2)+5/16*f^3*a^2/c^3*x*(c*x^2+b*x+a)^(1/2)-11/60*f^3*b/c^2*x^4*(c*x^2+b*x+a)^(1/2)+33/160*f^3*b^2/c^3*x^3*(c*x^2+b*x+a)^(1/2)-77/320*f^3*b^3/c^4*x^2*(c*x^2+b*x+a)^(1/2)+77/256*f^3*b^4/c^5*x*(c*x^2+b*x+a)^(1/2)-9/4*b/c^2*(c*x^2+b*x+a)^(1/2)*f*d^2-9/4*b/c^2*(c*x^2+b*x+a)^(1/2)*e^2*d+9/8*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f*d^2+9/8*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2*d-3/2*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f*d^2-3/2*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2*d-3/2*d^2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/2*x/c*(c*x^2+b*x+a)^(1/2)*f*d^2+3/2*x/c*(c*x^2+b*x+a)^(1/2)*e^2*d","B"
110,1,706,290,0.014000," ","int((f*x^2+e*x+d)^2/(c*x^2+b*x+a)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b x +a}\, f^{2} x^{3}}{4 c}-\frac{7 \sqrt{c \,x^{2}+b x +a}\, b \,f^{2} x^{2}}{24 c^{2}}+\frac{2 \sqrt{c \,x^{2}+b x +a}\, e f \,x^{2}}{3 c}+\frac{3 a^{2} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{15 a \,b^{2} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{16 c^{\frac{7}{2}}}+\frac{3 a b e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{5}{2}}}-\frac{a d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}-\frac{a \,e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{35 b^{4} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{128 c^{\frac{9}{2}}}-\frac{5 b^{3} e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{7}{2}}}+\frac{3 b^{2} d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{4 c^{\frac{5}{2}}}+\frac{3 b^{2} e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{b d e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}+\frac{d^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, a \,f^{2} x}{8 c^{2}}+\frac{35 \sqrt{c \,x^{2}+b x +a}\, b^{2} f^{2} x}{96 c^{3}}-\frac{5 \sqrt{c \,x^{2}+b x +a}\, b e f x}{6 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, d f x}{c}+\frac{\sqrt{c \,x^{2}+b x +a}\, e^{2} x}{2 c}+\frac{55 \sqrt{c \,x^{2}+b x +a}\, a b \,f^{2}}{48 c^{3}}-\frac{4 \sqrt{c \,x^{2}+b x +a}\, a e f}{3 c^{2}}-\frac{35 \sqrt{c \,x^{2}+b x +a}\, b^{3} f^{2}}{64 c^{4}}+\frac{5 \sqrt{c \,x^{2}+b x +a}\, b^{2} e f}{4 c^{3}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b d f}{2 c^{2}}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b \,e^{2}}{4 c^{2}}+\frac{2 \sqrt{c \,x^{2}+b x +a}\, d e}{c}"," ",0,"2*d*e/c*(c*x^2+b*x+a)^(1/2)+1/2*x/c*(c*x^2+b*x+a)^(1/2)*e^2-3/4*b/c^2*(c*x^2+b*x+a)^(1/2)*e^2+3/8*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2-1/2*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2-35/64*f^2*b^3/c^4*(c*x^2+b*x+a)^(1/2)+35/128*f^2*b^4/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3/8*f^2*a^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-5/6*e*f*b/c^2*x*(c*x^2+b*x+a)^(1/2)+1/4*f^2*x^3*(c*x^2+b*x+a)^(1/2)/c+3/2*e*f*b/c^(5/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+d^2*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)-5/8*e*f*b^3/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-4/3*e*f*a/c^2*(c*x^2+b*x+a)^(1/2)+x/c*(c*x^2+b*x+a)^(1/2)*d*f-3/2*b/c^2*(c*x^2+b*x+a)^(1/2)*d*f+3/4*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f-a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f-d*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3/8*f^2*a/c^2*x*(c*x^2+b*x+a)^(1/2)+55/48*f^2*b/c^3*a*(c*x^2+b*x+a)^(1/2)-7/24*f^2*b/c^2*x^2*(c*x^2+b*x+a)^(1/2)+35/96*f^2*b^2/c^3*x*(c*x^2+b*x+a)^(1/2)-15/16*f^2*b^2/c^(7/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+2/3*e*f*x^2/c*(c*x^2+b*x+a)^(1/2)+5/4*e*f*b^2/c^3*(c*x^2+b*x+a)^(1/2)","B"
111,1,185,98,0.008000," ","int((f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x)","-\frac{a f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{3 b^{2} f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{5}{2}}}-\frac{b e \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{3}{2}}}+\frac{d \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{\sqrt{c}}+\frac{\sqrt{c \,x^{2}+b x +a}\, f x}{2 c}-\frac{3 \sqrt{c \,x^{2}+b x +a}\, b f}{4 c^{2}}+\frac{\sqrt{c \,x^{2}+b x +a}\, e}{c}"," ",0,"1/2*f*x*(c*x^2+b*x+a)^(1/2)/c-3/4*f*b/c^2*(c*x^2+b*x+a)^(1/2)+3/8*f*b^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-1/2*f*a/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+e/c*(c*x^2+b*x+a)^(1/2)-1/2*e*b/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+d*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))/c^(1/2)","A"
112,1,761,330,0.025000," ","int(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x)","\frac{\sqrt{2}\, \ln \left(\frac{\frac{\left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c \right) \left(x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}-2 \sqrt{-4 d f +e^{2}}\, b f +2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x +\frac{e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}-\sqrt{-4 d f +e^{2}}\, b f +\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}-\frac{\sqrt{2}\, \ln \left(\frac{\frac{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}+\frac{\sqrt{2}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}\, \sqrt{4 \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)^{2} c +\frac{4 \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c \right) \left(x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}\right)}{f}+\frac{4 a \,f^{2}-2 b e f -4 c d f +2 c \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f -2 \sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}{2}}{x -\frac{-e +\sqrt{-4 d f +e^{2}}}{2 f}}\right)}{\sqrt{-4 d f +e^{2}}\, \sqrt{\frac{2 a \,f^{2}-b e f -2 c d f +c \,e^{2}+\sqrt{-4 d f +e^{2}}\, b f -\sqrt{-4 d f +e^{2}}\, c e}{f^{2}}}}"," ",0,"1/(-4*d*f+e^2)^(1/2)*2^(1/2)/((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln(((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+1/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*((-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4/f*(-c*(-4*d*f+e^2)^(1/2)+b*f-c*e)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)+2*(-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))-1/(-4*d*f+e^2)^(1/2)*2^(1/2)/(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*ln((((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2+(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+1/2*2^(1/2)*(((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(c*(-4*d*f+e^2)^(1/2)+b*f-c*e)/f*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)+2*((-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e+2*a*f^2-b*e*f-2*c*d*f+c*e^2)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))","B"
113,1,3858,735,0.031000," ","int(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d)^2,x)","\text{output too large to display}"," ",0,"2*f/(4*d*f-e^2)/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+2/(4*d*f-e^2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*f^2/(x-1/2/f*(-4*d*f+e^2)^(1/2)+1/2*e/f)*((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-1/(4*d*f-e^2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*(-4*d*f+e^2)^(1/2)-1/(4*d*f-e^2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*b+1/(4*d*f-e^2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))*c*e+2/(4*d*f-e^2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*f^2/(x+1/2/f*(-4*d*f+e^2)^(1/2)+1/2*e/f)*((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)+1/(4*d*f-e^2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*(-4*d*f+e^2)^(1/2)-1/(4*d*f-e^2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*b+1/(4*d*f-e^2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))*c*e-2*f/(4*d*f-e^2)/(-4*d*f+e^2)^(1/2)*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))","B"
114,1,2827,621,0.030000," ","int((f*x^2+e*x+d)^3/(c*x^2+b*x+a)^(3/2),x)","\text{output too large to display}"," ",0,"2*a/c^2/(c*x^2+b*x+a)^(1/2)*e^3+2*d^3*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+315/128*f^3*b^4/c^(11/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+15/8*f^3*a^2/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+315/256*f^3*b^5/c^6/(c*x^2+b*x+a)^(1/2)+1/4*f^3*x^5/c/(c*x^2+b*x+a)^(1/2)+3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*f*d^2+3/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2*d-3*d^2*e/c/(c*x^2+b*x+a)^(1/2)+x^2/c/(c*x^2+b*x+a)^(1/2)*e^3-3/4*b^2/c^3/(c*x^2+b*x+a)^(1/2)*e^3-3/2*b/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^3+115/4*e*f^2*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-9*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d*e*f+12*a/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d*e*f-39/2*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d*f^2-39/2*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*e^2*f-16*e*f^2*a^2/c^2*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+21/32*f^3*b^2/c^3*x^3/(c*x^2+b*x+a)^(1/2)-105/64*f^3*b^3/c^4*x^2/(c*x^2+b*x+a)^(1/2)-315/128*f^3*b^4/c^5*x/(c*x^2+b*x+a)^(1/2)+315/256*f^3*b^7/c^6/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-105/16*f^3*b^2/c^(9/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-5/8*f^3*a/c^2*x^3/(c*x^2+b*x+a)^(1/2)-15/8*f^3*a^2/c^3*x/(c*x^2+b*x+a)^(1/2)-3*x/c/(c*x^2+b*x+a)^(1/2)*f*d^2-3*x/c/(c*x^2+b*x+a)^(1/2)*e^2*d+3/2*x^3/c/(c*x^2+b*x+a)^(1/2)*d*f^2+3/2*x^3/c/(c*x^2+b*x+a)^(1/2)*e^2*f+45/16*b^3/c^4/(c*x^2+b*x+a)^(1/2)*d*f^2+45/16*b^3/c^4/(c*x^2+b*x+a)^(1/2)*e^2*f+45/8*b^2/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f^2+45/8*b^2/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2*f-9/2*a/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f^2-9/2*a/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2*f+3/2*b/c^2*x/(c*x^2+b*x+a)^(1/2)*e^3-3/4*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*e^3+e*f^2*x^4/c/(c*x^2+b*x+a)^(1/2)-105/32*e*f^2*b^4/c^5/(c*x^2+b*x+a)^(1/2)-105/16*e*f^2*b^3/c^(9/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-8*e*f^2*a^2/c^3/(c*x^2+b*x+a)^(1/2)+3/2*b/c^2/(c*x^2+b*x+a)^(1/2)*f*d^2+3/2*b/c^2/(c*x^2+b*x+a)^(1/2)*e^2*d-105/16*f^3*b^3/c^5*a/(c*x^2+b*x+a)^(1/2)+113/16*f^3*b/c^4*a^2/(c*x^2+b*x+a)^(1/2)+24*a/c*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d*e*f+9*b/c^2*x/(c*x^2+b*x+a)^(1/2)*d*e*f-9/2*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d*e*f+4*a/c*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*e^3+3*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*f*d^2+3*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*e^2*d-8*e*f^2*a^2/c^3*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+45/8*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d*f^2+45/8*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*e^2*f-39/4*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d*f^2-39/4*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*e^2*f-105/16*e*f^2*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+115/8*e*f^2*b^4/c^4*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-45/4*e*f^2*b/c^3*a*x/(c*x^2+b*x+a)^(1/2)+113/8*f^3*b^2/c^3*a^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-105/8*f^3*b^4/c^4*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+105/16*e*f^2*b^3/c^4*x/(c*x^2+b*x+a)^(1/2)-105/32*e*f^2*b^6/c^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+115/8*e*f^2*b^2/c^4*a/(c*x^2+b*x+a)^(1/2)+45/4*e*f^2*b/c^(7/2)*a*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-4*e*f^2*a/c^2*x^2/(c*x^2+b*x+a)^(1/2)+315/128*f^3*b^6/c^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-105/16*f^3*b^5/c^5*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+105/16*f^3*b^2/c^4*a*x/(c*x^2+b*x+a)^(1/2)+49/16*f^3*b/c^3*a*x^2/(c*x^2+b*x+a)^(1/2)+113/16*f^3*b^3/c^4*a^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+6*x^2/c/(c*x^2+b*x+a)^(1/2)*d*e*f-9/2*b^2/c^3/(c*x^2+b*x+a)^(1/2)*d*e*f-3/2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*e^3-9*b/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*e*f+12*a/c^2/(c*x^2+b*x+a)^(1/2)*d*e*f+2*a/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*e^3+3/2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*f*d^2+3/2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*e^2*d-6*d^2*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-3*d^2*e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-15/4*b/c^2*x^2/(c*x^2+b*x+a)^(1/2)*d*f^2-15/4*b/c^2*x^2/(c*x^2+b*x+a)^(1/2)*e^2*f-45/8*b^2/c^3*x/(c*x^2+b*x+a)^(1/2)*d*f^2-45/8*b^2/c^3*x/(c*x^2+b*x+a)^(1/2)*e^2*f-7/4*e*f^2*b/c^2*x^3/(c*x^2+b*x+a)^(1/2)+35/8*e*f^2*b^2/c^3*x^2/(c*x^2+b*x+a)^(1/2)+45/16*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*e^2*f-39/4*b/c^3*a/(c*x^2+b*x+a)^(1/2)*d*f^2-39/4*b/c^3*a/(c*x^2+b*x+a)^(1/2)*e^2*f+9/2*a/c^2*x/(c*x^2+b*x+a)^(1/2)*d*f^2+9/2*a/c^2*x/(c*x^2+b*x+a)^(1/2)*e^2*f-3/8*f^3*b/c^2*x^4/(c*x^2+b*x+a)^(1/2)+45/16*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d*f^2","B"
115,1,1011,289,0.015000," ","int((f*x^2+e*x+d)^2/(c*x^2+b*x+a)^(3/2),x)","-\frac{13 a \,b^{2} f^{2} x}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{8 a b e f x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}+\frac{15 b^{4} f^{2} x}{8 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}-\frac{3 b^{3} e f x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{2 b^{2} d f x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}+\frac{b^{2} e^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{4 b d e x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{f^{2} x^{3}}{2 \sqrt{c \,x^{2}+b x +a}\, c}-\frac{13 a \,b^{3} f^{2}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{4 a \,b^{2} e f}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{15 b^{5} f^{2}}{16 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{4}}-\frac{3 b^{4} e f}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{b^{3} d f}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{b^{3} e^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{2 b^{2} d e}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{5 b \,f^{2} x^{2}}{4 \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{2 e f \,x^{2}}{\sqrt{c \,x^{2}+b x +a}\, c}+\frac{3 a \,f^{2} x}{2 \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{15 b^{2} f^{2} x}{8 \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{3 b e f x}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{2 d f x}{\sqrt{c \,x^{2}+b x +a}\, c}-\frac{e^{2} x}{\sqrt{c \,x^{2}+b x +a}\, c}+\frac{2 \left(2 c x +b \right) d^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}-\frac{3 a \,f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{2 c^{\frac{5}{2}}}+\frac{15 b^{2} f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{8 c^{\frac{7}{2}}}-\frac{3 b e f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{5}{2}}}+\frac{2 d f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}+\frac{e^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}-\frac{13 a b \,f^{2}}{4 \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{4 a e f}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{15 b^{3} f^{2}}{16 \sqrt{c \,x^{2}+b x +a}\, c^{4}}-\frac{3 b^{2} e f}{2 \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{b d f}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{b \,e^{2}}{2 \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{2 d e}{\sqrt{c \,x^{2}+b x +a}\, c}"," ",0,"-2*d*e/c/(c*x^2+b*x+a)^(1/2)-x/c/(c*x^2+b*x+a)^(1/2)*e^2+1/2*b/c^2/(c*x^2+b*x+a)^(1/2)*e^2+2/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*d*f+1/2*f^2*x^3/c/(c*x^2+b*x+a)^(1/2)+15/16*f^2*b^3/c^4/(c*x^2+b*x+a)^(1/2)+15/8*f^2*b^2/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-3/2*f^2*a/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+2*d^2*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+4*e*f*a/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*d*f-13/2*f^2*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-3*e*f*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+8*e*f*a/c*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-13/4*f^2*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-4*d*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+15/8*f^2*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-2*d*e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+3*e*f*b/c^2*x/(c*x^2+b*x+a)^(1/2)-3/2*e*f*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*e^2+b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*d*f+1/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))*e^2+1/2*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*e^2+2*e*f*x^2/c/(c*x^2+b*x+a)^(1/2)-3/2*e*f*b^2/c^3/(c*x^2+b*x+a)^(1/2)-3*e*f*b/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+4*e*f*a/c^2/(c*x^2+b*x+a)^(1/2)-5/4*f^2*b/c^2*x^2/(c*x^2+b*x+a)^(1/2)-15/8*f^2*b^2/c^3*x/(c*x^2+b*x+a)^(1/2)+15/16*f^2*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-13/4*f^2*b/c^3*a/(c*x^2+b*x+a)^(1/2)+3/2*f^2*a/c^2*x/(c*x^2+b*x+a)^(1/2)-2*x/c/(c*x^2+b*x+a)^(1/2)*d*f+b/c^2/(c*x^2+b*x+a)^(1/2)*d*f","B"
116,1,249,101,0.006000," ","int((f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x)","\frac{b^{2} f x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{2 b e x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{b^{3} f}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{b^{2} e}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c}-\frac{f x}{\sqrt{c \,x^{2}+b x +a}\, c}+\frac{2 \left(2 c x +b \right) d}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}}+\frac{f \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{3}{2}}}+\frac{b f}{2 \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{e}{\sqrt{c \,x^{2}+b x +a}\, c}"," ",0,"-f*x/c/(c*x^2+b*x+a)^(1/2)+1/2*f*b/c^2/(c*x^2+b*x+a)^(1/2)+f*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x+1/2*f*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+f/c^(3/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-e/c/(c*x^2+b*x+a)^(1/2)-2*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+2*d*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)","B"
117,1,4099,609,0.028000," ","int(1/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x)","\text{output too large to display}"," ",0,"-2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*f^2/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-4*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2+4/(-4*d*f+e^2)^(1/2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*b*c-4/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2*e-2*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c+2/(-4*d*f+e^2)^(1/2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b^2-2/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c*e+2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)*f^2*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e-(-4*d*f+e^2)^(1/2)*c)*(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2-(-4*d*f+e^2)^(1/2)*b*f+(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x+1/2*(e+(-4*d*f+e^2)^(1/2))/f))+2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*f^2/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)-4*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2-4/(-4*d*f+e^2)^(1/2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*b*c+4/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*x*c^2*e-2*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c-2/(-4*d*f+e^2)^(1/2)*f^2/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b^2+2/(-4*d*f+e^2)^(1/2)*f/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/(4*a*c-4*c^2/f*d+c^2/f^2*e^2-1/f^2*(-4*d*f+e^2)*c^2-b^2)/((x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+1/2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*b*c*e-2/(-4*d*f+e^2)^(1/2)/(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)*f^2*2^(1/2)/((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*ln(((b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2+1/2*2^(1/2)*((2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2)*(4*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)^2*c+4*(b*f-c*e+(-4*d*f+e^2)^(1/2)*c)*(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f)/f+2*(2*a*f^2-b*e*f-2*c*d*f+c*e^2+(-4*d*f+e^2)^(1/2)*b*f-(-4*d*f+e^2)^(1/2)*c*e)/f^2)^(1/2))/(x-1/2*(-e+(-4*d*f+e^2)^(1/2))/f))","B"
118,1,4635,865,0.031000," ","int((f*x^2+e*x+d)^3/(c*x^2+b*x+a)^(5/2),x)","\text{output too large to display}"," 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1/2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*e^2*d+a/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b*f*d^2+a/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b*e^2*d+16*a*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x*f*d^2+16*a*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x*e^2*d+3/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x*e^2*f-1/8*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*d*f^2+1/2*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*f*d^2-5/4*f^3*a/c^4*b/(c*x^2+b*x+a)^(1/2)+173/96*f^3*b^3/c^5*a/(c*x^2+b*x+a)^(3/2)-35/8*f^3*b^2/c^4*x/(c*x^2+b*x+a)^(1/2)+35/16*f^3*b^5/c^5/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)-11/2*f^3*b/c^4*a^2/(c*x^2+b*x+a)^(3/2)-7/4*f^3*b/c^2*x^4/(c*x^2+b*x+a)^(3/2)-35/24*f^3*b^2/c^3*x^3/(c*x^2+b*x+a)^(3/2)+35/16*f^3*b^3/c^4*x^2/(c*x^2+b*x+a)^(3/2)+35/64*f^3*b^4/c^5*x/(c*x^2+b*x+a)^(3/2)-35/384*f^3*b^7/c^6/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-35/48*f^3*b^7/c^5/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+8*e*f^2*a^2/c^3/(c*x^2+b*x+a)^(3/2)-15/2*e*f^2*b/c^(7/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))+3*e*f^2*x^4/c/(c*x^2+b*x+a)^(3/2)+5/32*e*f^2*b^4/c^5/(c*x^2+b*x+a)^(3/2)-15/4*e*f^2*b^2/c^4/(c*x^2+b*x+a)^(1/2)-x^3/c/(c*x^2+b*x+a)^(3/2)*d*f^2-x^3/c/(c*x^2+b*x+a)^(3/2)*e^2*f-1/16*b^3/c^4/(c*x^2+b*x+a)^(3/2)*d*f^2-1/16*b^3/c^4/(c*x^2+b*x+a)^(3/2)*e^2*f-3/c^2*x/(c*x^2+b*x+a)^(1/2)*d*f^2-3/c^2*x/(c*x^2+b*x+a)^(1/2)*e^2*f+3/2/c^3*b/(c*x^2+b*x+a)^(1/2)*d*f^2+3/2/c^3*b/(c*x^2+b*x+a)^(1/2)*e^2*f-1/4*b/c^2*x/(c*x^2+b*x+a)^(3/2)*e^3+1/24*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*e^3+1/3*b^4/c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*e^3-3/2*x/c/(c*x^2+b*x+a)^(3/2)*f*d^2-3/2*x/c/(c*x^2+b*x+a)^(3/2)*e^2*d+1/4*b/c^2/(c*x^2+b*x+a)^(3/2)*f*d^2+1/4*b/c^2/(c*x^2+b*x+a)^(3/2)*e^2*d-8*d^2*e*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+4/3*d^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*c+32/3*d^3*c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+16/3*d^3*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*b","B"
119,1,1786,428,0.014000," ","int((f*x^2+e*x+d)^2/(c*x^2+b*x+a)^(5/2),x)","\frac{4 a \,b^{2} f^{2} x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}-\frac{16 a b e f x}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{32 a c d f x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{16 a c \,e^{2} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{b^{4} f^{2} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{4 b^{3} e f x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{8 b^{2} d f x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{4 b^{2} e^{2} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{32 b c d e x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{32 c^{2} d^{2} x}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{2 a \,b^{3} f^{2}}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{8 a \,b^{2} e f}{\left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{a \,b^{2} f^{2} x}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{2 a b e f x}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{16 a b d f}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{8 a b \,e^{2}}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{4 a d f x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{2 a \,e^{2} x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{b^{5} f^{2}}{6 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{2 b^{4} e f}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c^{2}}-\frac{b^{4} f^{2} x}{24 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{4 b^{3} d f}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{2 b^{3} e^{2}}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}\, c}+\frac{b^{3} e f x}{6 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{b^{2} d f x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{b^{2} e^{2} x}{6 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}-\frac{16 b^{2} d e}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}+\frac{16 b c \,d^{2}}{3 \left(4 a c -b^{2}\right)^{2} \sqrt{c \,x^{2}+b x +a}}-\frac{4 b d e x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}+\frac{4 c \,d^{2} x}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{f^{2} x^{3}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{a \,b^{3} f^{2}}{4 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{a \,b^{2} e f}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{2 a b d f}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{a b \,e^{2}}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}-\frac{b^{5} f^{2}}{48 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{b^{4} e f}{12 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{b^{3} d f}{6 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{b^{3} e^{2}}{12 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{2 b^{2} d e}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{b^{2} f^{2} x}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{b \,f^{2} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{2 b \,d^{2}}{3 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}}}-\frac{2 e f \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{b^{3} f^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{2}+b x +a}\, c^{3}}+\frac{b^{2} f^{2} x}{8 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{b e f x}{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{d f x}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}-\frac{e^{2} x}{2 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}+\frac{a b \,f^{2}}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}-\frac{4 a e f}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{b^{3} f^{2}}{48 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{4}}+\frac{b^{2} e f}{12 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{3}}+\frac{b d f}{6 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}+\frac{b \,e^{2}}{12 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c^{2}}-\frac{2 d e}{3 \left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} c}-\frac{f^{2} x}{\sqrt{c \,x^{2}+b x +a}\, c^{2}}+\frac{f^{2} \ln \left(\frac{c x +\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{2}+b x +a}\right)}{c^{\frac{5}{2}}}+\frac{b \,f^{2}}{2 \sqrt{c \,x^{2}+b x +a}\, c^{3}}"," ",0,"-2/3*d*e/c/(c*x^2+b*x+a)^(3/2)+2/3*d^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b-1/2*x/c/(c*x^2+b*x+a)^(3/2)*e^2+1/12*b/c^2/(c*x^2+b*x+a)^(3/2)*e^2-1/3*f^2*x^3/c/(c*x^2+b*x+a)^(3/2)-1/48*f^2*b^3/c^4/(c*x^2+b*x+a)^(3/2)-f^2/c^2*x/(c*x^2+b*x+a)^(1/2)+1/2*f^2/c^3*b/(c*x^2+b*x+a)^(1/2)-2*e*f*b/c*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+16/3*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*b*d*f-1/24*f^2*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-1/3*f^2*b^4/c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+1/4*f^2*b^3/c^3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+2*f^2*b^3/c^2*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+f^2/c^2*b^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)*x-4/3*d*e*b/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x-2/3*d*e*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-1/2*e*f*b/c^2*x/(c*x^2+b*x+a)^(3/2)+1/12*e*f*b^4/c^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)+2/3*e*f*b^4/c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+1/6*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*e^2+1/6*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*d*f+8/3*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x*d*f+4/3*b^3/c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*d*f+4/3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*d*f+1/3*a/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b*e^2+16/3*a*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x*e^2+f^2/c^(5/2)*ln((c*x+1/2*b)/c^(1/2)+(c*x^2+b*x+a)^(1/2))-2*e*f*x^2/c/(c*x^2+b*x+a)^(3/2)+1/12*e*f*b^2/c^3/(c*x^2+b*x+a)^(3/2)-4/3*e*f*a/c^2/(c*x^2+b*x+a)^(3/2)+1/2*f^2*b/c^2*x^2/(c*x^2+b*x+a)^(3/2)+1/8*f^2*b^2/c^3*x/(c*x^2+b*x+a)^(3/2)-1/48*f^2*b^5/c^4/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)-1/6*f^2*b^5/c^3/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+1/3*f^2*b/c^3*a/(c*x^2+b*x+a)^(3/2)+1/2*f^2/c^3*b^3/(4*a*c-b^2)/(c*x^2+b*x+a)^(1/2)+2/3*b^3/c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*e^2+2/3*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*e^2+8/3*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*b*e^2-16/3*d*e*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+4/3*d^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*c+32/3*d^2*c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+16/3*d^2*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*b-x/c/(c*x^2+b*x+a)^(3/2)*d*f+1/6*b/c^2/(c*x^2+b*x+a)^(3/2)*d*f+32/3*a*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x*d*f-32/3*d*e*b*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-16*e*f*b*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-8*e*f*b^2/c*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)+1/6*e*f*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+1/2*f^2*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x+4*f^2*b^2/c*a/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x+1/3*b^2/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*x*d*f+2/3*a/c/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*b*d*f+1/12*b^3/c^2/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)*e^2+4/3*b^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x*e^2+4/3*e*f*b^3/c/(4*a*c-b^2)^2/(c*x^2+b*x+a)^(1/2)*x-e*f*b^2/c^2*a/(4*a*c-b^2)/(c*x^2+b*x+a)^(3/2)","B"
120,1,185,123,0.007000," ","int((f*x^2+e*x+d)/(c*x^2+b*x+a)^(5/2),x)","\frac{\frac{16}{3} a \,c^{2} f \,x^{3}+\frac{4}{3} b^{2} c f \,x^{3}-\frac{16}{3} b \,c^{2} e \,x^{3}+\frac{32}{3} c^{3} d \,x^{3}+8 a b c f \,x^{2}+2 b^{3} f \,x^{2}-8 b^{2} c e \,x^{2}+16 b \,c^{2} d \,x^{2}+8 a \,b^{2} f x -8 a b c e x +16 a \,c^{2} d x -2 b^{3} e x +4 b^{2} c d x +\frac{16}{3} a^{2} b f -\frac{16}{3} a^{2} c e -\frac{4}{3} a \,b^{2} e +8 a b c d -\frac{2}{3} b^{3} d}{\left(c \,x^{2}+b x +a \right)^{\frac{3}{2}} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}"," ",0,"2/3/(c*x^2+b*x+a)^(3/2)*(8*a*c^2*f*x^3+2*b^2*c*f*x^3-8*b*c^2*e*x^3+16*c^3*d*x^3+12*a*b*c*f*x^2+3*b^3*f*x^2-12*b^2*c*e*x^2+24*b*c^2*d*x^2+12*a*b^2*f*x-12*a*b*c*e*x+24*a*c^2*d*x-3*b^3*e*x+6*b^2*c*d*x+8*a^2*b*f-8*a^2*c*e-2*a*b^2*e+12*a*b*c*d-b^3*d)/(16*a^2*c^2-8*a*b^2*c+b^4)","A"
121,1,144,41,0.024000," ","int(1/(5*x^2+12*x+8)/(5*x^2+2*x-7)^(1/2),x)","-\frac{\sqrt{-\frac{4 \left(x +2\right)^{2}}{\left(-x -1\right)^{2}}+9}\, \left(2 \arctanh \left(\frac{\sqrt{-\frac{4 \left(x +2\right)^{2}}{\left(-x -1\right)^{2}}+9}}{5}\right)+\arctan \left(\frac{5 \sqrt{-\frac{4 \left(x +2\right)^{2}}{\left(-x -1\right)^{2}}+9}\, \left(x +2\right)}{2 \left(\frac{4 \left(x +2\right)^{2}}{\left(-x -1\right)^{2}}-9\right) \left(-x -1\right)}\right)\right)}{10 \sqrt{-\frac{\frac{4 \left(x +2\right)^{2}}{\left(-x -1\right)^{2}}-9}{\left(1+\frac{x +2}{-x -1}\right)^{2}}}\, \left(1+\frac{x +2}{-x -1}\right)}"," ",0,"-1/10*(-4*(x+2)^2/(-1-x)^2+9)^(1/2)*(2*arctanh(1/5*(-4*(x+2)^2/(-1-x)^2+9)^(1/2))+arctan(5/2*(-4*(x+2)^2/(-1-x)^2+9)^(1/2)/(4*(x+2)^2/(-1-x)^2-9)*(x+2)/(-1-x)))/(-(4*(x+2)^2/(-1-x)^2-9)/(1+(x+2)/(-1-x))^2)^(1/2)/(1+(x+2)/(-1-x))","B"
122,1,928,1573,0.272000," ","int(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d)^(1/2),x)","\frac{8 \left(2 b \,f^{2} x^{2}-2 c e f \,x^{2}+2 b e f x -8 c d f x +2 \sqrt{-4 d f +e^{2}}\, c f \,x^{2}+2 \sqrt{-4 a c +b^{2}}\, f^{2} x^{2}-2 b d f +b \,e^{2}+2 \sqrt{-4 d f +e^{2}}\, b f x -2 c d e +2 \sqrt{-4 a c +b^{2}}\, e f x +\sqrt{-4 d f +e^{2}}\, b e -2 \sqrt{-4 d f +e^{2}}\, c d -2 \sqrt{-4 a c +b^{2}}\, d f +\sqrt{-4 a c +b^{2}}\, e^{2}+2 \sqrt{-4 d f +e^{2}}\, \sqrt{-4 a c +b^{2}}\, f x +\sqrt{-4 d f +e^{2}}\, \sqrt{-4 a c +b^{2}}\, e \right) \sqrt{\frac{\sqrt{-4 d f +e^{2}}\, \left(2 c x +b +\sqrt{-4 a c +b^{2}}\right) f}{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(2 f x +e +\sqrt{-4 d f +e^{2}}\right)}}\, \sqrt{-\frac{\sqrt{-4 d f +e^{2}}\, \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) f}{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c -\sqrt{-4 a c +b^{2}}\, f \right) \left(2 f x +e +\sqrt{-4 d f +e^{2}}\right)}}\, \sqrt{\frac{\left(-b f +c e +\sqrt{-4 d f +e^{2}}\, c -\sqrt{-4 a c +b^{2}}\, f \right) \left(-2 f x -e +\sqrt{-4 d f +e^{2}}\right)}{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(2 f x +e +\sqrt{-4 d f +e^{2}}\right)}}\, \sqrt{c \,x^{2}+b x +a}\, \sqrt{f \,x^{2}+e x +d}\, \EllipticF \left(\sqrt{\frac{\left(-b f +c e +\sqrt{-4 d f +e^{2}}\, c -\sqrt{-4 a c +b^{2}}\, f \right) \left(-2 f x -e +\sqrt{-4 d f +e^{2}}\right)}{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(2 f x +e +\sqrt{-4 d f +e^{2}}\right)}}, \sqrt{\frac{\left(-b f +c e +\sqrt{-4 d f +e^{2}}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \left(b f -c e +\sqrt{-4 d f +e^{2}}\, c +\sqrt{-4 a c +b^{2}}\, f \right)}{\left(b f -c e +\sqrt{-4 d f +e^{2}}\, c -\sqrt{-4 a c +b^{2}}\, f \right) \left(-b f +c e +\sqrt{-4 d f +e^{2}}\, c -\sqrt{-4 a c +b^{2}}\, f \right)}}\right)}{\sqrt{\frac{\left(-2 f x -e +\sqrt{-4 d f +e^{2}}\right) \left(2 f x +e +\sqrt{-4 d f +e^{2}}\right) \left(-2 c x -b +\sqrt{-4 a c +b^{2}}\right) \left(2 c x +b +\sqrt{-4 a c +b^{2}}\right)}{c f}}\, \sqrt{-4 d f +e^{2}}\, \left(b f -c e -\sqrt{-4 d f +e^{2}}\, c +\sqrt{-4 a c +b^{2}}\, f \right) \sqrt{c f \,x^{4}+b f \,x^{3}+c e \,x^{3}+a f \,x^{2}+b e \,x^{2}+c d \,x^{2}+a e x +b d x +a d}}"," ",0,"8*(2*b*f^2*x^2-2*c*e*f*x^2+2*x^2*c*f*(-4*d*f+e^2)^(1/2)+2*(-4*a*c+b^2)^(1/2)*f^2*x^2+2*b*e*f*x+2*x*b*f*(-4*d*f+e^2)^(1/2)-8*c*d*f*x+2*x*e*f*(-4*a*c+b^2)^(1/2)+2*x*f*(-4*d*f+e^2)^(1/2)*(-4*a*c+b^2)^(1/2)-2*b*d*f+b*e^2+b*e*(-4*d*f+e^2)^(1/2)-2*c*d*e-2*c*d*(-4*d*f+e^2)^(1/2)-2*(-4*a*c+b^2)^(1/2)*d*f+e^2*(-4*a*c+b^2)^(1/2)+e*(-4*d*f+e^2)^(1/2)*(-4*a*c+b^2)^(1/2))*EllipticF((((-4*d*f+e^2)^(1/2)*c-(-4*a*c+b^2)^(1/2)*f-b*f+c*e)*(-2*f*x+(-4*d*f+e^2)^(1/2)-e)/((-4*d*f+e^2)^(1/2)*c+(-4*a*c+b^2)^(1/2)*f+b*f-c*e)/(2*f*x+(-4*d*f+e^2)^(1/2)+e))^(1/2),(((-4*d*f+e^2)^(1/2)*c+(-4*a*c+b^2)^(1/2)*f-b*f+c*e)*((-4*d*f+e^2)^(1/2)*c+(-4*a*c+b^2)^(1/2)*f+b*f-c*e)/((-4*d*f+e^2)^(1/2)*c-(-4*a*c+b^2)^(1/2)*f+b*f-c*e)/((-4*d*f+e^2)^(1/2)*c-(-4*a*c+b^2)^(1/2)*f-b*f+c*e))^(1/2))*((-4*d*f+e^2)^(1/2)*(2*c*x+b+(-4*a*c+b^2)^(1/2))*f/((-4*d*f+e^2)^(1/2)*c+(-4*a*c+b^2)^(1/2)*f+b*f-c*e)/(2*f*x+(-4*d*f+e^2)^(1/2)+e))^(1/2)*(-(-4*d*f+e^2)^(1/2)*(-2*c*x-b+(-4*a*c+b^2)^(1/2))*f/((-4*d*f+e^2)^(1/2)*c-(-4*a*c+b^2)^(1/2)*f+b*f-c*e)/(2*f*x+(-4*d*f+e^2)^(1/2)+e))^(1/2)*(((-4*d*f+e^2)^(1/2)*c-(-4*a*c+b^2)^(1/2)*f-b*f+c*e)*(-2*f*x+(-4*d*f+e^2)^(1/2)-e)/((-4*d*f+e^2)^(1/2)*c+(-4*a*c+b^2)^(1/2)*f+b*f-c*e)/(2*f*x+(-4*d*f+e^2)^(1/2)+e))^(1/2)*(c*x^2+b*x+a)^(1/2)*(f*x^2+e*x+d)^(1/2)/(1/c/f*(-2*f*x+(-4*d*f+e^2)^(1/2)-e)*(2*f*x+(-4*d*f+e^2)^(1/2)+e)*(-2*c*x-b+(-4*a*c+b^2)^(1/2))*(2*c*x+b+(-4*a*c+b^2)^(1/2)))^(1/2)/(-4*d*f+e^2)^(1/2)/((-4*a*c+b^2)^(1/2)*f-(-4*d*f+e^2)^(1/2)*c+b*f-c*e)/(c*f*x^4+b*f*x^3+c*e*x^3+a*f*x^2+b*e*x^2+c*d*x^2+a*e*x+b*d*x+a*d)^(1/2)","A"
123,1,418,643,0.468000," ","int(1/(5*x^2+3*x+2)^(1/2)/(2*x^2-x+3)^(1/2),x)","-\frac{4 i \sqrt{5 x^{2}+3 x +2}\, \sqrt{2 x^{2}-x +3}\, \left(5 i \sqrt{23}+2 i \sqrt{31}-11\right) \sqrt{\frac{\left(5 i \sqrt{23}-2 i \sqrt{31}+11\right) \left(4 x -1+i \sqrt{23}\right)}{\left(5 i \sqrt{23}+2 i \sqrt{31}-11\right) \left(-4 x +i \sqrt{23}+1\right)}}\, \left(-4 x +i \sqrt{23}+1\right)^{2} \sqrt{-\frac{i \sqrt{23}\, \left(10 x +i \sqrt{31}+3\right)}{\left(5 i \sqrt{23}-2 i \sqrt{31}-11\right) \left(-4 x +i \sqrt{23}+1\right)}}\, \sqrt{\frac{i \sqrt{23}\, \left(-10 x +i \sqrt{31}-3\right)}{\left(5 i \sqrt{23}+2 i \sqrt{31}-11\right) \left(-4 x +i \sqrt{23}+1\right)}}\, \sqrt{23}\, \sqrt{10}\, \EllipticF \left(\sqrt{\frac{\left(5 i \sqrt{23}-2 i \sqrt{31}+11\right) \left(4 x -1+i \sqrt{23}\right)}{\left(5 i \sqrt{23}+2 i \sqrt{31}-11\right) \left(-4 x +i \sqrt{23}+1\right)}}, \sqrt{\frac{\left(5 i \sqrt{23}+2 i \sqrt{31}+11\right) \left(5 i \sqrt{23}+2 i \sqrt{31}-11\right)}{\left(5 i \sqrt{23}-2 i \sqrt{31}-11\right) \left(5 i \sqrt{23}-2 i \sqrt{31}+11\right)}}\right)}{23 \sqrt{10 x^{4}+x^{3}+16 x^{2}+7 x +6}\, \left(5 i \sqrt{23}-2 i \sqrt{31}+11\right) \sqrt{\left(4 x -1+i \sqrt{23}\right) \left(-4 x +i \sqrt{23}+1\right) \left(10 x +i \sqrt{31}+3\right) \left(-10 x +i \sqrt{31}-3\right)}}"," ",0,"-4/23*I*(5*x^2+3*x+2)^(1/2)*(2*x^2-x+3)^(1/2)*(5*I*23^(1/2)+2*I*31^(1/2)-11)*((5*I*23^(1/2)-2*I*31^(1/2)+11)*(-1+4*x+I*23^(1/2))/(5*I*23^(1/2)+2*I*31^(1/2)-11)/(I*23^(1/2)-4*x+1))^(1/2)*(I*23^(1/2)-4*x+1)^2*(-I*23^(1/2)*(I*31^(1/2)+10*x+3)/(5*I*23^(1/2)-2*I*31^(1/2)-11)/(I*23^(1/2)-4*x+1))^(1/2)*(I*23^(1/2)*(I*31^(1/2)-10*x-3)/(5*I*23^(1/2)+2*I*31^(1/2)-11)/(I*23^(1/2)-4*x+1))^(1/2)*23^(1/2)*10^(1/2)*EllipticF(((5*I*23^(1/2)-2*I*31^(1/2)+11)*(-1+4*x+I*23^(1/2))/(5*I*23^(1/2)+2*I*31^(1/2)-11)/(I*23^(1/2)-4*x+1))^(1/2),((5*I*23^(1/2)+2*I*31^(1/2)+11)*(5*I*23^(1/2)+2*I*31^(1/2)-11)/(5*I*23^(1/2)-2*I*31^(1/2)-11)/(5*I*23^(1/2)-2*I*31^(1/2)+11))^(1/2))/(10*x^4+x^3+16*x^2+7*x+6)^(1/2)/(5*I*23^(1/2)-2*I*31^(1/2)+11)/((-1+4*x+I*23^(1/2))*(I*23^(1/2)-4*x+1)*(I*31^(1/2)+10*x+3)*(I*31^(1/2)-10*x-3))^(1/2)","A"