1,1,77,106,0.031000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/4),x)","\frac{3 \sqrt{b \,x^{2}+a}\, a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{1}{4}} \sqrt{b}}+\frac{\left(2 b \,x^{2}+5 a \right) \left(b \,x^{2}+a \right) x}{8 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{1}{4}}}"," ",0,"1/8*x*(2*b*x^2+5*a)*(b*x^2+a)/((b*x^2+a)^2)^(1/4)+3/8*a^2*ln(x*b^(1/2)+(b*x^2+a)^(1/2))/b^(1/2)/((b*x^2+a)^2)^(1/4)*(b*x^2+a)^(1/2)","A"
2,1,58,73,0.014000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(1/4),x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{1}{4}} a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 \sqrt{b \,x^{2}+a}\, \sqrt{b}}+\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{1}{4}} x}{2}"," ",0,"1/2*x*((b*x^2+a)^2)^(1/4)+1/2*a*ln(b^(1/2)*x+(b*x^2+a)^(1/2))/b^(1/2)*((b*x^2+a)^2)^(1/4)/(b*x^2+a)^(1/2)","A"
3,0,0,48,0.035000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/4),x)","\int \frac{1}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/4),x)","F"
4,1,33,32,0.003000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/4),x)","\frac{\left(b \,x^{2}+a \right) x}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{3}{4}} a}"," ",0,"x*(b*x^2+a)/a/(b^2*x^4+2*a*b*x^2+a^2)^(3/4)","A"
5,1,44,60,0.003000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/4),x)","\frac{\left(b \,x^{2}+a \right) \left(2 b \,x^{2}+3 a \right) x}{3 \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{5}{4}} a^{2}}"," ",0,"1/3*(b*x^2+a)*x*(2*b*x^2+3*a)/a^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/4)","A"
6,1,55,93,0.004000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(7/4),x)","\frac{\left(b \,x^{2}+a \right) \left(8 b^{2} x^{4}+20 a b \,x^{2}+15 a^{2}\right) x}{15 \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{7}{4}} a^{3}}"," ",0,"1/15*(b*x^2+a)*x*(8*b^2*x^4+20*a*b*x^2+15*a^2)/a^3/(b^2*x^4+2*a*b*x^2+a^2)^(7/4)","A"
7,1,66,119,0.005000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(9/4),x)","\frac{\left(b \,x^{2}+a \right) \left(16 b^{3} x^{6}+56 b^{2} x^{4} a +70 a^{2} b \,x^{2}+35 a^{3}\right) x}{35 \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{9}{4}} a^{4}}"," ",0,"1/35*(b*x^2+a)*x*(16*b^3*x^6+56*a*b^2*x^4+70*a^2*b*x^2+35*a^3)/a^4/(b^2*x^4+2*a*b*x^2+a^2)^(9/4)","A"
8,1,1099,223,0.133000," ","int(1/(x^4+2*a*x^2+a^2+b),x)","\frac{a^{4} \arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{2 \left(a^{2}+b \right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+b}}\, b}-\frac{a^{4} \arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{2 \left(a^{2}+b \right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+b}}\, b}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, a^{3} \ln \left(x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, x +\sqrt{a^{2}+b}\right)}{8 \left(a^{2}+b \right)^{\frac{3}{2}} b}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, a^{3} \ln \left(-x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, x -\sqrt{a^{2}+b}\right)}{8 \left(a^{2}+b \right)^{\frac{3}{2}} b}+\frac{3 a^{2} \arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{2 \left(a^{2}+b \right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+b}}}-\frac{3 a^{2} \arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{2 \left(a^{2}+b \right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+b}}}-\frac{a^{2} \arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{2 \sqrt{a^{2}+b}\, \sqrt{2 a +2 \sqrt{a^{2}+b}}\, b}+\frac{a^{2} \arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{2 \sqrt{a^{2}+b}\, \sqrt{2 a +2 \sqrt{a^{2}+b}}\, b}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, a^{2} \ln \left(x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, x +\sqrt{a^{2}+b}\right)}{8 \left(a^{2}+b \right) b}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, a^{2} \ln \left(-x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, x -\sqrt{a^{2}+b}\right)}{8 \left(a^{2}+b \right) b}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, a \ln \left(x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, x +\sqrt{a^{2}+b}\right)}{8 \left(a^{2}+b \right)^{\frac{3}{2}}}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, a \ln \left(-x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, x -\sqrt{a^{2}+b}\right)}{8 \left(a^{2}+b \right)^{\frac{3}{2}}}+\frac{b \arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{\left(a^{2}+b \right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+b}}}-\frac{b \arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{\left(a^{2}+b \right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+b}}}-\frac{\arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{2 \sqrt{a^{2}+b}\, \sqrt{2 a +2 \sqrt{a^{2}+b}}}+\frac{\arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+b}}}{\sqrt{2 a +2 \sqrt{a^{2}+b}}}\right)}{2 \sqrt{a^{2}+b}\, \sqrt{2 a +2 \sqrt{a^{2}+b}}}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, \ln \left(x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, x +\sqrt{a^{2}+b}\right)}{8 a^{2}+8 b}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, \ln \left(-x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+b}}\, x -\sqrt{a^{2}+b}\right)}{8 \left(a^{2}+b \right)}"," ",0,"1/8/b/(a^2+b)*ln(x^2+x*(2*(a^2+b)^(1/2)-2*a)^(1/2)+(a^2+b)^(1/2))*(2*(a^2+b)^(1/2)-2*a)^(1/2)*a^2+1/8/b/(a^2+b)^(3/2)*ln(x^2+x*(2*(a^2+b)^(1/2)-2*a)^(1/2)+(a^2+b)^(1/2))*(2*(a^2+b)^(1/2)-2*a)^(1/2)*a^3+1/8/(a^2+b)*ln(x^2+x*(2*(a^2+b)^(1/2)-2*a)^(1/2)+(a^2+b)^(1/2))*(2*(a^2+b)^(1/2)-2*a)^(1/2)+1/8/(a^2+b)^(3/2)*ln(x^2+x*(2*(a^2+b)^(1/2)-2*a)^(1/2)+(a^2+b)^(1/2))*(2*(a^2+b)^(1/2)-2*a)^(1/2)*a-1/2/b/(a^2+b)^(1/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+b)^(1/2)-2*a)^(1/2))/(2*(a^2+b)^(1/2)+2*a)^(1/2))*a^2+1/2/b/(a^2+b)^(3/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+b)^(1/2)-2*a)^(1/2))/(2*(a^2+b)^(1/2)+2*a)^(1/2))*a^4-1/2/(a^2+b)^(1/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+b)^(1/2)-2*a)^(1/2))/(2*(a^2+b)^(1/2)+2*a)^(1/2))+3/2/(a^2+b)^(3/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+b)^(1/2)-2*a)^(1/2))/(2*(a^2+b)^(1/2)+2*a)^(1/2))*a^2+b/(a^2+b)^(3/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+b)^(1/2)-2*a)^(1/2))/(2*(a^2+b)^(1/2)+2*a)^(1/2))-1/8/b/(a^2+b)*ln(x*(2*(a^2+b)^(1/2)-2*a)^(1/2)-x^2-(a^2+b)^(1/2))*(2*(a^2+b)^(1/2)-2*a)^(1/2)*a^2-1/8/b/(a^2+b)^(3/2)*ln(x*(2*(a^2+b)^(1/2)-2*a)^(1/2)-x^2-(a^2+b)^(1/2))*(2*(a^2+b)^(1/2)-2*a)^(1/2)*a^3-1/8/(a^2+b)*ln(x*(2*(a^2+b)^(1/2)-2*a)^(1/2)-x^2-(a^2+b)^(1/2))*(2*(a^2+b)^(1/2)-2*a)^(1/2)-1/8/(a^2+b)^(3/2)*ln(x*(2*(a^2+b)^(1/2)-2*a)^(1/2)-x^2-(a^2+b)^(1/2))*(2*(a^2+b)^(1/2)-2*a)^(1/2)*a+1/2/b/(a^2+b)^(1/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+b)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+b)^(1/2)+2*a)^(1/2))*a^2-1/2/b/(a^2+b)^(3/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+b)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+b)^(1/2)+2*a)^(1/2))*a^4+1/2/(a^2+b)^(1/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+b)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+b)^(1/2)+2*a)^(1/2))-3/2/(a^2+b)^(3/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+b)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+b)^(1/2)+2*a)^(1/2))*a^2-b/(a^2+b)^(3/2)/(2*(a^2+b)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+b)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+b)^(1/2)+2*a)^(1/2))","B"
9,1,32,35,0.009000," ","int(1/(x^4+2*a*x^2+a^2-1),x)","-\frac{\arctan \left(\frac{x}{\sqrt{a +1}}\right)}{2 \sqrt{a +1}}+\frac{\arctan \left(\frac{x}{\sqrt{a -1}}\right)}{2 \sqrt{a -1}}"," ",0,"-1/2*arctan(x/(1+a)^(1/2))/(1+a)^(1/2)+1/2/(a-1)^(1/2)*arctan(x/(a-1)^(1/2))","A"
10,1,1073,223,0.106000," ","int(1/(x^4+2*a*x^2+a^2+1),x)","\frac{a^{4} \arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+1}}}-\frac{a^{4} \arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+1}}}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, a^{3} \ln \left(x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, x +\sqrt{a^{2}+1}\right)}{8 \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, a^{3} \ln \left(-x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, x -\sqrt{a^{2}+1}\right)}{8 \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{a^{2} \arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{2 \sqrt{a^{2}+1}\, \sqrt{2 a +2 \sqrt{a^{2}+1}}}+\frac{3 a^{2} \arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+1}}}+\frac{a^{2} \arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{2 \sqrt{a^{2}+1}\, \sqrt{2 a +2 \sqrt{a^{2}+1}}}-\frac{3 a^{2} \arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{2 \left(a^{2}+1\right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+1}}}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, a^{2} \ln \left(x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, x +\sqrt{a^{2}+1}\right)}{8 a^{2}+8}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, a^{2} \ln \left(-x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, x -\sqrt{a^{2}+1}\right)}{8 \left(a^{2}+1\right)}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, a \ln \left(x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, x +\sqrt{a^{2}+1}\right)}{8 \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, a \ln \left(-x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, x -\sqrt{a^{2}+1}\right)}{8 \left(a^{2}+1\right)^{\frac{3}{2}}}-\frac{\arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{2 \sqrt{a^{2}+1}\, \sqrt{2 a +2 \sqrt{a^{2}+1}}}+\frac{\arctan \left(\frac{2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+1}}}+\frac{\arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{2 \sqrt{a^{2}+1}\, \sqrt{2 a +2 \sqrt{a^{2}+1}}}-\frac{\arctan \left(\frac{-2 x +\sqrt{-2 a +2 \sqrt{a^{2}+1}}}{\sqrt{2 a +2 \sqrt{a^{2}+1}}}\right)}{\left(a^{2}+1\right)^{\frac{3}{2}} \sqrt{2 a +2 \sqrt{a^{2}+1}}}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, \ln \left(x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, x +\sqrt{a^{2}+1}\right)}{8 a^{2}+8}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, \ln \left(-x^{2}+\sqrt{-2 a +2 \sqrt{a^{2}+1}}\, x -\sqrt{a^{2}+1}\right)}{8 \left(a^{2}+1\right)}"," ",0,"-1/8/(a^2+1)*ln(x*(2*(a^2+1)^(1/2)-2*a)^(1/2)-x^2-(a^2+1)^(1/2))*(2*(a^2+1)^(1/2)-2*a)^(1/2)*a^2-1/8/(a^2+1)^(3/2)*ln(x*(2*(a^2+1)^(1/2)-2*a)^(1/2)-x^2-(a^2+1)^(1/2))*(2*(a^2+1)^(1/2)-2*a)^(1/2)*a^3-1/8/(a^2+1)*ln(x*(2*(a^2+1)^(1/2)-2*a)^(1/2)-x^2-(a^2+1)^(1/2))*(2*(a^2+1)^(1/2)-2*a)^(1/2)-1/8/(a^2+1)^(3/2)*ln(x*(2*(a^2+1)^(1/2)-2*a)^(1/2)-x^2-(a^2+1)^(1/2))*(2*(a^2+1)^(1/2)-2*a)^(1/2)*a+1/2/(a^2+1)^(1/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+1)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+1)^(1/2)+2*a)^(1/2))*a^2-1/2/(a^2+1)^(3/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+1)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+1)^(1/2)+2*a)^(1/2))*a^4+1/2/(a^2+1)^(1/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+1)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+1)^(1/2)+2*a)^(1/2))-3/2/(a^2+1)^(3/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+1)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+1)^(1/2)+2*a)^(1/2))*a^2-1/(a^2+1)^(3/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan(((2*(a^2+1)^(1/2)-2*a)^(1/2)-2*x)/(2*(a^2+1)^(1/2)+2*a)^(1/2))+1/8/(a^2+1)*ln(x^2+x*(2*(a^2+1)^(1/2)-2*a)^(1/2)+(a^2+1)^(1/2))*(2*(a^2+1)^(1/2)-2*a)^(1/2)*a^2+1/8/(a^2+1)^(3/2)*ln(x^2+x*(2*(a^2+1)^(1/2)-2*a)^(1/2)+(a^2+1)^(1/2))*(2*(a^2+1)^(1/2)-2*a)^(1/2)*a^3+1/8/(a^2+1)*ln(x^2+x*(2*(a^2+1)^(1/2)-2*a)^(1/2)+(a^2+1)^(1/2))*(2*(a^2+1)^(1/2)-2*a)^(1/2)+1/8/(a^2+1)^(3/2)*ln(x^2+x*(2*(a^2+1)^(1/2)-2*a)^(1/2)+(a^2+1)^(1/2))*(2*(a^2+1)^(1/2)-2*a)^(1/2)*a-1/2/(a^2+1)^(1/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+1)^(1/2)-2*a)^(1/2))/(2*(a^2+1)^(1/2)+2*a)^(1/2))*a^2+1/2/(a^2+1)^(3/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+1)^(1/2)-2*a)^(1/2))/(2*(a^2+1)^(1/2)+2*a)^(1/2))*a^4-1/2/(a^2+1)^(1/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+1)^(1/2)-2*a)^(1/2))/(2*(a^2+1)^(1/2)+2*a)^(1/2))+3/2/(a^2+1)^(3/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+1)^(1/2)-2*a)^(1/2))/(2*(a^2+1)^(1/2)+2*a)^(1/2))*a^2+1/(a^2+1)^(3/2)/(2*(a^2+1)^(1/2)+2*a)^(1/2)*arctan((2*x+(2*(a^2+1)^(1/2)-2*a)^(1/2))/(2*(a^2+1)^(1/2)+2*a)^(1/2))","B"
11,1,26,11,0.009000," ","int(1/(x^4-5*x^2+4),x)","\frac{\ln \left(x +1\right)}{6}-\frac{\ln \left(x +2\right)}{12}+\frac{\ln \left(x -2\right)}{12}-\frac{\ln \left(x -1\right)}{6}"," ",0,"-1/12*ln(x+2)+1/6*ln(1+x)+1/12*ln(x-2)-1/6*ln(x-1)","B"
12,1,18,17,0.006000," ","int(1/(x^4+4*x^2+3),x)","\frac{\arctan \left(x \right)}{2}-\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, x}{3}\right)}{6}"," ",0,"1/2*arctan(x)-1/6*arctan(1/3*x*3^(1/2))*3^(1/2)","A"
13,1,54,53,0.005000," ","int(1/(x^4+5*x^2+9),x)","\frac{\sqrt{11}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{11}}{11}\right)}{66}+\frac{\sqrt{11}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{11}}{11}\right)}{66}-\frac{\ln \left(x^{2}-x +3\right)}{12}+\frac{\ln \left(x^{2}+x +3\right)}{12}"," ",0,"-1/12*ln(x^2-x+3)+1/66*11^(1/2)*arctan(1/11*(2*x-1)*11^(1/2))+1/12*ln(x^2+x+3)+1/66*arctan(1/11*(2*x+1)*11^(1/2))*11^(1/2)","A"
14,1,57,56,0.036000," ","int(1/(x^4-x^2+1),x)","\frac{\arctan \left(2 x -\sqrt{3}\right)}{2}+\frac{\arctan \left(2 x +\sqrt{3}\right)}{2}-\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{12}+\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{12}"," ",0,"1/2*arctan(2*x-3^(1/2))+1/2*arctan(2*x+3^(1/2))-1/12*ln(1+x^2-3^(1/2)*x)*3^(1/2)+1/12*ln(1+x^2+3^(1/2)*x)*3^(1/2)","A"
15,1,386,124,0.109000," ","int(1/(x^4+2*x^2+2),x)","-\frac{\left(-2+2 \sqrt{2}\right) \sqrt{2}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{8 \sqrt{2+2 \sqrt{2}}}-\frac{\left(-2+2 \sqrt{2}\right) \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{4 \sqrt{2+2 \sqrt{2}}}+\frac{\sqrt{2}\, \arctan \left(\frac{2 x -\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{2 \sqrt{2+2 \sqrt{2}}}-\frac{\left(-2+2 \sqrt{2}\right) \sqrt{2}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{8 \sqrt{2+2 \sqrt{2}}}-\frac{\left(-2+2 \sqrt{2}\right) \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{4 \sqrt{2+2 \sqrt{2}}}+\frac{\sqrt{2}\, \arctan \left(\frac{2 x +\sqrt{-2+2 \sqrt{2}}}{\sqrt{2+2 \sqrt{2}}}\right)}{2 \sqrt{2+2 \sqrt{2}}}-\frac{\sqrt{-2+2 \sqrt{2}}\, \sqrt{2}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{2}}\, x +\sqrt{2}\right)}{16}-\frac{\sqrt{-2+2 \sqrt{2}}\, \ln \left(x^{2}-\sqrt{-2+2 \sqrt{2}}\, x +\sqrt{2}\right)}{8}+\frac{\sqrt{-2+2 \sqrt{2}}\, \sqrt{2}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{2}}\, x +\sqrt{2}\right)}{16}+\frac{\sqrt{-2+2 \sqrt{2}}\, \ln \left(x^{2}+\sqrt{-2+2 \sqrt{2}}\, x +\sqrt{2}\right)}{8}"," ",0,"-1/16*ln(x^2+2^(1/2)-x*(-2+2*2^(1/2))^(1/2))*(-2+2*2^(1/2))^(1/2)*2^(1/2)-1/8*ln(x^2+2^(1/2)-x*(-2+2*2^(1/2))^(1/2))*(-2+2*2^(1/2))^(1/2)-1/8/(2+2*2^(1/2))^(1/2)*arctan((2*x-(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))*(-2+2*2^(1/2))*2^(1/2)-1/4/(2+2*2^(1/2))^(1/2)*arctan((2*x-(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))*(-2+2*2^(1/2))+1/2/(2+2*2^(1/2))^(1/2)*arctan((2*x-(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))*2^(1/2)+1/16*ln(x^2+2^(1/2)+x*(-2+2*2^(1/2))^(1/2))*(-2+2*2^(1/2))^(1/2)*2^(1/2)+1/8*ln(x^2+2^(1/2)+x*(-2+2*2^(1/2))^(1/2))*(-2+2*2^(1/2))^(1/2)-1/8/(2+2*2^(1/2))^(1/2)*arctan((2*x+(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))*(-2+2*2^(1/2))*2^(1/2)-1/4/(2+2*2^(1/2))^(1/2)*arctan((2*x+(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))*(-2+2*2^(1/2))+1/2/(2+2*2^(1/2))^(1/2)*arctan((2*x+(-2+2*2^(1/2))^(1/2))/(2+2*2^(1/2))^(1/2))*2^(1/2)","B"
16,1,51,13,0.039000," ","int(1/(-3*x^4+5*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{3 x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{6}\right)}{2 \sqrt{-3 x^{4}+5 x^{2}+2}}"," ",0,"1/2*2^(1/2)*(-2*x^2+4)^(1/2)*(3*x^2+1)^(1/2)/(-3*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*2^(1/2),I*6^(1/2))","B"
17,1,84,37,0.107000," ","int(1/(-3*x^4+4*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-1+\frac{\sqrt{10}}{2}\right) x^{2}+1}\, \sqrt{-\left(-1-\frac{\sqrt{10}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-4+2 \sqrt{10}}\, x}{2}, \frac{i \sqrt{6}}{3}+\frac{i \sqrt{15}}{3}\right)}{\sqrt{-4+2 \sqrt{10}}\, \sqrt{-3 x^{4}+4 x^{2}+2}}"," ",0,"2/(-4+2*10^(1/2))^(1/2)*(1-(-1+1/2*10^(1/2))*x^2)^(1/2)*(1-(-1-1/2*10^(1/2))*x^2)^(1/2)/(-3*x^4+4*x^2+2)^(1/2)*EllipticF(1/2*x*(-4+2*10^(1/2))^(1/2),1/3*I*6^(1/2)+1/3*I*15^(1/2))","B"
18,1,80,37,0.097000," ","int(1/(-3*x^4+3*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{3}{4}+\frac{\sqrt{33}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{4}-\frac{\sqrt{33}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-3+\sqrt{33}}\, x}{2}, \frac{i \sqrt{6}}{4}+\frac{i \sqrt{22}}{4}\right)}{\sqrt{-3+\sqrt{33}}\, \sqrt{-3 x^{4}+3 x^{2}+2}}"," ",0,"2/(-3+33^(1/2))^(1/2)*(1-(-3/4+1/4*33^(1/2))*x^2)^(1/2)*(1-(-3/4-1/4*33^(1/2))*x^2)^(1/2)/(-3*x^4+3*x^2+2)^(1/2)*EllipticF(1/2*x*(-3+33^(1/2))^(1/2),1/4*I*6^(1/2)+1/4*I*22^(1/2))","B"
19,1,84,34,0.097000," ","int(1/(-3*x^4+2*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{1}{2}+\frac{\sqrt{7}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{\sqrt{7}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 \sqrt{7}}\, x}{2}, \frac{i \sqrt{6}}{6}+\frac{i \sqrt{42}}{6}\right)}{\sqrt{-2+2 \sqrt{7}}\, \sqrt{-3 x^{4}+2 x^{2}+2}}"," ",0,"2/(-2+2*7^(1/2))^(1/2)*(1-(-1/2+1/2*7^(1/2))*x^2)^(1/2)*(1-(-1/2-1/2*7^(1/2))*x^2)^(1/2)/(-3*x^4+2*x^2+2)^(1/2)*EllipticF(1/2*x*(-2+2*7^(1/2))^(1/2),1/6*I*6^(1/2)+1/6*I*42^(1/2))","B"
20,1,41,13,0.015000," ","int(1/(-3*x^4+x^2+2)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{6 x^{2}+4}\, \EllipticF \left(x , \frac{i \sqrt{6}}{2}\right)}{2 \sqrt{-3 x^{4}+x^{2}+2}}"," ",0,"1/2*(-x^2+1)^(1/2)*(6*x^2+4)^(1/2)/(-3*x^4+x^2+2)^(1/2)*EllipticF(x,1/2*I*6^(1/2))","B"
21,1,54,17,0.040000," ","int(1/(-3*x^4+2)^(1/2),x)","\frac{\sqrt{2}\, 6^{\frac{3}{4}} \sqrt{-2 \sqrt{6}\, x^{2}+4}\, \sqrt{2 \sqrt{6}\, x^{2}+4}\, \EllipticF \left(\frac{\sqrt{2}\, 6^{\frac{1}{4}} x}{2}, i\right)}{24 \sqrt{-3 x^{4}+2}}"," ",0,"1/24*2^(1/2)*6^(3/4)*(4-2*x^2*6^(1/2))^(1/2)*(4+2*x^2*6^(1/2))^(1/2)/(-3*x^4+2)^(1/2)*EllipticF(1/2*x*2^(1/2)*6^(1/4),I)","B"
22,1,49,18,0.031000," ","int(1/(-3*x^4-x^2+2)^(1/2),x)","\frac{\sqrt{6}\, \sqrt{-6 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{3}\right)}{6 \sqrt{-3 x^{4}-x^{2}+2}}"," ",0,"1/6*6^(1/2)*(-6*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-3*x^4-x^2+2)^(1/2)*EllipticF(1/2*6^(1/2)*x,1/3*I*6^(1/2))","B"
23,1,84,34,0.088000," ","int(1/(-3*x^4-2*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{\sqrt{7}}{2}+\frac{1}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{7}}{2}+\frac{1}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2+2 \sqrt{7}}\, x}{2}, \frac{i \sqrt{42}}{6}-\frac{i \sqrt{6}}{6}\right)}{\sqrt{2+2 \sqrt{7}}\, \sqrt{-3 x^{4}-2 x^{2}+2}}"," ",0,"2/(2+2*7^(1/2))^(1/2)*(1-(1/2*7^(1/2)+1/2)*x^2)^(1/2)*(1-(-1/2*7^(1/2)+1/2)*x^2)^(1/2)/(-3*x^4-2*x^2+2)^(1/2)*EllipticF(1/2*x*(2+2*7^(1/2))^(1/2),1/6*I*42^(1/2)-1/6*I*6^(1/2))","B"
24,1,80,37,0.094000," ","int(1/(-3*x^4-3*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{\sqrt{33}}{4}+\frac{3}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{33}}{4}+\frac{3}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3+\sqrt{33}}\, x}{2}, \frac{i \sqrt{22}}{4}-\frac{i \sqrt{6}}{4}\right)}{\sqrt{3+\sqrt{33}}\, \sqrt{-3 x^{4}-3 x^{2}+2}}"," ",0,"2/(3+33^(1/2))^(1/2)*(1-(1/4*33^(1/2)+3/4)*x^2)^(1/2)*(1-(-1/4*33^(1/2)+3/4)*x^2)^(1/2)/(-3*x^4-3*x^2+2)^(1/2)*EllipticF(1/2*x*(3+33^(1/2))^(1/2),1/4*I*22^(1/2)-1/4*I*6^(1/2))","B"
25,1,84,37,0.090000," ","int(1/(-3*x^4-4*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(1+\frac{\sqrt{10}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{10}}{2}+1\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{4+2 \sqrt{10}}\, x}{2}, \frac{i \sqrt{15}}{3}-\frac{i \sqrt{6}}{3}\right)}{\sqrt{4+2 \sqrt{10}}\, \sqrt{-3 x^{4}-4 x^{2}+2}}"," ",0,"2/(4+2*10^(1/2))^(1/2)*(1-(1+1/2*10^(1/2))*x^2)^(1/2)*(1-(-1/2*10^(1/2)+1)*x^2)^(1/2)/(-3*x^4-4*x^2+2)^(1/2)*EllipticF(1/2*x*(4+2*10^(1/2))^(1/2),1/3*I*15^(1/2)-1/3*I*6^(1/2))","B"
26,1,50,17,0.026000," ","int(1/(-3*x^4-5*x^2+2)^(1/2),x)","\frac{\sqrt{3}\, \sqrt{-3 x^{2}+1}\, \sqrt{2 x^{2}+4}\, \EllipticF \left(\sqrt{3}\, x , \frac{i \sqrt{6}}{6}\right)}{6 \sqrt{-3 x^{4}-5 x^{2}+2}}"," ",0,"1/6*3^(1/2)*(-3*x^2+1)^(1/2)*(2*x^2+4)^(1/2)/(-3*x^4-5*x^2+2)^(1/2)*EllipticF(3^(1/2)*x,1/6*I*6^(1/2))","B"
27,1,84,35,0.107000," ","int(1/(-2*x^4+7*x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{7}{6}+\frac{\sqrt{73}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{73}}{6}-\frac{7}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-42+6 \sqrt{73}}\, x}{6}, \frac{7 i \sqrt{6}}{12}+\frac{i \sqrt{438}}{12}\right)}{\sqrt{-42+6 \sqrt{73}}\, \sqrt{-2 x^{4}+7 x^{2}+3}}"," ",0,"6/(-42+6*73^(1/2))^(1/2)*(1-(-7/6+1/6*73^(1/2))*x^2)^(1/2)*(1-(-1/6*73^(1/2)-7/6)*x^2)^(1/2)/(-2*x^4+7*x^2+3)^(1/2)*EllipticF(1/6*x*(-42+6*73^(1/2))^(1/2),7/12*I*6^(1/2)+1/12*I*438^(1/2))","B"
28,1,84,37,0.107000," ","int(1/(-2*x^4+6*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(-1+\frac{\sqrt{15}}{3}\right) x^{2}+1}\, \sqrt{-\left(-1-\frac{\sqrt{15}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-9+3 \sqrt{15}}\, x}{3}, \frac{i \sqrt{6}}{2}+\frac{i \sqrt{10}}{2}\right)}{\sqrt{-9+3 \sqrt{15}}\, \sqrt{-2 x^{4}+6 x^{2}+3}}"," ",0,"3/(-9+3*15^(1/2))^(1/2)*(1-(-1+1/3*15^(1/2))*x^2)^(1/2)*(1-(-1-1/3*15^(1/2))*x^2)^(1/2)/(-2*x^4+6*x^2+3)^(1/2)*EllipticF(1/3*x*(-9+3*15^(1/2))^(1/2),1/2*I*6^(1/2)+1/2*I*10^(1/2))","B"
29,1,51,13,0.027000," ","int(1/(-2*x^4+5*x^2+3)^(1/2),x)","\frac{\sqrt{3}\, \sqrt{-3 x^{2}+9}\, \sqrt{2 x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3}\, x}{3}, i \sqrt{6}\right)}{3 \sqrt{-2 x^{4}+5 x^{2}+3}}"," ",0,"1/3*3^(1/2)*(-3*x^2+9)^(1/2)*(2*x^2+1)^(1/2)/(-2*x^4+5*x^2+3)^(1/2)*EllipticF(1/3*3^(1/2)*x,I*6^(1/2))","B"
30,1,84,34,0.078000," ","int(1/(-2*x^4+4*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{2}{3}+\frac{\sqrt{10}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{2}{3}-\frac{\sqrt{10}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+3 \sqrt{10}}\, x}{3}, \frac{i \sqrt{6}}{3}+\frac{i \sqrt{15}}{3}\right)}{\sqrt{-6+3 \sqrt{10}}\, \sqrt{-2 x^{4}+4 x^{2}+3}}"," ",0,"3/(-6+3*10^(1/2))^(1/2)*(1-(-2/3+1/3*10^(1/2))*x^2)^(1/2)*(1-(-2/3-1/3*10^(1/2))*x^2)^(1/2)/(-2*x^4+4*x^2+3)^(1/2)*EllipticF(1/3*x*(-6+3*10^(1/2))^(1/2),1/3*I*6^(1/2)+1/3*I*15^(1/2))","B"
31,1,84,35,0.079000," ","int(1/(-2*x^4+3*x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{1}{2}+\frac{\sqrt{33}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{\sqrt{33}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-18+6 \sqrt{33}}\, x}{6}, \frac{i \sqrt{6}}{4}+\frac{i \sqrt{22}}{4}\right)}{\sqrt{-18+6 \sqrt{33}}\, \sqrt{-2 x^{4}+3 x^{2}+3}}"," ",0,"6/(-18+6*33^(1/2))^(1/2)*(1-(-1/2+1/6*33^(1/2))*x^2)^(1/2)*(1-(-1/2-1/6*33^(1/2))*x^2)^(1/2)/(-2*x^4+3*x^2+3)^(1/2)*EllipticF(1/6*x*(-18+6*33^(1/2))^(1/2),1/4*I*6^(1/2)+1/4*I*22^(1/2))","B"
32,1,84,34,0.079000," ","int(1/(-2*x^4+2*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{1}{3}+\frac{\sqrt{7}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{3}-\frac{\sqrt{7}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-3+3 \sqrt{7}}\, x}{3}, \frac{i \sqrt{6}}{6}+\frac{i \sqrt{42}}{6}\right)}{\sqrt{-3+3 \sqrt{7}}\, \sqrt{-2 x^{4}+2 x^{2}+3}}"," ",0,"3/(-3+3*7^(1/2))^(1/2)*(1-(-1/3+1/3*7^(1/2))*x^2)^(1/2)*(1-(-1/3-1/3*7^(1/2))*x^2)^(1/2)/(-2*x^4+2*x^2+3)^(1/2)*EllipticF(1/3*x*(-3+3*7^(1/2))^(1/2),1/6*I*6^(1/2)+1/6*I*42^(1/2))","B"
33,1,47,18,0.027000," ","int(1/(-2*x^4+x^2+3)^(1/2),x)","\frac{\sqrt{6}\, \sqrt{-6 x^{2}+9}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6}\, x}{3}, \frac{i \sqrt{6}}{2}\right)}{6 \sqrt{-2 x^{4}+x^{2}+3}}"," ",0,"1/6*6^(1/2)*(-6*x^2+9)^(1/2)*(x^2+1)^(1/2)/(-2*x^4+x^2+3)^(1/2)*EllipticF(1/3*6^(1/2)*x,1/2*I*6^(1/2))","B"
34,1,54,17,0.039000," ","int(1/(-2*x^4+3)^(1/2),x)","\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{-3 \sqrt{6}\, x^{2}+9}\, \sqrt{3 \sqrt{6}\, x^{2}+9}\, \EllipticF \left(\frac{\sqrt{3}\, 6^{\frac{1}{4}} x}{3}, i\right)}{54 \sqrt{-2 x^{4}+3}}"," ",0,"1/54*3^(1/2)*6^(3/4)*(9-3*6^(1/2)*x^2)^(1/2)*(9+3*6^(1/2)*x^2)^(1/2)/(-2*x^4+3)^(1/2)*EllipticF(1/3*x*3^(1/2)*6^(1/4),I)","B"
35,1,43,13,0.011000," ","int(1/(-2*x^4-x^2+3)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{6 x^{2}+9}\, \EllipticF \left(x , \frac{i \sqrt{6}}{3}\right)}{3 \sqrt{-2 x^{4}-x^{2}+3}}"," ",0,"1/3*(-x^2+1)^(1/2)*(6*x^2+9)^(1/2)/(-2*x^4-x^2+3)^(1/2)*EllipticF(x,1/3*I*6^(1/2))","B"
36,1,84,34,0.076000," ","int(1/(-2*x^4-2*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(\frac{\sqrt{7}}{3}+\frac{1}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{7}}{3}+\frac{1}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3+3 \sqrt{7}}\, x}{3}, \frac{i \sqrt{42}}{6}-\frac{i \sqrt{6}}{6}\right)}{\sqrt{3+3 \sqrt{7}}\, \sqrt{-2 x^{4}-2 x^{2}+3}}"," ",0,"3/(3+3*7^(1/2))^(1/2)*(1-(1/3*7^(1/2)+1/3)*x^2)^(1/2)*(1-(-1/3*7^(1/2)+1/3)*x^2)^(1/2)/(-2*x^4-2*x^2+3)^(1/2)*EllipticF(1/3*x*(3+3*7^(1/2))^(1/2),1/6*I*42^(1/2)-1/6*I*6^(1/2))","B"
37,1,84,35,0.072000," ","int(1/(-2*x^4-3*x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(\frac{\sqrt{33}}{6}+\frac{1}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{33}}{6}+\frac{1}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{18+6 \sqrt{33}}\, x}{6}, \frac{i \sqrt{22}}{4}-\frac{i \sqrt{6}}{4}\right)}{\sqrt{18+6 \sqrt{33}}\, \sqrt{-2 x^{4}-3 x^{2}+3}}"," ",0,"6/(18+6*33^(1/2))^(1/2)*(1-(1/6*33^(1/2)+1/2)*x^2)^(1/2)*(1-(-1/6*33^(1/2)+1/2)*x^2)^(1/2)/(-2*x^4-3*x^2+3)^(1/2)*EllipticF(1/6*x*(18+6*33^(1/2))^(1/2),1/4*I*22^(1/2)-1/4*I*6^(1/2))","B"
38,1,84,34,0.076000," ","int(1/(-2*x^4-4*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(\frac{\sqrt{10}}{3}+\frac{2}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{10}}{3}+\frac{2}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6+3 \sqrt{10}}\, x}{3}, \frac{i \sqrt{15}}{3}-\frac{i \sqrt{6}}{3}\right)}{\sqrt{6+3 \sqrt{10}}\, \sqrt{-2 x^{4}-4 x^{2}+3}}"," ",0,"3/(6+3*10^(1/2))^(1/2)*(1-(1/3*10^(1/2)+2/3)*x^2)^(1/2)*(1-(-1/3*10^(1/2)+2/3)*x^2)^(1/2)/(-2*x^4-4*x^2+3)^(1/2)*EllipticF(1/3*x*(6+3*10^(1/2))^(1/2),1/3*I*15^(1/2)-1/3*I*6^(1/2))","B"
39,1,50,17,0.021000," ","int(1/(-2*x^4-5*x^2+3)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-2 x^{2}+1}\, \sqrt{3 x^{2}+9}\, \EllipticF \left(\sqrt{2}\, x , \frac{i \sqrt{6}}{6}\right)}{6 \sqrt{-2 x^{4}-5 x^{2}+3}}"," ",0,"1/6*2^(1/2)*(-2*x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-2*x^4-5*x^2+3)^(1/2)*EllipticF(2^(1/2)*x,1/6*I*6^(1/2))","B"
40,1,84,37,0.096000," ","int(1/(-2*x^4-6*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(1+\frac{\sqrt{15}}{3}\right) x^{2}+1}\, \sqrt{-\left(1-\frac{\sqrt{15}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{9+3 \sqrt{15}}\, x}{3}, \frac{i \sqrt{10}}{2}-\frac{i \sqrt{6}}{2}\right)}{\sqrt{9+3 \sqrt{15}}\, \sqrt{-2 x^{4}-6 x^{2}+3}}"," ",0,"3/(9+3*15^(1/2))^(1/2)*(1-(1+1/3*15^(1/2))*x^2)^(1/2)*(1-(1-1/3*15^(1/2))*x^2)^(1/2)/(-2*x^4-6*x^2+3)^(1/2)*EllipticF(1/3*x*(9+3*15^(1/2))^(1/2),1/2*I*10^(1/2)-1/2*I*6^(1/2))","B"
41,1,84,35,0.093000," ","int(1/(-2*x^4-7*x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(\frac{\sqrt{73}}{6}+\frac{7}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{7}{6}-\frac{\sqrt{73}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{42+6 \sqrt{73}}\, x}{6}, \frac{i \sqrt{438}}{12}-\frac{7 i \sqrt{6}}{12}\right)}{\sqrt{42+6 \sqrt{73}}\, \sqrt{-2 x^{4}-7 x^{2}+3}}"," ",0,"6/(42+6*73^(1/2))^(1/2)*(1-(1/6*73^(1/2)+7/6)*x^2)^(1/2)*(1-(7/6-1/6*73^(1/2))*x^2)^(1/2)/(-2*x^4-7*x^2+3)^(1/2)*EllipticF(1/6*x*(42+6*73^(1/2))^(1/2),1/12*I*438^(1/2)-7/12*I*6^(1/2))","B"
42,1,53,56,0.009000," ","int(1/(3*x^4+5*x^2-2)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{-3 x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, i \sqrt{6}\right)}{2 \sqrt{3 x^{4}+5 x^{2}-2}}"," ",0,"-1/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(-3*x^2+1)^(1/2)/(3*x^4+5*x^2-2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,I*6^(1/2))","C"
43,1,84,112,0.031000," ","int(1/(3*x^4+4*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{\sqrt{10}}{2}+1\right) x^{2}+1}\, \sqrt{-\left(1+\frac{\sqrt{10}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{4-2 \sqrt{10}}\, x}{2}, \frac{i \sqrt{6}}{3}+\frac{i \sqrt{15}}{3}\right)}{\sqrt{4-2 \sqrt{10}}\, \sqrt{3 x^{4}+4 x^{2}-2}}"," ",0,"2/(4-2*10^(1/2))^(1/2)*(-(-1/2*10^(1/2)+1)*x^2+1)^(1/2)*(-(1+1/2*10^(1/2))*x^2+1)^(1/2)/(3*x^4+4*x^2-2)^(1/2)*EllipticF(1/2*(4-2*10^(1/2))^(1/2)*x,1/3*I*6^(1/2)+1/3*I*15^(1/2))","C"
44,1,84,115,0.035000," ","int(1/(3*x^4+3*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{\sqrt{33}}{4}+\frac{3}{4}\right) x^{2}+1}\, \sqrt{-\left(\frac{\sqrt{33}}{4}+\frac{3}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3-\sqrt{33}}\, x}{2}, \frac{i \sqrt{6}}{4}+\frac{i \sqrt{22}}{4}\right)}{\sqrt{3-\sqrt{33}}\, \sqrt{3 x^{4}+3 x^{2}-2}}"," ",0,"2/(3-33^(1/2))^(1/2)*(-(-1/4*33^(1/2)+3/4)*x^2+1)^(1/2)*(-(1/4*33^(1/2)+3/4)*x^2+1)^(1/2)/(3*x^4+3*x^2-2)^(1/2)*EllipticF(1/2*(3-33^(1/2))^(1/2)*x,1/4*I*6^(1/2)+1/4*I*22^(1/2))","C"
45,1,84,112,0.035000," ","int(1/(3*x^4+2*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{\sqrt{7}}{2}+\frac{1}{2}\right) x^{2}+1}\, \sqrt{-\left(\frac{\sqrt{7}}{2}+\frac{1}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2-2 \sqrt{7}}\, x}{2}, \frac{i \sqrt{6}}{6}+\frac{i \sqrt{42}}{6}\right)}{\sqrt{2-2 \sqrt{7}}\, \sqrt{3 x^{4}+2 x^{2}-2}}"," ",0,"2/(2-2*7^(1/2))^(1/2)*(-(-1/2*7^(1/2)+1/2)*x^2+1)^(1/2)*(-(1/2*7^(1/2)+1/2)*x^2+1)^(1/2)/(3*x^4+2*x^2-2)^(1/2)*EllipticF(1/2*(2-2*7^(1/2))^(1/2)*x,1/6*I*6^(1/2)+1/6*I*42^(1/2))","C"
46,1,43,53,0.011000," ","int(1/(3*x^4+x^2-2)^(1/2),x)","-\frac{i \sqrt{x^{2}+1}\, \sqrt{-6 x^{2}+4}\, \EllipticF \left(i x , \frac{i \sqrt{6}}{2}\right)}{2 \sqrt{3 x^{4}+x^{2}-2}}"," ",0,"-1/2*I*(x^2+1)^(1/2)*(-6*x^2+4)^(1/2)/(3*x^4+x^2-2)^(1/2)*EllipticF(I*x,1/2*I*6^(1/2))","C"
47,1,56,88,0.022000," ","int(1/(3*x^4-2)^(1/2),x)","\frac{\sqrt{2 \sqrt{6}\, x^{2}+4}\, \sqrt{-2 \sqrt{6}\, x^{2}+4}\, \EllipticF \left(\frac{\sqrt{-2 \sqrt{6}}\, x}{2}, i\right)}{2 \sqrt{-2 \sqrt{6}}\, \sqrt{3 x^{4}-2}}"," ",0,"1/2/(-2*6^(1/2))^(1/2)*(2*6^(1/2)*x^2+4)^(1/2)*(-2*6^(1/2)*x^2+4)^(1/2)/(3*x^4-2)^(1/2)*EllipticF(1/2*(-2*6^(1/2))^(1/2)*x,I)","C"
48,1,53,54,0.031000," ","int(1/(3*x^4-x^2-2)^(1/2),x)","-\frac{i \sqrt{6}\, \sqrt{6 x^{2}+4}\, \sqrt{-x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{3}\right)}{6 \sqrt{3 x^{4}-x^{2}-2}}"," ",0,"-1/6*I*6^(1/2)*(6*x^2+4)^(1/2)*(-x^2+1)^(1/2)/(3*x^4-x^2-2)^(1/2)*EllipticF(1/2*I*x*6^(1/2),1/3*I*6^(1/2))","C"
49,1,84,117,0.035000," ","int(1/(3*x^4-2*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{1}{2}-\frac{\sqrt{7}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}+\frac{\sqrt{7}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2-2 \sqrt{7}}\, x}{2}, \frac{i \sqrt{42}}{6}-\frac{i \sqrt{6}}{6}\right)}{\sqrt{-2-2 \sqrt{7}}\, \sqrt{3 x^{4}-2 x^{2}-2}}"," ",0,"2/(-2-2*7^(1/2))^(1/2)*(-(-1/2-1/2*7^(1/2))*x^2+1)^(1/2)*(-(-1/2+1/2*7^(1/2))*x^2+1)^(1/2)/(3*x^4-2*x^2-2)^(1/2)*EllipticF(1/2*(-2-2*7^(1/2))^(1/2)*x,1/6*I*42^(1/2)-1/6*I*6^(1/2))","C"
50,1,84,120,0.034000," ","int(1/(3*x^4-3*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{3}{4}-\frac{\sqrt{33}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{4}+\frac{\sqrt{33}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-\sqrt{33}-3}\, x}{2}, \frac{i \sqrt{22}}{4}-\frac{i \sqrt{6}}{4}\right)}{\sqrt{-\sqrt{33}-3}\, \sqrt{3 x^{4}-3 x^{2}-2}}"," ",0,"2/(-33^(1/2)-3)^(1/2)*(-(-3/4-1/4*33^(1/2))*x^2+1)^(1/2)*(-(-3/4+1/4*33^(1/2))*x^2+1)^(1/2)/(3*x^4-3*x^2-2)^(1/2)*EllipticF(1/2*(-33^(1/2)-3)^(1/2)*x,1/4*I*22^(1/2)-1/4*I*6^(1/2))","C"
51,1,84,117,0.031000," ","int(1/(3*x^4-4*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-1-\frac{\sqrt{10}}{2}\right) x^{2}+1}\, \sqrt{-\left(-1+\frac{\sqrt{10}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-4-2 \sqrt{10}}\, x}{2}, \frac{i \sqrt{15}}{3}-\frac{i \sqrt{6}}{3}\right)}{\sqrt{-4-2 \sqrt{10}}\, \sqrt{3 x^{4}-4 x^{2}-2}}"," ",0,"2/(-4-2*10^(1/2))^(1/2)*(-(-1-1/2*10^(1/2))*x^2+1)^(1/2)*(-(-1+1/2*10^(1/2))*x^2+1)^(1/2)/(3*x^4-4*x^2-2)^(1/2)*EllipticF(1/2*(-4-2*10^(1/2))^(1/2)*x,1/3*I*15^(1/2)-1/3*I*6^(1/2))","C"
52,1,53,53,0.018000," ","int(1/(3*x^4-5*x^2-2)^(1/2),x)","-\frac{i \sqrt{3}\, \sqrt{3 x^{2}+1}\, \sqrt{-2 x^{2}+4}\, \EllipticF \left(i \sqrt{3}\, x , \frac{i \sqrt{6}}{6}\right)}{6 \sqrt{3 x^{4}-5 x^{2}-2}}"," ",0,"-1/6*I*3^(1/2)*(3*x^2+1)^(1/2)*(-2*x^2+4)^(1/2)/(3*x^4-5*x^2-2)^(1/2)*EllipticF(I*3^(1/2)*x,1/6*I*6^(1/2))","C"
53,1,84,115,0.033000," ","int(1/(2*x^4+7*x^2-3)^(1/2),x)","\frac{6 \sqrt{-\left(\frac{7}{6}-\frac{\sqrt{73}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{\sqrt{73}}{6}+\frac{7}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{42-6 \sqrt{73}}\, x}{6}, \frac{7 i \sqrt{6}}{12}+\frac{i \sqrt{438}}{12}\right)}{\sqrt{42-6 \sqrt{73}}\, \sqrt{2 x^{4}+7 x^{2}-3}}"," ",0,"6/(42-6*73^(1/2))^(1/2)*(-(7/6-1/6*73^(1/2))*x^2+1)^(1/2)*(-(1/6*73^(1/2)+7/6)*x^2+1)^(1/2)/(2*x^4+7*x^2-3)^(1/2)*EllipticF(1/6*(42-6*73^(1/2))^(1/2)*x,7/12*I*6^(1/2)+1/12*I*438^(1/2))","C"
54,1,84,118,0.032000," ","int(1/(2*x^4+6*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(1-\frac{\sqrt{15}}{3}\right) x^{2}+1}\, \sqrt{-\left(1+\frac{\sqrt{15}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{9-3 \sqrt{15}}\, x}{3}, \frac{i \sqrt{6}}{2}+\frac{i \sqrt{10}}{2}\right)}{\sqrt{9-3 \sqrt{15}}\, \sqrt{2 x^{4}+6 x^{2}-3}}"," ",0,"3/(9-3*15^(1/2))^(1/2)*(-(1-1/3*15^(1/2))*x^2+1)^(1/2)*(-(1+1/3*15^(1/2))*x^2+1)^(1/2)/(2*x^4+6*x^2-3)^(1/2)*EllipticF(1/3*(9-3*15^(1/2))^(1/2)*x,1/2*I*6^(1/2)+1/2*I*10^(1/2))","C"
55,1,53,56,0.006000," ","int(1/(2*x^4+5*x^2-3)^(1/2),x)","-\frac{i \sqrt{3}\, \sqrt{3 x^{2}+9}\, \sqrt{-2 x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{3}\, x}{3}, i \sqrt{6}\right)}{3 \sqrt{2 x^{4}+5 x^{2}-3}}"," ",0,"-1/3*I*3^(1/2)*(3*x^2+9)^(1/2)*(-2*x^2+1)^(1/2)/(2*x^4+5*x^2-3)^(1/2)*EllipticF(1/3*I*3^(1/2)*x,I*6^(1/2))","C"
56,1,84,118,0.036000," ","int(1/(2*x^4+4*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{\sqrt{10}}{3}+\frac{2}{3}\right) x^{2}+1}\, \sqrt{-\left(\frac{\sqrt{10}}{3}+\frac{2}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6-3 \sqrt{10}}\, x}{3}, \frac{i \sqrt{6}}{3}+\frac{i \sqrt{15}}{3}\right)}{\sqrt{6-3 \sqrt{10}}\, \sqrt{2 x^{4}+4 x^{2}-3}}"," ",0,"3/(6-3*10^(1/2))^(1/2)*(-(-1/3*10^(1/2)+2/3)*x^2+1)^(1/2)*(-(1/3*10^(1/2)+2/3)*x^2+1)^(1/2)/(2*x^4+4*x^2-3)^(1/2)*EllipticF(1/3*(6-3*10^(1/2))^(1/2)*x,1/3*I*6^(1/2)+1/3*I*15^(1/2))","C"
57,1,84,115,0.033000," ","int(1/(2*x^4+3*x^2-3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{\sqrt{33}}{6}+\frac{1}{2}\right) x^{2}+1}\, \sqrt{-\left(\frac{\sqrt{33}}{6}+\frac{1}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{18-6 \sqrt{33}}\, x}{6}, \frac{i \sqrt{6}}{4}+\frac{i \sqrt{22}}{4}\right)}{\sqrt{18-6 \sqrt{33}}\, \sqrt{2 x^{4}+3 x^{2}-3}}"," ",0,"6/(18-6*33^(1/2))^(1/2)*(-(-1/6*33^(1/2)+1/2)*x^2+1)^(1/2)*(-(1/6*33^(1/2)+1/2)*x^2+1)^(1/2)/(2*x^4+3*x^2-3)^(1/2)*EllipticF(1/6*(18-6*33^(1/2))^(1/2)*x,1/4*I*6^(1/2)+1/4*I*22^(1/2))","C"
58,1,84,115,0.034000," ","int(1/(2*x^4+2*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{\sqrt{7}}{3}+\frac{1}{3}\right) x^{2}+1}\, \sqrt{-\left(\frac{\sqrt{7}}{3}+\frac{1}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3-3 \sqrt{7}}\, x}{3}, \frac{i \sqrt{6}}{6}+\frac{i \sqrt{42}}{6}\right)}{\sqrt{3-3 \sqrt{7}}\, \sqrt{2 x^{4}+2 x^{2}-3}}"," ",0,"3/(3-3*7^(1/2))^(1/2)*(-(-1/3*7^(1/2)+1/3)*x^2+1)^(1/2)*(-(1/3*7^(1/2)+1/3)*x^2+1)^(1/2)/(2*x^4+2*x^2-3)^(1/2)*EllipticF(1/3*(3-3*7^(1/2))^(1/2)*x,1/6*I*6^(1/2)+1/6*I*42^(1/2))","C"
59,1,51,52,0.030000," ","int(1/(2*x^4+x^2-3)^(1/2),x)","-\frac{i \sqrt{6}\, \sqrt{6 x^{2}+9}\, \sqrt{-x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{6}\, x}{3}, \frac{i \sqrt{6}}{2}\right)}{6 \sqrt{2 x^{4}+x^{2}-3}}"," ",0,"-1/6*I*6^(1/2)*(6*x^2+9)^(1/2)*(-x^2+1)^(1/2)/(2*x^4+x^2-3)^(1/2)*EllipticF(1/3*I*x*6^(1/2),1/2*I*6^(1/2))","C"
60,1,56,88,0.020000," ","int(1/(2*x^4-3)^(1/2),x)","\frac{\sqrt{3 \sqrt{6}\, x^{2}+9}\, \sqrt{-3 \sqrt{6}\, x^{2}+9}\, \EllipticF \left(\frac{\sqrt{-3 \sqrt{6}}\, x}{3}, i\right)}{3 \sqrt{-3 \sqrt{6}}\, \sqrt{2 x^{4}-3}}"," ",0,"1/3/(-3*6^(1/2))^(1/2)*(3*6^(1/2)*x^2+9)^(1/2)*(-3*6^(1/2)*x^2+9)^(1/2)/(2*x^4-3)^(1/2)*EllipticF(1/3*(-3*6^(1/2))^(1/2)*x,I)","C"
61,1,45,55,0.010000," ","int(1/(2*x^4-x^2-3)^(1/2),x)","-\frac{i \sqrt{x^{2}+1}\, \sqrt{-6 x^{2}+9}\, \EllipticF \left(i x , \frac{i \sqrt{6}}{3}\right)}{3 \sqrt{2 x^{4}-x^{2}-3}}"," ",0,"-1/3*I*(x^2+1)^(1/2)*(-6*x^2+9)^(1/2)/(2*x^4-x^2-3)^(1/2)*EllipticF(I*x,1/3*I*6^(1/2))","C"
62,1,84,120,0.032000," ","int(1/(2*x^4-2*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{1}{3}-\frac{\sqrt{7}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{3}+\frac{\sqrt{7}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-3-3 \sqrt{7}}\, x}{3}, \frac{i \sqrt{42}}{6}-\frac{i \sqrt{6}}{6}\right)}{\sqrt{-3-3 \sqrt{7}}\, \sqrt{2 x^{4}-2 x^{2}-3}}"," ",0,"3/(-3-3*7^(1/2))^(1/2)*(-(-1/3-1/3*7^(1/2))*x^2+1)^(1/2)*(-(-1/3+1/3*7^(1/2))*x^2+1)^(1/2)/(2*x^4-2*x^2-3)^(1/2)*EllipticF(1/3*(-3-3*7^(1/2))^(1/2)*x,1/6*I*42^(1/2)-1/6*I*6^(1/2))","C"
63,1,84,120,0.032000," ","int(1/(2*x^4-3*x^2-3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{1}{2}-\frac{\sqrt{33}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}+\frac{\sqrt{33}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-18-6 \sqrt{33}}\, x}{6}, \frac{i \sqrt{22}}{4}-\frac{i \sqrt{6}}{4}\right)}{\sqrt{-18-6 \sqrt{33}}\, \sqrt{2 x^{4}-3 x^{2}-3}}"," ",0,"6/(-18-6*33^(1/2))^(1/2)*(-(-1/2-1/6*33^(1/2))*x^2+1)^(1/2)*(-(-1/2+1/6*33^(1/2))*x^2+1)^(1/2)/(2*x^4-3*x^2-3)^(1/2)*EllipticF(1/6*(-18-6*33^(1/2))^(1/2)*x,1/4*I*22^(1/2)-1/4*I*6^(1/2))","C"
64,1,84,123,0.033000," ","int(1/(2*x^4-4*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{2}{3}-\frac{\sqrt{10}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{2}{3}+\frac{\sqrt{10}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6-3 \sqrt{10}}\, x}{3}, \frac{i \sqrt{15}}{3}-\frac{i \sqrt{6}}{3}\right)}{\sqrt{-6-3 \sqrt{10}}\, \sqrt{2 x^{4}-4 x^{2}-3}}"," ",0,"3/(-6-3*10^(1/2))^(1/2)*(-(-2/3-1/3*10^(1/2))*x^2+1)^(1/2)*(-(-2/3+1/3*10^(1/2))*x^2+1)^(1/2)/(2*x^4-4*x^2-3)^(1/2)*EllipticF(1/3*(-6-3*10^(1/2))^(1/2)*x,1/3*I*15^(1/2)-1/3*I*6^(1/2))","C"
65,1,53,53,0.018000," ","int(1/(2*x^4-5*x^2-3)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+1}\, \sqrt{-3 x^{2}+9}\, \EllipticF \left(i \sqrt{2}\, x , \frac{i \sqrt{6}}{6}\right)}{6 \sqrt{2 x^{4}-5 x^{2}-3}}"," ",0,"-1/6*I*2^(1/2)*(2*x^2+1)^(1/2)*(-3*x^2+9)^(1/2)/(2*x^4-5*x^2-3)^(1/2)*EllipticF(I*2^(1/2)*x,1/6*I*6^(1/2))","C"
66,1,44,68,0.017000," ","int(1/(3*x^4+5*x^2+2)^(1/2),x)","-\frac{i \sqrt{x^{2}+1}\, \sqrt{6 x^{2}+4}\, \EllipticF \left(i x , \frac{\sqrt{6}}{2}\right)}{2 \sqrt{3 x^{4}+5 x^{2}+2}}"," ",0,"-1/2*I*(x^2+1)^(1/2)*(6*x^2+4)^(1/2)/(3*x^4+5*x^2+2)^(1/2)*EllipticF(I*x,1/2*6^(1/2))","A"
67,1,87,111,0.158000," ","int(1/(3*x^4+4*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-1+\frac{i \sqrt{2}}{2}\right) x^{2}+1}\, \sqrt{-\left(-1-\frac{i \sqrt{2}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-4+2 i \sqrt{2}}\, x}{2}, \frac{\sqrt{3+6 i \sqrt{2}}}{3}\right)}{\sqrt{-4+2 i \sqrt{2}}\, \sqrt{3 x^{4}+4 x^{2}+2}}"," ",0,"2/(-4+2*I*2^(1/2))^(1/2)*(1-(-1+1/2*I*2^(1/2))*x^2)^(1/2)*(1-(-1-1/2*I*2^(1/2))*x^2)^(1/2)/(3*x^4+4*x^2+2)^(1/2)*EllipticF(1/2*x*(-4+2*I*2^(1/2))^(1/2),1/3*(3+6*I*2^(1/2))^(1/2))","C"
68,1,87,111,0.131000," ","int(1/(3*x^4+3*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{3}{4}+\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{4}-\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-3+i \sqrt{15}}\, x}{2}, \frac{\sqrt{-1+i \sqrt{15}}}{2}\right)}{\sqrt{-3+i \sqrt{15}}\, \sqrt{3 x^{4}+3 x^{2}+2}}"," ",0,"2/(-3+I*15^(1/2))^(1/2)*(1-(-3/4+1/4*I*15^(1/2))*x^2)^(1/2)*(1-(-3/4-1/4*I*15^(1/2))*x^2)^(1/2)/(3*x^4+3*x^2+2)^(1/2)*EllipticF(1/2*x*(-3+I*15^(1/2))^(1/2),1/2*(-1+I*15^(1/2))^(1/2))","C"
69,1,87,111,0.135000," ","int(1/(3*x^4+2*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{5}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{5}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2+2 i \sqrt{5}}\, x}{2}, \frac{\sqrt{-6+3 i \sqrt{5}}}{3}\right)}{\sqrt{-2+2 i \sqrt{5}}\, \sqrt{3 x^{4}+2 x^{2}+2}}"," ",0,"2/(-2+2*I*5^(1/2))^(1/2)*(1-(-1/2+1/2*I*5^(1/2))*x^2)^(1/2)*(1-(-1/2-1/2*I*5^(1/2))*x^2)^(1/2)/(3*x^4+2*x^2+2)^(1/2)*EllipticF(1/2*x*(-2+2*I*5^(1/2))^(1/2),1/3*(-6+3*I*5^(1/2))^(1/2))","C"
70,1,85,107,0.133000," ","int(1/(3*x^4+x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{1}{4}+\frac{i \sqrt{23}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{4}-\frac{i \sqrt{23}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-1+i \sqrt{23}}\, x}{2}, \frac{\sqrt{-33+3 i \sqrt{23}}}{6}\right)}{\sqrt{-1+i \sqrt{23}}\, \sqrt{3 x^{4}+x^{2}+2}}"," ",0,"2/(-1+I*23^(1/2))^(1/2)*(1-(-1/4+1/4*I*23^(1/2))*x^2)^(1/2)*(1-(-1/4-1/4*I*23^(1/2))*x^2)^(1/2)/(3*x^4+x^2+2)^(1/2)*EllipticF(1/2*x*(-1+I*23^(1/2))^(1/2),1/6*(-33+3*I*23^(1/2))^(1/2))","C"
71,1,66,95,0.056000," ","int(1/(3*x^4+2)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-2 i \sqrt{6}\, x^{2}+4}\, \sqrt{2 i \sqrt{6}\, x^{2}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{i \sqrt{6}}\, x}{2}, i\right)}{4 \sqrt{i \sqrt{6}}\, \sqrt{3 x^{4}+2}}"," ",0,"1/4*2^(1/2)/(I*6^(1/2))^(1/2)*(4-2*I*6^(1/2)*x^2)^(1/2)*(4+2*I*6^(1/2)*x^2)^(1/2)/(3*x^4+2)^(1/2)*EllipticF(1/2*x*2^(1/2)*(I*6^(1/2))^(1/2),I)","C"
72,1,87,111,0.115000," ","int(1/(3*x^4-x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{1}{4}+\frac{i \sqrt{23}}{4}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{4}-\frac{i \sqrt{23}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{i \sqrt{23}+1}\, x}{2}, \frac{\sqrt{-33-3 i \sqrt{23}}}{6}\right)}{\sqrt{i \sqrt{23}+1}\, \sqrt{3 x^{4}-x^{2}+2}}"," ",0,"2/(I*23^(1/2)+1)^(1/2)*(1-(1/4+1/4*I*23^(1/2))*x^2)^(1/2)*(1-(1/4-1/4*I*23^(1/2))*x^2)^(1/2)/(3*x^4-x^2+2)^(1/2)*EllipticF(1/2*x*(I*23^(1/2)+1)^(1/2),1/6*(-33-3*I*23^(1/2))^(1/2))","C"
73,1,87,111,0.118000," ","int(1/(3*x^4-2*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{1}{2}+\frac{i \sqrt{5}}{2}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{2}-\frac{i \sqrt{5}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2+2 i \sqrt{5}}\, x}{2}, \frac{\sqrt{-6-3 i \sqrt{5}}}{3}\right)}{\sqrt{2+2 i \sqrt{5}}\, \sqrt{3 x^{4}-2 x^{2}+2}}"," ",0,"2/(2+2*I*5^(1/2))^(1/2)*(1-(1/2+1/2*I*5^(1/2))*x^2)^(1/2)*(1-(1/2-1/2*I*5^(1/2))*x^2)^(1/2)/(3*x^4-2*x^2+2)^(1/2)*EllipticF(1/2*x*(2+2*I*5^(1/2))^(1/2),1/3*(-6-3*I*5^(1/2))^(1/2))","C"
74,1,87,111,0.116000," ","int(1/(3*x^4-3*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{3}{4}+\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \sqrt{-\left(\frac{3}{4}-\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{i \sqrt{15}+3}\, x}{2}, \frac{\sqrt{-1-i \sqrt{15}}}{2}\right)}{\sqrt{i \sqrt{15}+3}\, \sqrt{3 x^{4}-3 x^{2}+2}}"," ",0,"2/(I*15^(1/2)+3)^(1/2)*(1-(3/4+1/4*I*15^(1/2))*x^2)^(1/2)*(1-(3/4-1/4*I*15^(1/2))*x^2)^(1/2)/(3*x^4-3*x^2+2)^(1/2)*EllipticF(1/2*x*(I*15^(1/2)+3)^(1/2),1/2*(-1-I*15^(1/2))^(1/2))","C"
75,1,87,111,0.117000," ","int(1/(3*x^4-4*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(1+\frac{i \sqrt{2}}{2}\right) x^{2}+1}\, \sqrt{-\left(1-\frac{i \sqrt{2}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{4+2 i \sqrt{2}}\, x}{2}, \frac{\sqrt{3-6 i \sqrt{2}}}{3}\right)}{\sqrt{4+2 i \sqrt{2}}\, \sqrt{3 x^{4}-4 x^{2}+2}}"," ",0,"2/(4+2*I*2^(1/2))^(1/2)*(1-(1+1/2*I*2^(1/2))*x^2)^(1/2)*(1-(1-1/2*I*2^(1/2))*x^2)^(1/2)/(3*x^4-4*x^2+2)^(1/2)*EllipticF(1/2*x*(4+2*I*2^(1/2))^(1/2),1/3*(3-6*I*2^(1/2))^(1/2))","C"
76,1,42,111,0.010000," ","int(1/(3*x^4-5*x^2+2)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{-6 x^{2}+4}\, \EllipticF \left(x , \frac{\sqrt{6}}{2}\right)}{2 \sqrt{3 x^{4}-5 x^{2}+2}}"," ",0,"1/2*(-x^2+1)^(1/2)*(-6*x^2+4)^(1/2)/(3*x^4-5*x^2+2)^(1/2)*EllipticF(x,1/2*6^(1/2))","A"
77,1,82,109,0.085000," ","int(1/(3*x^4-6*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{\sqrt{3}}{2}+\frac{3}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{\sqrt{3}}{2}+\frac{3}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6+2 \sqrt{3}}\, x}{2}, \frac{\sqrt{6}}{2}-\frac{\sqrt{2}}{2}\right)}{\sqrt{6+2 \sqrt{3}}\, \sqrt{3 x^{4}-6 x^{2}+2}}"," ",0,"2/(6+2*3^(1/2))^(1/2)*(1-(1/2*3^(1/2)+3/2)*x^2)^(1/2)*(1-(-1/2*3^(1/2)+3/2)*x^2)^(1/2)/(3*x^4-6*x^2+2)^(1/2)*EllipticF(1/2*x*(6+2*3^(1/2))^(1/2),1/2*6^(1/2)-1/2*2^(1/2))","A"
78,1,82,134,0.097000," ","int(1/(2*x^4+9*x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{3}{2}+\frac{\sqrt{57}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{2}-\frac{\sqrt{57}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-54+6 \sqrt{57}}\, x}{6}, \frac{3 \sqrt{6}}{4}+\frac{\sqrt{38}}{4}\right)}{\sqrt{-54+6 \sqrt{57}}\, \sqrt{2 x^{4}+9 x^{2}+3}}"," ",0,"6/(-54+6*57^(1/2))^(1/2)*(1-(-3/2+1/6*57^(1/2))*x^2)^(1/2)*(1-(-3/2-1/6*57^(1/2))*x^2)^(1/2)/(2*x^4+9*x^2+3)^(1/2)*EllipticF(1/6*x*(-54+6*57^(1/2))^(1/2),3/4*6^(1/2)+1/4*38^(1/2))","A"
79,1,82,134,0.091000," ","int(1/(2*x^4+8*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{4}{3}+\frac{\sqrt{10}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{4}{3}-\frac{\sqrt{10}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-12+3 \sqrt{10}}\, x}{3}, \frac{2 \sqrt{6}}{3}+\frac{\sqrt{15}}{3}\right)}{\sqrt{-12+3 \sqrt{10}}\, \sqrt{2 x^{4}+8 x^{2}+3}}"," ",0,"3/(-12+3*10^(1/2))^(1/2)*(1-(-4/3+1/3*10^(1/2))*x^2)^(1/2)*(1-(-4/3-1/3*10^(1/2))*x^2)^(1/2)/(2*x^4+8*x^2+3)^(1/2)*EllipticF(1/3*x*(-12+3*10^(1/2))^(1/2),2/3*6^(1/2)+1/3*15^(1/2))","A"
80,1,50,76,0.016000," ","int(1/(2*x^4+7*x^2+3)^(1/2),x)","-\frac{i \sqrt{3}\, \sqrt{3 x^{2}+9}\, \sqrt{2 x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{3}\, x}{3}, \sqrt{6}\right)}{3 \sqrt{2 x^{4}+7 x^{2}+3}}"," ",0,"-1/3*I*3^(1/2)*(3*x^2+9)^(1/2)*(2*x^2+1)^(1/2)/(2*x^4+7*x^2+3)^(1/2)*EllipticF(1/3*I*3^(1/2)*x,6^(1/2))","C"
81,1,82,130,0.084000," ","int(1/(2*x^4+6*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(-1+\frac{\sqrt{3}}{3}\right) x^{2}+1}\, \sqrt{-\left(-1-\frac{\sqrt{3}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-9+3 \sqrt{3}}\, x}{3}, \frac{\sqrt{6}}{2}+\frac{\sqrt{2}}{2}\right)}{\sqrt{-9+3 \sqrt{3}}\, \sqrt{2 x^{4}+6 x^{2}+3}}"," ",0,"3/(-9+3*3^(1/2))^(1/2)*(1-(-1+1/3*3^(1/2))*x^2)^(1/2)*(1-(-1-1/3*3^(1/2))*x^2)^(1/2)/(2*x^4+6*x^2+3)^(1/2)*EllipticF(1/3*x*(-9+3*3^(1/2))^(1/2),1/2*6^(1/2)+1/2*2^(1/2))","A"
82,1,50,67,0.015000," ","int(1/(2*x^4+5*x^2+3)^(1/2),x)","-\frac{i \sqrt{6}\, \sqrt{6 x^{2}+9}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{6}\, x}{3}, \frac{\sqrt{6}}{2}\right)}{6 \sqrt{2 x^{4}+5 x^{2}+3}}"," ",0,"-1/6*I*6^(1/2)*(6*x^2+9)^(1/2)*(x^2+1)^(1/2)/(2*x^4+5*x^2+3)^(1/2)*EllipticF(1/3*I*6^(1/2)*x,1/2*6^(1/2))","C"
83,1,87,111,0.105000," ","int(1/(2*x^4+4*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{2}{3}+\frac{i \sqrt{2}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{2}{3}-\frac{i \sqrt{2}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+3 i \sqrt{2}}\, x}{3}, \frac{\sqrt{3+6 i \sqrt{2}}}{3}\right)}{\sqrt{-6+3 i \sqrt{2}}\, \sqrt{2 x^{4}+4 x^{2}+3}}"," ",0,"3/(-6+3*I*2^(1/2))^(1/2)*(1-(-2/3+1/3*I*2^(1/2))*x^2)^(1/2)*(1-(-2/3-1/3*I*2^(1/2))*x^2)^(1/2)/(2*x^4+4*x^2+3)^(1/2)*EllipticF(1/3*x*(-6+3*I*2^(1/2))^(1/2),1/3*(3+6*I*2^(1/2))^(1/2))","C"
84,1,87,111,0.104000," ","int(1/(2*x^4+3*x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{15}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{15}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-18+6 i \sqrt{15}}\, x}{6}, \frac{\sqrt{-1+i \sqrt{15}}}{2}\right)}{\sqrt{-18+6 i \sqrt{15}}\, \sqrt{2 x^{4}+3 x^{2}+3}}"," ",0,"6/(-18+6*I*15^(1/2))^(1/2)*(1-(-1/2+1/6*I*15^(1/2))*x^2)^(1/2)*(1-(-1/2-1/6*I*15^(1/2))*x^2)^(1/2)/(2*x^4+3*x^2+3)^(1/2)*EllipticF(1/6*x*(-18+6*I*15^(1/2))^(1/2),1/2*(-1+I*15^(1/2))^(1/2))","C"
85,1,87,111,0.102000," ","int(1/(2*x^4+2*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{1}{3}+\frac{i \sqrt{5}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{3}-\frac{i \sqrt{5}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-3+3 i \sqrt{5}}\, x}{3}, \frac{\sqrt{-6+3 i \sqrt{5}}}{3}\right)}{\sqrt{-3+3 i \sqrt{5}}\, \sqrt{2 x^{4}+2 x^{2}+3}}"," ",0,"3/(-3+3*I*5^(1/2))^(1/2)*(1-(-1/3+1/3*I*5^(1/2))*x^2)^(1/2)*(1-(-1/3-1/3*I*5^(1/2))*x^2)^(1/2)/(2*x^4+2*x^2+3)^(1/2)*EllipticF(1/3*x*(-3+3*I*5^(1/2))^(1/2),1/3*(-6+3*I*5^(1/2))^(1/2))","C"
86,1,85,107,0.106000," ","int(1/(2*x^4+x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{1}{6}+\frac{i \sqrt{23}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{6}-\frac{i \sqrt{23}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6+6 i \sqrt{23}}\, x}{6}, \frac{\sqrt{-33+3 i \sqrt{23}}}{6}\right)}{\sqrt{-6+6 i \sqrt{23}}\, \sqrt{2 x^{4}+x^{2}+3}}"," ",0,"6/(-6+6*I*23^(1/2))^(1/2)*(1-(-1/6+1/6*I*23^(1/2))*x^2)^(1/2)*(1-(-1/6-1/6*I*23^(1/2))*x^2)^(1/2)/(2*x^4+x^2+3)^(1/2)*EllipticF(1/6*x*(-6+6*I*23^(1/2))^(1/2),1/6*(-33+3*I*23^(1/2))^(1/2))","C"
87,1,66,95,0.048000," ","int(1/(2*x^4+3)^(1/2),x)","\frac{\sqrt{3}\, \sqrt{-3 i \sqrt{6}\, x^{2}+9}\, \sqrt{3 i \sqrt{6}\, x^{2}+9}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \sqrt{6}}\, x}{3}, i\right)}{9 \sqrt{i \sqrt{6}}\, \sqrt{2 x^{4}+3}}"," ",0,"1/9*3^(1/2)/(I*6^(1/2))^(1/2)*(9-3*I*6^(1/2)*x^2)^(1/2)*(9+3*I*6^(1/2)*x^2)^(1/2)/(2*x^4+3)^(1/2)*EllipticF(1/3*x*3^(1/2)*(I*6^(1/2))^(1/2),I)","C"
88,1,87,111,0.102000," ","int(1/(2*x^4-x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(\frac{1}{6}+\frac{i \sqrt{23}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{6}-\frac{i \sqrt{23}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6+6 i \sqrt{23}}\, x}{6}, \frac{\sqrt{-33-3 i \sqrt{23}}}{6}\right)}{\sqrt{6+6 i \sqrt{23}}\, \sqrt{2 x^{4}-x^{2}+3}}"," ",0,"6/(6+6*I*23^(1/2))^(1/2)*(1-(1/6+1/6*I*23^(1/2))*x^2)^(1/2)*(1-(1/6-1/6*I*23^(1/2))*x^2)^(1/2)/(2*x^4-x^2+3)^(1/2)*EllipticF(1/6*x*(6+6*I*23^(1/2))^(1/2),1/6*(-33-3*I*23^(1/2))^(1/2))","C"
89,1,87,111,0.100000," ","int(1/(2*x^4-2*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(\frac{1}{3}+\frac{i \sqrt{5}}{3}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{3}-\frac{i \sqrt{5}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3+3 i \sqrt{5}}\, x}{3}, \frac{\sqrt{-6-3 i \sqrt{5}}}{3}\right)}{\sqrt{3+3 i \sqrt{5}}\, \sqrt{2 x^{4}-2 x^{2}+3}}"," ",0,"3/(3+3*I*5^(1/2))^(1/2)*(1-(1/3+1/3*I*5^(1/2))*x^2)^(1/2)*(1-(1/3-1/3*I*5^(1/2))*x^2)^(1/2)/(2*x^4-2*x^2+3)^(1/2)*EllipticF(1/3*x*(3+3*I*5^(1/2))^(1/2),1/3*(-6-3*I*5^(1/2))^(1/2))","C"
90,1,87,111,0.103000," ","int(1/(2*x^4-3*x^2+3)^(1/2),x)","\frac{6 \sqrt{-\left(\frac{1}{2}+\frac{i \sqrt{15}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{2}-\frac{i \sqrt{15}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{18+6 i \sqrt{15}}\, x}{6}, \frac{\sqrt{-1-i \sqrt{15}}}{2}\right)}{\sqrt{18+6 i \sqrt{15}}\, \sqrt{2 x^{4}-3 x^{2}+3}}"," ",0,"6/(18+6*I*15^(1/2))^(1/2)*(1-(1/2+1/6*I*15^(1/2))*x^2)^(1/2)*(1-(1/2-1/6*I*15^(1/2))*x^2)^(1/2)/(2*x^4-3*x^2+3)^(1/2)*EllipticF(1/6*x*(18+6*I*15^(1/2))^(1/2),1/2*(-1-I*15^(1/2))^(1/2))","C"
91,1,87,111,0.100000," ","int(1/(2*x^4-4*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(\frac{2}{3}+\frac{i \sqrt{2}}{3}\right) x^{2}+1}\, \sqrt{-\left(\frac{2}{3}-\frac{i \sqrt{2}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6+3 i \sqrt{2}}\, x}{3}, \frac{\sqrt{3-6 i \sqrt{2}}}{3}\right)}{\sqrt{6+3 i \sqrt{2}}\, \sqrt{2 x^{4}-4 x^{2}+3}}"," ",0,"3/(6+3*I*2^(1/2))^(1/2)*(1-(2/3+1/3*I*2^(1/2))*x^2)^(1/2)*(1-(2/3-1/3*I*2^(1/2))*x^2)^(1/2)/(2*x^4-4*x^2+3)^(1/2)*EllipticF(1/3*x*(6+3*I*2^(1/2))^(1/2),1/3*(3-6*I*2^(1/2))^(1/2))","C"
92,1,42,111,0.013000," ","int(1/(2*x^4-5*x^2+3)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{-6 x^{2}+9}\, \EllipticF \left(x , \frac{\sqrt{6}}{3}\right)}{3 \sqrt{2 x^{4}-5 x^{2}+3}}"," ",0,"1/3*(-x^2+1)^(1/2)*(-6*x^2+9)^(1/2)/(2*x^4-5*x^2+3)^(1/2)*EllipticF(x,1/3*6^(1/2))","A"
93,1,82,109,0.067000," ","int(1/(2*x^4-6*x^2+3)^(1/2),x)","\frac{3 \sqrt{-\left(1+\frac{\sqrt{3}}{3}\right) x^{2}+1}\, \sqrt{-\left(1-\frac{\sqrt{3}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{9+3 \sqrt{3}}\, x}{3}, \frac{\sqrt{6}}{2}-\frac{\sqrt{2}}{2}\right)}{\sqrt{9+3 \sqrt{3}}\, \sqrt{2 x^{4}-6 x^{2}+3}}"," ",0,"3/(9+3*3^(1/2))^(1/2)*(1-(1+1/3*3^(1/2))*x^2)^(1/2)*(1-(1-1/3*3^(1/2))*x^2)^(1/2)/(2*x^4-6*x^2+3)^(1/2)*EllipticF(1/3*x*(9+3*3^(1/2))^(1/2),1/2*6^(1/2)-1/2*2^(1/2))","A"
94,1,49,111,0.011000," ","int(1/(2*x^4-7*x^2+3)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-2 x^{2}+1}\, \sqrt{-3 x^{2}+9}\, \EllipticF \left(\sqrt{2}\, x , \frac{\sqrt{6}}{6}\right)}{6 \sqrt{2 x^{4}-7 x^{2}+3}}"," ",0,"1/6*2^(1/2)*(-2*x^2+1)^(1/2)*(-3*x^2+9)^(1/2)/(2*x^4-7*x^2+3)^(1/2)*EllipticF(2^(1/2)*x,1/6*6^(1/2))","A"
95,1,48,30,0.010000," ","int(1/(-2*x^4+7*x^2-3)^(1/2),x)","\frac{\sqrt{3}\, \sqrt{-3 x^{2}+9}\, \sqrt{-2 x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3}\, x}{3}, \sqrt{6}\right)}{3 \sqrt{-2 x^{4}+7 x^{2}-3}}"," ",0,"1/3*3^(1/2)*(-3*x^2+9)^(1/2)*(-2*x^2+1)^(1/2)/(-2*x^4+7*x^2-3)^(1/2)*EllipticF(1/3*3^(1/2)*x,6^(1/2))","A"
96,1,82,63,0.024000," ","int(1/(-2*x^4+6*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(1-\frac{\sqrt{3}}{3}\right) x^{2}+1}\, \sqrt{-\left(1+\frac{\sqrt{3}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{9-3 \sqrt{3}}\, x}{3}, \frac{\sqrt{6}}{2}+\frac{\sqrt{2}}{2}\right)}{\sqrt{9-3 \sqrt{3}}\, \sqrt{-2 x^{4}+6 x^{2}-3}}"," ",0,"3/(9-3*3^(1/2))^(1/2)*(-(1-1/3*3^(1/2))*x^2+1)^(1/2)*(-(1+1/3*3^(1/2))*x^2+1)^(1/2)/(-2*x^4+6*x^2-3)^(1/2)*EllipticF(1/3*x*(9-3*3^(1/2))^(1/2),1/2*6^(1/2)+1/2*2^(1/2))","A"
97,1,50,25,0.012000," ","int(1/(-2*x^4+5*x^2-3)^(1/2),x)","\frac{\sqrt{6}\, \sqrt{-6 x^{2}+9}\, \sqrt{-x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6}\, x}{3}, \frac{\sqrt{6}}{2}\right)}{6 \sqrt{-2 x^{4}+5 x^{2}-3}}"," ",0,"1/6*6^(1/2)*(-6*x^2+9)^(1/2)*(-x^2+1)^(1/2)/(-2*x^4+5*x^2-3)^(1/2)*EllipticF(1/3*6^(1/2)*x,1/2*6^(1/2))","A"
98,1,87,111,0.053000," ","int(1/(-2*x^4+4*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(\frac{2}{3}-\frac{i \sqrt{2}}{3}\right) x^{2}+1}\, \sqrt{-\left(\frac{2}{3}+\frac{i \sqrt{2}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6-3 i \sqrt{2}}\, x}{3}, \frac{\sqrt{3+6 i \sqrt{2}}}{3}\right)}{\sqrt{6-3 i \sqrt{2}}\, \sqrt{-2 x^{4}+4 x^{2}-3}}"," ",0,"3/(6-3*I*2^(1/2))^(1/2)*(-(2/3-1/3*I*2^(1/2))*x^2+1)^(1/2)*(-(2/3+1/3*I*2^(1/2))*x^2+1)^(1/2)/(-2*x^4+4*x^2-3)^(1/2)*EllipticF(1/3*(6-3*I*2^(1/2))^(1/2)*x,1/3*(3+6*I*2^(1/2))^(1/2))","C"
99,1,87,111,0.058000," ","int(1/(-2*x^4+3*x^2-3)^(1/2),x)","\frac{6 \sqrt{-\left(\frac{1}{2}-\frac{i \sqrt{15}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{2}+\frac{i \sqrt{15}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{18-6 i \sqrt{15}}\, x}{6}, \frac{\sqrt{-1+i \sqrt{15}}}{2}\right)}{\sqrt{18-6 i \sqrt{15}}\, \sqrt{-2 x^{4}+3 x^{2}-3}}"," ",0,"6/(18-6*I*15^(1/2))^(1/2)*(-(1/2-1/6*I*15^(1/2))*x^2+1)^(1/2)*(-(1/2+1/6*I*15^(1/2))*x^2+1)^(1/2)/(-2*x^4+3*x^2-3)^(1/2)*EllipticF(1/6*(18-6*I*15^(1/2))^(1/2)*x,1/2*(-1+I*15^(1/2))^(1/2))","C"
100,1,87,111,0.068000," ","int(1/(-2*x^4+2*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(\frac{1}{3}-\frac{i \sqrt{5}}{3}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{3}+\frac{i \sqrt{5}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3-3 i \sqrt{5}}\, x}{3}, \frac{\sqrt{-6+3 i \sqrt{5}}}{3}\right)}{\sqrt{3-3 i \sqrt{5}}\, \sqrt{-2 x^{4}+2 x^{2}-3}}"," ",0,"3/(3-3*I*5^(1/2))^(1/2)*(-(1/3-1/3*I*5^(1/2))*x^2+1)^(1/2)*(-(1/3+1/3*I*5^(1/2))*x^2+1)^(1/2)/(-2*x^4+2*x^2-3)^(1/2)*EllipticF(1/3*(3-3*I*5^(1/2))^(1/2)*x,1/3*(-6+3*I*5^(1/2))^(1/2))","C"
101,1,85,109,0.049000," ","int(1/(-2*x^4+x^2-3)^(1/2),x)","\frac{6 \sqrt{-\left(\frac{1}{6}-\frac{i \sqrt{23}}{6}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{6}+\frac{i \sqrt{23}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6-6 i \sqrt{23}}\, x}{6}, \frac{\sqrt{-33+3 i \sqrt{23}}}{6}\right)}{\sqrt{6-6 i \sqrt{23}}\, \sqrt{-2 x^{4}+x^{2}-3}}"," ",0,"6/(6-6*I*23^(1/2))^(1/2)*(-(1/6-1/6*I*23^(1/2))*x^2+1)^(1/2)*(-(1/6+1/6*I*23^(1/2))*x^2+1)^(1/2)/(-2*x^4+x^2-3)^(1/2)*EllipticF(1/6*(6-6*I*23^(1/2))^(1/2)*x,1/6*(-33+3*I*23^(1/2))^(1/2))","C"
102,1,66,95,0.022000," ","int(1/(-2*x^4-3)^(1/2),x)","\frac{\sqrt{3}\, \sqrt{3 i \sqrt{6}\, x^{2}+9}\, \sqrt{-3 i \sqrt{6}\, x^{2}+9}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-i \sqrt{6}}\, x}{3}, i\right)}{9 \sqrt{-i \sqrt{6}}\, \sqrt{-2 x^{4}-3}}"," ",0,"1/9*3^(1/2)/(-I*6^(1/2))^(1/2)*(3*I*6^(1/2)*x^2+9)^(1/2)*(-3*I*6^(1/2)*x^2+9)^(1/2)/(-2*x^4-3)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*6^(1/2))^(1/2)*x,I)","C"
103,1,87,109,0.047000," ","int(1/(-2*x^4-x^2-3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{1}{6}-\frac{i \sqrt{23}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{6}+\frac{i \sqrt{23}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6-6 i \sqrt{23}}\, x}{6}, \frac{\sqrt{-33-3 i \sqrt{23}}}{6}\right)}{\sqrt{-6-6 i \sqrt{23}}\, \sqrt{-2 x^{4}-x^{2}-3}}"," ",0,"6/(-6-6*I*23^(1/2))^(1/2)*(-(-1/6-1/6*I*23^(1/2))*x^2+1)^(1/2)*(-(-1/6+1/6*I*23^(1/2))*x^2+1)^(1/2)/(-2*x^4-x^2-3)^(1/2)*EllipticF(1/6*(-6-6*I*23^(1/2))^(1/2)*x,1/6*(-33-3*I*23^(1/2))^(1/2))","C"
104,1,87,111,0.048000," ","int(1/(-2*x^4-2*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{1}{3}-\frac{i \sqrt{5}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{3}+\frac{i \sqrt{5}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-3-3 i \sqrt{5}}\, x}{3}, \frac{\sqrt{-6-3 i \sqrt{5}}}{3}\right)}{\sqrt{-3-3 i \sqrt{5}}\, \sqrt{-2 x^{4}-2 x^{2}-3}}"," ",0,"3/(-3-3*I*5^(1/2))^(1/2)*(-(-1/3-1/3*I*5^(1/2))*x^2+1)^(1/2)*(-(-1/3+1/3*I*5^(1/2))*x^2+1)^(1/2)/(-2*x^4-2*x^2-3)^(1/2)*EllipticF(1/3*(-3-3*I*5^(1/2))^(1/2)*x,1/3*(-6-3*I*5^(1/2))^(1/2))","C"
105,1,87,111,0.049000," ","int(1/(-2*x^4-3*x^2-3)^(1/2),x)","\frac{6 \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{15}}{6}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{15}}{6}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-18-6 i \sqrt{15}}\, x}{6}, \frac{\sqrt{-1-i \sqrt{15}}}{2}\right)}{\sqrt{-18-6 i \sqrt{15}}\, \sqrt{-2 x^{4}-3 x^{2}-3}}"," ",0,"6/(-18-6*I*15^(1/2))^(1/2)*(-(-1/2-1/6*I*15^(1/2))*x^2+1)^(1/2)*(-(-1/2+1/6*I*15^(1/2))*x^2+1)^(1/2)/(-2*x^4-3*x^2-3)^(1/2)*EllipticF(1/6*(-18-6*I*15^(1/2))^(1/2)*x,1/2*(-1-I*15^(1/2))^(1/2))","C"
106,1,87,111,0.048000," ","int(1/(-2*x^4-4*x^2-3)^(1/2),x)","\frac{3 \sqrt{-\left(-\frac{2}{3}-\frac{i \sqrt{2}}{3}\right) x^{2}+1}\, \sqrt{-\left(-\frac{2}{3}+\frac{i \sqrt{2}}{3}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-6-3 i \sqrt{2}}\, x}{3}, \frac{\sqrt{3-6 i \sqrt{2}}}{3}\right)}{\sqrt{-6-3 i \sqrt{2}}\, \sqrt{-2 x^{4}-4 x^{2}-3}}"," ",0,"3/(-6-3*I*2^(1/2))^(1/2)*(-(-2/3-1/3*I*2^(1/2))*x^2+1)^(1/2)*(-(-2/3+1/3*I*2^(1/2))*x^2+1)^(1/2)/(-2*x^4-4*x^2-3)^(1/2)*EllipticF(1/3*(-6-3*I*2^(1/2))^(1/2)*x,1/3*(3-6*I*2^(1/2))^(1/2))","C"
107,1,44,71,0.013000," ","int(1/(-2*x^4-5*x^2-3)^(1/2),x)","-\frac{i \sqrt{x^{2}+1}\, \sqrt{6 x^{2}+9}\, \EllipticF \left(i x , \frac{\sqrt{6}}{3}\right)}{3 \sqrt{-2 x^{4}-5 x^{2}-3}}"," ",0,"-1/3*I*(x^2+1)^(1/2)*(6*x^2+9)^(1/2)/(-2*x^4-5*x^2-3)^(1/2)*EllipticF(I*x,1/3*6^(1/2))","C"
108,1,82,59,0.025000," ","int(1/(-3*x^4+6*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{\sqrt{3}}{2}+\frac{3}{2}\right) x^{2}+1}\, \sqrt{-\left(\frac{\sqrt{3}}{2}+\frac{3}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{6-2 \sqrt{3}}\, x}{2}, \frac{\sqrt{6}}{2}+\frac{\sqrt{2}}{2}\right)}{\sqrt{6-2 \sqrt{3}}\, \sqrt{-3 x^{4}+6 x^{2}-2}}"," ",0,"2/(6-2*3^(1/2))^(1/2)*(-(-1/2*3^(1/2)+3/2)*x^2+1)^(1/2)*(-(1/2*3^(1/2)+3/2)*x^2+1)^(1/2)/(-3*x^4+6*x^2-2)^(1/2)*EllipticF(1/2*(6-2*3^(1/2))^(1/2)*x,1/2*6^(1/2)+1/2*2^(1/2))","A"
109,1,42,23,0.008000," ","int(1/(-3*x^4+5*x^2-2)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{-6 x^{2}+4}\, \EllipticF \left(x , \frac{\sqrt{6}}{2}\right)}{2 \sqrt{-3 x^{4}+5 x^{2}-2}}"," ",0,"1/2*(-x^2+1)^(1/2)*(-6*x^2+4)^(1/2)/(-3*x^4+5*x^2-2)^(1/2)*EllipticF(x,1/2*6^(1/2))","A"
110,1,87,111,0.048000," ","int(1/(-3*x^4+4*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(1-\frac{i \sqrt{2}}{2}\right) x^{2}+1}\, \sqrt{-\left(1+\frac{i \sqrt{2}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{4-2 i \sqrt{2}}\, x}{2}, \frac{\sqrt{3+6 i \sqrt{2}}}{3}\right)}{\sqrt{4-2 i \sqrt{2}}\, \sqrt{-3 x^{4}+4 x^{2}-2}}"," ",0,"2/(4-2*I*2^(1/2))^(1/2)*(-(1-1/2*I*2^(1/2))*x^2+1)^(1/2)*(-(1+1/2*I*2^(1/2))*x^2+1)^(1/2)/(-3*x^4+4*x^2-2)^(1/2)*EllipticF(1/2*(4-2*I*2^(1/2))^(1/2)*x,1/3*(3+6*I*2^(1/2))^(1/2))","C"
111,1,87,111,0.051000," ","int(1/(-3*x^4+3*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{3}{4}-\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \sqrt{-\left(\frac{3}{4}+\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{3-i \sqrt{15}}\, x}{2}, \frac{\sqrt{-1+i \sqrt{15}}}{2}\right)}{\sqrt{3-i \sqrt{15}}\, \sqrt{-3 x^{4}+3 x^{2}-2}}"," ",0,"2/(3-I*15^(1/2))^(1/2)*(-(3/4-1/4*I*15^(1/2))*x^2+1)^(1/2)*(-(3/4+1/4*I*15^(1/2))*x^2+1)^(1/2)/(-3*x^4+3*x^2-2)^(1/2)*EllipticF(1/2*(3-I*15^(1/2))^(1/2)*x,1/2*(-1+I*15^(1/2))^(1/2))","C"
112,1,87,111,0.063000," ","int(1/(-3*x^4+2*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{1}{2}-\frac{i \sqrt{5}}{2}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{2}+\frac{i \sqrt{5}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2-2 i \sqrt{5}}\, x}{2}, \frac{\sqrt{-6+3 i \sqrt{5}}}{3}\right)}{\sqrt{2-2 i \sqrt{5}}\, \sqrt{-3 x^{4}+2 x^{2}-2}}"," ",0,"2/(2-2*I*5^(1/2))^(1/2)*(-(1/2-1/2*I*5^(1/2))*x^2+1)^(1/2)*(-(1/2+1/2*I*5^(1/2))*x^2+1)^(1/2)/(-3*x^4+2*x^2-2)^(1/2)*EllipticF(1/2*(2-2*I*5^(1/2))^(1/2)*x,1/3*(-6+3*I*5^(1/2))^(1/2))","C"
113,1,85,109,0.047000," ","int(1/(-3*x^4+x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(\frac{1}{4}-\frac{i \sqrt{23}}{4}\right) x^{2}+1}\, \sqrt{-\left(\frac{1}{4}+\frac{i \sqrt{23}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{1-i \sqrt{23}}\, x}{2}, \frac{\sqrt{-33+3 i \sqrt{23}}}{6}\right)}{\sqrt{1-i \sqrt{23}}\, \sqrt{-3 x^{4}+x^{2}-2}}"," ",0,"2/(1-I*23^(1/2))^(1/2)*(-(1/4-1/4*I*23^(1/2))*x^2+1)^(1/2)*(-(1/4+1/4*I*23^(1/2))*x^2+1)^(1/2)/(-3*x^4+x^2-2)^(1/2)*EllipticF(1/2*(1-I*23^(1/2))^(1/2)*x,1/6*(-33+3*I*23^(1/2))^(1/2))","C"
114,1,66,95,0.020000," ","int(1/(-3*x^4-2)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{2 i \sqrt{6}\, x^{2}+4}\, \sqrt{-2 i \sqrt{6}\, x^{2}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{-i \sqrt{6}}\, x}{2}, i\right)}{4 \sqrt{-i \sqrt{6}}\, \sqrt{-3 x^{4}-2}}"," ",0,"1/4*2^(1/2)/(-I*6^(1/2))^(1/2)*(2*I*6^(1/2)*x^2+4)^(1/2)*(-2*I*6^(1/2)*x^2+4)^(1/2)/(-3*x^4-2)^(1/2)*EllipticF(1/2*2^(1/2)*(-I*6^(1/2))^(1/2)*x,I)","C"
115,1,87,109,0.046000," ","int(1/(-3*x^4-x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{1}{4}-\frac{i \sqrt{23}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{4}+\frac{i \sqrt{23}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-1-i \sqrt{23}}\, x}{2}, \frac{\sqrt{-33-3 i \sqrt{23}}}{6}\right)}{\sqrt{-1-i \sqrt{23}}\, \sqrt{-3 x^{4}-x^{2}-2}}"," ",0,"2/(-1-I*23^(1/2))^(1/2)*(-(-1/4-1/4*I*23^(1/2))*x^2+1)^(1/2)*(-(-1/4+1/4*I*23^(1/2))*x^2+1)^(1/2)/(-3*x^4-x^2-2)^(1/2)*EllipticF(1/2*(-1-I*23^(1/2))^(1/2)*x,1/6*(-33-3*I*23^(1/2))^(1/2))","C"
116,1,87,111,0.046000," ","int(1/(-3*x^4-2*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{1}{2}-\frac{i \sqrt{5}}{2}\right) x^{2}+1}\, \sqrt{-\left(-\frac{1}{2}+\frac{i \sqrt{5}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-2-2 i \sqrt{5}}\, x}{2}, \frac{\sqrt{-6-3 i \sqrt{5}}}{3}\right)}{\sqrt{-2-2 i \sqrt{5}}\, \sqrt{-3 x^{4}-2 x^{2}-2}}"," ",0,"2/(-2-2*I*5^(1/2))^(1/2)*(-(-1/2-1/2*I*5^(1/2))*x^2+1)^(1/2)*(-(-1/2+1/2*I*5^(1/2))*x^2+1)^(1/2)/(-3*x^4-2*x^2-2)^(1/2)*EllipticF(1/2*(-2-2*I*5^(1/2))^(1/2)*x,1/3*(-6-3*I*5^(1/2))^(1/2))","C"
117,1,87,111,0.046000," ","int(1/(-3*x^4-3*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{3}{4}-\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{3}{4}+\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-3-i \sqrt{15}}\, x}{2}, \frac{\sqrt{-1-i \sqrt{15}}}{2}\right)}{\sqrt{-3-i \sqrt{15}}\, \sqrt{-3 x^{4}-3 x^{2}-2}}"," ",0,"2/(-3-I*15^(1/2))^(1/2)*(-(-3/4-1/4*I*15^(1/2))*x^2+1)^(1/2)*(-(-3/4+1/4*I*15^(1/2))*x^2+1)^(1/2)/(-3*x^4-3*x^2-2)^(1/2)*EllipticF(1/2*(-3-I*15^(1/2))^(1/2)*x,1/2*(-1-I*15^(1/2))^(1/2))","C"
118,1,87,111,0.046000," ","int(1/(-3*x^4-4*x^2-2)^(1/2),x)","\frac{2 \sqrt{-\left(-1-\frac{i \sqrt{2}}{2}\right) x^{2}+1}\, \sqrt{-\left(-1+\frac{i \sqrt{2}}{2}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-4-2 i \sqrt{2}}\, x}{2}, \frac{\sqrt{3-6 i \sqrt{2}}}{3}\right)}{\sqrt{-4-2 i \sqrt{2}}\, \sqrt{-3 x^{4}-4 x^{2}-2}}"," ",0,"2/(-4-2*I*2^(1/2))^(1/2)*(-(-1-1/2*I*2^(1/2))*x^2+1)^(1/2)*(-(-1+1/2*I*2^(1/2))*x^2+1)^(1/2)/(-3*x^4-4*x^2-2)^(1/2)*EllipticF(1/2*(-4-2*I*2^(1/2))^(1/2)*x,1/3*(3-6*I*2^(1/2))^(1/2))","C"
119,1,50,56,0.013000," ","int(1/(-3*x^4-5*x^2-2)^(1/2),x)","-\frac{i \sqrt{6}\, \sqrt{6 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{6}\, x}{2}, \frac{\sqrt{6}}{3}\right)}{6 \sqrt{-3 x^{4}-5 x^{2}-2}}"," ",0,"-1/6*I*6^(1/2)*(6*x^2+4)^(1/2)*(x^2+1)^(1/2)/(-3*x^4-5*x^2-2)^(1/2)*EllipticF(1/2*I*6^(1/2)*x,1/3*6^(1/2))","A"
120,1,87,111,0.115000," ","int(1/(5*x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{i \sqrt{15}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+i \sqrt{15}}\, x}{2}, \frac{\sqrt{1+i \sqrt{15}}}{2}\right)}{\sqrt{-5+i \sqrt{15}}\, \sqrt{5 x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+I*15^(1/2))^(1/2)*(1-(-5/4+1/4*I*15^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*I*15^(1/2))*x^2)^(1/2)/(5*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+I*15^(1/2))^(1/2),1/2*(1+I*15^(1/2))^(1/2))","C"
121,1,87,99,0.124000," ","int(1/(4*x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{i \sqrt{7}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{i \sqrt{7}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+i \sqrt{7}}\, x}{2}, \frac{\sqrt{9+5 i \sqrt{7}}}{4}\right)}{\sqrt{-5+i \sqrt{7}}\, \sqrt{4 x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+I*7^(1/2))^(1/2)*(1-(-5/4+1/4*I*7^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*I*7^(1/2))*x^2)^(1/2)/(4*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+I*7^(1/2))^(1/2),1/4*(9+5*I*7^(1/2))^(1/2))","C"
122,1,44,68,0.000000," ","int(1/(3*x^4+5*x^2+2)^(1/2),x)","-\frac{i \sqrt{x^{2}+1}\, \sqrt{6 x^{2}+4}\, \EllipticF \left(i x , \frac{\sqrt{6}}{2}\right)}{2 \sqrt{3 x^{4}+5 x^{2}+2}}"," ",0,"-1/2*I*(x^2+1)^(1/2)*(6*x^2+4)^(1/2)/(3*x^4+5*x^2+2)^(1/2)*EllipticF(I*x,1/2*6^(1/2))","A"
123,1,48,73,0.014000," ","int(1/(2*x^4+5*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{2 x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, 2\right)}{2 \sqrt{2 x^{4}+5 x^{2}+2}}"," ",0,"-1/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(2*x^2+1)^(1/2)/(2*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2)","C"
124,1,76,112,0.084000," ","int(1/(x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{\sqrt{17}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{\sqrt{17}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+\sqrt{17}}\, x}{2}, \frac{5 \sqrt{2}}{4}+\frac{\sqrt{34}}{4}\right)}{\sqrt{-5+\sqrt{17}}\, \sqrt{x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+17^(1/2))^(1/2)*(1-(-5/4+1/4*17^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*17^(1/2))*x^2)^(1/2)/(x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+17^(1/2))^(1/2),5/4*2^(1/2)+1/4*34^(1/2))","A"
125,1,80,37,0.099000," ","int(1/(-x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{\sqrt{33}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{\sqrt{33}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+\sqrt{33}}\, x}{2}, \frac{5 i \sqrt{2}}{4}+\frac{i \sqrt{66}}{4}\right)}{\sqrt{-5+\sqrt{33}}\, \sqrt{-x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+33^(1/2))^(1/2)*(1-(-5/4+1/4*33^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*33^(1/2))*x^2)^(1/2)/(-x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+33^(1/2))^(1/2),5/4*I*2^(1/2)+1/4*I*66^(1/2))","B"
126,1,76,31,0.092000," ","int(1/(-2*x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{\sqrt{41}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{\sqrt{41}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+\sqrt{41}}\, x}{2}, \frac{5 i}{4}+\frac{i \sqrt{41}}{4}\right)}{\sqrt{-5+\sqrt{41}}\, \sqrt{-2 x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+41^(1/2))^(1/2)*(1-(-5/4+1/4*41^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*41^(1/2))*x^2)^(1/2)/(-2*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+41^(1/2))^(1/2),5/4*I+1/4*I*41^(1/2))","B"
127,1,51,13,0.000000," ","int(1/(-3*x^4+5*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-2 x^{2}+4}\, \sqrt{3 x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{6}\right)}{2 \sqrt{-3 x^{4}+5 x^{2}+2}}"," ",0,"1/2*2^(1/2)*(-2*x^2+4)^(1/2)*(3*x^2+1)^(1/2)/(-3*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*2^(1/2)*x,I*6^(1/2))","B"
128,1,80,38,0.101000," ","int(1/(-4*x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{\sqrt{57}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{\sqrt{57}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+\sqrt{57}}\, x}{2}, \frac{5 i \sqrt{2}}{8}+\frac{i \sqrt{114}}{8}\right)}{\sqrt{-5+\sqrt{57}}\, \sqrt{-4 x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+57^(1/2))^(1/2)*(1-(-5/4+1/4*57^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*57^(1/2))*x^2)^(1/2)/(-4*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+57^(1/2))^(1/2),5/8*I*2^(1/2)+1/8*I*114^(1/2))","B"
129,1,80,37,0.108000," ","int(1/(-5*x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{\sqrt{65}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{\sqrt{65}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+\sqrt{65}}\, x}{2}, \frac{i \sqrt{10}}{4}+\frac{i \sqrt{26}}{4}\right)}{\sqrt{-5+\sqrt{65}}\, \sqrt{-5 x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+65^(1/2))^(1/2)*(1-(-5/4+1/4*65^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*65^(1/2))*x^2)^(1/2)/(-5*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+65^(1/2))^(1/2),1/4*I*10^(1/2)+1/4*I*26^(1/2))","B"
130,1,80,38,0.100000," ","int(1/(-6*x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{\sqrt{73}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{\sqrt{73}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+\sqrt{73}}\, x}{2}, \frac{5 i \sqrt{3}}{12}+\frac{i \sqrt{219}}{12}\right)}{\sqrt{-5+\sqrt{73}}\, \sqrt{-6 x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+73^(1/2))^(1/2)*(1-(-5/4+1/4*73^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*73^(1/2))*x^2)^(1/2)/(-6*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+73^(1/2))^(1/2),5/12*I*3^(1/2)+1/12*I*219^(1/2))","B"
131,1,43,13,0.016000," ","int(1/(-7*x^4+5*x^2+2)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{14 x^{2}+4}\, \EllipticF \left(x , \frac{i \sqrt{14}}{2}\right)}{2 \sqrt{-7 x^{4}+5 x^{2}+2}}"," ",0,"1/2*(-x^2+1)^(1/2)*(14*x^2+4)^(1/2)/(-7*x^4+5*x^2+2)^(1/2)*EllipticF(x,1/2*I*14^(1/2))","B"
132,1,76,31,0.097000," ","int(1/(-8*x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{\sqrt{89}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{\sqrt{89}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+\sqrt{89}}\, x}{2}, \frac{5 i}{8}+\frac{i \sqrt{89}}{8}\right)}{\sqrt{-5+\sqrt{89}}\, \sqrt{-8 x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+89^(1/2))^(1/2)*(1-(-5/4+1/4*89^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*89^(1/2))*x^2)^(1/2)/(-8*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+89^(1/2))^(1/2),5/8*I+1/8*I*89^(1/2))","B"
133,1,80,38,0.102000," ","int(1/(-9*x^4+5*x^2+2)^(1/2),x)","\frac{2 \sqrt{-\left(-\frac{5}{4}+\frac{\sqrt{97}}{4}\right) x^{2}+1}\, \sqrt{-\left(-\frac{5}{4}-\frac{\sqrt{97}}{4}\right) x^{2}+1}\, \EllipticF \left(\frac{\sqrt{-5+\sqrt{97}}\, x}{2}, \frac{5 i \sqrt{2}}{12}+\frac{i \sqrt{194}}{12}\right)}{\sqrt{-5+\sqrt{97}}\, \sqrt{-9 x^{4}+5 x^{2}+2}}"," ",0,"2/(-5+97^(1/2))^(1/2)*(1-(-5/4+1/4*97^(1/2))*x^2)^(1/2)*(1-(-5/4-1/4*97^(1/2))*x^2)^(1/2)/(-9*x^4+5*x^2+2)^(1/2)*EllipticF(1/2*x*(-5+97^(1/2))^(1/2),5/12*I*2^(1/2)+1/12*I*194^(1/2))","B"
134,1,14,13,0.001000," ","int(x^2*(c*x^4+b*x^2),x)","\frac{1}{7} c \,x^{7}+\frac{1}{5} b \,x^{5}"," ",0,"1/5*b*x^5+1/7*c*x^7","A"
135,1,14,13,0.001000," ","int(x*(c*x^4+b*x^2),x)","\frac{1}{6} c \,x^{6}+\frac{1}{4} b \,x^{4}"," ",0,"1/4*b*x^4+1/6*c*x^6","A"
136,1,14,13,0.001000," ","int(c*x^4+b*x^2,x)","\frac{1}{5} c \,x^{5}+\frac{1}{3} b \,x^{3}"," ",0,"1/3*b*x^3+1/5*c*x^5","A"
137,1,14,13,0.001000," ","int((c*x^4+b*x^2)/x,x)","\frac{1}{4} c \,x^{4}+\frac{1}{2} b \,x^{2}"," ",0,"1/2*b*x^2+1/4*c*x^4","A"
138,1,11,10,0.000000," ","int((c*x^4+b*x^2)/x^2,x)","\frac{1}{3} c \,x^{3}+b x"," ",0,"b*x+1/3*c*x^3","A"
139,1,12,11,0.003000," ","int((c*x^4+b*x^2)/x^3,x)","\frac{c \,x^{2}}{2}+b \ln \left(x \right)"," ",0,"1/2*c*x^2+b*ln(x)","A"
140,1,11,10,0.005000," ","int((c*x^4+b*x^2)/x^4,x)","c x -\frac{b}{x}"," ",0,"-b/x+c*x","A"
141,1,12,11,0.007000," ","int((c*x^4+b*x^2)/x^5,x)","c \ln \left(x \right)-\frac{b}{2 x^{2}}"," ",0,"-1/2*b/x^2+c*ln(x)","A"
142,1,14,13,0.005000," ","int((c*x^4+b*x^2)/x^6,x)","-\frac{c}{x}-\frac{b}{3 x^{3}}"," ",0,"-1/3*b/x^3-c/x","A"
143,1,14,13,0.004000," ","int((c*x^4+b*x^2)/x^7,x)","-\frac{c}{2 x^{2}}-\frac{b}{4 x^{4}}"," ",0,"-1/4*b/x^4-1/2*c/x^2","A"
144,1,14,13,0.005000," ","int((c*x^4+b*x^2)/x^8,x)","-\frac{c}{3 x^{3}}-\frac{b}{5 x^{5}}"," ",0,"-1/5*b/x^5-1/3*c/x^3","A"
145,1,25,24,0.001000," ","int((c*x^4+b*x^2)^2,x)","\frac{1}{9} c^{2} x^{9}+\frac{2}{7} b c \,x^{7}+\frac{1}{5} b^{2} x^{5}"," ",0,"1/5*b^2*x^5+2/7*b*c*x^7+1/9*c^2*x^9","A"
146,1,25,24,0.001000," ","int((c*x^4+b*x^2)^2/x,x)","\frac{1}{8} c^{2} x^{8}+\frac{1}{3} b c \,x^{6}+\frac{1}{4} b^{2} x^{4}"," ",0,"1/4*b^2*x^4+1/3*b*c*x^6+1/8*c^2*x^8","A"
147,1,25,24,0.001000," ","int((c*x^4+b*x^2)^2/x^2,x)","\frac{1}{7} c^{2} x^{7}+\frac{2}{5} b c \,x^{5}+\frac{1}{3} b^{2} x^{3}"," ",0,"1/3*b^2*x^3+2/5*b*c*x^5+1/7*c^2*x^7","A"
148,1,25,14,0.001000," ","int((c*x^4+b*x^2)^2/x^3,x)","\frac{1}{6} c^{2} x^{6}+\frac{1}{2} b c \,x^{4}+\frac{1}{2} b^{2} x^{2}"," ",0,"1/6*c^2*x^6+1/2*b*c*x^4+1/2*b^2*x^2","A"
149,1,22,21,0.001000," ","int((c*x^4+b*x^2)^2/x^4,x)","\frac{1}{5} c^{2} x^{5}+\frac{2}{3} b c \,x^{3}+b^{2} x"," ",0,"b^2*x+2/3*b*c*x^3+1/5*c^2*x^5","A"
150,1,22,21,0.003000," ","int((c*x^4+b*x^2)^2/x^5,x)","\frac{c^{2} x^{4}}{4}+b c \,x^{2}+b^{2} \ln \left(x \right)"," ",0,"b*c*x^2+1/4*c^2*x^4+b^2*ln(x)","A"
151,1,23,22,0.004000," ","int((c*x^4+b*x^2)^2/x^6,x)","\frac{c^{2} x^{3}}{3}+2 b c x -\frac{b^{2}}{x}"," ",0,"-b^2/x+2*b*c*x+1/3*c^2*x^3","A"
152,1,24,23,0.005000," ","int((c*x^4+b*x^2)^2/x^7,x)","\frac{c^{2} x^{2}}{2}+2 b c \ln \left(x \right)-\frac{b^{2}}{2 x^{2}}"," ",0,"-1/2*b^2/x^2+1/2*c^2*x^2+2*b*c*ln(x)","A"
153,1,22,21,0.007000," ","int((c*x^4+b*x^2)^2/x^8,x)","c^{2} x -\frac{2 b c}{x}-\frac{b^{2}}{3 x^{3}}"," ",0,"-1/3*b^2/x^3-2*b*c/x+c^2*x","A"
154,1,23,22,0.005000," ","int((c*x^4+b*x^2)^2/x^9,x)","c^{2} \ln \left(x \right)-\frac{b c}{x^{2}}-\frac{b^{2}}{4 x^{4}}"," ",0,"-1/4*b^2/x^4-b*c/x^2+c^2*ln(x)","A"
155,1,25,24,0.004000," ","int((c*x^4+b*x^2)^2/x^10,x)","-\frac{c^{2}}{x}-\frac{2 b c}{3 x^{3}}-\frac{b^{2}}{5 x^{5}}"," ",0,"-1/5*b^2/x^5-2/3*b*c/x^3-c^2/x","A"
156,1,25,17,0.006000," ","int((c*x^4+b*x^2)^2/x^11,x)","-\frac{c^{2}}{2 x^{2}}-\frac{b c}{2 x^{4}}-\frac{b^{2}}{6 x^{6}}"," ",0,"-1/2*b*c/x^4-1/2*c^2/x^2-1/6*b^2/x^6","A"
157,1,25,24,0.005000," ","int((c*x^4+b*x^2)^2/x^12,x)","-\frac{c^{2}}{3 x^{3}}-\frac{2 b c}{5 x^{5}}-\frac{b^{2}}{7 x^{7}}"," ",0,"-1/7*b^2/x^7-2/5*b*c/x^5-1/3*c^2/x^3","A"
158,1,36,35,0.001000," ","int((c*x^4+b*x^2)^3/x^2,x)","\frac{1}{11} c^{3} x^{11}+\frac{1}{3} b \,c^{2} x^{9}+\frac{3}{7} b^{2} c \,x^{7}+\frac{1}{5} b^{3} x^{5}"," ",0,"1/5*b^3*x^5+3/7*b^2*c*x^7+1/3*b*c^2*x^9+1/11*c^3*x^11","A"
159,1,36,30,0.001000," ","int((c*x^4+b*x^2)^3/x^3,x)","\frac{1}{10} c^{3} x^{10}+\frac{3}{8} b \,c^{2} x^{8}+\frac{1}{2} b^{2} c \,x^{6}+\frac{1}{4} b^{3} x^{4}"," ",0,"1/10*c^3*x^10+3/8*b*c^2*x^8+1/2*b^2*c*x^6+1/4*b^3*x^4","A"
160,1,36,35,0.002000," ","int((c*x^4+b*x^2)^3/x^4,x)","\frac{1}{9} c^{3} x^{9}+\frac{3}{7} b \,c^{2} x^{7}+\frac{3}{5} b^{2} c \,x^{5}+\frac{1}{3} b^{3} x^{3}"," ",0,"1/3*b^3*x^3+3/5*b^2*c*x^5+3/7*b*c^2*x^7+1/9*c^3*x^9","A"
161,1,36,14,0.001000," ","int((c*x^4+b*x^2)^3/x^5,x)","\frac{1}{8} c^{3} x^{8}+\frac{1}{2} b \,c^{2} x^{6}+\frac{3}{4} b^{2} c \,x^{4}+\frac{1}{2} b^{3} x^{2}"," ",0,"1/8*c^3*x^8+1/2*b*c^2*x^6+3/4*b^2*c*x^4+1/2*b^3*x^2","B"
162,1,32,31,0.000000," ","int((c*x^4+b*x^2)^3/x^6,x)","\frac{1}{7} c^{3} x^{7}+\frac{3}{5} b \,c^{2} x^{5}+b^{2} c \,x^{3}+b^{3} x"," ",0,"b^3*x+b^2*c*x^3+3/5*b*c^2*x^5+1/7*c^3*x^7","A"
163,1,34,33,0.003000," ","int((c*x^4+b*x^2)^3/x^7,x)","\frac{c^{3} x^{6}}{6}+\frac{3 b \,c^{2} x^{4}}{4}+\frac{3 b^{2} c \,x^{2}}{2}+b^{3} \ln \left(x \right)"," ",0,"3/2*b^2*c*x^2+3/4*b*c^2*x^4+1/6*c^3*x^6+b^3*ln(x)","A"
164,1,33,32,0.004000," ","int((c*x^4+b*x^2)^3/x^8,x)","\frac{c^{3} x^{5}}{5}+b \,c^{2} x^{3}+3 b^{2} c x -\frac{b^{3}}{x}"," ",0,"-b^3/x+3*b^2*c*x+b*c^2*x^3+1/5*c^3*x^5","A"
165,1,35,34,0.007000," ","int((c*x^4+b*x^2)^3/x^9,x)","\frac{c^{3} x^{4}}{4}+\frac{3 b \,c^{2} x^{2}}{2}+3 b^{2} c \ln \left(x \right)-\frac{b^{3}}{2 x^{2}}"," ",0,"-1/2*b^3/x^2+3/2*b*c^2*x^2+1/4*c^3*x^4+3*b^2*c*ln(x)","A"
166,1,34,33,0.006000," ","int((c*x^4+b*x^2)^3/x^10,x)","\frac{c^{3} x^{3}}{3}+3 b \,c^{2} x -\frac{3 b^{2} c}{x}-\frac{b^{3}}{3 x^{3}}"," ",0,"-1/3*b^3/x^3-3*b^2*c/x+3*b*c^2*x+1/3*c^3*x^3","A"
167,1,35,34,0.006000," ","int((c*x^4+b*x^2)^3/x^11,x)","\frac{c^{3} x^{2}}{2}+3 b \,c^{2} \ln \left(x \right)-\frac{3 b^{2} c}{2 x^{2}}-\frac{b^{3}}{4 x^{4}}"," ",0,"-1/4*b^3/x^4-3/2*b^2*c/x^2+1/2*c^3*x^2+3*b*c^2*ln(x)","A"
168,1,33,32,0.006000," ","int((c*x^4+b*x^2)^3/x^12,x)","c^{3} x -\frac{3 b \,c^{2}}{x}-\frac{b^{2} c}{x^{3}}-\frac{b^{3}}{5 x^{5}}"," ",0,"-1/5*b^3/x^5-b^2*c/x^3-3*b*c^2/x+c^3*x","A"
169,1,34,33,0.007000," ","int((c*x^4+b*x^2)^3/x^13,x)","c^{3} \ln \left(x \right)-\frac{3 b \,c^{2}}{2 x^{2}}-\frac{3 b^{2} c}{4 x^{4}}-\frac{b^{3}}{6 x^{6}}"," ",0,"-1/6*b^3/x^6-3/4*b^2*c/x^4-3/2*b*c^2/x^2+c^3*ln(x)","A"
170,1,36,35,0.006000," ","int((c*x^4+b*x^2)^3/x^14,x)","-\frac{c^{3}}{x}-\frac{b \,c^{2}}{x^{3}}-\frac{3 b^{2} c}{5 x^{5}}-\frac{b^{3}}{7 x^{7}}"," ",0,"-1/7*b^3/x^7-3/5*b^2*c/x^5-b*c^2/x^3-c^3/x","A"
171,1,36,17,0.005000," ","int((c*x^4+b*x^2)^3/x^15,x)","-\frac{c^{3}}{2 x^{2}}-\frac{3 b \,c^{2}}{4 x^{4}}-\frac{b^{2} c}{2 x^{6}}-\frac{b^{3}}{8 x^{8}}"," ",0,"-1/2*c^3/x^2-1/2*b^2*c/x^6-3/4*b*c^2/x^4-1/8*b^3/x^8","B"
172,1,36,35,0.006000," ","int((c*x^4+b*x^2)^3/x^16,x)","-\frac{c^{3}}{3 x^{3}}-\frac{3 b \,c^{2}}{5 x^{5}}-\frac{3 b^{2} c}{7 x^{7}}-\frac{b^{3}}{9 x^{9}}"," ",0,"-1/9*b^3/x^9-3/7*b^2*c/x^7-3/5*b*c^2/x^5-1/3*c^3/x^3","A"
173,1,36,36,0.005000," ","int((c*x^4+b*x^2)^3/x^17,x)","-\frac{c^{3}}{4 x^{4}}-\frac{b \,c^{2}}{2 x^{6}}-\frac{3 b^{2} c}{8 x^{8}}-\frac{b^{3}}{10 x^{10}}"," ",0,"-3/8*b^2*c/x^8-1/2*b*c^2/x^6-1/4*c^3/x^4-1/10*b^3/x^10","A"
174,1,60,54,0.008000," ","int(x^10/(c*x^4+b*x^2),x)","\frac{x^{7}}{7 c}-\frac{b \,x^{5}}{5 c^{2}}+\frac{b^{2} x^{3}}{3 c^{3}}+\frac{b^{4} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}\, c^{4}}-\frac{b^{3} x}{c^{4}}"," ",0,"1/7*x^7/c-1/5*b*x^5/c^2+1/3*b^2*x^3/c^3-b^3*x/c^4+b^4/c^4/(b*c)^(1/2)*arctan(x*c/(b*c)^(1/2))","A"
175,1,46,45,0.004000," ","int(x^9/(c*x^4+b*x^2),x)","\frac{x^{6}}{6 c}-\frac{b \,x^{4}}{4 c^{2}}+\frac{b^{2} x^{2}}{2 c^{3}}-\frac{b^{3} \ln \left(c \,x^{2}+b \right)}{2 c^{4}}"," ",0,"1/2*b^2*x^2/c^3-1/4*b*x^4/c^2+1/6*x^6/c-1/2*b^3*ln(c*x^2+b)/c^4","A"
176,1,49,43,0.004000," ","int(x^8/(c*x^4+b*x^2),x)","\frac{x^{5}}{5 c}-\frac{b \,x^{3}}{3 c^{2}}-\frac{b^{3} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}\, c^{3}}+\frac{b^{2} x}{c^{3}}"," ",0,"1/5*x^5/c-1/3*b*x^3/c^2+b^2*x/c^3-b^3/c^3/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
177,1,35,34,0.003000," ","int(x^7/(c*x^4+b*x^2),x)","\frac{x^{4}}{4 c}-\frac{b \,x^{2}}{2 c^{2}}+\frac{b^{2} \ln \left(c \,x^{2}+b \right)}{2 c^{3}}"," ",0,"-1/2*b*x^2/c^2+1/4*x^4/c+1/2*b^2*ln(c*x^2+b)/c^3","A"
178,1,38,32,0.003000," ","int(x^6/(c*x^4+b*x^2),x)","\frac{x^{3}}{3 c}+\frac{b^{2} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}\, c^{2}}-\frac{b x}{c^{2}}"," ",0,"1/3*x^3/c-b*x/c^2+b^2/c^2/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
179,1,24,23,0.002000," ","int(x^5/(c*x^4+b*x^2),x)","\frac{x^{2}}{2 c}-\frac{b \ln \left(c \,x^{2}+b \right)}{2 c^{2}}"," ",0,"1/2*x^2/c-1/2*b*ln(c*x^2+b)/c^2","A"
180,1,27,23,0.004000," ","int(x^4/(c*x^4+b*x^2),x)","-\frac{b \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}\, c}+\frac{x}{c}"," ",0,"x/c-b/c/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
181,1,14,13,0.001000," ","int(x^3/(c*x^4+b*x^2),x)","\frac{\ln \left(c \,x^{2}+b \right)}{2 c}"," ",0,"1/2*ln(c*x^2+b)/c","A"
182,1,16,16,0.003000," ","int(x^2/(c*x^4+b*x^2),x)","\frac{\arctan \left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}}"," ",0,"1/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
183,1,21,20,0.005000," ","int(x/(c*x^4+b*x^2),x)","\frac{\ln \left(x \right)}{b}-\frac{\ln \left(c \,x^{2}+b \right)}{2 b}"," ",0,"ln(x)/b-1/2*ln(c*x^2+b)/b","A"
184,1,30,26,0.005000," ","int(1/(c*x^4+b*x^2),x)","-\frac{c \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}\, b}-\frac{1}{b x}"," ",0,"-c/b/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/b/x","A"
185,1,32,31,0.006000," ","int(1/x/(c*x^4+b*x^2),x)","-\frac{c \ln \left(x \right)}{b^{2}}+\frac{c \ln \left(c \,x^{2}+b \right)}{2 b^{2}}-\frac{1}{2 b \,x^{2}}"," ",0,"-1/2/b/x^2-c*ln(x)/b^2+1/2*c*ln(c*x^2+b)/b^2","A"
186,1,39,33,0.007000," ","int(1/x^2/(c*x^4+b*x^2),x)","\frac{c^{2} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}\, b^{2}}+\frac{c}{b^{2} x}-\frac{1}{3 b \,x^{3}}"," ",0,"c^2/b^2/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/3/b/x^3+c/b^2/x","A"
187,1,44,43,0.006000," ","int(1/x^3/(c*x^4+b*x^2),x)","\frac{c^{2} \ln \left(x \right)}{b^{3}}-\frac{c^{2} \ln \left(c \,x^{2}+b \right)}{2 b^{3}}+\frac{c}{2 b^{2} x^{2}}-\frac{1}{4 b \,x^{4}}"," ",0,"-1/4/b/x^4+1/2*c/b^2/x^2+c^2*ln(x)/b^3-1/2*c^2*ln(c*x^2+b)/b^3","A"
188,1,52,46,0.007000," ","int(1/x^4/(c*x^4+b*x^2),x)","-\frac{c^{3} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{\sqrt{b c}\, b^{3}}-\frac{c^{2}}{b^{3} x}+\frac{c}{3 b^{2} x^{3}}-\frac{1}{5 b \,x^{5}}"," ",0,"-c^3/b^3/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/5/b/x^5-c^2/b^3/x+1/3*c/b^2/x^3","A"
189,1,56,55,0.007000," ","int(1/x^5/(c*x^4+b*x^2),x)","-\frac{c^{3} \ln \left(x \right)}{b^{4}}+\frac{c^{3} \ln \left(c \,x^{2}+b \right)}{2 b^{4}}-\frac{c^{2}}{2 b^{3} x^{2}}+\frac{c}{4 b^{2} x^{4}}-\frac{1}{6 b \,x^{6}}"," ",0,"-1/6/b/x^6+1/4*c/b^2/x^4-1/2*c^2/b^3/x^2-c^3*ln(x)/b^4+1/2*c^3*ln(c*x^2+b)/b^4","A"
190,1,68,61,0.010000," ","int(x^12/(c*x^4+b*x^2)^2,x)","\frac{x^{5}}{5 c^{2}}-\frac{2 b \,x^{3}}{3 c^{3}}+\frac{b^{3} x}{2 \left(c \,x^{2}+b \right) c^{4}}-\frac{7 b^{3} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{2 \sqrt{b c}\, c^{4}}+\frac{3 b^{2} x}{c^{4}}"," ",0,"1/5*x^5/c^2-2/3*b*x^3/c^3+3*b^2*x/c^4+1/2/c^4*b^3*x/(c*x^2+b)-7/2/c^4*b^3/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
191,1,52,51,0.011000," ","int(x^11/(c*x^4+b*x^2)^2,x)","\frac{x^{4}}{4 c^{2}}-\frac{b \,x^{2}}{c^{3}}+\frac{b^{3}}{2 \left(c \,x^{2}+b \right) c^{4}}+\frac{3 b^{2} \ln \left(c \,x^{2}+b \right)}{2 c^{4}}"," ",0,"-b*x^2/c^3+1/4*x^4/c^2+1/2*b^3/c^4/(c*x^2+b)+3/2*b^2*ln(c*x^2+b)/c^4","A"
192,1,57,50,0.009000," ","int(x^10/(c*x^4+b*x^2)^2,x)","\frac{x^{3}}{3 c^{2}}-\frac{b^{2} x}{2 \left(c \,x^{2}+b \right) c^{3}}+\frac{5 b^{2} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{2 \sqrt{b c}\, c^{3}}-\frac{2 b x}{c^{3}}"," ",0,"1/3*x^3/c^2-2*b*x/c^3-1/2/c^3*b^2*x/(c*x^2+b)+5/2/c^3*b^2/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
193,1,41,40,0.008000," ","int(x^9/(c*x^4+b*x^2)^2,x)","\frac{x^{2}}{2 c^{2}}-\frac{b^{2}}{2 \left(c \,x^{2}+b \right) c^{3}}-\frac{b \ln \left(c \,x^{2}+b \right)}{c^{3}}"," ",0,"1/2*x^2/c^2-1/2*b^2/c^3/(c*x^2+b)-b*ln(c*x^2+b)/c^3","A"
194,1,43,41,0.010000," ","int(x^8/(c*x^4+b*x^2)^2,x)","\frac{b x}{2 \left(c \,x^{2}+b \right) c^{2}}-\frac{3 b \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{2 \sqrt{b c}\, c^{2}}+\frac{x}{c^{2}}"," ",0,"x/c^2+1/2/c^2*b*x/(c*x^2+b)-3/2/c^2*b/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
195,1,30,29,0.009000," ","int(x^7/(c*x^4+b*x^2)^2,x)","\frac{b}{2 \left(c \,x^{2}+b \right) c^{2}}+\frac{\ln \left(c \,x^{2}+b \right)}{2 c^{2}}"," ",0,"1/2*b/c^2/(c*x^2+b)+1/2*ln(c*x^2+b)/c^2","A"
196,1,36,33,0.008000," ","int(x^6/(c*x^4+b*x^2)^2,x)","-\frac{x}{2 \left(c \,x^{2}+b \right) c}+\frac{\arctan \left(\frac{c x}{\sqrt{b c}}\right)}{2 \sqrt{b c}\, c}"," ",0,"-1/2*x/c/(c*x^2+b)+1/2/c/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
197,1,15,14,0.000000," ","int(x^5/(c*x^4+b*x^2)^2,x)","-\frac{1}{2 \left(c \,x^{2}+b \right) c}"," ",0,"-1/2/c/(c*x^2+b)","A"
198,1,36,33,0.005000," ","int(x^4/(c*x^4+b*x^2)^2,x)","\frac{x}{2 \left(c \,x^{2}+b \right) b}+\frac{\arctan \left(\frac{c x}{\sqrt{b c}}\right)}{2 \sqrt{b c}\, b}"," ",0,"1/2*x/b/(c*x^2+b)+1/2/b/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
199,1,35,34,0.012000," ","int(x^3/(c*x^4+b*x^2)^2,x)","\frac{1}{2 \left(c \,x^{2}+b \right) b}+\frac{\ln \left(x \right)}{b^{2}}-\frac{\ln \left(c \,x^{2}+b \right)}{2 b^{2}}"," ",0,"1/2/b/(c*x^2+b)+ln(x)/b^2-1/2*ln(c*x^2+b)/b^2","A"
200,1,46,43,0.010000," ","int(x^2/(c*x^4+b*x^2)^2,x)","-\frac{c x}{2 \left(c \,x^{2}+b \right) b^{2}}-\frac{3 c \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{2 \sqrt{b c}\, b^{2}}-\frac{1}{b^{2} x}"," ",0,"-1/2/b^2*c*x/(c*x^2+b)-3/2/b^2*c/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/b^2/x","A"
201,1,46,45,0.012000," ","int(x/(c*x^4+b*x^2)^2,x)","-\frac{c}{2 \left(c \,x^{2}+b \right) b^{2}}-\frac{2 c \ln \left(x \right)}{b^{3}}+\frac{c \ln \left(c \,x^{2}+b \right)}{b^{3}}-\frac{1}{2 b^{2} x^{2}}"," ",0,"-1/2/b^2/x^2-1/2*c/b^2/(c*x^2+b)-2*c*ln(x)/b^3+c*ln(c*x^2+b)/b^3","A"
202,1,59,52,0.014000," ","int(1/(c*x^4+b*x^2)^2,x)","\frac{c^{2} x}{2 \left(c \,x^{2}+b \right) b^{3}}+\frac{5 c^{2} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{2 \sqrt{b c}\, b^{3}}+\frac{2 c}{b^{3} x}-\frac{1}{3 b^{2} x^{3}}"," ",0,"1/2/b^3*c^2*x/(c*x^2+b)+5/2/b^3*c^2/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/3/b^2/x^3+2*c/b^3/x","A"
203,1,61,60,0.013000," ","int(1/x/(c*x^4+b*x^2)^2,x)","\frac{c^{2}}{2 \left(c \,x^{2}+b \right) b^{3}}+\frac{3 c^{2} \ln \left(x \right)}{b^{4}}-\frac{3 c^{2} \ln \left(c \,x^{2}+b \right)}{2 b^{4}}+\frac{c}{b^{3} x^{2}}-\frac{1}{4 b^{2} x^{4}}"," ",0,"-1/4/b^2/x^4+c/b^3/x^2+1/2*c^2/b^3/(c*x^2+b)+3*c^2*ln(x)/b^4-3/2*c^2*ln(c*x^2+b)/b^4","A"
204,1,70,63,0.012000," ","int(1/x^2/(c*x^4+b*x^2)^2,x)","-\frac{c^{3} x}{2 \left(c \,x^{2}+b \right) b^{4}}-\frac{7 c^{3} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{2 \sqrt{b c}\, b^{4}}-\frac{3 c^{2}}{b^{4} x}+\frac{2 c}{3 b^{3} x^{3}}-\frac{1}{5 b^{2} x^{5}}"," ",0,"-1/2/b^4*c^3*x/(c*x^2+b)-7/2/b^4*c^3/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/5/b^2/x^5-3*c^2/b^4/x+2/3*c/b^3/x^3","A"
205,1,77,67,0.011000," ","int(x^14/(c*x^4+b*x^2)^3,x)","-\frac{13 b^{2} x^{3}}{8 \left(c \,x^{2}+b \right)^{2} c^{3}}-\frac{11 b^{3} x}{8 \left(c \,x^{2}+b \right)^{2} c^{4}}+\frac{x^{3}}{3 c^{3}}+\frac{35 b^{2} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{8 \sqrt{b c}\, c^{4}}-\frac{3 b x}{c^{4}}"," ",0,"1/3*x^3/c^3-3*b*x/c^4-13/8/c^3*b^2/(c*x^2+b)^2*x^3-11/8/c^4*b^3/(c*x^2+b)^2*x+35/8/c^4*b^2/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
206,1,58,57,0.010000," ","int(x^13/(c*x^4+b*x^2)^3,x)","\frac{b^{3}}{4 \left(c \,x^{2}+b \right)^{2} c^{4}}+\frac{x^{2}}{2 c^{3}}-\frac{3 b^{2}}{2 \left(c \,x^{2}+b \right) c^{4}}-\frac{3 b \ln \left(c \,x^{2}+b \right)}{2 c^{4}}"," ",0,"1/2*x^2/c^3+1/4*b^3/c^4/(c*x^2+b)^2-3/2*b^2/c^4/(c*x^2+b)-3/2*b*ln(c*x^2+b)/c^4","A"
207,1,63,58,0.011000," ","int(x^12/(c*x^4+b*x^2)^3,x)","\frac{9 b \,x^{3}}{8 \left(c \,x^{2}+b \right)^{2} c^{2}}+\frac{7 b^{2} x}{8 \left(c \,x^{2}+b \right)^{2} c^{3}}-\frac{15 b \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{8 \sqrt{b c}\, c^{3}}+\frac{x}{c^{3}}"," ",0,"x/c^3+9/8/c^2*b/(c*x^2+b)^2*x^3+7/8/c^3*b^2/(c*x^2+b)^2*x-15/8/c^3*b/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
208,1,46,45,0.009000," ","int(x^11/(c*x^4+b*x^2)^3,x)","-\frac{b^{2}}{4 \left(c \,x^{2}+b \right)^{2} c^{3}}+\frac{b}{\left(c \,x^{2}+b \right) c^{3}}+\frac{\ln \left(c \,x^{2}+b \right)}{2 c^{3}}"," ",0,"-1/4*b^2/c^3/(c*x^2+b)^2+b/c^3/(c*x^2+b)+1/2*ln(c*x^2+b)/c^3","A"
209,1,47,50,0.010000," ","int(x^10/(c*x^4+b*x^2)^3,x)","\frac{3 \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{8 \sqrt{b c}\, c^{2}}+\frac{-\frac{5 x^{3}}{8 c}-\frac{3 b x}{8 c^{2}}}{\left(c \,x^{2}+b \right)^{2}}"," ",0,"(-5/8/c*x^3-3/8*b/c^2*x)/(c*x^2+b)^2+3/8/c^2/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
210,1,31,17,0.008000," ","int(x^9/(c*x^4+b*x^2)^3,x)","\frac{b}{4 \left(c \,x^{2}+b \right)^{2} c^{2}}-\frac{1}{2 \left(c \,x^{2}+b \right) c^{2}}"," ",0,"1/4*b/c^2/(c*x^2+b)^2-1/2/c^2/(c*x^2+b)","A"
211,1,49,51,0.008000," ","int(x^8/(c*x^4+b*x^2)^3,x)","\frac{\arctan \left(\frac{c x}{\sqrt{b c}}\right)}{8 \sqrt{b c}\, b c}+\frac{\frac{x^{3}}{8 b}-\frac{x}{8 c}}{\left(c \,x^{2}+b \right)^{2}}"," ",0,"(1/8/b*x^3-1/8/c*x)/(c*x^2+b)^2+1/8/c/b/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
212,1,15,14,0.002000," ","int(x^7/(c*x^4+b*x^2)^3,x)","-\frac{1}{4 \left(c \,x^{2}+b \right)^{2} c}"," ",0,"-1/4/c/(c*x^2+b)^2","A"
213,1,51,48,0.006000," ","int(x^6/(c*x^4+b*x^2)^3,x)","\frac{x}{4 \left(c \,x^{2}+b \right)^{2} b}+\frac{3 x}{8 \left(c \,x^{2}+b \right) b^{2}}+\frac{3 \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{8 \sqrt{b c}\, b^{2}}"," ",0,"1/4*x/b/(c*x^2+b)^2+3/8*x/b^2/(c*x^2+b)+3/8/b^2/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)","A"
214,1,49,48,0.012000," ","int(x^5/(c*x^4+b*x^2)^3,x)","\frac{1}{4 \left(c \,x^{2}+b \right)^{2} b}+\frac{1}{2 \left(c \,x^{2}+b \right) b^{2}}+\frac{\ln \left(x \right)}{b^{3}}-\frac{\ln \left(c \,x^{2}+b \right)}{2 b^{3}}"," ",0,"1/4/b/(c*x^2+b)^2+1/2/b^2/(c*x^2+b)+ln(x)/b^3-1/2*ln(c*x^2+b)/b^3","A"
215,1,66,60,0.013000," ","int(x^4/(c*x^4+b*x^2)^3,x)","-\frac{7 c^{2} x^{3}}{8 \left(c \,x^{2}+b \right)^{2} b^{3}}-\frac{9 c x}{8 \left(c \,x^{2}+b \right)^{2} b^{2}}-\frac{15 c \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{8 \sqrt{b c}\, b^{3}}-\frac{1}{b^{3} x}"," ",0,"-7/8/b^3*c^2/(c*x^2+b)^2*x^3-9/8/b^2*c/(c*x^2+b)^2*x-15/8/b^3*c/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/b^3/x","A"
216,1,62,61,0.015000," ","int(x^3/(c*x^4+b*x^2)^3,x)","-\frac{c}{4 \left(c \,x^{2}+b \right)^{2} b^{2}}-\frac{c}{\left(c \,x^{2}+b \right) b^{3}}-\frac{3 c \ln \left(x \right)}{b^{4}}+\frac{3 c \ln \left(c \,x^{2}+b \right)}{2 b^{4}}-\frac{1}{2 b^{3} x^{2}}"," ",0,"-1/2/b^3/x^2-1/4*c/b^2/(c*x^2+b)^2-c/b^3/(c*x^2+b)-3*c*ln(x)/b^4+3/2*c*ln(c*x^2+b)/b^4","A"
217,1,79,69,0.013000," ","int(x^2/(c*x^4+b*x^2)^3,x)","\frac{11 c^{3} x^{3}}{8 \left(c \,x^{2}+b \right)^{2} b^{4}}+\frac{13 c^{2} x}{8 \left(c \,x^{2}+b \right)^{2} b^{3}}+\frac{35 c^{2} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{8 \sqrt{b c}\, b^{4}}+\frac{3 c}{b^{4} x}-\frac{1}{3 b^{3} x^{3}}"," ",0,"11/8/b^4*c^3/(c*x^2+b)^2*x^3+13/8/b^3*c^2/(c*x^2+b)^2*x+35/8/b^4*c^2/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/3/b^3/x^3+3*c/b^4/x","A"
218,1,79,78,0.014000," ","int(x/(c*x^4+b*x^2)^3,x)","\frac{c^{2}}{4 \left(c \,x^{2}+b \right)^{2} b^{3}}+\frac{3 c^{2}}{2 \left(c \,x^{2}+b \right) b^{4}}+\frac{6 c^{2} \ln \left(x \right)}{b^{5}}-\frac{3 c^{2} \ln \left(c \,x^{2}+b \right)}{b^{5}}+\frac{3 c}{2 b^{4} x^{2}}-\frac{1}{4 b^{3} x^{4}}"," ",0,"-1/4/b^3/x^4+3/2*c/b^4/x^2+1/4*c^2/b^3/(c*x^2+b)^2+3/2*c^2/b^4/(c*x^2+b)+6*c^2*ln(x)/b^5-3*c^2*ln(c*x^2+b)/b^5","A"
219,1,89,80,0.015000," ","int(1/(c*x^4+b*x^2)^3,x)","-\frac{15 c^{4} x^{3}}{8 \left(c \,x^{2}+b \right)^{2} b^{5}}-\frac{17 c^{3} x}{8 \left(c \,x^{2}+b \right)^{2} b^{4}}-\frac{63 c^{3} \arctan \left(\frac{c x}{\sqrt{b c}}\right)}{8 \sqrt{b c}\, b^{5}}-\frac{6 c^{2}}{b^{5} x}+\frac{c}{b^{4} x^{3}}-\frac{1}{5 b^{3} x^{5}}"," ",0,"-15/8/b^5*c^4/(c*x^2+b)^2*x^3-17/8/b^4*c^3/(c*x^2+b)^2*x-63/8/b^5*c^3/(b*c)^(1/2)*arctan(1/(b*c)^(1/2)*c*x)-1/5/b^3/x^5-6*c^2/b^5/x+c/b^4/x^3","A"
220,1,90,89,0.015000," ","int(1/x/(c*x^4+b*x^2)^3,x)","-\frac{c^{3}}{4 \left(c \,x^{2}+b \right)^{2} b^{4}}-\frac{2 c^{3}}{\left(c \,x^{2}+b \right) b^{5}}-\frac{10 c^{3} \ln \left(x \right)}{b^{6}}+\frac{5 c^{3} \ln \left(c \,x^{2}+b \right)}{b^{6}}-\frac{3 c^{2}}{b^{5} x^{2}}+\frac{3 c}{4 b^{4} x^{4}}-\frac{1}{6 b^{3} x^{6}}"," ",0,"-1/6/b^3/x^6+3/4*c/b^4/x^4-3*c^2/b^5/x^2-1/4*c^3/b^4/(c*x^2+b)^2-2*c^3/b^5/(c*x^2+b)-10*c^3*ln(x)/b^6+5*c^3*ln(c*x^2+b)/b^6","A"
221,1,124,99,0.016000," ","int(x^5*(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(48 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{\frac{5}{2}} x^{5}-40 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b \,c^{\frac{3}{2}} x^{3}-15 b^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)-15 \sqrt{c \,x^{2}+b}\, b^{3} \sqrt{c}\, x +30 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{2} \sqrt{c}\, x \right)}{384 \sqrt{c \,x^{2}+b}\, c^{\frac{7}{2}} x}"," ",0,"1/384*(c*x^4+b*x^2)^(1/2)*(48*x^5*(c*x^2+b)^(3/2)*c^(5/2)-40*(c*x^2+b)^(3/2)*c^(3/2)*x^3*b+30*(c*x^2+b)^(3/2)*c^(1/2)*x*b^2-15*(c*x^2+b)^(1/2)*c^(1/2)*x*b^3-15*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*b^4)/x/(c*x^2+b)^(1/2)/c^(7/2)","A"
222,1,104,75,0.008000," ","int(x^3*(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(8 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{\frac{3}{2}} x^{3}+3 b^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+3 \sqrt{c \,x^{2}+b}\, b^{2} \sqrt{c}\, x -6 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b \sqrt{c}\, x \right)}{48 \sqrt{c \,x^{2}+b}\, c^{\frac{5}{2}} x}"," ",0,"1/48*(c*x^4+b*x^2)^(1/2)*(8*x^3*(c*x^2+b)^(3/2)*c^(3/2)-6*c^(1/2)*(c*x^2+b)^(3/2)*x*b+3*c^(1/2)*(c*x^2+b)^(1/2)*x*b^2+3*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*b^3)/x/(c*x^2+b)^(1/2)/c^(5/2)","A"
223,1,84,56,0.007000," ","int(x*(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(-b^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)-\sqrt{c \,x^{2}+b}\, b \sqrt{c}\, x +2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} \sqrt{c}\, x \right)}{8 \sqrt{c \,x^{2}+b}\, c^{\frac{3}{2}} x}"," ",0,"1/8*(c*x^4+b*x^2)^(1/2)*(2*x*(c*x^2+b)^(3/2)*c^(1/2)-c^(1/2)*(c*x^2+b)^(1/2)*x*b-ln(c^(1/2)*x+(c*x^2+b)^(1/2))*b^2)/x/(c*x^2+b)^(1/2)/c^(3/2)","A"
224,1,64,43,0.005000," ","int((c*x^4+b*x^2)^(1/2)/x,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(b \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+\sqrt{c \,x^{2}+b}\, \sqrt{c}\, x \right)}{2 \sqrt{c \,x^{2}+b}\, \sqrt{c}\, x}"," ",0,"1/2*(c*x^4+b*x^2)^(1/2)*(x*(c*x^2+b)^(1/2)*c^(1/2)+b*ln(c^(1/2)*x+(c*x^2+b)^(1/2)))/x/(c*x^2+b)^(1/2)/c^(1/2)","A"
225,1,84,44,0.007000," ","int((c*x^4+b*x^2)^(1/2)/x^3,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(b c x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+\sqrt{c \,x^{2}+b}\, c^{\frac{3}{2}} x^{2}-\left(c \,x^{2}+b \right)^{\frac{3}{2}} \sqrt{c}\right)}{\sqrt{c \,x^{2}+b}\, b \sqrt{c}\, x^{2}}"," ",0,"(c*x^4+b*x^2)^(1/2)*(c^(3/2)*(c*x^2+b)^(1/2)*x^2-(c*x^2+b)^(3/2)*c^(1/2)+ln(c^(1/2)*x+(c*x^2+b)^(1/2))*x*b*c)/x^2/(c*x^2+b)^(1/2)/b/c^(1/2)","A"
226,1,29,21,0.004000," ","int((c*x^4+b*x^2)^(1/2)/x^5,x)","-\frac{\left(c \,x^{2}+b \right) \sqrt{c \,x^{4}+b \,x^{2}}}{3 b \,x^{4}}"," ",0,"-1/3/x^4*(c*x^2+b)/b*(c*x^4+b*x^2)^(1/2)","A"
227,1,39,44,0.004000," ","int((c*x^4+b*x^2)^(1/2)/x^7,x)","-\frac{\left(c \,x^{2}+b \right) \left(-2 c \,x^{2}+3 b \right) \sqrt{c \,x^{4}+b \,x^{2}}}{15 b^{2} x^{6}}"," ",0,"-1/15*(c*x^2+b)*(-2*c*x^2+3*b)*(c*x^4+b*x^2)^(1/2)/b^2/x^6","A"
228,1,50,68,0.005000," ","int((c*x^4+b*x^2)^(1/2)/x^9,x)","-\frac{\left(c \,x^{2}+b \right) \left(8 c^{2} x^{4}-12 b c \,x^{2}+15 b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}}}{105 b^{3} x^{8}}"," ",0,"-1/105*(c*x^2+b)*(8*c^2*x^4-12*b*c*x^2+15*b^2)*(c*x^4+b*x^2)^(1/2)/x^8/b^3","A"
229,1,61,92,0.007000," ","int((c*x^4+b*x^2)^(1/2)/x^11,x)","-\frac{\left(c \,x^{2}+b \right) \left(-16 c^{3} x^{6}+24 b \,c^{2} x^{4}-30 b^{2} c \,x^{2}+35 b^{3}\right) \sqrt{c \,x^{4}+b \,x^{2}}}{315 b^{4} x^{10}}"," ",0,"-1/315*(c*x^2+b)*(-16*c^3*x^6+24*b*c^2*x^4-30*b^2*c*x^2+35*b^3)*(c*x^4+b*x^2)^(1/2)/x^10/b^4","A"
230,1,72,116,0.006000," ","int((c*x^4+b*x^2)^(1/2)/x^13,x)","-\frac{\left(c \,x^{2}+b \right) \left(128 c^{4} x^{8}-192 c^{3} x^{6} b +240 c^{2} x^{4} b^{2}-280 c \,x^{2} b^{3}+315 b^{4}\right) \sqrt{c \,x^{4}+b \,x^{2}}}{3465 b^{5} x^{12}}"," ",0,"-1/3465*(c*x^2+b)*(128*c^4*x^8-192*b*c^3*x^6+240*b^2*c^2*x^4-280*b^3*c*x^2+315*b^4)*(c*x^4+b*x^2)^(1/2)/x^12/b^5","A"
231,1,50,66,0.005000," ","int(x^4*(c*x^4+b*x^2)^(1/2),x)","\frac{\left(c \,x^{2}+b \right) \left(15 c^{2} x^{4}-12 b c \,x^{2}+8 b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}}}{105 c^{3} x}"," ",0,"1/105*(c*x^2+b)*(15*c^2*x^4-12*b*c*x^2+8*b^2)*(c*x^4+b*x^2)^(1/2)/c^3/x","A"
232,1,39,44,0.005000," ","int(x^2*(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-3 c \,x^{2}+2 b \right) \sqrt{c \,x^{4}+b \,x^{2}}}{15 c^{2} x}"," ",0,"-1/15*(c*x^2+b)*(-3*c*x^2+2*b)*(c*x^4+b*x^2)^(1/2)/c^2/x","A"
233,1,29,21,0.003000," ","int((c*x^4+b*x^2)^(1/2),x)","\frac{\left(c \,x^{2}+b \right) \sqrt{c \,x^{4}+b \,x^{2}}}{3 c x}"," ",0,"1/3*(c*x^2+b)/c/x*(c*x^4+b*x^2)^(1/2)","A"
234,1,65,42,0.006000," ","int((c*x^4+b*x^2)^(1/2)/x^2,x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(\sqrt{b}\, \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-\sqrt{c \,x^{2}+b}\right)}{\sqrt{c \,x^{2}+b}\, x}"," ",0,"-(c*x^4+b*x^2)^(1/2)*(b^(1/2)*ln(2*(b^(1/2)*(c*x^2+b)^(1/2)+b)/x)-(c*x^2+b)^(1/2))/x/(c*x^2+b)^(1/2)","A"
235,1,85,44,0.006000," ","int((c*x^4+b*x^2)^(1/2)/x^4,x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(\sqrt{b}\, c \,x^{2} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-\sqrt{c \,x^{2}+b}\, c \,x^{2}+\left(c \,x^{2}+b \right)^{\frac{3}{2}}\right)}{2 \sqrt{c \,x^{2}+b}\, b \,x^{3}}"," ",0,"-1/2*(c*x^4+b*x^2)^(1/2)*(b^(1/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^2*c-(c*x^2+b)^(1/2)*x^2*c+(c*x^2+b)^(3/2))/x^3/(c*x^2+b)^(1/2)/b","A"
236,1,106,68,0.007000," ","int((c*x^4+b*x^2)^(1/2)/x^6,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(\sqrt{b}\, c^{2} x^{4} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-\sqrt{c \,x^{2}+b}\, c^{2} x^{4}+\left(c \,x^{2}+b \right)^{\frac{3}{2}} c \,x^{2}-2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b \right)}{8 \sqrt{c \,x^{2}+b}\, b^{2} x^{5}}"," ",0,"1/8*(c*x^4+b*x^2)^(1/2)*(b^(1/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^4*c^2-(c*x^2+b)^(1/2)*x^4*c^2+(c*x^2+b)^(3/2)*x^2*c-2*(c*x^2+b)^(3/2)*b)/x^5/(c*x^2+b)^(1/2)/b^2","A"
237,1,128,92,0.010000," ","int((c*x^4+b*x^2)^(1/2)/x^8,x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}}\, \left(3 \sqrt{b}\, c^{3} x^{6} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-3 \sqrt{c \,x^{2}+b}\, c^{3} x^{6}+3 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{2} x^{4}-6 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b c \,x^{2}+8 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{2}\right)}{48 \sqrt{c \,x^{2}+b}\, b^{3} x^{7}}"," ",0,"-1/48*(c*x^4+b*x^2)^(1/2)*(3*b^(1/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^6*c^3-3*(c*x^2+b)^(1/2)*x^6*c^3+3*(c*x^2+b)^(3/2)*x^4*c^2-6*(c*x^2+b)^(3/2)*x^2*b*c+8*(c*x^2+b)^(3/2)*b^2)/x^7/(c*x^2+b)^(1/2)/b^3","A"
238,1,142,104,0.010000," ","int(x^3*(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(128 \left(c \,x^{2}+b \right)^{\frac{5}{2}} c^{\frac{5}{2}} x^{5}-15 b^{5} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)-15 \sqrt{c \,x^{2}+b}\, b^{4} \sqrt{c}\, x -80 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b \,c^{\frac{3}{2}} x^{3}-10 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{3} \sqrt{c}\, x +40 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b^{2} \sqrt{c}\, x \right)}{1280 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{\frac{7}{2}} x^{3}}"," ",0,"1/1280*(c*x^4+b*x^2)^(3/2)*(128*x^5*(c*x^2+b)^(5/2)*c^(5/2)-80*c^(3/2)*(c*x^2+b)^(5/2)*x^3*b+40*c^(1/2)*(c*x^2+b)^(5/2)*x*b^2-10*c^(1/2)*(c*x^2+b)^(3/2)*x*b^3-15*c^(1/2)*(c*x^2+b)^(1/2)*x*b^4-15*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*b^5)/x^3/(c*x^2+b)^(3/2)/c^(7/2)","A"
239,1,122,85,0.010000," ","int(x*(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{4} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+3 \sqrt{c \,x^{2}+b}\, b^{3} \sqrt{c}\, x +16 \left(c \,x^{2}+b \right)^{\frac{5}{2}} c^{\frac{3}{2}} x^{3}+2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{2} \sqrt{c}\, x -8 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b \sqrt{c}\, x \right)}{128 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{\frac{5}{2}} x^{3}}"," ",0,"1/128*(c*x^4+b*x^2)^(3/2)*(16*x^3*(c*x^2+b)^(5/2)*c^(3/2)-8*c^(1/2)*(c*x^2+b)^(5/2)*x*b+2*(c*x^2+b)^(3/2)*b^2*c^(1/2)*x+3*(c*x^2+b)^(1/2)*b^3*c^(1/2)*x+3*b^4*ln(c^(1/2)*x+(c*x^2+b)^(1/2)))/x^3/(c*x^2+b)^(3/2)/c^(5/2)","A"
240,1,102,72,0.008000," ","int((c*x^4+b*x^2)^(3/2)/x,x)","\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(-3 b^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)-3 \sqrt{c \,x^{2}+b}\, b^{2} \sqrt{c}\, x -2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b \sqrt{c}\, x +8 \left(c \,x^{2}+b \right)^{\frac{5}{2}} \sqrt{c}\, x \right)}{48 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{\frac{3}{2}} x^{3}}"," ",0,"1/48*(c*x^4+b*x^2)^(3/2)*(8*x*(c*x^2+b)^(5/2)*c^(1/2)-2*(c*x^2+b)^(3/2)*b*c^(1/2)*x-3*(c*x^2+b)^(1/2)*b^2*c^(1/2)*x-3*b^3*ln(c^(1/2)*x+(c*x^2+b)^(1/2)))/x^3/(c*x^2+b)^(3/2)/c^(3/2)","A"
241,1,84,64,0.005000," ","int((c*x^4+b*x^2)^(3/2)/x^3,x)","\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{2} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+3 \sqrt{c \,x^{2}+b}\, b \sqrt{c}\, x +2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} \sqrt{c}\, x \right)}{8 \left(c \,x^{2}+b \right)^{\frac{3}{2}} \sqrt{c}\, x^{3}}"," ",0,"1/8*(c*x^4+b*x^2)^(3/2)*(2*(c*x^2+b)^(3/2)*c^(1/2)*x+3*(c*x^2+b)^(1/2)*b*c^(1/2)*x+3*b^2*ln(c^(1/2)*x+(c*x^2+b)^(1/2)))/x^3/(c*x^2+b)^(3/2)/c^(1/2)","A"
242,1,107,62,0.007000," ","int((c*x^4+b*x^2)^(3/2)/x^5,x)","\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{2} c x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+3 \sqrt{c \,x^{2}+b}\, b \,c^{\frac{3}{2}} x^{2}+2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{\frac{3}{2}} x^{2}-2 \left(c \,x^{2}+b \right)^{\frac{5}{2}} \sqrt{c}\right)}{2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b \sqrt{c}\, x^{4}}"," ",0,"1/2*(c*x^4+b*x^2)^(3/2)*(2*c^(3/2)*(c*x^2+b)^(3/2)*x^2+3*c^(3/2)*(c*x^2+b)^(1/2)*x^2*b-2*(c*x^2+b)^(5/2)*c^(1/2)+3*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*x*b^2*c)/x^4/(c*x^2+b)^(3/2)/b/c^(1/2)","A"
243,1,129,63,0.007000," ","int((c*x^4+b*x^2)^(3/2)/x^7,x)","\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{2} c^{2} x^{3} \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+3 \sqrt{c \,x^{2}+b}\, b \,c^{\frac{5}{2}} x^{4}+2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{\frac{5}{2}} x^{4}-2 \left(c \,x^{2}+b \right)^{\frac{5}{2}} c^{\frac{3}{2}} x^{2}-\left(c \,x^{2}+b \right)^{\frac{5}{2}} b \sqrt{c}\right)}{3 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{2} \sqrt{c}\, x^{6}}"," ",0,"1/3*(c*x^4+b*x^2)^(3/2)*(2*c^(5/2)*(c*x^2+b)^(3/2)*x^4+3*c^(5/2)*(c*x^2+b)^(1/2)*x^4*b-2*c^(3/2)*(c*x^2+b)^(5/2)*x^2+3*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*x^3*b^2*c^2-(c*x^2+b)^(5/2)*b*c^(1/2))/x^6/(c*x^2+b)^(3/2)/b^2/c^(1/2)","B"
244,1,29,21,0.004000," ","int((c*x^4+b*x^2)^(3/2)/x^9,x)","-\frac{\left(c \,x^{2}+b \right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{5 b \,x^{8}}"," ",0,"-1/5/x^8*(c*x^2+b)/b*(c*x^4+b*x^2)^(3/2)","A"
245,1,39,44,0.005000," ","int((c*x^4+b*x^2)^(3/2)/x^11,x)","-\frac{\left(c \,x^{2}+b \right) \left(-2 c \,x^{2}+5 b \right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{35 b^{2} x^{10}}"," ",0,"-1/35*(c*x^2+b)*(-2*c*x^2+5*b)*(c*x^4+b*x^2)^(3/2)/x^10/b^2","A"
246,1,50,68,0.005000," ","int((c*x^4+b*x^2)^(3/2)/x^13,x)","-\frac{\left(c \,x^{2}+b \right) \left(8 c^{2} x^{4}-20 b c \,x^{2}+35 b^{2}\right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{315 b^{3} x^{12}}"," ",0,"-1/315*(c*x^2+b)*(8*c^2*x^4-20*b*c*x^2+35*b^2)*(c*x^4+b*x^2)^(3/2)/x^12/b^3","A"
247,1,61,92,0.005000," ","int((c*x^4+b*x^2)^(3/2)/x^15,x)","-\frac{\left(c \,x^{2}+b \right) \left(-16 c^{3} x^{6}+40 b \,c^{2} x^{4}-70 b^{2} c \,x^{2}+105 b^{3}\right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{1155 b^{4} x^{14}}"," ",0,"-1/1155*(c*x^2+b)*(-16*c^3*x^6+40*b*c^2*x^4-70*b^2*c*x^2+105*b^3)*(c*x^4+b*x^2)^(3/2)/x^14/b^4","A"
248,1,72,116,0.007000," ","int((c*x^4+b*x^2)^(3/2)/x^17,x)","-\frac{\left(c \,x^{2}+b \right) \left(128 c^{4} x^{8}-320 c^{3} x^{6} b +560 c^{2} x^{4} b^{2}-840 c \,x^{2} b^{3}+1155 b^{4}\right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{15015 b^{5} x^{16}}"," ",0,"-1/15015*(c*x^2+b)*(128*c^4*x^8-320*b*c^3*x^6+560*b^2*c^2*x^4-840*b^3*c*x^2+1155*b^4)*(c*x^4+b*x^2)^(3/2)/x^16/b^5","A"
249,1,72,114,0.007000," ","int(x^6*(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(1155 c^{4} x^{8}-840 c^{3} x^{6} b +560 c^{2} x^{4} b^{2}-320 c \,x^{2} b^{3}+128 b^{4}\right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{15015 c^{5} x^{3}}"," ",0,"1/15015*(c*x^2+b)*(1155*c^4*x^8-840*b*c^3*x^6+560*b^2*c^2*x^4-320*b^3*c*x^2+128*b^4)*(c*x^4+b*x^2)^(3/2)/c^5/x^3","A"
250,1,61,90,0.008000," ","int(x^4*(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-105 c^{3} x^{6}+70 b \,c^{2} x^{4}-40 b^{2} c \,x^{2}+16 b^{3}\right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{1155 c^{4} x^{3}}"," ",0,"-1/1155*(c*x^2+b)*(-105*c^3*x^6+70*b*c^2*x^4-40*b^2*c*x^2+16*b^3)*(c*x^4+b*x^2)^(3/2)/c^4/x^3","A"
251,1,50,68,0.006000," ","int(x^2*(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(35 c^{2} x^{4}-20 b c \,x^{2}+8 b^{2}\right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{315 c^{3} x^{3}}"," ",0,"1/315*(c*x^2+b)*(35*c^2*x^4-20*b*c*x^2+8*b^2)*(c*x^4+b*x^2)^(3/2)/c^3/x^3","A"
252,1,39,44,0.006000," ","int((c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-5 c \,x^{2}+2 b \right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{35 c^{2} x^{3}}"," ",0,"-1/35*(c*x^2+b)*(-5*c*x^2+2*b)*(c*x^4+b*x^2)^(3/2)/c^2/x^3","A"
253,1,29,21,0.003000," ","int((c*x^4+b*x^2)^(3/2)/x^2,x)","\frac{\left(c \,x^{2}+b \right) \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}}}{5 c \,x^{3}}"," ",0,"1/5*(c*x^2+b)/c/x^3*(c*x^4+b*x^2)^(3/2)","A"
254,1,78,61,0.006000," ","int((c*x^4+b*x^2)^(3/2)/x^4,x)","-\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{\frac{3}{2}} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-3 \sqrt{c \,x^{2}+b}\, b -\left(c \,x^{2}+b \right)^{\frac{3}{2}}\right)}{3 \left(c \,x^{2}+b \right)^{\frac{3}{2}} x^{3}}"," ",0,"-1/3*(c*x^4+b*x^2)^(3/2)*(3*b^(3/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)-(c*x^2+b)^(3/2)-3*(c*x^2+b)^(1/2)*b)/x^3/(c*x^2+b)^(3/2)","A"
255,1,102,63,0.006000," ","int((c*x^4+b*x^2)^(3/2)/x^6,x)","-\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{\frac{3}{2}} c \,x^{2} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-3 \sqrt{c \,x^{2}+b}\, b c \,x^{2}-\left(c \,x^{2}+b \right)^{\frac{3}{2}} c \,x^{2}+\left(c \,x^{2}+b \right)^{\frac{5}{2}}\right)}{2 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b \,x^{5}}"," ",0,"-1/2*(c*x^4+b*x^2)^(3/2)*(3*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*b^(3/2)*x^2*c-(c*x^2+b)^(3/2)*c*x^2+(c*x^2+b)^(5/2)-3*(c*x^2+b)^(1/2)*x^2*b*c)/x^5/(c*x^2+b)^(3/2)/b","A"
256,1,125,65,0.008000," ","int((c*x^4+b*x^2)^(3/2)/x^8,x)","-\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{\frac{3}{2}} c^{2} x^{4} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-3 \sqrt{c \,x^{2}+b}\, b \,c^{2} x^{4}-\left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{2} x^{4}+\left(c \,x^{2}+b \right)^{\frac{5}{2}} c \,x^{2}+2 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b \right)}{8 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{2} x^{7}}"," ",0,"-1/8*(c*x^4+b*x^2)^(3/2)*(3*b^(3/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^4*c^2-(c*x^2+b)^(3/2)*c^2*x^4+(c*x^2+b)^(5/2)*x^2*c-3*(c*x^2+b)^(1/2)*x^4*b*c^2+2*(c*x^2+b)^(5/2)*b)/x^7/(c*x^2+b)^(3/2)/b^2","A"
257,1,145,89,0.011000," ","int((c*x^4+b*x^2)^(3/2)/x^10,x)","\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{\frac{3}{2}} c^{3} x^{6} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-3 \sqrt{c \,x^{2}+b}\, b \,c^{3} x^{6}-\left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{3} x^{6}+\left(c \,x^{2}+b \right)^{\frac{5}{2}} c^{2} x^{4}+2 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b c \,x^{2}-8 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b^{2}\right)}{48 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{3} x^{9}}"," ",0,"1/48*(c*x^4+b*x^2)^(3/2)*(3*b^(3/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^6*c^3-(c*x^2+b)^(3/2)*x^6*c^3+(c*x^2+b)^(5/2)*x^4*c^2-3*(c*x^2+b)^(1/2)*x^6*b*c^3+2*(c*x^2+b)^(5/2)*x^2*b*c-8*(c*x^2+b)^(5/2)*b^2)/x^9/(c*x^2+b)^(3/2)/b^3","A"
258,1,165,113,0.016000," ","int((c*x^4+b*x^2)^(3/2)/x^12,x)","-\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(3 b^{\frac{3}{2}} c^{4} x^{8} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-3 \sqrt{c \,x^{2}+b}\, b \,c^{4} x^{8}-\left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{4} x^{8}+\left(c \,x^{2}+b \right)^{\frac{5}{2}} c^{3} x^{6}+2 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b \,c^{2} x^{4}-8 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b^{2} c \,x^{2}+16 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b^{3}\right)}{128 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{4} x^{11}}"," ",0,"-1/128*(c*x^4+b*x^2)^(3/2)*(3*b^(3/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^8*c^4-(c*x^2+b)^(3/2)*x^8*c^4+(c*x^2+b)^(5/2)*x^6*c^3-3*(c*x^2+b)^(1/2)*x^8*b*c^4+2*(c*x^2+b)^(5/2)*x^4*b*c^2-8*(c*x^2+b)^(5/2)*x^2*b^2*c+16*(c*x^2+b)^(5/2)*b^3)/x^11/(c*x^2+b)^(3/2)/b^4","A"
259,1,186,137,0.031000," ","int((c*x^4+b*x^2)^(3/2)/x^14,x)","\frac{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(15 b^{\frac{3}{2}} c^{5} x^{10} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-15 \sqrt{c \,x^{2}+b}\, b \,c^{5} x^{10}-5 \left(c \,x^{2}+b \right)^{\frac{3}{2}} c^{5} x^{10}+5 \left(c \,x^{2}+b \right)^{\frac{5}{2}} c^{4} x^{8}+10 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b \,c^{3} x^{6}-40 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b^{2} c^{2} x^{4}+80 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b^{3} c \,x^{2}-128 \left(c \,x^{2}+b \right)^{\frac{5}{2}} b^{4}\right)}{1280 \left(c \,x^{2}+b \right)^{\frac{3}{2}} b^{5} x^{13}}"," ",0,"1/1280*(c*x^4+b*x^2)^(3/2)*(-5*(c*x^2+b)^(3/2)*x^10*c^5+15*b^(3/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^10*c^5+5*(c*x^2+b)^(5/2)*x^8*c^4-15*(c*x^2+b)^(1/2)*x^10*b*c^5+10*(c*x^2+b)^(5/2)*x^6*b*c^3-40*(c*x^2+b)^(5/2)*x^4*b^2*c^2+80*(c*x^2+b)^(5/2)*x^2*b^3*c-128*(c*x^2+b)^(5/2)*b^4)/x^13/(c*x^2+b)^(3/2)/b^5","A"
260,1,105,94,0.009000," ","int(x^7/(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b}\, \left(8 \sqrt{c \,x^{2}+b}\, c^{\frac{7}{2}} x^{5}-10 \sqrt{c \,x^{2}+b}\, b \,c^{\frac{5}{2}} x^{3}-15 b^{3} c \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+15 \sqrt{c \,x^{2}+b}\, b^{2} c^{\frac{3}{2}} x \right) x}{48 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{\frac{9}{2}}}"," ",0,"1/48*x*(c*x^2+b)^(1/2)*(8*x^5*(c*x^2+b)^(1/2)*c^(7/2)-10*c^(5/2)*(c*x^2+b)^(1/2)*x^3*b+15*c^(3/2)*(c*x^2+b)^(1/2)*x*b^2-15*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*b^3*c)/(c*x^4+b*x^2)^(1/2)/c^(9/2)","A"
261,1,85,70,0.009000," ","int(x^5/(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b}\, \left(2 \sqrt{c \,x^{2}+b}\, c^{\frac{5}{2}} x^{3}+3 b^{2} c \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)-3 \sqrt{c \,x^{2}+b}\, b \,c^{\frac{3}{2}} x \right) x}{8 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{\frac{7}{2}}}"," ",0,"1/8*x*(c*x^2+b)^(1/2)*(2*x^3*(c*x^2+b)^(1/2)*c^(5/2)-3*c^(3/2)*(c*x^2+b)^(1/2)*x*b+3*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*b^2*c)/(c*x^4+b*x^2)^(1/2)/c^(7/2)","A"
262,1,64,46,0.007000," ","int(x^3/(c*x^4+b*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b}\, \left(b c \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)-\sqrt{c \,x^{2}+b}\, c^{\frac{3}{2}} x \right) x}{2 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{\frac{5}{2}}}"," ",0,"-1/2*x*(c*x^2+b)^(1/2)*(-x*(c*x^2+b)^(1/2)*c^(3/2)+b*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*c)/(c*x^4+b*x^2)^(1/2)/c^(5/2)","A"
263,1,44,25,0.003000," ","int(x/(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b}\, x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)}{\sqrt{c \,x^{4}+b \,x^{2}}\, \sqrt{c}}"," ",0,"1/(c*x^4+b*x^2)^(1/2)*x*(c*x^2+b)^(1/2)*ln(c^(1/2)*x+(c*x^2+b)^(1/2))/c^(1/2)","A"
264,1,26,21,0.005000," ","int(1/x/(c*x^4+b*x^2)^(1/2),x)","-\frac{c \,x^{2}+b}{\sqrt{c \,x^{4}+b \,x^{2}}\, b}"," ",0,"-(c*x^2+b)/b/(c*x^4+b*x^2)^(1/2)","A"
265,1,37,44,0.004000," ","int(1/x^3/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-2 c \,x^{2}+b \right)}{3 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{2} x^{2}}"," ",0,"-1/3*(c*x^2+b)*(-2*c*x^2+b)/x^2/b^2/(c*x^4+b*x^2)^(1/2)","A"
266,1,50,68,0.005000," ","int(1/x^5/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(8 c^{2} x^{4}-4 b c \,x^{2}+3 b^{2}\right)}{15 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{3} x^{4}}"," ",0,"-1/15*(c*x^2+b)*(8*c^2*x^4-4*b*c*x^2+3*b^2)/x^4/b^3/(c*x^4+b*x^2)^(1/2)","A"
267,1,61,92,0.007000," ","int(1/x^7/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-16 c^{3} x^{6}+8 b \,c^{2} x^{4}-6 b^{2} c \,x^{2}+5 b^{3}\right)}{35 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{4} x^{6}}"," ",0,"-1/35*(c*x^2+b)*(-16*c^3*x^6+8*b*c^2*x^4-6*b^2*c*x^2+5*b^3)/x^6/b^4/(c*x^4+b*x^2)^(1/2)","A"
268,1,37,42,0.004000," ","int(x^4/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-c \,x^{2}+2 b \right) x}{3 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{2}}"," ",0,"-1/3*(c*x^2+b)*(-c*x^2+2*b)*x/c^2/(c*x^4+b*x^2)^(1/2)","A"
269,1,26,20,0.003000," ","int(x^2/(c*x^4+b*x^2)^(1/2),x)","\frac{\left(c \,x^{2}+b \right) x}{\sqrt{c \,x^{4}+b \,x^{2}}\, c}"," ",0,"(c*x^2+b)/c*x/(c*x^4+b*x^2)^(1/2)","A"
270,1,50,24,0.005000," ","int(1/(c*x^4+b*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b}\, x \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)}{\sqrt{c \,x^{4}+b \,x^{2}}\, \sqrt{b}}"," ",0,"-1/(c*x^4+b*x^2)^(1/2)*x*(c*x^2+b)^(1/2)/b^(1/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)","B"
271,1,73,47,0.006000," ","int(1/x^2/(c*x^4+b*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b}\, \left(-b c \,x^{2} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)+\sqrt{c \,x^{2}+b}\, b^{\frac{3}{2}}\right)}{2 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{\frac{5}{2}} x}"," ",0,"-1/2/x*(c*x^2+b)^(1/2)*(-c*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^2*b+(c*x^2+b)^(1/2)*b^(3/2))/(c*x^4+b*x^2)^(1/2)/b^(5/2)","A"
272,1,94,71,0.009000," ","int(1/x^4/(c*x^4+b*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b}\, \left(3 b \,c^{2} x^{4} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-3 \sqrt{c \,x^{2}+b}\, b^{\frac{3}{2}} c \,x^{2}+2 \sqrt{c \,x^{2}+b}\, b^{\frac{5}{2}}\right)}{8 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{\frac{7}{2}} x^{3}}"," ",0,"-1/8*(c*x^2+b)^(1/2)*(3*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^4*b*c^2-3*b^(3/2)*(c*x^2+b)^(1/2)*x^2*c+2*(c*x^2+b)^(1/2)*b^(5/2))/x^3/(c*x^4+b*x^2)^(1/2)/b^(7/2)","A"
273,1,87,91,0.010000," ","int(x^9/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(2 c^{\frac{7}{2}} x^{5}-5 b \,c^{\frac{5}{2}} x^{3}-15 b^{2} c^{\frac{3}{2}} x +15 \sqrt{c \,x^{2}+b}\, b^{2} c \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)\right) x^{3}}{8 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{\frac{9}{2}}}"," ",0,"1/8*x^3*(c*x^2+b)*(2*x^5*c^(7/2)-5*c^(5/2)*x^3*b-15*c^(3/2)*x*b^2+15*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*(c*x^2+b)^(1/2)*b^2*c)/(c*x^4+b*x^2)^(3/2)/c^(9/2)","A"
274,1,73,67,0.007000," ","int(x^7/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(c^{\frac{5}{2}} x^{3}+3 b \,c^{\frac{3}{2}} x -3 \sqrt{c \,x^{2}+b}\, b c \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)\right) x^{3}}{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{\frac{7}{2}}}"," ",0,"1/2*x^3*(c*x^2+b)*(x^3*c^(5/2)+3*c^(3/2)*x*b-3*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*(c*x^2+b)^(1/2)*b*c)/(c*x^4+b*x^2)^(3/2)/c^(7/2)","A"
275,1,63,47,0.007000," ","int(x^5/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(c^{\frac{3}{2}} x -\sqrt{c \,x^{2}+b}\, c \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)\right) x^{3}}{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{\frac{5}{2}}}"," ",0,"-x^3*(c*x^2+b)*(x*c^(3/2)-ln(c^(1/2)*x+(c*x^2+b)^(1/2))*c*(c*x^2+b)^(1/2))/(c*x^4+b*x^2)^(3/2)/c^(5/2)","A"
276,1,28,20,0.003000," ","int(x^3/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) x^{4}}{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b}"," ",0,"(c*x^2+b)/b*x^4/(c*x^4+b*x^2)^(3/2)","A"
277,1,37,27,0.005000," ","int(x/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(2 c \,x^{2}+b \right) x^{2}}{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"-x^2*(c*x^2+b)*(2*c*x^2+b)/b^2/(c*x^4+b*x^2)^(3/2)","A"
278,1,45,64,0.006000," ","int(1/x/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-8 c^{2} x^{4}-4 b c \,x^{2}+b^{2}\right)}{3 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"-1/3*(c*x^2+b)*(-8*c^2*x^4-4*b*c*x^2+b^2)/b^3/(c*x^4+b*x^2)^(3/2)","A"
279,1,59,88,0.005000," ","int(1/x^3/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(16 c^{3} x^{6}+8 b \,c^{2} x^{4}-2 b^{2} c \,x^{2}+b^{3}\right)}{5 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{4} x^{2}}"," ",0,"-1/5*(c*x^2+b)*(16*c^3*x^6+8*b*c^2*x^4-2*b^2*c*x^2+b^3)/x^2/b^4/(c*x^4+b*x^2)^(3/2)","A"
280,1,72,112,0.006000," ","int(1/x^5/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-128 c^{4} x^{8}-64 c^{3} x^{6} b +16 c^{2} x^{4} b^{2}-8 c \,x^{2} b^{3}+5 b^{4}\right)}{35 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{5} x^{4}}"," ",0,"-1/35*(c*x^2+b)*(-128*c^4*x^8-64*b*c^3*x^6+16*b^2*c^2*x^4-8*b^3*c*x^2+5*b^4)/x^4/b^5/(c*x^4+b*x^2)^(3/2)","A"
281,1,37,43,0.004000," ","int(x^6/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(c \,x^{2}+2 b \right) x^{3}}{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{2}}"," ",0,"(c*x^2+b)*(c*x^2+2*b)*x^3/c^2/(c*x^4+b*x^2)^(3/2)","A"
282,1,29,19,0.003000," ","int(x^4/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) x^{3}}{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c}"," ",0,"-(c*x^2+b)/c*x^3/(c*x^4+b*x^2)^(3/2)","A"
283,1,65,43,0.007000," ","int(x^2/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(-\sqrt{c \,x^{2}+b}\, b \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)+b^{\frac{3}{2}}\right) x^{3}}{\left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{\frac{5}{2}}}"," ",0,"x^3*(c*x^2+b)*(b^(3/2)-ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*b*(c*x^2+b)^(1/2))/(c*x^4+b*x^2)^(3/2)/b^(5/2)","A"
284,1,77,67,0.006000," ","int(1/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-3 \sqrt{c \,x^{2}+b}\, b c \,x^{2} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)+3 b^{\frac{3}{2}} c \,x^{2}+b^{\frac{5}{2}}\right) x}{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{\frac{7}{2}}}"," ",0,"-1/2*x*(c*x^2+b)*(3*b^(3/2)*x^2*c-3*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*(c*x^2+b)^(1/2)*x^2*b*c+b^(5/2))/(c*x^4+b*x^2)^(3/2)/b^(7/2)","A"
285,1,94,91,0.008000," ","int(1/x^2/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(15 \sqrt{c \,x^{2}+b}\, b \,c^{2} x^{4} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-15 b^{\frac{3}{2}} c^{2} x^{4}-5 b^{\frac{5}{2}} c \,x^{2}+2 b^{\frac{7}{2}}\right)}{8 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{\frac{9}{2}} x}"," ",0,"-1/8/x*(c*x^2+b)*(15*(c*x^2+b)^(1/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^4*b*c^2-15*b^(3/2)*x^4*c^2-5*b^(5/2)*x^2*c+2*b^(7/2))/(c*x^4+b*x^2)^(3/2)/b^(9/2)","A"
286,1,48,26,0.008000," ","int(x^3/(-4*x^4+3*x^2)^(1/2),x)","\frac{\sqrt{-4 x^{2}+3}\, \left(-2 \sqrt{-4 x^{2}+3}\, x +3 \arcsin \left(\frac{2 \sqrt{3}\, x}{3}\right)\right) x}{16 \sqrt{-4 x^{4}+3 x^{2}}}"," ",0,"1/16*x*(-4*x^2+3)^(1/2)*(-2*x*(-4*x^2+3)^(1/2)+3*arcsin(2/3*3^(1/2)*x))/(-4*x^4+3*x^2)^(1/2)","A"
287,1,54,26,0.006000," ","int(x^3/(-4*x^4-3*x^2)^(1/2),x)","-\frac{\sqrt{-4 x^{2}-3}\, \left(2 \sqrt{-4 x^{2}-3}\, x +3 \arctan \left(\frac{2 x}{\sqrt{-4 x^{2}-3}}\right)\right) x}{16 \sqrt{-4 x^{4}-3 x^{2}}}"," ",0,"-1/16*x*(-4*x^2-3)^(1/2)*(2*x*(-4*x^2-3)^(1/2)+3*arctan(2*x/(-4*x^2-3)^(1/2)))/(-4*x^4-3*x^2)^(1/2)","B"
288,1,48,37,0.007000," ","int(x^3/(4*x^4+3*x^2)^(1/2),x)","-\frac{\sqrt{4 x^{2}+3}\, \left(-2 \sqrt{4 x^{2}+3}\, x +3 \arcsinh \left(\frac{2 \sqrt{3}\, x}{3}\right)\right) x}{16 \sqrt{4 x^{4}+3 x^{2}}}"," ",0,"-1/16*x*(4*x^2+3)^(1/2)*(-2*x*(4*x^2+3)^(1/2)+3*arcsinh(2/3*3^(1/2)*x))/(4*x^4+3*x^2)^(1/2)","A"
289,1,60,37,0.007000," ","int(x^3/(4*x^4-3*x^2)^(1/2),x)","\frac{\sqrt{4 x^{2}-3}\, \left(4 \sqrt{4 x^{2}-3}\, x +3 \sqrt{4}\, \ln \left(\sqrt{4}\, x +\sqrt{4 x^{2}-3}\right)\right) x}{32 \sqrt{4 x^{4}-3 x^{2}}}"," ",0,"1/32*x*(4*x^2-3)^(1/2)*(3*ln(x*4^(1/2)+(4*x^2-3)^(1/2))*4^(1/2)+4*x*(4*x^2-3)^(1/2))/(4*x^4-3*x^2)^(1/2)","A"
290,1,64,46,0.007000," ","int(x^3/(b*x^4+a*x^2)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \left(-a b \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)+\sqrt{b \,x^{2}+a}\, b^{\frac{3}{2}} x \right) x}{2 \sqrt{b \,x^{4}+a \,x^{2}}\, b^{\frac{5}{2}}}"," ",0,"1/2*x*(b*x^2+a)^(1/2)*(x*(b*x^2+a)^(1/2)*b^(3/2)-a*ln(b^(1/2)*x+(b*x^2+a)^(1/2))*b)/(b*x^4+a*x^2)^(1/2)/b^(5/2)","A"
291,1,67,48,0.009000," ","int(x^3/(-b*x^4+a*x^2)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \left(a b \arctan \left(\frac{\sqrt{b}\, x}{\sqrt{-b \,x^{2}+a}}\right)-\sqrt{-b \,x^{2}+a}\, b^{\frac{3}{2}} x \right) x}{2 \sqrt{-b \,x^{4}+a \,x^{2}}\, b^{\frac{5}{2}}}"," ",0,"1/2*x*(-b*x^2+a)^(1/2)*(-x*(-b*x^2+a)^(1/2)*b^(3/2)+a*arctan(b^(1/2)*x/(-b*x^2+a)^(1/2))*b)/(-b*x^4+a*x^2)^(1/2)/b^(5/2)","A"
292,1,16,13,0.003000," ","int(x^(7/2)*(c*x^4+b*x^2),x)","\frac{2 \left(13 c \,x^{2}+17 b \right) x^{\frac{13}{2}}}{221}"," ",0,"2/221*x^(13/2)*(13*c*x^2+17*b)","A"
293,1,16,13,0.004000," ","int(x^(5/2)*(c*x^4+b*x^2),x)","\frac{2 \left(11 c \,x^{2}+15 b \right) x^{\frac{11}{2}}}{165}"," ",0,"2/165*x^(11/2)*(11*c*x^2+15*b)","A"
294,1,16,13,0.004000," ","int(x^(3/2)*(c*x^4+b*x^2),x)","\frac{2 \left(9 c \,x^{2}+13 b \right) x^{\frac{9}{2}}}{117}"," ",0,"2/117*x^(9/2)*(9*c*x^2+13*b)","A"
295,1,16,13,0.003000," ","int(x^(1/2)*(c*x^4+b*x^2),x)","\frac{2 \left(7 c \,x^{2}+11 b \right) x^{\frac{7}{2}}}{77}"," ",0,"2/77*x^(7/2)*(7*c*x^2+11*b)","A"
296,1,16,13,0.003000," ","int((c*x^4+b*x^2)/x^(1/2),x)","\frac{2 \left(5 c \,x^{2}+9 b \right) x^{\frac{5}{2}}}{45}"," ",0,"2/45*x^(5/2)*(5*c*x^2+9*b)","A"
297,1,16,13,0.004000," ","int((c*x^4+b*x^2)/x^(3/2),x)","\frac{2 \left(3 c \,x^{2}+7 b \right) x^{\frac{3}{2}}}{21}"," ",0,"2/21*x^(3/2)*(3*c*x^2+7*b)","A"
298,1,15,13,0.003000," ","int((c*x^4+b*x^2)/x^(5/2),x)","\frac{2 \left(c \,x^{2}+5 b \right) \sqrt{x}}{5}"," ",0,"2/5*x^(1/2)*(c*x^2+5*b)","A"
299,1,16,13,0.004000," ","int((c*x^4+b*x^2)/x^(7/2),x)","-\frac{2 \left(-c \,x^{2}+3 b \right)}{3 \sqrt{x}}"," ",0,"-2/3/x^(1/2)*(-c*x^2+3*b)","A"
300,1,27,24,0.006000," ","int(x^(7/2)*(c*x^4+b*x^2)^2,x)","\frac{2 \left(357 c^{2} x^{4}+850 b c \,x^{2}+525 b^{2}\right) x^{\frac{17}{2}}}{8925}"," ",0,"2/8925*x^(17/2)*(357*c^2*x^4+850*b*c*x^2+525*b^2)","A"
301,1,27,24,0.006000," ","int(x^(5/2)*(c*x^4+b*x^2)^2,x)","\frac{2 \left(285 c^{2} x^{4}+690 b c \,x^{2}+437 b^{2}\right) x^{\frac{15}{2}}}{6555}"," ",0,"2/6555*x^(15/2)*(285*c^2*x^4+690*b*c*x^2+437*b^2)","A"
302,1,27,24,0.006000," ","int(x^(3/2)*(c*x^4+b*x^2)^2,x)","\frac{2 \left(221 c^{2} x^{4}+546 b c \,x^{2}+357 b^{2}\right) x^{\frac{13}{2}}}{4641}"," ",0,"2/4641*x^(13/2)*(221*c^2*x^4+546*b*c*x^2+357*b^2)","A"
303,1,27,24,0.005000," ","int(x^(1/2)*(c*x^4+b*x^2)^2,x)","\frac{2 \left(165 c^{2} x^{4}+418 b c \,x^{2}+285 b^{2}\right) x^{\frac{11}{2}}}{3135}"," ",0,"2/3135*x^(11/2)*(165*c^2*x^4+418*b*c*x^2+285*b^2)","A"
304,1,27,24,0.006000," ","int((c*x^4+b*x^2)^2/x^(1/2),x)","\frac{2 \left(117 c^{2} x^{4}+306 b c \,x^{2}+221 b^{2}\right) x^{\frac{9}{2}}}{1989}"," ",0,"2/1989*x^(9/2)*(117*c^2*x^4+306*b*c*x^2+221*b^2)","A"
305,1,27,24,0.006000," ","int((c*x^4+b*x^2)^2/x^(3/2),x)","\frac{2 \left(77 c^{2} x^{4}+210 b c \,x^{2}+165 b^{2}\right) x^{\frac{7}{2}}}{1155}"," ",0,"2/1155*x^(7/2)*(77*c^2*x^4+210*b*c*x^2+165*b^2)","A"
306,1,27,24,0.004000," ","int((c*x^4+b*x^2)^2/x^(5/2),x)","\frac{2 \left(45 c^{2} x^{4}+130 b c \,x^{2}+117 b^{2}\right) x^{\frac{5}{2}}}{585}"," ",0,"2/585*x^(5/2)*(45*c^2*x^4+130*b*c*x^2+117*b^2)","A"
307,1,27,24,0.007000," ","int((c*x^4+b*x^2)^2/x^(7/2),x)","\frac{2 \left(21 c^{2} x^{4}+66 b c \,x^{2}+77 b^{2}\right) x^{\frac{3}{2}}}{231}"," ",0,"2/231*x^(3/2)*(21*c^2*x^4+66*b*c*x^2+77*b^2)","A"
308,1,38,35,0.006000," ","int(x^(7/2)*(c*x^4+b*x^2)^3,x)","\frac{2 \left(5075 c^{3} x^{6}+17325 b \,c^{2} x^{4}+20097 b^{2} c \,x^{2}+7975 b^{3}\right) x^{\frac{21}{2}}}{167475}"," ",0,"2/167475*x^(21/2)*(5075*c^3*x^6+17325*b*c^2*x^4+20097*b^2*c*x^2+7975*b^3)","A"
309,1,38,35,0.005000," ","int(x^(5/2)*(c*x^4+b*x^2)^3,x)","\frac{2 \left(3933 c^{3} x^{6}+13547 b \,c^{2} x^{4}+15903 b^{2} c \,x^{2}+6417 b^{3}\right) x^{\frac{19}{2}}}{121923}"," ",0,"2/121923*x^(19/2)*(3933*c^3*x^6+13547*b*c^2*x^4+15903*b^2*c*x^2+6417*b^3)","A"
310,1,38,35,0.005000," ","int(x^(3/2)*(c*x^4+b*x^2)^3,x)","\frac{2 \left(2975 c^{3} x^{6}+10353 b \,c^{2} x^{4}+12325 b^{2} c \,x^{2}+5075 b^{3}\right) x^{\frac{17}{2}}}{86275}"," ",0,"2/86275*x^(17/2)*(2975*c^3*x^6+10353*b*c^2*x^4+12325*b^2*c*x^2+5075*b^3)","A"
311,1,38,35,0.007000," ","int(x^(1/2)*(c*x^4+b*x^2)^3,x)","\frac{2 \left(2185 c^{3} x^{6}+7695 b \,c^{2} x^{4}+9315 b^{2} c \,x^{2}+3933 b^{3}\right) x^{\frac{15}{2}}}{58995}"," ",0,"2/58995*x^(15/2)*(2185*c^3*x^6+7695*b*c^2*x^4+9315*b^2*c*x^2+3933*b^3)","A"
312,1,38,35,0.005000," ","int((c*x^4+b*x^2)^3/x^(1/2),x)","\frac{2 \left(1547 c^{3} x^{6}+5525 b \,c^{2} x^{4}+6825 b^{2} c \,x^{2}+2975 b^{3}\right) x^{\frac{13}{2}}}{38675}"," ",0,"2/38675*x^(13/2)*(1547*c^3*x^6+5525*b*c^2*x^4+6825*b^2*c*x^2+2975*b^3)","A"
313,1,38,35,0.006000," ","int((c*x^4+b*x^2)^3/x^(3/2),x)","\frac{2 \left(1045 c^{3} x^{6}+3795 b \,c^{2} x^{4}+4807 b^{2} c \,x^{2}+2185 b^{3}\right) x^{\frac{11}{2}}}{24035}"," ",0,"2/24035*x^(11/2)*(1045*c^3*x^6+3795*b*c^2*x^4+4807*b^2*c*x^2+2185*b^3)","A"
314,1,38,35,0.006000," ","int((c*x^4+b*x^2)^3/x^(5/2),x)","\frac{2 \left(663 c^{3} x^{6}+2457 b \,c^{2} x^{4}+3213 b^{2} c \,x^{2}+1547 b^{3}\right) x^{\frac{9}{2}}}{13923}"," ",0,"2/13923*x^(9/2)*(663*c^3*x^6+2457*b*c^2*x^4+3213*b^2*c*x^2+1547*b^3)","A"
315,1,38,35,0.004000," ","int((c*x^4+b*x^2)^3/x^(7/2),x)","\frac{2 \left(385 c^{3} x^{6}+1463 b \,c^{2} x^{4}+1995 b^{2} c \,x^{2}+1045 b^{3}\right) x^{\frac{7}{2}}}{7315}"," ",0,"2/7315*x^(7/2)*(385*c^3*x^6+1463*b*c^2*x^4+1995*b^2*c*x^2+1045*b^3)","A"
316,1,158,142,0.014000," ","int(x^(13/2)/(c*x^4+b*x^2),x)","\frac{2 x^{\frac{7}{2}}}{7 c}-\frac{2 b \,x^{\frac{3}{2}}}{3 c^{2}}+\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}+\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}+\frac{\sqrt{2}\, b^{2} \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}"," ",0,"2/7*x^(7/2)/c-2/3*b*x^(3/2)/c^2+1/4*b^2/c^3/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*x^(1/2)*2^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*x^(1/2)*2^(1/2)+(b/c)^(1/2)))+1/2*b^2/c^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+1/2*b^2/c^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
317,1,152,142,0.008000," ","int(x^(11/2)/(c*x^4+b*x^2),x)","\frac{2 x^{\frac{5}{2}}}{5 c}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 c^{2}}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 c^{2}}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 c^{2}}-\frac{2 b \sqrt{x}}{c^{2}}"," ",0,"2/5*x^(5/2)/c-2*b*x^(1/2)/c^2+1/4*b/c^2*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+1/2*b/c^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+1/2*b/c^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
318,1,143,133,0.006000," ","int(x^(9/2)/(c*x^4+b*x^2),x)","\frac{2 x^{\frac{3}{2}}}{3 c}-\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{2}}-\frac{\sqrt{2}\, b \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{2}}"," ",0,"2/3*x^(3/2)/c-1/4*b/c^2/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-1/2*b/c^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-1/2*b/c^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
319,1,140,133,0.007000," ","int(x^(7/2)/(c*x^4+b*x^2),x)","-\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 c}-\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 c}-\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 c}+\frac{2 \sqrt{x}}{c}"," ",0,"2*x^(1/2)/c-1/4/c*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-1/2/c*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-1/2/c*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
320,1,132,125,0.005000," ","int(x^(5/2)/(c*x^4+b*x^2),x)","\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 \left(\frac{b}{c}\right)^{\frac{1}{4}} c}"," ",0,"1/4/c/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+1/2/c/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+1/2/c/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
321,1,132,125,0.006000," ","int(x^(3/2)/(c*x^4+b*x^2),x)","\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 b}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 b}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 b}"," ",0,"1/4*(b/c)^(1/4)/b*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+1/2*(b/c)^(1/4)/b*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+1/2*(b/c)^(1/4)/b*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
322,1,140,133,0.008000," ","int(x^(1/2)/(c*x^4+b*x^2),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} b}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} b}-\frac{\sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 \left(\frac{b}{c}\right)^{\frac{1}{4}} b}-\frac{2}{b \sqrt{x}}"," ",0,"-1/4/b/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-1/2/b/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-1/2/b/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/b/x^(1/2)","A"
323,1,143,133,0.011000," ","int(1/(c*x^4+b*x^2)/x^(1/2),x)","-\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 b^{2}}-\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 b^{2}}-\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 b^{2}}-\frac{2}{3 b \,x^{\frac{3}{2}}}"," ",0,"-1/4*c/b^2*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-1/2*c/b^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-1/2*c/b^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/3/b/x^(3/2)","A"
324,1,152,142,0.011000," ","int(1/x^(3/2)/(c*x^4+b*x^2),x)","\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2}}+\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2}}+\frac{\sqrt{2}\, c \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2}}+\frac{2 c}{b^{2} \sqrt{x}}-\frac{2}{5 b \,x^{\frac{5}{2}}}"," ",0,"1/4*c/b^2/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+1/2*c/b^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+1/2*c/b^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/5/b/x^(5/2)+2*c/b^2/x^(1/2)","A"
325,1,158,142,0.011000," ","int(1/x^(5/2)/(c*x^4+b*x^2),x)","\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 b^{3}}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 b^{3}}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 b^{3}}+\frac{2 c}{3 b^{2} x^{\frac{3}{2}}}-\frac{2}{7 b \,x^{\frac{7}{2}}}"," ",0,"1/4*c^2/b^3*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+1/2*c^2/b^3*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+1/2*c^2/b^3*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/7/b/x^(7/2)+2/3*c/b^2/x^(3/2)","A"
326,1,169,153,0.013000," ","int(1/x^(7/2)/(c*x^4+b*x^2),x)","-\frac{\sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}-\frac{\sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{2 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}-\frac{\sqrt{2}\, c^{2} \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{4 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}-\frac{2 c^{2}}{b^{3} \sqrt{x}}+\frac{2 c}{5 b^{2} x^{\frac{5}{2}}}-\frac{2}{9 b \,x^{\frac{9}{2}}}"," ",0,"-1/4*c^2/b^3/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-1/2*c^2/b^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-1/2*c^2/b^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/9/b/x^(9/2)-2*c^2/b^3/x^(1/2)+2/5*c/b^2/x^(5/2)","A"
327,1,172,159,0.014000," ","int(x^(19/2)/(c*x^4+b*x^2)^2,x)","\frac{2 x^{\frac{5}{2}}}{5 c^{2}}-\frac{b^{2} \sqrt{x}}{2 \left(c \,x^{2}+b \right) c^{3}}+\frac{9 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 c^{3}}+\frac{9 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 c^{3}}+\frac{9 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 c^{3}}-\frac{4 b \sqrt{x}}{c^{3}}"," ",0,"2/5*x^(5/2)/c^2-4*b*x^(1/2)/c^3-1/2/c^3*b^2*x^(1/2)/(c*x^2+b)+9/16/c^3*b*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+9/8/c^3*b*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+9/8/c^3*b*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
328,1,161,150,0.011000," ","int(x^(17/2)/(c*x^4+b*x^2)^2,x)","\frac{b \,x^{\frac{3}{2}}}{2 \left(c \,x^{2}+b \right) c^{2}}+\frac{2 x^{\frac{3}{2}}}{3 c^{2}}-\frac{7 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}-\frac{7 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}-\frac{7 \sqrt{2}\, b \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}"," ",0,"2/3*x^(3/2)/c^2+1/2*b/c^2*x^(3/2)/(c*x^2+b)-7/16*b/c^3/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-7/8*b/c^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-7/8*b/c^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
329,1,158,150,0.013000," ","int(x^(15/2)/(c*x^4+b*x^2)^2,x)","\frac{b \sqrt{x}}{2 \left(c \,x^{2}+b \right) c^{2}}-\frac{5 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 c^{2}}-\frac{5 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 c^{2}}-\frac{5 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 c^{2}}+\frac{2 \sqrt{x}}{c^{2}}"," ",0,"2*x^(1/2)/c^2+1/2*b/c^2*x^(1/2)/(c*x^2+b)-5/16/c^2*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-5/8/c^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-5/8/c^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
330,1,149,142,0.013000," ","int(x^(13/2)/(c*x^4+b*x^2)^2,x)","-\frac{x^{\frac{3}{2}}}{2 \left(c \,x^{2}+b \right) c}+\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{2}}+\frac{3 \sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{2}}"," ",0,"-1/2*x^(3/2)/c/(c*x^2+b)+3/16/c^2/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+3/8/c^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+3/8/c^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
331,1,158,142,0.012000," ","int(x^(11/2)/(c*x^4+b*x^2)^2,x)","-\frac{\sqrt{x}}{2 \left(c \,x^{2}+b \right) c}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 b c}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 b c}+\frac{\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 b c}"," ",0,"-1/2*x^(1/2)/c/(c*x^2+b)+1/16/c*(b/c)^(1/4)/b*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+1/8/c*(b/c)^(1/4)/b*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+1/8/c*(b/c)^(1/4)/b*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
332,1,158,142,0.010000," ","int(x^(9/2)/(c*x^4+b*x^2)^2,x)","\frac{x^{\frac{3}{2}}}{2 \left(c \,x^{2}+b \right) b}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} b c}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} b c}+\frac{\sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 \left(\frac{b}{c}\right)^{\frac{1}{4}} b c}"," ",0,"1/2*x^(3/2)/b/(c*x^2+b)+1/16/b/c/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+1/8/b/c/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+1/8/b/c/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
333,1,149,142,0.006000," ","int(x^(7/2)/(c*x^4+b*x^2)^2,x)","\frac{\sqrt{x}}{2 \left(c \,x^{2}+b \right) b}+\frac{3 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}+\frac{3 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}+\frac{3 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 b^{2}}"," ",0,"1/2*x^(1/2)/b/(c*x^2+b)+3/16/b^2*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+3/8/b^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+3/8/b^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
334,1,158,150,0.017000," ","int(x^(5/2)/(c*x^4+b*x^2)^2,x)","-\frac{c \,x^{\frac{3}{2}}}{2 \left(c \,x^{2}+b \right) b^{2}}-\frac{5 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2}}-\frac{5 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2}}-\frac{5 \sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2}}-\frac{2}{b^{2} \sqrt{x}}"," ",0,"-1/2/b^2*c*x^(3/2)/(c*x^2+b)-5/16/b^2/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-5/8/b^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-5/8/b^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/b^2/x^(1/2)","A"
335,1,161,150,0.015000," ","int(x^(3/2)/(c*x^4+b*x^2)^2,x)","-\frac{c \sqrt{x}}{2 \left(c \,x^{2}+b \right) b^{2}}-\frac{7 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 b^{3}}-\frac{7 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 b^{3}}-\frac{7 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 b^{3}}-\frac{2}{3 b^{2} x^{\frac{3}{2}}}"," ",0,"-1/2/b^2*c*x^(1/2)/(c*x^2+b)-7/16/b^3*c*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-7/8/b^3*c*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-7/8/b^3*c*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/3/b^2/x^(3/2)","A"
336,1,172,159,0.020000," ","int(x^(1/2)/(c*x^4+b*x^2)^2,x)","\frac{c^{2} x^{\frac{3}{2}}}{2 \left(c \,x^{2}+b \right) b^{3}}+\frac{9 \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}+\frac{9 \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}+\frac{9 \sqrt{2}\, c \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}+\frac{4 c}{b^{3} \sqrt{x}}-\frac{2}{5 b^{2} x^{\frac{5}{2}}}"," ",0,"1/2/b^3*c^2*x^(3/2)/(c*x^2+b)+9/16/b^3*c/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+9/8/b^3*c/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+9/8/b^3*c/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/5/b^2/x^(5/2)+4*c/b^3/x^(1/2)","A"
337,1,178,159,0.018000," ","int(1/(c*x^4+b*x^2)^2/x^(1/2),x)","\frac{c^{2} \sqrt{x}}{2 \left(c \,x^{2}+b \right) b^{3}}+\frac{11 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 b^{4}}+\frac{11 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 b^{4}}+\frac{11 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 b^{4}}+\frac{4 c}{3 b^{3} x^{\frac{3}{2}}}-\frac{2}{7 b^{2} x^{\frac{7}{2}}}"," ",0,"1/2/b^3*c^2*x^(1/2)/(c*x^2+b)+11/16/b^4*c^2*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+11/8/b^4*c^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+11/8/b^4*c^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/7/b^2/x^(7/2)+4/3*c/b^3/x^(3/2)","A"
338,1,189,170,0.017000," ","int(1/x^(3/2)/(c*x^4+b*x^2)^2,x)","-\frac{c^{3} x^{\frac{3}{2}}}{2 \left(c \,x^{2}+b \right) b^{4}}-\frac{13 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{4}}-\frac{13 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{4}}-\frac{13 \sqrt{2}\, c^{2} \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{16 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{4}}-\frac{6 c^{2}}{b^{4} \sqrt{x}}+\frac{4 c}{5 b^{3} x^{\frac{5}{2}}}-\frac{2}{9 b^{2} x^{\frac{9}{2}}}"," ",0,"-1/2/b^4*c^3*x^(3/2)/(c*x^2+b)-13/16/b^4*c^2/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-13/8/b^4*c^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-13/8/b^4*c^2/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/9/b^2/x^(9/2)-6*c^2/b^4/x^(1/2)+4/5*c/b^3/x^(5/2)","A"
339,1,178,167,0.017000," ","int(x^(23/2)/(c*x^4+b*x^2)^3,x)","\frac{17 b \,x^{\frac{5}{2}}}{16 \left(c \,x^{2}+b \right)^{2} c^{2}}+\frac{13 b^{2} \sqrt{x}}{16 \left(c \,x^{2}+b \right)^{2} c^{3}}-\frac{45 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 c^{3}}-\frac{45 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 c^{3}}-\frac{45 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 c^{3}}+\frac{2 \sqrt{x}}{c^{3}}"," ",0,"2*x^(1/2)/c^3+17/16/c^2*b/(c*x^2+b)^2*x^(5/2)+13/16/c^3*b^2/(c*x^2+b)^2*x^(1/2)-45/128/c^3*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-45/64/c^3*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-45/64/c^3*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
340,1,161,159,0.017000," ","int(x^(21/2)/(c*x^4+b*x^2)^3,x)","\frac{21 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}+\frac{21 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}+\frac{21 \sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 \left(\frac{b}{c}\right)^{\frac{1}{4}} c^{3}}+\frac{-\frac{11 x^{\frac{7}{2}}}{16 c}-\frac{7 b \,x^{\frac{3}{2}}}{16 c^{2}}}{\left(c \,x^{2}+b \right)^{2}}"," ",0,"2*(-11/32/c*x^(7/2)-7/32*b/c^2*x^(3/2))/(c*x^2+b)^2+21/128/c^3/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+21/64/c^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+21/64/c^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
341,1,170,159,0.016000," ","int(x^(19/2)/(c*x^4+b*x^2)^3,x)","\frac{5 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 b \,c^{2}}+\frac{5 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 b \,c^{2}}+\frac{5 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 b \,c^{2}}+\frac{-\frac{9 x^{\frac{5}{2}}}{16 c}-\frac{5 b \sqrt{x}}{16 c^{2}}}{\left(c \,x^{2}+b \right)^{2}}"," ",0,"2*(-9/32/c*x^(5/2)-5/32*b/c^2*x^(1/2))/(c*x^2+b)^2+5/128/c^2*(b/c)^(1/4)/b*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+5/64/c^2*(b/c)^(1/4)/b*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+5/64/c^2*(b/c)^(1/4)/b*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
342,1,169,162,0.017000," ","int(x^(17/2)/(c*x^4+b*x^2)^3,x)","\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b \,c^{2}}+\frac{3 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b \,c^{2}}+\frac{3 \sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 \left(\frac{b}{c}\right)^{\frac{1}{4}} b \,c^{2}}+\frac{\frac{3 x^{\frac{7}{2}}}{16 b}-\frac{x^{\frac{3}{2}}}{16 c}}{\left(c \,x^{2}+b \right)^{2}}"," ",0,"2*(3/32/b*x^(7/2)-1/32/c*x^(3/2))/(c*x^2+b)^2+3/128/c^2/b/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+3/64/c^2/b/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+3/64/c^2/b/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
343,1,169,162,0.015000," ","int(x^(15/2)/(c*x^4+b*x^2)^3,x)","\frac{3 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 b^{2} c}+\frac{3 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 b^{2} c}+\frac{3 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 b^{2} c}+\frac{\frac{x^{\frac{5}{2}}}{16 b}-\frac{3 \sqrt{x}}{16 c}}{\left(c \,x^{2}+b \right)^{2}}"," ",0,"2*(1/32/b*x^(5/2)-3/32/c*x^(1/2))/(c*x^2+b)^2+3/128/c/b^2*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+3/64/c/b^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+3/64/c/b^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
344,1,175,159,0.010000," ","int(x^(13/2)/(c*x^4+b*x^2)^3,x)","\frac{x^{\frac{3}{2}}}{4 \left(c \,x^{2}+b \right)^{2} b}+\frac{5 x^{\frac{3}{2}}}{16 \left(c \,x^{2}+b \right) b^{2}}+\frac{5 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2} c}+\frac{5 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2} c}+\frac{5 \sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{2} c}"," ",0,"1/4*x^(3/2)/b/(c*x^2+b)^2+5/16*x^(3/2)/b^2/(c*x^2+b)+5/128/b^2/c/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+5/64/b^2/c/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+5/64/b^2/c/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
345,1,166,159,0.008000," ","int(x^(11/2)/(c*x^4+b*x^2)^3,x)","\frac{\sqrt{x}}{4 \left(c \,x^{2}+b \right)^{2} b}+\frac{7 \sqrt{x}}{16 \left(c \,x^{2}+b \right) b^{2}}+\frac{21 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 b^{3}}+\frac{21 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 b^{3}}+\frac{21 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 b^{3}}"," ",0,"1/4*x^(1/2)/b/(c*x^2+b)^2+7/16*x^(1/2)/b^2/(c*x^2+b)+21/128/b^3*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+21/64/b^3*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+21/64/b^3*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)","A"
346,1,178,167,0.019000," ","int(x^(9/2)/(c*x^4+b*x^2)^3,x)","-\frac{13 c^{2} x^{\frac{7}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{3}}-\frac{17 c \,x^{\frac{3}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{2}}-\frac{45 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}-\frac{45 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}-\frac{45 \sqrt{2}\, \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{3}}-\frac{2}{b^{3} \sqrt{x}}"," ",0,"-13/16*c^2/b^3/(c*x^2+b)^2*x^(7/2)-17/16*c/b^2/(c*x^2+b)^2*x^(3/2)-45/128/b^3/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-45/64/b^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-45/64/b^3/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/b^3/x^(1/2)","A"
347,1,181,167,0.018000," ","int(x^(7/2)/(c*x^4+b*x^2)^3,x)","-\frac{15 c^{2} x^{\frac{5}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{3}}-\frac{19 c \sqrt{x}}{16 \left(c \,x^{2}+b \right)^{2} b^{2}}-\frac{77 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 b^{4}}-\frac{77 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 b^{4}}-\frac{77 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 b^{4}}-\frac{2}{3 b^{3} x^{\frac{3}{2}}}"," ",0,"-15/16*c^2/b^3/(c*x^2+b)^2*x^(5/2)-19/16*c/b^2/(c*x^2+b)^2*x^(1/2)-77/128*c/b^4*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-77/64*c/b^4*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-77/64*c/b^4*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/3/b^3/x^(3/2)","A"
348,1,192,176,0.022000," ","int(x^(5/2)/(c*x^4+b*x^2)^3,x)","\frac{21 c^{3} x^{\frac{7}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{4}}+\frac{25 c^{2} x^{\frac{3}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{3}}+\frac{117 \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{4}}+\frac{117 \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{4}}+\frac{117 \sqrt{2}\, c \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{4}}+\frac{6 c}{b^{4} \sqrt{x}}-\frac{2}{5 b^{3} x^{\frac{5}{2}}}"," ",0,"21/16*c^3/b^4/(c*x^2+b)^2*x^(7/2)+25/16*c^2/b^3/(c*x^2+b)^2*x^(3/2)+117/128*c/b^4/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+117/64*c/b^4/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+117/64*c/b^4/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/5/b^3/x^(5/2)+6*c/b^4/x^(1/2)","A"
349,1,198,176,0.022000," ","int(x^(3/2)/(c*x^4+b*x^2)^3,x)","\frac{23 c^{3} x^{\frac{5}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{4}}+\frac{27 c^{2} \sqrt{x}}{16 \left(c \,x^{2}+b \right)^{2} b^{3}}+\frac{165 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 b^{5}}+\frac{165 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 b^{5}}+\frac{165 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 b^{5}}+\frac{2 c}{b^{4} x^{\frac{3}{2}}}-\frac{2}{7 b^{3} x^{\frac{7}{2}}}"," ",0,"23/16/b^4*c^3/(c*x^2+b)^2*x^(5/2)+27/16/b^3*c^2/(c*x^2+b)^2*x^(1/2)+165/128/b^5*c^2*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))+165/64/b^5*c^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)+165/64/b^5*c^2*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/7/b^3/x^(7/2)+2*c/b^4/x^(3/2)","A"
350,1,209,187,0.022000," ","int(x^(1/2)/(c*x^4+b*x^2)^3,x)","-\frac{29 c^{4} x^{\frac{7}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{5}}-\frac{33 c^{3} x^{\frac{3}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{4}}-\frac{221 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{5}}-\frac{221 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{5}}-\frac{221 \sqrt{2}\, c^{2} \ln \left(\frac{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 \left(\frac{b}{c}\right)^{\frac{1}{4}} b^{5}}-\frac{12 c^{2}}{b^{5} \sqrt{x}}+\frac{6 c}{5 b^{4} x^{\frac{5}{2}}}-\frac{2}{9 b^{3} x^{\frac{9}{2}}}"," ",0,"-29/16*c^4/b^5/(c*x^2+b)^2*x^(7/2)-33/16*c^3/b^4/(c*x^2+b)^2*x^(3/2)-221/128*c^2/b^5/(b/c)^(1/4)*2^(1/2)*ln((x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-221/64*c^2/b^5/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-221/64*c^2/b^5/(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/9/b^3/x^(9/2)-12*c^2/b^5/x^(1/2)+6/5*c/b^4/x^(5/2)","A"
351,1,209,187,0.021000," ","int(1/(c*x^4+b*x^2)^3/x^(1/2),x)","-\frac{31 c^{4} x^{\frac{5}{2}}}{16 \left(c \,x^{2}+b \right)^{2} b^{5}}-\frac{35 c^{3} \sqrt{x}}{16 \left(c \,x^{2}+b \right)^{2} b^{4}}-\frac{285 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}-1\right)}{64 b^{6}}-\frac{285 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{x}}{\left(\frac{b}{c}\right)^{\frac{1}{4}}}+1\right)}{64 b^{6}}-\frac{285 \left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \ln \left(\frac{x +\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}{x -\left(\frac{b}{c}\right)^{\frac{1}{4}} \sqrt{2}\, \sqrt{x}+\sqrt{\frac{b}{c}}}\right)}{128 b^{6}}-\frac{4 c^{2}}{b^{5} x^{\frac{3}{2}}}+\frac{6 c}{7 b^{4} x^{\frac{7}{2}}}-\frac{2}{11 b^{3} x^{\frac{11}{2}}}"," ",0,"-31/16*c^4/b^5/(c*x^2+b)^2*x^(5/2)-35/16*c^3/b^4/(c*x^2+b)^2*x^(1/2)-285/128*c^3/b^6*(b/c)^(1/4)*2^(1/2)*ln((x+(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2))/(x-(b/c)^(1/4)*2^(1/2)*x^(1/2)+(b/c)^(1/2)))-285/64*c^3/b^6*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)+1)-285/64*c^3/b^6*(b/c)^(1/4)*2^(1/2)*arctan(2^(1/2)/(b/c)^(1/4)*x^(1/2)-1)-2/11/b^3/x^(11/2)-4*c^2/b^5/x^(3/2)+6/7*c/b^4/x^(7/2)","A"
352,1,237,319,0.062000," ","int(x^(7/2)*(c*x^4+b*x^2)^(1/2),x)","\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(45 c^{4} x^{8}+55 b \,c^{3} x^{6}-4 b^{2} c^{2} x^{4}-14 b^{3} c \,x^{2}+42 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{4} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{4} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{585 \left(c \,x^{2}+b \right) c^{3} x^{\frac{3}{2}}}"," ",0,"2/585*(c*x^4+b*x^2)^(1/2)/x^(3/2)/(c*x^2+b)/c^3*(45*c^4*x^8+55*c^3*x^6*b+42*b^4*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-x*c/(-b*c)^(1/2))^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-21*b^4*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-x*c/(-b*c)^(1/2))^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-4*c^2*x^4*b^2-14*c*x^2*b^3)","A"
353,1,157,171,0.029000," ","int(x^(5/2)*(c*x^4+b*x^2)^(1/2),x)","\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(21 c^{4} x^{7}+27 b \,c^{3} x^{5}-4 b^{2} c^{2} x^{3}-10 b^{3} c x +5 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{231 \left(c \,x^{2}+b \right) c^{3} x^{\frac{3}{2}}}"," ",0,"2/231*(c*x^4+b*x^2)^(1/2)/x^(3/2)/(c*x^2+b)*(21*x^7*c^4+5*b^3*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+27*x^5*b*c^3-4*x^3*b^2*c^2-10*x*b^3*c)/c^3","A"
354,1,226,295,0.030000," ","int(x^(3/2)*(c*x^4+b*x^2)^(1/2),x)","-\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(-5 c^{3} x^{6}-7 b \,c^{2} x^{4}-2 b^{2} c \,x^{2}+6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{45 \left(c \,x^{2}+b \right) c^{2} x^{\frac{3}{2}}}"," ",0,"-2/45*(c*x^4+b*x^2)^(1/2)/x^(3/2)/(c*x^2+b)/c^2*(-5*c^3*x^6+6*b^3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-3*b^3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-7*b*c^2*x^4-2*b^2*c*x^2)","A"
355,1,145,147,0.028000," ","int(x^(1/2)*(c*x^4+b*x^2)^(1/2),x)","-\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(-3 c^{3} x^{5}-5 b \,c^{2} x^{3}-2 b^{2} c x +\sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{21 \left(c \,x^{2}+b \right) c^{2} x^{\frac{3}{2}}}"," ",0,"-2/21*(c*x^4+b*x^2)^(1/2)/x^(3/2)/(c*x^2+b)*(b^2*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-3*c^3*x^5-5*b*c^2*x^3-2*b^2*c*x)/c^2","A"
356,1,213,271,0.028000," ","int((c*x^4+b*x^2)^(1/2)/x^(1/2),x)","\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(c^{2} x^{4}+b c \,x^{2}+2 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{5 \left(c \,x^{2}+b \right) c \,x^{\frac{3}{2}}}"," ",0,"2/5*(c*x^4+b*x^2)^(1/2)/x^(3/2)/(c*x^2+b)/c*(2*b^2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-b^2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+c^2*x^4+b*c*x^2)","A"
357,1,130,125,0.028000," ","int((c*x^4+b*x^2)^(1/2)/x^(3/2),x)","\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(c^{2} x^{3}+b c x +\sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{3 \left(c \,x^{2}+b \right) c \,x^{\frac{3}{2}}}"," ",0,"2/3*(c*x^4+b*x^2)^(1/2)/x^(3/2)/(c*x^2+b)*(b*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+c^2*x^3+b*c*x)/c","A"
358,1,202,270,0.034000," ","int((c*x^4+b*x^2)^(1/2)/x^(5/2),x)","\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(-c \,x^{2}+2 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-b \right)}{\left(c \,x^{2}+b \right) x^{\frac{3}{2}}}"," ",0,"2*(c*x^4+b*x^2)^(1/2)/x^(3/2)/(c*x^2+b)*(2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-c*x^2-b)","A"
359,1,125,125,0.032000," ","int((c*x^4+b*x^2)^(1/2)/x^(7/2),x)","\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(-c \,x^{2}+\sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, x \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-b \right)}{3 \left(c \,x^{2}+b \right) x^{\frac{5}{2}}}"," ",0,"2/3*(c*x^4+b*x^2)^(1/2)/x^(5/2)/(c*x^2+b)*((-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x-c*x^2-b)","A"
360,1,224,295,0.035000," ","int((c*x^4+b*x^2)^(1/2)/x^(9/2),x)","\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(-2 c^{2} x^{4}+2 \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, b c \,x^{2} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, b c \,x^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-3 b c \,x^{2}-b^{2}\right)}{5 \left(c \,x^{2}+b \right) b \,x^{\frac{7}{2}}}"," ",0,"2/5*(c*x^4+b*x^2)^(1/2)/x^(7/2)/(c*x^2+b)*(2*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*x^2*b*c-(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*x^2*b*c-2*c^2*x^4-3*b*c*x^2-b^2)/b","A"
361,1,142,147,0.033000," ","int((c*x^4+b*x^2)^(1/2)/x^(11/2),x)","-\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(2 c^{2} x^{4}+\sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, c \,x^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+5 b c \,x^{2}+3 b^{2}\right)}{21 \left(c \,x^{2}+b \right) b \,x^{\frac{9}{2}}}"," ",0,"-2/21*(c*x^4+b*x^2)^(1/2)/x^(9/2)/(c*x^2+b)*(((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*x^3*c+2*c^2*x^4+5*b*c*x^2+3*b^2)/b","A"
362,1,239,319,0.036000," ","int((c*x^4+b*x^2)^(1/2)/x^(13/2),x)","-\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(-6 c^{3} x^{6}+6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{2} x^{4} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{2} x^{4} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-4 b \,c^{2} x^{4}+7 b^{2} c \,x^{2}+5 b^{3}\right)}{45 \left(c \,x^{2}+b \right) b^{2} x^{\frac{11}{2}}}"," ",0,"-2/45*(c*x^4+b*x^2)^(1/2)/x^(11/2)/(c*x^2+b)*(6*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b*c^2-3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b*c^2-6*c^3*x^6-4*b*c^2*x^4+7*b^2*c*x^2+5*b^3)/b^2","A"
363,1,156,171,0.035000," ","int((c*x^4+b*x^2)^(1/2)/x^(15/2),x)","\frac{2 \sqrt{c \,x^{4}+b \,x^{2}}\, \left(10 c^{3} x^{6}+5 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, c^{2} x^{5} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+4 b \,c^{2} x^{4}-27 b^{2} c \,x^{2}-21 b^{3}\right)}{231 \left(c \,x^{2}+b \right) b^{2} x^{\frac{13}{2}}}"," ",0,"2/231*(c*x^4+b*x^2)^(1/2)/x^(13/2)/(c*x^2+b)*(5*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*x^5*c^2+10*c^3*x^6+4*b*c^2*x^4-27*b^2*c*x^2-21*b^3)/b^2","A"
364,1,248,340,0.030000," ","int(x^(3/2)*(c*x^4+b*x^2)^(3/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(195 c^{5} x^{10}+480 b \,c^{4} x^{8}+305 b^{2} c^{3} x^{6}-8 b^{3} c^{2} x^{4}-28 b^{4} c \,x^{2}+84 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{5} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-42 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{5} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{3315 \left(c \,x^{2}+b \right)^{2} c^{3} x^{\frac{7}{2}}}"," ",0,"2/3315*(c*x^4+b*x^2)^(3/2)/x^(7/2)/(c*x^2+b)^2/c^3*(195*x^10*c^5+480*x^8*b*c^4+305*x^6*b^2*c^3+84*b^5*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-42*b^5*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-8*x^4*b^3*c^2-28*x^2*b^4*c)","A"
365,1,168,192,0.030000," ","int((c*x^4+b*x^2)^(3/2)*x^(1/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(77 c^{5} x^{9}+196 b \,c^{4} x^{7}+131 b^{2} c^{3} x^{5}-8 b^{3} c^{2} x^{3}-20 b^{4} c x +10 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{4} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{1155 \left(c \,x^{2}+b \right)^{2} c^{3} x^{\frac{7}{2}}}"," ",0,"2/1155*(c*x^4+b*x^2)^(3/2)/x^(7/2)/(c*x^2+b)^2*(77*x^9*c^5+196*x^7*b*c^4+10*b^4*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+131*x^5*b^2*c^3-8*x^3*b^3*c^2-20*x*b^4*c)/c^3","A"
366,1,237,316,0.014000," ","int((c*x^4+b*x^2)^(3/2)/x^(1/2),x)","-\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(-15 c^{4} x^{8}-40 b \,c^{3} x^{6}-29 b^{2} c^{2} x^{4}-4 b^{3} c \,x^{2}+12 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{4} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{4} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{195 \left(c \,x^{2}+b \right)^{2} c^{2} x^{\frac{7}{2}}}"," ",0,"-2/195*(c*x^4+b*x^2)^(3/2)/x^(7/2)/(c*x^2+b)^2/c^2*(-15*c^4*x^8-40*b*c^3*x^6+12*b^4*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-6*b^4*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-29*b^2*c^2*x^4-4*b^3*c*x^2)","A"
367,1,157,168,0.014000," ","int((c*x^4+b*x^2)^(3/2)/x^(3/2),x)","-\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(-7 c^{4} x^{7}-20 b \,c^{3} x^{5}-17 b^{2} c^{2} x^{3}-4 b^{3} c x +2 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{77 \left(c \,x^{2}+b \right)^{2} c^{2} x^{\frac{7}{2}}}"," ",0,"-2/77*(c*x^4+b*x^2)^(3/2)/x^(7/2)/(c*x^2+b)^2*(-7*c^4*x^7+2*b^3*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-20*b*c^3*x^5-17*b^2*c^2*x^3-4*b^3*c*x)/c^2","A"
368,1,226,292,0.013000," ","int((c*x^4+b*x^2)^(3/2)/x^(5/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(5 c^{3} x^{6}+16 b \,c^{2} x^{4}+11 b^{2} c \,x^{2}+12 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{45 \left(c \,x^{2}+b \right)^{2} c \,x^{\frac{7}{2}}}"," ",0,"2/45*(c*x^4+b*x^2)^(3/2)/x^(7/2)/(c*x^2+b)^2/c*(5*c^3*x^6+12*b^3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-6*b^3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+16*b*c^2*x^4+11*b^2*c*x^2)","A"
369,1,145,144,0.015000," ","int((c*x^4+b*x^2)^(3/2)/x^(7/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(c^{3} x^{5}+4 b \,c^{2} x^{3}+3 b^{2} c x +2 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right)}{7 \left(c \,x^{2}+b \right)^{2} c \,x^{\frac{7}{2}}}"," ",0,"2/7*(c*x^4+b*x^2)^(3/2)/x^(7/2)/(c*x^2+b)^2*(2*b^2*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+c^3*x^5+4*b*c^2*x^3+3*b^2*c*x)/c","A"
370,1,216,290,0.019000," ","int((c*x^4+b*x^2)^(3/2)/x^(9/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(c^{2} x^{4}-4 b c \,x^{2}+12 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-5 b^{2}\right)}{5 \left(c \,x^{2}+b \right)^{2} x^{\frac{7}{2}}}"," ",0,"2/5*(c*x^4+b*x^2)^(3/2)/x^(7/2)/(c*x^2+b)^2*(12*b^2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-6*b^2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+c^2*x^4-4*b*c*x^2-5*b^2)","A"
371,1,130,144,0.016000," ","int((c*x^4+b*x^2)^(3/2)/x^(11/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(c^{2} x^{4}+2 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, b x \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-b^{2}\right)}{3 \left(c \,x^{2}+b \right)^{2} x^{\frac{9}{2}}}"," ",0,"2/3*(c*x^4+b*x^2)^(3/2)/x^(9/2)/(c*x^2+b)^2*(2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*x*b+c^2*x^4-b^2)","A"
372,1,221,289,0.019000," ","int((c*x^4+b*x^2)^(3/2)/x^(13/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(-7 c^{2} x^{4}+12 \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, b c \,x^{2} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, b c \,x^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-8 b c \,x^{2}-b^{2}\right)}{5 \left(c \,x^{2}+b \right)^{2} x^{\frac{11}{2}}}"," ",0,"2/5*(c*x^4+b*x^2)^(3/2)/x^(11/2)/(c*x^2+b)^2*(12*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*x^2*b*c-6*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*x^2*b*c-7*c^2*x^4-8*b*c*x^2-b^2)","A"
373,1,140,144,0.015000," ","int((c*x^4+b*x^2)^(3/2)/x^(15/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(-3 c^{2} x^{4}+2 \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, c \,x^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-4 b c \,x^{2}-b^{2}\right)}{7 \left(c \,x^{2}+b \right)^{2} x^{\frac{13}{2}}}"," ",0,"2/7*(c*x^4+b*x^2)^(3/2)/x^(13/2)/(c*x^2+b)^2*(2*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*x^3*c-3*c^2*x^4-4*b*c*x^2-b^2)","A"
374,1,239,316,0.020000," ","int((c*x^4+b*x^2)^(3/2)/x^(17/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(-12 c^{3} x^{6}+12 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{2} x^{4} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{2} x^{4} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-23 b \,c^{2} x^{4}-16 b^{2} c \,x^{2}-5 b^{3}\right)}{45 \left(c \,x^{2}+b \right)^{2} b \,x^{\frac{15}{2}}}"," ",0,"2/45*(c*x^4+b*x^2)^(3/2)/x^(15/2)/(c*x^2+b)^2*(12*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b*c^2-6*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b*c^2-12*c^3*x^6-23*b*c^2*x^4-16*b^2*c*x^2-5*b^3)/b","A"
375,1,156,168,0.016000," ","int((c*x^4+b*x^2)^(3/2)/x^(19/2),x)","-\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(4 c^{3} x^{6}+2 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, c^{2} x^{5} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+17 b \,c^{2} x^{4}+20 b^{2} c \,x^{2}+7 b^{3}\right)}{77 \left(c \,x^{2}+b \right)^{2} b \,x^{\frac{17}{2}}}"," ",0,"-2/77*(c*x^4+b*x^2)^(3/2)/x^(17/2)/(c*x^2+b)^2*(2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*x^5*c^2+4*c^3*x^6+17*b*c^2*x^4+20*b^2*c*x^2+7*b^3)/b","A"
376,1,250,340,0.044000," ","int((c*x^4+b*x^2)^(3/2)/x^(21/2),x)","-\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(-12 c^{4} x^{8}+12 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{3} x^{6} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{3} x^{6} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-8 b \,c^{3} x^{6}+29 b^{2} c^{2} x^{4}+40 b^{3} c \,x^{2}+15 b^{4}\right)}{195 \left(c \,x^{2}+b \right)^{2} b^{2} x^{\frac{19}{2}}}"," ",0,"-2/195*(c*x^4+b*x^2)^(3/2)/x^(19/2)/(c*x^2+b)^2*(12*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^6*b*c^3-6*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^6*b*c^3-12*c^4*x^8-8*b*c^3*x^6+29*b^2*c^2*x^4+40*b^3*c*x^2+15*b^4)/b^2","A"
377,1,167,192,0.039000," ","int((c*x^4+b*x^2)^(3/2)/x^(23/2),x)","\frac{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} \left(20 c^{4} x^{8}+10 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, c^{3} x^{7} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+8 b \,c^{3} x^{6}-131 b^{2} c^{2} x^{4}-196 b^{3} c \,x^{2}-77 b^{4}\right)}{1155 \left(c \,x^{2}+b \right)^{2} b^{2} x^{\frac{21}{2}}}"," ",0,"2/1155*(c*x^4+b*x^2)^(3/2)/x^(21/2)/(c*x^2+b)^2*(10*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*x^7*c^3+20*c^4*x^8+8*b*c^3*x^6-131*b^2*c^2*x^4-196*b^3*c*x^2-77*b^4)/b^2","A"
378,1,148,174,0.032000," ","int(x^(13/2)/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(-14 c^{4} x^{7}+4 b \,c^{3} x^{5}-12 b^{2} c^{2} x^{3}-30 b^{3} c x +15 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{x}}{77 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{4}}"," ",0,"-1/77/(c*x^4+b*x^2)^(1/2)*x^(1/2)*(-14*c^4*x^7+15*b^3*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+4*b*c^3*x^5-12*b^2*c^2*x^3-30*b^3*c*x)/c^4","A"
379,1,217,298,0.032000," ","int(x^(11/2)/(c*x^4+b*x^2)^(1/2),x)","\frac{\left(10 c^{3} x^{6}-4 b \,c^{2} x^{4}-14 b^{2} c \,x^{2}+42 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{x}}{45 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{3}}"," ",0,"1/45/(c*x^4+b*x^2)^(1/2)*x^(1/2)/c^3*(10*c^3*x^6+42*b^3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-21*b^3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-4*b*c^2*x^4-14*b^2*c*x^2)","A"
380,1,137,150,0.016000," ","int(x^(9/2)/(c*x^4+b*x^2)^(1/2),x)","\frac{\left(6 c^{3} x^{5}-4 b \,c^{2} x^{3}-10 b^{2} c x +5 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{x}}{21 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{3}}"," ",0,"1/21/(c*x^4+b*x^2)^(1/2)*x^(1/2)*(5*b^2*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+6*c^3*x^5-4*b*c^2*x^3-10*b^2*c*x)/c^3","A"
381,1,206,274,0.015000," ","int(x^(7/2)/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(-2 c^{2} x^{4}-2 b c \,x^{2}+6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{x}}{5 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{2}}"," ",0,"-1/5/(c*x^4+b*x^2)^(1/2)*x^(1/2)/c^2*(6*b^2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-3*b^2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-2*c^2*x^4-2*b*c*x^2)","A"
382,1,123,128,0.013000," ","int(x^(5/2)/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(-2 c^{2} x^{3}-2 b c x +\sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) \sqrt{x}}{3 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{2}}"," ",0,"-1/3/(c*x^4+b*x^2)^(1/2)*x^(1/2)*(b*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-2*c^2*x^3-2*b*c*x)/c^2","A"
383,1,131,251,0.013000," ","int(x^(3/2)/(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \left(2 \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-\EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) b \sqrt{x}}{\sqrt{c \,x^{4}+b \,x^{2}}\, c}"," ",0,"1/(c*x^4+b*x^2)^(1/2)*x^(1/2)*b/c*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*(2*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2)))","A"
384,1,106,105,0.016000," ","int(x^(1/2)/(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{x}\, \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)}{\sqrt{c \,x^{4}+b \,x^{2}}\, c}"," ",0,"1/(c*x^4+b*x^2)^(1/2)*x^(1/2)*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))/c","A"
385,1,195,275,0.017000," ","int(1/x^(1/2)/(c*x^4+b*x^2)^(1/2),x)","\frac{\left(-2 c \,x^{2}+2 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-2 b \right) \sqrt{x}}{\sqrt{c \,x^{4}+b \,x^{2}}\, b}"," ",0,"1/(c*x^4+b*x^2)^(1/2)*x^(1/2)*(2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-2*c*x^2-2*b)/b","A"
386,1,119,128,0.015000," ","int(1/x^(3/2)/(c*x^4+b*x^2)^(1/2),x)","-\frac{2 c \,x^{2}+\sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, x \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+2 b}{3 \sqrt{c \,x^{4}+b \,x^{2}}\, b \sqrt{x}}"," ",0,"-1/3/(c*x^4+b*x^2)^(1/2)/x^(1/2)*((-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x+2*c*x^2+2*b)/b","A"
387,1,215,298,0.017000," ","int(1/x^(5/2)/(c*x^4+b*x^2)^(1/2),x)","-\frac{-6 c^{2} x^{4}+6 \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, b c \,x^{2} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, b c \,x^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-4 b c \,x^{2}+2 b^{2}}{5 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{2} x^{\frac{3}{2}}}"," ",0,"-1/5/(c*x^4+b*x^2)^(1/2)/x^(3/2)*(6*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*x^2*b*c-3*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*x^2*b*c-6*c^2*x^4-4*b*c*x^2+2*b^2)/b^2","A"
388,1,134,150,0.016000," ","int(1/x^(7/2)/(c*x^4+b*x^2)^(1/2),x)","\frac{10 c^{2} x^{4}+5 \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, c \,x^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+4 b c \,x^{2}-6 b^{2}}{21 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{2} x^{\frac{5}{2}}}"," ",0,"1/21/(c*x^4+b*x^2)^(1/2)/x^(5/2)*(5*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*x^3*c+10*c^2*x^4+4*b*c*x^2-6*b^2)/b^2","A"
389,1,230,322,0.019000," ","int(1/x^(9/2)/(c*x^4+b*x^2)^(1/2),x)","\frac{-42 c^{3} x^{6}+42 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{2} x^{4} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{2} x^{4} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-28 b \,c^{2} x^{4}+4 b^{2} c \,x^{2}-10 b^{3}}{45 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{3} x^{\frac{7}{2}}}"," ",0,"1/45/(c*x^4+b*x^2)^(1/2)/x^(7/2)*(42*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b*c^2-21*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b*c^2-42*c^3*x^6-28*b*c^2*x^4+4*b^2*c*x^2-10*b^3)/b^3","A"
390,1,147,174,0.019000," ","int(1/x^(11/2)/(c*x^4+b*x^2)^(1/2),x)","-\frac{30 c^{3} x^{6}+15 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, c^{2} x^{5} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+12 b \,c^{2} x^{4}-4 b^{2} c \,x^{2}+14 b^{3}}{77 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{3} x^{\frac{9}{2}}}"," ",0,"-1/77/(c*x^4+b*x^2)^(1/2)/x^(9/2)*(15*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*x^5*c^2+30*c^3*x^6+12*b*c^2*x^4-4*b^2*c*x^2+14*b^3)/b^3","A"
391,1,144,171,0.044000," ","int(x^(17/2)/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(4 c^{3} x^{5}-12 b \,c^{2} x^{3}-30 b^{2} c x +15 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) x^{\frac{5}{2}}}{14 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{4}}"," ",0,"1/14/(c*x^4+b*x^2)^(3/2)*x^(5/2)*(c*x^2+b)*(15*b^2*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+4*c^3*x^5-12*b*c^2*x^3-30*b^2*c*x)/c^4","A"
392,1,213,295,0.039000," ","int(x^(15/2)/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-4 c^{2} x^{4}-14 b c \,x^{2}+42 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) x^{\frac{5}{2}}}{10 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{3}}"," ",0,"-1/10/(c*x^4+b*x^2)^(3/2)*x^(5/2)*(c*x^2+b)*(42*b^2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-21*b^2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-4*c^2*x^4-14*b*c*x^2)/c^3","A"
393,1,131,149,0.017000," ","int(x^(13/2)/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-4 c^{2} x^{3}-10 b c x +5 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) x^{\frac{5}{2}}}{6 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{3}}"," ",0,"-1/6/(c*x^4+b*x^2)^(3/2)*x^(5/2)*(c*x^2+b)*(5*b*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-4*c^2*x^3-10*b*c*x)/c^3","A"
394,1,200,273,0.018000," ","int(x^(11/2)/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(-2 c \,x^{2}+6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) x^{\frac{5}{2}}}{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{2}}"," ",0,"1/2/(c*x^4+b*x^2)^(3/2)*x^(5/2)*(c*x^2+b)*(6*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-2*c*x^2)/c^2","A"
395,1,120,128,0.016000," ","int(x^(9/2)/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(-2 c x +\sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) x^{\frac{5}{2}}}{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} c^{2}}"," ",0,"1/2/(c*x^4+b*x^2)^(3/2)*x^(5/2)*(c*x^2+b)*((-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))-2*c*x)/c^2","A"
396,1,203,274,0.014000," ","int(x^(7/2)/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-2 c \,x^{2}+2 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) x^{\frac{5}{2}}}{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b c}"," ",0,"-1/2/(c*x^4+b*x^2)^(3/2)*x^(5/2)*(c*x^2+b)*(2*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-2*c*x^2)/c/b","A"
397,1,123,127,0.022000," ","int(x^(5/2)/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(2 c x +\sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)\right) x^{\frac{5}{2}}}{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b c}"," ",0,"1/2/(c*x^4+b*x^2)^(3/2)*x^(5/2)*(c*x^2+b)*((-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))+2*c*x)/c/b","A"
398,1,203,296,0.020000," ","int(x^(3/2)/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(-6 c \,x^{2}+6 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-3 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-4 b \right) x^{\frac{5}{2}}}{2 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"1/2/(c*x^4+b*x^2)^(3/2)*x^(5/2)*(c*x^2+b)*(6*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-3*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*b-6*c*x^2-4*b)/b^2","A"
399,1,127,148,0.023000," ","int(x^(1/2)/(c*x^4+b*x^2)^(3/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(10 c \,x^{2}+5 \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, x \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+4 b \right) x^{\frac{3}{2}}}{6 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"-1/6/(c*x^4+b*x^2)^(3/2)*x^(3/2)*(c*x^2+b)*(5*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x+10*c*x^2+4*b)/b^2","A"
400,1,222,318,0.021000," ","int(1/(c*x^4+b*x^2)^(3/2)/x^(1/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-42 c^{2} x^{4}+42 \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, b c \,x^{2} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-21 \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, b c \,x^{2} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-28 b c \,x^{2}+4 b^{2}\right) \sqrt{x}}{10 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"-1/10/(c*x^4+b*x^2)^(3/2)*x^(1/2)*(c*x^2+b)*(42*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*x^2*b*c-21*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*x^2*b*c-42*c^2*x^4-28*b*c*x^2+4*b^2)/b^3","A"
401,1,141,170,0.020000," ","int(1/x^(3/2)/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(30 c^{2} x^{4}+15 \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, \sqrt{-b c}\, \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, c \,x^{3} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)+12 b c \,x^{2}-4 b^{2}\right)}{14 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{3} \sqrt{x}}"," ",0,"1/14/(c*x^4+b*x^2)^(3/2)/x^(1/2)*(c*x^2+b)*(15*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*(-b*c)^(1/2)*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*x^3*c+30*c^2*x^4+12*b*c*x^2-4*b^2)/b^3","A"
402,1,237,342,0.022000," ","int(1/x^(5/2)/(c*x^4+b*x^2)^(3/2),x)","\frac{\left(c \,x^{2}+b \right) \left(-462 c^{3} x^{6}+462 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{2} x^{4} \EllipticE \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-231 \sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{2}\, \sqrt{\frac{-c x +\sqrt{-b c}}{\sqrt{-b c}}}\, \sqrt{-\frac{c x}{\sqrt{-b c}}}\, b \,c^{2} x^{4} \EllipticF \left(\sqrt{\frac{c x +\sqrt{-b c}}{\sqrt{-b c}}}, \frac{\sqrt{2}}{2}\right)-308 b \,c^{2} x^{4}+44 b^{2} c \,x^{2}-20 b^{3}\right)}{90 \left(c \,x^{4}+b \,x^{2}\right)^{\frac{3}{2}} b^{4} x^{\frac{3}{2}}}"," ",0,"1/90/(c*x^4+b*x^2)^(3/2)/x^(3/2)*(c*x^2+b)*(462*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticE(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b*c^2-231*((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*2^(1/2)*((-c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2)*(-1/(-b*c)^(1/2)*c*x)^(1/2)*EllipticF(((c*x+(-b*c)^(1/2))/(-b*c)^(1/2))^(1/2),1/2*2^(1/2))*x^4*b*c^2-462*c^3*x^6-308*b*c^2*x^4+44*b^2*c*x^2-20*b^3)/b^4","A"
403,1,181,73,0.007000," ","int((c*x)^m*(c*x^4+b*x^2)^3,x)","\frac{\left(c^{3} m^{3} x^{6}+27 c^{3} m^{2} x^{6}+3 b \,c^{2} m^{3} x^{4}+239 c^{3} m \,x^{6}+87 b \,c^{2} m^{2} x^{4}+693 c^{3} x^{6}+3 b^{2} c \,m^{3} x^{2}+813 b \,c^{2} m \,x^{4}+93 b^{2} c \,m^{2} x^{2}+2457 b \,c^{2} x^{4}+b^{3} m^{3}+933 b^{2} c m \,x^{2}+33 b^{3} m^{2}+3003 b^{2} c \,x^{2}+359 b^{3} m +1287 b^{3}\right) x^{7} \left(c x \right)^{m}}{\left(m +13\right) \left(m +11\right) \left(m +9\right) \left(m +7\right)}"," ",0,"(c*x)^m*(c^3*m^3*x^6+27*c^3*m^2*x^6+3*b*c^2*m^3*x^4+239*c^3*m*x^6+87*b*c^2*m^2*x^4+693*c^3*x^6+3*b^2*c*m^3*x^2+813*b*c^2*m*x^4+93*b^2*c*m^2*x^2+2457*b*c^2*x^4+b^3*m^3+933*b^2*c*m*x^2+33*b^3*m^2+3003*b^2*c*x^2+359*b^3*m+1287*b^3)*x^7/(13+m)/(11+m)/(9+m)/(7+m)","B"
404,1,96,52,0.006000," ","int((c*x)^m*(c*x^4+b*x^2)^2,x)","\frac{\left(c^{2} m^{2} x^{4}+12 c^{2} m \,x^{4}+2 b c \,m^{2} x^{2}+35 c^{2} x^{4}+28 b c m \,x^{2}+b^{2} m^{2}+90 b c \,x^{2}+16 b^{2} m +63 b^{2}\right) x^{5} \left(c x \right)^{m}}{\left(m +9\right) \left(m +7\right) \left(m +5\right)}"," ",0,"(c*x)^m*(c^2*m^2*x^4+12*c^2*m*x^4+2*b*c*m^2*x^2+35*c^2*x^4+28*b*c*m*x^2+b^2*m^2+90*b*c*x^2+16*b^2*m+63*b^2)*x^5/(m+9)/(m+7)/(5+m)","A"
405,1,39,34,0.003000," ","int((c*x)^m*(c*x^4+b*x^2),x)","\frac{\left(c m \,x^{2}+3 c \,x^{2}+b m +5 b \right) x^{3} \left(c x \right)^{m}}{\left(m +5\right) \left(m +3\right)}"," ",0,"(c*x)^m*(c*m*x^2+3*c*x^2+b*m+5*b)*x^3/(m+5)/(3+m)","A"
406,0,0,43,0.053000," ","int((c*x)^m/(c*x^4+b*x^2),x)","\int \frac{\left(c x \right)^{m}}{c \,x^{4}+b \,x^{2}}\, dx"," ",0,"int((c*x)^m/(c*x^4+b*x^2),x)","F"
407,0,0,43,0.047000," ","int((c*x)^m/(c*x^4+b*x^2)^2,x)","\int \frac{\left(c x \right)^{m}}{\left(c \,x^{4}+b \,x^{2}\right)^{2}}\, dx"," ",0,"int((c*x)^m/(c*x^4+b*x^2)^2,x)","F"
408,0,0,43,0.049000," ","int((c*x)^m/(c*x^4+b*x^2)^3,x)","\int \frac{\left(c x \right)^{m}}{\left(c \,x^{4}+b \,x^{2}\right)^{3}}\, dx"," ",0,"int((c*x)^m/(c*x^4+b*x^2)^3,x)","F"
409,1,25,24,0.001000," ","int(x^3*(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{1}{8} b^{2} x^{8}+\frac{1}{3} a b \,x^{6}+\frac{1}{4} a^{2} x^{4}"," ",0,"1/4*a^2*x^4+1/3*a*b*x^6+1/8*b^2*x^8","A"
410,1,25,24,0.000000," ","int(x^2*(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{1}{7} b^{2} x^{7}+\frac{2}{5} a b \,x^{5}+\frac{1}{3} a^{2} x^{3}"," ",0,"1/3*a^2*x^3+2/5*a*b*x^5+1/7*b^2*x^7","A"
411,1,25,24,0.001000," ","int(x*(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{1}{6} b^{2} x^{6}+\frac{1}{2} a b \,x^{4}+\frac{1}{2} a^{2} x^{2}"," ",0,"1/2*a^2*x^2+1/2*a*b*x^4+1/6*b^2*x^6","A"
412,1,22,21,0.001000," ","int(b^2*x^4+2*a*b*x^2+a^2,x)","\frac{1}{5} b^{2} x^{5}+\frac{2}{3} a b \,x^{3}+a^{2} x"," ",0,"a^2*x+2/3*a*b*x^3+1/5*b^2*x^5","A"
413,1,22,21,0.004000," ","int((b^2*x^4+2*a*b*x^2+a^2)/x,x)","\frac{b^{2} x^{4}}{4}+a b \,x^{2}+a^{2} \ln \left(x \right)"," ",0,"a*b*x^2+1/4*b^2*x^4+a^2*ln(x)","A"
414,1,23,22,0.004000," ","int((b^2*x^4+2*a*b*x^2+a^2)/x^2,x)","\frac{b^{2} x^{3}}{3}+2 a b x -\frac{a^{2}}{x}"," ",0,"-a^2/x+2*a*b*x+1/3*b^2*x^3","A"
415,1,24,23,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)/x^3,x)","\frac{b^{2} x^{2}}{2}+2 a b \ln \left(x \right)-\frac{a^{2}}{2 x^{2}}"," ",0,"-1/2*a^2/x^2+1/2*b^2*x^2+2*a*b*ln(x)","A"
416,1,22,21,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)/x^4,x)","b^{2} x -\frac{2 a b}{x}-\frac{a^{2}}{3 x^{3}}"," ",0,"-1/3*a^2/x^3-2*a*b/x+b^2*x","A"
417,1,23,22,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)/x^5,x)","b^{2} \ln \left(x \right)-\frac{a b}{x^{2}}-\frac{a^{2}}{4 x^{4}}"," ",0,"-1/4*a^2/x^4-a*b/x^2+b^2*ln(x)","A"
418,1,25,24,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)/x^6,x)","-\frac{b^{2}}{x}-\frac{2 a b}{3 x^{3}}-\frac{a^{2}}{5 x^{5}}"," ",0,"-1/5*a^2/x^5-2/3*a*b/x^3-b^2/x","A"
419,1,25,24,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)/x^7,x)","-\frac{b^{2}}{2 x^{2}}-\frac{a b}{2 x^{4}}-\frac{a^{2}}{6 x^{6}}"," ",0,"-1/6*a^2/x^6-1/2*a*b/x^4-1/2*b^2/x^2","A"
420,1,25,24,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)/x^8,x)","-\frac{b^{2}}{3 x^{3}}-\frac{2 a b}{5 x^{5}}-\frac{a^{2}}{7 x^{7}}"," ",0,"-1/7*a^2/x^7-2/5*a*b/x^5-1/3*b^2/x^3","A"
421,1,47,46,0.001000," ","int(x^6*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{1}{15} b^{4} x^{15}+\frac{4}{13} a \,b^{3} x^{13}+\frac{6}{11} a^{2} b^{2} x^{11}+\frac{4}{9} a^{3} b \,x^{9}+\frac{1}{7} a^{4} x^{7}"," ",0,"1/7*a^4*x^7+4/9*a^3*b*x^9+6/11*a^2*b^2*x^11+4/13*a*b^3*x^13+1/15*b^4*x^15","A"
422,1,47,47,0.000000," ","int(x^5*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{1}{14} b^{4} x^{14}+\frac{1}{3} a \,b^{3} x^{12}+\frac{3}{5} a^{2} b^{2} x^{10}+\frac{1}{2} a^{3} b \,x^{8}+\frac{1}{6} a^{4} x^{6}"," ",0,"1/14*b^4*x^14+1/3*a*b^3*x^12+3/5*a^2*b^2*x^10+1/2*a^3*b*x^8+1/6*a^4*x^6","A"
423,1,47,46,0.001000," ","int(x^4*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{1}{13} b^{4} x^{13}+\frac{4}{11} a \,b^{3} x^{11}+\frac{2}{3} a^{2} b^{2} x^{9}+\frac{4}{7} a^{3} b \,x^{7}+\frac{1}{5} a^{4} x^{5}"," ",0,"1/5*a^4*x^5+4/7*a^3*b*x^7+2/3*a^2*b^2*x^9+4/11*a*b^3*x^11+1/13*b^4*x^13","A"
424,1,47,30,0.002000," ","int(x^3*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{1}{12} b^{4} x^{12}+\frac{2}{5} a \,b^{3} x^{10}+\frac{3}{4} a^{2} b^{2} x^{8}+\frac{2}{3} a^{3} b \,x^{6}+\frac{1}{4} a^{4} x^{4}"," ",0,"1/12*b^4*x^12+2/5*a*b^3*x^10+3/4*a^2*b^2*x^8+2/3*a^3*b*x^6+1/4*a^4*x^4","A"
425,1,47,46,0.001000," ","int(x^2*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{1}{11} b^{4} x^{11}+\frac{4}{9} a \,b^{3} x^{9}+\frac{6}{7} a^{2} b^{2} x^{7}+\frac{4}{5} a^{3} b \,x^{5}+\frac{1}{3} a^{4} x^{3}"," ",0,"1/3*a^4*x^3+4/5*a^3*b*x^5+6/7*a^2*b^2*x^7+4/9*a*b^3*x^9+1/11*b^4*x^11","A"
426,1,45,14,0.001000," ","int(x*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{1}{10} b^{4} x^{10}+\frac{1}{2} a \,b^{3} x^{8}+a^{2} b^{2} x^{6}+a^{3} b \,x^{4}+\frac{1}{2} a^{4} x^{2}"," ",0,"1/10*b^4*x^10+1/2*a*b^3*x^8+a^2*b^2*x^6+a^3*b*x^4+1/2*a^4*x^2","B"
427,1,44,43,0.001000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{1}{9} b^{4} x^{9}+\frac{4}{7} a \,b^{3} x^{7}+\frac{6}{5} a^{2} b^{2} x^{5}+\frac{4}{3} a^{3} b \,x^{3}+a^{4} x"," ",0,"a^4*x+4/3*a^3*b*x^3+6/5*a^2*b^2*x^5+4/7*a*b^3*x^7+1/9*b^4*x^9","A"
428,1,45,44,0.003000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x,x)","\frac{b^{4} x^{8}}{8}+\frac{2 a \,b^{3} x^{6}}{3}+\frac{3 a^{2} b^{2} x^{4}}{2}+2 a^{3} b \,x^{2}+a^{4} \ln \left(x \right)"," ",0,"2*a^3*b*x^2+3/2*a^2*b^2*x^4+2/3*a*b^3*x^6+1/8*b^4*x^8+a^4*ln(x)","A"
429,1,45,44,0.003000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^2,x)","\frac{b^{4} x^{7}}{7}+\frac{4 a \,b^{3} x^{5}}{5}+2 a^{2} b^{2} x^{3}+4 a^{3} b x -\frac{a^{4}}{x}"," ",0,"-a^4/x+4*a^3*b*x+2*a^2*b^2*x^3+4/5*a*b^3*x^5+1/7*b^4*x^7","A"
430,1,45,44,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^3,x)","\frac{b^{4} x^{6}}{6}+a \,b^{3} x^{4}+3 a^{2} b^{2} x^{2}+4 a^{3} b \ln \left(x \right)-\frac{a^{4}}{2 x^{2}}"," ",0,"-1/2*a^4/x^2+3*a^2*b^2*x^2+a*b^3*x^4+1/6*b^4*x^6+4*a^3*b*ln(x)","A"
431,1,45,44,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^4,x)","\frac{b^{4} x^{5}}{5}+\frac{4 a \,b^{3} x^{3}}{3}+6 a^{2} b^{2} x -\frac{4 a^{3} b}{x}-\frac{a^{4}}{3 x^{3}}"," ",0,"-1/3*a^4/x^3-4*a^3*b/x+6*a^2*b^2*x+4/3*a*b^3*x^3+1/5*b^4*x^5","A"
432,1,46,45,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^5,x)","\frac{b^{4} x^{4}}{4}+2 a \,b^{3} x^{2}+6 a^{2} b^{2} \ln \left(x \right)-\frac{2 a^{3} b}{x^{2}}-\frac{a^{4}}{4 x^{4}}"," ",0,"-1/4*a^4/x^4-2*a^3*b/x^2+2*a*b^3*x^2+1/4*b^4*x^4+6*a^2*b^2*ln(x)","A"
433,1,45,44,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^6,x)","\frac{b^{4} x^{3}}{3}+4 a \,b^{3} x -\frac{6 a^{2} b^{2}}{x}-\frac{4 a^{3} b}{3 x^{3}}-\frac{a^{4}}{5 x^{5}}"," ",0,"-1/5*a^4/x^5-4/3*a^3*b/x^3-6*a^2*b^2/x+4*a*b^3*x+1/3*b^4*x^3","A"
434,1,46,45,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^7,x)","\frac{b^{4} x^{2}}{2}+4 a \,b^{3} \ln \left(x \right)-\frac{3 a^{2} b^{2}}{x^{2}}-\frac{a^{3} b}{x^{4}}-\frac{a^{4}}{6 x^{6}}"," ",0,"-1/6*a^4/x^6-a^3*b/x^4-3*a^2*b^2/x^2+1/2*b^4*x^2+4*a*b^3*ln(x)","A"
435,1,44,43,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^8,x)","b^{4} x -\frac{4 a \,b^{3}}{x}-\frac{2 a^{2} b^{2}}{x^{3}}-\frac{4 a^{3} b}{5 x^{5}}-\frac{a^{4}}{7 x^{7}}"," ",0,"-1/7*a^4/x^7-4/5*a^3*b/x^5-2*a^2*b^2/x^3-4*a*b^3/x+b^4*x","A"
436,1,45,44,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^9,x)","b^{4} \ln \left(x \right)-\frac{2 a \,b^{3}}{x^{2}}-\frac{3 a^{2} b^{2}}{2 x^{4}}-\frac{2 a^{3} b}{3 x^{6}}-\frac{a^{4}}{8 x^{8}}"," ",0,"-1/8*a^4/x^8-2/3*a^3*b/x^6-3/2*a^2*b^2/x^4-2*a*b^3/x^2+b^4*ln(x)","A"
437,1,47,46,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^10,x)","-\frac{b^{4}}{x}-\frac{4 a \,b^{3}}{3 x^{3}}-\frac{6 a^{2} b^{2}}{5 x^{5}}-\frac{4 a^{3} b}{7 x^{7}}-\frac{a^{4}}{9 x^{9}}"," ",0,"-1/9*a^4/x^9-4/7*a^3*b/x^7-6/5*a^2*b^2/x^5-4/3*a*b^3/x^3-b^4/x","A"
438,1,47,17,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^11,x)","-\frac{b^{4}}{2 x^{2}}-\frac{a \,b^{3}}{x^{4}}-\frac{a^{2} b^{2}}{x^{6}}-\frac{a^{3} b}{2 x^{8}}-\frac{a^{4}}{10 x^{10}}"," ",0,"-1/2*b^4/x^2-a^2*b^2/x^6-1/2*a^3*b/x^8-1/10*a^4/x^10-a*b^3/x^4","B"
439,1,47,46,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^12,x)","-\frac{b^{4}}{3 x^{3}}-\frac{4 a \,b^{3}}{5 x^{5}}-\frac{6 a^{2} b^{2}}{7 x^{7}}-\frac{4 a^{3} b}{9 x^{9}}-\frac{a^{4}}{11 x^{11}}"," ",0,"-1/11*a^4/x^11-4/9*a^3*b/x^9-6/7*a^2*b^2/x^7-4/5*a*b^3/x^5-1/3*b^4/x^3","A"
440,1,47,36,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^13,x)","-\frac{b^{4}}{4 x^{4}}-\frac{2 a \,b^{3}}{3 x^{6}}-\frac{3 a^{2} b^{2}}{4 x^{8}}-\frac{2 a^{3} b}{5 x^{10}}-\frac{a^{4}}{12 x^{12}}"," ",0,"-2/3*a*b^3/x^6-2/5*a^3*b/x^10-1/12*a^4/x^12-3/4*a^2*b^2/x^8-1/4*b^4/x^4","A"
441,1,47,46,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^14,x)","-\frac{b^{4}}{5 x^{5}}-\frac{4 a \,b^{3}}{7 x^{7}}-\frac{2 a^{2} b^{2}}{3 x^{9}}-\frac{4 a^{3} b}{11 x^{11}}-\frac{a^{4}}{13 x^{13}}"," ",0,"-1/13*a^4/x^13-4/11*a^3*b/x^11-2/3*a^2*b^2/x^9-4/7*a*b^3/x^7-1/5*b^4/x^5","A"
442,1,47,46,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^15,x)","-\frac{b^{4}}{6 x^{6}}-\frac{a \,b^{3}}{2 x^{8}}-\frac{3 a^{2} b^{2}}{5 x^{10}}-\frac{a^{3} b}{3 x^{12}}-\frac{a^{4}}{14 x^{14}}"," ",0,"-1/14*a^4/x^14-1/3*a^3*b/x^12-3/5*a^2*b^2/x^10-1/2*a*b^3/x^8-1/6*b^4/x^6","A"
443,1,47,46,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/x^16,x)","-\frac{b^{4}}{7 x^{7}}-\frac{4 a \,b^{3}}{9 x^{9}}-\frac{6 a^{2} b^{2}}{11 x^{11}}-\frac{4 a^{3} b}{13 x^{13}}-\frac{a^{4}}{15 x^{15}}"," ",0,"-1/15*a^4/x^15-4/13*a^3*b/x^13-6/11*a^2*b^2/x^11-4/9*a*b^3/x^9-1/7*b^4/x^7","A"
444,1,69,68,0.001000," ","int(x^8*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{21} b^{6} x^{21}+\frac{6}{19} a \,b^{5} x^{19}+\frac{15}{17} a^{2} b^{4} x^{17}+\frac{4}{3} a^{3} b^{3} x^{15}+\frac{15}{13} a^{4} b^{2} x^{13}+\frac{6}{11} a^{5} b \,x^{11}+\frac{1}{9} a^{6} x^{9}"," ",0,"1/9*a^6*x^9+6/11*a^5*b*x^11+15/13*a^4*b^2*x^13+4/3*a^3*b^3*x^15+15/17*a^2*b^4*x^17+6/19*a*b^5*x^19+1/21*b^6*x^21","A"
445,1,69,64,0.001000," ","int(x^7*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{20} b^{6} x^{20}+\frac{1}{3} a \,b^{5} x^{18}+\frac{15}{16} a^{2} b^{4} x^{16}+\frac{10}{7} a^{3} b^{3} x^{14}+\frac{5}{4} a^{4} b^{2} x^{12}+\frac{3}{5} a^{5} b \,x^{10}+\frac{1}{8} a^{6} x^{8}"," ",0,"1/20*b^6*x^20+1/3*a*b^5*x^18+15/16*a^2*b^4*x^16+10/7*a^3*b^3*x^14+5/4*a^4*b^2*x^12+3/5*a^5*b*x^10+1/8*a^6*x^8","A"
446,1,68,67,0.001000," ","int(x^6*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{19} b^{6} x^{19}+\frac{6}{17} a \,b^{5} x^{17}+a^{2} b^{4} x^{15}+\frac{20}{13} a^{3} b^{3} x^{13}+\frac{15}{11} a^{4} b^{2} x^{11}+\frac{2}{3} a^{5} b \,x^{9}+\frac{1}{7} a^{6} x^{7}"," ",0,"1/7*a^6*x^7+2/3*a^5*b*x^9+15/11*a^4*b^2*x^11+20/13*a^3*b^3*x^13+a^2*b^4*x^15+6/17*a*b^5*x^17+1/19*b^6*x^19","A"
447,1,69,47,0.001000," ","int(x^5*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{18} b^{6} x^{18}+\frac{3}{8} a \,b^{5} x^{16}+\frac{15}{14} a^{2} b^{4} x^{14}+\frac{5}{3} a^{3} b^{3} x^{12}+\frac{3}{2} a^{4} b^{2} x^{10}+\frac{3}{4} a^{5} b \,x^{8}+\frac{1}{6} a^{6} x^{6}"," ",0,"1/18*b^6*x^18+3/8*a*b^5*x^16+15/14*a^2*b^4*x^14+5/3*a^3*b^3*x^12+3/2*a^4*b^2*x^10+3/4*a^5*b*x^8+1/6*a^6*x^6","A"
448,1,69,68,0.000000," ","int(x^4*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{17} b^{6} x^{17}+\frac{2}{5} a \,b^{5} x^{15}+\frac{15}{13} a^{2} b^{4} x^{13}+\frac{20}{11} a^{3} b^{3} x^{11}+\frac{5}{3} a^{4} b^{2} x^{9}+\frac{6}{7} a^{5} b \,x^{7}+\frac{1}{5} a^{6} x^{5}"," ",0,"1/5*a^6*x^5+6/7*a^5*b*x^7+5/3*a^4*b^2*x^9+20/11*a^3*b^3*x^11+15/13*a^2*b^4*x^13+2/5*a*b^5*x^15+1/17*b^6*x^17","A"
449,1,68,30,0.000000," ","int(x^3*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{16} b^{6} x^{16}+\frac{3}{7} a \,b^{5} x^{14}+\frac{5}{4} a^{2} b^{4} x^{12}+2 a^{3} b^{3} x^{10}+\frac{15}{8} a^{4} b^{2} x^{8}+a^{5} b \,x^{6}+\frac{1}{4} a^{6} x^{4}"," ",0,"1/16*b^6*x^16+3/7*a*b^5*x^14+5/4*a^2*b^4*x^12+2*a^3*b^3*x^10+15/8*a^4*b^2*x^8+a^5*b*x^6+1/4*a^6*x^4","B"
450,1,69,68,0.002000," ","int(x^2*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{15} b^{6} x^{15}+\frac{6}{13} a \,b^{5} x^{13}+\frac{15}{11} a^{2} b^{4} x^{11}+\frac{20}{9} a^{3} b^{3} x^{9}+\frac{15}{7} a^{4} b^{2} x^{7}+\frac{6}{5} a^{5} b \,x^{5}+\frac{1}{3} a^{6} x^{3}"," ",0,"1/3*a^6*x^3+6/5*a^5*b*x^5+15/7*a^4*b^2*x^7+20/9*a^3*b^3*x^9+15/11*a^2*b^4*x^11+6/13*a*b^5*x^13+1/15*b^6*x^15","A"
451,1,69,14,0.002000," ","int(x*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{14} b^{6} x^{14}+\frac{1}{2} a \,b^{5} x^{12}+\frac{3}{2} a^{2} b^{4} x^{10}+\frac{5}{2} a^{3} b^{3} x^{8}+\frac{5}{2} a^{4} b^{2} x^{6}+\frac{3}{2} a^{5} b \,x^{4}+\frac{1}{2} a^{6} x^{2}"," ",0,"1/14*b^6*x^14+1/2*a*b^5*x^12+3/2*a^2*b^4*x^10+5/2*a^3*b^3*x^8+5/2*a^4*b^2*x^6+3/2*a^5*b*x^4+1/2*a^6*x^2","B"
452,1,66,65,0.001000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{13} b^{6} x^{13}+\frac{6}{11} a \,b^{5} x^{11}+\frac{5}{3} a^{2} b^{4} x^{9}+\frac{20}{7} a^{3} b^{3} x^{7}+3 a^{4} b^{2} x^{5}+2 a^{5} b \,x^{3}+a^{6} x"," ",0,"a^6*x+2*a^5*b*x^3+3*a^4*b^2*x^5+20/7*a^3*b^3*x^7+5/3*a^2*b^4*x^9+6/11*a*b^5*x^11+1/13*b^6*x^13","A"
453,1,67,66,0.003000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x,x)","\frac{b^{6} x^{12}}{12}+\frac{3 a \,b^{5} x^{10}}{5}+\frac{15 a^{2} b^{4} x^{8}}{8}+\frac{10 a^{3} b^{3} x^{6}}{3}+\frac{15 a^{4} b^{2} x^{4}}{4}+3 a^{5} b \,x^{2}+a^{6} \ln \left(x \right)"," ",0,"3*a^5*b*x^2+15/4*a^4*b^2*x^4+10/3*a^3*b^3*x^6+15/8*a^2*b^4*x^8+3/5*a*b^5*x^10+1/12*b^6*x^12+a^6*ln(x)","A"
454,1,67,66,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^2,x)","\frac{b^{6} x^{11}}{11}+\frac{2 a \,b^{5} x^{9}}{3}+\frac{15 a^{2} b^{4} x^{7}}{7}+4 a^{3} b^{3} x^{5}+5 a^{4} b^{2} x^{3}+6 a^{5} b x -\frac{a^{6}}{x}"," ",0,"-a^6/x+6*a^5*b*x+5*a^4*b^2*x^3+4*a^3*b^3*x^5+15/7*a^2*b^4*x^7+2/3*a*b^5*x^9+1/11*b^6*x^11","A"
455,1,68,67,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^3,x)","\frac{b^{6} x^{10}}{10}+\frac{3 a \,b^{5} x^{8}}{4}+\frac{5 a^{2} b^{4} x^{6}}{2}+5 a^{3} b^{3} x^{4}+\frac{15 a^{4} b^{2} x^{2}}{2}+6 a^{5} b \ln \left(x \right)-\frac{a^{6}}{2 x^{2}}"," ",0,"-1/2*a^6/x^2+15/2*a^4*b^2*x^2+5*a^3*b^3*x^4+5/2*a^2*b^4*x^6+3/4*a*b^5*x^8+1/10*b^6*x^10+6*a^5*b*ln(x)","A"
456,1,67,66,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^4,x)","\frac{b^{6} x^{9}}{9}+\frac{6 a \,b^{5} x^{7}}{7}+3 a^{2} b^{4} x^{5}+\frac{20 a^{3} b^{3} x^{3}}{3}+15 a^{4} b^{2} x -\frac{6 a^{5} b}{x}-\frac{a^{6}}{3 x^{3}}"," ",0,"-1/3*a^6/x^3-6*a^5*b/x+15*a^4*b^2*x+20/3*a^3*b^3*x^3+3*a^2*b^4*x^5+6/7*a*b^5*x^7+1/9*b^6*x^9","A"
457,1,67,66,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^5,x)","\frac{b^{6} x^{8}}{8}+a \,b^{5} x^{6}+\frac{15 a^{2} b^{4} x^{4}}{4}+10 a^{3} b^{3} x^{2}+15 a^{4} b^{2} \ln \left(x \right)-\frac{3 a^{5} b}{x^{2}}-\frac{a^{6}}{4 x^{4}}"," ",0,"-1/4*a^6/x^4-3*a^5*b/x^2+10*a^3*b^3*x^2+15/4*a^2*b^4*x^4+a*b^5*x^6+1/8*b^6*x^8+15*a^4*b^2*ln(x)","A"
458,1,67,66,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^6,x)","\frac{b^{6} x^{7}}{7}+\frac{6 a \,b^{5} x^{5}}{5}+5 a^{2} b^{4} x^{3}+20 a^{3} b^{3} x -\frac{15 a^{4} b^{2}}{x}-\frac{2 a^{5} b}{x^{3}}-\frac{a^{6}}{5 x^{5}}"," ",0,"-1/5*a^6/x^5-2*a^5*b/x^3-15*a^4*b^2/x+20*a^3*b^3*x+5*a^2*b^4*x^3+6/5*a*b^5*x^5+1/7*b^6*x^7","A"
459,1,68,67,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^7,x)","\frac{b^{6} x^{6}}{6}+\frac{3 a \,b^{5} x^{4}}{2}+\frac{15 a^{2} b^{4} x^{2}}{2}+20 a^{3} b^{3} \ln \left(x \right)-\frac{15 a^{4} b^{2}}{2 x^{2}}-\frac{3 a^{5} b}{2 x^{4}}-\frac{a^{6}}{6 x^{6}}"," ",0,"-1/6*a^6/x^6-3/2*a^5*b/x^4-15/2*a^4*b^2/x^2+15/2*a^2*b^4*x^2+3/2*a*b^5*x^4+1/6*b^6*x^6+20*a^3*b^3*ln(x)","A"
460,1,67,66,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^8,x)","\frac{b^{6} x^{5}}{5}+2 a \,b^{5} x^{3}+15 a^{2} b^{4} x -\frac{20 a^{3} b^{3}}{x}-\frac{5 a^{4} b^{2}}{x^{3}}-\frac{6 a^{5} b}{5 x^{5}}-\frac{a^{6}}{7 x^{7}}"," ",0,"-1/7*a^6/x^7-6/5*a^5*b/x^5-5*a^4*b^2/x^3-20*a^3*b^3/x+15*a^2*b^4*x+2*a*b^5*x^3+1/5*b^6*x^5","A"
461,1,68,67,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^9,x)","\frac{b^{6} x^{4}}{4}+3 a \,b^{5} x^{2}+15 a^{2} b^{4} \ln \left(x \right)-\frac{10 a^{3} b^{3}}{x^{2}}-\frac{15 a^{4} b^{2}}{4 x^{4}}-\frac{a^{5} b}{x^{6}}-\frac{a^{6}}{8 x^{8}}"," ",0,"-1/8*a^6/x^8-a^5*b/x^6-15/4*a^4*b^2/x^4-10*a^3*b^3/x^2+3*a*b^5*x^2+1/4*b^6*x^4+15*a^2*b^4*ln(x)","A"
462,1,67,66,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^10,x)","\frac{b^{6} x^{3}}{3}+6 a \,b^{5} x -\frac{15 a^{2} b^{4}}{x}-\frac{20 a^{3} b^{3}}{3 x^{3}}-\frac{3 a^{4} b^{2}}{x^{5}}-\frac{6 a^{5} b}{7 x^{7}}-\frac{a^{6}}{9 x^{9}}"," ",0,"-1/9*a^6/x^9-6/7*a^5*b/x^7-3*a^4*b^2/x^5-20/3*a^3*b^3/x^3-15*a^2*b^4/x+6*a*b^5*x+1/3*b^6*x^3","A"
463,1,68,67,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^11,x)","\frac{b^{6} x^{2}}{2}+6 a \,b^{5} \ln \left(x \right)-\frac{15 a^{2} b^{4}}{2 x^{2}}-\frac{5 a^{3} b^{3}}{x^{4}}-\frac{5 a^{4} b^{2}}{2 x^{6}}-\frac{3 a^{5} b}{4 x^{8}}-\frac{a^{6}}{10 x^{10}}"," ",0,"-1/10*a^6/x^10-3/4*a^5*b/x^8-5/2*a^4*b^2/x^6-5*a^3*b^3/x^4-15/2*a^2*b^4/x^2+1/2*b^6*x^2+6*a*b^5*ln(x)","A"
464,1,66,65,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^12,x)","b^{6} x -\frac{6 a \,b^{5}}{x}-\frac{5 a^{2} b^{4}}{x^{3}}-\frac{4 a^{3} b^{3}}{x^{5}}-\frac{15 a^{4} b^{2}}{7 x^{7}}-\frac{2 a^{5} b}{3 x^{9}}-\frac{a^{6}}{11 x^{11}}"," ",0,"-1/11*a^6/x^11-2/3*a^5*b/x^9-15/7*a^4*b^2/x^7-4*a^3*b^3/x^5-5*a^2*b^4/x^3-6*a*b^5/x+b^6*x","A"
465,1,67,66,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^13,x)","b^{6} \ln \left(x \right)-\frac{3 a \,b^{5}}{x^{2}}-\frac{15 a^{2} b^{4}}{4 x^{4}}-\frac{10 a^{3} b^{3}}{3 x^{6}}-\frac{15 a^{4} b^{2}}{8 x^{8}}-\frac{3 a^{5} b}{5 x^{10}}-\frac{a^{6}}{12 x^{12}}"," ",0,"-1/12*a^6/x^12-3/5*a^5*b/x^10-15/8*a^4*b^2/x^8-10/3*a^3*b^3/x^6-15/4*a^2*b^4/x^4-3*a*b^5/x^2+b^6*ln(x)","A"
466,1,69,68,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^14,x)","-\frac{b^{6}}{x}-\frac{2 a \,b^{5}}{x^{3}}-\frac{3 a^{2} b^{4}}{x^{5}}-\frac{20 a^{3} b^{3}}{7 x^{7}}-\frac{5 a^{4} b^{2}}{3 x^{9}}-\frac{6 a^{5} b}{11 x^{11}}-\frac{a^{6}}{13 x^{13}}"," ",0,"-1/13*a^6/x^13-6/11*a^5*b/x^11-5/3*a^4*b^2/x^9-20/7*a^3*b^3/x^7-3*a^2*b^4/x^5-2*a*b^5/x^3-b^6/x","A"
467,1,69,17,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^15,x)","-\frac{b^{6}}{2 x^{2}}-\frac{3 a \,b^{5}}{2 x^{4}}-\frac{5 a^{2} b^{4}}{2 x^{6}}-\frac{5 a^{3} b^{3}}{2 x^{8}}-\frac{3 a^{4} b^{2}}{2 x^{10}}-\frac{a^{5} b}{2 x^{12}}-\frac{a^{6}}{14 x^{14}}"," ",0,"-1/2*b^6/x^2-3/2*a^4*b^2/x^10-1/14*a^6/x^14-1/2*a^5*b/x^12-5/2*a^2*b^4/x^6-5/2*a^3*b^3/x^8-3/2*a*b^5/x^4","B"
468,1,69,68,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^16,x)","-\frac{b^{6}}{3 x^{3}}-\frac{6 a \,b^{5}}{5 x^{5}}-\frac{15 a^{2} b^{4}}{7 x^{7}}-\frac{20 a^{3} b^{3}}{9 x^{9}}-\frac{15 a^{4} b^{2}}{11 x^{11}}-\frac{6 a^{5} b}{13 x^{13}}-\frac{a^{6}}{15 x^{15}}"," ",0,"-1/15*a^6/x^15-6/13*a^5*b/x^13-15/11*a^4*b^2/x^11-20/9*a^3*b^3/x^9-15/7*a^2*b^4/x^7-6/5*a*b^5/x^5-1/3*b^6/x^3","A"
469,1,69,36,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^17,x)","-\frac{b^{6}}{4 x^{4}}-\frac{a \,b^{5}}{x^{6}}-\frac{15 a^{2} b^{4}}{8 x^{8}}-\frac{2 a^{3} b^{3}}{x^{10}}-\frac{5 a^{4} b^{2}}{4 x^{12}}-\frac{3 a^{5} b}{7 x^{14}}-\frac{a^{6}}{16 x^{16}}"," ",0,"-2*a^3*b^3/x^10-1/16*a^6/x^16-5/4*a^4*b^2/x^12-a*b^5/x^6-15/8*a^2*b^4/x^8-3/7*a^5*b/x^14-1/4*b^6/x^4","A"
470,1,69,68,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^18,x)","-\frac{b^{6}}{5 x^{5}}-\frac{6 a \,b^{5}}{7 x^{7}}-\frac{5 a^{2} b^{4}}{3 x^{9}}-\frac{20 a^{3} b^{3}}{11 x^{11}}-\frac{15 a^{4} b^{2}}{13 x^{13}}-\frac{2 a^{5} b}{5 x^{15}}-\frac{a^{6}}{17 x^{17}}"," ",0,"-1/17*a^6/x^17-2/5*a^5*b/x^15-15/13*a^4*b^2/x^13-20/11*a^3*b^3/x^11-5/3*a^2*b^4/x^9-6/7*a*b^5/x^7-1/5*b^6/x^5","A"
471,1,69,56,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^19,x)","-\frac{b^{6}}{6 x^{6}}-\frac{3 a \,b^{5}}{4 x^{8}}-\frac{3 a^{2} b^{4}}{2 x^{10}}-\frac{5 a^{3} b^{3}}{3 x^{12}}-\frac{15 a^{4} b^{2}}{14 x^{14}}-\frac{3 a^{5} b}{8 x^{16}}-\frac{a^{6}}{18 x^{18}}"," ",0,"-3/2*a^2*b^4/x^10-1/6*b^6/x^6-15/14*a^4*b^2/x^14-3/4*a*b^5/x^8-3/8*a^5*b/x^16-1/18*a^6/x^18-5/3*a^3*b^3/x^12","A"
472,1,69,68,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^20,x)","-\frac{b^{6}}{7 x^{7}}-\frac{2 a \,b^{5}}{3 x^{9}}-\frac{15 a^{2} b^{4}}{11 x^{11}}-\frac{20 a^{3} b^{3}}{13 x^{13}}-\frac{a^{4} b^{2}}{x^{15}}-\frac{6 a^{5} b}{17 x^{17}}-\frac{a^{6}}{19 x^{19}}"," ",0,"-1/19*a^6/x^19-6/17*a^5*b/x^17-a^4*b^2/x^15-20/13*a^3*b^3/x^13-15/11*a^2*b^4/x^11-2/3*a*b^5/x^9-1/7*b^6/x^7","A"
473,1,69,76,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^21,x)","-\frac{b^{6}}{8 x^{8}}-\frac{3 a \,b^{5}}{5 x^{10}}-\frac{5 a^{2} b^{4}}{4 x^{12}}-\frac{10 a^{3} b^{3}}{7 x^{14}}-\frac{15 a^{4} b^{2}}{16 x^{16}}-\frac{a^{5} b}{3 x^{18}}-\frac{a^{6}}{20 x^{20}}"," ",0,"-3/5*a*b^5/x^10-1/3*a^5*b/x^18-1/20*a^6/x^20-1/8*b^6/x^8-15/16*a^4*b^2/x^16-10/7*a^3*b^3/x^14-5/4*a^2*b^4/x^12","A"
474,1,69,68,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/x^22,x)","-\frac{b^{6}}{9 x^{9}}-\frac{6 a \,b^{5}}{11 x^{11}}-\frac{15 a^{2} b^{4}}{13 x^{13}}-\frac{4 a^{3} b^{3}}{3 x^{15}}-\frac{15 a^{4} b^{2}}{17 x^{17}}-\frac{6 a^{5} b}{19 x^{19}}-\frac{a^{6}}{21 x^{21}}"," ",0,"-1/21*a^6/x^21-6/19*a^5*b/x^19-15/17*a^4*b^2/x^17-4/3*a^3*b^3/x^15-15/13*a^2*b^4/x^13-6/11*a*b^5/x^11-1/9*b^6/x^9","A"
475,1,74,73,0.009000," ","int(x^11/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{x^{8}}{8 b^{2}}-\frac{a \,x^{6}}{3 b^{3}}+\frac{3 a^{2} x^{4}}{4 b^{4}}-\frac{2 a^{3} x^{2}}{b^{5}}+\frac{a^{5}}{2 \left(b \,x^{2}+a \right) b^{6}}+\frac{5 a^{4} \ln \left(b \,x^{2}+a \right)}{2 b^{6}}"," ",0,"-2*a^3*x^2/b^5+3/4*a^2*x^4/b^4-1/3*a*x^6/b^3+1/8*x^8/b^2+1/2*a^5/b^6/(b*x^2+a)+5/2*a^4*ln(b*x^2+a)/b^6","A"
476,1,63,62,0.010000," ","int(x^9/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{x^{6}}{6 b^{2}}-\frac{a \,x^{4}}{2 b^{3}}+\frac{3 a^{2} x^{2}}{2 b^{4}}-\frac{a^{4}}{2 \left(b \,x^{2}+a \right) b^{5}}-\frac{2 a^{3} \ln \left(b \,x^{2}+a \right)}{b^{5}}"," ",0,"3/2*a^2*x^2/b^4-1/2*a*x^4/b^3+1/6*x^6/b^2-1/2*a^4/b^5/(b*x^2+a)-2*a^3*ln(b*x^2+a)/b^5","A"
477,1,52,51,0.008000," ","int(x^7/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{x^{4}}{4 b^{2}}-\frac{a \,x^{2}}{b^{3}}+\frac{a^{3}}{2 \left(b \,x^{2}+a \right) b^{4}}+\frac{3 a^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{4}}"," ",0,"-a*x^2/b^3+1/4*x^4/b^2+1/2*a^3/b^4/(b*x^2+a)+3/2*a^2*ln(b*x^2+a)/b^4","A"
478,1,41,40,0.006000," ","int(x^5/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{x^{2}}{2 b^{2}}-\frac{a^{2}}{2 \left(b \,x^{2}+a \right) b^{3}}-\frac{a \ln \left(b \,x^{2}+a \right)}{b^{3}}"," ",0,"1/2*x^2/b^2-1/2*a^2/b^3/(b*x^2+a)-a*ln(b*x^2+a)/b^3","A"
479,1,30,29,0.006000," ","int(x^3/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{a}{2 \left(b \,x^{2}+a \right) b^{2}}+\frac{\ln \left(b \,x^{2}+a \right)}{2 b^{2}}"," ",0,"1/2*a/b^2/(b*x^2+a)+1/2*ln(b*x^2+a)/b^2","A"
480,1,15,14,0.003000," ","int(x/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{1}{2 \left(b \,x^{2}+a \right) b}"," ",0,"-1/2/b/(b*x^2+a)","A"
481,1,35,34,0.012000," ","int(1/x/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{1}{2 \left(b \,x^{2}+a \right) a}+\frac{\ln \left(x \right)}{a^{2}}-\frac{\ln \left(b \,x^{2}+a \right)}{2 a^{2}}"," ",0,"1/2/a/(b*x^2+a)+ln(x)/a^2-1/2*ln(b*x^2+a)/a^2","A"
482,1,46,45,0.014000," ","int(1/x^3/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{b}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{2 b \ln \left(x \right)}{a^{3}}+\frac{b \ln \left(b \,x^{2}+a \right)}{a^{3}}-\frac{1}{2 a^{2} x^{2}}"," ",0,"-1/2/a^2/x^2-1/2*b/a^2/(b*x^2+a)-2*b*ln(x)/a^3+b*ln(b*x^2+a)/a^3","A"
483,1,61,60,0.014000," ","int(1/x^5/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{b^{2}}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{3 b^{2} \ln \left(x \right)}{a^{4}}-\frac{3 b^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{4}}+\frac{b}{a^{3} x^{2}}-\frac{1}{4 a^{2} x^{4}}"," ",0,"-1/4/a^2/x^4+b/a^3/x^2+1/2*b^2/a^3/(b*x^2+a)+3*b^2*ln(x)/a^4-3/2*b^2*ln(b*x^2+a)/a^4","A"
484,1,78,72,0.013000," ","int(x^10/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{x^{7}}{7 b^{2}}-\frac{2 a \,x^{5}}{5 b^{3}}+\frac{a^{2} x^{3}}{b^{4}}-\frac{a^{4} x}{2 \left(b \,x^{2}+a \right) b^{5}}+\frac{9 a^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{5}}-\frac{4 a^{3} x}{b^{5}}"," ",0,"1/7*x^7/b^2-2/5*a*x^5/b^3+a^2*x^3/b^4-4*a^3*x/b^5-1/2/b^5*a^4*x/(b*x^2+a)+9/2/b^5*a^4/(a*b)^(1/2)*arctan(x*b/(a*b)^(1/2))","A"
485,1,68,61,0.010000," ","int(x^8/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{x^{5}}{5 b^{2}}-\frac{2 a \,x^{3}}{3 b^{3}}+\frac{a^{3} x}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{7 a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{4}}+\frac{3 a^{2} x}{b^{4}}"," ",0,"1/5*x^5/b^2-2/3*a*x^3/b^3+3*a^2*x/b^4+1/2/b^4*a^3*x/(b*x^2+a)-7/2/b^4*a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
486,1,57,50,0.009000," ","int(x^6/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{x^{3}}{3 b^{2}}-\frac{a^{2} x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{5 a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}-\frac{2 a x}{b^{3}}"," ",0,"1/3*x^3/b^2-2*a*x/b^3-1/2/b^3*a^2*x/(b*x^2+a)+5/2/b^3*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
487,1,43,41,0.008000," ","int(x^4/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{a x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}+\frac{x}{b^{2}}"," ",0,"x/b^2+1/2/b^2*a*x/(b*x^2+a)-3/2/b^2*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
488,1,36,33,0.007000," ","int(x^2/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{x}{2 \left(b \,x^{2}+a \right) b}+\frac{\arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}"," ",0,"-1/2*x/b/(b*x^2+a)+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
489,1,36,33,0.004000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{x}{2 \left(b \,x^{2}+a \right) a}+\frac{\arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}"," ",0,"1/2*x/a/(b*x^2+a)+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
490,1,46,43,0.011000," ","int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{b x}{2 \left(b \,x^{2}+a \right) a^{2}}-\frac{3 b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{2}}-\frac{1}{a^{2} x}"," ",0,"-1/a^2/x-1/2/a^2*b*x/(b*x^2+a)-3/2/a^2*b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
491,1,59,52,0.011000," ","int(1/x^4/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{b^{2} x}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{5 b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{3}}+\frac{2 b}{a^{3} x}-\frac{1}{3 a^{2} x^{3}}"," ",0,"-1/3/a^2/x^3+2*b/a^3/x+1/2/a^3*b^2*x/(b*x^2+a)+5/2/a^3*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
492,1,70,63,0.013000," ","int(1/x^6/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{b^{3} x}{2 \left(b \,x^{2}+a \right) a^{4}}-\frac{7 b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a^{4}}-\frac{3 b^{2}}{a^{4} x}+\frac{2 b}{3 a^{3} x^{3}}-\frac{1}{5 a^{2} x^{5}}"," ",0,"-1/5/a^2/x^5-3*b^2/a^4/x+2/3*b/a^3/x^3-1/2/a^4*b^3*x/(b*x^2+a)-7/2/a^4*b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
493,1,86,85,0.013000," ","int(x^11/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{x^{4}}{4 b^{4}}+\frac{a^{5}}{6 \left(b \,x^{2}+a \right)^{3} b^{6}}-\frac{5 a^{4}}{4 \left(b \,x^{2}+a \right)^{2} b^{6}}-\frac{2 a \,x^{2}}{b^{5}}+\frac{5 a^{3}}{\left(b \,x^{2}+a \right) b^{6}}+\frac{5 a^{2} \ln \left(b \,x^{2}+a \right)}{b^{6}}"," ",0,"-2*a*x^2/b^5+1/4*x^4/b^4+1/6*a^5/b^6/(b*x^2+a)^3-5/4*a^4/b^6/(b*x^2+a)^2+5*a^3/b^6/(b*x^2+a)+5*a^2*ln(b*x^2+a)/b^6","A"
494,1,74,73,0.013000," ","int(x^9/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{a^{4}}{6 \left(b \,x^{2}+a \right)^{3} b^{5}}+\frac{a^{3}}{\left(b \,x^{2}+a \right)^{2} b^{5}}+\frac{x^{2}}{2 b^{4}}-\frac{3 a^{2}}{\left(b \,x^{2}+a \right) b^{5}}-\frac{2 a \ln \left(b \,x^{2}+a \right)}{b^{5}}"," ",0,"1/2*x^2/b^4-1/6*a^4/b^5/(b*x^2+a)^3+a^3/b^5/(b*x^2+a)^2-3*a^2/b^5/(b*x^2+a)-2*a*ln(b*x^2+a)/b^5","A"
495,1,64,63,0.010000," ","int(x^7/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{a^{3}}{6 \left(b \,x^{2}+a \right)^{3} b^{4}}-\frac{3 a^{2}}{4 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{3 a}{2 \left(b \,x^{2}+a \right) b^{4}}+\frac{\ln \left(b \,x^{2}+a \right)}{2 b^{4}}"," ",0,"1/6*a^3/b^4/(b*x^2+a)^3-3/4*a^2/b^4/(b*x^2+a)^2+3/2*a/b^4/(b*x^2+a)+1/2*ln(b*x^2+a)/b^4","A"
496,1,48,17,0.008000," ","int(x^5/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{a^{2}}{6 \left(b \,x^{2}+a \right)^{3} b^{3}}+\frac{a}{2 \left(b \,x^{2}+a \right)^{2} b^{3}}-\frac{1}{2 \left(b \,x^{2}+a \right) b^{3}}"," ",0,"-1/6*a^2/b^3/(b*x^2+a)^3+1/2*a/b^3/(b*x^2+a)^2-1/2/b^3/(b*x^2+a)","B"
497,1,31,30,0.006000," ","int(x^3/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{a}{6 \left(b \,x^{2}+a \right)^{3} b^{2}}-\frac{1}{4 \left(b \,x^{2}+a \right)^{2} b^{2}}"," ",0,"1/6*a/b^2/(b*x^2+a)^3-1/4/b^2/(b*x^2+a)^2","A"
498,1,15,14,0.004000," ","int(x/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{1}{6 \left(b \,x^{2}+a \right)^{3} b}"," ",0,"-1/6/b/(b*x^2+a)^3","A"
499,1,63,62,0.014000," ","int(1/x/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{1}{6 \left(b \,x^{2}+a \right)^{3} a}+\frac{1}{4 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{1}{2 \left(b \,x^{2}+a \right) a^{3}}+\frac{\ln \left(x \right)}{a^{4}}-\frac{\ln \left(b \,x^{2}+a \right)}{2 a^{4}}"," ",0,"1/6/a/(b*x^2+a)^3+1/4/a^2/(b*x^2+a)^2+1/2/a^3/(b*x^2+a)+ln(x)/a^4-1/2*ln(b*x^2+a)/a^4","A"
500,1,77,76,0.015000," ","int(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{b}{6 \left(b \,x^{2}+a \right)^{3} a^{2}}-\frac{b}{2 \left(b \,x^{2}+a \right)^{2} a^{3}}-\frac{3 b}{2 \left(b \,x^{2}+a \right) a^{4}}-\frac{4 b \ln \left(x \right)}{a^{5}}+\frac{2 b \ln \left(b \,x^{2}+a \right)}{a^{5}}-\frac{1}{2 a^{4} x^{2}}"," ",0,"-1/2/a^4/x^2-1/6*b/a^2/(b*x^2+a)^3-1/2*b/a^3/(b*x^2+a)^2-3/2*b/a^4/(b*x^2+a)-4*b*ln(x)/a^5+2*b*ln(b*x^2+a)/a^5","A"
501,1,96,95,0.015000," ","int(1/x^5/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{b^{2}}{6 \left(b \,x^{2}+a \right)^{3} a^{3}}+\frac{3 b^{2}}{4 \left(b \,x^{2}+a \right)^{2} a^{4}}+\frac{3 b^{2}}{\left(b \,x^{2}+a \right) a^{5}}+\frac{10 b^{2} \ln \left(x \right)}{a^{6}}-\frac{5 b^{2} \ln \left(b \,x^{2}+a \right)}{a^{6}}+\frac{2 b}{a^{5} x^{2}}-\frac{1}{4 a^{4} x^{4}}"," ",0,"-1/4/a^4/x^4+2*b/a^5/x^2+1/6*b^2/a^3/(b*x^2+a)^3+3/4*b^2/a^4/(b*x^2+a)^2+3*b^2/a^5/(b*x^2+a)+10*b^2*ln(x)/a^6-5*b^2*ln(b*x^2+a)/a^6","A"
502,1,108,95,0.015000," ","int(x^12/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{89 a^{3} x^{5}}{16 \left(b \,x^{2}+a \right)^{3} b^{4}}+\frac{59 a^{4} x^{3}}{6 \left(b \,x^{2}+a \right)^{3} b^{5}}+\frac{x^{5}}{5 b^{4}}+\frac{71 a^{5} x}{16 \left(b \,x^{2}+a \right)^{3} b^{6}}-\frac{4 a \,x^{3}}{3 b^{5}}-\frac{231 a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, b^{6}}+\frac{10 a^{2} x}{b^{6}}"," ",0,"1/5*x^5/b^4-4/3*a*x^3/b^5+10*a^2*x/b^6+89/16/b^4*a^3/(b*x^2+a)^3*x^5+59/6/b^5*a^4/(b*x^2+a)^3*x^3+71/16/b^6*a^5/(b*x^2+a)^3*x-231/16/b^6*a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
503,1,97,84,0.013000," ","int(x^10/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{55 a^{2} x^{5}}{16 \left(b \,x^{2}+a \right)^{3} b^{3}}-\frac{35 a^{3} x^{3}}{6 \left(b \,x^{2}+a \right)^{3} b^{4}}-\frac{41 a^{4} x}{16 \left(b \,x^{2}+a \right)^{3} b^{5}}+\frac{x^{3}}{3 b^{4}}+\frac{105 a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, b^{5}}-\frac{4 a x}{b^{5}}"," ",0,"1/3*x^3/b^4-4*a*x/b^5-55/16/b^3*a^2/(b*x^2+a)^3*x^5-35/6/b^4*a^3/(b*x^2+a)^3*x^3-41/16/b^5*a^4/(b*x^2+a)^3*x+105/16/b^5*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
504,1,83,75,0.012000," ","int(x^8/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{29 a \,x^{5}}{16 \left(b \,x^{2}+a \right)^{3} b^{2}}+\frac{17 a^{2} x^{3}}{6 \left(b \,x^{2}+a \right)^{3} b^{3}}+\frac{19 a^{3} x}{16 \left(b \,x^{2}+a \right)^{3} b^{4}}-\frac{35 a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, b^{4}}+\frac{x}{b^{4}}"," ",0,"x/b^4+29/16/b^2*a/(b*x^2+a)^3*x^5+17/6/b^3*a^2/(b*x^2+a)^3*x^3+19/16/b^4*a^3/(b*x^2+a)^3*x-35/16/b^4*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
505,1,58,67,0.008000," ","int(x^6/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{5 \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, b^{3}}+\frac{-\frac{11 x^{5}}{16 b}-\frac{5 a \,x^{3}}{6 b^{2}}-\frac{5 a^{2} x}{16 b^{3}}}{\left(b \,x^{2}+a \right)^{3}}"," ",0,"(-11/16/b*x^5-5/6*a/b^2*x^3-5/16*a^2/b^3*x)/(b*x^2+a)^3+5/16/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
506,1,58,68,0.010000," ","int(x^4/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{\arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, a \,b^{2}}+\frac{\frac{x^{5}}{16 a}-\frac{x^{3}}{6 b}-\frac{a x}{16 b^{2}}}{\left(b \,x^{2}+a \right)^{3}}"," ",0,"(1/16/a*x^5-1/6/b*x^3-1/16*a/b^2*x)/(b*x^2+a)^3+1/16/a/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
507,1,58,69,0.011000," ","int(x^2/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{\arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, a^{2} b}+\frac{\frac{b \,x^{5}}{16 a^{2}}+\frac{x^{3}}{6 a}-\frac{x}{16 b}}{\left(b \,x^{2}+a \right)^{3}}"," ",0,"(1/16/a^2*b*x^5+1/6/a*x^3-1/16/b*x)/(b*x^2+a)^3+1/16/a^2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
508,1,66,63,0.004000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{x}{6 \left(b \,x^{2}+a \right)^{3} a}+\frac{5 x}{24 \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{5 x}{16 \left(b \,x^{2}+a \right) a^{3}}+\frac{5 \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, a^{3}}"," ",0,"1/6*x/a/(b*x^2+a)^3+5/24*x/a^2/(b*x^2+a)^2+5/16*x/a^3/(b*x^2+a)+5/16/a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
509,1,86,77,0.014000," ","int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{19 b^{3} x^{5}}{16 \left(b \,x^{2}+a \right)^{3} a^{4}}-\frac{17 b^{2} x^{3}}{6 \left(b \,x^{2}+a \right)^{3} a^{3}}-\frac{29 b x}{16 \left(b \,x^{2}+a \right)^{3} a^{2}}-\frac{35 b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, a^{4}}-\frac{1}{a^{4} x}"," ",0,"-1/a^4/x-19/16*b^3/a^4/(b*x^2+a)^3*x^5-17/6*b^2/a^3/(b*x^2+a)^3*x^3-29/16*b/a^2/(b*x^2+a)^3*x-35/16*b/a^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
510,1,99,86,0.016000," ","int(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{41 b^{4} x^{5}}{16 \left(b \,x^{2}+a \right)^{3} a^{5}}+\frac{35 b^{3} x^{3}}{6 \left(b \,x^{2}+a \right)^{3} a^{4}}+\frac{55 b^{2} x}{16 \left(b \,x^{2}+a \right)^{3} a^{3}}+\frac{105 b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, a^{5}}+\frac{4 b}{a^{5} x}-\frac{1}{3 a^{4} x^{3}}"," ",0,"-1/3/a^4/x^3+4*b/a^5/x+41/16*b^4/a^5/(b*x^2+a)^3*x^5+35/6*b^3/a^4/(b*x^2+a)^3*x^3+55/16*b^2/a^3/(b*x^2+a)^3*x+105/16*b^2/a^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
511,1,110,97,0.015000," ","int(1/x^6/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{71 b^{5} x^{5}}{16 \left(b \,x^{2}+a \right)^{3} a^{6}}-\frac{59 b^{4} x^{3}}{6 \left(b \,x^{2}+a \right)^{3} a^{5}}-\frac{89 b^{3} x}{16 \left(b \,x^{2}+a \right)^{3} a^{4}}-\frac{231 b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{16 \sqrt{a b}\, a^{6}}-\frac{10 b^{2}}{a^{6} x}+\frac{4 b}{3 a^{5} x^{3}}-\frac{1}{5 a^{4} x^{5}}"," ",0,"-1/5/a^4/x^5-10*b^2/a^6/x+4/3*b/a^5/x^3-71/16/a^6*b^5/(b*x^2+a)^3*x^5-59/6/a^5*b^4/(b*x^2+a)^3*x^3-89/16/a^4*b^3/(b*x^2+a)^3*x-231/16/a^6*b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
512,1,120,119,0.015000," ","int(x^15/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{a^{7}}{10 \left(b \,x^{2}+a \right)^{5} b^{8}}-\frac{7 a^{6}}{8 \left(b \,x^{2}+a \right)^{4} b^{8}}+\frac{x^{4}}{4 b^{6}}+\frac{7 a^{5}}{2 \left(b \,x^{2}+a \right)^{3} b^{8}}-\frac{35 a^{4}}{4 \left(b \,x^{2}+a \right)^{2} b^{8}}-\frac{3 a \,x^{2}}{b^{7}}+\frac{35 a^{3}}{2 \left(b \,x^{2}+a \right) b^{8}}+\frac{21 a^{2} \ln \left(b \,x^{2}+a \right)}{2 b^{8}}"," ",0,"-3*a*x^2/b^7+1/4*x^4/b^6+1/10*a^7/b^8/(b*x^2+a)^5-7/8*a^6/b^8/(b*x^2+a)^4+7/2*a^5/b^8/(b*x^2+a)^3-35/4*a^4/b^8/(b*x^2+a)^2+35/2*a^3/b^8/(b*x^2+a)+21/2*a^2*ln(b*x^2+a)/b^8","A"
513,1,109,108,0.014000," ","int(x^13/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{a^{6}}{10 \left(b \,x^{2}+a \right)^{5} b^{7}}+\frac{3 a^{5}}{4 \left(b \,x^{2}+a \right)^{4} b^{7}}-\frac{5 a^{4}}{2 \left(b \,x^{2}+a \right)^{3} b^{7}}+\frac{5 a^{3}}{\left(b \,x^{2}+a \right)^{2} b^{7}}+\frac{x^{2}}{2 b^{6}}-\frac{15 a^{2}}{2 \left(b \,x^{2}+a \right) b^{7}}-\frac{3 a \ln \left(b \,x^{2}+a \right)}{b^{7}}"," ",0,"1/2*x^2/b^6-1/10*a^6/b^7/(b*x^2+a)^5+3/4*a^5/b^7/(b*x^2+a)^4-5/2*a^4/b^7/(b*x^2+a)^3+5*a^3/b^7/(b*x^2+a)^2-15/2*a^2/b^7/(b*x^2+a)-3*a*ln(b*x^2+a)/b^7","A"
514,1,98,97,0.011000," ","int(x^11/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{a^{5}}{10 \left(b \,x^{2}+a \right)^{5} b^{6}}-\frac{5 a^{4}}{8 \left(b \,x^{2}+a \right)^{4} b^{6}}+\frac{5 a^{3}}{3 \left(b \,x^{2}+a \right)^{3} b^{6}}-\frac{5 a^{2}}{2 \left(b \,x^{2}+a \right)^{2} b^{6}}+\frac{5 a}{2 \left(b \,x^{2}+a \right) b^{6}}+\frac{\ln \left(b \,x^{2}+a \right)}{2 b^{6}}"," ",0,"1/10*a^5/b^6/(b*x^2+a)^5-5/8*a^4/b^6/(b*x^2+a)^4+5/3*a^3/b^6/(b*x^2+a)^3-5/2*a^2/b^6/(b*x^2+a)^2+5/2*a/b^6/(b*x^2+a)+1/2*ln(b*x^2+a)/b^6","A"
515,1,81,17,0.008000," ","int(x^9/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{a^{4}}{10 \left(b \,x^{2}+a \right)^{5} b^{5}}+\frac{a^{3}}{2 \left(b \,x^{2}+a \right)^{4} b^{5}}-\frac{a^{2}}{\left(b \,x^{2}+a \right)^{3} b^{5}}+\frac{a}{\left(b \,x^{2}+a \right)^{2} b^{5}}-\frac{1}{2 \left(b \,x^{2}+a \right) b^{5}}"," ",0,"-a^2/b^5/(b*x^2+a)^3+1/2*a^3/b^5/(b*x^2+a)^4-1/10*a^4/b^5/(b*x^2+a)^5+a/b^5/(b*x^2+a)^2-1/2/b^5/(b*x^2+a)","B"
516,1,65,35,0.008000," ","int(x^7/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{a^{3}}{10 \left(b \,x^{2}+a \right)^{5} b^{4}}-\frac{3 a^{2}}{8 \left(b \,x^{2}+a \right)^{4} b^{4}}+\frac{a}{2 \left(b \,x^{2}+a \right)^{3} b^{4}}-\frac{1}{4 \left(b \,x^{2}+a \right)^{2} b^{4}}"," ",0,"1/2*a/b^4/(b*x^2+a)^3-3/8*a^2/b^4/(b*x^2+a)^4+1/10*a^3/b^4/(b*x^2+a)^5-1/4/b^4/(b*x^2+a)^2","A"
517,1,48,47,0.009000," ","int(x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{a^{2}}{10 \left(b \,x^{2}+a \right)^{5} b^{3}}+\frac{a}{4 \left(b \,x^{2}+a \right)^{4} b^{3}}-\frac{1}{6 \left(b \,x^{2}+a \right)^{3} b^{3}}"," ",0,"-1/10*a^2/b^3/(b*x^2+a)^5+1/4*a/b^3/(b*x^2+a)^4-1/6/b^3/(b*x^2+a)^3","A"
518,1,31,30,0.009000," ","int(x^3/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{a}{10 \left(b \,x^{2}+a \right)^{5} b^{2}}-\frac{1}{8 \left(b \,x^{2}+a \right)^{4} b^{2}}"," ",0,"1/10*a/b^2/(b*x^2+a)^5-1/8/b^2/(b*x^2+a)^4","A"
519,1,15,14,0.005000," ","int(x/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{1}{10 \left(b \,x^{2}+a \right)^{5} b}"," ",0,"-1/10/b/(b*x^2+a)^5","A"
520,1,91,90,0.015000," ","int(1/x/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1}{10 \left(b \,x^{2}+a \right)^{5} a}+\frac{1}{8 \left(b \,x^{2}+a \right)^{4} a^{2}}+\frac{1}{6 \left(b \,x^{2}+a \right)^{3} a^{3}}+\frac{1}{4 \left(b \,x^{2}+a \right)^{2} a^{4}}+\frac{1}{2 \left(b \,x^{2}+a \right) a^{5}}+\frac{\ln \left(x \right)}{a^{6}}-\frac{\ln \left(b \,x^{2}+a \right)}{2 a^{6}}"," ",0,"1/10/a/(b*x^2+a)^5+1/8/a^2/(b*x^2+a)^4+1/6/a^3/(b*x^2+a)^3+1/4/a^4/(b*x^2+a)^2+1/2/a^5/(b*x^2+a)+ln(x)/a^6-1/2*ln(b*x^2+a)/a^6","A"
521,1,107,106,0.018000," ","int(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{b}{10 \left(b \,x^{2}+a \right)^{5} a^{2}}-\frac{b}{4 \left(b \,x^{2}+a \right)^{4} a^{3}}-\frac{b}{2 \left(b \,x^{2}+a \right)^{3} a^{4}}-\frac{b}{\left(b \,x^{2}+a \right)^{2} a^{5}}-\frac{5 b}{2 \left(b \,x^{2}+a \right) a^{6}}-\frac{6 b \ln \left(x \right)}{a^{7}}+\frac{3 b \ln \left(b \,x^{2}+a \right)}{a^{7}}-\frac{1}{2 a^{6} x^{2}}"," ",0,"-1/2/a^6/x^2-1/10*b/a^2/(b*x^2+a)^5-1/4*b/a^3/(b*x^2+a)^4-1/2*b/a^4/(b*x^2+a)^3-b/a^5/(b*x^2+a)^2-5/2*b/a^6/(b*x^2+a)-6*b*ln(x)/a^7+3*b*ln(b*x^2+a)/a^7","A"
522,1,129,128,0.018000," ","int(1/x^5/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{b^{2}}{10 \left(b \,x^{2}+a \right)^{5} a^{3}}+\frac{3 b^{2}}{8 \left(b \,x^{2}+a \right)^{4} a^{4}}+\frac{b^{2}}{\left(b \,x^{2}+a \right)^{3} a^{5}}+\frac{5 b^{2}}{2 \left(b \,x^{2}+a \right)^{2} a^{6}}+\frac{15 b^{2}}{2 \left(b \,x^{2}+a \right) a^{7}}+\frac{21 b^{2} \ln \left(x \right)}{a^{8}}-\frac{21 b^{2} \ln \left(b \,x^{2}+a \right)}{2 a^{8}}+\frac{3 b}{a^{7} x^{2}}-\frac{1}{4 a^{6} x^{4}}"," ",0,"-1/4/a^6/x^4+3*b/a^7/x^2+1/10*b^2/a^3/(b*x^2+a)^5+3/8*b^2/a^4/(b*x^2+a)^4+b^2/a^5/(b*x^2+a)^3+5/2*b^2/a^6/(b*x^2+a)^2+15/2*b^2/a^7/(b*x^2+a)+21*b^2*ln(x)/a^8-21/2*b^2*ln(b*x^2+a)/a^8","A"
523,1,148,129,0.016000," ","int(x^16/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{5327 a^{3} x^{9}}{256 \left(b \,x^{2}+a \right)^{5} b^{4}}+\frac{9443 a^{4} x^{7}}{128 \left(b \,x^{2}+a \right)^{5} b^{5}}+\frac{1001 a^{5} x^{5}}{10 \left(b \,x^{2}+a \right)^{5} b^{6}}+\frac{7837 a^{6} x^{3}}{128 \left(b \,x^{2}+a \right)^{5} b^{7}}+\frac{3633 a^{7} x}{256 \left(b \,x^{2}+a \right)^{5} b^{8}}+\frac{x^{5}}{5 b^{6}}-\frac{2 a \,x^{3}}{b^{7}}-\frac{9009 a^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, b^{8}}+\frac{21 a^{2} x}{b^{8}}"," ",0,"1/5*x^5/b^6-2*a*x^3/b^7+21*a^2*x/b^8+5327/256/b^4*a^3/(b*x^2+a)^5*x^9+9443/128/b^5*a^4/(b*x^2+a)^5*x^7+1001/10/b^6*a^5/(b*x^2+a)^5*x^5+7837/128/b^7*a^6/(b*x^2+a)^5*x^3+3633/256/b^8*a^7/(b*x^2+a)^5*x-9009/256/b^8*a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
524,1,137,118,0.017000," ","int(x^14/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{2373 a^{2} x^{9}}{256 \left(b \,x^{2}+a \right)^{5} b^{3}}-\frac{12131 a^{3} x^{7}}{384 \left(b \,x^{2}+a \right)^{5} b^{4}}-\frac{1253 a^{4} x^{5}}{30 \left(b \,x^{2}+a \right)^{5} b^{5}}-\frac{9629 a^{5} x^{3}}{384 \left(b \,x^{2}+a \right)^{5} b^{6}}-\frac{1467 a^{6} x}{256 \left(b \,x^{2}+a \right)^{5} b^{7}}+\frac{x^{3}}{3 b^{6}}+\frac{3003 a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, b^{7}}-\frac{6 a x}{b^{7}}"," ",0,"1/3*x^3/b^6-6*a*x/b^7-2373/256/b^3*a^2/(b*x^2+a)^5*x^9-12131/384/b^4*a^3/(b*x^2+a)^5*x^7-1253/30/b^5*a^4/(b*x^2+a)^5*x^5-9629/384/b^6*a^5/(b*x^2+a)^5*x^3-1467/256/b^7*a^6/(b*x^2+a)^5*x+3003/256/b^7*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
525,1,123,109,0.016000," ","int(x^12/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{843 a \,x^{9}}{256 \left(b \,x^{2}+a \right)^{5} b^{2}}+\frac{1327 a^{2} x^{7}}{128 \left(b \,x^{2}+a \right)^{5} b^{3}}+\frac{131 a^{3} x^{5}}{10 \left(b \,x^{2}+a \right)^{5} b^{4}}+\frac{977 a^{4} x^{3}}{128 \left(b \,x^{2}+a \right)^{5} b^{5}}+\frac{437 a^{5} x}{256 \left(b \,x^{2}+a \right)^{5} b^{6}}-\frac{693 a \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, b^{6}}+\frac{x}{b^{6}}"," ",0,"x/b^6+843/256/b^2*a/(b*x^2+a)^5*x^9+1327/128/b^3*a^2/(b*x^2+a)^5*x^7+131/10/b^4*a^3/(b*x^2+a)^5*x^5+977/128/b^5*a^4/(b*x^2+a)^5*x^3+437/256/b^6*a^5/(b*x^2+a)^5*x-693/256/b^6*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
526,1,80,101,0.013000," ","int(x^10/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{63 \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, b^{5}}+\frac{-\frac{193 x^{9}}{256 b}-\frac{237 a \,x^{7}}{128 b^{2}}-\frac{21 a^{2} x^{5}}{10 b^{3}}-\frac{147 a^{3} x^{3}}{128 b^{4}}-\frac{63 a^{4} x}{256 b^{5}}}{\left(b \,x^{2}+a \right)^{5}}"," ",0,"(-193/256/b*x^9-237/128*a/b^2*x^7-21/10*a^2/b^3*x^5-147/128*a^3/b^4*x^3-63/256*a^4/b^5*x)/(b*x^2+a)^5+63/256/b^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
527,1,80,102,0.012000," ","int(x^8/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{7 \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, a \,b^{4}}+\frac{\frac{7 x^{9}}{256 a}-\frac{79 x^{7}}{384 b}-\frac{7 a \,x^{5}}{30 b^{2}}-\frac{49 a^{2} x^{3}}{384 b^{3}}-\frac{7 a^{3} x}{256 b^{4}}}{\left(b \,x^{2}+a \right)^{5}}"," ",0,"(7/256/a*x^9-79/384/b*x^7-7/30*a/b^2*x^5-49/384*a^2/b^3*x^3-7/256*a^3/b^4*x)/(b*x^2+a)^5+7/256/a/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
528,1,78,103,0.012000," ","int(x^6/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{3 \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, a^{2} b^{3}}+\frac{\frac{3 b \,x^{9}}{256 a^{2}}+\frac{7 x^{7}}{128 a}-\frac{x^{5}}{10 b}-\frac{7 a \,x^{3}}{128 b^{2}}-\frac{3 a^{2} x}{256 b^{3}}}{\left(b \,x^{2}+a \right)^{5}}"," ",0,"(3/256/a^2*b*x^9+7/128/a*x^7-1/10/b*x^5-7/128*a/b^2*x^3-3/256*a^2/b^3*x)/(b*x^2+a)^5+3/256/a^2/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
529,1,78,104,0.012000," ","int(x^4/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{3 \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, a^{3} b^{2}}+\frac{\frac{3 b^{2} x^{9}}{256 a^{3}}+\frac{7 b \,x^{7}}{128 a^{2}}+\frac{x^{5}}{10 a}-\frac{7 x^{3}}{128 b}-\frac{3 a x}{256 b^{2}}}{\left(b \,x^{2}+a \right)^{5}}"," ",0,"(3/256/a^3*b^2*x^9+7/128/a^2*b*x^7+1/10/a*x^5-7/128/b*x^3-3/256*a/b^2*x)/(b*x^2+a)^5+3/256/a^3/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
530,1,80,105,0.012000," ","int(x^2/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{7 \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, a^{4} b}+\frac{\frac{7 b^{3} x^{9}}{256 a^{4}}+\frac{49 b^{2} x^{7}}{384 a^{3}}+\frac{7 b \,x^{5}}{30 a^{2}}+\frac{79 x^{3}}{384 a}-\frac{7 x}{256 b}}{\left(b \,x^{2}+a \right)^{5}}"," ",0,"(7/256/a^4*b^3*x^9+49/384/a^3*b^2*x^7+7/30/a^2*b*x^5+79/384/a*x^3-7/256/b*x)/(b*x^2+a)^5+7/256/a^4/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
531,1,96,93,0.006000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{x}{10 \left(b \,x^{2}+a \right)^{5} a}+\frac{9 x}{80 \left(b \,x^{2}+a \right)^{4} a^{2}}+\frac{21 x}{160 \left(b \,x^{2}+a \right)^{3} a^{3}}+\frac{21 x}{128 \left(b \,x^{2}+a \right)^{2} a^{4}}+\frac{63 x}{256 \left(b \,x^{2}+a \right) a^{5}}+\frac{63 \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, a^{5}}"," ",0,"1/10*x/a/(b*x^2+a)^5+9/80*x/a^2/(b*x^2+a)^4+21/160*x/a^3/(b*x^2+a)^3+21/128*x/a^4/(b*x^2+a)^2+63/256*x/a^5/(b*x^2+a)+63/256/a^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
532,1,126,111,0.017000," ","int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{437 b^{5} x^{9}}{256 \left(b \,x^{2}+a \right)^{5} a^{6}}-\frac{977 b^{4} x^{7}}{128 \left(b \,x^{2}+a \right)^{5} a^{5}}-\frac{131 b^{3} x^{5}}{10 \left(b \,x^{2}+a \right)^{5} a^{4}}-\frac{1327 b^{2} x^{3}}{128 \left(b \,x^{2}+a \right)^{5} a^{3}}-\frac{843 b x}{256 \left(b \,x^{2}+a \right)^{5} a^{2}}-\frac{693 b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, a^{6}}-\frac{1}{a^{6} x}"," ",0,"-1/a^6/x-437/256*b^5/a^6/(b*x^2+a)^5*x^9-977/128*b^4/a^5/(b*x^2+a)^5*x^7-131/10*b^3/a^4/(b*x^2+a)^5*x^5-1327/128*b^2/a^3/(b*x^2+a)^5*x^3-843/256*b/a^2/(b*x^2+a)^5*x-693/256*b/a^6/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
533,1,139,120,0.019000," ","int(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{1467 b^{6} x^{9}}{256 \left(b \,x^{2}+a \right)^{5} a^{7}}+\frac{9629 b^{5} x^{7}}{384 \left(b \,x^{2}+a \right)^{5} a^{6}}+\frac{1253 b^{4} x^{5}}{30 \left(b \,x^{2}+a \right)^{5} a^{5}}+\frac{12131 b^{3} x^{3}}{384 \left(b \,x^{2}+a \right)^{5} a^{4}}+\frac{2373 b^{2} x}{256 \left(b \,x^{2}+a \right)^{5} a^{3}}+\frac{3003 b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, a^{7}}+\frac{6 b}{a^{7} x}-\frac{1}{3 a^{6} x^{3}}"," ",0,"-1/3/a^6/x^3+6*b/a^7/x+1467/256/a^7*b^6/(b*x^2+a)^5*x^9+9629/384/a^6*b^5/(b*x^2+a)^5*x^7+1253/30/a^5*b^4/(b*x^2+a)^5*x^5+12131/384/a^4*b^3/(b*x^2+a)^5*x^3+2373/256/a^3*b^2/(b*x^2+a)^5*x+3003/256/a^7*b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
534,1,150,131,0.019000," ","int(1/x^6/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{3633 b^{7} x^{9}}{256 \left(b \,x^{2}+a \right)^{5} a^{8}}-\frac{7837 b^{6} x^{7}}{128 \left(b \,x^{2}+a \right)^{5} a^{7}}-\frac{1001 b^{5} x^{5}}{10 \left(b \,x^{2}+a \right)^{5} a^{6}}-\frac{9443 b^{4} x^{3}}{128 \left(b \,x^{2}+a \right)^{5} a^{5}}-\frac{5327 b^{3} x}{256 \left(b \,x^{2}+a \right)^{5} a^{4}}-\frac{9009 b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{256 \sqrt{a b}\, a^{8}}-\frac{21 b^{2}}{a^{8} x}+\frac{2 b}{a^{7} x^{3}}-\frac{1}{5 a^{6} x^{5}}"," ",0,"-1/5/a^6/x^5-21*b^2/a^8/x+2*b/a^7/x^3-3633/256*b^7/a^8/(b*x^2+a)^5*x^9-7837/128*b^6/a^7/(b*x^2+a)^5*x^7-1001/10*b^5/a^6/(b*x^2+a)^5*x^5-9443/128*b^4/a^5/(b*x^2+a)^5*x^3-5327/256*b^3/a^4/(b*x^2+a)^5*x-9009/256*b^3/a^8/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
535,1,16,15,0.005000," ","int(1/(x^4+2*x^2+1),x)","\frac{x}{2 x^{2}+2}+\frac{\arctan \left(x \right)}{2}"," ",0,"1/2/(x^2+1)*x+1/2*arctan(x)","A"
536,1,10,9,0.005000," ","int(x/(x^4+2*x^2+1),x)","-\frac{1}{2 \left(x^{2}+1\right)}"," ",0,"-1/2/(x^2+1)","A"
537,1,16,15,0.006000," ","int(x^2/(x^4+2*x^2+1),x)","-\frac{x}{2 \left(x^{2}+1\right)}+\frac{\arctan \left(x \right)}{2}"," ",0,"-1/2/(x^2+1)*x+1/2*arctan(x)","A"
538,1,19,18,0.004000," ","int(x^3/(x^4+2*x^2+1),x)","\frac{\ln \left(x^{2}+1\right)}{2}+\frac{1}{2 x^{2}+2}"," ",0,"1/2/(x^2+1)+1/2*ln(x^2+1)","A"
539,1,10,11,0.004000," ","int(x/(x^4-18*x^2+81),x)","-\frac{1}{2 \left(x^{2}-9\right)}"," ",0,"-1/2/(x^2-9)","A"
540,1,19,22,0.005000," ","int(x^3/(x^4-8*x^2+16),x)","\frac{\ln \left(x^{2}-4\right)}{2}-\frac{2}{x^{2}-4}"," ",0,"1/2*ln(x^2-4)-2/(x^2-4)","A"
541,1,36,53,0.008000," ","int(x^5*((b*x^2+a)^2)^(1/2),x)","\frac{\left(3 b \,x^{2}+4 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x^{6}}{24 b \,x^{2}+24 a}"," ",0,"1/24*x^6*(3*b*x^2+4*a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
542,1,36,50,0.004000," ","int(x^3*((b*x^2+a)^2)^(1/2),x)","\frac{\left(2 b \,x^{2}+3 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x^{4}}{12 b \,x^{2}+12 a}"," ",0,"1/12*x^4*(2*b*x^2+3*a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
543,1,35,23,0.010000," ","int(x*((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+2 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x^{2}}{4 b \,x^{2}+4 a}"," ",0,"1/4*x^2*(b*x^2+2*a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
544,1,34,51,0.014000," ","int(((b*x^2+a)^2)^(1/2)/x,x)","\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(b \,x^{2}+2 a \ln \left(x \right)\right)}{2 b \,x^{2}+2 a}"," ",0,"1/2*((b*x^2+a)^2)^(1/2)*(b*x^2+2*a*ln(x))/(b*x^2+a)","A"
545,1,38,51,0.009000," ","int(((b*x^2+a)^2)^(1/2)/x^3,x)","\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(2 b \,x^{2} \ln \left(x \right)-a \right)}{2 \left(b \,x^{2}+a \right) x^{2}}"," ",0,"1/2*((b*x^2+a)^2)^(1/2)*(2*b*ln(x)*x^2-a)/(b*x^2+a)/x^2","A"
546,1,34,26,0.003000," ","int(((b*x^2+a)^2)^(1/2)/x^5,x)","-\frac{\left(2 b \,x^{2}+a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{4 \left(b \,x^{2}+a \right) x^{4}}"," ",0,"-1/4*(2*b*x^2+a)*((b*x^2+a)^2)^(1/2)/x^4/(b*x^2+a)","A"
547,1,36,55,0.003000," ","int(((b*x^2+a)^2)^(1/2)/x^7,x)","-\frac{\left(3 b \,x^{2}+2 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{12 \left(b \,x^{2}+a \right) x^{6}}"," ",0,"-1/12*(3*b*x^2+2*a)*((b*x^2+a)^2)^(1/2)/x^6/(b*x^2+a)","A"
548,1,36,53,0.005000," ","int(((b*x^2+a)^2)^(1/2)/x^9,x)","-\frac{\left(4 b \,x^{2}+3 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{24 \left(b \,x^{2}+a \right) x^{8}}"," ",0,"-1/24*(4*b*x^2+3*a)*((b*x^2+a)^2)^(1/2)/x^8/(b*x^2+a)","A"
549,1,36,53,0.004000," ","int(((b*x^2+a)^2)^(1/2)/x^11,x)","-\frac{\left(5 b \,x^{2}+4 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{40 \left(b \,x^{2}+a \right) x^{10}}"," ",0,"-1/40*(5*b*x^2+4*a)*((b*x^2+a)^2)^(1/2)/x^10/(b*x^2+a)","A"
550,1,36,53,0.004000," ","int(x^4*((b*x^2+a)^2)^(1/2),x)","\frac{\left(5 b \,x^{2}+7 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x^{5}}{35 b \,x^{2}+35 a}"," ",0,"1/35*x^5*(5*b*x^2+7*a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
551,1,36,53,0.003000," ","int(x^2*((b*x^2+a)^2)^(1/2),x)","\frac{\left(3 b \,x^{2}+5 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x^{3}}{15 b \,x^{2}+15 a}"," ",0,"1/15*x^3*(3*b*x^2+5*a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
552,1,33,50,0.003000," ","int(((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+3 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x}{3 b \,x^{2}+3 a}"," ",0,"1/3*x*(b*x^2+3*a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
553,1,34,50,0.003000," ","int(((b*x^2+a)^2)^(1/2)/x^2,x)","-\frac{\left(-b \,x^{2}+a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{\left(b \,x^{2}+a \right) x}"," ",0,"-(-b*x^2+a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)/x","A"
554,1,34,53,0.003000," ","int(((b*x^2+a)^2)^(1/2)/x^4,x)","-\frac{\left(3 b \,x^{2}+a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{3 \left(b \,x^{2}+a \right) x^{3}}"," ",0,"-1/3*(3*b*x^2+a)*((b*x^2+a)^2)^(1/2)/x^3/(b*x^2+a)","A"
555,1,36,53,0.004000," ","int(((b*x^2+a)^2)^(1/2)/x^6,x)","-\frac{\left(5 b \,x^{2}+3 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{15 \left(b \,x^{2}+a \right) x^{5}}"," ",0,"-1/15*(5*b*x^2+3*a)*((b*x^2+a)^2)^(1/2)/x^5/(b*x^2+a)","A"
556,1,36,53,0.002000," ","int(((b*x^2+a)^2)^(1/2)/x^8,x)","-\frac{\left(7 b \,x^{2}+5 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{35 \left(b \,x^{2}+a \right) x^{7}}"," ",0,"-1/35*(7*b*x^2+5*a)*((b*x^2+a)^2)^(1/2)/x^7/(b*x^2+a)","A"
557,1,36,53,0.006000," ","int(((b*x^2+a)^2)^(1/2)/x^10,x)","-\frac{\left(9 b \,x^{2}+7 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}}{63 \left(b \,x^{2}+a \right) x^{9}}"," ",0,"-1/63*(9*b*x^2+7*a)*((b*x^2+a)^2)^(1/2)/x^9/(b*x^2+a)","A"
558,1,58,115,0.007000," ","int(x^9*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(35 b^{3} x^{6}+120 a \,b^{2} x^{4}+140 a^{2} b \,x^{2}+56 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{10}}{560 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/560*x^10*(35*b^3*x^6+120*a*b^2*x^4+140*a^2*b*x^2+56*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
559,1,58,115,0.007000," ","int(x^7*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(20 b^{3} x^{6}+70 a \,b^{2} x^{4}+84 a^{2} b \,x^{2}+35 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{8}}{280 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/280*x^8*(20*b^3*x^6+70*a*b^2*x^4+84*a^2*b*x^2+35*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
560,1,58,94,0.007000," ","int(x^5*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(10 b^{3} x^{6}+36 a \,b^{2} x^{4}+45 a^{2} b \,x^{2}+20 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{6}}{120 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/120*x^6*(10*b^3*x^6+36*a*b^2*x^4+45*a^2*b*x^2+20*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
561,1,58,59,0.006000," ","int(x^3*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(4 b^{3} x^{6}+15 a \,b^{2} x^{4}+20 a^{2} b \,x^{2}+10 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{4}}{40 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/40*x^4*(4*b^3*x^6+15*a*b^2*x^4+20*a^2*b*x^2+10*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
562,1,57,32,0.005000," ","int(x*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(b^{3} x^{6}+4 a \,b^{2} x^{4}+6 a^{2} b \,x^{2}+4 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{2}}{8 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/8*x^2*(b^3*x^6+4*a*b^2*x^4+6*a^2*b*x^2+4*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
563,1,57,113,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} \left(2 b^{3} x^{6}+9 a \,b^{2} x^{4}+18 a^{2} b \,x^{2}+12 a^{3} \ln \left(x \right)\right)}{12 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/12*((b*x^2+a)^2)^(3/2)*(2*b^3*x^6+9*a*b^2*x^4+18*a^2*b*x^2+12*a^3*ln(x))/(b*x^2+a)^3","A"
564,1,59,114,0.012000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^3,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} \left(b^{3} x^{6}+6 a \,b^{2} x^{4}+12 a^{2} b \,x^{2} \ln \left(x \right)-2 a^{3}\right)}{4 \left(b \,x^{2}+a \right)^{3} x^{2}}"," ",0,"1/4*((b*x^2+a)^2)^(3/2)*(b^3*x^6+6*a*b^2*x^4+12*a^2*b*ln(x)*x^2-2*a^3)/(b*x^2+a)^3/x^2","A"
565,1,60,114,0.014000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^5,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} \left(2 b^{3} x^{6}+12 a \,b^{2} x^{4} \ln \left(x \right)-6 a^{2} b \,x^{2}-a^{3}\right)}{4 \left(b \,x^{2}+a \right)^{3} x^{4}}"," ",0,"1/4*((b*x^2+a)^2)^(3/2)*(2*b^3*x^6+12*a*b^2*ln(x)*x^4-6*a^2*b*x^2-a^3)/(b*x^2+a)^3/x^4","A"
566,1,60,113,0.014000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^7,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} \left(12 b^{3} x^{6} \ln \left(x \right)-18 a \,b^{2} x^{4}-9 a^{2} b \,x^{2}-2 a^{3}\right)}{12 \left(b \,x^{2}+a \right)^{3} x^{6}}"," ",0,"1/12*((b*x^2+a)^2)^(3/2)*(12*b^3*ln(x)*x^6-18*a*b^2*x^4-9*a^2*b*x^2-2*a^3)/(b*x^2+a)^3/x^6","A"
567,1,56,28,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^9,x)","-\frac{\left(4 b^{3} x^{6}+6 a \,b^{2} x^{4}+4 a^{2} b \,x^{2}+a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{8 \left(b \,x^{2}+a \right)^{3} x^{8}}"," ",0,"-1/8*(4*b^3*x^6+6*a*b^2*x^4+4*a^2*b*x^2+a^3)*((b*x^2+a)^2)^(3/2)/x^8/(b*x^2+a)^3","A"
568,1,58,64,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^11,x)","-\frac{\left(10 b^{3} x^{6}+20 a \,b^{2} x^{4}+15 a^{2} b \,x^{2}+4 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{40 \left(b \,x^{2}+a \right)^{3} x^{10}}"," ",0,"-1/40*(10*b^3*x^6+20*a*b^2*x^4+15*a^2*b*x^2+4*a^3)*((b*x^2+a)^2)^(3/2)/x^10/(b*x^2+a)^3","A"
569,1,58,115,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^13,x)","-\frac{\left(20 b^{3} x^{6}+45 a \,b^{2} x^{4}+36 a^{2} b \,x^{2}+10 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{120 \left(b \,x^{2}+a \right)^{3} x^{12}}"," ",0,"-1/120*(20*b^3*x^6+45*a*b^2*x^4+36*a^2*b*x^2+10*a^3)*((b*x^2+a)^2)^(3/2)/x^12/(b*x^2+a)^3","A"
570,1,58,115,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^15,x)","-\frac{\left(35 b^{3} x^{6}+84 a \,b^{2} x^{4}+70 a^{2} b \,x^{2}+20 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{280 \left(b \,x^{2}+a \right)^{3} x^{14}}"," ",0,"-1/280*(35*b^3*x^6+84*a*b^2*x^4+70*a^2*b*x^2+20*a^3)*((b*x^2+a)^2)^(3/2)/x^14/(b*x^2+a)^3","A"
571,1,58,115,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^17,x)","-\frac{\left(56 b^{3} x^{6}+140 a \,b^{2} x^{4}+120 a^{2} b \,x^{2}+35 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{560 \left(b \,x^{2}+a \right)^{3} x^{16}}"," ",0,"-1/560*(56*b^3*x^6+140*a*b^2*x^4+120*a^2*b*x^2+35*a^3)*((b*x^2+a)^2)^(3/2)/x^16/(b*x^2+a)^3","A"
572,1,58,115,0.009000," ","int(x^8*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(429 b^{3} x^{6}+1485 a \,b^{2} x^{4}+1755 a^{2} b \,x^{2}+715 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{9}}{6435 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/6435*x^9*(429*b^3*x^6+1485*a*b^2*x^4+1755*a^2*b*x^2+715*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
573,1,58,115,0.008000," ","int(x^6*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(231 b^{3} x^{6}+819 a \,b^{2} x^{4}+1001 a^{2} b \,x^{2}+429 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{7}}{3003 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/3003*x^7*(231*b^3*x^6+819*a*b^2*x^4+1001*a^2*b*x^2+429*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
574,1,58,115,0.007000," ","int(x^4*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(105 b^{3} x^{6}+385 a \,b^{2} x^{4}+495 a^{2} b \,x^{2}+231 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{5}}{1155 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/1155*x^5*(105*b^3*x^6+385*a*b^2*x^4+495*a^2*b*x^2+231*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
575,1,58,115,0.007000," ","int(x^2*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(35 b^{3} x^{6}+135 a \,b^{2} x^{4}+189 a^{2} b \,x^{2}+105 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x^{3}}{315 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/315*x^3*(35*b^3*x^6+135*a*b^2*x^4+189*a^2*b*x^2+105*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
576,1,56,147,0.004000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(5 b^{3} x^{6}+21 a \,b^{2} x^{4}+35 a^{2} b \,x^{2}+35 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x}{35 \left(b \,x^{2}+a \right)^{3}}"," ",0,"1/35*x*(5*b^3*x^6+21*a*b^2*x^4+35*a^2*b*x^2+35*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
577,1,58,112,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^2,x)","-\frac{\left(-b^{3} x^{6}-5 a \,b^{2} x^{4}-15 a^{2} b \,x^{2}+5 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{5 \left(b \,x^{2}+a \right)^{3} x}"," ",0,"-1/5*(-b^3*x^6-5*a*b^2*x^4-15*a^2*b*x^2+5*a^3)*((b*x^2+a)^2)^(3/2)/x/(b*x^2+a)^3","A"
578,1,56,113,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^4,x)","-\frac{\left(-b^{3} x^{6}-9 a \,b^{2} x^{4}+9 a^{2} b \,x^{2}+a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{3 \left(b \,x^{2}+a \right)^{3} x^{3}}"," ",0,"-1/3*(-b^3*x^6-9*a*b^2*x^4+9*a^2*b*x^2+a^3)*((b*x^2+a)^2)^(3/2)/x^3/(b*x^2+a)^3","A"
579,1,56,112,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^6,x)","-\frac{\left(-5 b^{3} x^{6}+15 a \,b^{2} x^{4}+5 a^{2} b \,x^{2}+a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{5 \left(b \,x^{2}+a \right)^{3} x^{5}}"," ",0,"-1/5*(-5*b^3*x^6+15*a*b^2*x^4+5*a^2*b*x^2+a^3)*((b*x^2+a)^2)^(3/2)/x^5/(b*x^2+a)^3","A"
580,1,58,115,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^8,x)","-\frac{\left(35 b^{3} x^{6}+35 a \,b^{2} x^{4}+21 a^{2} b \,x^{2}+5 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{35 \left(b \,x^{2}+a \right)^{3} x^{7}}"," ",0,"-1/35*(35*b^3*x^6+35*a*b^2*x^4+21*a^2*b*x^2+5*a^3)*((b*x^2+a)^2)^(3/2)/x^7/(b*x^2+a)^3","A"
581,1,58,115,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^10,x)","-\frac{\left(105 b^{3} x^{6}+189 a \,b^{2} x^{4}+135 a^{2} b \,x^{2}+35 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{315 \left(b \,x^{2}+a \right)^{3} x^{9}}"," ",0,"-1/315*(105*b^3*x^6+189*a*b^2*x^4+135*a^2*b*x^2+35*a^3)*((b*x^2+a)^2)^(3/2)/x^9/(b*x^2+a)^3","A"
582,1,58,115,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^12,x)","-\frac{\left(231 b^{3} x^{6}+495 a \,b^{2} x^{4}+385 a^{2} b \,x^{2}+105 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{1155 \left(b \,x^{2}+a \right)^{3} x^{11}}"," ",0,"-1/1155*(231*b^3*x^6+495*a*b^2*x^4+385*a^2*b*x^2+105*a^3)*((b*x^2+a)^2)^(3/2)/x^11/(b*x^2+a)^3","A"
583,1,58,115,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^14,x)","-\frac{\left(429 b^{3} x^{6}+1001 a \,b^{2} x^{4}+819 a^{2} b \,x^{2}+231 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{3003 \left(b \,x^{2}+a \right)^{3} x^{13}}"," ",0,"-1/3003*(429*b^3*x^6+1001*a*b^2*x^4+819*a^2*b*x^2+231*a^3)*((b*x^2+a)^2)^(3/2)/x^13/(b*x^2+a)^3","A"
584,1,58,115,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/x^16,x)","-\frac{\left(715 b^{3} x^{6}+1755 a \,b^{2} x^{4}+1485 a^{2} b \,x^{2}+429 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}}}{6435 \left(b \,x^{2}+a \right)^{3} x^{15}}"," ",0,"-1/6435*(715*b^3*x^6+1755*a*b^2*x^4+1485*a^2*b*x^2+429*a^3)*((b*x^2+a)^2)^(3/2)/x^15/(b*x^2+a)^3","A"
585,1,80,177,0.010000," ","int(x^13*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(462 b^{5} x^{10}+2520 a \,b^{4} x^{8}+5544 a^{2} b^{3} x^{6}+6160 a^{3} b^{2} x^{4}+3465 a^{4} b \,x^{2}+792 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{14}}{11088 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/11088*x^14*(462*b^5*x^10+2520*a*b^4*x^8+5544*a^2*b^3*x^6+6160*a^3*b^2*x^4+3465*a^4*b*x^2+792*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
586,1,80,177,0.010000," ","int(x^11*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(252 b^{5} x^{10}+1386 a \,b^{4} x^{8}+3080 a^{2} b^{3} x^{6}+3465 a^{3} b^{2} x^{4}+1980 a^{4} b \,x^{2}+462 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{12}}{5544 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/5544*x^12*(252*b^5*x^10+1386*a*b^4*x^8+3080*a^2*b^3*x^6+3465*a^3*b^2*x^4+1980*a^4*b*x^2+462*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
587,1,80,136,0.009000," ","int(x^9*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(126 b^{5} x^{10}+700 a \,b^{4} x^{8}+1575 a^{2} b^{3} x^{6}+1800 a^{3} b^{2} x^{4}+1050 a^{4} b \,x^{2}+252 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{10}}{2520 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/2520*x^10*(126*b^5*x^10+700*a*b^4*x^8+1575*a^2*b^3*x^6+1800*a^3*b^2*x^4+1050*a^4*b*x^2+252*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
588,1,80,108,0.008000," ","int(x^7*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(56 b^{5} x^{10}+315 a \,b^{4} x^{8}+720 a^{2} b^{3} x^{6}+840 a^{3} b^{2} x^{4}+504 a^{4} b \,x^{2}+126 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{8}}{1008 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/1008*x^8*(56*b^5*x^10+315*a*b^4*x^8+720*a^2*b^3*x^6+840*a^3*b^2*x^4+504*a^4*b*x^2+126*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
589,1,80,80,0.008000," ","int(x^5*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(21 b^{5} x^{10}+120 a \,b^{4} x^{8}+280 a^{2} b^{3} x^{6}+336 a^{3} b^{2} x^{4}+210 a^{4} b \,x^{2}+56 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{6}}{336 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/336*x^6*(21*b^5*x^10+120*a*b^4*x^8+280*a^2*b^3*x^6+336*a^3*b^2*x^4+210*a^4*b*x^2+56*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
590,1,80,59,0.008000," ","int(x^3*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(6 b^{5} x^{10}+35 a \,b^{4} x^{8}+84 a^{2} b^{3} x^{6}+105 a^{3} b^{2} x^{4}+70 a^{4} b \,x^{2}+21 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{4}}{84 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/84*x^4*(6*b^5*x^10+35*a*b^4*x^8+84*a^2*b^3*x^6+105*a^3*b^2*x^4+70*a^4*b*x^2+21*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
591,1,79,32,0.006000," ","int(x*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(b^{5} x^{10}+6 a \,b^{4} x^{8}+15 a^{2} b^{3} x^{6}+20 a^{3} b^{2} x^{4}+15 a^{4} b \,x^{2}+6 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{2}}{12 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/12*x^2*(b^5*x^10+6*a*b^4*x^8+15*a^2*b^3*x^6+20*a^3*b^2*x^4+15*a^4*b*x^2+6*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","B"
592,1,79,175,0.011000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} \left(12 b^{5} x^{10}+75 a \,b^{4} x^{8}+200 a^{2} b^{3} x^{6}+300 a^{3} b^{2} x^{4}+300 a^{4} b \,x^{2}+120 a^{5} \ln \left(x \right)\right)}{120 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/120*((b*x^2+a)^2)^(5/2)*(12*b^5*x^10+75*a*b^4*x^8+200*a^2*b^3*x^6+300*a^3*b^2*x^4+300*a^4*b*x^2+120*a^5*ln(x))/(b*x^2+a)^5","A"
593,1,82,176,0.012000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^3,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} \left(3 b^{5} x^{10}+20 a \,b^{4} x^{8}+60 a^{2} b^{3} x^{6}+120 a^{3} b^{2} x^{4}+120 a^{4} b \,x^{2} \ln \left(x \right)-12 a^{5}\right)}{24 \left(b \,x^{2}+a \right)^{5} x^{2}}"," ",0,"1/24*((b*x^2+a)^2)^(5/2)*(3*b^5*x^10+20*a*b^4*x^8+60*a^2*b^3*x^6+120*a^3*b^2*x^4+120*a^4*b*ln(x)*x^2-12*a^5)/(b*x^2+a)^5/x^2","A"
594,1,82,176,0.014000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^5,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} \left(2 b^{5} x^{10}+15 a \,b^{4} x^{8}+60 a^{2} b^{3} x^{6}+120 a^{3} b^{2} x^{4} \ln \left(x \right)-30 a^{4} b \,x^{2}-3 a^{5}\right)}{12 \left(b \,x^{2}+a \right)^{5} x^{4}}"," ",0,"1/12*((b*x^2+a)^2)^(5/2)*(2*b^5*x^10+15*a*b^4*x^8+60*a^2*b^3*x^6+120*a^3*b^2*ln(x)*x^4-30*a^4*b*x^2-3*a^5)/(b*x^2+a)^5/x^4","A"
595,1,82,176,0.013000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^7,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} \left(3 b^{5} x^{10}+30 a \,b^{4} x^{8}+120 a^{2} b^{3} x^{6} \ln \left(x \right)-60 a^{3} b^{2} x^{4}-15 a^{4} b \,x^{2}-2 a^{5}\right)}{12 \left(b \,x^{2}+a \right)^{5} x^{6}}"," ",0,"1/12*((b*x^2+a)^2)^(5/2)*(3*b^5*x^10+30*a*b^4*x^8+120*a^2*b^3*ln(x)*x^6-60*a^3*b^2*x^4-15*a^4*b*x^2-2*a^5)/(b*x^2+a)^5/x^6","A"
596,1,82,176,0.013000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^9,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} \left(12 b^{5} x^{10}+120 a \,b^{4} x^{8} \ln \left(x \right)-120 a^{2} b^{3} x^{6}-60 a^{3} b^{2} x^{4}-20 a^{4} b \,x^{2}-3 a^{5}\right)}{24 \left(b \,x^{2}+a \right)^{5} x^{8}}"," ",0,"1/24*((b*x^2+a)^2)^(5/2)*(12*b^5*x^10+120*a*b^4*ln(x)*x^8-120*a^2*b^3*x^6-60*a^3*b^2*x^4-20*a^4*b*x^2-3*a^5)/(b*x^2+a)^5/x^8","A"
597,1,82,175,0.014000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^11,x)","\frac{\left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} \left(120 b^{5} x^{10} \ln \left(x \right)-300 a \,b^{4} x^{8}-300 a^{2} b^{3} x^{6}-200 a^{3} b^{2} x^{4}-75 a^{4} b \,x^{2}-12 a^{5}\right)}{120 \left(b \,x^{2}+a \right)^{5} x^{10}}"," ",0,"1/120*((b*x^2+a)^2)^(5/2)*(120*b^5*ln(x)*x^10-300*a*b^4*x^8-300*a^2*b^3*x^6-200*a^3*b^2*x^4-75*a^4*b*x^2-12*a^5)/(b*x^2+a)^5/x^10","A"
598,1,78,28,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^13,x)","-\frac{\left(6 b^{5} x^{10}+15 a \,b^{4} x^{8}+20 a^{2} b^{3} x^{6}+15 a^{3} b^{2} x^{4}+6 a^{4} b \,x^{2}+a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{12 \left(b \,x^{2}+a \right)^{5} x^{12}}"," ",0,"-1/12*(6*b^5*x^10+15*a*b^4*x^8+20*a^2*b^3*x^6+15*a^3*b^2*x^4+6*a^4*b*x^2+a^5)*((b*x^2+a)^2)^(5/2)/x^12/(b*x^2+a)^5","B"
599,1,80,64,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^15,x)","-\frac{\left(21 b^{5} x^{10}+70 a \,b^{4} x^{8}+105 a^{2} b^{3} x^{6}+84 a^{3} b^{2} x^{4}+35 a^{4} b \,x^{2}+6 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{84 \left(b \,x^{2}+a \right)^{5} x^{14}}"," ",0,"-1/84*(21*b^5*x^10+70*a*b^4*x^8+105*a^2*b^3*x^6+84*a^3*b^2*x^4+35*a^4*b*x^2+6*a^5)*((b*x^2+a)^2)^(5/2)/x^14/(b*x^2+a)^5","A"
600,1,80,89,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^17,x)","-\frac{\left(56 b^{5} x^{10}+210 a \,b^{4} x^{8}+336 a^{2} b^{3} x^{6}+280 a^{3} b^{2} x^{4}+120 a^{4} b \,x^{2}+21 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{336 \left(b \,x^{2}+a \right)^{5} x^{16}}"," ",0,"-1/336*(56*b^5*x^10+210*a*b^4*x^8+336*a^2*b^3*x^6+280*a^3*b^2*x^4+120*a^4*b*x^2+21*a^5)*((b*x^2+a)^2)^(5/2)/x^16/(b*x^2+a)^5","A"
601,1,80,177,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^19,x)","-\frac{\left(126 b^{5} x^{10}+504 a \,b^{4} x^{8}+840 a^{2} b^{3} x^{6}+720 a^{3} b^{2} x^{4}+315 a^{4} b \,x^{2}+56 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{1008 \left(b \,x^{2}+a \right)^{5} x^{18}}"," ",0,"-1/1008*(126*b^5*x^10+504*a*b^4*x^8+840*a^2*b^3*x^6+720*a^3*b^2*x^4+315*a^4*b*x^2+56*a^5)*((b*x^2+a)^2)^(5/2)/x^18/(b*x^2+a)^5","A"
602,1,80,177,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^21,x)","-\frac{\left(252 b^{5} x^{10}+1050 a \,b^{4} x^{8}+1800 a^{2} b^{3} x^{6}+1575 a^{3} b^{2} x^{4}+700 a^{4} b \,x^{2}+126 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{2520 \left(b \,x^{2}+a \right)^{5} x^{20}}"," ",0,"-1/2520*(252*b^5*x^10+1050*a*b^4*x^8+1800*a^2*b^3*x^6+1575*a^3*b^2*x^4+700*a^4*b*x^2+126*a^5)*((b*x^2+a)^2)^(5/2)/x^20/(b*x^2+a)^5","A"
603,1,80,177,0.010000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^23,x)","-\frac{\left(462 b^{5} x^{10}+1980 a \,b^{4} x^{8}+3465 a^{2} b^{3} x^{6}+3080 a^{3} b^{2} x^{4}+1386 a^{4} b \,x^{2}+252 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{5544 \left(b \,x^{2}+a \right)^{5} x^{22}}"," ",0,"-1/5544*(462*b^5*x^10+1980*a*b^4*x^8+3465*a^2*b^3*x^6+3080*a^3*b^2*x^4+1386*a^4*b*x^2+252*a^5)*((b*x^2+a)^2)^(5/2)/x^22/(b*x^2+a)^5","A"
604,1,80,177,0.011000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^25,x)","-\frac{\left(792 b^{5} x^{10}+3465 a \,b^{4} x^{8}+6160 a^{2} b^{3} x^{6}+5544 a^{3} b^{2} x^{4}+2520 a^{4} b \,x^{2}+462 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{11088 \left(b \,x^{2}+a \right)^{5} x^{24}}"," ",0,"-1/11088*(792*b^5*x^10+3465*a*b^4*x^8+6160*a^2*b^3*x^6+5544*a^3*b^2*x^4+2520*a^4*b*x^2+462*a^5)*((b*x^2+a)^2)^(5/2)/x^24/(b*x^2+a)^5","A"
605,1,80,177,0.008000," ","int(x^12*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(88179 b^{5} x^{10}+482885 a \,b^{4} x^{8}+1067430 a^{2} b^{3} x^{6}+1193010 a^{3} b^{2} x^{4}+676039 a^{4} b \,x^{2}+156009 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{13}}{2028117 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/2028117*x^13*(88179*b^5*x^10+482885*a*b^4*x^8+1067430*a^2*b^3*x^6+1193010*a^3*b^2*x^4+676039*a^4*b*x^2+156009*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
606,1,80,177,0.009000," ","int(x^10*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(46189 b^{5} x^{10}+255255 a \,b^{4} x^{8}+570570 a^{2} b^{3} x^{6}+646646 a^{3} b^{2} x^{4}+373065 a^{4} b \,x^{2}+88179 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{11}}{969969 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/969969*x^11*(46189*b^5*x^10+255255*a*b^4*x^8+570570*a^2*b^3*x^6+646646*a^3*b^2*x^4+373065*a^4*b*x^2+88179*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
607,1,80,177,0.007000," ","int(x^8*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(21879 b^{5} x^{10}+122265 a \,b^{4} x^{8}+277134 a^{2} b^{3} x^{6}+319770 a^{3} b^{2} x^{4}+188955 a^{4} b \,x^{2}+46189 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{9}}{415701 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/415701*x^9*(21879*b^5*x^10+122265*a*b^4*x^8+277134*a^2*b^3*x^6+319770*a^3*b^2*x^4+188955*a^4*b*x^2+46189*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
608,1,80,177,0.008000," ","int(x^6*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(9009 b^{5} x^{10}+51051 a \,b^{4} x^{8}+117810 a^{2} b^{3} x^{6}+139230 a^{3} b^{2} x^{4}+85085 a^{4} b \,x^{2}+21879 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{7}}{153153 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/153153*x^7*(9009*b^5*x^10+51051*a*b^4*x^8+117810*a^2*b^3*x^6+139230*a^3*b^2*x^4+85085*a^4*b*x^2+21879*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
609,1,80,177,0.010000," ","int(x^4*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(3003 b^{5} x^{10}+17325 a \,b^{4} x^{8}+40950 a^{2} b^{3} x^{6}+50050 a^{3} b^{2} x^{4}+32175 a^{4} b \,x^{2}+9009 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{5}}{45045 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/45045*x^5*(3003*b^5*x^10+17325*a*b^4*x^8+40950*a^2*b^3*x^6+50050*a^3*b^2*x^4+32175*a^4*b*x^2+9009*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
610,1,80,176,0.008000," ","int(x^2*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(693 b^{5} x^{10}+4095 a \,b^{4} x^{8}+10010 a^{2} b^{3} x^{6}+12870 a^{3} b^{2} x^{4}+9009 a^{4} b \,x^{2}+3003 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x^{3}}{9009 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/9009*x^3*(693*b^5*x^10+4095*a*b^4*x^8+10010*a^2*b^3*x^6+12870*a^3*b^2*x^4+9009*a^4*b*x^2+3003*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
611,1,78,228,0.004000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(63 b^{5} x^{10}+385 a \,b^{4} x^{8}+990 a^{2} b^{3} x^{6}+1386 a^{3} b^{2} x^{4}+1155 a^{4} b \,x^{2}+693 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x}{693 \left(b \,x^{2}+a \right)^{5}}"," ",0,"1/693*x*(63*b^5*x^10+385*a*b^4*x^8+990*a^2*b^3*x^6+1386*a^3*b^2*x^4+1155*a^4*b*x^2+693*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
612,1,80,175,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^2,x)","-\frac{\left(-7 b^{5} x^{10}-45 a \,b^{4} x^{8}-126 a^{2} b^{3} x^{6}-210 a^{3} b^{2} x^{4}-315 a^{4} b \,x^{2}+63 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{63 \left(b \,x^{2}+a \right)^{5} x}"," ",0,"-1/63*(-7*b^5*x^10-45*a*b^4*x^8-126*a^2*b^3*x^6-210*a^3*b^2*x^4-315*a^4*b*x^2+63*a^5)*((b*x^2+a)^2)^(5/2)/x/(b*x^2+a)^5","A"
613,1,80,174,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^4,x)","-\frac{\left(-3 b^{5} x^{10}-21 a \,b^{4} x^{8}-70 a^{2} b^{3} x^{6}-210 a^{3} b^{2} x^{4}+105 a^{4} b \,x^{2}+7 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{21 \left(b \,x^{2}+a \right)^{5} x^{3}}"," ",0,"-1/21*(-3*b^5*x^10-21*a*b^4*x^8-70*a^2*b^3*x^6-210*a^3*b^2*x^4+105*a^4*b*x^2+7*a^5)*((b*x^2+a)^2)^(5/2)/x^3/(b*x^2+a)^5","A"
614,1,80,175,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^6,x)","-\frac{\left(-3 b^{5} x^{10}-25 a \,b^{4} x^{8}-150 a^{2} b^{3} x^{6}+150 a^{3} b^{2} x^{4}+25 a^{4} b \,x^{2}+3 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{15 \left(b \,x^{2}+a \right)^{5} x^{5}}"," ",0,"-1/15*(-3*b^5*x^10-25*a*b^4*x^8-150*a^2*b^3*x^6+150*a^3*b^2*x^4+25*a^4*b*x^2+3*a^5)*((b*x^2+a)^2)^(5/2)/x^5/(b*x^2+a)^5","A"
615,1,80,175,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^8,x)","-\frac{\left(-7 b^{5} x^{10}-105 a \,b^{4} x^{8}+210 a^{2} b^{3} x^{6}+70 a^{3} b^{2} x^{4}+21 a^{4} b \,x^{2}+3 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{21 \left(b \,x^{2}+a \right)^{5} x^{7}}"," ",0,"-1/21*(-7*b^5*x^10-105*a*b^4*x^8+210*a^2*b^3*x^6+70*a^3*b^2*x^4+21*a^4*b*x^2+3*a^5)*((b*x^2+a)^2)^(5/2)/x^7/(b*x^2+a)^5","A"
616,1,80,174,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^10,x)","-\frac{\left(-63 b^{5} x^{10}+315 a \,b^{4} x^{8}+210 a^{2} b^{3} x^{6}+126 a^{3} b^{2} x^{4}+45 a^{4} b \,x^{2}+7 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{63 \left(b \,x^{2}+a \right)^{5} x^{9}}"," ",0,"-1/63*(-63*b^5*x^10+315*a*b^4*x^8+210*a^2*b^3*x^6+126*a^3*b^2*x^4+45*a^4*b*x^2+7*a^5)*((b*x^2+a)^2)^(5/2)/x^9/(b*x^2+a)^5","A"
617,1,80,177,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^12,x)","-\frac{\left(693 b^{5} x^{10}+1155 a \,b^{4} x^{8}+1386 a^{2} b^{3} x^{6}+990 a^{3} b^{2} x^{4}+385 a^{4} b \,x^{2}+63 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{693 \left(b \,x^{2}+a \right)^{5} x^{11}}"," ",0,"-1/693*(693*b^5*x^10+1155*a*b^4*x^8+1386*a^2*b^3*x^6+990*a^3*b^2*x^4+385*a^4*b*x^2+63*a^5)*((b*x^2+a)^2)^(5/2)/x^11/(b*x^2+a)^5","A"
618,1,80,177,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^14,x)","-\frac{\left(3003 b^{5} x^{10}+9009 a \,b^{4} x^{8}+12870 a^{2} b^{3} x^{6}+10010 a^{3} b^{2} x^{4}+4095 a^{4} b \,x^{2}+693 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{9009 \left(b \,x^{2}+a \right)^{5} x^{13}}"," ",0,"-1/9009*(3003*b^5*x^10+9009*a*b^4*x^8+12870*a^2*b^3*x^6+10010*a^3*b^2*x^4+4095*a^4*b*x^2+693*a^5)*((b*x^2+a)^2)^(5/2)/x^13/(b*x^2+a)^5","A"
619,1,80,177,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^16,x)","-\frac{\left(9009 b^{5} x^{10}+32175 a \,b^{4} x^{8}+50050 a^{2} b^{3} x^{6}+40950 a^{3} b^{2} x^{4}+17325 a^{4} b \,x^{2}+3003 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{45045 \left(b \,x^{2}+a \right)^{5} x^{15}}"," ",0,"-1/45045*(9009*b^5*x^10+32175*a*b^4*x^8+50050*a^2*b^3*x^6+40950*a^3*b^2*x^4+17325*a^4*b*x^2+3003*a^5)*((b*x^2+a)^2)^(5/2)/x^15/(b*x^2+a)^5","A"
620,1,80,177,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^18,x)","-\frac{\left(21879 b^{5} x^{10}+85085 a \,b^{4} x^{8}+139230 a^{2} b^{3} x^{6}+117810 a^{3} b^{2} x^{4}+51051 a^{4} b \,x^{2}+9009 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{153153 \left(b \,x^{2}+a \right)^{5} x^{17}}"," ",0,"-1/153153*(21879*b^5*x^10+85085*a*b^4*x^8+139230*a^2*b^3*x^6+117810*a^3*b^2*x^4+51051*a^4*b*x^2+9009*a^5)*((b*x^2+a)^2)^(5/2)/x^17/(b*x^2+a)^5","A"
621,1,80,177,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^20,x)","-\frac{\left(46189 b^{5} x^{10}+188955 a \,b^{4} x^{8}+319770 a^{2} b^{3} x^{6}+277134 a^{3} b^{2} x^{4}+122265 a^{4} b \,x^{2}+21879 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{415701 \left(b \,x^{2}+a \right)^{5} x^{19}}"," ",0,"-1/415701*(46189*b^5*x^10+188955*a*b^4*x^8+319770*a^2*b^3*x^6+277134*a^3*b^2*x^4+122265*a^4*b*x^2+21879*a^5)*((b*x^2+a)^2)^(5/2)/x^19/(b*x^2+a)^5","A"
622,1,80,177,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^22,x)","-\frac{\left(88179 b^{5} x^{10}+373065 a \,b^{4} x^{8}+646646 a^{2} b^{3} x^{6}+570570 a^{3} b^{2} x^{4}+255255 a^{4} b \,x^{2}+46189 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{969969 \left(b \,x^{2}+a \right)^{5} x^{21}}"," ",0,"-1/969969*(88179*b^5*x^10+373065*a*b^4*x^8+646646*a^2*b^3*x^6+570570*a^3*b^2*x^4+255255*a^4*b*x^2+46189*a^5)*((b*x^2+a)^2)^(5/2)/x^21/(b*x^2+a)^5","A"
623,1,80,177,0.010000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/x^24,x)","-\frac{\left(156009 b^{5} x^{10}+676039 a \,b^{4} x^{8}+1193010 a^{2} b^{3} x^{6}+1067430 a^{3} b^{2} x^{4}+482885 a^{4} b \,x^{2}+88179 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}}}{2028117 \left(b \,x^{2}+a \right)^{5} x^{23}}"," ",0,"-1/2028117*(156009*b^5*x^10+676039*a*b^4*x^8+1193010*a^2*b^3*x^6+1067430*a^3*b^2*x^4+482885*a^4*b*x^2+88179*a^5)*((b*x^2+a)^2)^(5/2)/x^23/(b*x^2+a)^5","A"
624,1,52,88,0.009000," ","int(x^5/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(b^{2} x^{4}-2 a b \,x^{2}+2 a^{2} \ln \left(b \,x^{2}+a \right)\right)}{4 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, b^{3}}"," ",0,"1/4*(b*x^2+a)*(b^2*x^4-2*a*b*x^2+2*a^2*ln(b*x^2+a))/((b*x^2+a)^2)^(1/2)/b^3","A"
625,1,41,49,0.007000," ","int(x^3/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(-b \,x^{2}+a \ln \left(b \,x^{2}+a \right)\right)}{2 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, b^{2}}"," ",0,"-1/2*(b*x^2+a)*(-b*x^2+a*ln(b*x^2+a))/((b*x^2+a)^2)^(1/2)/b^2","A"
626,1,32,31,0.004000," ","int(x/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \ln \left(b \,x^{2}+a \right)}{2 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, b}"," ",0,"1/2*(b*x^2+a)*ln(b*x^2+a)/b/((b*x^2+a)^2)^(1/2)","A"
627,1,39,56,0.008000," ","int(1/x/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(2 \ln \left(x \right)-\ln \left(b \,x^{2}+a \right)\right)}{2 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, a}"," ",0,"1/2*(b*x^2+a)*(2*ln(x)-ln(b*x^2+a))/((b*x^2+a)^2)^(1/2)/a","A"
628,1,51,88,0.012000," ","int(1/x^3/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(2 b \,x^{2} \ln \left(x \right)-b \,x^{2} \ln \left(b \,x^{2}+a \right)+a \right)}{2 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, a^{2} x^{2}}"," ",0,"-1/2*(b*x^2+a)*(2*b*x^2*ln(x)-b*ln(b*x^2+a)*x^2+a)/((b*x^2+a)^2)^(1/2)/x^2/a^2","A"
629,1,63,86,0.009000," ","int(x^4/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(\sqrt{a b}\, b \,x^{3}+3 a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-3 \sqrt{a b}\, a x \right)}{3 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, \sqrt{a b}\, b^{2}}"," ",0,"1/3*(b*x^2+a)*((a*b)^(1/2)*x^3*b-3*(a*b)^(1/2)*x*a+3*a^2*arctan(1/(a*b)^(1/2)*b*x))/((b*x^2+a)^2)^(1/2)/b^2/(a*b)^(1/2)","A"
630,1,48,59,0.007000," ","int(x^2/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(-a \arctan \left(\frac{b x}{\sqrt{a b}}\right)+\sqrt{a b}\, x \right)}{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \sqrt{a b}\, b}"," ",0,"(b*x^2+a)*(x*(a*b)^(1/2)-a*arctan(1/(a*b)^(1/2)*b*x))/((b*x^2+a)^2)^(1/2)/b/(a*b)^(1/2)","A"
631,1,34,34,0.005000," ","int(1/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \sqrt{a b}}"," ",0,"1/((b*x^2+a)^2)^(1/2)*(b*x^2+a)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
632,1,50,64,0.009000," ","int(1/x^2/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(b x \arctan \left(\frac{b x}{\sqrt{a b}}\right)+\sqrt{a b}\right)}{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \sqrt{a b}\, a x}"," ",0,"-(b*x^2+a)*(b*arctan(1/(a*b)^(1/2)*b*x)*x+(a*b)^(1/2))/((b*x^2+a)^2)^(1/2)/a/x/(a*b)^(1/2)","A"
633,1,69,90,0.011000," ","int(1/x^4/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(3 b^{2} x^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 \sqrt{a b}\, b \,x^{2}-\sqrt{a b}\, a \right)}{3 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, \sqrt{a b}\, a^{2} x^{3}}"," ",0,"1/3*(b*x^2+a)*(3*b^2*arctan(1/(a*b)^(1/2)*b*x)*x^3+3*b*x^2*(a*b)^(1/2)-a*(a*b)^(1/2))/((b*x^2+a)^2)^(1/2)/a^2/x^3/(a*b)^(1/2)","A"
634,1,103,106,0.018000," ","int(x^7/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(-2 b^{3} x^{6}+6 a \,b^{2} x^{4} \ln \left(b \,x^{2}+a \right)-4 a \,b^{2} x^{4}+12 a^{2} b \,x^{2} \ln \left(b \,x^{2}+a \right)+4 a^{2} b \,x^{2}+6 a^{3} \ln \left(b \,x^{2}+a \right)+5 a^{3}\right) \left(b \,x^{2}+a \right)}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{4}}"," ",0,"-1/4*(-2*b^3*x^6+6*ln(b*x^2+a)*x^4*a*b^2-4*a*b^2*x^4+12*ln(b*x^2+a)*x^2*a^2*b+4*a^2*b*x^2+6*ln(b*x^2+a)*a^3+5*a^3)*(b*x^2+a)/b^4/((b*x^2+a)^2)^(3/2)","A"
635,1,81,76,0.015000," ","int(x^5/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(2 b^{2} x^{4} \ln \left(b \,x^{2}+a \right)+4 a b \,x^{2} \ln \left(b \,x^{2}+a \right)+4 a b \,x^{2}+2 a^{2} \ln \left(b \,x^{2}+a \right)+3 a^{2}\right) \left(b \,x^{2}+a \right)}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"1/4*(2*ln(b*x^2+a)*x^4*b^2+4*ln(b*x^2+a)*x^2*a*b+4*a*b*x^2+2*a^2*ln(b*x^2+a)+3*a^2)*(b*x^2+a)/b^3/((b*x^2+a)^2)^(3/2)","A"
636,1,32,28,0.006000," ","int(x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(2 b \,x^{2}+a \right)}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"-1/4*(b*x^2+a)*(2*b*x^2+a)/b^2/((b*x^2+a)^2)^(3/2)","A"
637,1,24,25,0.004000," ","int(x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{b \,x^{2}+a}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b}"," ",0,"-1/4*(b*x^2+a)/b/((b*x^2+a)^2)^(3/2)","A"
638,1,107,97,0.018000," ","int(1/x/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(4 b^{2} x^{4} \ln \left(x \right)-2 b^{2} x^{4} \ln \left(b \,x^{2}+a \right)+8 a b \,x^{2} \ln \left(x \right)-4 a b \,x^{2} \ln \left(b \,x^{2}+a \right)+2 a b \,x^{2}+4 a^{2} \ln \left(x \right)-2 a^{2} \ln \left(b \,x^{2}+a \right)+3 a^{2}\right) \left(b \,x^{2}+a \right)}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{3}}"," ",0,"1/4*(4*ln(x)*x^4*b^2-2*b^2*x^4*ln(b*x^2+a)+8*ln(x)*x^2*a*b-4*a*b*x^2*ln(b*x^2+a)+2*a*b*x^2+4*a^2*ln(x)-2*a^2*ln(b*x^2+a)+3*a^2)*(b*x^2+a)/a^3/((b*x^2+a)^2)^(3/2)","A"
639,1,133,131,0.021000," ","int(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(12 b^{3} x^{6} \ln \left(x \right)-6 b^{3} x^{6} \ln \left(b \,x^{2}+a \right)+24 a \,b^{2} x^{4} \ln \left(x \right)-12 a \,b^{2} x^{4} \ln \left(b \,x^{2}+a \right)+6 a \,b^{2} x^{4}+12 a^{2} b \,x^{2} \ln \left(x \right)-6 a^{2} b \,x^{2} \ln \left(b \,x^{2}+a \right)+9 a^{2} b \,x^{2}+2 a^{3}\right) \left(b \,x^{2}+a \right)}{4 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{4} x^{2}}"," ",0,"-1/4*(12*b^3*x^6*ln(x)-6*ln(b*x^2+a)*x^6*b^3+24*a*b^2*x^4*ln(x)-12*a*b^2*x^4*ln(b*x^2+a)+6*a*b^2*x^4+12*a^2*b*x^2*ln(x)-6*a^2*b*x^2*ln(b*x^2+a)+9*a^2*b*x^2+2*a^3)*(b*x^2+a)/a^4/x^2/((b*x^2+a)^2)^(3/2)","A"
640,1,97,81,0.016000," ","int(x^4/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(-3 b^{2} x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-6 a b \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+5 \sqrt{a b}\, b \,x^{3}-3 a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 \sqrt{a b}\, a x \right) \left(b \,x^{2}+a \right)}{8 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{2}}"," ",0,"-1/8*(-3*arctan(1/(a*b)^(1/2)*b*x)*x^4*b^2+5*(a*b)^(1/2)*b*x^3-6*arctan(1/(a*b)^(1/2)*b*x)*x^2*a*b+3*(a*b)^(1/2)*a*x-3*a^2*arctan(1/(a*b)^(1/2)*b*x))*(b*x^2+a)/(a*b)^(1/2)/b^2/((b*x^2+a)^2)^(3/2)","A"
641,1,97,82,0.018000," ","int(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(b^{2} x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+2 a b \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+\sqrt{a b}\, b \,x^{3}+a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-\sqrt{a b}\, a x \right) \left(b \,x^{2}+a \right)}{8 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a b}"," ",0,"1/8*(b^2*x^4*arctan(1/(a*b)^(1/2)*b*x)+(a*b)^(1/2)*b*x^3+2*a*b*x^2*arctan(1/(a*b)^(1/2)*b*x)-(a*b)^(1/2)*a*x+a^2*arctan(1/(a*b)^(1/2)*b*x))*(b*x^2+a)/(a*b)^(1/2)/b/a/((b*x^2+a)^2)^(3/2)","A"
642,1,97,115,0.008000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(3 b^{2} x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+6 a b \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 \sqrt{a b}\, b \,x^{3}+3 a^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+5 \sqrt{a b}\, a x \right) \left(b \,x^{2}+a \right)}{8 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{2}}"," ",0,"1/8*(3*b^2*x^4*arctan(1/(a*b)^(1/2)*b*x)+3*(a*b)^(1/2)*b*x^3+6*a*b*x^2*arctan(1/(a*b)^(1/2)*b*x)+5*(a*b)^(1/2)*a*x+3*a^2*arctan(1/(a*b)^(1/2)*b*x))*(b*x^2+a)/(a*b)^(1/2)/a^2/((b*x^2+a)^2)^(3/2)","A"
643,1,119,109,0.018000," ","int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(15 b^{3} x^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+30 a \,b^{2} x^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+15 \sqrt{a b}\, b^{2} x^{4}+15 a^{2} b x \arctan \left(\frac{b x}{\sqrt{a b}}\right)+25 \sqrt{a b}\, a b \,x^{2}+8 \sqrt{a b}\, a^{2}\right) \left(b \,x^{2}+a \right)}{8 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{3} x}"," ",0,"-1/8*(15*arctan(1/(a*b)^(1/2)*b*x)*x^5*b^3+15*(a*b)^(1/2)*x^4*b^2+30*arctan(1/(a*b)^(1/2)*b*x)*x^3*a*b^2+25*(a*b)^(1/2)*x^2*a*b+15*arctan(1/(a*b)^(1/2)*b*x)*x*a^2*b+8*(a*b)^(1/2)*a^2)*(b*x^2+a)/(a*b)^(1/2)/x/a^3/((b*x^2+a)^2)^(3/2)","A"
644,1,139,136,0.021000," ","int(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(105 b^{4} x^{7} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+210 a \,b^{3} x^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+105 \sqrt{a b}\, b^{3} x^{6}+105 a^{2} b^{2} x^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+175 \sqrt{a b}\, a \,b^{2} x^{4}+56 \sqrt{a b}\, a^{2} b \,x^{2}-8 \sqrt{a b}\, a^{3}\right) \left(b \,x^{2}+a \right)}{24 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{4} x^{3}}"," ",0,"1/24*(105*arctan(1/(a*b)^(1/2)*b*x)*x^7*b^4+105*(a*b)^(1/2)*x^6*b^3+210*arctan(1/(a*b)^(1/2)*b*x)*x^5*a*b^3+175*(a*b)^(1/2)*x^4*a*b^2+105*arctan(1/(a*b)^(1/2)*b*x)*x^3*a^2*b^2+56*(a*b)^(1/2)*x^2*a^2*b-8*(a*b)^(1/2)*a^3)*(b*x^2+a)/(a*b)^(1/2)/x^3/a^4/((b*x^2+a)^2)^(3/2)","A"
645,1,163,162,0.021000," ","int(x^11/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(-12 b^{5} x^{10}+60 a \,b^{4} x^{8} \ln \left(b \,x^{2}+a \right)-48 a \,b^{4} x^{8}+240 a^{2} b^{3} x^{6} \ln \left(b \,x^{2}+a \right)+48 a^{2} b^{3} x^{6}+360 a^{3} b^{2} x^{4} \ln \left(b \,x^{2}+a \right)+252 a^{3} b^{2} x^{4}+240 a^{4} b \,x^{2} \ln \left(b \,x^{2}+a \right)+248 a^{4} b \,x^{2}+60 a^{5} \ln \left(b \,x^{2}+a \right)+77 a^{5}\right) \left(b \,x^{2}+a \right)}{24 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{6}}"," ",0,"-1/24*(-12*b^5*x^10+60*ln(b*x^2+a)*x^8*a*b^4-48*a*b^4*x^8+240*ln(b*x^2+a)*x^6*a^2*b^3+48*a^2*b^3*x^6+360*ln(b*x^2+a)*x^4*a^3*b^2+252*a^3*b^2*x^4+240*ln(b*x^2+a)*x^2*a^4*b+248*a^4*b*x^2+60*ln(b*x^2+a)*a^5+77*a^5)*(b*x^2+a)/b^6/((b*x^2+a)^2)^(5/2)","A"
646,1,141,133,0.017000," ","int(x^9/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(12 b^{4} x^{8} \ln \left(b \,x^{2}+a \right)+48 a \,b^{3} x^{6} \ln \left(b \,x^{2}+a \right)+48 a \,b^{3} x^{6}+72 a^{2} b^{2} x^{4} \ln \left(b \,x^{2}+a \right)+108 a^{2} b^{2} x^{4}+48 a^{3} b \,x^{2} \ln \left(b \,x^{2}+a \right)+88 a^{3} b \,x^{2}+12 a^{4} \ln \left(b \,x^{2}+a \right)+25 a^{4}\right) \left(b \,x^{2}+a \right)}{24 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{5}}"," ",0,"1/24*(12*ln(b*x^2+a)*x^8*b^4+48*ln(b*x^2+a)*x^6*a*b^3+48*a*b^3*x^6+72*ln(b*x^2+a)*x^4*a^2*b^2+108*a^2*b^2*x^4+48*ln(b*x^2+a)*x^2*a^3*b+88*a^3*b*x^2+12*ln(b*x^2+a)*a^4+25*a^4)*(b*x^2+a)/b^5/((b*x^2+a)^2)^(5/2)","A"
647,1,54,28,0.007000," ","int(x^7/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(4 b^{3} x^{6}+6 a \,b^{2} x^{4}+4 a^{2} b \,x^{2}+a^{3}\right)}{8 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{4}}"," ",0,"-1/8*(b*x^2+a)*(4*b^3*x^6+6*a*b^2*x^4+4*a^2*b*x^2+a^3)/b^4/((b*x^2+a)^2)^(5/2)","A"
648,1,43,66,0.008000," ","int(x^5/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(6 b^{2} x^{4}+4 a b \,x^{2}+a^{2}\right)}{24 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{3}}"," ",0,"-1/24*(b*x^2+a)*(6*b^2*x^4+4*a*b*x^2+a^2)/b^3/((b*x^2+a)^2)^(5/2)","A"
649,1,32,61,0.008000," ","int(x^3/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(4 b \,x^{2}+a \right)}{24 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{2}}"," ",0,"-1/24*(b*x^2+a)*(4*b*x^2+a)/b^2/((b*x^2+a)^2)^(5/2)","A"
650,1,24,34,0.007000," ","int(x/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{b \,x^{2}+a}{8 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b}"," ",0,"-1/8*(b*x^2+a)/b/((b*x^2+a)^2)^(5/2)","A"
651,1,193,147,0.019000," ","int(1/x/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(24 b^{4} x^{8} \ln \left(x \right)-12 b^{4} x^{8} \ln \left(b \,x^{2}+a \right)+96 a \,b^{3} x^{6} \ln \left(x \right)-48 a \,b^{3} x^{6} \ln \left(b \,x^{2}+a \right)+12 a \,b^{3} x^{6}+144 a^{2} b^{2} x^{4} \ln \left(x \right)-72 a^{2} b^{2} x^{4} \ln \left(b \,x^{2}+a \right)+42 a^{2} b^{2} x^{4}+96 a^{3} b \,x^{2} \ln \left(x \right)-48 a^{3} b \,x^{2} \ln \left(b \,x^{2}+a \right)+52 a^{3} b \,x^{2}+24 a^{4} \ln \left(x \right)-12 a^{4} \ln \left(b \,x^{2}+a \right)+25 a^{4}\right) \left(b \,x^{2}+a \right)}{24 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{5}}"," ",0,"1/24*(24*ln(x)*x^8*b^4-12*b^4*x^8*ln(b*x^2+a)+96*ln(x)*x^6*a*b^3-48*a*b^3*x^6*ln(b*x^2+a)+12*a*b^3*x^6+144*ln(x)*x^4*a^2*b^2-72*a^2*b^2*x^4*ln(b*x^2+a)+42*a^2*b^2*x^4+96*ln(x)*x^2*a^3*b-48*a^3*b*x^2*ln(b*x^2+a)+52*a^3*b*x^2+24*a^4*ln(x)-12*a^4*ln(b*x^2+a)+25*a^4)*(b*x^2+a)/a^5/((b*x^2+a)^2)^(5/2)","A"
652,1,219,183,0.023000," ","int(1/x^3/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(120 b^{5} x^{10} \ln \left(x \right)-60 b^{5} x^{10} \ln \left(b \,x^{2}+a \right)+480 a \,b^{4} x^{8} \ln \left(x \right)-240 a \,b^{4} x^{8} \ln \left(b \,x^{2}+a \right)+60 a \,b^{4} x^{8}+720 a^{2} b^{3} x^{6} \ln \left(x \right)-360 a^{2} b^{3} x^{6} \ln \left(b \,x^{2}+a \right)+210 a^{2} b^{3} x^{6}+480 a^{3} b^{2} x^{4} \ln \left(x \right)-240 a^{3} b^{2} x^{4} \ln \left(b \,x^{2}+a \right)+260 a^{3} b^{2} x^{4}+120 a^{4} b \,x^{2} \ln \left(x \right)-60 a^{4} b \,x^{2} \ln \left(b \,x^{2}+a \right)+125 a^{4} b \,x^{2}+12 a^{5}\right) \left(b \,x^{2}+a \right)}{24 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{6} x^{2}}"," ",0,"-1/24*(120*b^5*x^10*ln(x)-60*ln(b*x^2+a)*x^10*b^5+480*a*b^4*x^8*ln(x)-240*a*b^4*x^8*ln(b*x^2+a)+60*a*b^4*x^8+720*a^2*b^3*x^6*ln(x)-360*a^2*b^3*x^6*ln(b*x^2+a)+210*a^2*b^3*x^6+480*a^3*b^2*x^4*ln(x)-240*a^3*b^2*x^4*ln(b*x^2+a)+260*a^3*b^2*x^4+120*a^4*b*x^2*ln(x)-60*a^4*b*x^2*ln(b*x^2+a)+125*a^4*b*x^2+12*a^5)*(b*x^2+a)/x^2/a^6/((b*x^2+a)^2)^(5/2)","A"
653,1,172,138,0.018000," ","int(x^6/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(15 b^{4} x^{8} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+60 a \,b^{3} x^{6} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+15 \sqrt{a b}\, b^{3} x^{7}+90 a^{2} b^{2} x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-73 \sqrt{a b}\, a \,b^{2} x^{5}+60 a^{3} b \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-55 \sqrt{a b}\, a^{2} b \,x^{3}+15 a^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-15 \sqrt{a b}\, a^{3} x \right) \left(b \,x^{2}+a \right)}{384 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a \,b^{3}}"," ",0,"1/384*(15*arctan(1/(a*b)^(1/2)*b*x)*x^8*b^4+15*(a*b)^(1/2)*x^7*b^3+60*arctan(1/(a*b)^(1/2)*b*x)*x^6*a*b^3-73*(a*b)^(1/2)*x^5*a*b^2+90*arctan(1/(a*b)^(1/2)*b*x)*x^4*a^2*b^2-55*(a*b)^(1/2)*x^3*a^2*b+60*arctan(1/(a*b)^(1/2)*b*x)*x^2*a^3*b-15*(a*b)^(1/2)*x*a^3+15*arctan(1/(a*b)^(1/2)*b*x)*a^4)*(b*x^2+a)/(a*b)^(1/2)/b^3/a/((b*x^2+a)^2)^(5/2)","A"
654,1,172,139,0.018000," ","int(x^4/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(3 b^{4} x^{8} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+12 a \,b^{3} x^{6} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3 \sqrt{a b}\, b^{3} x^{7}+18 a^{2} b^{2} x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+11 \sqrt{a b}\, a \,b^{2} x^{5}+12 a^{3} b \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-11 \sqrt{a b}\, a^{2} b \,x^{3}+3 a^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-3 \sqrt{a b}\, a^{3} x \right) \left(b \,x^{2}+a \right)}{128 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{2} b^{2}}"," ",0,"1/128*(3*b^4*x^8*arctan(1/(a*b)^(1/2)*b*x)+3*(a*b)^(1/2)*b^3*x^7+12*a*b^3*x^6*arctan(1/(a*b)^(1/2)*b*x)+11*(a*b)^(1/2)*a*b^2*x^5+18*a^2*b^2*x^4*arctan(1/(a*b)^(1/2)*b*x)-11*(a*b)^(1/2)*a^2*b*x^3+12*a^3*b*x^2*arctan(1/(a*b)^(1/2)*b*x)-3*(a*b)^(1/2)*a^3*x+3*a^4*arctan(1/(a*b)^(1/2)*b*x))*(b*x^2+a)/(a*b)^(1/2)/b^2/a^2/((b*x^2+a)^2)^(5/2)","A"
655,1,172,140,0.017000," ","int(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(15 b^{4} x^{8} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+60 a \,b^{3} x^{6} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+15 \sqrt{a b}\, b^{3} x^{7}+90 a^{2} b^{2} x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+55 \sqrt{a b}\, a \,b^{2} x^{5}+60 a^{3} b \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+73 \sqrt{a b}\, a^{2} b \,x^{3}+15 a^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)-15 \sqrt{a b}\, a^{3} x \right) \left(b \,x^{2}+a \right)}{384 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{3} b}"," ",0,"1/384*(15*b^4*x^8*arctan(1/(a*b)^(1/2)*b*x)+15*(a*b)^(1/2)*b^3*x^7+60*a*b^3*x^6*arctan(1/(a*b)^(1/2)*b*x)+55*(a*b)^(1/2)*a*b^2*x^5+90*a^2*b^2*x^4*arctan(1/(a*b)^(1/2)*b*x)+73*(a*b)^(1/2)*a^2*b*x^3+60*a^3*b*x^2*arctan(1/(a*b)^(1/2)*b*x)-15*(a*b)^(1/2)*a^3*x+15*a^4*arctan(1/(a*b)^(1/2)*b*x))*(b*x^2+a)/(a*b)^(1/2)/b/a^3/((b*x^2+a)^2)^(5/2)","A"
656,1,169,185,0.008000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(105 b^{4} x^{8} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+420 a \,b^{3} x^{6} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+105 \sqrt{a b}\, b^{3} x^{7}+630 a^{2} b^{2} x^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+385 \sqrt{a b}\, a \,b^{2} x^{5}+420 a^{3} b \,x^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+511 \sqrt{a b}\, a^{2} b \,x^{3}+105 a^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+279 \sqrt{a b}\, a^{3} x \right) \left(b \,x^{2}+a \right)}{384 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{4}}"," ",0,"1/384*(105*b^4*x^8*arctan(1/(a*b)^(1/2)*b*x)+105*(a*b)^(1/2)*b^3*x^7+420*a*b^3*x^6*arctan(1/(a*b)^(1/2)*b*x)+385*(a*b)^(1/2)*a*b^2*x^5+630*a^2*b^2*x^4*arctan(1/(a*b)^(1/2)*b*x)+511*(a*b)^(1/2)*a^2*b*x^3+420*a^3*b*x^2*arctan(1/(a*b)^(1/2)*b*x)+279*(a*b)^(1/2)*a^3*x+105*a^4*arctan(1/(a*b)^(1/2)*b*x))*(b*x^2+a)/(a*b)^(1/2)/a^4/((b*x^2+a)^2)^(5/2)","A"
657,1,191,165,0.022000," ","int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(315 b^{5} x^{9} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+1260 a \,b^{4} x^{7} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+315 \sqrt{a b}\, b^{4} x^{8}+1890 a^{2} b^{3} x^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+1155 \sqrt{a b}\, a \,b^{3} x^{6}+1260 a^{3} b^{2} x^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+1533 \sqrt{a b}\, a^{2} b^{2} x^{4}+315 a^{4} b x \arctan \left(\frac{b x}{\sqrt{a b}}\right)+837 \sqrt{a b}\, a^{3} b \,x^{2}+128 \sqrt{a b}\, a^{4}\right) \left(b \,x^{2}+a \right)}{128 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{5} x}"," ",0,"-1/128*(315*arctan(1/(a*b)^(1/2)*b*x)*x^9*b^5+315*(a*b)^(1/2)*x^8*b^4+1260*arctan(1/(a*b)^(1/2)*b*x)*x^7*a*b^4+1155*(a*b)^(1/2)*x^6*a*b^3+1890*arctan(1/(a*b)^(1/2)*b*x)*x^5*a^2*b^3+1533*(a*b)^(1/2)*x^4*a^2*b^2+1260*arctan(1/(a*b)^(1/2)*b*x)*x^3*a^3*b^2+837*(a*b)^(1/2)*x^2*a^3*b+315*arctan(1/(a*b)^(1/2)*b*x)*x*a^4*b+128*(a*b)^(1/2)*a^4)*(b*x^2+a)/(a*b)^(1/2)/x/a^5/((b*x^2+a)^2)^(5/2)","A"
658,1,211,192,0.024000," ","int(1/x^4/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(3465 b^{6} x^{11} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+13860 a \,b^{5} x^{9} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+3465 \sqrt{a b}\, b^{5} x^{10}+20790 a^{2} b^{4} x^{7} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+12705 \sqrt{a b}\, a \,b^{4} x^{8}+13860 a^{3} b^{3} x^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+16863 \sqrt{a b}\, a^{2} b^{3} x^{6}+3465 a^{4} b^{2} x^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)+9207 \sqrt{a b}\, a^{3} b^{2} x^{4}+1408 \sqrt{a b}\, a^{4} b \,x^{2}-128 \sqrt{a b}\, a^{5}\right) \left(b \,x^{2}+a \right)}{384 \sqrt{a b}\, \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{6} x^{3}}"," ",0,"1/384*(3465*arctan(1/(a*b)^(1/2)*b*x)*x^11*b^6+3465*(a*b)^(1/2)*x^10*b^5+13860*arctan(1/(a*b)^(1/2)*b*x)*x^9*a*b^5+12705*(a*b)^(1/2)*x^8*a*b^4+20790*arctan(1/(a*b)^(1/2)*b*x)*x^7*a^2*b^4+16863*(a*b)^(1/2)*x^6*a^2*b^3+13860*arctan(1/(a*b)^(1/2)*b*x)*x^5*a^3*b^3+9207*(a*b)^(1/2)*x^4*a^3*b^2+3465*arctan(1/(a*b)^(1/2)*b*x)*x^3*a^4*b^2+1408*(a*b)^(1/2)*x^2*a^4*b-128*(a*b)^(1/2)*a^5)*(b*x^2+a)/(a*b)^(1/2)/x^3/a^6/((b*x^2+a)^2)^(5/2)","A"
659,0,0,252,0.097000," ","int(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x)","\int \frac{x^{2}}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x)","F"
660,0,0,216,0.022000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x)","\int \frac{1}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x)","F"
661,0,0,250,0.070000," ","int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x)","\int \frac{1}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{1}{3}} x^{2}}\, dx"," ",0,"int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(1/3),x)","F"
662,0,0,524,0.058000," ","int(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x)","\int \frac{x^{2}}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{2}{3}}}\, dx"," ",0,"int(x^2/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x)","F"
663,0,0,516,0.033000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x)","\int \frac{1}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x)","F"
664,0,0,551,0.102000," ","int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x)","\int \frac{1}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{2}{3}} x^{2}}\, dx"," ",0,"int(1/x^2/(b^2*x^4+2*a*b*x^2+a^2)^(2/3),x)","F"
665,1,30,39,0.008000," ","int((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{2 \left(77 b^{2} x^{4}+210 a b \,x^{2}+165 a^{2}\right) \left(d x \right)^{\frac{5}{2}} x}{1155}"," ",0,"2/1155*x*(77*b^2*x^4+210*a*b*x^2+165*a^2)*(d*x)^(5/2)","A"
666,1,30,39,0.008000," ","int((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{2 \left(45 b^{2} x^{4}+130 a b \,x^{2}+117 a^{2}\right) \left(d x \right)^{\frac{3}{2}} x}{585}"," ",0,"2/585*x*(45*b^2*x^4+130*a*b*x^2+117*a^2)*(d*x)^(3/2)","A"
667,1,30,39,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)*(d*x)^(1/2),x)","\frac{2 \left(21 b^{2} x^{4}+66 a b \,x^{2}+77 a^{2}\right) \sqrt{d x}\, x}{231}"," ",0,"2/231*x*(21*b^2*x^4+66*a*b*x^2+77*a^2)*(d*x)^(1/2)","A"
668,1,30,39,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(1/2),x)","\frac{2 \left(5 b^{2} x^{4}+18 a b \,x^{2}+45 a^{2}\right) x}{45 \sqrt{d x}}"," ",0,"2/45*(5*b^2*x^4+18*a*b*x^2+45*a^2)*x/(d*x)^(1/2)","A"
669,1,30,39,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(3/2),x)","-\frac{2 \left(-3 b^{2} x^{4}-14 a b \,x^{2}+21 a^{2}\right) x}{21 \left(d x \right)^{\frac{3}{2}}}"," ",0,"-2/21*(-3*b^2*x^4-14*a*b*x^2+21*a^2)*x/(d*x)^(3/2)","A"
670,1,30,39,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(5/2),x)","-\frac{2 \left(-3 b^{2} x^{4}-30 a b \,x^{2}+5 a^{2}\right) x}{15 \left(d x \right)^{\frac{5}{2}}}"," ",0,"-2/15*(-3*b^2*x^4-30*a*b*x^2+5*a^2)*x/(d*x)^(5/2)","A"
671,1,30,39,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(7/2),x)","-\frac{2 \left(-5 b^{2} x^{4}+30 a b \,x^{2}+3 a^{2}\right) x}{15 \left(d x \right)^{\frac{7}{2}}}"," ",0,"-2/15*(-5*b^2*x^4+30*a*b*x^2+3*a^2)*x/(d*x)^(7/2)","A"
672,1,52,71,0.008000," ","int((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{2 \left(7315 b^{4} x^{8}+35420 a \,b^{3} x^{6}+67298 a^{2} b^{2} x^{4}+61180 a^{3} b \,x^{2}+24035 a^{4}\right) \left(d x \right)^{\frac{5}{2}} x}{168245}"," ",0,"2/168245*x*(7315*b^4*x^8+35420*a*b^3*x^6+67298*a^2*b^2*x^4+61180*a^3*b*x^2+24035*a^4)*(d*x)^(5/2)","A"
673,1,52,71,0.009000," ","int((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{2 \left(3315 b^{4} x^{8}+16380 a \,b^{3} x^{6}+32130 a^{2} b^{2} x^{4}+30940 a^{3} b \,x^{2}+13923 a^{4}\right) \left(d x \right)^{\frac{3}{2}} x}{69615}"," ",0,"2/69615*x*(3315*b^4*x^8+16380*a*b^3*x^6+32130*a^2*b^2*x^4+30940*a^3*b*x^2+13923*a^4)*(d*x)^(3/2)","A"
674,1,52,71,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2*(d*x)^(1/2),x)","\frac{2 \left(1155 b^{4} x^{8}+5852 a \,b^{3} x^{6}+11970 a^{2} b^{2} x^{4}+12540 a^{3} b \,x^{2}+7315 a^{4}\right) \sqrt{d x}\, x}{21945}"," ",0,"2/21945*x*(1155*b^4*x^8+5852*a*b^3*x^6+11970*a^2*b^2*x^4+12540*a^3*b*x^2+7315*a^4)*(d*x)^(1/2)","A"
675,1,52,71,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(1/2),x)","\frac{2 \left(195 b^{4} x^{8}+1020 a \,b^{3} x^{6}+2210 a^{2} b^{2} x^{4}+2652 a^{3} b \,x^{2}+3315 a^{4}\right) x}{3315 \sqrt{d x}}"," ",0,"2/3315*(195*b^4*x^8+1020*a*b^3*x^6+2210*a^2*b^2*x^4+2652*a^3*b*x^2+3315*a^4)*x/(d*x)^(1/2)","A"
676,1,52,71,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(3/2),x)","-\frac{2 \left(-77 b^{4} x^{8}-420 a \,b^{3} x^{6}-990 a^{2} b^{2} x^{4}-1540 a^{3} b \,x^{2}+1155 a^{4}\right) x}{1155 \left(d x \right)^{\frac{3}{2}}}"," ",0,"-2/1155*(-77*b^4*x^8-420*a*b^3*x^6-990*a^2*b^2*x^4-1540*a^3*b*x^2+1155*a^4)*x/(d*x)^(3/2)","A"
677,1,52,71,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(5/2),x)","-\frac{2 \left(-45 b^{4} x^{8}-260 a \,b^{3} x^{6}-702 a^{2} b^{2} x^{4}-2340 a^{3} b \,x^{2}+195 a^{4}\right) x}{585 \left(d x \right)^{\frac{5}{2}}}"," ",0,"-2/585*(-45*b^4*x^8-260*a*b^3*x^6-702*a^2*b^2*x^4-2340*a^3*b*x^2+195*a^4)*x/(d*x)^(5/2)","A"
678,1,52,71,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(7/2),x)","-\frac{2 \left(-35 b^{4} x^{8}-220 a \,b^{3} x^{6}-770 a^{2} b^{2} x^{4}+1540 a^{3} b \,x^{2}+77 a^{4}\right) x}{385 \left(d x \right)^{\frac{7}{2}}}"," ",0,"-2/385*(-35*b^4*x^8-220*a*b^3*x^6-770*a^2*b^2*x^4+1540*a^3*b*x^2+77*a^4)*x/(d*x)^(7/2)","A"
679,1,74,103,0.009000," ","int((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{2 \left(302841 b^{6} x^{12}+2086238 a \,b^{5} x^{10}+6122655 a^{2} b^{4} x^{8}+9882180 a^{3} b^{3} x^{6}+9388071 a^{4} b^{2} x^{4}+5120766 a^{5} b \,x^{2}+1341153 a^{6}\right) \left(d x \right)^{\frac{5}{2}} x}{9388071}"," ",0,"2/9388071*x*(302841*b^6*x^12+2086238*a*b^5*x^10+6122655*a^2*b^4*x^8+9882180*a^3*b^3*x^6+9388071*a^4*b^2*x^4+5120766*a^5*b*x^2+1341153*a^6)*(d*x)^(5/2)","A"
680,1,74,103,0.010000," ","int((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{2 \left(116025 b^{6} x^{12}+807534 a \,b^{5} x^{10}+2403375 a^{2} b^{4} x^{8}+3958500 a^{3} b^{3} x^{6}+3882375 a^{4} b^{2} x^{4}+2243150 a^{5} b \,x^{2}+672945 a^{6}\right) \left(d x \right)^{\frac{3}{2}} x}{3364725}"," ",0,"2/3364725*x*(116025*b^6*x^12+807534*a*b^5*x^10+2403375*a^2*b^4*x^8+3958500*a^3*b^3*x^6+3882375*a^4*b^2*x^4+2243150*a^5*b*x^2+672945*a^6)*(d*x)^(3/2)","A"
681,1,74,103,0.008000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3*(d*x)^(1/2),x)","\frac{2 \left(33649 b^{6} x^{12}+237006 a \,b^{5} x^{10}+717255 a^{2} b^{4} x^{8}+1211364 a^{3} b^{3} x^{6}+1238895 a^{4} b^{2} x^{4}+778734 a^{5} b \,x^{2}+302841 a^{6}\right) \sqrt{d x}\, x}{908523}"," ",0,"2/908523*x*(33649*b^6*x^12+237006*a*b^5*x^10+717255*a^2*b^4*x^8+1211364*a^3*b^3*x^6+1238895*a^4*b^2*x^4+778734*a^5*b*x^2+302841*a^6)*(d*x)^(1/2)","A"
682,1,74,103,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(1/2),x)","\frac{2 \left(4641 b^{6} x^{12}+33150 a \,b^{5} x^{10}+102375 a^{2} b^{4} x^{8}+178500 a^{3} b^{3} x^{6}+193375 a^{4} b^{2} x^{4}+139230 a^{5} b \,x^{2}+116025 a^{6}\right) x}{116025 \sqrt{d x}}"," ",0,"2/116025*(4641*b^6*x^12+33150*a*b^5*x^10+102375*a^2*b^4*x^8+178500*a^3*b^3*x^6+193375*a^4*b^2*x^4+139230*a^5*b*x^2+116025*a^6)*x/(d*x)^(1/2)","A"
683,1,74,103,0.010000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(3/2),x)","-\frac{2 \left(-1463 b^{6} x^{12}-10626 a \,b^{5} x^{10}-33649 a^{2} b^{4} x^{8}-61180 a^{3} b^{3} x^{6}-72105 a^{4} b^{2} x^{4}-67298 a^{5} b \,x^{2}+33649 a^{6}\right) x}{33649 \left(d x \right)^{\frac{3}{2}}}"," ",0,"-2/33649*(-1463*b^6*x^12-10626*a*b^5*x^10-33649*a^2*b^4*x^8-61180*a^3*b^3*x^6-72105*a^4*b^2*x^4-67298*a^5*b*x^2+33649*a^6)*x/(d*x)^(3/2)","A"
684,1,74,103,0.009000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(5/2),x)","-\frac{2 \left(-663 b^{6} x^{12}-4914 a \,b^{5} x^{10}-16065 a^{2} b^{4} x^{8}-30940 a^{3} b^{3} x^{6}-41769 a^{4} b^{2} x^{4}-83538 a^{5} b \,x^{2}+4641 a^{6}\right) x}{13923 \left(d x \right)^{\frac{5}{2}}}"," ",0,"-2/13923*(-663*b^6*x^12-4914*a*b^5*x^10-16065*a^2*b^4*x^8-30940*a^3*b^3*x^6-41769*a^4*b^2*x^4-83538*a^5*b*x^2+4641*a^6)*x/(d*x)^(5/2)","A"
685,1,74,103,0.010000," ","int((b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(7/2),x)","-\frac{2 \left(-385 b^{6} x^{12}-2926 a \,b^{5} x^{10}-9975 a^{2} b^{4} x^{8}-20900 a^{3} b^{3} x^{6}-36575 a^{4} b^{2} x^{4}+43890 a^{5} b \,x^{2}+1463 a^{6}\right) x}{7315 \left(d x \right)^{\frac{7}{2}}}"," ",0,"-2/7315*(-385*b^6*x^12-2926*a*b^5*x^10-9975*a^2*b^4*x^8-20900*a^3*b^3*x^6-36575*a^4*b^2*x^4+43890*a^5*b*x^2+1463*a^6)*x/(d*x)^(7/2)","A"
686,1,242,212,0.023000," ","int((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{\sqrt{d x}\, a^{2} d^{7}}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) b^{3}}+\frac{9 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{3}}+\frac{9 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{3}}+\frac{9 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{5} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 b^{3}}-\frac{4 \sqrt{d x}\, a \,d^{5}}{b^{3}}+\frac{2 \left(d x \right)^{\frac{5}{2}} d^{3}}{5 b^{2}}"," ",0,"2/5*d^3*(d*x)^(5/2)/b^2-4*a*d^5*(d*x)^(1/2)/b^3-1/2*d^7/b^3*a^2*(d*x)^(1/2)/(b*d^2*x^2+a*d^2)+9/16*d^5/b^3*a*(d^2*a/b)^(1/4)*2^(1/2)*ln((d*x+(d^2*a/b)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2*a/b)^(1/2))/(d*x-(d^2*a/b)^(1/4)*(d*x)^(1/2)*2^(1/2)+(d^2*a/b)^(1/2)))+9/8*d^5/b^3*a*(d^2*a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2*a/b)^(1/4)*(d*x)^(1/2)+1)+9/8*d^5/b^3*a*(d^2*a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(d^2*a/b)^(1/4)*(d*x)^(1/2)-1)","A"
687,1,226,198,0.018000," ","int((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{\left(d x \right)^{\frac{3}{2}} a \,d^{5}}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) b^{2}}-\frac{7 \sqrt{2}\, a \,d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{7 \sqrt{2}\, a \,d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{3}}-\frac{7 \sqrt{2}\, a \,d^{5} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{3}}+\frac{2 \left(d x \right)^{\frac{3}{2}} d^{3}}{3 b^{2}}"," ",0,"2/3*d^3*(d*x)^(3/2)/b^2+1/2*d^5*a/b^2*(d*x)^(3/2)/(b*d^2*x^2+a*d^2)-7/16*d^5*a/b^3/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-7/8*d^5*a/b^3/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-7/8*d^5*a/b^3/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
688,1,223,198,0.018000," ","int((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{\sqrt{d x}\, a \,d^{5}}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) b^{2}}-\frac{5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 b^{2}}+\frac{2 \sqrt{d x}\, d^{3}}{b^{2}}"," ",0,"2*d^3*(d*x)^(1/2)/b^2+1/2*d^5/b^2*a*(d*x)^(1/2)/(b*d^2*x^2+a*d^2)-5/16*d^3/b^2*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-5/8*d^3/b^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-5/8*d^3/b^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
689,1,209,185,0.016000," ","int((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{\left(d x \right)^{\frac{3}{2}} d^{3}}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) b}+\frac{3 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, d^{3} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{2}}"," ",0,"-1/2*d^3/b*(d*x)^(3/2)/(b*d^2*x^2+a*d^2)+3/16*d^3/b^2/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+3/8*d^3/b^2/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+3/8*d^3/b^2/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
690,1,212,185,0.014000," ","int((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{\sqrt{d x}\, d^{3}}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) b}+\frac{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a b}+\frac{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a b}+\frac{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 a b}"," ",0,"-1/2*d^3/b*(d*x)^(1/2)/(b*d^2*x^2+a*d^2)+1/16*d/b*(a/b*d^2)^(1/4)/a*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1/8*d/b*(a/b*d^2)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+1/8*d/b*(a/b*d^2)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
691,1,210,187,0.012000," ","int((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, d \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a b}+\frac{\left(d x \right)^{\frac{3}{2}} d}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) a}"," ",0,"1/2*d*(d*x)^(3/2)/a/(b*d^2*x^2+a*d^2)+1/16*d/a/b/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1/8*d/a/b/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+1/8*d/a/b/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
692,1,207,187,0.011000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)/(d*x)^(1/2),x)","\frac{\sqrt{d x}\, d}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) a}+\frac{3 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{2} d}+\frac{3 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{2} d}+\frac{3 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 a^{2} d}"," ",0,"1/2*d*(d*x)^(1/2)/a/(b*d^2*x^2+a*d^2)+3/16/d/a^2*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+3/8/d/a^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+3/8/d/a^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
693,1,223,200,0.019000," ","int(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{\left(d x \right)^{\frac{3}{2}} b}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) a^{2} d}-\frac{5 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} d}-\frac{5 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} d}-\frac{5 \sqrt{2}\, \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} d}-\frac{2}{\sqrt{d x}\, a^{2} d}"," ",0,"-1/2/d*b/a^2*(d*x)^(3/2)/(b*d^2*x^2+a*d^2)-5/16/d/a^2/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-5/8/d/a^2/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-5/8/d/a^2/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/a^2/d/(d*x)^(1/2)","A"
694,1,226,200,0.019000," ","int(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{\sqrt{d x}\, b}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) a^{2} d}-\frac{2}{3 \left(d x \right)^{\frac{3}{2}} a^{2} d}-\frac{7 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a^{3} d^{3}}-\frac{7 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a^{3} d^{3}}-\frac{7 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 a^{3} d^{3}}"," ",0,"-1/2/d/a^2*b*(d*x)^(1/2)/(b*d^2*x^2+a*d^2)-7/16/d^3/a^3*b*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-7/8/d^3/a^3*b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-7/8/d^3/a^3*b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/3/a^2/d/(d*x)^(3/2)","A"
695,1,242,214,0.021000," ","int(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2),x)","-\frac{2}{5 \left(d x \right)^{\frac{5}{2}} a^{2} d}+\frac{\left(d x \right)^{\frac{3}{2}} b^{2}}{2 \left(b \,d^{2} x^{2}+d^{2} a \right) a^{3} d^{3}}+\frac{9 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} d^{3}}+\frac{9 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} d^{3}}+\frac{9 \sqrt{2}\, b \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{16 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} d^{3}}+\frac{4 b}{\sqrt{d x}\, a^{3} d^{3}}"," ",0,"1/2/d^3*b^2/a^3*(d*x)^(3/2)/(b*d^2*x^2+a*d^2)+9/16/d^3*b/a^3/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+9/8/d^3*b/a^3/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+9/8/d^3*b/a^3/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/5/a^2/d/(d*x)^(5/2)+4*b/a^3/d^3/(d*x)^(1/2)","A"
696,1,306,256,0.023000," ","int((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{151 \sqrt{d x}\, a^{4} d^{15}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{5}}-\frac{173 \left(d x \right)^{\frac{5}{2}} a^{3} d^{13}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{4}}-\frac{617 \left(d x \right)^{\frac{9}{2}} a^{2} d^{11}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{3}}+\frac{663 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 b^{5}}+\frac{663 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 b^{5}}+\frac{663 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{9} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 b^{5}}-\frac{8 \sqrt{d x}\, a \,d^{9}}{b^{5}}+\frac{2 \left(d x \right)^{\frac{5}{2}} d^{7}}{5 b^{4}}"," ",0,"2/5*d^7*(d*x)^(5/2)/b^4-8*a*d^9*(d*x)^(1/2)/b^5-617/192*d^11/b^3*a^2/(b*d^2*x^2+a*d^2)^3*(d*x)^(9/2)-173/32*d^13/b^4*a^3/(b*d^2*x^2+a*d^2)^3*(d*x)^(5/2)-151/64*d^15/b^5*a^4/(b*d^2*x^2+a*d^2)^3*(d*x)^(1/2)+663/512*d^9/b^5*a*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+663/256*d^9/b^5*a*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+663/256*d^9/b^5*a*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
697,1,290,242,0.023000," ","int((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{257 \left(d x \right)^{\frac{3}{2}} a^{3} d^{13}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{4}}+\frac{101 \left(d x \right)^{\frac{7}{2}} a^{2} d^{11}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{3}}+\frac{127 \left(d x \right)^{\frac{11}{2}} a \,d^{9}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{2}}-\frac{385 \sqrt{2}\, a \,d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{5}}-\frac{385 \sqrt{2}\, a \,d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{5}}-\frac{385 \sqrt{2}\, a \,d^{9} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{5}}+\frac{2 \left(d x \right)^{\frac{3}{2}} d^{7}}{3 b^{4}}"," ",0,"2/3*d^7*(d*x)^(3/2)/b^4+127/64*d^9*a/b^2/(b*d^2*x^2+a*d^2)^3*(d*x)^(11/2)+101/32*d^11*a^2/b^3/(b*d^2*x^2+a*d^2)^3*(d*x)^(7/2)+257/192*d^13*a^3/b^4/(b*d^2*x^2+a*d^2)^3*(d*x)^(3/2)-385/512*d^9*a/b^5/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-385/256*d^9*a/b^5/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-385/256*d^9*a/b^5/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
698,1,287,242,0.024000," ","int((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{67 \sqrt{d x}\, a^{3} d^{13}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{4}}+\frac{81 \left(d x \right)^{\frac{5}{2}} a^{2} d^{11}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{3}}+\frac{317 \left(d x \right)^{\frac{9}{2}} a \,d^{9}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{2}}-\frac{195 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 b^{4}}-\frac{195 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 b^{4}}-\frac{195 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{7} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 b^{4}}+\frac{2 \sqrt{d x}\, d^{7}}{b^{4}}"," ",0,"2*d^7*(d*x)^(1/2)/b^4+317/192*d^9/b^2*a/(b*d^2*x^2+a*d^2)^3*(d*x)^(9/2)+81/32*d^11/b^3*a^2/(b*d^2*x^2+a*d^2)^3*(d*x)^(5/2)+67/64*d^13/b^4*a^3/(b*d^2*x^2+a*d^2)^3*(d*x)^(1/2)-195/512*d^7/b^4*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-195/256*d^7/b^4*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-195/256*d^7/b^4*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
699,1,271,229,0.019000," ","int((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{77 \left(d x \right)^{\frac{3}{2}} a^{2} d^{11}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{3}}-\frac{33 \left(d x \right)^{\frac{7}{2}} a \,d^{9}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{2}}-\frac{51 \left(d x \right)^{\frac{11}{2}} d^{7}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b}+\frac{77 \sqrt{2}\, d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{4}}+\frac{77 \sqrt{2}\, d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{4}}+\frac{77 \sqrt{2}\, d^{7} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{4}}"," ",0,"-51/64*d^7/(b*d^2*x^2+a*d^2)^3/b*(d*x)^(11/2)-33/32*d^9/(b*d^2*x^2+a*d^2)^3/b^2*a*(d*x)^(7/2)-77/192*d^11/(b*d^2*x^2+a*d^2)^3/b^3*a^2*(d*x)^(3/2)+77/512*d^7/b^4/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+77/256*d^7/b^4/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+77/256*d^7/b^4/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
700,1,280,229,0.021000," ","int((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{15 \sqrt{d x}\, a^{2} d^{11}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{3}}-\frac{21 \left(d x \right)^{\frac{5}{2}} a \,d^{9}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{2}}-\frac{113 \left(d x \right)^{\frac{9}{2}} d^{7}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b}+\frac{15 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 a \,b^{3}}+\frac{15 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 a \,b^{3}}+\frac{15 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{5} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 a \,b^{3}}"," ",0,"-113/192*d^7/(b*d^2*x^2+a*d^2)^3/b*(d*x)^(9/2)-21/32*d^9/(b*d^2*x^2+a*d^2)^3/b^2*a*(d*x)^(5/2)-15/64*d^11/(b*d^2*x^2+a*d^2)^3/b^3*a^2*(d*x)^(1/2)+15/512*d^5/b^3*(a/b*d^2)^(1/4)/a*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+15/256*d^5/b^3*(a/b*d^2)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+15/256*d^5/b^3*(a/b*d^2)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
701,1,277,232,0.021000," ","int((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{7 \left(d x \right)^{\frac{3}{2}} a \,d^{9}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{2}}-\frac{3 \left(d x \right)^{\frac{7}{2}} d^{7}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b}+\frac{7 \left(d x \right)^{\frac{11}{2}} d^{5}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a}+\frac{7 \sqrt{2}\, d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{3}}+\frac{7 \sqrt{2}\, d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{3}}+\frac{7 \sqrt{2}\, d^{5} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{3}}"," ",0,"7/64*d^5/(b*d^2*x^2+a*d^2)^3/a*(d*x)^(11/2)-3/32*d^7/(b*d^2*x^2+a*d^2)^3/b*(d*x)^(7/2)-7/192*d^9/(b*d^2*x^2+a*d^2)^3/b^2*a*(d*x)^(3/2)+7/512*d^5/a/b^3/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+7/256*d^5/a/b^3/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+7/256*d^5/a/b^3/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
702,1,277,232,0.019000," ","int((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{5 \sqrt{d x}\, a \,d^{9}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b^{2}}-\frac{7 \left(d x \right)^{\frac{5}{2}} d^{7}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b}+\frac{5 \left(d x \right)^{\frac{9}{2}} d^{5}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a}+\frac{5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 a^{2} b^{2}}+\frac{5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 a^{2} b^{2}}+\frac{5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 a^{2} b^{2}}"," ",0,"5/192*d^5/(b*d^2*x^2+a*d^2)^3/a*(d*x)^(9/2)-7/32*d^7/(b*d^2*x^2+a*d^2)^3/b*(d*x)^(5/2)-5/64*d^9/(b*d^2*x^2+a*d^2)^3/b^2*a*(d*x)^(1/2)+5/512*d^3/a^2/b^2*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+5/256*d^3/a^2/b^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+5/256*d^3/a^2/b^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
703,1,277,231,0.019000," ","int((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{5 \left(d x \right)^{\frac{3}{2}} d^{7}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b}+\frac{7 \left(d x \right)^{\frac{7}{2}} d^{5}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a}+\frac{5 \left(d x \right)^{\frac{11}{2}} b \,d^{3}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{2}}+\frac{5 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{5 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{5 \sqrt{2}\, d^{3} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}"," ",0,"5/64*d^3/(b*d^2*x^2+a*d^2)^3/a^2*b*(d*x)^(11/2)+7/32*d^5/(b*d^2*x^2+a*d^2)^3/a*(d*x)^(7/2)-5/192*d^7/(b*d^2*x^2+a*d^2)^3/b*(d*x)^(3/2)+5/512*d^3/a^2/b^2/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+5/256*d^3/a^2/b^2/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+5/256*d^3/a^2/b^2/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
704,1,271,231,0.021000," ","int((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{7 \sqrt{d x}\, d^{7}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} b}+\frac{3 \left(d x \right)^{\frac{5}{2}} d^{5}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a}+\frac{7 \left(d x \right)^{\frac{9}{2}} b \,d^{3}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{2}}+\frac{7 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 a^{3} b}+\frac{7 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 a^{3} b}+\frac{7 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 a^{3} b}"," ",0,"7/192*d^3/(b*d^2*x^2+a*d^2)^3/a^2*b*(d*x)^(9/2)+3/32*d^5/(b*d^2*x^2+a*d^2)^3/a*(d*x)^(5/2)-7/64*d^7/(b*d^2*x^2+a*d^2)^3/b*(d*x)^(1/2)+7/512*d/a^3/b*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+7/256*d/a^3/b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+7/256*d/a^3/b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
705,1,272,231,0.019000," ","int((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{113 \left(d x \right)^{\frac{3}{2}} d^{5}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a}+\frac{21 \left(d x \right)^{\frac{7}{2}} b \,d^{3}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{2}}+\frac{15 \left(d x \right)^{\frac{11}{2}} b^{2} d}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{3}}+\frac{15 \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, d \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b}"," ",0,"15/64*d/(b*d^2*x^2+a*d^2)^3/a^3*b^2*(d*x)^(11/2)+21/32*d^3/(b*d^2*x^2+a*d^2)^3/a^2*b*(d*x)^(7/2)+113/192*d^5/(b*d^2*x^2+a*d^2)^3/a*(d*x)^(3/2)+15/512*d/a^3/b/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+15/256*d/a^3/b/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+15/256*d/a^3/b/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
706,1,269,231,0.018000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^2/(d*x)^(1/2),x)","\frac{51 \sqrt{d x}\, d^{5}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a}+\frac{33 \left(d x \right)^{\frac{5}{2}} b \,d^{3}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{2}}+\frac{77 \left(d x \right)^{\frac{9}{2}} b^{2} d}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{3}}+\frac{77 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 a^{4} d}+\frac{77 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 a^{4} d}+\frac{77 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 a^{4} d}"," ",0,"77/192*d/(b*d^2*x^2+a*d^2)^3/a^3*b^2*(d*x)^(9/2)+33/32*d^3/(b*d^2*x^2+a*d^2)^3/a^2*b*(d*x)^(5/2)+51/64*d^5/(b*d^2*x^2+a*d^2)^3/a*(d*x)^(1/2)+77/512/d/a^4*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+77/256/d/a^4*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+77/256/d/a^4*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
707,1,285,244,0.025000," ","int(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{317 \left(d x \right)^{\frac{3}{2}} b \,d^{3}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{2}}-\frac{81 \left(d x \right)^{\frac{7}{2}} b^{2} d}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{3}}-\frac{67 \left(d x \right)^{\frac{11}{2}} b^{3}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{4} d}-\frac{195 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4} d}-\frac{195 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4} d}-\frac{195 \sqrt{2}\, \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4} d}-\frac{2}{\sqrt{d x}\, a^{4} d}"," ",0,"-67/64/d*b^3/a^4/(b*d^2*x^2+a*d^2)^3*(d*x)^(11/2)-81/32*d*b^2/a^3/(b*d^2*x^2+a*d^2)^3*(d*x)^(7/2)-317/192*d^3*b/a^2/(b*d^2*x^2+a*d^2)^3*(d*x)^(3/2)-195/512/d/a^4/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-195/256/d/a^4/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-195/256/d/a^4/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/a^4/d/(d*x)^(1/2)","A"
708,1,288,244,0.024000," ","int(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","-\frac{127 \sqrt{d x}\, b \,d^{3}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{2}}-\frac{101 \left(d x \right)^{\frac{5}{2}} b^{2} d}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{3}}-\frac{257 \left(d x \right)^{\frac{9}{2}} b^{3}}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{4} d}-\frac{2}{3 \left(d x \right)^{\frac{3}{2}} a^{4} d}-\frac{385 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 a^{5} d^{3}}-\frac{385 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 a^{5} d^{3}}-\frac{385 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 a^{5} d^{3}}"," ",0,"-257/192/d/a^4*b^3/(b*d^2*x^2+a*d^2)^3*(d*x)^(9/2)-101/32*d/a^3*b^2/(b*d^2*x^2+a*d^2)^3*(d*x)^(5/2)-127/64*d^3/a^2*b/(b*d^2*x^2+a*d^2)^3*(d*x)^(1/2)-385/512/d^3/a^5*b*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-385/256/d^3/a^5*b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-385/256/d^3/a^5*b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/3/a^4/d/(d*x)^(3/2)","A"
709,1,304,258,0.027000," ","int(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{617 \left(d x \right)^{\frac{3}{2}} b^{2} d}{192 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{3}}+\frac{173 \left(d x \right)^{\frac{7}{2}} b^{3}}{32 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{4} d}+\frac{151 \left(d x \right)^{\frac{11}{2}} b^{4}}{64 \left(b \,d^{2} x^{2}+d^{2} a \right)^{3} a^{5} d^{3}}-\frac{2}{5 \left(d x \right)^{\frac{5}{2}} a^{4} d}+\frac{663 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{5} d^{3}}+\frac{663 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{5} d^{3}}+\frac{663 \sqrt{2}\, b \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{512 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{5} d^{3}}+\frac{8 b}{\sqrt{d x}\, a^{5} d^{3}}"," ",0,"151/64/d^3*b^4/a^5/(b*d^2*x^2+a*d^2)^3*(d*x)^(11/2)+173/32/d*b^3/a^4/(b*d^2*x^2+a*d^2)^3*(d*x)^(7/2)+617/192*d*b^2/a^3/(b*d^2*x^2+a*d^2)^3*(d*x)^(3/2)+663/512/d^3*b/a^5/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+663/256/d^3*b/a^5/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+663/256/d^3*b/a^5/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/5/a^4/d/(d*x)^(5/2)+8*b/a^5/d^3/(d*x)^(1/2)","A"
710,1,370,300,0.029000," ","int((d*x)^(27/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{20463 \sqrt{d x}\, a^{6} d^{23}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{7}}-\frac{56269 \left(d x \right)^{\frac{5}{2}} a^{5} d^{21}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{6}}-\frac{75471 \left(d x \right)^{\frac{9}{2}} a^{4} d^{19}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{5}}-\frac{3597 \left(d x \right)^{\frac{13}{2}} a^{3} d^{17}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{4}}-\frac{34139 \left(d x \right)^{\frac{17}{2}} a^{2} d^{15}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}+\frac{69615 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{13} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 b^{7}}+\frac{69615 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{13} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 b^{7}}+\frac{69615 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{13} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 b^{7}}-\frac{12 \sqrt{d x}\, a \,d^{13}}{b^{7}}+\frac{2 \left(d x \right)^{\frac{5}{2}} d^{11}}{5 b^{6}}"," ",0,"2/5*d^11*(d*x)^(5/2)/b^6-12*a*d^13*(d*x)^(1/2)/b^7-20463/4096*d^23/b^7*a^6/(b*d^2*x^2+a*d^2)^5*(d*x)^(1/2)-56269/2560*d^21/b^6*a^5/(b*d^2*x^2+a*d^2)^5*(d*x)^(5/2)-75471/2048*d^19/b^5*a^4/(b*d^2*x^2+a*d^2)^5*(d*x)^(9/2)-3597/128*d^17/b^4*a^3/(b*d^2*x^2+a*d^2)^5*(d*x)^(13/2)-34139/4096*d^15/b^3*a^2/(b*d^2*x^2+a*d^2)^5*(d*x)^(17/2)+69615/32768*d^13/b^7*a*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+69615/16384*d^13/b^7*a*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+69615/16384*d^13/b^7*a*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
711,1,354,286,0.031000," ","int((d*x)^(25/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{25457 \left(d x \right)^{\frac{3}{2}} a^{5} d^{21}}{12288 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{6}}+\frac{3527 \left(d x \right)^{\frac{7}{2}} a^{4} d^{19}}{384 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{5}}+\frac{95821 \left(d x \right)^{\frac{11}{2}} a^{3} d^{17}}{6144 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{4}}+\frac{31149 \left(d x \right)^{\frac{15}{2}} a^{2} d^{15}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}+\frac{15503 \left(d x \right)^{\frac{19}{2}} a \,d^{13}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{33649 \sqrt{2}\, a \,d^{13} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{7}}-\frac{33649 \sqrt{2}\, a \,d^{13} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{7}}-\frac{33649 \sqrt{2}\, a \,d^{13} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{7}}+\frac{2 \left(d x \right)^{\frac{3}{2}} d^{11}}{3 b^{6}}"," ",0,"2/3*d^11*(d*x)^(3/2)/b^6+25457/12288*d^21*a^5/b^6/(b*d^2*x^2+a*d^2)^5*(d*x)^(3/2)+3527/384*d^19*a^4/b^5/(b*d^2*x^2+a*d^2)^5*(d*x)^(7/2)+95821/6144*d^17*a^3/b^4/(b*d^2*x^2+a*d^2)^5*(d*x)^(11/2)+31149/2560*d^15*a^2/b^3/(b*d^2*x^2+a*d^2)^5*(d*x)^(15/2)+15503/4096*d^13*a/b^2/(b*d^2*x^2+a*d^2)^5*(d*x)^(19/2)-33649/32768*d^13*a/b^7/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-33649/16384*d^13*a/b^7/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-33649/16384*d^13*a/b^7/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
712,1,351,286,0.031000," ","int((d*x)^(23/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{5731 \sqrt{d x}\, a^{5} d^{21}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{6}}+\frac{16169 \left(d x \right)^{\frac{5}{2}} a^{4} d^{19}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{5}}+\frac{22467 \left(d x \right)^{\frac{9}{2}} a^{3} d^{17}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{4}}+\frac{1129 \left(d x \right)^{\frac{13}{2}} a^{2} d^{15}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}+\frac{11743 \left(d x \right)^{\frac{17}{2}} a \,d^{13}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{13923 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{11} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 b^{6}}-\frac{13923 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{11} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 b^{6}}-\frac{13923 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{11} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 b^{6}}+\frac{2 \sqrt{d x}\, d^{11}}{b^{6}}"," ",0,"2*d^11*(d*x)^(1/2)/b^6+5731/4096*d^21/b^6*a^5/(b*d^2*x^2+a*d^2)^5*(d*x)^(1/2)+16169/2560*d^19/b^5*a^4/(b*d^2*x^2+a*d^2)^5*(d*x)^(5/2)+22467/2048*d^17/b^4*a^3/(b*d^2*x^2+a*d^2)^5*(d*x)^(9/2)+1129/128*d^15/b^3*a^2/(b*d^2*x^2+a*d^2)^5*(d*x)^(13/2)+11743/4096*d^13/b^2*a/(b*d^2*x^2+a*d^2)^5*(d*x)^(17/2)-13923/32768*d^11/b^6*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-13923/16384*d^11/b^6*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-13923/16384*d^11/b^6*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
713,1,335,273,0.025000," ","int((d*x)^(21/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{1463 \left(d x \right)^{\frac{3}{2}} a^{4} d^{19}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{5}}-\frac{209 \left(d x \right)^{\frac{7}{2}} a^{3} d^{17}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{4}}-\frac{5947 \left(d x \right)^{\frac{11}{2}} a^{2} d^{15}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}-\frac{6289 \left(d x \right)^{\frac{15}{2}} a \,d^{13}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{3803 \left(d x \right)^{\frac{19}{2}} d^{11}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{4389 \sqrt{2}\, d^{11} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{6}}+\frac{4389 \sqrt{2}\, d^{11} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{6}}+\frac{4389 \sqrt{2}\, d^{11} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{6}}"," ",0,"-1463/4096*d^19/(b*d^2*x^2+a*d^2)^5/b^5*a^4*(d*x)^(3/2)-209/128*d^17/(b*d^2*x^2+a*d^2)^5/b^4*a^3*(d*x)^(7/2)-5947/2048*d^15/(b*d^2*x^2+a*d^2)^5/b^3*a^2*(d*x)^(11/2)-6289/2560*d^13/(b*d^2*x^2+a*d^2)^5/b^2*a*(d*x)^(15/2)-3803/4096*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(19/2)+4389/32768*d^11/b^6/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+4389/16384*d^11/b^6/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+4389/16384*d^11/b^6/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
714,1,344,273,0.026000," ","int((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{663 \sqrt{d x}\, a^{4} d^{19}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{5}}-\frac{1989 \left(d x \right)^{\frac{5}{2}} a^{3} d^{17}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{4}}-\frac{9061 \left(d x \right)^{\frac{9}{2}} a^{2} d^{15}}{6144 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}-\frac{527 \left(d x \right)^{\frac{13}{2}} a \,d^{13}}{384 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{7529 \left(d x \right)^{\frac{17}{2}} d^{11}}{12288 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{663 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 a \,b^{5}}+\frac{663 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 a \,b^{5}}+\frac{663 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{9} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 a \,b^{5}}"," ",0,"-663/4096*d^19/(b*d^2*x^2+a*d^2)^5/b^5*a^4*(d*x)^(1/2)-1989/2560*d^17/(b*d^2*x^2+a*d^2)^5/b^4*a^3*(d*x)^(5/2)-9061/6144*d^15/(b*d^2*x^2+a*d^2)^5/b^3*a^2*(d*x)^(9/2)-527/384*d^13/(b*d^2*x^2+a*d^2)^5/b^2*a*(d*x)^(13/2)-7529/12288*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(17/2)+663/32768*d^9/b^5*(a/b*d^2)^(1/4)/a*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+663/16384*d^9/b^5*(a/b*d^2)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+663/16384*d^9/b^5*(a/b*d^2)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
715,1,341,276,0.026000," ","int((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{77 \left(d x \right)^{\frac{3}{2}} a^{3} d^{17}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{4}}-\frac{11 \left(d x \right)^{\frac{7}{2}} a^{2} d^{15}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}-\frac{313 \left(d x \right)^{\frac{11}{2}} a \,d^{13}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{331 \left(d x \right)^{\frac{15}{2}} d^{11}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{231 \left(d x \right)^{\frac{19}{2}} d^{9}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{231 \sqrt{2}\, d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{5}}+\frac{231 \sqrt{2}\, d^{9} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{5}}+\frac{231 \sqrt{2}\, d^{9} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{5}}"," ",0,"-77/4096*d^17/(b*d^2*x^2+a*d^2)^5/b^4*a^3*(d*x)^(3/2)-11/128*d^15/(b*d^2*x^2+a*d^2)^5/b^3*a^2*(d*x)^(7/2)-313/2048*d^13/(b*d^2*x^2+a*d^2)^5/b^2*a*(d*x)^(11/2)-331/2560*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(15/2)+231/4096*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(19/2)+231/32768*d^9/a/b^5/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+231/16384*d^9/a/b^5/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+231/16384*d^9/a/b^5/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
716,1,341,276,0.025000," ","int((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{117 \sqrt{d x}\, a^{3} d^{17}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{4}}-\frac{351 \left(d x \right)^{\frac{5}{2}} a^{2} d^{15}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}-\frac{533 \left(d x \right)^{\frac{9}{2}} a \,d^{13}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{31 \left(d x \right)^{\frac{13}{2}} d^{11}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{39 \left(d x \right)^{\frac{17}{2}} d^{9}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{117 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 a^{2} b^{4}}+\frac{117 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 a^{2} b^{4}}+\frac{117 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{7} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 a^{2} b^{4}}"," ",0,"-117/4096*d^17/(b*d^2*x^2+a*d^2)^5/b^4*a^3*(d*x)^(1/2)-351/2560*d^15/(b*d^2*x^2+a*d^2)^5/b^3*a^2*(d*x)^(5/2)-533/2048*d^13/(b*d^2*x^2+a*d^2)^5/b^2*a*(d*x)^(9/2)-31/128*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(13/2)+39/4096*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(17/2)+117/32768*d^7/a^2/b^4*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+117/16384*d^7/a^2/b^4*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+117/16384*d^7/a^2/b^4*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
717,1,339,279,0.025000," ","int((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{77 \left(d x \right)^{\frac{3}{2}} a^{2} d^{15}}{12288 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}-\frac{11 \left(d x \right)^{\frac{7}{2}} a \,d^{13}}{384 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{313 \left(d x \right)^{\frac{11}{2}} d^{11}}{6144 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{231 \left(d x \right)^{\frac{15}{2}} d^{9}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{77 \left(d x \right)^{\frac{19}{2}} b \,d^{7}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}+\frac{77 \sqrt{2}\, d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{4}}+\frac{77 \sqrt{2}\, d^{7} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{4}}+\frac{77 \sqrt{2}\, d^{7} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{4}}"," ",0,"-77/12288*d^15/(b*d^2*x^2+a*d^2)^5/b^3*a^2*(d*x)^(3/2)-11/384*d^13/(b*d^2*x^2+a*d^2)^5/b^2*a*(d*x)^(7/2)-313/6144*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(11/2)+231/2560*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(15/2)+77/4096*d^7/(b*d^2*x^2+a*d^2)^5/a^2*b*(d*x)^(19/2)+77/32768*d^7/a^2/b^4/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+77/16384*d^7/a^2/b^4/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+77/16384*d^7/a^2/b^4/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
718,1,339,279,0.025000," ","int((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{63 \sqrt{d x}\, a^{2} d^{15}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{3}}-\frac{189 \left(d x \right)^{\frac{5}{2}} a \,d^{13}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{287 \left(d x \right)^{\frac{9}{2}} d^{11}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{3 \left(d x \right)^{\frac{13}{2}} d^{9}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{21 \left(d x \right)^{\frac{17}{2}} b \,d^{7}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}+\frac{63 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 a^{3} b^{3}}+\frac{63 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 a^{3} b^{3}}+\frac{63 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{5} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 a^{3} b^{3}}"," ",0,"-63/4096*d^15/(b*d^2*x^2+a*d^2)^5/b^3*a^2*(d*x)^(1/2)-189/2560*d^13/(b*d^2*x^2+a*d^2)^5/b^2*a*(d*x)^(5/2)-287/2048*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(9/2)+3/128*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(13/2)+21/4096*d^7/(b*d^2*x^2+a*d^2)^5/a^2*b*(d*x)^(17/2)+63/32768*d^5/a^3/b^3*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+63/16384*d^5/a^3/b^3*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+63/16384*d^5/a^3/b^3*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
719,1,339,282,0.028000," ","int((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{21 \left(d x \right)^{\frac{3}{2}} a \,d^{13}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{3 \left(d x \right)^{\frac{7}{2}} d^{11}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{287 \left(d x \right)^{\frac{11}{2}} d^{9}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{189 \left(d x \right)^{\frac{15}{2}} b \,d^{7}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}+\frac{63 \left(d x \right)^{\frac{19}{2}} b^{2} d^{5}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}+\frac{63 \sqrt{2}\, d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b^{3}}+\frac{63 \sqrt{2}\, d^{5} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b^{3}}+\frac{63 \sqrt{2}\, d^{5} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b^{3}}"," ",0,"-21/4096*d^13/(b*d^2*x^2+a*d^2)^5/b^2*a*(d*x)^(3/2)-3/128*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(7/2)+287/2048*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(11/2)+189/2560*d^7/(b*d^2*x^2+a*d^2)^5/a^2*b*(d*x)^(15/2)+63/4096*d^5/(b*d^2*x^2+a*d^2)^5/a^3*b^2*(d*x)^(19/2)+63/32768*d^5/a^3/b^3/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+63/16384*d^5/a^3/b^3/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+63/16384*d^5/a^3/b^3/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
720,1,339,282,0.025000," ","int((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{77 \sqrt{d x}\, a \,d^{13}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b^{2}}-\frac{231 \left(d x \right)^{\frac{5}{2}} d^{11}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{313 \left(d x \right)^{\frac{9}{2}} d^{9}}{6144 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{11 \left(d x \right)^{\frac{13}{2}} b \,d^{7}}{384 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}+\frac{77 \left(d x \right)^{\frac{17}{2}} b^{2} d^{5}}{12288 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}+\frac{77 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 a^{4} b^{2}}+\frac{77 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 a^{4} b^{2}}+\frac{77 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{3} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 a^{4} b^{2}}"," ",0,"-77/4096*d^13/(b*d^2*x^2+a*d^2)^5/b^2*a*(d*x)^(1/2)-231/2560*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(5/2)+313/6144*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(9/2)+11/384*d^7/(b*d^2*x^2+a*d^2)^5/a^2*b*(d*x)^(13/2)+77/12288*d^5/(b*d^2*x^2+a*d^2)^5/a^3*b^2*(d*x)^(17/2)+77/32768*d^3/a^4/b^2*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+77/16384*d^3/a^4/b^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+77/16384*d^3/a^4/b^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
721,1,341,277,0.025000," ","int((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{39 \left(d x \right)^{\frac{3}{2}} d^{11}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{31 \left(d x \right)^{\frac{7}{2}} d^{9}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{533 \left(d x \right)^{\frac{11}{2}} b \,d^{7}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}+\frac{351 \left(d x \right)^{\frac{15}{2}} b^{2} d^{5}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}+\frac{117 \left(d x \right)^{\frac{19}{2}} b^{3} d^{3}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{4}}+\frac{117 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4} b^{2}}+\frac{117 \sqrt{2}\, d^{3} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4} b^{2}}+\frac{117 \sqrt{2}\, d^{3} \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4} b^{2}}"," ",0,"-39/4096*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(3/2)+31/128*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(7/2)+533/2048*d^7/(b*d^2*x^2+a*d^2)^5/a^2*b*(d*x)^(11/2)+351/2560*d^5/(b*d^2*x^2+a*d^2)^5/a^3*b^2*(d*x)^(15/2)+117/4096*d^3/(b*d^2*x^2+a*d^2)^5/a^4*b^3*(d*x)^(19/2)+117/32768*d^3/a^4/b^2/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+117/16384*d^3/a^4/b^2/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+117/16384*d^3/a^4/b^2/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
722,1,335,277,0.025000," ","int((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{231 \sqrt{d x}\, d^{11}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} b}+\frac{331 \left(d x \right)^{\frac{5}{2}} d^{9}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{313 \left(d x \right)^{\frac{9}{2}} b \,d^{7}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}+\frac{11 \left(d x \right)^{\frac{13}{2}} b^{2} d^{5}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}+\frac{77 \left(d x \right)^{\frac{17}{2}} b^{3} d^{3}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{4}}+\frac{231 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 a^{5} b}+\frac{231 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 a^{5} b}+\frac{231 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 a^{5} b}"," ",0,"-231/4096*d^11/(b*d^2*x^2+a*d^2)^5/b*(d*x)^(1/2)+331/2560*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(5/2)+313/2048*d^7/(b*d^2*x^2+a*d^2)^5/a^2*b*(d*x)^(9/2)+11/128*d^5/(b*d^2*x^2+a*d^2)^5/a^3*b^2*(d*x)^(13/2)+77/4096*d^3/(b*d^2*x^2+a*d^2)^5/a^4*b^3*(d*x)^(17/2)+231/32768*d/a^5/b*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+231/16384*d/a^5/b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+231/16384*d/a^5/b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
723,1,336,275,0.026000," ","int((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{7529 \left(d x \right)^{\frac{3}{2}} d^{9}}{12288 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{527 \left(d x \right)^{\frac{7}{2}} b \,d^{7}}{384 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}+\frac{9061 \left(d x \right)^{\frac{11}{2}} b^{2} d^{5}}{6144 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}+\frac{1989 \left(d x \right)^{\frac{15}{2}} b^{3} d^{3}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{4}}+\frac{663 \left(d x \right)^{\frac{19}{2}} b^{4} d}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{5}}+\frac{663 \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{5} b}+\frac{663 \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{5} b}+\frac{663 \sqrt{2}\, d \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{5} b}"," ",0,"7529/12288*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(3/2)+527/384*d^7/(b*d^2*x^2+a*d^2)^5/a^2*b*(d*x)^(7/2)+9061/6144*d^5/(b*d^2*x^2+a*d^2)^5/a^3*b^2*(d*x)^(11/2)+1989/2560*d^3/(b*d^2*x^2+a*d^2)^5/a^4*b^3*(d*x)^(15/2)+663/4096*d/(b*d^2*x^2+a*d^2)^5/a^5*b^4*(d*x)^(19/2)+663/32768*d/a^5/b/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+663/16384*d/a^5/b/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+663/16384*d/a^5/b/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
724,1,333,275,0.026000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^3/(d*x)^(1/2),x)","\frac{3803 \sqrt{d x}\, d^{9}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a}+\frac{6289 \left(d x \right)^{\frac{5}{2}} b \,d^{7}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}+\frac{5947 \left(d x \right)^{\frac{9}{2}} b^{2} d^{5}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}+\frac{209 \left(d x \right)^{\frac{13}{2}} b^{3} d^{3}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{4}}+\frac{1463 \left(d x \right)^{\frac{17}{2}} b^{4} d}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{5}}+\frac{4389 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 a^{6} d}+\frac{4389 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 a^{6} d}+\frac{4389 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 a^{6} d}"," ",0,"3803/4096*d^9/(b*d^2*x^2+a*d^2)^5/a*(d*x)^(1/2)+6289/2560*d^7/(b*d^2*x^2+a*d^2)^5/a^2*b*(d*x)^(5/2)+5947/2048*d^5/(b*d^2*x^2+a*d^2)^5/a^3*b^2*(d*x)^(9/2)+209/128*d^3/(b*d^2*x^2+a*d^2)^5/a^4*b^3*(d*x)^(13/2)+1463/4096*d/(b*d^2*x^2+a*d^2)^5/a^5*b^4*(d*x)^(17/2)+4389/32768/d/a^6*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+4389/16384/d/a^6*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+4389/16384/d/a^6*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)","A"
725,1,349,288,0.031000," ","int(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{11743 \left(d x \right)^{\frac{3}{2}} b \,d^{7}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}-\frac{1129 \left(d x \right)^{\frac{7}{2}} b^{2} d^{5}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}-\frac{22467 \left(d x \right)^{\frac{11}{2}} b^{3} d^{3}}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{4}}-\frac{16169 \left(d x \right)^{\frac{15}{2}} b^{4} d}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{5}}-\frac{5731 \left(d x \right)^{\frac{19}{2}} b^{5}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{6} d}-\frac{13923 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{6} d}-\frac{13923 \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{6} d}-\frac{13923 \sqrt{2}\, \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{6} d}-\frac{2}{\sqrt{d x}\, a^{6} d}"," ",0,"-11743/4096*d^7*b/a^2/(b*d^2*x^2+a*d^2)^5*(d*x)^(3/2)-1129/128*d^5*b^2/a^3/(b*d^2*x^2+a*d^2)^5*(d*x)^(7/2)-22467/2048*d^3*b^3/a^4/(b*d^2*x^2+a*d^2)^5*(d*x)^(11/2)-16169/2560*d*b^4/a^5/(b*d^2*x^2+a*d^2)^5*(d*x)^(15/2)-5731/4096/d*b^5/a^6/(b*d^2*x^2+a*d^2)^5*(d*x)^(19/2)-13923/32768/d/a^6/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-13923/16384/d/a^6/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-13923/16384/d/a^6/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/a^6/d/(d*x)^(1/2)","A"
726,1,352,288,0.031000," ","int(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","-\frac{15503 \sqrt{d x}\, b \,d^{7}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{2}}-\frac{31149 \left(d x \right)^{\frac{5}{2}} b^{2} d^{5}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}-\frac{95821 \left(d x \right)^{\frac{9}{2}} b^{3} d^{3}}{6144 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{4}}-\frac{3527 \left(d x \right)^{\frac{13}{2}} b^{4} d}{384 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{5}}-\frac{25457 \left(d x \right)^{\frac{17}{2}} b^{5}}{12288 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{6} d}-\frac{2}{3 \left(d x \right)^{\frac{3}{2}} a^{6} d}-\frac{33649 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 a^{7} d^{3}}-\frac{33649 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 a^{7} d^{3}}-\frac{33649 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 a^{7} d^{3}}"," ",0,"-15503/4096*d^7/a^2*b/(b*d^2*x^2+a*d^2)^5*(d*x)^(1/2)-31149/2560*d^5/a^3*b^2/(b*d^2*x^2+a*d^2)^5*(d*x)^(5/2)-95821/6144*d^3/a^4*b^3/(b*d^2*x^2+a*d^2)^5*(d*x)^(9/2)-3527/384*d/a^5*b^4/(b*d^2*x^2+a*d^2)^5*(d*x)^(13/2)-25457/12288/d/a^6*b^5/(b*d^2*x^2+a*d^2)^5*(d*x)^(17/2)-33649/32768/d^3/a^7*b*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))-33649/16384/d^3/a^7*b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)-33649/16384/d^3/a^7*b*(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/3/a^6/d/(d*x)^(3/2)","A"
727,1,368,302,0.041000," ","int(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{34139 \left(d x \right)^{\frac{3}{2}} b^{2} d^{5}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{3}}+\frac{3597 \left(d x \right)^{\frac{7}{2}} b^{3} d^{3}}{128 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{4}}+\frac{75471 \left(d x \right)^{\frac{11}{2}} b^{4} d}{2048 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{5}}+\frac{56269 \left(d x \right)^{\frac{15}{2}} b^{5}}{2560 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{6} d}+\frac{20463 \left(d x \right)^{\frac{19}{2}} b^{6}}{4096 \left(b \,d^{2} x^{2}+d^{2} a \right)^{5} a^{7} d^{3}}-\frac{2}{5 \left(d x \right)^{\frac{5}{2}} a^{6} d}+\frac{69615 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}-1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{7} d^{3}}+\frac{69615 \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}+1\right)}{16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{7} d^{3}}+\frac{69615 \sqrt{2}\, b \ln \left(\frac{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)}{32768 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{7} d^{3}}+\frac{12 b}{\sqrt{d x}\, a^{7} d^{3}}"," ",0,"34139/4096*d^5*b^2/a^3/(b*d^2*x^2+a*d^2)^5*(d*x)^(3/2)+3597/128*d^3*b^3/a^4/(b*d^2*x^2+a*d^2)^5*(d*x)^(7/2)+75471/2048*d*b^4/a^5/(b*d^2*x^2+a*d^2)^5*(d*x)^(11/2)+56269/2560/d*b^5/a^6/(b*d^2*x^2+a*d^2)^5*(d*x)^(15/2)+20463/4096/d^3*b^6/a^7/(b*d^2*x^2+a*d^2)^5*(d*x)^(19/2)+69615/32768/d^3*b/a^7/(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+69615/16384/d^3*b/a^7/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)+1)+69615/16384/d^3*b/a^7/(a/b*d^2)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b*d^2)^(1/4)*(d*x)^(1/2)-1)-2/5/a^6/d/(d*x)^(5/2)+12*b/a^7/d^3/(d*x)^(1/2)","A"
728,1,39,63,0.004000," ","int((d*x)^(5/2)*((b*x^2+a)^2)^(1/2),x)","\frac{2 \left(7 b \,x^{2}+11 a \right) \left(d x \right)^{\frac{5}{2}} \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x}{77 \left(b \,x^{2}+a \right)}"," ",0,"2/77*x*(7*b*x^2+11*a)*(d*x)^(5/2)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
729,1,39,63,0.002000," ","int((d*x)^(3/2)*((b*x^2+a)^2)^(1/2),x)","\frac{2 \left(5 b \,x^{2}+9 a \right) \left(d x \right)^{\frac{3}{2}} \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x}{45 \left(b \,x^{2}+a \right)}"," ",0,"2/45*x*(5*b*x^2+9*a)*(d*x)^(3/2)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
730,1,39,63,0.004000," ","int((d*x)^(1/2)*((b*x^2+a)^2)^(1/2),x)","\frac{2 \left(3 b \,x^{2}+7 a \right) \sqrt{d x}\, \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x}{21 \left(b \,x^{2}+a \right)}"," ",0,"2/21*x*(3*b*x^2+7*a)*(d*x)^(1/2)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)","A"
731,1,38,63,0.003000," ","int(((b*x^2+a)^2)^(1/2)/(d*x)^(1/2),x)","\frac{2 \left(b \,x^{2}+5 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x}{5 \left(b \,x^{2}+a \right) \sqrt{d x}}"," ",0,"2/5*x*(b*x^2+5*a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)/(d*x)^(1/2)","A"
732,1,39,63,0.003000," ","int(((b*x^2+a)^2)^(1/2)/(d*x)^(3/2),x)","-\frac{2 \left(-b \,x^{2}+3 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x}{3 \left(b \,x^{2}+a \right) \left(d x \right)^{\frac{3}{2}}}"," ",0,"-2/3*x*(-b*x^2+3*a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)/(d*x)^(3/2)","A"
733,1,37,63,0.003000," ","int(((b*x^2+a)^2)^(1/2)/(d*x)^(5/2),x)","-\frac{2 \left(-3 b \,x^{2}+a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x}{3 \left(b \,x^{2}+a \right) \left(d x \right)^{\frac{5}{2}}}"," ",0,"-2/3*x*(-3*b*x^2+a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)/(d*x)^(5/2)","A"
734,1,37,63,0.003000," ","int(((b*x^2+a)^2)^(1/2)/(d*x)^(7/2),x)","-\frac{2 \left(5 b \,x^{2}+a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x}{5 \left(b \,x^{2}+a \right) \left(d x \right)^{\frac{7}{2}}}"," ",0,"-2/5*x*(5*b*x^2+a)*((b*x^2+a)^2)^(1/2)/(b*x^2+a)/(d*x)^(7/2)","A"
735,1,61,135,0.006000," ","int((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{2 \left(385 b^{3} x^{6}+1463 a \,b^{2} x^{4}+1995 a^{2} b \,x^{2}+1045 a^{3}\right) \left(d x \right)^{\frac{5}{2}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x}{7315 \left(b \,x^{2}+a \right)^{3}}"," ",0,"2/7315*x*(385*b^3*x^6+1463*a*b^2*x^4+1995*a^2*b*x^2+1045*a^3)*(d*x)^(5/2)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
736,1,61,135,0.007000," ","int((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{2 \left(195 b^{3} x^{6}+765 a \,b^{2} x^{4}+1105 a^{2} b \,x^{2}+663 a^{3}\right) \left(d x \right)^{\frac{3}{2}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x}{3315 \left(b \,x^{2}+a \right)^{3}}"," ",0,"2/3315*x*(195*b^3*x^6+765*a*b^2*x^4+1105*a^2*b*x^2+663*a^3)*(d*x)^(3/2)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3","A"
737,1,61,135,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)*(d*x)^(1/2),x)","\frac{2 \left(77 b^{3} x^{6}+315 a \,b^{2} x^{4}+495 a^{2} b \,x^{2}+385 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} \sqrt{d x}\, x}{1155 \left(b \,x^{2}+a \right)^{3}}"," ",0,"2/1155*x*(77*b^3*x^6+315*a*b^2*x^4+495*a^2*b*x^2+385*a^3)*((b*x^2+a)^2)^(3/2)*(d*x)^(1/2)/(b*x^2+a)^3","A"
738,1,61,135,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(1/2),x)","\frac{2 \left(15 b^{3} x^{6}+65 a \,b^{2} x^{4}+117 a^{2} b \,x^{2}+195 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x}{195 \left(b \,x^{2}+a \right)^{3} \sqrt{d x}}"," ",0,"2/195*x*(15*b^3*x^6+65*a*b^2*x^4+117*a^2*b*x^2+195*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3/(d*x)^(1/2)","A"
739,1,61,135,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(3/2),x)","-\frac{2 \left(-7 b^{3} x^{6}-33 a \,b^{2} x^{4}-77 a^{2} b \,x^{2}+77 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x}{77 \left(b \,x^{2}+a \right)^{3} \left(d x \right)^{\frac{3}{2}}}"," ",0,"-2/77*x*(-7*b^3*x^6-33*a*b^2*x^4-77*a^2*b*x^2+77*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3/(d*x)^(3/2)","A"
740,1,61,135,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(5/2),x)","-\frac{2 \left(-5 b^{3} x^{6}-27 a \,b^{2} x^{4}-135 a^{2} b \,x^{2}+15 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x}{45 \left(b \,x^{2}+a \right)^{3} \left(d x \right)^{\frac{5}{2}}}"," ",0,"-2/45*x*(-5*b^3*x^6-27*a*b^2*x^4-135*a^2*b*x^2+15*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3/(d*x)^(5/2)","A"
741,1,61,135,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(7/2),x)","-\frac{2 \left(-5 b^{3} x^{6}-35 a \,b^{2} x^{4}+105 a^{2} b \,x^{2}+7 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x}{35 \left(b \,x^{2}+a \right)^{3} \left(d x \right)^{\frac{7}{2}}}"," ",0,"-2/35*x*(-5*b^3*x^6-35*a*b^2*x^4+105*a^2*b*x^2+7*a^3)*((b*x^2+a)^2)^(3/2)/(b*x^2+a)^3/(d*x)^(7/2)","A"
742,1,83,207,0.006000," ","int((d*x)^(5/2)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{2 \left(33649 b^{5} x^{10}+197505 a \,b^{4} x^{8}+478170 a^{2} b^{3} x^{6}+605682 a^{3} b^{2} x^{4}+412965 a^{4} b \,x^{2}+129789 a^{5}\right) \left(d x \right)^{\frac{5}{2}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x}{908523 \left(b \,x^{2}+a \right)^{5}}"," ",0,"2/908523*x*(33649*b^5*x^10+197505*a*b^4*x^8+478170*a^2*b^3*x^6+605682*a^3*b^2*x^4+412965*a^4*b*x^2+129789*a^5)*(d*x)^(5/2)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
743,1,83,207,0.007000," ","int((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{2 \left(13923 b^{5} x^{10}+82875 a \,b^{4} x^{8}+204750 a^{2} b^{3} x^{6}+267750 a^{3} b^{2} x^{4}+193375 a^{4} b \,x^{2}+69615 a^{5}\right) \left(d x \right)^{\frac{3}{2}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x}{348075 \left(b \,x^{2}+a \right)^{5}}"," ",0,"2/348075*x*(13923*b^5*x^10+82875*a*b^4*x^8+204750*a^2*b^3*x^6+267750*a^3*b^2*x^4+193375*a^4*b*x^2+69615*a^5)*(d*x)^(3/2)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5","A"
744,1,83,207,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)*(d*x)^(1/2),x)","\frac{2 \left(4389 b^{5} x^{10}+26565 a \,b^{4} x^{8}+67298 a^{2} b^{3} x^{6}+91770 a^{3} b^{2} x^{4}+72105 a^{4} b \,x^{2}+33649 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} \sqrt{d x}\, x}{100947 \left(b \,x^{2}+a \right)^{5}}"," ",0,"2/100947*x*(4389*b^5*x^10+26565*a*b^4*x^8+67298*a^2*b^3*x^6+91770*a^3*b^2*x^4+72105*a^4*b*x^2+33649*a^5)*((b*x^2+a)^2)^(5/2)*(d*x)^(1/2)/(b*x^2+a)^5","A"
745,1,83,207,0.006000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(1/2),x)","\frac{2 \left(663 b^{5} x^{10}+4095 a \,b^{4} x^{8}+10710 a^{2} b^{3} x^{6}+15470 a^{3} b^{2} x^{4}+13923 a^{4} b \,x^{2}+13923 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x}{13923 \left(b \,x^{2}+a \right)^{5} \sqrt{d x}}"," ",0,"2/13923*x*(663*b^5*x^10+4095*a*b^4*x^8+10710*a^2*b^3*x^6+15470*a^3*b^2*x^4+13923*a^4*b*x^2+13923*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5/(d*x)^(1/2)","A"
746,1,83,207,0.005000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(3/2),x)","-\frac{2 \left(-231 b^{5} x^{10}-1463 a \,b^{4} x^{8}-3990 a^{2} b^{3} x^{6}-6270 a^{3} b^{2} x^{4}-7315 a^{4} b \,x^{2}+4389 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x}{4389 \left(b \,x^{2}+a \right)^{5} \left(d x \right)^{\frac{3}{2}}}"," ",0,"-2/4389*x*(-231*b^5*x^10-1463*a*b^4*x^8-3990*a^2*b^3*x^6-6270*a^3*b^2*x^4-7315*a^4*b*x^2+4389*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5/(d*x)^(3/2)","A"
747,1,83,207,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(5/2),x)","-\frac{2 \left(-117 b^{5} x^{10}-765 a \,b^{4} x^{8}-2210 a^{2} b^{3} x^{6}-3978 a^{3} b^{2} x^{4}-9945 a^{4} b \,x^{2}+663 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x}{1989 \left(b \,x^{2}+a \right)^{5} \left(d x \right)^{\frac{5}{2}}}"," ",0,"-2/1989*x*(-117*b^5*x^10-765*a*b^4*x^8-2210*a^2*b^3*x^6-3978*a^3*b^2*x^4-9945*a^4*b*x^2+663*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5/(d*x)^(5/2)","A"
748,1,83,207,0.007000," ","int((b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(7/2),x)","-\frac{2 \left(-77 b^{5} x^{10}-525 a \,b^{4} x^{8}-1650 a^{2} b^{3} x^{6}-3850 a^{3} b^{2} x^{4}+5775 a^{4} b \,x^{2}+231 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x}{1155 \left(b \,x^{2}+a \right)^{5} \left(d x \right)^{\frac{7}{2}}}"," ",0,"-2/1155*x*(-77*b^5*x^10-525*a*b^4*x^8-1650*a^2*b^3*x^6-3850*a^3*b^2*x^4+5775*a^4*b*x^2+231*a^5)*((b*x^2+a)^2)^(5/2)/(b*x^2+a)^5/(d*x)^(7/2)","A"
749,1,239,298,0.011000," ","int((d*x)^(7/2)/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(10 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+10 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-40 \sqrt{d x}\, a \,d^{2}+8 \left(d x \right)^{\frac{5}{2}} b \right) d}{20 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, b^{2}}"," ",0,"1/20*(b*x^2+a)*d*(5*a*d^2*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+10*a*d^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+10*a*d^2*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+8*(d*x)^(5/2)*b-40*d^2*a*(d*x)^(1/2))/((b*x^2+a)^2)^(1/2)/b^2","A"
750,1,221,266,0.009000," ","int((d*x)^(5/2)/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(6 \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6 \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+3 \sqrt{2}\, a \,d^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-8 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b \right) d}{12 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{2}}"," ",0,"-1/12*(b*x^2+a)*d*(3*a*d^2*2^(1/2)*ln(-((a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-d*x-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+6*a*d^2*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+6*a*d^2*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-8*(d*x)^(3/2)*b*(a/b*d^2)^(1/4))/((b*x^2+a)^2)^(1/2)/b^2/(a/b*d^2)^(1/4)","A"
751,1,214,266,0.008000," ","int((d*x)^(3/2)/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(2 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-8 \sqrt{d x}\right) d}{4 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, b}"," ",0,"-1/4*(b*x^2+a)*d*((a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+2*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-8*(d*x)^(1/2))/((b*x^2+a)^2)^(1/2)/b","A"
752,1,183,237,0.008000," ","int((d*x)^(1/2)/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \sqrt{2}\, \left(2 \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2 \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+\ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)\right) d}{4 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b}"," ",0,"1/4/((b*x^2+a)^2)^(1/2)*(b*x^2+a)*d/b/(a/b*d^2)^(1/4)*2^(1/2)*(ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4)))","A"
753,1,182,237,0.007000," ","int(1/(d*x)^(1/2)/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \left(2 \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2 \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+\ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)\right)}{4 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, a d}"," ",0,"1/4/((b*x^2+a)^2)^(1/2)*(b*x^2+a)/d*(a/b*d^2)^(1/4)/a*2^(1/2)*(ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4)))","A"
754,1,224,268,0.010000," ","int(1/(d*x)^(3/2)/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(2 \sqrt{2}\, \sqrt{d x}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2 \sqrt{2}\, \sqrt{d x}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+\sqrt{2}\, \sqrt{d x}\, \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}\right)}{4 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, a d}"," ",0,"-1/4*(b*x^2+a)/d*(2^(1/2)*(d*x)^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+2*2^(1/2)*(d*x)^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2*2^(1/2)*(d*x)^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+8*(a/b*d^2)^(1/4))/((b*x^2+a)^2)^(1/2)/a/(a/b*d^2)^(1/4)/(d*x)^(1/2)","A"
755,1,239,268,0.010000," ","int(1/(d*x)^(5/2)/((b*x^2+a)^2)^(1/2),x)","-\frac{\left(b \,x^{2}+a \right) \left(8 a \,d^{2}+6 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \left(d x \right)^{\frac{3}{2}} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \left(d x \right)^{\frac{3}{2}} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+3 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \left(d x \right)^{\frac{3}{2}} b \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)\right)}{12 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(d x \right)^{\frac{3}{2}} a^{2} d^{3}}"," ",0,"-1/12*(b*x^2+a)/d^3*(3*b*(a/b*d^2)^(1/4)*2^(1/2)*(d*x)^(3/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+6*b*(a/b*d^2)^(1/4)*2^(1/2)*(d*x)^(3/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+6*b*(a/b*d^2)^(1/4)*2^(1/2)*(d*x)^(3/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+8*d^2*a)/((b*x^2+a)^2)^(1/2)/a^2/(d*x)^(3/2)","A"
756,1,251,300,0.013000," ","int(1/(d*x)^(7/2)/((b*x^2+a)^2)^(1/2),x)","\frac{\left(b \,x^{2}+a \right) \left(40 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b \,d^{2} x^{2}-8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,d^{2}+10 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+10 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+5 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} b \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)\right)}{20 \sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{5}{2}} a^{2} d^{3}}"," ",0,"1/20*(b*x^2+a)/d^3*(5*b*2^(1/2)*(d*x)^(5/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+10*b*2^(1/2)*(d*x)^(5/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+10*b*2^(1/2)*(d*x)^(5/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+40*b*(a/b*d^2)^(1/4)*d^2*x^2-8*d^2*a*(a/b*d^2)^(1/4))/((b*x^2+a)^2)^(1/2)/a^2/(a/b*d^2)^(1/4)/(d*x)^(5/2)","A"
757,1,737,355,0.023000," ","int((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+585 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{2} d^{2} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-3840 \sqrt{d x}\, a \,b^{2} d^{2} x^{4}+2340 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2340 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b \,d^{2} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-7680 \sqrt{d x}\, a^{2} b \,d^{2} x^{2}+256 \left(d x \right)^{\frac{5}{2}} b^{3} x^{4}+1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+585 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-4680 \sqrt{d x}\, a^{3} d^{2}+512 \left(d x \right)^{\frac{5}{2}} a \,b^{2} x^{2}-744 \left(d x \right)^{\frac{5}{2}} a^{2} b \right) \left(b \,x^{2}+a \right) d^{5}}{640 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{4}}"," ",0,"1/640*(1170*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*x^4*a*b^2*d^2+585*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a*b^2*d^2+1170*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a*b^2*d^2+256*(d*x)^(5/2)*x^4*b^3+2340*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*x^2*a^2*b*d^2+1170*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^2*b*d^2+2340*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^2*b*d^2+512*(d*x)^(5/2)*x^2*a*b^2-3840*(d*x)^(1/2)*x^4*a*b^2*d^2+1170*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*a^3*d^2+585*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^3*d^2+1170*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^3*d^2-744*(d*x)^(5/2)*a^2*b-7680*(d*x)^(1/2)*x^2*a^2*b*d^2-4680*(d*x)^(1/2)*a^3*d^2)*d^5*(b*x^2+a)/b^4/((b*x^2+a)^2)^(3/2)","B"
758,1,679,323,0.023000," ","int((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(-462 \sqrt{2}\, a \,b^{2} d^{4} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-462 \sqrt{2}\, a \,b^{2} d^{4} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-231 \sqrt{2}\, a \,b^{2} d^{4} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-924 \sqrt{2}\, a^{2} b \,d^{4} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-924 \sqrt{2}\, a^{2} b \,d^{4} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-462 \sqrt{2}\, a^{2} b \,d^{4} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} b^{3} d^{2} x^{4}-462 \sqrt{2}\, a^{3} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-462 \sqrt{2}\, a^{3} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-231 \sqrt{2}\, a^{3} d^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+512 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a \,b^{2} d^{2} x^{2}+616 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a^{2} b \,d^{2}+456 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{7}{2}} a \,b^{2}\right) \left(b \,x^{2}+a \right) d^{3}}{384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{4}}"," ",0,"1/384*(256*(a/b*d^2)^(1/4)*(d*x)^(3/2)*x^4*b^3*d^2-231*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a*b^2*d^4-462*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a*b^2*d^4-462*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a*b^2*d^4+456*(a/b*d^2)^(1/4)*(d*x)^(7/2)*a*b^2+512*(a/b*d^2)^(1/4)*(d*x)^(3/2)*x^2*a*b^2*d^2-462*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^2*b*d^4-924*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^2*b*d^4-924*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^2*b*d^4+616*(a/b*d^2)^(1/4)*(d*x)^(3/2)*a^2*b*d^2-231*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^3*d^4-462*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^3*d^4-462*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^3*d^4)*d^3*(b*x^2+a)/(a/b*d^2)^(1/4)/b^4/((b*x^2+a)^2)^(3/2)","B"
759,1,696,323,0.022000," ","int((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+45 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-256 \sqrt{d x}\, b^{2} d^{2} x^{4}+180 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+180 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-512 \sqrt{d x}\, a b \,d^{2} x^{2}+90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+45 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-360 \sqrt{d x}\, a^{2} d^{2}-136 \left(d x \right)^{\frac{5}{2}} a b \right) \left(b \,x^{2}+a \right) d^{3}}{128 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"-1/128*(45*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*b^2*d^2+90*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*b^2*d^2+90*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*b^2*d^2+90*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a*b*d^2+180*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a*b*d^2+180*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a*b*d^2-256*(d*x)^(1/2)*x^4*b^2*d^2+45*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^2*d^2+90*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^2*d^2+90*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^2*d^2-136*(d*x)^(5/2)*a*b-512*(d*x)^(1/2)*x^2*a*b*d^2-360*(d*x)^(1/2)*a^2*d^2)*d^3*(b*x^2+a)/b^3/((b*x^2+a)^2)^(3/2)","B"
760,1,612,292,0.020000," ","int((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(-42 \sqrt{2}\, b^{2} d^{4} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-42 \sqrt{2}\, b^{2} d^{4} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-21 \sqrt{2}\, b^{2} d^{4} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-84 \sqrt{2}\, a b \,d^{4} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-84 \sqrt{2}\, a b \,d^{4} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-42 \sqrt{2}\, a b \,d^{4} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-42 \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-42 \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-21 \sqrt{2}\, a^{2} d^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+56 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a b \,d^{2}+88 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{7}{2}} b^{2}\right) \left(b \,x^{2}+a \right) d}{128 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} b^{3}}"," ",0,"-1/128*(-21*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*b^2*d^4-42*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*b^2*d^4-42*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*b^2*d^4+88*(a/b*d^2)^(1/4)*(d*x)^(7/2)*b^2-42*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a*b*d^4-84*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a*b*d^4-84*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a*b*d^4+56*(a/b*d^2)^(1/4)*(d*x)^(3/2)*a*b*d^2-21*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^2*d^4-42*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^2*d^4-42*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^2*d^4)*d*(b*x^2+a)/(a/b*d^2)^(1/4)/b^3/((b*x^2+a)^2)^(3/2)","B"
761,1,666,292,0.019000," ","int((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(10 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+10 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+20 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+20 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+10 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+10 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+10 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+5 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-40 \sqrt{d x}\, a^{2} d^{2}-72 \left(d x \right)^{\frac{5}{2}} a b \right) \left(b \,x^{2}+a \right) d}{128 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a \,b^{2}}"," ",0,"1/128*(5*(a/b*d^2)^(1/4)*2^(1/2)*b^2*d^2*x^4*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+10*(a/b*d^2)^(1/4)*2^(1/2)*b^2*d^2*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+10*(a/b*d^2)^(1/4)*2^(1/2)*b^2*d^2*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+10*(a/b*d^2)^(1/4)*2^(1/2)*a*b*d^2*x^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+20*(a/b*d^2)^(1/4)*2^(1/2)*a*b*d^2*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+20*(a/b*d^2)^(1/4)*2^(1/2)*a*b*d^2*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+5*(a/b*d^2)^(1/4)*2^(1/2)*a^2*d^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+10*(a/b*d^2)^(1/4)*2^(1/2)*a^2*d^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+10*(a/b*d^2)^(1/4)*2^(1/2)*a^2*d^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-72*(d*x)^(5/2)*a*b-40*(d*x)^(1/2)*a^2*d^2)*d*(b*x^2+a)/a/b^2/((b*x^2+a)^2)^(3/2)","B"
762,1,617,293,0.018000," ","int((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(6 \sqrt{2}\, b^{2} d^{4} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6 \sqrt{2}\, b^{2} d^{4} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+3 \sqrt{2}\, b^{2} d^{4} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+12 \sqrt{2}\, a b \,d^{4} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+12 \sqrt{2}\, a b \,d^{4} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6 \sqrt{2}\, a b \,d^{4} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+6 \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6 \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+3 \sqrt{2}\, a^{2} d^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-8 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a b \,d^{2}+24 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{7}{2}} b^{2}\right) \left(b \,x^{2}+a \right)}{128 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a \,b^{2} d}"," ",0,"1/128*(3*2^(1/2)*b^2*d^4*x^4*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+6*2^(1/2)*b^2*d^4*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+6*2^(1/2)*b^2*d^4*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+24*(a/b*d^2)^(1/4)*(d*x)^(7/2)*b^2+6*2^(1/2)*a*b*d^4*x^2*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+12*2^(1/2)*a*b*d^4*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+12*2^(1/2)*a*b*d^4*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-8*(a/b*d^2)^(1/4)*(d*x)^(3/2)*a*b*d^2+3*2^(1/2)*a^2*d^4*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+6*2^(1/2)*a^2*d^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+6*2^(1/2)*a^2*d^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4)))/d*(b*x^2+a)/(a/b*d^2)^(1/4)/b^2/a/((b*x^2+a)^2)^(3/2)","B"
763,1,668,293,0.019000," ","int((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(6 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+3 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d^{2} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+12 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+12 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,d^{2} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+6 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+3 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-24 \sqrt{d x}\, a^{2} d^{2}+8 \left(d x \right)^{\frac{5}{2}} a b \right) \left(b \,x^{2}+a \right)}{128 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{2} b d}"," ",0,"1/128*(3*(a/b*d^2)^(1/4)*2^(1/2)*b^2*d^2*x^4*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+6*(a/b*d^2)^(1/4)*2^(1/2)*b^2*d^2*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+6*(a/b*d^2)^(1/4)*2^(1/2)*b^2*d^2*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+6*(a/b*d^2)^(1/4)*2^(1/2)*a*b*d^2*x^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+12*(a/b*d^2)^(1/4)*2^(1/2)*a*b*d^2*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+12*(a/b*d^2)^(1/4)*2^(1/2)*a*b*d^2*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+3*(a/b*d^2)^(1/4)*2^(1/2)*a^2*d^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+6*(a/b*d^2)^(1/4)*2^(1/2)*a^2*d^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+6*(a/b*d^2)^(1/4)*2^(1/2)*a^2*d^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+8*(d*x)^(5/2)*a*b-24*(d*x)^(1/2)*a^2*d^2)/d*(b*x^2+a)/b/a^2/((b*x^2+a)^2)^(3/2)","B"
764,1,617,294,0.012000," ","int((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(10 \sqrt{2}\, b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+10 \sqrt{2}\, b^{2} d^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+5 \sqrt{2}\, b^{2} d^{2} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+20 \sqrt{2}\, a b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+20 \sqrt{2}\, a b \,d^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+10 \sqrt{2}\, a b \,d^{2} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+10 \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+10 \sqrt{2}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+5 \sqrt{2}\, a^{2} d^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+40 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} b^{2} x^{2}+72 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a b \right) \left(b \,x^{2}+a \right)}{128 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{2} b d}"," ",0,"1/128*(5*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*b^2*d^2+10*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*b^2*d^2+10*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*b^2*d^2+40*(a/b*d^2)^(1/4)*(d*x)^(3/2)*x^2*b^2+10*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a*b*d^2+20*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a*b*d^2+20*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a*b*d^2+72*(d*x)^(3/2)*a*b*(a/b*d^2)^(1/4)+5*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^2*d^2+10*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^2*d^2+10*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^2*d^2)/d*(b*x^2+a)/(a/b*d^2)^(1/4)/b/a^2/((b*x^2+a)^2)^(3/2)","B"
765,1,638,294,0.010000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(3/2)/(d*x)^(1/2),x)","\frac{\left(42 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+42 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+21 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+84 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+84 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+42 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a b \,x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+56 \sqrt{d x}\, a b \,x^{2}+42 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+42 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+21 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+88 \sqrt{d x}\, a^{2}\right) \left(b \,x^{2}+a \right)}{128 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{3} d}"," ",0,"1/128*(42*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*x^4*b^2+42*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*x^4*b^2+21*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*b^2+84*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*x^2*a*b+84*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*x^2*a*b+42*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a*b+42*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*a^2+42*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(a/b*d^2)^(1/4)*2^(1/2)*a^2+21*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^2+56*(d*x)^(1/2)*x^2*a*b+88*(d*x)^(1/2)*a^2)/d*(b*x^2+a)/a^3/((b*x^2+a)^2)^(3/2)","B"
766,1,645,325,0.021000," ","int(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(90 \sqrt{2}\, \sqrt{d x}\, b^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \sqrt{2}\, \sqrt{d x}\, b^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+45 \sqrt{2}\, \sqrt{d x}\, b^{2} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+360 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{2} x^{4}+180 \sqrt{2}\, \sqrt{d x}\, a b \,x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+180 \sqrt{2}\, \sqrt{d x}\, a b \,x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \sqrt{2}\, \sqrt{d x}\, a b \,x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+648 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a b \,x^{2}+90 \sqrt{2}\, \sqrt{d x}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \sqrt{2}\, \sqrt{d x}\, a^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+45 \sqrt{2}\, \sqrt{d x}\, a^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2}\right) \left(b \,x^{2}+a \right)}{128 \sqrt{d x}\, \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{3} d}"," ",0,"-1/128/d*(45*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*(d*x)^(1/2)*x^4*b^2+90*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(1/2)*x^4*b^2+90*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(1/2)*x^4*b^2+360*(a/b*d^2)^(1/4)*x^4*b^2+90*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*(d*x)^(1/2)*x^2*a*b+180*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(1/2)*x^2*a*b+180*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(1/2)*x^2*a*b+648*(a/b*d^2)^(1/4)*x^2*a*b+45*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*(d*x)^(1/2)*a^2+90*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(1/2)*a^2+90*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(1/2)*a^2+256*(a/b*d^2)^(1/4)*a^2)*(b*x^2+a)/(d*x)^(1/2)/(a/b*d^2)^(1/4)/a^3/((b*x^2+a)^2)^(3/2)","A"
767,1,707,325,0.022000," ","int(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","-\frac{\left(616 a \,b^{2} d^{2} x^{4}+462 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+462 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+231 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+968 a^{2} b \,d^{2} x^{2}+924 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+924 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+462 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{2} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+256 a^{3} d^{2}+462 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+462 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+231 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)\right) \left(b \,x^{2}+a \right)}{384 \left(d x \right)^{\frac{3}{2}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{4} d^{3}}"," ",0,"-1/384/d^3*(231*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*b^3+462*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*b^3+462*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*b^3+462*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a*b^2+924*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a*b^2+924*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a*b^2+231*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^2*b+462*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^2*b+462*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^2*b+616*a*d^2*b^2*x^4+968*x^2*a^2*b*d^2+256*a^3*d^2)*(b*x^2+a)/(d*x)^(3/2)/a^4/((b*x^2+a)^2)^(3/2)","B"
768,1,687,357,0.026000," ","int(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(4680 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{3} d^{2} x^{6}+8424 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{2} d^{2} x^{4}+1170 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} b^{3} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} b^{3} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+585 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} b^{3} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+3328 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b \,d^{2} x^{2}+2340 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} a \,b^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2340 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} a \,b^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} a \,b^{2} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-256 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} d^{2}+1170 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} a^{2} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} a^{2} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+585 \sqrt{2}\, \left(d x \right)^{\frac{5}{2}} a^{2} b \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)\right) \left(b \,x^{2}+a \right)}{640 \left(d x \right)^{\frac{5}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} a^{4} d^{3}}"," ",0,"1/640/d^3*(585*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*(d*x)^(5/2)*x^4*b^3+1170*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(5/2)*x^4*b^3+1170*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(5/2)*x^4*b^3+4680*(a/b*d^2)^(1/4)*x^6*b^3*d^2+1170*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*(d*x)^(5/2)*x^2*a*b^2+2340*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(5/2)*x^2*a*b^2+2340*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(5/2)*x^2*a*b^2+8424*(a/b*d^2)^(1/4)*x^4*a*b^2*d^2+585*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*(d*x)^(5/2)*a^2*b+1170*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(5/2)*a^2*b+1170*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*(d*x)^(5/2)*a^2*b+3328*(a/b*d^2)^(1/4)*x^2*a^2*b*d^2-256*(a/b*d^2)^(1/4)*a^3*d^2)*(b*x^2+a)/(d*x)^(5/2)/(a/b*d^2)^(1/4)/a^4/((b*x^2+a)^2)^(3/2)","A"
769,1,1287,421,0.027000," ","int((d*x)^(23/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(-139230 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-139230 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-69615 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{4} d^{6} x^{8} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+409600 \sqrt{d x}\, a \,b^{4} d^{6} x^{8}-556920 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-556920 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-278460 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{3} d^{6} x^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1638400 \sqrt{d x}\, a^{2} b^{3} d^{6} x^{6}-16384 \left(d x \right)^{\frac{5}{2}} b^{5} d^{4} x^{8}-835380 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-835380 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-417690 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b^{2} d^{6} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+2457600 \sqrt{d x}\, a^{3} b^{2} d^{6} x^{4}-65536 \left(d x \right)^{\frac{5}{2}} a \,b^{4} d^{4} x^{6}-556920 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-556920 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-278460 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} b \,d^{6} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1638400 \sqrt{d x}\, a^{4} b \,d^{6} x^{2}-98304 \left(d x \right)^{\frac{5}{2}} a^{2} b^{3} d^{4} x^{4}-139230 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{5} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-139230 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{5} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-69615 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{5} d^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+556920 \sqrt{d x}\, a^{5} d^{6}-65536 \left(d x \right)^{\frac{5}{2}} a^{3} b^{2} d^{4} x^{2}+477896 \left(d x \right)^{\frac{5}{2}} a^{4} b \,d^{4}+565800 \left(d x \right)^{\frac{9}{2}} a^{3} b^{2} d^{2}+223960 \left(d x \right)^{\frac{13}{2}} a^{2} b^{3}\right) \left(b \,x^{2}+a \right) d^{5}}{40960 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{6}}"," ",0,"-1/40960*(477896*(d*x)^(5/2)*a^4*b*d^4+565800*(d*x)^(9/2)*a^3*b^2*d^2-16384*(d*x)^(5/2)*x^8*b^5*d^4-65536*(d*x)^(5/2)*x^6*a*b^4*d^4+409600*(d*x)^(1/2)*x^8*a*b^4*d^6-98304*(d*x)^(5/2)*x^4*a^2*b^3*d^4+1638400*(d*x)^(1/2)*x^6*a^2*b^3*d^6-65536*(d*x)^(5/2)*x^2*a^3*b^2*d^4+2457600*(d*x)^(1/2)*x^4*a^3*b^2*d^6+1638400*(d*x)^(1/2)*x^2*a^4*b*d^6-69615*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^5*d^6-139230*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^5*d^6-139230*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^5*d^6-556920*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^4*b*d^6-69615*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^8*a*b^4*d^6-139230*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*a*b^4*d^6-139230*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*a*b^4*d^6-278460*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^6*a^2*b^3*d^6-556920*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a^2*b^3*d^6-556920*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a^2*b^3*d^6-417690*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a^3*b^2*d^6-835380*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^3*b^2*d^6-278460*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^4*b*d^6-556920*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^4*b*d^6-835380*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^3*b^2*d^6+223960*(d*x)^(13/2)*a^2*b^3+556920*(d*x)^(1/2)*a^5*d^6)*d^5*(b*x^2+a)/b^6/((b*x^2+a)^2)^(5/2)","B"
770,1,1171,389,0.027000," ","int((d*x)^(21/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(-43890 \sqrt{2}\, a \,b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-43890 \sqrt{2}\, a \,b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-21945 \sqrt{2}\, a \,b^{4} d^{8} x^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-175560 \sqrt{2}\, a^{2} b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-175560 \sqrt{2}\, a^{2} b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-87780 \sqrt{2}\, a^{2} b^{3} d^{8} x^{6} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+16384 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{5} d^{6} x^{8}-263340 \sqrt{2}\, a^{3} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-263340 \sqrt{2}\, a^{3} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-131670 \sqrt{2}\, a^{3} b^{2} d^{8} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+65536 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{4} d^{6} x^{6}-175560 \sqrt{2}\, a^{4} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-175560 \sqrt{2}\, a^{4} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-87780 \sqrt{2}\, a^{4} b \,d^{8} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+98304 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{3} d^{6} x^{4}-43890 \sqrt{2}\, a^{5} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-43890 \sqrt{2}\, a^{5} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-21945 \sqrt{2}\, a^{5} d^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+65536 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b^{2} d^{6} x^{2}+58520 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4} b \,d^{6}+143464 \left(d x \right)^{\frac{7}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b^{2} d^{4}+168456 \left(d x \right)^{\frac{11}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{3} d^{2}+70200 \left(d x \right)^{\frac{15}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{4}\right) \left(b \,x^{2}+a \right) d^{3}}{24576 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{6}}"," ",0,"1/24576*(16384*(d*x)^(3/2)*(a/b*d^2)^(1/4)*x^8*b^5*d^6-21945*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^8*a*b^4*d^8-43890*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*a*b^4*d^8-43890*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*a*b^4*d^8+70200*(d*x)^(15/2)*(a/b*d^2)^(1/4)*a*b^4+65536*(d*x)^(3/2)*(a/b*d^2)^(1/4)*x^6*a*b^4*d^6-87780*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^6*a^2*b^3*d^8-175560*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a^2*b^3*d^8-175560*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a^2*b^3*d^8+168456*(d*x)^(11/2)*(a/b*d^2)^(1/4)*a^2*b^3*d^2+98304*(d*x)^(3/2)*(a/b*d^2)^(1/4)*x^4*a^2*b^3*d^6-131670*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a^3*b^2*d^8-263340*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^3*b^2*d^8-263340*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^3*b^2*d^8+143464*(d*x)^(7/2)*(a/b*d^2)^(1/4)*a^3*b^2*d^4+65536*(d*x)^(3/2)*(a/b*d^2)^(1/4)*x^2*a^3*b^2*d^6-87780*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^4*b*d^8-175560*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^4*b*d^8-175560*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^4*b*d^8+58520*(d*x)^(3/2)*(a/b*d^2)^(1/4)*a^4*b*d^6-21945*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^5*d^8-43890*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^5*d^8-43890*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^5*d^8)*d^3*(b*x^2+a)/(a/b*d^2)^(1/4)/b^6/((b*x^2+a)^2)^(5/2)","B"
771,1,1202,389,0.028000," ","int((d*x)^(19/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(19890 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+19890 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+9945 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-49152 \sqrt{d x}\, b^{4} d^{6} x^{8}+79560 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+79560 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+39780 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-196608 \sqrt{d x}\, a \,b^{3} d^{6} x^{6}+119340 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+119340 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+59670 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-294912 \sqrt{d x}\, a^{2} b^{2} d^{6} x^{4}+79560 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+79560 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+39780 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-196608 \sqrt{d x}\, a^{3} b \,d^{6} x^{2}+19890 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+19890 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+9945 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-79560 \sqrt{d x}\, a^{4} d^{6}-105720 \left(d x \right)^{\frac{5}{2}} a^{3} b \,d^{4}-127640 \left(d x \right)^{\frac{9}{2}} a^{2} b^{2} d^{2}-55400 \left(d x \right)^{\frac{13}{2}} a \,b^{3}\right) \left(b \,x^{2}+a \right) d^{3}}{24576 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{5}}"," ",0,"-1/24576*(9945*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^8*b^4*d^6+19890*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^4*d^6+19890*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^4*d^6+39780*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^6*a*b^3*d^6+79560*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^3*d^6+79560*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^3*d^6-49152*(d*x)^(1/2)*x^8*b^4*d^6+59670*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a^2*b^2*d^6+119340*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^2*d^6+119340*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^2*d^6-55400*(d*x)^(13/2)*a*b^3-196608*(d*x)^(1/2)*x^6*a*b^3*d^6+39780*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^3*b*d^6+79560*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b*d^6+79560*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b*d^6-127640*(d*x)^(9/2)*a^2*b^2*d^2-294912*(d*x)^(1/2)*x^4*a^2*b^2*d^6+9945*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^4*d^6+19890*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4*d^6+19890*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4*d^6-105720*(d*x)^(5/2)*a^3*b*d^4-196608*(d*x)^(1/2)*x^2*a^3*b*d^6-79560*(d*x)^(1/2)*a^4*d^6)*d^3*(b*x^2+a)/b^5/((b*x^2+a)^2)^(5/2)","B"
772,1,1046,358,0.025000," ","int((d*x)^(17/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(-2310 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-2310 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-1155 \sqrt{2}\, b^{4} d^{8} x^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-9240 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-9240 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-4620 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-13860 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-13860 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-6930 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-9240 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-9240 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-4620 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-2310 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-2310 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)-1155 \sqrt{2}\, a^{4} d^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+3080 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a^{3} b \,d^{6}+11000 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{7}{2}} a^{2} b^{2} d^{4}+14040 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{11}{2}} a \,b^{3} d^{2}+7144 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{15}{2}} b^{4}\right) \left(b \,x^{2}+a \right) d}{8192 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} b^{5}}"," ",0,"-1/8192*(-1155*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^8*b^4*d^8-2310*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^4*d^8-2310*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^4*d^8+7144*(a/b*d^2)^(1/4)*(d*x)^(15/2)*b^4-4620*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^6*a*b^3*d^8-9240*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^3*d^8-9240*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^3*d^8+14040*(a/b*d^2)^(1/4)*(d*x)^(11/2)*a*b^3*d^2-6930*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a^2*b^2*d^8-13860*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^2*d^8-13860*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^2*d^8+11000*(a/b*d^2)^(1/4)*(d*x)^(7/2)*a^2*b^2*d^4-4620*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^3*b*d^8-9240*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b*d^8-9240*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b*d^8+3080*(a/b*d^2)^(1/4)*(d*x)^(3/2)*a^3*b*d^6-1155*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^4*d^8-2310*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4*d^8-2310*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4*d^8)*d*(b*x^2+a)/(a/b*d^2)^(1/4)/b^5/((b*x^2+a)^2)^(5/2)","B"
773,1,1134,358,0.025000," ","int((d*x)^(15/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+585 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+4680 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+4680 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2340 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+7020 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+7020 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+3510 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+4680 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+4680 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2340 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+585 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-4680 \sqrt{d x}\, a^{4} d^{6}-17784 \left(d x \right)^{\frac{5}{2}} a^{3} b \,d^{4}-24856 \left(d x \right)^{\frac{9}{2}} a^{2} b^{2} d^{2}-14824 \left(d x \right)^{\frac{13}{2}} a \,b^{3}\right) \left(b \,x^{2}+a \right) d}{24576 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a \,b^{4}}"," ",0,"1/24576*(585*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1170*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1170*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2340*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+4680*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+4680*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+3510*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+7020*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+7020*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-14824*(d*x)^(13/2)*a*b^3+2340*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+4680*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+4680*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-24856*(d*x)^(9/2)*a^2*b^2*d^2+585*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1170*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1170*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-17784*(d*x)^(5/2)*a^3*b*d^4-4680*(d*x)^(1/2)*a^4*d^6)*d*(b*x^2+a)/a/b^4/((b*x^2+a)^2)^(5/2)","B"
774,1,1051,361,0.024000," ","int((d*x)^(13/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(462 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+462 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+231 \sqrt{2}\, b^{4} d^{8} x^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1848 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1848 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+924 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+2772 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2772 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1386 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1848 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1848 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+924 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+462 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+462 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+231 \sqrt{2}\, a^{4} d^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-616 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a^{3} b \,d^{6}-2200 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{7}{2}} a^{2} b^{2} d^{4}-2808 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{11}{2}} a \,b^{3} d^{2}+1848 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{15}{2}} b^{4}\right) \left(b \,x^{2}+a \right)}{24576 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a \,b^{4} d}"," ",0,"1/24576*(231*2^(1/2)*b^4*d^8*x^8*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+462*2^(1/2)*b^4*d^8*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+462*2^(1/2)*b^4*d^8*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1848*(a/b*d^2)^(1/4)*(d*x)^(15/2)*b^4+924*2^(1/2)*a*b^3*d^8*x^6*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1848*2^(1/2)*a*b^3*d^8*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1848*2^(1/2)*a*b^3*d^8*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-2808*(a/b*d^2)^(1/4)*(d*x)^(11/2)*a*b^3*d^2+1386*2^(1/2)*a^2*b^2*d^8*x^4*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+2772*2^(1/2)*a^2*b^2*d^8*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2772*2^(1/2)*a^2*b^2*d^8*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-2200*(a/b*d^2)^(1/4)*(d*x)^(7/2)*a^2*b^2*d^4+924*2^(1/2)*a^3*b*d^8*x^2*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1848*2^(1/2)*a^3*b*d^8*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1848*2^(1/2)*a^3*b*d^8*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-616*(a/b*d^2)^(1/4)*(d*x)^(3/2)*a^3*b*d^6+231*2^(1/2)*a^4*d^8*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+462*2^(1/2)*a^4*d^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+462*2^(1/2)*a^4*d^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4)))/d*(b*x^2+a)/(a/b*d^2)^(1/4)/b^4/a/((b*x^2+a)^2)^(5/2)","B"
775,1,1136,361,0.023000," ","int((d*x)^(11/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+45 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+360 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+360 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+180 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+540 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+540 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+270 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+360 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+360 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+180 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+45 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-360 \sqrt{d x}\, a^{4} d^{6}-1368 \left(d x \right)^{\frac{5}{2}} a^{3} b \,d^{4}-1912 \left(d x \right)^{\frac{9}{2}} a^{2} b^{2} d^{2}+120 \left(d x \right)^{\frac{13}{2}} a \,b^{3}\right) \left(b \,x^{2}+a \right)}{8192 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{2} b^{3} d}"," ",0,"1/8192*(45*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+90*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+90*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+180*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+360*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+360*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+270*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+540*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+540*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+120*(d*x)^(13/2)*a*b^3+180*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+360*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+360*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-1912*(d*x)^(9/2)*a^2*b^2*d^2+45*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+90*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+90*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-1368*(d*x)^(5/2)*a^3*b*d^4-360*(d*x)^(1/2)*a^4*d^6)/d*(b*x^2+a)/b^3/a^2/((b*x^2+a)^2)^(5/2)","B"
776,1,1051,364,0.026000," ","int((d*x)^(9/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(210 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+210 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+105 \sqrt{2}\, b^{4} d^{8} x^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+840 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+840 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+420 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1260 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1260 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+630 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+840 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+840 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+420 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+210 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+210 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+105 \sqrt{2}\, a^{4} d^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-280 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a^{3} b \,d^{6}-1000 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{7}{2}} a^{2} b^{2} d^{4}+3192 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{11}{2}} a \,b^{3} d^{2}+840 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{15}{2}} b^{4}\right) \left(b \,x^{2}+a \right)}{24576 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{2} b^{3} d^{3}}"," ",0,"1/24576*(105*2^(1/2)*b^4*d^8*x^8*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+210*2^(1/2)*b^4*d^8*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+210*2^(1/2)*b^4*d^8*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+840*(a/b*d^2)^(1/4)*(d*x)^(15/2)*b^4+420*2^(1/2)*a*b^3*d^8*x^6*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+840*2^(1/2)*a*b^3*d^8*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+840*2^(1/2)*a*b^3*d^8*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+3192*(a/b*d^2)^(1/4)*(d*x)^(11/2)*a*b^3*d^2+630*2^(1/2)*a^2*b^2*d^8*x^4*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1260*2^(1/2)*a^2*b^2*d^8*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1260*2^(1/2)*a^2*b^2*d^8*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-1000*(a/b*d^2)^(1/4)*(d*x)^(7/2)*a^2*b^2*d^4+420*2^(1/2)*a^3*b*d^8*x^2*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+840*2^(1/2)*a^3*b*d^8*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+840*2^(1/2)*a^3*b*d^8*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-280*(a/b*d^2)^(1/4)*(d*x)^(3/2)*a^3*b*d^6+105*2^(1/2)*a^4*d^8*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+210*2^(1/2)*a^4*d^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+210*2^(1/2)*a^4*d^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4)))/d^3*(b*x^2+a)/(a/b*d^2)^(1/4)/b^3/a^2/((b*x^2+a)^2)^(5/2)","B"
777,1,1136,364,0.024000," ","int((d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(210 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+210 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+105 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+840 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+840 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+420 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1260 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1260 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+630 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+840 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+840 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+420 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+210 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+210 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+105 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-840 \sqrt{d x}\, a^{4} d^{6}-3192 \left(d x \right)^{\frac{5}{2}} a^{3} b \,d^{4}+1000 \left(d x \right)^{\frac{9}{2}} a^{2} b^{2} d^{2}+280 \left(d x \right)^{\frac{13}{2}} a \,b^{3}\right) \left(b \,x^{2}+a \right)}{24576 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{3} b^{2} d^{3}}"," ",0,"1/24576*(105*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+210*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+210*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+420*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+840*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+840*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+630*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1260*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1260*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+280*(d*x)^(13/2)*a*b^3+420*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+840*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+840*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1000*(d*x)^(9/2)*a^2*b^2*d^2+105*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+210*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+210*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-3192*(d*x)^(5/2)*a^3*b*d^4-840*(d*x)^(1/2)*a^4*d^6)/d^3*(b*x^2+a)/b^2/a^3/((b*x^2+a)^2)^(5/2)","B"
778,1,1051,361,0.024000," ","int((d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(90 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+45 \sqrt{2}\, b^{4} d^{8} x^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+360 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+360 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+180 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+540 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+540 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+270 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+360 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+360 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+180 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+90 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+90 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+45 \sqrt{2}\, a^{4} d^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-120 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a^{3} b \,d^{6}+1912 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{7}{2}} a^{2} b^{2} d^{4}+1368 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{11}{2}} a \,b^{3} d^{2}+360 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{15}{2}} b^{4}\right) \left(b \,x^{2}+a \right)}{8192 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{3} b^{2} d^{5}}"," ",0,"1/8192*(45*2^(1/2)*b^4*d^8*x^8*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+90*2^(1/2)*b^4*d^8*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+90*2^(1/2)*b^4*d^8*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+360*(a/b*d^2)^(1/4)*(d*x)^(15/2)*b^4+180*2^(1/2)*a*b^3*d^8*x^6*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+360*2^(1/2)*a*b^3*d^8*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+360*2^(1/2)*a*b^3*d^8*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1368*(a/b*d^2)^(1/4)*(d*x)^(11/2)*a*b^3*d^2+270*2^(1/2)*a^2*b^2*d^8*x^4*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+540*2^(1/2)*a^2*b^2*d^8*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+540*2^(1/2)*a^2*b^2*d^8*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1912*(a/b*d^2)^(1/4)*(d*x)^(7/2)*a^2*b^2*d^4+180*2^(1/2)*a^3*b*d^8*x^2*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+360*2^(1/2)*a^3*b*d^8*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+360*2^(1/2)*a^3*b*d^8*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))-120*(a/b*d^2)^(1/4)*(d*x)^(3/2)*a^3*b*d^6+45*2^(1/2)*a^4*d^8*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+90*2^(1/2)*a^4*d^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+90*2^(1/2)*a^4*d^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4)))/d^5*(b*x^2+a)/(a/b*d^2)^(1/4)/b^2/a^3/((b*x^2+a)^2)^(5/2)","B"
779,1,1136,361,0.024000," ","int((d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(462 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+462 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+231 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1848 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1848 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+924 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+2772 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2772 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1386 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1848 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1848 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+924 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+462 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+462 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+231 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-1848 \sqrt{d x}\, a^{4} d^{6}+2808 \left(d x \right)^{\frac{5}{2}} a^{3} b \,d^{4}+2200 \left(d x \right)^{\frac{9}{2}} a^{2} b^{2} d^{2}+616 \left(d x \right)^{\frac{13}{2}} a \,b^{3}\right) \left(b \,x^{2}+a \right)}{24576 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{4} b \,d^{5}}"," ",0,"1/24576*(231*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+462*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+462*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+924*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1848*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1848*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1386*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+2772*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2772*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+616*(d*x)^(13/2)*a*b^3+924*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1848*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1848*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2200*(d*x)^(9/2)*a^2*b^2*d^2+231*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+462*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+462*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2808*(d*x)^(5/2)*a^3*b*d^4-1848*(d*x)^(1/2)*a^4*d^6)/d^5*(b*x^2+a)/b/a^4/((b*x^2+a)^2)^(5/2)","B"
780,1,1051,360,0.023000," ","int((d*x)^(1/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(1170 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \sqrt{2}\, b^{4} d^{8} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+585 \sqrt{2}\, b^{4} d^{8} x^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+4680 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+4680 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2340 \sqrt{2}\, a \,b^{3} d^{8} x^{6} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+7020 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+7020 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+3510 \sqrt{2}\, a^{2} b^{2} d^{8} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+4680 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+4680 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2340 \sqrt{2}\, a^{3} b \,d^{8} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1170 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1170 \sqrt{2}\, a^{4} d^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+585 \sqrt{2}\, a^{4} d^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+14824 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{3}{2}} a^{3} b \,d^{6}+24856 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{7}{2}} a^{2} b^{2} d^{4}+17784 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{11}{2}} a \,b^{3} d^{2}+4680 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(d x \right)^{\frac{15}{2}} b^{4}\right) \left(b \,x^{2}+a \right)}{24576 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{4} b \,d^{7}}"," ",0,"1/24576*(585*2^(1/2)*b^4*d^8*x^8*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1170*2^(1/2)*b^4*d^8*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1170*2^(1/2)*b^4*d^8*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+4680*(a/b*d^2)^(1/4)*(d*x)^(15/2)*b^4+2340*2^(1/2)*a*b^3*d^8*x^6*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+4680*2^(1/2)*a*b^3*d^8*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+4680*2^(1/2)*a*b^3*d^8*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+17784*(a/b*d^2)^(1/4)*(d*x)^(11/2)*a*b^3*d^2+3510*2^(1/2)*a^2*b^2*d^8*x^4*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+7020*2^(1/2)*a^2*b^2*d^8*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+7020*2^(1/2)*a^2*b^2*d^8*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+24856*(a/b*d^2)^(1/4)*(d*x)^(7/2)*a^2*b^2*d^4+2340*2^(1/2)*a^3*b*d^8*x^2*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+4680*2^(1/2)*a^3*b*d^8*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+4680*2^(1/2)*a^3*b*d^8*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+14824*(a/b*d^2)^(1/4)*(d*x)^(3/2)*a^3*b*d^6+585*2^(1/2)*a^4*d^8*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+1170*2^(1/2)*a^4*d^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+1170*2^(1/2)*a^4*d^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4)))/d^7*(b*x^2+a)/(a/b*d^2)^(1/4)/b/a^4/((b*x^2+a)^2)^(5/2)","B"
781,1,1133,360,0.024000," ","int(1/(b^2*x^4+2*a*b*x^2+a^2)^(5/2)/(d*x)^(1/2),x)","\frac{\left(2310 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2310 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1155 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{4} d^{6} x^{8} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+9240 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+9240 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+4620 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{3} d^{6} x^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+13860 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+13860 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+6930 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{2} d^{6} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+9240 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+9240 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+4620 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b \,d^{6} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+2310 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+2310 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+1155 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} d^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+7144 \sqrt{d x}\, a^{4} d^{6}+14040 \left(d x \right)^{\frac{5}{2}} a^{3} b \,d^{4}+11000 \left(d x \right)^{\frac{9}{2}} a^{2} b^{2} d^{2}+3080 \left(d x \right)^{\frac{13}{2}} a \,b^{3}\right) \left(b \,x^{2}+a \right)}{8192 \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{5} d^{7}}"," ",0,"1/8192*(1155*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+2310*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2310*(a/b*d^2)^(1/4)*2^(1/2)*b^4*d^6*x^8*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+4620*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+9240*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+9240*(a/b*d^2)^(1/4)*2^(1/2)*a*b^3*d^6*x^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+6930*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+13860*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+13860*(a/b*d^2)^(1/4)*2^(1/2)*a^2*b^2*d^6*x^4*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+3080*(d*x)^(13/2)*a*b^3+4620*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+9240*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+9240*(a/b*d^2)^(1/4)*2^(1/2)*a^3*b*d^6*x^2*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+11000*(d*x)^(9/2)*a^2*b^2*d^2+1155*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))+2310*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+2310*(a/b*d^2)^(1/4)*2^(1/2)*a^4*d^6*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))+14040*(d*x)^(5/2)*a^3*b*d^4+7144*(d*x)^(1/2)*a^4*d^6)/d^7*(b*x^2+a)/a^5/((b*x^2+a)^2)^(5/2)","B"
782,1,1081,391,0.030000," ","int(1/(d*x)^(3/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(19890 \sqrt{d x}\, \sqrt{2}\, b^{4} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+19890 \sqrt{d x}\, \sqrt{2}\, b^{4} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+9945 \sqrt{d x}\, \sqrt{2}\, b^{4} x^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+79560 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{4} x^{8}+79560 \sqrt{d x}\, \sqrt{2}\, a \,b^{3} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+79560 \sqrt{d x}\, \sqrt{2}\, a \,b^{3} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+39780 \sqrt{d x}\, \sqrt{2}\, a \,b^{3} x^{6} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+302328 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{3} x^{6}+119340 \sqrt{d x}\, \sqrt{2}\, a^{2} b^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+119340 \sqrt{d x}\, \sqrt{2}\, a^{2} b^{2} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+59670 \sqrt{d x}\, \sqrt{2}\, a^{2} b^{2} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+422552 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{2} x^{4}+79560 \sqrt{d x}\, \sqrt{2}\, a^{3} b \,x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+79560 \sqrt{d x}\, \sqrt{2}\, a^{3} b \,x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+39780 \sqrt{d x}\, \sqrt{2}\, a^{3} b \,x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+252008 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b \,x^{2}+19890 \sqrt{d x}\, \sqrt{2}\, a^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+19890 \sqrt{d x}\, \sqrt{2}\, a^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+9945 \sqrt{d x}\, \sqrt{2}\, a^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+49152 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4}\right) \left(b \,x^{2}+a \right)}{24576 \sqrt{d x}\, \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{5} d}"," ",0,"-1/24576/d*(9945*(d*x)^(1/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^8*b^4+19890*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^4+19890*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^4+39780*(d*x)^(1/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^6*a*b^3+79560*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^3+79560*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^3+79560*(a/b*d^2)^(1/4)*x^8*b^4+59670*(d*x)^(1/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a^2*b^2+119340*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^2+119340*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^2+302328*(a/b*d^2)^(1/4)*x^6*a*b^3+39780*(d*x)^(1/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^3*b+79560*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b+79560*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b+422552*(a/b*d^2)^(1/4)*x^4*a^2*b^2+9945*(d*x)^(1/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^4+19890*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4+19890*(d*x)^(1/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4+252008*(a/b*d^2)^(1/4)*x^2*a^3*b+49152*(a/b*d^2)^(1/4)*a^4)*(b*x^2+a)/(d*x)^(1/2)/(a/b*d^2)^(1/4)/a^5/((b*x^2+a)^2)^(5/2)","B"
783,1,1183,391,0.029000," ","int(1/(d*x)^(5/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","-\frac{\left(58520 a \,b^{4} d^{2} x^{8}+43890 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{5} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+43890 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{5} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+21945 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{5} x^{8} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+209000 a^{2} b^{3} d^{2} x^{6}+175560 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{4} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+175560 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{4} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+87780 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,b^{4} x^{6} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+266760 a^{3} b^{2} d^{2} x^{4}+263340 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{3} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+263340 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{3} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+131670 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} b^{3} x^{4} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+135736 a^{4} b \,d^{2} x^{2}+175560 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+175560 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+87780 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} b^{2} x^{2} \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+16384 a^{5} d^{2}+43890 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+43890 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+21945 \left(d x \right)^{\frac{3}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{4} b \ln \left(\frac{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}{d x -\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)\right) \left(b \,x^{2}+a \right)}{24576 \left(d x \right)^{\frac{3}{2}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{6} d^{3}}"," ",0,"-1/24576/d^3*(21945*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^8*b^5+43890*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^5+43890*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^5+87780*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^6*a*b^4+175560*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^4+175560*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^4+131670*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a^2*b^3+263340*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^3+263340*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^3+58520*x^8*a*b^4*d^2+87780*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^3*b^2+175560*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b^2+175560*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b^2+209000*x^6*a^2*b^3*d^2+21945*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*ln((d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2))/(d*x-(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^4*b+43890*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4*b+43890*(d*x)^(3/2)*(a/b*d^2)^(1/4)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4*b+266760*x^4*a^3*b^2*d^2+135736*x^2*a^4*b*d^2+16384*a^5*d^2)*(b*x^2+a)/(d*x)^(3/2)/a^6/((b*x^2+a)^2)^(5/2)","B"
784,1,1129,423,0.032000," ","int(1/(d*x)^(7/2)/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(556920 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} b^{5} d^{2} x^{10}+2116296 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a \,b^{4} d^{2} x^{8}+139230 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, b^{5} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+139230 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, b^{5} x^{8} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+69615 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, b^{5} x^{8} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+2957864 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{2} b^{3} d^{2} x^{6}+556920 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a \,b^{4} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+556920 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a \,b^{4} x^{6} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+278460 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a \,b^{4} x^{6} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+1764056 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{3} b^{2} d^{2} x^{4}+835380 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{2} b^{3} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+835380 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{2} b^{3} x^{4} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+417690 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{2} b^{3} x^{4} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)+344064 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{4} b \,d^{2} x^{2}+556920 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{3} b^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+556920 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{3} b^{2} x^{2} \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+278460 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{3} b^{2} x^{2} \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)-16384 \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} a^{5} d^{2}+139230 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{4} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}-\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+139230 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{4} b \arctan \left(\frac{\sqrt{2}\, \sqrt{d x}+\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}{\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}}}\right)+69615 \left(d x \right)^{\frac{5}{2}} \sqrt{2}\, a^{4} b \ln \left(-\frac{-d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}-\sqrt{\frac{a \,d^{2}}{b}}}{d x +\left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \sqrt{d x}\, \sqrt{2}+\sqrt{\frac{a \,d^{2}}{b}}}\right)\right) \left(b \,x^{2}+a \right)}{40960 \left(d x \right)^{\frac{5}{2}} \left(\frac{a \,d^{2}}{b}\right)^{\frac{1}{4}} \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} a^{6} d^{3}}"," ",0,"1/40960/d^3*(69615*(d*x)^(5/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^8*b^5+139230*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^5+139230*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^8*b^5+278460*(d*x)^(5/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^6*a*b^4+556920*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^4+556920*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^6*a*b^4+556920*(a/b*d^2)^(1/4)*x^10*b^5*d^2+417690*(d*x)^(5/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^4*a^2*b^3+835380*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^3+835380*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^4*a^2*b^3+2116296*(a/b*d^2)^(1/4)*x^8*a*b^4*d^2+278460*(d*x)^(5/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*x^2*a^3*b^2+556920*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b^2+556920*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*x^2*a^3*b^2+2957864*(a/b*d^2)^(1/4)*x^6*a^2*b^3*d^2+69615*(d*x)^(5/2)*2^(1/2)*ln(-(-d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)-(a/b*d^2)^(1/2))/(d*x+(a/b*d^2)^(1/4)*(d*x)^(1/2)*2^(1/2)+(a/b*d^2)^(1/2)))*a^4*b+139230*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)+(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4*b+139230*(d*x)^(5/2)*2^(1/2)*arctan((2^(1/2)*(d*x)^(1/2)-(a/b*d^2)^(1/4))/(a/b*d^2)^(1/4))*a^4*b+1764056*(a/b*d^2)^(1/4)*x^4*a^3*b^2*d^2+344064*(a/b*d^2)^(1/4)*x^2*a^4*b*d^2-16384*(a/b*d^2)^(1/4)*a^5*d^2)*(b*x^2+a)/(d*x)^(5/2)/(a/b*d^2)^(1/4)/a^6/((b*x^2+a)^2)^(5/2)","B"
785,1,602,150,0.011000," ","int((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\frac{\left(b^{6} m^{6} x^{12}+36 b^{6} m^{5} x^{12}+6 a \,b^{5} m^{6} x^{10}+505 b^{6} m^{4} x^{12}+228 a \,b^{5} m^{5} x^{10}+3480 b^{6} m^{3} x^{12}+15 a^{2} b^{4} m^{6} x^{8}+3330 a \,b^{5} m^{4} x^{10}+12139 b^{6} m^{2} x^{12}+600 a^{2} b^{4} m^{5} x^{8}+23640 a \,b^{5} m^{3} x^{10}+19524 b^{6} m \,x^{12}+20 a^{3} b^{3} m^{6} x^{6}+9195 a^{2} b^{4} m^{4} x^{8}+84234 a \,b^{5} m^{2} x^{10}+10395 b^{6} x^{12}+840 a^{3} b^{3} m^{5} x^{6}+67920 a^{2} b^{4} m^{3} x^{8}+137412 a \,b^{5} m \,x^{10}+15 a^{4} b^{2} m^{6} x^{4}+13580 a^{3} b^{3} m^{4} x^{6}+249405 a^{2} b^{4} m^{2} x^{8}+73710 a \,b^{5} x^{10}+660 a^{4} b^{2} m^{5} x^{4}+105840 a^{3} b^{3} m^{3} x^{6}+415320 a^{2} b^{4} m \,x^{8}+6 a^{5} b \,m^{6} x^{2}+11295 a^{4} b^{2} m^{4} x^{4}+406700 a^{3} b^{3} m^{2} x^{6}+225225 a^{2} b^{4} x^{8}+276 a^{5} b \,m^{5} x^{2}+94200 a^{4} b^{2} m^{3} x^{4}+699720 a^{3} b^{3} m \,x^{6}+a^{6} m^{6}+5010 a^{5} b \,m^{4} x^{2}+389685 a^{4} b^{2} m^{2} x^{4}+386100 a^{3} b^{3} x^{6}+48 a^{6} m^{5}+45240 a^{5} b \,m^{3} x^{2}+711540 a^{4} b^{2} m \,x^{4}+925 a^{6} m^{4}+208554 a^{5} b \,m^{2} x^{2}+405405 a^{4} b^{2} x^{4}+9120 a^{6} m^{3}+438324 a^{5} b m \,x^{2}+48259 a^{6} m^{2}+270270 a^{5} b \,x^{2}+129072 a^{6} m +135135 a^{6}\right) x \left(d x \right)^{m}}{\left(m +13\right) \left(m +11\right) \left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"(d*x)^m*(b^6*m^6*x^12+36*b^6*m^5*x^12+6*a*b^5*m^6*x^10+505*b^6*m^4*x^12+228*a*b^5*m^5*x^10+3480*b^6*m^3*x^12+15*a^2*b^4*m^6*x^8+3330*a*b^5*m^4*x^10+12139*b^6*m^2*x^12+600*a^2*b^4*m^5*x^8+23640*a*b^5*m^3*x^10+19524*b^6*m*x^12+20*a^3*b^3*m^6*x^6+9195*a^2*b^4*m^4*x^8+84234*a*b^5*m^2*x^10+10395*b^6*x^12+840*a^3*b^3*m^5*x^6+67920*a^2*b^4*m^3*x^8+137412*a*b^5*m*x^10+15*a^4*b^2*m^6*x^4+13580*a^3*b^3*m^4*x^6+249405*a^2*b^4*m^2*x^8+73710*a*b^5*x^10+660*a^4*b^2*m^5*x^4+105840*a^3*b^3*m^3*x^6+415320*a^2*b^4*m*x^8+6*a^5*b*m^6*x^2+11295*a^4*b^2*m^4*x^4+406700*a^3*b^3*m^2*x^6+225225*a^2*b^4*x^8+276*a^5*b*m^5*x^2+94200*a^4*b^2*m^3*x^4+699720*a^3*b^3*m*x^6+a^6*m^6+5010*a^5*b*m^4*x^2+389685*a^4*b^2*m^2*x^4+386100*a^3*b^3*x^6+48*a^6*m^5+45240*a^5*b*m^3*x^2+711540*a^4*b^2*m*x^4+925*a^6*m^4+208554*a^5*b*m^2*x^2+405405*a^4*b^2*x^4+9120*a^6*m^3+438324*a^5*b*m*x^2+48259*a^6*m^2+270270*a^5*b*x^2+129072*a^6*m+135135*a^6)*x/(m+13)/(m+11)/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)","B"
786,1,292,104,0.009000," ","int((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\frac{\left(b^{4} m^{4} x^{8}+16 b^{4} m^{3} x^{8}+4 a \,b^{3} m^{4} x^{6}+86 b^{4} m^{2} x^{8}+72 a \,b^{3} m^{3} x^{6}+176 b^{4} m \,x^{8}+6 a^{2} b^{2} m^{4} x^{4}+416 a \,b^{3} m^{2} x^{6}+105 b^{4} x^{8}+120 a^{2} b^{2} m^{3} x^{4}+888 a \,b^{3} m \,x^{6}+4 a^{3} b \,m^{4} x^{2}+780 a^{2} b^{2} m^{2} x^{4}+540 a \,b^{3} x^{6}+88 a^{3} b \,m^{3} x^{2}+1800 a^{2} b^{2} m \,x^{4}+a^{4} m^{4}+656 a^{3} b \,m^{2} x^{2}+1134 a^{2} b^{2} x^{4}+24 a^{4} m^{3}+1832 a^{3} b m \,x^{2}+206 a^{4} m^{2}+1260 a^{3} b \,x^{2}+744 a^{4} m +945 a^{4}\right) x \left(d x \right)^{m}}{\left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"(d*x)^m*(b^4*m^4*x^8+16*b^4*m^3*x^8+4*a*b^3*m^4*x^6+86*b^4*m^2*x^8+72*a*b^3*m^3*x^6+176*b^4*m*x^8+6*a^2*b^2*m^4*x^4+416*a*b^3*m^2*x^6+105*b^4*x^8+120*a^2*b^2*m^3*x^4+888*a*b^3*m*x^6+4*a^3*b*m^4*x^2+780*a^2*b^2*m^2*x^4+540*a*b^3*x^6+88*a^3*b*m^3*x^2+1800*a^2*b^2*m*x^4+a^4*m^4+656*a^3*b*m^2*x^2+1134*a^2*b^2*x^4+24*a^4*m^3+1832*a^3*b*m*x^2+206*a^4*m^2+1260*a^3*b*x^2+744*a^4*m+945*a^4)*x/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)","B"
787,1,94,58,0.006000," ","int((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2),x)","\frac{\left(b^{2} m^{2} x^{4}+4 b^{2} m \,x^{4}+2 a b \,m^{2} x^{2}+3 b^{2} x^{4}+12 a b m \,x^{2}+a^{2} m^{2}+10 a b \,x^{2}+8 a^{2} m +15 a^{2}\right) x \left(d x \right)^{m}}{\left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"(d*x)^m*(b^2*m^2*x^4+4*b^2*m*x^4+2*a*b*m^2*x^2+3*b^2*x^4+12*a*b*m*x^2+a^2*m^2+10*a*b*x^2+8*a^2*m+15*a^2)*x/(m+5)/(m+3)/(m+1)","A"
788,0,0,42,0.052000," ","int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2),x)","\int \frac{\left(d x \right)^{m}}{b^{2} x^{4}+2 a b \,x^{2}+a^{2}}\, dx"," ",0,"int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2),x)","F"
789,0,0,42,0.032000," ","int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","\int \frac{\left(d x \right)^{m}}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{2}}\, dx"," ",0,"int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^2,x)","F"
790,0,0,42,0.041000," ","int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","\int \frac{\left(d x \right)^{m}}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{3}}\, dx"," ",0,"int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^3,x)","F"
791,1,453,247,0.006000," ","int((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\frac{\left(b^{5} m^{5} x^{10}+25 b^{5} m^{4} x^{10}+5 a \,b^{4} m^{5} x^{8}+230 b^{5} m^{3} x^{10}+135 a \,b^{4} m^{4} x^{8}+950 b^{5} m^{2} x^{10}+10 a^{2} b^{3} m^{5} x^{6}+1310 a \,b^{4} m^{3} x^{8}+1689 b^{5} m \,x^{10}+290 a^{2} b^{3} m^{4} x^{6}+5610 a \,b^{4} m^{2} x^{8}+945 b^{5} x^{10}+10 a^{3} b^{2} m^{5} x^{4}+3020 a^{2} b^{3} m^{3} x^{6}+10205 a \,b^{4} m \,x^{8}+310 a^{3} b^{2} m^{4} x^{4}+13660 a^{2} b^{3} m^{2} x^{6}+5775 a \,b^{4} x^{8}+5 a^{4} b \,m^{5} x^{2}+3500 a^{3} b^{2} m^{3} x^{4}+25770 a^{2} b^{3} m \,x^{6}+165 a^{4} b \,m^{4} x^{2}+17300 a^{3} b^{2} m^{2} x^{4}+14850 a^{2} b^{3} x^{6}+a^{5} m^{5}+2030 a^{4} b \,m^{3} x^{2}+34890 a^{3} b^{2} m \,x^{4}+35 a^{5} m^{4}+11310 a^{4} b \,m^{2} x^{2}+20790 a^{3} b^{2} x^{4}+470 a^{5} m^{3}+26765 a^{4} b m \,x^{2}+3010 a^{5} m^{2}+17325 a^{4} b \,x^{2}+9129 a^{5} m +10395 a^{5}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{5}{2}} x \left(d x \right)^{m}}{\left(m +11\right) \left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right) \left(b \,x^{2}+a \right)^{5}}"," ",0,"x*(b^5*m^5*x^10+25*b^5*m^4*x^10+5*a*b^4*m^5*x^8+230*b^5*m^3*x^10+135*a*b^4*m^4*x^8+950*b^5*m^2*x^10+10*a^2*b^3*m^5*x^6+1310*a*b^4*m^3*x^8+1689*b^5*m*x^10+290*a^2*b^3*m^4*x^6+5610*a*b^4*m^2*x^8+945*b^5*x^10+10*a^3*b^2*m^5*x^4+3020*a^2*b^3*m^3*x^6+10205*a*b^4*m*x^8+310*a^3*b^2*m^4*x^4+13660*a^2*b^3*m^2*x^6+5775*a*b^4*x^8+5*a^4*b*m^5*x^2+3500*a^3*b^2*m^3*x^4+25770*a^2*b^3*m*x^6+165*a^4*b*m^4*x^2+17300*a^3*b^2*m^2*x^4+14850*a^2*b^3*x^6+a^5*m^5+2030*a^4*b*m^3*x^2+34890*a^3*b^2*m*x^4+35*a^5*m^4+11310*a^4*b*m^2*x^2+20790*a^3*b^2*x^4+470*a^5*m^3+26765*a^4*b*m*x^2+3010*a^5*m^2+17325*a^4*b*x^2+9129*a^5*m+10395*a^5)*(d*x)^m*((b*x^2+a)^2)^(5/2)/(m+11)/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)/(b*x^2+a)^5","A"
792,1,199,161,0.006000," ","int((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\frac{\left(b^{3} m^{3} x^{6}+9 b^{3} m^{2} x^{6}+3 a \,b^{2} m^{3} x^{4}+23 b^{3} m \,x^{6}+33 a \,b^{2} m^{2} x^{4}+15 b^{3} x^{6}+3 a^{2} b \,m^{3} x^{2}+93 a \,b^{2} m \,x^{4}+39 a^{2} b \,m^{2} x^{2}+63 a \,b^{2} x^{4}+a^{3} m^{3}+141 a^{2} b m \,x^{2}+15 a^{3} m^{2}+105 a^{2} b \,x^{2}+71 a^{3} m +105 a^{3}\right) \left(\left(b \,x^{2}+a \right)^{2}\right)^{\frac{3}{2}} x \left(d x \right)^{m}}{\left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right) \left(b \,x^{2}+a \right)^{3}}"," ",0,"x*(b^3*m^3*x^6+9*b^3*m^2*x^6+3*a*b^2*m^3*x^4+23*b^3*m*x^6+33*a*b^2*m^2*x^4+15*b^3*x^6+3*a^2*b*m^3*x^2+93*a*b^2*m*x^4+39*a^2*b*m^2*x^2+63*a*b^2*x^4+a^3*m^3+141*a^2*b*m*x^2+15*a^3*m^2+105*a^2*b*x^2+71*a^3*m+105*a^3)*(d*x)^m*((b*x^2+a)^2)^(3/2)/(m+7)/(m+5)/(m+3)/(m+1)/(b*x^2+a)^3","A"
793,1,56,75,0.004000," ","int((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x)","\frac{\left(b m \,x^{2}+b \,x^{2}+a m +3 a \right) \sqrt{\left(b \,x^{2}+a \right)^{2}}\, x \left(d x \right)^{m}}{\left(m +3\right) \left(m +1\right) \left(b \,x^{2}+a \right)}"," ",0,"x*(b*m*x^2+b*x^2+a*m+3*a)*(d*x)^m*((b*x^2+a)^2)^(1/2)/(m+3)/(m+1)/(b*x^2+a)","A"
794,0,0,60,0.041000," ","int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x)","\int \frac{\left(d x \right)^{m}}{\sqrt{b^{2} x^{4}+2 a b \,x^{2}+a^{2}}}\, dx"," ",0,"int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(1/2),x)","F"
795,0,0,60,0.024000," ","int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","\int \frac{\left(d x \right)^{m}}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(3/2),x)","F"
796,0,0,60,0.039000," ","int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","\int \frac{\left(d x \right)^{m}}{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*x)^m/(b^2*x^4+2*a*b*x^2+a^2)^(5/2),x)","F"
797,0,0,72,0.135000," ","int((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\int \left(d x \right)^{m} \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((d*x)^m*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","F"
798,1,150,166,0.010000," ","int(x^7*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","-\frac{\left(-4 b^{3} p^{3} x^{6}-12 b^{3} p^{2} x^{6}-11 b^{3} p \,x^{6}+6 a \,b^{2} p^{2} x^{4}-3 b^{3} x^{6}+9 a \,b^{2} p \,x^{4}+3 a \,b^{2} x^{4}-6 a^{2} b p \,x^{2}-3 a^{2} b \,x^{2}+3 a^{3}\right) \left(b \,x^{2}+a \right) \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{4 \left(4 p^{4}+20 p^{3}+35 p^{2}+25 p +6\right) b^{4}}"," ",0,"-1/4*(b^2*x^4+2*a*b*x^2+a^2)^p*(-4*b^3*p^3*x^6-12*b^3*p^2*x^6-11*b^3*p*x^6+6*a*b^2*p^2*x^4-3*b^3*x^6+9*a*b^2*p*x^4+3*a*b^2*x^4-6*a^2*b*p*x^2-3*a^2*b*x^2+3*a^3)*(b*x^2+a)/b^4/(4*p^4+20*p^3+35*p^2+25*p+6)","A"
799,1,96,124,0.008000," ","int(x^5*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\frac{\left(b \,x^{2}+a \right) \left(2 b^{2} p^{2} x^{4}+3 b^{2} p \,x^{4}+b^{2} x^{4}-2 a b p \,x^{2}-a b \,x^{2}+a^{2}\right) \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{2 \left(4 p^{3}+12 p^{2}+11 p +3\right) b^{3}}"," ",0,"1/2*(b*x^2+a)*(2*b^2*p^2*x^4+3*b^2*p*x^4+b^2*x^4-2*a*b*p*x^2-a*b*x^2+a^2)*(b^2*x^4+2*a*b*x^2+a^2)^p/b^3/(4*p^3+12*p^2+11*p+3)","A"
800,1,60,80,0.007000," ","int(x^3*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","-\frac{\left(-2 x^{2} p b -b \,x^{2}+a \right) \left(b \,x^{2}+a \right) \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{4 \left(2 p^{2}+3 p +1\right) b^{2}}"," ",0,"-1/4*(b^2*x^4+2*a*b*x^2+a^2)^p*(-2*b*p*x^2-b*x^2+a)*(b*x^2+a)/b^2/(2*p^2+3*p+1)","A"
801,1,40,39,0.004000," ","int(x*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\frac{\left(b \,x^{2}+a \right) \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{2 \left(2 p +1\right) b}"," ",0,"1/2*(b*x^2+a)*(b^2*x^4+2*a*b*x^2+a^2)^p/b/(1+2*p)","A"
802,0,0,63,0.027000," ","int((b^2*x^4+2*a*b*x^2+a^2)^p/x,x)","\int \frac{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{x}\, dx"," ",0,"int((b^2*x^4+2*a*b*x^2+a^2)^p/x,x)","F"
803,0,0,64,0.045000," ","int((b^2*x^4+2*a*b*x^2+a^2)^p/x^3,x)","\int \frac{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{x^{3}}\, dx"," ",0,"int((b^2*x^4+2*a*b*x^2+a^2)^p/x^3,x)","F"
804,0,0,58,0.067000," ","int(x^4*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\int x^{4} \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int(x^4*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","F"
805,0,0,58,0.044000," ","int(x^2*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\int x^{2} \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int(x^2*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","F"
806,0,0,55,0.015000," ","int((b^2*x^4+2*a*b*x^2+a^2)^p,x)","\int \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((b^2*x^4+2*a*b*x^2+a^2)^p,x)","F"
807,0,0,58,0.041000," ","int((b^2*x^4+2*a*b*x^2+a^2)^p/x^2,x)","\int \frac{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"int((b^2*x^4+2*a*b*x^2+a^2)^p/x^2,x)","F"
808,0,0,58,0.055000," ","int((b^2*x^4+2*a*b*x^2+a^2)^p/x^4,x)","\int \frac{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{x^{4}}\, dx"," ",0,"int((b^2*x^4+2*a*b*x^2+a^2)^p/x^4,x)","F"
809,0,0,63,0.012000," ","int((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\int \left(d x \right)^{\frac{3}{2}} \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((d*x)^(3/2)*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","F"
810,0,0,63,0.012000," ","int((d*x)^(1/2)*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","\int \sqrt{d x}\, \left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}\, dx"," ",0,"int((d*x)^(1/2)*(b^2*x^4+2*a*b*x^2+a^2)^p,x)","F"
811,0,0,63,0.013000," ","int((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(1/2),x)","\int \frac{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{\sqrt{d x}}\, dx"," ",0,"int((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(1/2),x)","F"
812,0,0,63,0.013000," ","int((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(3/2),x)","\int \frac{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{\left(d x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(3/2),x)","F"
813,0,0,63,0.012000," ","int((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(5/2),x)","\int \frac{\left(b^{2} x^{4}+2 a b \,x^{2}+a^{2}\right)^{p}}{\left(d x \right)^{\frac{5}{2}}}\, dx"," ",0,"int((b^2*x^4+2*a*b*x^2+a^2)^p/(d*x)^(5/2),x)","F"
814,1,20,19,0.002000," ","int(x^2*(c*x^4+b*x^2+a),x)","\frac{1}{7} c \,x^{7}+\frac{1}{5} b \,x^{5}+\frac{1}{3} a \,x^{3}"," ",0,"1/3*a*x^3+1/5*b*x^5+1/7*c*x^7","A"
815,1,20,19,0.000000," ","int(x*(c*x^4+b*x^2+a),x)","\frac{1}{6} c \,x^{6}+\frac{1}{4} b \,x^{4}+\frac{1}{2} a \,x^{2}"," ",0,"1/2*a*x^2+1/4*b*x^4+1/6*c*x^6","A"
816,1,17,16,0.001000," ","int(c*x^4+b*x^2+a,x)","\frac{1}{5} c \,x^{5}+\frac{1}{3} b \,x^{3}+a x"," ",0,"a*x+1/3*b*x^3+1/5*c*x^5","A"
817,1,18,17,0.003000," ","int((c*x^4+b*x^2+a)/x,x)","\frac{c \,x^{4}}{4}+\frac{b \,x^{2}}{2}+a \ln \left(x \right)"," ",0,"1/2*b*x^2+1/4*c*x^4+a*ln(x)","A"
818,1,17,16,0.004000," ","int((c*x^4+b*x^2+a)/x^2,x)","\frac{c \,x^{3}}{3}+b x -\frac{a}{x}"," ",0,"-a/x+b*x+1/3*c*x^3","A"
819,1,18,17,0.005000," ","int((c*x^4+b*x^2+a)/x^3,x)","\frac{c \,x^{2}}{2}+b \ln \left(x \right)-\frac{a}{2 x^{2}}"," ",0,"-1/2*a/x^2+1/2*c*x^2+b*ln(x)","A"
820,1,17,16,0.006000," ","int((c*x^4+b*x^2+a)/x^4,x)","c x -\frac{b}{x}-\frac{a}{3 x^{3}}"," ",0,"-1/3*a/x^3-b/x+c*x","A"
821,1,18,17,0.005000," ","int((c*x^4+b*x^2+a)/x^5,x)","c \ln \left(x \right)-\frac{b}{2 x^{2}}-\frac{a}{4 x^{4}}"," ",0,"-1/4*a/x^4-1/2*b/x^2+c*ln(x)","A"
822,1,20,19,0.005000," ","int((c*x^4+b*x^2+a)/x^6,x)","-\frac{c}{x}-\frac{b}{3 x^{3}}-\frac{a}{5 x^{5}}"," ",0,"-1/5*a/x^5-1/3*b/x^3-c/x","A"
823,1,20,19,0.005000," ","int((c*x^4+b*x^2+a)/x^7,x)","-\frac{c}{2 x^{2}}-\frac{b}{4 x^{4}}-\frac{a}{6 x^{6}}"," ",0,"-1/6*a/x^6-1/4*b/x^4-1/2*c/x^2","A"
824,1,20,19,0.005000," ","int((c*x^4+b*x^2+a)/x^8,x)","-\frac{c}{3 x^{3}}-\frac{b}{5 x^{5}}-\frac{a}{7 x^{7}}"," ",0,"-1/7*a/x^7-1/5*b/x^5-1/3*c/x^3","A"
825,1,45,44,0.000000," ","int(x^2*(c*x^4+b*x^2+a)^2,x)","\frac{c^{2} x^{11}}{11}+\frac{2 b c \,x^{9}}{9}+\frac{2 a b \,x^{5}}{5}+\frac{\left(2 a c +b^{2}\right) x^{7}}{7}+\frac{a^{2} x^{3}}{3}"," ",0,"1/3*a^2*x^3+2/5*a*b*x^5+1/7*(2*a*c+b^2)*x^7+2/9*b*c*x^9+1/11*c^2*x^11","A"
826,1,45,44,0.001000," ","int(x*(c*x^4+b*x^2+a)^2,x)","\frac{c^{2} x^{10}}{10}+\frac{b c \,x^{8}}{4}+\frac{a b \,x^{4}}{2}+\frac{\left(2 a c +b^{2}\right) x^{6}}{6}+\frac{a^{2} x^{2}}{2}"," ",0,"1/2*a^2*x^2+1/2*a*b*x^4+1/6*(2*a*c+b^2)*x^6+1/4*b*c*x^8+1/10*c^2*x^10","A"
827,1,42,41,0.001000," ","int((c*x^4+b*x^2+a)^2,x)","\frac{c^{2} x^{9}}{9}+\frac{2 b c \,x^{7}}{7}+\frac{2 a b \,x^{3}}{3}+\frac{\left(2 a c +b^{2}\right) x^{5}}{5}+a^{2} x"," ",0,"a^2*x+2/3*a*b*x^3+1/5*(2*a*c+b^2)*x^5+2/7*b*c*x^7+1/9*c^2*x^9","A"
828,1,44,41,0.001000," ","int((c*x^4+b*x^2+a)^2/x,x)","\frac{c^{2} x^{8}}{8}+\frac{b c \,x^{6}}{3}+\frac{a c \,x^{4}}{2}+\frac{b^{2} x^{4}}{4}+a b \,x^{2}+a^{2} \ln \left(x \right)"," ",0,"1/8*c^2*x^8+1/3*b*c*x^6+1/2*x^4*a*c+1/4*b^2*x^4+a*b*x^2+a^2*ln(x)","A"
829,1,45,42,0.004000," ","int((c*x^4+b*x^2+a)^2/x^2,x)","\frac{c^{2} x^{7}}{7}+\frac{2 b c \,x^{5}}{5}+\frac{2 a c \,x^{3}}{3}+\frac{b^{2} x^{3}}{3}+2 a b x -\frac{a^{2}}{x}"," ",0,"1/7*c^2*x^7+2/5*b*c*x^5+2/3*x^3*a*c+1/3*b^2*x^3+2*a*b*x-a^2/x","A"
830,1,45,43,0.006000," ","int((c*x^4+b*x^2+a)^2/x^3,x)","\frac{c^{2} x^{6}}{6}+\frac{b c \,x^{4}}{2}+a c \,x^{2}+\frac{b^{2} x^{2}}{2}+2 a b \ln \left(x \right)-\frac{a^{2}}{2 x^{2}}"," ",0,"1/6*c^2*x^6+1/2*b*c*x^4+x^2*a*c+1/2*b^2*x^2-1/2*a^2/x^2+2*a*b*ln(x)","A"
831,1,42,41,0.006000," ","int((c*x^4+b*x^2+a)^2/x^4,x)","\frac{c^{2} x^{5}}{5}+\frac{2 b c \,x^{3}}{3}+2 a c x +b^{2} x -\frac{2 a b}{x}-\frac{a^{2}}{3 x^{3}}"," ",0,"1/5*c^2*x^5+2/3*b*c*x^3+2*a*c*x+b^2*x-2*a*b/x-1/3*a^2/x^3","A"
832,1,43,41,0.008000," ","int((c*x^4+b*x^2+a)^2/x^5,x)","\frac{c^{2} x^{4}}{4}+b c \,x^{2}+2 a c \ln \left(x \right)+b^{2} \ln \left(x \right)-\frac{a b}{x^{2}}-\frac{a^{2}}{4 x^{4}}"," ",0,"1/4*c^2*x^4+b*c*x^2-a*b/x^2-1/4*a^2/x^4+2*ln(x)*a*c+b^2*ln(x)","A"
833,1,43,43,0.006000," ","int((c*x^4+b*x^2+a)^2/x^6,x)","\frac{c^{2} x^{3}}{3}+2 b c x -\frac{2 a b}{3 x^{3}}-\frac{2 a c +b^{2}}{x}-\frac{a^{2}}{5 x^{5}}"," ",0,"1/3*c^2*x^3+2*b*c*x-1/5*a^2/x^5-(2*a*c+b^2)/x-2/3*a*b/x^3","A"
834,1,46,45,0.008000," ","int((c*x^4+b*x^2+a)^2/x^7,x)","\frac{c^{2} x^{2}}{2}+2 b c \ln \left(x \right)-\frac{a c}{x^{2}}-\frac{b^{2}}{2 x^{2}}-\frac{a b}{2 x^{4}}-\frac{a^{2}}{6 x^{6}}"," ",0,"1/2*c^2*x^2-1/x^2*a*c-1/2*b^2/x^2-1/6*a^2/x^6-1/2*a*b/x^4+2*b*c*ln(x)","A"
835,1,42,43,0.006000," ","int((c*x^4+b*x^2+a)^2/x^8,x)","c^{2} x -\frac{2 b c}{x}-\frac{2 a b}{5 x^{5}}-\frac{2 a c +b^{2}}{3 x^{3}}-\frac{a^{2}}{7 x^{7}}"," ",0,"c^2*x-1/7*a^2/x^7-2/5*a*b/x^5-2*b*c/x-1/3*(2*a*c+b^2)/x^3","A"
836,1,45,44,0.006000," ","int((c*x^4+b*x^2+a)^2/x^9,x)","c^{2} \ln \left(x \right)-\frac{b c}{x^{2}}-\frac{a c}{2 x^{4}}-\frac{b^{2}}{4 x^{4}}-\frac{a b}{3 x^{6}}-\frac{a^{2}}{8 x^{8}}"," ",0,"-b*c/x^2-1/8*a^2/x^8-1/3*a*b/x^6-1/2/x^4*a*c-1/4*b^2/x^4+c^2*ln(x)","A"
837,1,45,46,0.005000," ","int((c*x^4+b*x^2+a)^2/x^10,x)","-\frac{c^{2}}{x}-\frac{2 b c}{3 x^{3}}-\frac{2 a b}{7 x^{7}}-\frac{2 a c +b^{2}}{5 x^{5}}-\frac{a^{2}}{9 x^{9}}"," ",0,"-2/7*a*b/x^7-1/9*a^2/x^9-1/5*(2*a*c+b^2)/x^5-c^2/x-2/3*b*c/x^3","A"
838,1,45,46,0.005000," ","int((c*x^4+b*x^2+a)^2/x^11,x)","-\frac{c^{2}}{2 x^{2}}-\frac{b c}{2 x^{4}}-\frac{a b}{4 x^{8}}-\frac{2 a c +b^{2}}{6 x^{6}}-\frac{a^{2}}{10 x^{10}}"," ",0,"-1/2*c^2/x^2-1/6*(2*a*c+b^2)/x^6-1/10*a^2/x^10-1/2*b*c/x^4-1/4*a*b/x^8","A"
839,1,45,46,0.006000," ","int((c*x^4+b*x^2+a)^2/x^12,x)","-\frac{c^{2}}{3 x^{3}}-\frac{2 b c}{5 x^{5}}-\frac{2 a b}{9 x^{9}}-\frac{2 a c +b^{2}}{7 x^{7}}-\frac{a^{2}}{11 x^{11}}"," ",0,"-1/7*(2*a*c+b^2)/x^7-1/11*a^2/x^11-2/5*b*c/x^5-1/3*c^2/x^3-2/9*a*b/x^9","A"
840,1,45,46,0.005000," ","int((c*x^4+b*x^2+a)^2/x^13,x)","-\frac{c^{2}}{4 x^{4}}-\frac{b c}{3 x^{6}}-\frac{a b}{5 x^{10}}-\frac{2 a c +b^{2}}{8 x^{8}}-\frac{a^{2}}{12 x^{12}}"," ",0,"-1/3*b*c/x^6-1/12*a^2/x^12-1/5*a*b/x^10-1/8*(2*a*c+b^2)/x^8-1/4*c^2/x^4","A"
841,1,111,75,0.000000," ","int(x^2*(c*x^4+b*x^2+a)^3,x)","\frac{c^{3} x^{15}}{15}+\frac{3 b \,c^{2} x^{13}}{13}+\frac{\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) x^{11}}{11}+\frac{\left(4 a b c +\left(2 a c +b^{2}\right) b \right) x^{9}}{9}+\frac{3 a^{2} b \,x^{5}}{5}+\frac{\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) x^{7}}{7}+\frac{a^{3} x^{3}}{3}"," ",0,"1/15*c^3*x^15+3/13*b*c^2*x^13+1/11*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)*x^11+1/9*(4*a*b*c+(2*a*c+b^2)*b)*x^9+1/7*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*x^7+3/5*a^2*b*x^5+1/3*a^3*x^3","A"
842,1,111,75,0.002000," ","int(x*(c*x^4+b*x^2+a)^3,x)","\frac{c^{3} x^{14}}{14}+\frac{b \,c^{2} x^{12}}{4}+\frac{\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) x^{10}}{10}+\frac{\left(4 a b c +\left(2 a c +b^{2}\right) b \right) x^{8}}{8}+\frac{3 a^{2} b \,x^{4}}{4}+\frac{\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) x^{6}}{6}+\frac{a^{3} x^{2}}{2}"," ",0,"1/14*c^3*x^14+1/4*b*c^2*x^12+1/10*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)*x^10+1/8*(4*a*b*c+(2*a*c+b^2)*b)*x^8+1/6*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*x^6+3/4*a^2*b*x^4+1/2*a^3*x^2","A"
843,1,107,71,0.001000," ","int((c*x^4+b*x^2+a)^3,x)","\frac{c^{3} x^{13}}{13}+\frac{3 b \,c^{2} x^{11}}{11}+\frac{\left(a \,c^{2}+2 b^{2} c +\left(2 a c +b^{2}\right) c \right) x^{9}}{9}+\frac{\left(4 a b c +\left(2 a c +b^{2}\right) b \right) x^{7}}{7}+a^{2} b \,x^{3}+\frac{\left(a^{2} c +2 a \,b^{2}+\left(2 a c +b^{2}\right) a \right) x^{5}}{5}+a^{3} x"," ",0,"1/13*c^3*x^13+3/11*b*c^2*x^11+1/9*(a*c^2+2*b^2*c+(2*a*c+b^2)*c)*x^9+1/7*(4*a*b*c+(2*a*c+b^2)*b)*x^7+1/5*(a^2*c+2*a*b^2+(2*a*c+b^2)*a)*x^5+a^2*b*x^3+a^3*x","A"
844,1,85,73,0.002000," ","int((c*x^4+b*x^2+a)^3/x,x)","\frac{c^{3} x^{12}}{12}+\frac{3 b \,c^{2} x^{10}}{10}+\frac{3 a \,c^{2} x^{8}}{8}+\frac{3 b^{2} c \,x^{8}}{8}+a b c \,x^{6}+\frac{b^{3} x^{6}}{6}+\frac{3 a^{2} c \,x^{4}}{4}+\frac{3 a \,b^{2} x^{4}}{4}+\frac{3 a^{2} b \,x^{2}}{2}+a^{3} \ln \left(x \right)"," ",0,"1/12*c^3*x^12+3/10*b*c^2*x^10+3/8*x^8*a*c^2+3/8*x^8*b^2*c+x^6*a*b*c+1/6*b^3*x^6+3/4*x^4*a^2*c+3/4*a*b^2*x^4+3/2*a^2*b*x^2+a^3*ln(x)","A"
845,1,84,72,0.004000," ","int((c*x^4+b*x^2+a)^3/x^2,x)","\frac{c^{3} x^{11}}{11}+\frac{b \,c^{2} x^{9}}{3}+\frac{3 a \,c^{2} x^{7}}{7}+\frac{3 b^{2} c \,x^{7}}{7}+\frac{6 a b c \,x^{5}}{5}+\frac{b^{3} x^{5}}{5}+a^{2} c \,x^{3}+a \,b^{2} x^{3}+3 a^{2} b x -\frac{a^{3}}{x}"," ",0,"1/11*c^3*x^11+1/3*b*c^2*x^9+3/7*x^7*a*c^2+3/7*b^2*c*x^7+6/5*x^5*a*b*c+1/5*b^3*x^5+x^3*a^2*c+a*b^2*x^3+3*a^2*b*x-a^3/x","A"
846,1,87,74,0.007000," ","int((c*x^4+b*x^2+a)^3/x^3,x)","\frac{c^{3} x^{10}}{10}+\frac{3 b \,c^{2} x^{8}}{8}+\frac{a \,c^{2} x^{6}}{2}+\frac{b^{2} c \,x^{6}}{2}+\frac{3 a b c \,x^{4}}{2}+\frac{b^{3} x^{4}}{4}+\frac{3 a^{2} c \,x^{2}}{2}+\frac{3 a \,b^{2} x^{2}}{2}+3 a^{2} b \ln \left(x \right)-\frac{a^{3}}{2 x^{2}}"," ",0,"1/10*c^3*x^10+3/8*b*c^2*x^8+1/2*x^6*a*c^2+1/2*x^6*b^2*c+3/2*x^4*a*b*c+1/4*b^3*x^4+3/2*x^2*a^2*c+3/2*a*b^2*x^2-1/2*a^3/x^2+3*a^2*b*ln(x)","A"
847,1,84,73,0.006000," ","int((c*x^4+b*x^2+a)^3/x^4,x)","\frac{c^{3} x^{9}}{9}+\frac{3 b \,c^{2} x^{7}}{7}+\frac{3 a \,c^{2} x^{5}}{5}+\frac{3 b^{2} c \,x^{5}}{5}+2 a b c \,x^{3}+\frac{b^{3} x^{3}}{3}+3 a^{2} c x +3 a \,b^{2} x -\frac{3 a^{2} b}{x}-\frac{a^{3}}{3 x^{3}}"," ",0,"1/9*c^3*x^9+3/7*b*c^2*x^7+3/5*x^5*a*c^2+3/5*b^2*c*x^5+2*x^3*a*b*c+1/3*b^3*x^3+3*a^2*c*x+3*a*b^2*x-3*a^2*b/x-1/3*a^3/x^3","A"
848,1,142,88,0.008000," ","int(x^7/(c*x^4+b*x^2+a),x)","\frac{x^{4}}{4 c}+\frac{3 a b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{3}}-\frac{b \,x^{2}}{2 c^{2}}-\frac{a \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}+\frac{b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{3}}"," ",0,"1/4/c*x^4-1/2*b/c^2*x^2-1/4/c^2*ln(c*x^4+b*x^2+a)*a+1/4/c^3*ln(c*x^4+b*x^2+a)*b^2+3/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b-1/2/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3","A"
849,1,111,71,0.004000," ","int(x^5/(c*x^4+b*x^2+a),x)","-\frac{a \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}+\frac{x^{2}}{2 c}-\frac{b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c^{2}}"," ",0,"1/2/c*x^2-1/4*b*ln(c*x^4+b*x^2+a)/c^2-1/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a+1/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2","A"
850,1,60,55,0.002000," ","int(x^3/(c*x^4+b*x^2+a),x)","-\frac{b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c}+\frac{\ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 c}"," ",0,"1/4*ln(c*x^4+b*x^2+a)/c-1/2*b/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
851,1,36,32,0.002000," ","int(x/(c*x^4+b*x^2+a),x)","\frac{\arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}"," ",0,"1/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
852,1,66,61,0.006000," ","int(1/x/(c*x^4+b*x^2+a),x)","-\frac{b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a}+\frac{\ln \left(x \right)}{a}-\frac{\ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a}"," ",0,"-1/4*ln(c*x^4+b*x^2+a)/a-1/2/a*b/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))+ln(x)/a","A"
853,1,119,79,0.009000," ","int(1/x^3/(c*x^4+b*x^2+a),x)","-\frac{c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}-\frac{1}{2 a \,x^{2}}"," ",0,"1/4*b*ln(c*x^4+b*x^2+a)/a^2-1/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c+1/2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2-1/2/a/x^2-b*ln(x)/a^2","A"
854,1,159,102,0.011000," ","int(1/x^5/(c*x^4+b*x^2+a),x)","\frac{3 b c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{3}}-\frac{c \ln \left(x \right)}{a^{2}}+\frac{c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{2}}+\frac{b^{2} \ln \left(x \right)}{a^{3}}-\frac{b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 a^{3}}+\frac{b}{2 a^{2} x^{2}}-\frac{1}{4 a \,x^{4}}"," ",0,"1/4/a^2*c*ln(c*x^4+b*x^2+a)-1/4/a^3*ln(c*x^4+b*x^2+a)*b^2+3/2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c-1/2/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3-1/4/a/x^4-1/a^2*ln(x)*c+1/a^3*ln(x)*b^2+1/2*b/a^2/x^2","A"
855,1,467,167,0.046000," ","int(x^6/(c*x^4+b*x^2+a),x)","-\frac{3 \sqrt{2}\, a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{x^{3}}{3 c}+\frac{\sqrt{2}\, a \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{b x}{c^{2}}"," ",0,"1/3/c*x^3-b/c^2*x+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(x*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a-1/2/c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(x*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(x*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a*b+1/2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(x*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^3-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(x*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a+1/2/c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(x*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2-3/2/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(x*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a*b+1/2/c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(x*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^3","B"
856,1,343,144,0.026000," ","int(x^4/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, a \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{x}{c}"," ",0,"1/c*x+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/2/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/2/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2","B"
857,1,208,115,0.018000," ","int(x^2/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}"," ",0,"-1/2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b","A"
858,1,116,114,0.016000," ","int(1/(c*x^4+b*x^2+a),x)","-\frac{\sqrt{2}\, c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}"," ",0,"-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","A"
859,1,232,138,0.022000," ","int(1/x^2/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{1}{a x}"," ",0,"1/2*c/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/2*c/a/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-1/2*c/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/2*c/a/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-1/a/x","A"
860,1,368,161,0.023000," ","int(1/x^4/(c*x^4+b*x^2+a),x)","\frac{\sqrt{2}\, c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{\sqrt{2}\, b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{b}{a^{2} x}-\frac{1}{3 a \,x^{3}}"," ",0,"-1/2/a^2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+1/2/a^2*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/a*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/a^2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-1/3/a/x^3+b/a^2/x","B"
861,1,222,120,0.016000," ","int(x^7/(c*x^4+b*x^2+a)^2,x)","-\frac{3 a b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{b^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{a \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) c}-\frac{b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) c^{2}}+\frac{\frac{\left(3 a c -b^{2}\right) b \,x^{2}}{\left(4 a c -b^{2}\right) c^{2}}+\frac{\left(2 a c -b^{2}\right) a}{\left(4 a c -b^{2}\right) c^{2}}}{2 c \,x^{4}+2 b \,x^{2}+2 a}"," ",0,"1/2*(b*(3*a*c-b^2)/c^2/(4*a*c-b^2)*x^2+a*(2*a*c-b^2)/(4*a*c-b^2)/c^2)/(c*x^4+b*x^2+a)+1/c/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*a-1/4/c^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2-3/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b+1/2/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3","A"
862,1,104,72,0.010000," ","int(x^5/(c*x^4+b*x^2+a)^2,x)","\frac{2 a \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{\frac{a b}{\left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) x^{2}}{\left(4 a c -b^{2}\right) c}}{2 c \,x^{4}+2 b \,x^{2}+2 a}"," ",0,"1/2*(-(2*a*c-b^2)/c/(4*a*c-b^2)*x^2+a*b/c/(4*a*c-b^2))/(c*x^4+b*x^2+a)+2*a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
863,1,77,69,0.006000," ","int(x^3/(c*x^4+b*x^2+a)^2,x)","-\frac{b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{-b \,x^{2}-2 a}{2 \left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{2}+a \right)}"," ",0,"1/2*(-b*x^2-2*a)/(4*a*c-b^2)/(c*x^4+b*x^2+a)-b/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
864,1,75,70,0.006000," ","int(x/(c*x^4+b*x^2+a)^2,x)","\frac{2 c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c \,x^{2}+b}{2 \left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{2}+a \right)}"," ",0,"1/2*(2*c*x^2+b)/(4*a*c-b^2)/(c*x^4+b*x^2+a)+2*c/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
865,1,253,112,0.018000," ","int(1/x/(c*x^4+b*x^2+a)^2,x)","-\frac{b c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{3 b c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{b^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a}+\frac{b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(4 a c -b^{2}\right) a^{2}}+\frac{c}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{\ln \left(x \right)}{a^{2}}"," ",0,"-1/2/a/(c*x^4+b*x^2+a)*b*c/(4*a*c-b^2)*x^2+1/(c*x^4+b*x^2+a)/(4*a*c-b^2)*c-1/2/a/(c*x^4+b*x^2+a)/(4*a*c-b^2)*b^2-1/a/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)+1/4/a^2/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^2-3/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c+1/2/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3+1/a^2*ln(x)","B"
866,1,352,155,0.020000," ","int(1/x^3/(c*x^4+b*x^2+a)^2,x)","-\frac{c^{2} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c \,x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{6 c^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{6 b^{2} c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{4} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}-\frac{3 b c}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{2 b c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{2 \left(4 a c -b^{2}\right) a^{3}}-\frac{2 b \ln \left(x \right)}{a^{3}}-\frac{1}{2 a^{2} x^{2}}"," ",0,"-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^2+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^2*b^2-3/2/a/(c*x^4+b*x^2+a)*b/(4*a*c-b^2)*c+1/2/a^2/(c*x^4+b*x^2+a)*b^3/(4*a*c-b^2)+2/a^2/(4*a*c-b^2)*c*ln(c*x^4+b*x^2+a)*b-1/2/a^3/(4*a*c-b^2)*ln(c*x^4+b*x^2+a)*b^3-6/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c^2+6/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*c-1/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4-1/2/a^2/x^2-2/a^3*b*ln(x)","B"
867,1,844,284,0.038000," ","int(x^8/(c*x^4+b*x^2+a)^2,x)","\frac{3 a b \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{b^{3} x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{5 \sqrt{2}\, a^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{5 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{19 \sqrt{2}\, a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{19 \sqrt{2}\, a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{3 \sqrt{2}\, b^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{a^{2} x}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c}-\frac{a \,b^{2} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{13 \sqrt{2}\, a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{13 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{x}{c^{2}}"," ",0,"1/c^2*x+3/2/c/(c*x^4+b*x^2+a)*b/(4*a*c-b^2)*x^3*a-1/2/c^2/(c*x^4+b*x^2+a)*b^3/(4*a*c-b^2)*x^3+1/c/(c*x^4+b*x^2+a)*a^2/(4*a*c-b^2)*x-1/2/c^2/(c*x^4+b*x^2+a)*a/(4*a*c-b^2)*x*b^2+13/4/c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b-3/4/c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4-13/4/c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b+3/4/c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3+5/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2-19/4/c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2+3/4/c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4","B"
868,1,602,227,0.033000," ","int(x^6/(c*x^4+b*x^2+a)^2,x)","\frac{2 \sqrt{2}\, a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{2 \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, a \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\frac{a b x}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) x^{3}}{2 \left(4 a c -b^{2}\right) c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2*(2*a*c-b^2)/c/(4*a*c-b^2)*x^3+1/2/(4*a*c-b^2)*a*b/c*x)/(c*x^4+b*x^2+a)-3/2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a+1/4/(4*a*c-b^2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3+3/2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/4/(4*a*c-b^2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b-1/4/(4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3","B"
869,1,452,194,0.027000," ","int(x^4/(c*x^4+b*x^2+a)^2,x)","-\frac{\sqrt{2}\, a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{-\frac{b \,x^{3}}{2 \left(4 a c -b^{2}\right)}-\frac{a x}{4 a c -b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"(-1/2*b/(4*a*c-b^2)*x^3-a/(4*a*c-b^2)*x)/(c*x^4+b*x^2+a)+1/4/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-1/4/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-1/(4*a*c-b^2)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/4/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2","B"
870,1,342,180,0.083000," ","int(x^2/(c*x^4+b*x^2+a)^2,x)","\frac{\sqrt{2}\, b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{x}{2 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}+\frac{x}{2 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}"," ",0,"1/2/(4*a*c-b^2)*x/(x^2+1/2*b/c-1/2/c*(-4*a*c+b^2)^(1/2))+c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-1/2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/2/(4*a*c-b^2)*x/(x^2+1/2/c*(-4*a*c+b^2)^(1/2)+1/2*b/c)+c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","A"
871,1,733,206,0.065000," ","int(1/(c*x^4+b*x^2+a)^2,x)","\frac{\sqrt{2}\, b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{b^{2} x}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}+\frac{b^{2} x}{4 \sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}+\frac{\sqrt{2}\, b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{c x}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{c x}{\sqrt{-4 a c +b^{2}}\, \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right)}-\frac{b x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}-\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}-\frac{b x}{4 \left(4 a c -b^{2}\right) \left(x^{2}+\frac{b}{2 c}+\frac{\sqrt{-4 a c +b^{2}}}{2 c}\right) a}"," ",0,"-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*b+c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)-1/4/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*x/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)*b^2+1/4*c/(4*a*c-b^2)/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3*c^2/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-1/4/(4*a*c-b^2)/a*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*b-c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)+1/4/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*x/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)*b^2-1/4*c/(4*a*c-b^2)/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3*c^2/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+1/4*c/(-4*a*c+b^2)^(1/2)/(4*a*c-b^2)/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2","B"
872,1,712,260,0.038000," ","int(1/x^2/(c*x^4+b*x^2+a)^2,x)","-\frac{c^{2} x^{3}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c \,x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{4 \sqrt{2}\, b \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{4 \sqrt{2}\, b \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{3 \sqrt{2}\, b^{3} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{3 b c x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{5 \sqrt{2}\, c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{5 \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{b^{3} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 \sqrt{2}\, b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{3 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{1}{a^{2} x}"," ",0,"-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^3+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^3*b^2-3/2/a/(c*x^4+b*x^2+a)*b*c/(4*a*c-b^2)*x+1/2/a^2/(c*x^4+b*x^2+a)*b^3/(4*a*c-b^2)*x+5/2/a*c^2/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3/4/a^2*c/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+4/a*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3/4/a^2*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3-5/2/a*c^2/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+3/4/a^2*c/(4*a*c-b^2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+4/a*c^2/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3/4/a^2*c/(4*a*c-b^2)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3-1/a^2/x","B"
873,1,547,195,0.024000," ","int(x^11/(c*x^4+b*x^2+a)^3,x)","-\frac{15 a^{2} b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c}+\frac{5 a \,b^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b^{5} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{4 a^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{2 a \,b^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{b^{4} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{\frac{\left(25 a^{2} c^{2}-15 a \,b^{2} c +2 b^{4}\right) b \,x^{6}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{\left(31 a^{2} c^{2}-22 a \,b^{2} c +3 b^{4}\right) a b \,x^{2}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{\left(32 a^{3} c^{3}+11 a^{2} b^{2} c^{2}-19 a \,b^{4} c +3 b^{6}\right) x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{3 \left(8 a^{2} c^{2}-7 a \,b^{2} c +b^{4}\right) a^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/2*(1/c^2*b*(25*a^2*c^2-15*a*b^2*c+2*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+1/2*(32*a^3*c^3+11*a^2*b^2*c^2-19*a*b^4*c+3*b^6)/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4+a*b*(31*a^2*c^2-22*a*b^2*c+3*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^3*x^2+3/2*a^2*(8*a^2*c^2-7*a*b^2*c+b^4)/c^3/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^4+b*x^2+a)^2+4/c/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*a^2-2/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*a*b^2+1/4/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*b^4-15/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a^2*b+5/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*b^3-1/2/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^5","B"
874,1,267,113,0.017000," ","int(x^9/(c*x^4+b*x^2+a)^3,x)","\frac{6 a^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{\left(10 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) x^{6}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{\left(2 a^{2} c^{2}+8 a \,b^{2} c -b^{4}\right) b \,x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{\left(10 a c -b^{2}\right) a^{2} b}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(6 a^{2} c^{2}-10 a \,b^{2} c +b^{4}\right) a \,x^{2}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/2*(-1/c*(10*a^2*c^2-8*a*b^2*c+b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+1/2*b*(2*a^2*c^2+8*a*b^2*c-b^4)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-a*(6*a^2*c^2-10*a*b^2*c+b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^2*x^2+1/2*a^2*b*(10*a*c-b^2)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^4+b*x^2+a)^2+6*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","B"
875,1,230,111,0.016000," ","int(x^7/(c*x^4+b*x^2+a)^3,x)","-\frac{3 a b \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{3 a b c \,x^{6}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{\left(5 a c +b^{2}\right) a b \,x^{2}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(16 a^{2} c^{2}+a \,b^{2} c +b^{4}\right) x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(8 a c +b^{2}\right) a^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/2*(-3*a*b*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6-1/2*(16*a^2*c^2+a*b^2*c+b^4)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-(5*a*c+b^2)*a*b/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-1/2*a^2*(8*a*c+b^2)/c/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^4+b*x^2+a)^2-3*a*b/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","B"
876,1,270,122,0.016000," ","int(x^5/(c*x^4+b*x^2+a)^3,x)","\frac{2 a c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{\frac{\left(2 a c +b^{2}\right) c \,x^{6}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{3 \left(2 a c +b^{2}\right) b \,x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 a^{2} b}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{\left(2 a c -5 b^{2}\right) a \,x^{2}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/2*((2*a*c+b^2)*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+3/2*b*(2*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-a*(2*a*c-5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+3*a^2*b/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^4+b*x^2+a)^2+2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*a*c+1/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2","B"
877,1,142,105,0.009000," ","int(x^3/(c*x^4+b*x^2+a)^3,x)","-\frac{3 b c \,x^{2}}{2 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{4}+b \,x^{2}+a \right)}-\frac{3 b c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}}}-\frac{3 b^{2}}{4 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{4}+b \,x^{2}+a \right)}+\frac{-b \,x^{2}-2 a}{4 \left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/4*(-b*x^2-2*a)/(4*a*c-b^2)/(c*x^4+b*x^2+a)^2-3/2*b/(4*a*c-b^2)^2/(c*x^4+b*x^2+a)*x^2*c-3/4*b^2/(4*a*c-b^2)^2/(c*x^4+b*x^2+a)-3*b/(4*a*c-b^2)^(5/2)*c*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
878,1,141,107,0.008000," ","int(x/(c*x^4+b*x^2+a)^3,x)","\frac{3 c^{2} x^{2}}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{4}+b \,x^{2}+a \right)}+\frac{6 c^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}}}+\frac{3 b c}{2 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{4}+b \,x^{2}+a \right)}+\frac{2 c \,x^{2}+b}{4 \left(4 a c -b^{2}\right) \left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"1/4*(2*c*x^2+b)/(4*a*c-b^2)/(c*x^4+b*x^2+a)^2+3*c^2/(4*a*c-b^2)^2/(c*x^4+b*x^2+a)*x^2+3/2*c/(4*a*c-b^2)^2/(c*x^4+b*x^2+a)*b+6*c^2/(4*a*c-b^2)^(5/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))","A"
879,1,822,188,0.028000," ","int(1/x/(c*x^4+b*x^2+a)^3,x)","-\frac{7 b \,c^{3} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{b^{3} c^{2} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{29 b^{2} c^{2} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{b^{4} c \,x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{4 c^{3} x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 b^{3} c \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{b^{5} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{b \,c^{2} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{6 a \,c^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 b^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{15 b \,c^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a}+\frac{5 b^{3} c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b^{5} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{3}}-\frac{21 b^{2} c}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{4 c^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{2 b^{2} c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{b^{4} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{\ln \left(x \right)}{a^{3}}"," ",0,"-7/2/a/(c*x^4+b*x^2+a)^2*b*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+1/2/a^2/(c*x^4+b*x^2+a)^2*b^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+4/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-29/4/a/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^2+1/a^2/(c*x^4+b*x^2+a)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^4-1/2/(c*x^4+b*x^2+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*c^2-3/a/(c*x^4+b*x^2+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*c+1/2/a^2/(c*x^4+b*x^2+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+6*a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2-21/4/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^2*c+3/4/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4-4/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^4+b*x^2+a)+2/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^4+b*x^2+a)*b^2-1/4/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*b^4-15/a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b*c^2+5/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^3*c-1/2/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^5+ln(x)/a^3","B"
880,1,1002,241,0.033000," ","int(1/x^3/(c*x^4+b*x^2+a)^3,x)","-\frac{7 c^{4} x^{6}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{13 b^{2} c^{3} x^{6}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{b^{4} c^{2} x^{6}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{37 b \,c^{3} x^{4}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{55 b^{3} c^{2} x^{4}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{2 b^{5} c \,x^{4}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{7 b^{2} c^{2} x^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{6 b^{4} c \,x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{b^{6} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{9 c^{3} x^{2}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{9 b^{3} c}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{30 c^{3} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a}-\frac{5 b^{5}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{45 b^{2} c^{2} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{15 b^{4} c \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{3}}+\frac{3 b^{6} \arctan \left(\frac{2 c \,x^{2}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{4}}-\frac{29 b \,c^{2}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{12 b \,c^{2} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{6 b^{3} c \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{3 b^{5} \ln \left(c \,x^{4}+b \,x^{2}+a \right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{4}}-\frac{3 b \ln \left(x \right)}{a^{4}}-\frac{1}{2 a^{3} x^{2}}"," ",0,"-7/a/(c*x^4+b*x^2+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+13/2/a^2/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*b^2-1/a^3/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6*b^4-37/2/a/(c*x^4+b*x^2+a)^2*b*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4+55/4/a^2/(c*x^4+b*x^2+a)^2*b^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-2/a^3/(c*x^4+b*x^2+a)^2*b^5*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-9/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*c^3-7/2/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^2*c^2+6/a^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^4*c-1/a^3/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^6-29/2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b*c^2+9/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^3*c-5/4/a^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^5+12/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^4+b*x^2+a)*b-6/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^4+b*x^2+a)*b^3+3/4/a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^4+b*x^2+a)*b^5-30/a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*c^3+45/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^2*c^2-15/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^4*c+3/2/a^4/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2+b)/(4*a*c-b^2)^(1/2))*b^6-1/2/a^3/x^2-3*b*ln(x)/a^4","B"
881,1,1141,353,0.049000," ","int(x^10/(c*x^4+b*x^2+a)^3,x)","\frac{33 \sqrt{2}\, a^{2} b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{33 \sqrt{2}\, a^{2} b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{33 \sqrt{2}\, a \,b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{33 \sqrt{2}\, a \,b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{3 \sqrt{2}\, b^{5} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{5} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}-\frac{21 \sqrt{2}\, a^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{21 \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{27 \sqrt{2}\, a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{27 \sqrt{2}\, a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{3 \sqrt{2}\, b^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{3 \sqrt{2}\, b^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c^{2}}+\frac{-\frac{\left(44 a^{2} c^{2}-37 a \,b^{2} c +5 b^{4}\right) x^{7}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{\left(4 a^{2} c^{2}+20 a \,b^{2} c -3 b^{4}\right) b \,x^{5}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{3 \left(8 a c -b^{2}\right) a^{2} b x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(28 a^{2} c^{2}-49 a \,b^{2} c +6 b^{4}\right) a \,x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"(-1/8*(44*a^2*c^2-37*a*b^2*c+5*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c*x^7+1/8*b*(4*a^2*c^2+20*a*b^2*c-3*b^4)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-1/8*a/c^2*(28*a^2*c^2-49*a*b^2*c+6*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+3/8*a^2*b*(8*a*c-b^2)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x)/(c*x^4+b*x^2+a)^2-21/4/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2+27/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2-3/16/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4+33/4/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*b-33/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3+3/16/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5+21/4/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2-27/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2+3/16/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4+33/4/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2*b-33/16/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^3+3/16/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5","B"
882,1,953,303,0.045000," ","int(x^8/(c*x^4+b*x^2+a)^3,x)","-\frac{5 \sqrt{2}\, a^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{5 \sqrt{2}\, a^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, a \,b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, a \,b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b^{4} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{4} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, a b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{-\frac{\left(16 a c -b^{2}\right) b \,x^{7}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(14 a c +b^{2}\right) a b \,x^{3}}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(36 a^{2} c^{2}+5 a \,b^{2} c +b^{4}\right) x^{5}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(20 a c +b^{2}\right) a^{2} x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"(-1/8*b*(16*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7-1/8*(36*a^2*c^2+5*a*b^2*c+b^4)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-1/4*a/c*b*(14*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-1/8*a^2*(20*a*c+b^2)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x)/(c*x^4+b*x^2+a)^2+1/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b-1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3-5/2/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2+1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4-1/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b+1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3-5/2/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a^2-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b^2+1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4","B"
883,1,753,254,0.038000," ","int(x^6/(c*x^4+b*x^2+a)^3,x)","\frac{9 \sqrt{2}\, a b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{9 \sqrt{2}\, a b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, a c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, a c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\frac{3 \left(4 a c +b^{2}\right) c \,x^{7}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{\left(16 a c +5 b^{2}\right) b \,x^{5}}{128 a^{2} c^{2}-64 a \,b^{2} c +8 b^{4}}+\frac{3 a^{2} b x}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(4 a c -19 b^{2}\right) a \,x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"(3/8*c*(4*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7+1/8*b*(16*a*c+5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-1/8*(4*a*c-19*b^2)*a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+3/2/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*b*x)/(c*x^4+b*x^2+a)^2-3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-3/16/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+9/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3+3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+9/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a*b+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3","B"
884,1,617,241,0.038000," ","int(x^4/(c*x^4+b*x^2+a)^3,x)","-\frac{3 \sqrt{2}\, a \,c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, a \,c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, b^{2} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{9 \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{3 \sqrt{2}\, b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{3 \sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{-\frac{3 b \,c^{2} x^{7}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{\left(4 a c -19 b^{2}\right) c \,x^{5}}{128 a^{2} c^{2}-64 a \,b^{2} c +8 b^{4}}-\frac{\left(16 a c +5 b^{2}\right) b \,x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \left(4 a c +b^{2}\right) a x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"(-3/2*b*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7+1/8*c*(4*a*c-19*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-1/8*b*(16*a*c+5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-3/8*a*(4*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x)/(c*x^4+b*x^2+a)^2+3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3/2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3/2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-9/8/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2","B"
885,1,2958,267,0.161000," ","int(x^2/(c*x^4+b*x^2+a)^3,x)","\text{output too large to display}"," ",0,"52*c^4/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*a^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+9*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-9*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-27*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3-1/16*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^7+1/16*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^6-1/16*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^6+52*c^4/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*a^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-1/16*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^7-27*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3+1/16/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x^3*b^6+1/16/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x^3*b^6+20*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a^2*x^3+3/4*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*b^5-56*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a^3+3/4*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*b^4+3/4*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*b^4+20*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a^2*x^3-3/4*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*b^5+56*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a^3-1/16/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x^3*b^7-9*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x^3*b^2+12*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a^2*b-6*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a*b^3+12*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a^2*b-6*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a*b^3+20*c^4/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*a^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+3/4*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4+4*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a^2*x^3*b-3*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x^3*b^3+42*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a^2*b^2-21/2*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a*b^4+15/4*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5-4*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a^2*x^3*b+3*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x^3*b^3-42*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a^2*b^2+21/2*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*a*b^4+15/4*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5-20*c^4/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*a^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-3/4*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4-9*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x^3*b^2+7/8/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*b^6+3/4/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*b^5-7/8/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*b^6+1/16/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x^3*b^7+3/4/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*b^5","B"
886,1,3360,310,0.131000," ","int(1/(c*x^4+b*x^2+a)^3,x)","\text{output too large to display}"," ",0,"-24*c^4/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-3*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5-168*c^5/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*a^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+27/8*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x^3*b^6-3*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x^3*b^5+27*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x*b^2+27*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x*b^2+15*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3-24*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x^3*b-57/2*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4-15*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3-24*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x^3*b+20*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a^2*b*x+66*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*b^2*x^3-66*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*b^2*x^3-20*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a^2*b*x-57/2*c^3/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4-15*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x*b^3-3*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x^3*b^5-168*c^5/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*a^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-27/8*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x^3*b^6+15*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a*x*b^3+27/8*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^6-3/16*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/a^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^8+114*c^4/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+27/8*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^6-3/16*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/a^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^8+114*c^4/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2*a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+24*c^4/(-4*a*c+b^2)^2/(4*a*c-b^2)^2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+3*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5-3/16*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/a^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^7+3/16*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/a^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^7-72*c^4/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*a^2+5/16/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x*b^7-3/16/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2/a^2*x^3*b^8+3/16/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2/a^2*x^3*b^7+3/16/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2/a^2*x^3*b^7+5/16/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x*b^6+5/16/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x*b^6-5/16/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2/a*x*b^7+3/16/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2/a^2*x^3*b^8+72*c^4/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*a^2+45/2*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*b^4-15/4*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*b^5-44*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*a^2*x-44*c^3/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*a^2*x+15*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*b^3-21/4*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*b^4-45/2*c^2/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*b^4+15*c^2/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x^3*b^3-21/4*c/(-4*a*c+b^2)^2/(4*a*c-b^2)^2/(x^2+1/2*b/c-1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*b^4+15/4*c/(-4*a*c+b^2)^(5/2)/(4*a*c-b^2)^2/(x^2+1/2*b/c+1/2*(-4*a*c+b^2)^(1/2)/c)^2*x*b^5","B"
887,1,1567,378,0.055000," ","int(1/x^2/(c*x^4+b*x^2+a)^3,x)","-\frac{13 c^{4} x^{7}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{47 b^{2} c^{3} x^{7}}{8 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{7 b^{4} c^{2} x^{7}}{8 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{17 b \,c^{3} x^{5}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{99 b^{3} c^{2} x^{5}}{8 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{7 b^{5} c \,x^{5}}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{25 b^{2} c^{2} x^{3}}{8 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{43 b^{4} c \,x^{3}}{8 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{7 b^{6} x^{3}}{8 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{17 c^{3} x^{3}}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{33 b^{3} c x}{4 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{93 \sqrt{2}\, b \,c^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{93 \sqrt{2}\, b \,c^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{9 b^{5} x}{8 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{141 \sqrt{2}\, b^{3} c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}-\frac{141 \sqrt{2}\, b^{3} c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{15 \sqrt{2}\, b^{5} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}+\frac{15 \sqrt{2}\, b^{5} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{27 b \,c^{2} x}{2 \left(c \,x^{4}+b \,x^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{45 \sqrt{2}\, c^{3} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{45 \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{111 \sqrt{2}\, b^{2} c^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{111 \sqrt{2}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{2}}+\frac{15 \sqrt{2}\, b^{4} c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{15 \sqrt{2}\, b^{4} c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a^{3}}-\frac{1}{a^{3} x}"," ",0,"-17/2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*c^3+45/4/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-45/4/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)+43/8/a^2/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^4*c+33/4/a/(c*x^4+b*x^2+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c-25/8/a/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^2*c^2+47/8/a^2/(c*x^4+b*x^2+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7*b^2-17/a/(c*x^4+b*x^2+a)^2*c^3*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-13/2/a/(c*x^4+b*x^2+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7-27/2/(c*x^4+b*x^2+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c^2-141/16/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3+15/16/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5+15/16/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^5-141/16/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^3+93/4/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+93/4/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-111/16/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+111/16/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+15/16/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4-15/16/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^4-9/8/a^2/(c*x^4+b*x^2+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x-7/8/a^3/(c*x^4+b*x^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^6-1/a^3/x+99/8/a^2/(c*x^4+b*x^2+a)^2*c^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-7/8/a^3/(c*x^4+b*x^2+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7*b^4-7/4/a^3/(c*x^4+b*x^2+a)^2*c*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5","B"
888,1,116,72,0.005000," ","int(x^5/(c*x^4-b*x^2+a),x)","-\frac{a \arctan \left(\frac{2 c \,x^{2}-b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{2}-b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c^{2}}+\frac{x^{2}}{2 c}+\frac{b \ln \left(c \,x^{4}-b \,x^{2}+a \right)}{4 c^{2}}"," ",0,"1/2/c*x^2+1/4*b*ln(c*x^4-b*x^2+a)/c^2-1/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2-b)/(4*a*c-b^2)^(1/2))*a+1/2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2-b)/(4*a*c-b^2)^(1/2))*b^2","A"
889,1,63,56,0.004000," ","int(x^3/(c*x^4-b*x^2+a),x)","\frac{b \arctan \left(\frac{2 c \,x^{2}-b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c}+\frac{\ln \left(c \,x^{4}-b \,x^{2}+a \right)}{4 c}"," ",0,"1/4*ln(c*x^4-b*x^2+a)/c+1/2*b/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2-b)/(4*a*c-b^2)^(1/2))","A"
890,1,38,31,0.002000," ","int(x/(c*x^4-b*x^2+a),x)","\frac{\arctan \left(\frac{2 c \,x^{2}-b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}"," ",0,"1/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2-b)/(4*a*c-b^2)^(1/2))","A"
891,1,69,62,0.008000," ","int(1/x/(c*x^4-b*x^2+a),x)","\frac{b \arctan \left(\frac{2 c \,x^{2}-b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a}+\frac{\ln \left(x \right)}{a}-\frac{\ln \left(c \,x^{4}-b \,x^{2}+a \right)}{4 a}"," ",0,"1/a*ln(x)-1/4*ln(c*x^4-b*x^2+a)/a+1/2/a*b/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2-b)/(4*a*c-b^2)^(1/2))","A"
892,1,123,79,0.008000," ","int(1/x^3/(c*x^4-b*x^2+a),x)","-\frac{c \arctan \left(\frac{2 c \,x^{2}-b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{2}-b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a^{2}}+\frac{b \ln \left(x \right)}{a^{2}}-\frac{b \ln \left(c \,x^{4}-b \,x^{2}+a \right)}{4 a^{2}}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2/a/x^2+1/a^2*b*ln(x)-1/4*b*ln(c*x^4-b*x^2+a)/a^2-1/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2-b)/(4*a*c-b^2)^(1/2))*c+1/2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^2-b)/(4*a*c-b^2)^(1/2))*b^2","A"
893,1,343,144,0.028000," ","int(x^4/(c*x^4-b*x^2+a),x)","\frac{\sqrt{2}\, a \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{x}{c}"," ",0,"1/c*x-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/2/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/2/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2","B"
894,1,208,115,0.013000," ","int(x^2/(c*x^4-b*x^2+a),x)","-\frac{\sqrt{2}\, b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}"," ",0,"-1/2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b","A"
895,1,116,114,0.013000," ","int(1/(c*x^4-b*x^2+a),x)","-\frac{\sqrt{2}\, c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}"," ",0,"-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)","A"
896,1,232,138,0.016000," ","int(1/x^2/(c*x^4-b*x^2+a),x)","-\frac{\sqrt{2}\, b c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{1}{a x}"," ",0,"-1/a/x+1/2*c/a*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2*c/a/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b-1/2*c/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)-1/2*c/a/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b","A"
897,1,86,55,0.005000," ","int(x^5/(a*x^4+2*a*x^2+a-b),x)","-\frac{b \arctanh \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \sqrt{a b}\, a}+\frac{x^{2}}{2 a}-\frac{\arctanh \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \sqrt{a b}}-\frac{\ln \left(a \,x^{4}+2 a \,x^{2}+a -b \right)}{2 a}"," ",0,"1/2*x^2/a-1/2*ln(a*x^4+2*a*x^2+a-b)/a-1/2/(a*b)^(1/2)*arctanh(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))-1/2/a/(a*b)^(1/2)*arctanh(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))*b","A"
898,1,49,44,0.002000," ","int(x^3/(a*x^4+2*a*x^2+a-b),x)","\frac{\arctanh \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \sqrt{a b}}+\frac{\ln \left(a \,x^{4}+2 a \,x^{2}+a -b \right)}{4 a}"," ",0,"1/4/a*ln(a*x^4+2*a*x^2+a-b)+1/2/(a*b)^(1/2)*arctanh(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))","A"
899,1,26,21,0.002000," ","int(x/(a*x^4+2*a*x^2+a-b),x)","-\frac{\arctanh \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \sqrt{a b}}"," ",0,"-1/2/(a*b)^(1/2)*arctanh(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))","A"
900,1,71,65,0.006000," ","int(1/x/(a*x^4+2*a*x^2+a-b),x)","\frac{a \arctanh \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \left(a -b \right) \sqrt{a b}}+\frac{\ln \left(x \right)}{a -b}-\frac{\ln \left(a \,x^{4}+2 a \,x^{2}+a -b \right)}{4 \left(a -b \right)}"," ",0,"ln(x)/(a-b)-1/4*ln(a*x^4+2*a*x^2+a-b)/(a-b)+1/2*a/(a-b)/(a*b)^(1/2)*arctanh(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))","A"
901,1,122,83,0.010000," ","int(1/x^3/(a*x^4+2*a*x^2+a-b),x)","-\frac{a^{2} \arctanh \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \left(a -b \right)^{2} \sqrt{a b}}-\frac{a b \arctanh \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \left(a -b \right)^{2} \sqrt{a b}}-\frac{2 a \ln \left(x \right)}{\left(a -b \right)^{2}}+\frac{a \ln \left(a \,x^{4}+2 a \,x^{2}+a -b \right)}{2 \left(a -b \right)^{2}}-\frac{1}{2 \left(a -b \right) x^{2}}"," ",0,"-1/2/(a-b)/x^2-2*a*ln(x)/(a-b)^2+1/2*a*ln(a*x^4+2*a*x^2+a-b)/(a-b)^2-1/2/(a-b)^2*a^2/(a*b)^(1/2)*arctanh(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))-1/2/(a-b)^2*a/(a*b)^(1/2)*arctanh(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))*b","A"
902,1,210,74,0.030000," ","int(x^4/(a*x^4+2*a*x^2+a-b),x)","-\frac{a \arctanh \left(\frac{a x}{\sqrt{\left(-a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{a b}\, \sqrt{\left(-a +\sqrt{a b}\right) a}}-\frac{a \arctan \left(\frac{a x}{\sqrt{\left(a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{a b}\, \sqrt{\left(a +\sqrt{a b}\right) a}}-\frac{b \arctanh \left(\frac{a x}{\sqrt{\left(-a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{a b}\, \sqrt{\left(-a +\sqrt{a b}\right) a}}-\frac{b \arctan \left(\frac{a x}{\sqrt{\left(a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{a b}\, \sqrt{\left(a +\sqrt{a b}\right) a}}+\frac{\arctanh \left(\frac{a x}{\sqrt{\left(-a +\sqrt{a b}\right) a}}\right)}{\sqrt{\left(-a +\sqrt{a b}\right) a}}-\frac{\arctan \left(\frac{a x}{\sqrt{\left(a +\sqrt{a b}\right) a}}\right)}{\sqrt{\left(a +\sqrt{a b}\right) a}}+\frac{x}{a}"," ",0,"x/a+1/(((a*b)^(1/2)-a)*a)^(1/2)*arctanh(a*x/(((a*b)^(1/2)-a)*a)^(1/2))-1/2/(a*b)^(1/2)/(((a*b)^(1/2)-a)*a)^(1/2)*arctanh(a*x/(((a*b)^(1/2)-a)*a)^(1/2))*a-1/2/(a*b)^(1/2)/(((a*b)^(1/2)-a)*a)^(1/2)*arctanh(a*x/(((a*b)^(1/2)-a)*a)^(1/2))*b-1/(((a*b)^(1/2)+a)*a)^(1/2)*arctan(a*x/(((a*b)^(1/2)+a)*a)^(1/2))-1/2/(a*b)^(1/2)/(((a*b)^(1/2)+a)*a)^(1/2)*arctan(a*x/(((a*b)^(1/2)+a)*a)^(1/2))*a-1/2/(a*b)^(1/2)/(((a*b)^(1/2)+a)*a)^(1/2)*arctan(a*x/(((a*b)^(1/2)+a)*a)^(1/2))*b","B"
903,1,134,69,0.011000," ","int(x^2/(a*x^4+2*a*x^2+a-b),x)","\frac{a \arctanh \left(\frac{a x}{\sqrt{\left(-a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{a b}\, \sqrt{\left(-a +\sqrt{a b}\right) a}}+\frac{a \arctan \left(\frac{a x}{\sqrt{\left(a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{a b}\, \sqrt{\left(a +\sqrt{a b}\right) a}}-\frac{\arctanh \left(\frac{a x}{\sqrt{\left(-a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{\left(-a +\sqrt{a b}\right) a}}+\frac{\arctan \left(\frac{a x}{\sqrt{\left(a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{\left(a +\sqrt{a b}\right) a}}"," ",0,"-1/2/((-a+(a*b)^(1/2))*a)^(1/2)*arctanh(1/((-a+(a*b)^(1/2))*a)^(1/2)*a*x)+1/2/(a*b)^(1/2)/((-a+(a*b)^(1/2))*a)^(1/2)*arctanh(1/((-a+(a*b)^(1/2))*a)^(1/2)*a*x)*a+1/2/((a+(a*b)^(1/2))*a)^(1/2)*arctan(1/((a+(a*b)^(1/2))*a)^(1/2)*a*x)+1/2/(a*b)^(1/2)/((a+(a*b)^(1/2))*a)^(1/2)*a*arctan(1/((a+(a*b)^(1/2))*a)^(1/2)*a*x)","A"
904,1,74,69,0.012000," ","int(1/(a*x^4+2*a*x^2+a-b),x)","-\frac{a \arctanh \left(\frac{a x}{\sqrt{\left(-a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{a b}\, \sqrt{\left(-a +\sqrt{a b}\right) a}}-\frac{a \arctan \left(\frac{a x}{\sqrt{\left(a +\sqrt{a b}\right) a}}\right)}{2 \sqrt{a b}\, \sqrt{\left(a +\sqrt{a b}\right) a}}"," ",0,"-1/2/(a*b)^(1/2)/((-a+(a*b)^(1/2))*a)^(1/2)*arctanh(1/((-a+(a*b)^(1/2))*a)^(1/2)*a*x)*a-1/2/(a*b)^(1/2)/((a+(a*b)^(1/2))*a)^(1/2)*a*arctan(1/((a+(a*b)^(1/2))*a)^(1/2)*a*x)","A"
905,1,180,81,0.013000," ","int(1/x^2/(a*x^4+2*a*x^2+a-b),x)","\frac{a^{2} \arctanh \left(\frac{a x}{\sqrt{\left(-a +\sqrt{a b}\right) a}}\right)}{2 \left(a -b \right) \sqrt{a b}\, \sqrt{\left(-a +\sqrt{a b}\right) a}}+\frac{a^{2} \arctan \left(\frac{a x}{\sqrt{\left(a +\sqrt{a b}\right) a}}\right)}{2 \left(a -b \right) \sqrt{a b}\, \sqrt{\left(a +\sqrt{a b}\right) a}}+\frac{a \arctanh \left(\frac{a x}{\sqrt{\left(-a +\sqrt{a b}\right) a}}\right)}{2 \left(a -b \right) \sqrt{\left(-a +\sqrt{a b}\right) a}}-\frac{a \arctan \left(\frac{a x}{\sqrt{\left(a +\sqrt{a b}\right) a}}\right)}{2 \left(a -b \right) \sqrt{\left(a +\sqrt{a b}\right) a}}-\frac{1}{\left(a -b \right) x}"," ",0,"-1/(a-b)/x+1/2*a/(a-b)/((-a+(a*b)^(1/2))*a)^(1/2)*arctanh(1/((-a+(a*b)^(1/2))*a)^(1/2)*a*x)+1/2*a^2/(a-b)/(a*b)^(1/2)/((-a+(a*b)^(1/2))*a)^(1/2)*arctanh(1/((-a+(a*b)^(1/2))*a)^(1/2)*a*x)-1/2*a/(a-b)/((a+(a*b)^(1/2))*a)^(1/2)*arctan(1/((a+(a*b)^(1/2))*a)^(1/2)*a*x)+1/2*a^2/(a-b)/(a*b)^(1/2)/((a+(a*b)^(1/2))*a)^(1/2)*arctan(1/((a+(a*b)^(1/2))*a)^(1/2)*a*x)","B"
906,1,84,55,0.006000," ","int(x^5/(a*x^4+2*a*x^2+a+b),x)","-\frac{b \arctan \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \sqrt{a b}\, a}+\frac{x^{2}}{2 a}+\frac{\arctan \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \sqrt{a b}}-\frac{\ln \left(a \,x^{4}+2 a \,x^{2}+a +b \right)}{2 a}"," ",0,"1/2/a*x^2-1/2*ln(a*x^4+2*a*x^2+a+b)/a+1/2/(a*b)^(1/2)*arctan(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))-1/2/a/(a*b)^(1/2)*arctan(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))*b","A"
907,1,47,42,0.003000," ","int(x^3/(a*x^4+2*a*x^2+a+b),x)","-\frac{\arctan \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \sqrt{a b}}+\frac{\ln \left(a \,x^{4}+2 a \,x^{2}+a +b \right)}{4 a}"," ",0,"1/4/a*ln(a*x^4+2*a*x^2+a+b)-1/2/(a*b)^(1/2)*arctan(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))","A"
908,1,26,21,0.003000," ","int(x/(a*x^4+2*a*x^2+a+b),x)","\frac{\arctan \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \sqrt{a b}}"," ",0,"1/2/(a*b)^(1/2)*arctan(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))","A"
909,1,63,57,0.009000," ","int(1/x/(a*x^4+2*a*x^2+a+b),x)","-\frac{a \arctan \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \left(a +b \right) \sqrt{a b}}+\frac{\ln \left(x \right)}{a +b}-\frac{\ln \left(a \,x^{4}+2 a \,x^{2}+a +b \right)}{4 \left(a +b \right)}"," ",0,"-1/4*ln(a*x^4+2*a*x^2+a+b)/(a+b)-1/2*a/(a+b)/(a*b)^(1/2)*arctan(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))+ln(x)/(a+b)","A"
910,1,110,75,0.010000," ","int(1/x^3/(a*x^4+2*a*x^2+a+b),x)","\frac{a^{2} \arctan \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \left(a +b \right)^{2} \sqrt{a b}}-\frac{a b \arctan \left(\frac{2 a \,x^{2}+2 a}{2 \sqrt{a b}}\right)}{2 \left(a +b \right)^{2} \sqrt{a b}}-\frac{2 a \ln \left(x \right)}{\left(a +b \right)^{2}}+\frac{a \ln \left(a \,x^{4}+2 a \,x^{2}+a +b \right)}{2 \left(a +b \right)^{2}}-\frac{1}{2 \left(a +b \right) x^{2}}"," ",0,"1/2*a*ln(a*x^4+2*a*x^2+a+b)/(a+b)^2+1/2/(a+b)^2*a^2/(a*b)^(1/2)*arctan(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))-1/2/(a+b)^2*a/(a*b)^(1/2)*arctan(1/2*(2*a*x^2+2*a)/(a*b)^(1/2))*b-1/2/(a+b)/x^2-2*a*ln(x)/(a+b)^2","A"
911,1,1658,300,0.138000," ","int(x^4/(a*x^4+2*a*x^2+a+b),x)","\frac{x}{a}+\frac{\sqrt{a +b}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a}-\frac{\sqrt{a +b}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a}+\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{2 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, \sqrt{a}\, b}-\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{2 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, \sqrt{a}\, b}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(-\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x -\sqrt{a +b}\right)}{4 \sqrt{a}\, b}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x +\sqrt{a +b}\right)}{4 \sqrt{a}\, b}-\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{a +b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a b}+\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{a +b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a b}+\frac{\sqrt{a +b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(-\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x -\sqrt{a +b}\right)}{8 a b}-\frac{\sqrt{a +b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x +\sqrt{a +b}\right)}{8 a b}+\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{a^{2}+a b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{2 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a^{\frac{3}{2}} b}-\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{a^{2}+a b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{2 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a^{\frac{3}{2}} b}-\frac{\sqrt{a^{2}+a b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(-\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x -\sqrt{a +b}\right)}{4 a^{\frac{3}{2}} b}+\frac{\sqrt{a^{2}+a b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x +\sqrt{a +b}\right)}{4 a^{\frac{3}{2}} b}-\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{a^{2}+a b}\, \sqrt{a +b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a^{2} b}+\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{a^{2}+a b}\, \sqrt{a +b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a^{2} b}+\frac{\sqrt{a^{2}+a b}\, \sqrt{a +b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(-\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x -\sqrt{a +b}\right)}{8 a^{2} b}-\frac{\sqrt{a^{2}+a b}\, \sqrt{a +b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x +\sqrt{a +b}\right)}{8 a^{2} b}"," ",0,"1/a*x+1/8/a/b*ln(-x^2*a^(1/2)+x*(2*(a*(a+b))^(1/2)-2*a)^(1/2)-(a+b)^(1/2))*(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/8/a^2/b*ln(-x^2*a^(1/2)+x*(2*(a*(a+b))^(1/2)-2*a)^(1/2)-(a+b)^(1/2))*(a^2+a*b)^(1/2)*(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/4/a^(3/2)/b*ln(-x^2*a^(1/2)+x*(2*(a*(a+b))^(1/2)-2*a)^(1/2)-(a+b)^(1/2))*(a^2+a*b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/4/a^(1/2)/b*ln(-x^2*a^(1/2)+x*(2*(a*(a+b))^(1/2)-2*a)^(1/2)-(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/a/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(a+b)^(1/2)-1/4/a/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/4/a^2/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)*(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/2/a^(3/2)/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/2/a^(1/2)/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((-2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/8/a/b*ln(x^2*a^(1/2)+x*(2*(a*(a+b))^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/8/a^2/b*ln(x^2*a^(1/2)+x*(2*(a*(a+b))^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(a^2+a*b)^(1/2)*(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/4/a^(3/2)/b*ln(x^2*a^(1/2)+x*(2*(a*(a+b))^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(a^2+a*b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/4/a^(1/2)/b*ln(x^2*a^(1/2)+x*(2*(a*(a+b))^(1/2)-2*a)^(1/2)+(a+b)^(1/2))*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/a/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(a+b)^(1/2)+1/4/a/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)+1/4/a^2/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)*(a+b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/2/a^(3/2)/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(a^2+a*b)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)-1/2/a^(1/2)/b/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2)*arctan((2*a^(1/2)*x+(2*(a*(a+b))^(1/2)-2*a)^(1/2))/(4*a^(1/2)*(a+b)^(1/2)-2*(a*(a+b))^(1/2)+2*a)^(1/2))*(2*(a*(a+b))^(1/2)-2*a)^(1/2)*(2*(a^2+a*b)^(1/2)-2*a)^(1/2)","B"
912,1,724,223,0.059000," ","int(x^2/(a*x^4+2*a*x^2+a+b),x)","-\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, \sqrt{a}\, b}+\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, \sqrt{a}\, b}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(-\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x -\sqrt{a +b}\right)}{8 \sqrt{a}\, b}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x +\sqrt{a +b}\right)}{8 \sqrt{a}\, b}-\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{a^{2}+a b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a^{\frac{3}{2}} b}+\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{a^{2}+a b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a^{\frac{3}{2}} b}+\frac{\sqrt{a^{2}+a b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(-\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x -\sqrt{a +b}\right)}{8 a^{\frac{3}{2}} b}-\frac{\sqrt{a^{2}+a b}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x +\sqrt{a +b}\right)}{8 a^{\frac{3}{2}} b}"," ",0,"1/8*(a^2+a*b)^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)/a^(3/2)/b*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))-1/4/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(a^2+a*b)^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)/a^(3/2)/b*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))+1/8*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)/a^(1/2)/b*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))-1/4/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)/a^(1/2)/b*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))-1/8*(a^2+a*b)^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)/a^(3/2)/b*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))+1/4/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(a^2+a*b)^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)/a^(3/2)/b*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))-1/8*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)/a^(1/2)/b*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))+1/4/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)/a^(1/2)/b*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))","B"
913,1,913,243,0.079000," ","int(1/(a*x^4+2*a*x^2+a+b),x)","-\frac{\arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{\sqrt{a +b}\, \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}+\frac{\arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{\sqrt{a +b}\, \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}+\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{a +b}\, \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, b}-\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{a +b}\, \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, b}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(-\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x -\sqrt{a +b}\right)}{8 \sqrt{a +b}\, b}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \ln \left(\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x +\sqrt{a +b}\right)}{8 \sqrt{a +b}\, b}+\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \sqrt{a^{2}+a b}\, \arctan \left(\frac{-2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{a +b}\, \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a b}-\frac{\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, \sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \sqrt{a^{2}+a b}\, \arctan \left(\frac{2 \sqrt{a}\, x +\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}}{\sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}}\right)}{4 \sqrt{a +b}\, \sqrt{2 a +4 \sqrt{a +b}\, \sqrt{a}-2 \sqrt{\left(a +b \right) a}}\, a b}-\frac{\sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \sqrt{a^{2}+a b}\, \ln \left(-\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x -\sqrt{a +b}\right)}{8 \sqrt{a +b}\, a b}+\frac{\sqrt{-2 a +2 \sqrt{a^{2}+a b}}\, \sqrt{a^{2}+a b}\, \ln \left(\sqrt{a}\, x^{2}+\sqrt{-2 a +2 \sqrt{\left(a +b \right) a}}\, x +\sqrt{a +b}\right)}{8 \sqrt{a +b}\, a b}"," ",0,"-1/8/(a+b)^(1/2)/a/b*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/8/(a+b)^(1/2)/b*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-1/(a+b)^(1/2)/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))+1/4/(a+b)^(1/2)/a/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)+1/4/(a+b)^(1/2)/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+1/8/(a+b)^(1/2)/a/b*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)+1/8/(a+b)^(1/2)/b*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+1/(a+b)^(1/2)/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))-1/4/(a+b)^(1/2)/a/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/4/(a+b)^(1/2)/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)","B"
914,1,3318,301,0.070000," ","int(1/x^2/(a*x^4+2*a*x^2+a+b),x)","\text{output too large to display}"," ",0,"1/4*a^(3/2)/(a+b)^2/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-1/2*a^2/(a+b)^(5/2)/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-1/4/a^(1/2)/(a+b)^2/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)+1/2*a^2/(a+b)^(5/2)/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-1/4*a^(3/2)/(a+b)^2/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+1/4/a^(1/2)/(a+b)^2/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/4/(a+b)^(5/2)*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/8*a^(1/2)/(a+b)^2*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+1/8*a^(1/2)/(a+b)^2*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-1/4*a/(a+b)^(5/2)*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-2*a^2/(a+b)^(5/2)/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))+1/4*a/(a+b)^(5/2)*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+2*a^2/(a+b)^(5/2)/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))+1/4/(a+b)^(5/2)*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/(a+b)/x-1/2*a/(a+b)^(5/2)/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)+1/2*a/(a+b)^(5/2)/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/4*a^(1/2)/(a+b)^2/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)+1/4*a^(1/2)/(a+b)^2/b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-2*a/(a+b)^(5/2)*b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))+1/8/a^(1/2)/(a+b)^2*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/8/a^(1/2)/(a+b)^2*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/8*a^(3/2)/(a+b)^2/b*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+1/4*a^2/(a+b)^(5/2)/b*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+2*a/(a+b)^(5/2)*b/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))+1/2*a/(a+b)^(5/2)/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-1/4*a^(1/2)/(a+b)^2/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-1/8*a^(1/2)/(a+b)^2/b*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/2/(a+b)^(5/2)/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)+1/2/(a+b)^(5/2)/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/2*a/(a+b)^(5/2)/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+1/4*a/(a+b)^(5/2)/b*ln(-a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x-(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)-1/4*a/(a+b)^(5/2)/b*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)+1/8*a^(1/2)/(a+b)^2/b*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)*(a^2+a*b)^(1/2)+1/4*a^(1/2)/(a+b)^2/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2)*arctan((-2*a^(1/2)*x+(-2*a+2*((a+b)*a)^(1/2))^(1/2))/(2*a+4*(a+b)^(1/2)*a^(1/2)-2*((a+b)*a)^(1/2))^(1/2))*(-2*a+2*((a+b)*a)^(1/2))^(1/2)*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)+1/8*a^(3/2)/(a+b)^2/b*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)-1/4*a^2/(a+b)^(5/2)/b*ln(a^(1/2)*x^2+(-2*a+2*((a+b)*a)^(1/2))^(1/2)*x+(a+b)^(1/2))*(-2*a+2*(a^2+a*b)^(1/2))^(1/2)","B"
915,1,19,18,0.002000," ","int(x/(x^4+x^2+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}+1\right) \sqrt{3}}{3}\right)}{3}"," ",0,"1/3*arctan(1/3*(2*x^2+1)*3^(1/2))*3^(1/2)","A"
916,1,11,10,0.003000," ","int(x/(x^4+2*x^2+10),x)","\frac{\arctan \left(\frac{x^{2}}{3}+\frac{1}{3}\right)}{6}"," ",0,"1/6*arctan(1/3*x^2+1/3)","A"
917,1,19,18,0.009000," ","int(x^2/(x^4+9*x^2+20),x)","-2 \arctan \left(\frac{x}{2}\right)+\sqrt{5}\, \arctan \left(\frac{\sqrt{5}\, x}{5}\right)"," ",0,"-2*arctan(1/2*x)+arctan(1/5*x*5^(1/2))*5^(1/2)","A"
918,1,57,56,0.022000," ","int(x^2/(x^4-x^2+1),x)","\frac{\arctan \left(2 x -\sqrt{3}\right)}{2}+\frac{\arctan \left(2 x +\sqrt{3}\right)}{2}+\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{12}-\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{12}"," ",0,"1/2*arctan(2*x-3^(1/2))+1/2*arctan(2*x+3^(1/2))+1/12*3^(1/2)*ln(x^2-3^(1/2)*x+1)-1/12*3^(1/2)*ln(x^2+3^(1/2)*x+1)","A"
919,1,308,132,0.105000," ","int(x^2/(x^4-2*x^2+2),x)","\frac{\sqrt{2}\, \left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 x -\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 x -\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2}\, \left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 x +\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}-\frac{\left(2+2 \sqrt{2}\right) \arctan \left(\frac{2 x +\sqrt{2+2 \sqrt{2}}}{\sqrt{-2+2 \sqrt{2}}}\right)}{4 \sqrt{-2+2 \sqrt{2}}}+\frac{\sqrt{2+2 \sqrt{2}}\, \sqrt{2}\, \ln \left(x^{2}-\sqrt{2+2 \sqrt{2}}\, x +\sqrt{2}\right)}{8}-\frac{\sqrt{2+2 \sqrt{2}}\, \ln \left(x^{2}-\sqrt{2+2 \sqrt{2}}\, x +\sqrt{2}\right)}{8}-\frac{\sqrt{2+2 \sqrt{2}}\, \sqrt{2}\, \ln \left(x^{2}+\sqrt{2+2 \sqrt{2}}\, x +\sqrt{2}\right)}{8}+\frac{\sqrt{2+2 \sqrt{2}}\, \ln \left(x^{2}+\sqrt{2+2 \sqrt{2}}\, x +\sqrt{2}\right)}{8}"," ",0,"-1/8*(2+2*2^(1/2))^(1/2)*2^(1/2)*ln(x^2+2^(1/2)+x*(2+2*2^(1/2))^(1/2))+1/4*2^(1/2)*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*x+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))+1/8*(2+2*2^(1/2))^(1/2)*ln(x^2+2^(1/2)+x*(2+2*2^(1/2))^(1/2))-1/4*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*x+(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))+1/8*(2+2*2^(1/2))^(1/2)*2^(1/2)*ln(x^2+2^(1/2)-x*(2+2*2^(1/2))^(1/2))+1/4*2^(1/2)*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*x-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))-1/8*(2+2*2^(1/2))^(1/2)*ln(x^2+2^(1/2)-x*(2+2*2^(1/2))^(1/2))-1/4*(2+2*2^(1/2))/(-2+2*2^(1/2))^(1/2)*arctan((2*x-(2+2*2^(1/2))^(1/2))/(-2+2*2^(1/2))^(1/2))","B"
920,1,296,149,0.024000," ","int(x^7*(c*x^4+b*x^2+a)^(1/2),x)","\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} x^{4}}{10 c}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b \,x^{2}}{32 c^{2}}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} x^{2}}{128 c^{3}}+\frac{3 a^{2} b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{5}{2}}}-\frac{5 a \,b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{64 c^{\frac{7}{2}}}+\frac{7 b^{5} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{512 c^{\frac{9}{2}}}-\frac{7 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b \,x^{2}}{80 c^{2}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{2}}{64 c^{3}}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4}}{256 c^{4}}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} a}{15 c^{2}}+\frac{7 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}{96 c^{3}}"," ",0,"1/10*x^4*(c*x^4+b*x^2+a)^(3/2)/c-7/80*b/c^2*x^2*(c*x^4+b*x^2+a)^(3/2)+7/96*b^2/c^3*(c*x^4+b*x^2+a)^(3/2)-7/128*b^3/c^3*(c*x^4+b*x^2+a)^(1/2)*x^2-7/256*b^4/c^4*(c*x^4+b*x^2+a)^(1/2)-5/64*b^3/c^(7/2)*ln((1/2*b+c*x^2)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*a+7/512*b^5/c^(9/2)*ln((1/2*b+c*x^2)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/32*b/c^2*a*(c*x^4+b*x^2+a)^(1/2)*x^2+3/64*b^2/c^3*a*(c*x^4+b*x^2+a)^(1/2)+3/32*b/c^(5/2)*a^2*ln((1/2*b+c*x^2)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/15*a/c^2*(c*x^4+b*x^2+a)^(3/2)","A"
921,1,247,131,0.017000," ","int(x^5*(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{2}}{16 c}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} x^{2}}{64 c^{2}}-\frac{a^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 c^{\frac{3}{2}}}+\frac{3 a \,b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{5}{2}}}-\frac{5 b^{4} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{256 c^{\frac{7}{2}}}+\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} x^{2}}{8 c}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a b}{32 c^{2}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3}}{128 c^{3}}-\frac{5 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b}{48 c^{2}}"," ",0,"1/8*x^2*(c*x^4+b*x^2+a)^(3/2)/c-5/48*b*(c*x^4+b*x^2+a)^(3/2)/c^2+5/64*b^2/c^2*(c*x^4+b*x^2+a)^(1/2)*x^2+5/128*b^3/c^3*(c*x^4+b*x^2+a)^(1/2)+3/32*b^2/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*a-5/256*b^4/c^(7/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/16*a/c*(c*x^4+b*x^2+a)^(1/2)*x^2-1/32*a/c^2*(c*x^4+b*x^2+a)^(1/2)*b-1/16*a^2/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","A"
922,1,139,90,0.014000," ","int(x^3*(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{2}}{8 c}-\frac{a b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{8 c^{\frac{3}{2}}}+\frac{b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{5}{2}}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{16 c^{2}}+\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{6 c}"," ",0,"1/6*(c*x^4+b*x^2+a)^(3/2)/c-1/8*b/c*x^2*(c*x^4+b*x^2+a)^(1/2)-1/16*b^2/c^2*(c*x^4+b*x^2+a)^(1/2)-1/8*b/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*a+1/32*b^3/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","A"
923,1,101,69,0.010000," ","int(x*(c*x^4+b*x^2+a)^(1/2),x)","\frac{a \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 \sqrt{c}}-\frac{b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 c^{\frac{3}{2}}}+\frac{\left(2 c \,x^{2}+b \right) \sqrt{c \,x^{4}+b \,x^{2}+a}}{8 c}"," ",0,"1/8*(2*c*x^2+b)*(c*x^4+b*x^2+a)^(1/2)/c+1/4/c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*a-1/16/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))*b^2","A"
924,1,91,85,0.012000," ","int((c*x^4+b*x^2+a)^(1/2)/x,x)","-\frac{\sqrt{a}\, \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 \sqrt{c}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{2}"," ",0,"1/2*(c*x^4+b*x^2+a)^(1/2)+1/4*b*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)-1/2*a^(1/2)*ln((2*a+b*x^2+2*a^(1/2)*(c*x^4+b*x^2+a)^(1/2))/x^2)","A"
925,1,140,88,0.011000," ","int((c*x^4+b*x^2+a)^(1/2)/x^3,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{2}}{2 a}-\frac{b \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4 \sqrt{a}}+\frac{\sqrt{c}\, \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{2 a}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{2 a \,x^{2}}"," ",0,"-1/2/a/x^2*(c*x^4+b*x^2+a)^(3/2)+1/2*b/a*(c*x^4+b*x^2+a)^(1/2)-1/4*b/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/2*c/a*(c*x^4+b*x^2+a)^(1/2)*x^2+1/2*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","A"
926,1,193,74,0.012000," ","int((c*x^4+b*x^2+a)^(1/2)/x^5,x)","-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b c \,x^{2}}{8 a^{2}}-\frac{c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4 \sqrt{a}}+\frac{b^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{16 a^{\frac{3}{2}}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c}{4 a}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{8 a^{2}}+\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b}{8 a^{2} x^{2}}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{4 a \,x^{4}}"," ",0,"-1/4/a/x^4*(c*x^4+b*x^2+a)^(3/2)+1/8*b/a^2/x^2*(c*x^4+b*x^2+a)^(3/2)-1/8*b^2/a^2*(c*x^4+b*x^2+a)^(1/2)+1/16*b^2/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/8*b/a^2*c*(c*x^4+b*x^2+a)^(1/2)*x^2+1/4*c/a*(c*x^4+b*x^2+a)^(1/2)-1/4*c/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","B"
927,1,222,98,0.013000," ","int((c*x^4+b*x^2+a)^(1/2)/x^7,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} c \,x^{2}}{16 a^{3}}+\frac{b c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{8 a^{\frac{3}{2}}}-\frac{b^{3} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{5}{2}}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b c}{8 a^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3}}{16 a^{3}}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}{16 a^{3} x^{2}}+\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b}{8 a^{2} x^{4}}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{6 a \,x^{6}}"," ",0,"-1/6*(c*x^4+b*x^2+a)^(3/2)/a/x^6+1/8*b/a^2/x^4*(c*x^4+b*x^2+a)^(3/2)-1/16*b^2/a^3/x^2*(c*x^4+b*x^2+a)^(3/2)+1/16*b^3/a^3*(c*x^4+b*x^2+a)^(1/2)-1/32*b^3/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/16*b^2/a^3*c*(c*x^4+b*x^2+a)^(1/2)*x^2-1/8*b/a^2*c*(c*x^4+b*x^2+a)^(1/2)+1/8*b/a^(3/2)*c*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","B"
928,1,387,139,0.017000," ","int((c*x^4+b*x^2+a)^(1/2)/x^9,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,c^{2} x^{2}}{32 a^{3}}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} c \,x^{2}}{128 a^{4}}+\frac{c^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{16 a^{\frac{3}{2}}}-\frac{3 b^{2} c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{5}{2}}}+\frac{5 b^{4} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{256 a^{\frac{7}{2}}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}{16 a^{2}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} c}{64 a^{3}}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4}}{128 a^{4}}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b c}{32 a^{3} x^{2}}+\frac{5 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b^{3}}{128 a^{4} x^{2}}+\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} c}{16 a^{2} x^{4}}-\frac{5 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}{64 a^{3} x^{4}}+\frac{5 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b}{48 a^{2} x^{6}}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{8 a \,x^{8}}"," ",0,"-1/8*(c*x^4+b*x^2+a)^(3/2)/a/x^8+5/48*b*(c*x^4+b*x^2+a)^(3/2)/a^2/x^6-5/64*b^2/a^3/x^4*(c*x^4+b*x^2+a)^(3/2)+5/128*b^3/a^4/x^2*(c*x^4+b*x^2+a)^(3/2)-5/128*b^4/a^4*(c*x^4+b*x^2+a)^(1/2)+5/256*b^4/a^(7/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-5/128*b^3/a^4*c*(c*x^4+b*x^2+a)^(1/2)*x^2+7/64*b^2/a^3*c*(c*x^4+b*x^2+a)^(1/2)-3/32*b^2/a^(5/2)*c*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/16*c/a^2/x^4*(c*x^4+b*x^2+a)^(3/2)-1/32*c/a^3*b/x^2*(c*x^4+b*x^2+a)^(3/2)+1/32*c^2/a^3*b*(c*x^4+b*x^2+a)^(1/2)*x^2-1/16*c^2/a^2*(c*x^4+b*x^2+a)^(1/2)+1/16*c^2/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","B"
929,1,442,173,0.020000," ","int((c*x^4+b*x^2+a)^(1/2)/x^11,x)","-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} c^{2} x^{2}}{64 a^{4}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4} c \,x^{2}}{256 a^{5}}-\frac{3 b \,c^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{5}{2}}}+\frac{5 b^{3} c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{64 a^{\frac{7}{2}}}-\frac{7 b^{5} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{512 a^{\frac{9}{2}}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,c^{2}}{32 a^{3}}-\frac{13 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} c}{128 a^{4}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{5}}{256 a^{5}}+\frac{3 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b^{2} c}{64 a^{4} x^{2}}-\frac{7 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b^{4}}{256 a^{5} x^{2}}-\frac{3 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b c}{32 a^{3} x^{4}}+\frac{7 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b^{3}}{128 a^{4} x^{4}}+\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} c}{15 a^{2} x^{6}}-\frac{7 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}{96 a^{3} x^{6}}+\frac{7 \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} b}{80 a^{2} x^{8}}-\frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{10 a \,x^{10}}"," ",0,"-1/10*(c*x^4+b*x^2+a)^(3/2)/a/x^10+7/80*b*(c*x^4+b*x^2+a)^(3/2)/a^2/x^8-7/96*b^2/a^3/x^6*(c*x^4+b*x^2+a)^(3/2)+7/128*b^3/a^4/x^4*(c*x^4+b*x^2+a)^(3/2)-7/256*b^4/a^5/x^2*(c*x^4+b*x^2+a)^(3/2)+7/256*b^5/a^5*(c*x^4+b*x^2+a)^(1/2)-7/512*b^5/a^(9/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+7/256*b^4/a^5*c*(c*x^4+b*x^2+a)^(1/2)*x^2-13/128*b^3/a^4*c*(c*x^4+b*x^2+a)^(1/2)+5/64*b^3/a^(7/2)*c*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-3/32*b/a^3*c/x^4*(c*x^4+b*x^2+a)^(3/2)+3/64*b^2/a^4*c/x^2*(c*x^4+b*x^2+a)^(3/2)-3/64*b^2/a^4*c^2*(c*x^4+b*x^2+a)^(1/2)*x^2+3/32*b/a^3*c^2*(c*x^4+b*x^2+a)^(1/2)-3/32*b/a^(5/2)*c^2*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/15*c/a^2/x^6*(c*x^4+b*x^2+a)^(3/2)","B"
930,1,476,383,0.052000," ","int(x^4*(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{5}}{7}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{3}}{35 c}-\frac{\left(\frac{2 a}{7}-\frac{4 b^{2}}{35 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}-\frac{\left(-\frac{3 a b}{35 c}-\frac{2 \left(\frac{2 a}{7}-\frac{4 b^{2}}{35 c}\right) b}{3 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\left(\frac{2 a}{7}-\frac{4 b^{2}}{35 c}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}"," ",0,"1/7*x^5*(c*x^4+b*x^2+a)^(1/2)+1/35*b/c*x^3*(c*x^4+b*x^2+a)^(1/2)+1/3*(2/7*a-4/35*b^2/c)/c*x*(c*x^4+b*x^2+a)^(1/2)-1/12*(2/7*a-4/35*b^2/c)/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-1/2*(-3/35*b/c*a-2/3*(2/7*a-4/35*b^2/c)/c*b)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(-4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2))-EllipticE(1/2*x*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4+2*b*(b+(-4*a*c+b^2)^(1/2))/a/c)^(1/2)))","A"
931,1,417,334,0.010000," ","int(x^2*(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{3}}{5}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{60 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}-\frac{\left(\frac{2 a}{5}-\frac{2 b^{2}}{15 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b x}{15 c}"," ",0,"1/5*x^3*(c*x^4+b*x^2+a)^(1/2)+1/15*b/c*x*(c*x^4+b*x^2+a)^(1/2)-1/60*a*b/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(2/5*a-2/15*b^2/c)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
932,1,379,301,0.011000," ","int((c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{6 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{6 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3}"," ",0,"1/3*x*(c*x^4+b*x^2+a)^(1/2)+1/6*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/6*b*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
933,1,381,301,0.013000," ","int((c*x^4+b*x^2+a)^(1/2)/x^2,x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a c}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{x}"," ",0,"-(c*x^4+b*x^2+a)^(1/2)/x+1/4*b*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
934,1,404,329,0.015000," ","int((c*x^4+b*x^2+a)^(1/2)/x^4,x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) b c}{6 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{6 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{3 a x}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{3 x^{3}}"," ",0,"-1/3*(c*x^4+b*x^2+a)^(1/2)/x^3-1/3*b*(c*x^4+b*x^2+a)^(1/2)/a/x+1/6*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/6*b*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
935,1,452,381,0.019000," ","int((c*x^4+b*x^2+a)^(1/2)/x^6,x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, b c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{60 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, a}-\frac{\left(3 a c -b^{2}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) c}{15 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) a}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{15 a \,x^{3}}-\frac{2 \left(3 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}}{15 a^{2} x}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{5 x^{5}}"," ",0,"-1/5*(c*x^4+b*x^2+a)^(1/2)/x^5-1/15*b*(c*x^4+b*x^2+a)^(1/2)/a/x^3-2/15*(3*a*c-b^2)/a^2*(c*x^4+b*x^2+a)^(1/2)/x-1/60*b*c/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/15*c*(3*a*c-b^2)/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
936,1,534,197,0.035000," ","int(x^7*(c*x^4+b*x^2+a)^(3/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{12}}{14}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{10}}{56}+\frac{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{8}}{35}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} x^{8}}{560 c}+\frac{11 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b \,x^{6}}{1120 c}-\frac{9 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} x^{6}}{4480 c^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} x^{4}}{70 c}-\frac{31 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{2} x^{4}}{2240 c^{2}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4} x^{4}}{1280 c^{3}}-\frac{73 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} b \,x^{2}}{2240 c^{2}}+\frac{13 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{3} x^{2}}{640 c^{3}}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{5} x^{2}}{1024 c^{4}}+\frac{3 a^{3} b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{64 c^{\frac{5}{2}}}-\frac{15 a^{2} b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{256 c^{\frac{7}{2}}}+\frac{21 a \,b^{5} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{1024 c^{\frac{9}{2}}}-\frac{9 b^{7} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4096 c^{\frac{11}{2}}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{3}}{35 c^{2}}+\frac{49 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} b^{2}}{640 c^{3}}-\frac{9 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{4}}{256 c^{4}}+\frac{9 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{6}}{2048 c^{5}}"," ",0,"1/560*b^2*x^8/c*(c*x^4+b*x^2+a)^(1/2)-9/4480*b^3/c^2*x^6*(c*x^4+b*x^2+a)^(1/2)+3/1280*b^4/c^3*x^4*(c*x^4+b*x^2+a)^(1/2)-3/1024*b^5/c^4*x^2*(c*x^4+b*x^2+a)^(1/2)+1/70*a^2*x^4/c*(c*x^4+b*x^2+a)^(1/2)+49/640*a^2*b^2/c^3*(c*x^4+b*x^2+a)^(1/2)+3/64*a^3*b/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-9/256*a*b^4/c^4*(c*x^4+b*x^2+a)^(1/2)+21/1024*a*b^5/c^(9/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-15/256*a^2*b^3/c^(7/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+4/35*a*x^8*(c*x^4+b*x^2+a)^(1/2)+9/2048*b^6/c^5*(c*x^4+b*x^2+a)^(1/2)+1/14*c*x^12*(c*x^4+b*x^2+a)^(1/2)+11/1120*a*b*x^6/c*(c*x^4+b*x^2+a)^(1/2)-31/2240*a*b^2/c^2*x^4*(c*x^4+b*x^2+a)^(1/2)+13/640*a*b^3/c^3*x^2*(c*x^4+b*x^2+a)^(1/2)-73/2240*a^2*b/c^2*x^2*(c*x^4+b*x^2+a)^(1/2)+5/56*b*x^10*(c*x^4+b*x^2+a)^(1/2)-9/4096*b^7/c^(11/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/35*a^3/c^2*(c*x^4+b*x^2+a)^(1/2)","B"
937,1,432,178,0.024000," ","int(x^5*(c*x^4+b*x^2+a)^(3/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{10}}{12}+\frac{13 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{8}}{120}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{6}}{48}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} x^{6}}{320 c}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b \,x^{4}}{160 c}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} x^{4}}{1920 c^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} x^{2}}{32 c}-\frac{9 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{2} x^{2}}{320 c^{2}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4} x^{2}}{1536 c^{3}}-\frac{a^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}}}+\frac{9 a^{2} b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{128 c^{\frac{5}{2}}}-\frac{15 a \,b^{4} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{512 c^{\frac{7}{2}}}+\frac{7 b^{6} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2048 c^{\frac{9}{2}}}-\frac{27 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} b}{320 c^{2}}+\frac{19 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{3}}{384 c^{3}}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{5}}{1024 c^{4}}"," ",0,"7/1536*b^4/c^3*x^2*(c*x^4+b*x^2+a)^(1/2)+1/320*b^2*x^6/c*(c*x^4+b*x^2+a)^(1/2)-7/1920*b^3/c^2*x^4*(c*x^4+b*x^2+a)^(1/2)+1/32*a^2*x^2/c*(c*x^4+b*x^2+a)^(1/2)-15/512*a*b^4/c^(7/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+9/128*a^2*b^2/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-27/320*a^2*b/c^2*(c*x^4+b*x^2+a)^(1/2)+19/384*a*b^3/c^3*(c*x^4+b*x^2+a)^(1/2)+13/120*b*x^8*(c*x^4+b*x^2+a)^(1/2)+3/160*a*b*x^4/c*(c*x^4+b*x^2+a)^(1/2)-9/320*a*b^2/c^2*x^2*(c*x^4+b*x^2+a)^(1/2)-1/32*a^3/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/12*c*x^10*(c*x^4+b*x^2+a)^(1/2)+7/48*a*x^6*(c*x^4+b*x^2+a)^(1/2)-7/1024*b^5/c^4*(c*x^4+b*x^2+a)^(1/2)+7/2048*b^6/c^(9/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","B"
938,1,316,128,0.020000," ","int(x^3*(c*x^4+b*x^2+a)^(3/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{8}}{10}+\frac{11 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{6}}{80}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{4}}{5}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} x^{4}}{160 c}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b \,x^{2}}{160 c}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} x^{2}}{128 c^{2}}-\frac{3 a^{2} b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}}}+\frac{3 a \,b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{64 c^{\frac{5}{2}}}-\frac{3 b^{5} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{512 c^{\frac{7}{2}}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2}}{10 c}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,b^{2}}{64 c^{2}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4}}{256 c^{3}}"," ",0,"1/160*b^2*x^4/c*(c*x^4+b*x^2+a)^(1/2)-1/128*b^3/c^2*x^2*(c*x^4+b*x^2+a)^(1/2)+3/64*a*b^3/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-3/32*a^2*b/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-5/64*a*b^2/c^2*(c*x^4+b*x^2+a)^(1/2)+7/160*a*b*x^2/c*(c*x^4+b*x^2+a)^(1/2)+1/10*c*x^8*(c*x^4+b*x^2+a)^(1/2)+1/5*a*x^4*(c*x^4+b*x^2+a)^(1/2)+3/256*b^4/c^3*(c*x^4+b*x^2+a)^(1/2)-3/512*b^5/c^(7/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/10*a^2/c*(c*x^4+b*x^2+a)^(1/2)+11/80*b*x^6*(c*x^4+b*x^2+a)^(1/2)","B"
939,1,242,106,0.015000," ","int(x*(c*x^4+b*x^2+a)^(3/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{6}}{8}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{4}}{16}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{2}}{16}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} x^{2}}{64 c}+\frac{3 a^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 \sqrt{c}}-\frac{3 a \,b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}}}+\frac{3 b^{4} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{256 c^{\frac{5}{2}}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a b}{32 c}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3}}{128 c^{2}}"," ",0,"5/16*a*x^2*(c*x^4+b*x^2+a)^(1/2)-3/128*b^3/c^2*(c*x^4+b*x^2+a)^(1/2)+3/256*b^4/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/64*b^2*x^2/c*(c*x^4+b*x^2+a)^(1/2)+5/32*a*b/c*(c*x^4+b*x^2+a)^(1/2)-3/32*a*b^2/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/16*a^2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+3/16*b*x^4*(c*x^4+b*x^2+a)^(1/2)+1/8*c*x^6*(c*x^4+b*x^2+a)^(1/2)","B"
940,1,192,127,0.019000," ","int((c*x^4+b*x^2+a)^(3/2)/x,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{4}}{6}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{2}}{24}-\frac{a^{\frac{3}{2}} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{3 a b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{8 \sqrt{c}}-\frac{b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{3}{2}}}+\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{3}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{16 c}"," ",0,"1/6*c*x^4*(c*x^4+b*x^2+a)^(1/2)+7/24*b*x^2*(c*x^4+b*x^2+a)^(1/2)+1/16/c*b^2*(c*x^4+b*x^2+a)^(1/2)-1/32/c^(3/2)*b^3*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/8*a*b*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+2/3*a*(c*x^4+b*x^2+a)^(1/2)-1/2*a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
941,1,170,122,0.019000," ","int((c*x^4+b*x^2+a)^(3/2)/x^3,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{2}}{4}+\frac{3 a \sqrt{c}\, \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4}-\frac{3 \sqrt{a}\, b \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4}+\frac{3 b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 \sqrt{c}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{8}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{2 x^{2}}"," ",0,"1/4*c*x^2*(c*x^4+b*x^2+a)^(1/2)+5/8*b*(c*x^4+b*x^2+a)^(1/2)+3/16*b^2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)+3/4*a*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/2*a/x^2*(c*x^4+b*x^2+a)^(1/2)-3/4*a^(1/2)*b*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
942,1,174,123,0.018000," ","int((c*x^4+b*x^2+a)^(3/2)/x^5,x)","-\frac{3 \sqrt{a}\, c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4}-\frac{3 b^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{16 \sqrt{a}}+\frac{3 b \sqrt{c}\, \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c}{2}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{8 x^{2}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{4 x^{4}}"," ",0,"1/2*c*(c*x^4+b*x^2+a)^(1/2)+3/4*b*c^(1/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/4*a/x^4*(c*x^4+b*x^2+a)^(1/2)-5/8*b/x^2*(c*x^4+b*x^2+a)^(1/2)-3/16/a^(1/2)*b^2*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-3/4*a^(1/2)*c*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
943,1,202,135,0.019000," ","int((c*x^4+b*x^2+a)^(3/2)/x^7,x)","-\frac{3 b c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{8 \sqrt{a}}+\frac{b^{3} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{3}{2}}}+\frac{c^{\frac{3}{2}} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{16 a \,x^{2}}-\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}{3 x^{2}}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{24 x^{4}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{6 x^{6}}"," ",0,"1/2*c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-7/24*b/x^4*(c*x^4+b*x^2+a)^(1/2)-1/16/a*b^2/x^2*(c*x^4+b*x^2+a)^(1/2)+1/32/a^(3/2)*b^3*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-3/8*b*c/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-2/3*c/x^2*(c*x^4+b*x^2+a)^(1/2)-1/6*a/x^6*(c*x^4+b*x^2+a)^(1/2)","A"
944,1,260,115,0.020000," ","int((c*x^4+b*x^2+a)^(3/2)/x^9,x)","-\frac{3 c^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{16 \sqrt{a}}+\frac{3 b^{2} c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{3}{2}}}-\frac{3 b^{4} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{256 a^{\frac{5}{2}}}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b c}{32 a \,x^{2}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3}}{128 a^{2} x^{2}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{64 a \,x^{4}}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}{16 x^{4}}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{16 x^{6}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{8 x^{8}}"," ",0,"-1/64*b^2/a/x^4*(c*x^4+b*x^2+a)^(1/2)+3/128*b^3/a^2/x^2*(c*x^4+b*x^2+a)^(1/2)-3/16*c^2/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-5/16*c/x^4*(c*x^4+b*x^2+a)^(1/2)-3/256*b^4/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/8*a/x^8*(c*x^4+b*x^2+a)^(1/2)-5/32/a*c*b/x^2*(c*x^4+b*x^2+a)^(1/2)+3/32/a^(3/2)*c*b^2*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-3/16*b/x^6*(c*x^4+b*x^2+a)^(1/2)","B"
945,1,337,140,0.024000," ","int((c*x^4+b*x^2+a)^(3/2)/x^11,x)","\frac{3 b \,c^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{3}{2}}}-\frac{3 b^{3} c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{64 a^{\frac{5}{2}}}+\frac{3 b^{5} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{512 a^{\frac{7}{2}}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}{10 a \,x^{2}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} c}{64 a^{2} x^{2}}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4}}{256 a^{3} x^{2}}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b c}{160 a \,x^{4}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3}}{128 a^{2} x^{4}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{160 a \,x^{6}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c}{5 x^{6}}-\frac{11 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{80 x^{8}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{10 x^{10}}"," ",0,"-1/160/a*b^2/x^6*(c*x^4+b*x^2+a)^(1/2)+1/128/a^2*b^3/x^4*(c*x^4+b*x^2+a)^(1/2)-3/256/a^3*b^4/x^2*(c*x^4+b*x^2+a)^(1/2)+3/512/a^(7/2)*b^5*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/10/a*c^2/x^2*(c*x^4+b*x^2+a)^(1/2)+3/32*b*c^2/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-3/64*b^3*c/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-7/160*b*c/a/x^4*(c*x^4+b*x^2+a)^(1/2)+5/64*b^2*c/a^2/x^2*(c*x^4+b*x^2+a)^(1/2)-1/10*a/x^10*(c*x^4+b*x^2+a)^(1/2)-11/80*b/x^8*(c*x^4+b*x^2+a)^(1/2)-1/5*c/x^6*(c*x^4+b*x^2+a)^(1/2)","B"
946,1,457,190,0.027000," ","int((c*x^4+b*x^2+a)^(3/2)/x^13,x)","\frac{c^{3} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{3}{2}}}-\frac{9 b^{2} c^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{128 a^{\frac{5}{2}}}+\frac{15 b^{4} c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{512 a^{\frac{7}{2}}}-\frac{7 b^{6} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2048 a^{\frac{9}{2}}}+\frac{27 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,c^{2}}{320 a^{2} x^{2}}-\frac{19 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3} c}{384 a^{3} x^{2}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{5}}{1024 a^{4} x^{2}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}{32 a \,x^{4}}+\frac{9 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2} c}{320 a^{2} x^{4}}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{4}}{1536 a^{3} x^{4}}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b c}{160 a \,x^{6}}+\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{3}}{1920 a^{2} x^{6}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{320 a \,x^{8}}-\frac{7 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}{48 x^{8}}-\frac{13 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{120 x^{10}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{12 x^{12}}"," ",0,"-1/320/a*b^2/x^8*(c*x^4+b*x^2+a)^(1/2)+7/1920/a^2*b^3/x^6*(c*x^4+b*x^2+a)^(1/2)-7/1536/a^3*b^4/x^4*(c*x^4+b*x^2+a)^(1/2)+7/1024/a^4*b^5/x^2*(c*x^4+b*x^2+a)^(1/2)-7/2048/a^(9/2)*b^6*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-9/128*c^2*b^2/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-1/32*c^2/a/x^4*(c*x^4+b*x^2+a)^(1/2)-1/12*a/x^12*(c*x^4+b*x^2+a)^(1/2)-7/48*c/x^8*(c*x^4+b*x^2+a)^(1/2)-13/120*b/x^10*(c*x^4+b*x^2+a)^(1/2)+1/32*c^3/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+27/320*c^2*b/a^2/x^2*(c*x^4+b*x^2+a)^(1/2)+15/512/a^(7/2)*b^4*c*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-19/384/a^3*b^3*c/x^2*(c*x^4+b*x^2+a)^(1/2)+9/320/a^2*b^2*c/x^4*(c*x^4+b*x^2+a)^(1/2)-3/160/a*b*c/x^6*(c*x^4+b*x^2+a)^(1/2)","B"
947,1,674,479,0.011000," ","int(x^4*(c*x^4+b*x^2+a)^(3/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{9}}{11}+\frac{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{7}}{33}+\frac{\left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{5}}{7 c}+\frac{\left(\frac{38 a b}{33}-\frac{6 \left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) b}{7 c}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{3}}{5 c}-\frac{\left(a^{2}-\frac{5 \left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) a}{7 c}-\frac{4 \left(\frac{38 a b}{33}-\frac{6 \left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) b}{7 c}\right) b}{5 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}-\frac{\left(-\frac{3 \left(\frac{38 a b}{33}-\frac{6 \left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) b}{7 c}\right) a}{5 c}-\frac{2 \left(a^{2}-\frac{5 \left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) a}{7 c}-\frac{4 \left(\frac{38 a b}{33}-\frac{6 \left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) b}{7 c}\right) b}{5 c}\right) b}{3 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\left(a^{2}-\frac{5 \left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) a}{7 c}-\frac{4 \left(\frac{38 a b}{33}-\frac{6 \left(\frac{13 a c}{11}+\frac{b^{2}}{33}\right) b}{7 c}\right) b}{5 c}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}"," ",0,"1/11*c*x^9*(c*x^4+b*x^2+a)^(1/2)+4/33*b*x^7*(c*x^4+b*x^2+a)^(1/2)+1/7*(13/11*a*c+1/33*b^2)/c*x^5*(c*x^4+b*x^2+a)^(1/2)+1/5*(38/33*a*b-6/7*(13/11*a*c+1/33*b^2)/c*b)/c*x^3*(c*x^4+b*x^2+a)^(1/2)+1/3*(a^2-5/7*(13/11*a*c+1/33*b^2)/c*a-4/5*(38/33*a*b-6/7*(13/11*a*c+1/33*b^2)/c*b)/c*b)/c*x*(c*x^4+b*x^2+a)^(1/2)-1/12*(a^2-5/7*(13/11*a*c+1/33*b^2)/c*a-4/5*(38/33*a*b-6/7*(13/11*a*c+1/33*b^2)/c*b)/c*b)/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(-3/5*(38/33*a*b-6/7*(13/11*a*c+1/33*b^2)/c*b)/c*a-2/3*(a^2-5/7*(13/11*a*c+1/33*b^2)/c*a-4/5*(38/33*a*b-6/7*(13/11*a*c+1/33*b^2)/c*b)/c*b)/c*b)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
948,1,545,431,0.010000," ","int(x^2*(c*x^4+b*x^2+a)^(3/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{7}}{9}+\frac{10 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{5}}{63}+\frac{\left(\frac{11 a c}{9}+\frac{b^{2}}{21}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{3}}{5 c}-\frac{\left(\frac{76 a b}{63}-\frac{4 \left(\frac{11 a c}{9}+\frac{b^{2}}{21}\right) b}{5 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}-\frac{\left(a^{2}-\frac{3 \left(\frac{11 a c}{9}+\frac{b^{2}}{21}\right) a}{5 c}-\frac{2 \left(\frac{76 a b}{63}-\frac{4 \left(\frac{11 a c}{9}+\frac{b^{2}}{21}\right) b}{5 c}\right) b}{3 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\left(\frac{76 a b}{63}-\frac{4 \left(\frac{11 a c}{9}+\frac{b^{2}}{21}\right) b}{5 c}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}"," ",0,"1/9*c*x^7*(c*x^4+b*x^2+a)^(1/2)+10/63*b*x^5*(c*x^4+b*x^2+a)^(1/2)+1/5*(11/9*a*c+1/21*b^2)/c*x^3*(c*x^4+b*x^2+a)^(1/2)+1/3*(76/63*a*b-4/5*(11/9*a*c+1/21*b^2)/c*b)/c*x*(c*x^4+b*x^2+a)^(1/2)-1/12*(76/63*a*b-4/5*(11/9*a*c+1/21*b^2)/c*b)/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(a^2-3/5*(11/9*a*c+1/21*b^2)/c*a-2/3*(76/63*a*b-4/5*(11/9*a*c+1/21*b^2)/c*b)/c*b)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
949,1,471,369,0.009000," ","int((c*x^4+b*x^2+a)^(3/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{5}}{7}+\frac{8 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{3}}{35}-\frac{\left(\frac{46 a b}{35}-\frac{2 \left(\frac{9 a c}{7}+\frac{3 b^{2}}{35}\right) b}{3 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\left(a^{2}-\frac{\left(\frac{9 a c}{7}+\frac{3 b^{2}}{35}\right) a}{3 c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\frac{\left(\frac{9 a c}{7}+\frac{3 b^{2}}{35}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}"," ",0,"1/7*c*x^5*(c*x^4+b*x^2+a)^(1/2)+8/35*b*x^3*(c*x^4+b*x^2+a)^(1/2)+1/3*(9/7*a*c+3/35*b^2)/c*x*(c*x^4+b*x^2+a)^(1/2)+1/4*(a^2-1/3*(9/7*a*c+3/35*b^2)/c*a)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(46/35*a*b-2/3*(9/7*a*c+3/35*b^2)/c*b)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
950,1,430,351,0.015000," ","int((c*x^4+b*x^2+a)^(3/2)/x^2,x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c \,x^{3}}{5}+\frac{2 \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{5 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b x}{5}-\frac{\left(\frac{12 a c}{5}+\frac{b^{2}}{5}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{x}"," ",0,"-a*(c*x^4+b*x^2+a)^(1/2)/x+1/5*c*x^3*(c*x^4+b*x^2+a)^(1/2)+2/5*b*x*(c*x^4+b*x^2+a)^(1/2)+2/5*a*b*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(12/5*a*c+1/5*b^2)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
951,1,428,341,0.015000," ","int((c*x^4+b*x^2+a)^(3/2)/x^4,x)","-\frac{4 \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b c}{3 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c x}{3}+\frac{\left(\frac{4 a c}{3}+b^{2}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{3 x}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{3 x^{3}}"," ",0,"-1/3*a*(c*x^4+b*x^2+a)^(1/2)/x^3-4/3*b*(c*x^4+b*x^2+a)^(1/2)/x+1/3*c*x*(c*x^4+b*x^2+a)^(1/2)+1/4*(4/3*a*c+b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-4/3*b*c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
952,1,450,384,0.018000," ","int((c*x^4+b*x^2+a)^(3/2)/x^6,x)","\frac{2 \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, b c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{5 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{\left(c^{2}+\frac{\left(7 a c +b^{2}\right) c}{5 a}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{\left(7 a c +b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}}{5 a x}-\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{5 x^{3}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{5 x^{5}}"," ",0,"-1/5*a*(c*x^4+b*x^2+a)^(1/2)/x^5-2/5*b*(c*x^4+b*x^2+a)^(1/2)/x^3-1/5*(7*a*c+b^2)/a*(c*x^4+b*x^2+a)^(1/2)/x+2/5*b*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(c^2+1/5*c*(7*a*c+b^2)/a)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
953,1,495,427,0.021000," ","int((c*x^4+b*x^2+a)^(3/2)/x^8,x)","-\frac{\left(8 a c -b^{2}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) b c}{35 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) a}+\frac{\left(c^{2}-\frac{\left(15 a c +b^{2}\right) c}{35 a}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{2 \left(8 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{35 a^{2} x}-\frac{\left(15 a c +b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}}{35 a \,x^{3}}-\frac{8 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{35 x^{5}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{7 x^{7}}"," ",0,"-1/7*a*(c*x^4+b*x^2+a)^(1/2)/x^7-8/35*b*(c*x^4+b*x^2+a)^(1/2)/x^5-1/35*(15*a*c+b^2)/a*(c*x^4+b*x^2+a)^(1/2)/x^3-2/35*b*(8*a*c-b^2)/a^2*(c*x^4+b*x^2+a)^(1/2)/x+1/4*(c^2-1/35*c*(15*a*c+b^2)/a)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/35*b*c*(8*a*c-b^2)/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
954,1,114,44,0.016000," ","int((-x^4-2*x^2+3)^(1/2),x)","\frac{\sqrt{-x^{4}-2 x^{2}+3}\, x}{3}+\frac{2 \sqrt{-x^{2}+1}\, \sqrt{3 x^{2}+9}\, \EllipticF \left(x , \frac{i \sqrt{3}}{3}\right)}{3 \sqrt{-x^{4}-2 x^{2}+3}}+\frac{2 \sqrt{-x^{2}+1}\, \sqrt{3 x^{2}+9}\, \left(-\EllipticE \left(x , \frac{i \sqrt{3}}{3}\right)+\EllipticF \left(x , \frac{i \sqrt{3}}{3}\right)\right)}{3 \sqrt{-x^{4}-2 x^{2}+3}}"," ",0,"1/3*x*(-x^4-2*x^2+3)^(1/2)+2/3*(-x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-x^4-2*x^2+3)^(1/2)*EllipticF(x,1/3*I*3^(1/2))+2/3*(-x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-x^4-2*x^2+3)^(1/2)*(EllipticF(x,1/3*I*3^(1/2))-EllipticE(x,1/3*I*3^(1/2)))","B"
955,1,162,103,0.017000," ","int(x^7/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{4}}{6 c}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{2}}{24 c^{2}}+\frac{3 a b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{8 c^{\frac{5}{2}}}-\frac{5 b^{3} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{32 c^{\frac{7}{2}}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, a}{3 c^{2}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{16 c^{3}}"," ",0,"1/6*x^4*(c*x^4+b*x^2+a)^(1/2)/c-5/24*b/c^2*x^2*(c*x^4+b*x^2+a)^(1/2)+5/16*b^2/c^3*(c*x^4+b*x^2+a)^(1/2)-5/32*b^3/c^(7/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+3/8*b/c^(5/2)*a*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/3*a/c^2*(c*x^4+b*x^2+a)^(1/2)","A"
956,1,116,86,0.014000," ","int(x^5/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{2}}{4 c}-\frac{a \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{3}{2}}}+\frac{3 b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 c^{\frac{5}{2}}}-\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{8 c^{2}}"," ",0,"1/4*x^2*(c*x^4+b*x^2+a)^(1/2)/c-3/8*b*(c*x^4+b*x^2+a)^(1/2)/c^2+3/16*b^2/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-1/4*a/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","A"
957,1,56,54,0.011000," ","int(x^3/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{3}{2}}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{2 c}"," ",0,"1/2*(c*x^4+b*x^2+a)^(1/2)/c-1/4*b/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","A"
958,1,35,33,0.009000," ","int(x/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 \sqrt{c}}"," ",0,"1/2*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))/c^(1/2)","A"
959,1,39,34,0.011000," ","int(1/x/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{a}}"," ",0,"-1/2/a^(1/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
960,1,63,58,0.013000," ","int(1/x^3/(c*x^4+b*x^2+a)^(1/2),x)","\frac{b \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4 a^{\frac{3}{2}}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{2 a \,x^{2}}"," ",0,"-1/2*(c*x^4+b*x^2+a)^(1/2)/a/x^2+1/4*b/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
961,1,127,90,0.014000," ","int(1/x^5/(c*x^4+b*x^2+a)^(1/2),x)","\frac{c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4 a^{\frac{3}{2}}}-\frac{3 b^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{16 a^{\frac{5}{2}}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{8 a^{2} x^{2}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{4 a \,x^{4}}"," ",0,"-1/4*(c*x^4+b*x^2+a)^(1/2)/a/x^4+3/8*b*(c*x^4+b*x^2+a)^(1/2)/a^2/x^2-3/16*b^2/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/4*c/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
962,1,176,123,0.016000," ","int(1/x^7/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{3 b c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{8 a^{\frac{5}{2}}}+\frac{5 b^{3} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{7}{2}}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c}{3 a^{2} x^{2}}-\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b^{2}}{16 a^{3} x^{2}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{24 a^{2} x^{4}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{6 a \,x^{6}}"," ",0,"-1/6*(c*x^4+b*x^2+a)^(1/2)/a/x^6+5/24*b*(c*x^4+b*x^2+a)^(1/2)/a^2/x^4-5/16*b^2/a^3/x^2*(c*x^4+b*x^2+a)^(1/2)+5/32*b^3/a^(7/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-3/8*b/a^(5/2)*c*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+1/3*c/a^2/x^2*(c*x^4+b*x^2+a)^(1/2)","A"
963,1,388,305,0.011000," ","int(x^4/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{3 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) c}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}"," ",0,"1/3*x*(c*x^4+b*x^2+a)^(1/2)/c-1/12/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/3*b/c*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
964,1,216,271,0.009000," ","int(x^2/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}"," ",0,"-1/2*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
965,1,144,119,0.007000," ","int(1/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}"," ",0,"1/4*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
966,1,239,296,0.013000," ","int(1/x^2/(c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) c}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{a x}"," ",0,"-(c*x^4+b*x^2+a)^(1/2)/a/x-1/2*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
967,1,413,333,0.015000," ","int(1/x^4/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) b c}{3 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) a}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, a}+\frac{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b}{3 a^{2} x}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{3 a \,x^{3}}"," ",0,"-1/3*(c*x^4+b*x^2+a)^(1/2)/a/x^3+2/3*b*(c*x^4+b*x^2+a)^(1/2)/a^2/x-1/12*c/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/3*b*c/a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
968,1,168,106,0.022000," ","int(x^7/(-c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, x^{4}}{6 c}-\frac{5 \sqrt{-c \,x^{4}+b \,x^{2}+a}\, b \,x^{2}}{24 c^{2}}+\frac{3 a b \arctan \left(\frac{\left(x^{2}-\frac{b}{2 c}\right) \sqrt{c}}{\sqrt{-c \,x^{4}+b \,x^{2}+a}}\right)}{8 c^{\frac{5}{2}}}+\frac{5 b^{3} \arctan \left(\frac{\left(x^{2}-\frac{b}{2 c}\right) \sqrt{c}}{\sqrt{-c \,x^{4}+b \,x^{2}+a}}\right)}{32 c^{\frac{7}{2}}}-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, a}{3 c^{2}}-\frac{5 \sqrt{-c \,x^{4}+b \,x^{2}+a}\, b^{2}}{16 c^{3}}"," ",0,"-1/6*x^4*(-c*x^4+b*x^2+a)^(1/2)/c-5/24*b/c^2*x^2*(-c*x^4+b*x^2+a)^(1/2)-5/16*b^2/c^3*(-c*x^4+b*x^2+a)^(1/2)+5/32*b^3/c^(7/2)*arctan(c^(1/2)*(x^2-1/2*b/c)/(-c*x^4+b*x^2+a)^(1/2))+3/8*b/c^(5/2)*a*arctan(c^(1/2)*(x^2-1/2*b/c)/(-c*x^4+b*x^2+a)^(1/2))-1/3/c^2*a*(-c*x^4+b*x^2+a)^(1/2)","A"
969,1,120,89,0.017000," ","int(x^5/(-c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, x^{2}}{4 c}+\frac{a \arctan \left(\frac{\left(x^{2}-\frac{b}{2 c}\right) \sqrt{c}}{\sqrt{-c \,x^{4}+b \,x^{2}+a}}\right)}{4 c^{\frac{3}{2}}}+\frac{3 b^{2} \arctan \left(\frac{\left(x^{2}-\frac{b}{2 c}\right) \sqrt{c}}{\sqrt{-c \,x^{4}+b \,x^{2}+a}}\right)}{16 c^{\frac{5}{2}}}-\frac{3 \sqrt{-c \,x^{4}+b \,x^{2}+a}\, b}{8 c^{2}}"," ",0,"-1/4*x^2*(-c*x^4+b*x^2+a)^(1/2)/c-3/8*b*(-c*x^4+b*x^2+a)^(1/2)/c^2+3/16*b^2/c^(5/2)*arctan((x^2-1/2*b/c)/(-c*x^4+b*x^2+a)^(1/2)*c^(1/2))+1/4*a/c^(3/2)*arctan((x^2-1/2*b/c)/(-c*x^4+b*x^2+a)^(1/2)*c^(1/2))","A"
970,1,58,56,0.014000," ","int(x^3/(-c*x^4+b*x^2+a)^(1/2),x)","\frac{b \arctan \left(\frac{\left(x^{2}-\frac{b}{2 c}\right) \sqrt{c}}{\sqrt{-c \,x^{4}+b \,x^{2}+a}}\right)}{4 c^{\frac{3}{2}}}-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}}{2 c}"," ",0,"-1/2*(-c*x^4+b*x^2+a)^(1/2)/c+1/4*b/c^(3/2)*arctan((x^2-1/2*b/c)/(-c*x^4+b*x^2+a)^(1/2)*c^(1/2))","A"
971,1,36,34,0.010000," ","int(x/(-c*x^4+b*x^2+a)^(1/2),x)","\frac{\arctan \left(\frac{\left(x^{2}-\frac{b}{2 c}\right) \sqrt{c}}{\sqrt{-c \,x^{4}+b \,x^{2}+a}}\right)}{2 \sqrt{c}}"," ",0,"1/2/c^(1/2)*arctan((x^2-1/2*b/c)/(-c*x^4+b*x^2+a)^(1/2)*c^(1/2))","A"
972,1,45,37,0.016000," ","int(1/x/(c*x^4+b*x^2-a)^(1/2),x)","-\frac{\ln \left(\frac{b \,x^{2}-2 a +2 \sqrt{-a}\, \sqrt{c \,x^{4}+b \,x^{2}-a}}{x^{2}}\right)}{2 \sqrt{-a}}"," ",0,"-1/2/(-a)^(1/2)*ln((-2*a+b*x^2+2*(-a)^(1/2)*(c*x^4+b*x^2-a)^(1/2))/x^2)","A"
973,1,74,63,0.012000," ","int(1/x^3/(c*x^4+b*x^2-a)^(1/2),x)","-\frac{b \ln \left(\frac{b \,x^{2}-2 a +2 \sqrt{-a}\, \sqrt{c \,x^{4}+b \,x^{2}-a}}{x^{2}}\right)}{4 \sqrt{-a}\, a}+\frac{\sqrt{c \,x^{4}+b \,x^{2}-a}}{2 a \,x^{2}}"," ",0,"1/2*(c*x^4+b*x^2-a)^(1/2)/a/x^2-1/4*b/a/(-a)^(1/2)*ln((b*x^2-2*a+2*(-a)^(1/2)*(c*x^4+b*x^2-a)^(1/2))/x^2)","A"
974,1,149,97,0.014000," ","int(1/x^5/(c*x^4+b*x^2-a)^(1/2),x)","-\frac{c \ln \left(\frac{b \,x^{2}-2 a +2 \sqrt{-a}\, \sqrt{c \,x^{4}+b \,x^{2}-a}}{x^{2}}\right)}{4 \sqrt{-a}\, a}-\frac{3 b^{2} \ln \left(\frac{b \,x^{2}-2 a +2 \sqrt{-a}\, \sqrt{c \,x^{4}+b \,x^{2}-a}}{x^{2}}\right)}{16 \sqrt{-a}\, a^{2}}+\frac{3 \sqrt{c \,x^{4}+b \,x^{2}-a}\, b}{8 a^{2} x^{2}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}-a}}{4 a \,x^{4}}"," ",0,"1/4*(c*x^4+b*x^2-a)^(1/2)/a/x^4+3/8*b*(c*x^4+b*x^2-a)^(1/2)/a^2/x^2-3/16*b^2/a^2/(-a)^(1/2)*ln((b*x^2-2*a+2*(-a)^(1/2)*(c*x^4+b*x^2-a)^(1/2))/x^2)-1/4*c/a/(-a)^(1/2)*ln((b*x^2-2*a+2*(-a)^(1/2)*(c*x^4+b*x^2-a)^(1/2))/x^2)","A"
975,1,202,132,0.018000," ","int(1/x^7/(c*x^4+b*x^2-a)^(1/2),x)","-\frac{3 b c \ln \left(\frac{b \,x^{2}-2 a +2 \sqrt{-a}\, \sqrt{c \,x^{4}+b \,x^{2}-a}}{x^{2}}\right)}{8 \sqrt{-a}\, a^{2}}-\frac{5 b^{3} \ln \left(\frac{b \,x^{2}-2 a +2 \sqrt{-a}\, \sqrt{c \,x^{4}+b \,x^{2}-a}}{x^{2}}\right)}{32 \sqrt{-a}\, a^{3}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}-a}\, c}{3 a^{2} x^{2}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}-a}\, b^{2}}{16 a^{3} x^{2}}+\frac{5 \sqrt{c \,x^{4}+b \,x^{2}-a}\, b}{24 a^{2} x^{4}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}-a}}{6 a \,x^{6}}"," ",0,"1/6*(c*x^4+b*x^2-a)^(1/2)/a/x^6+5/24*b*(c*x^4+b*x^2-a)^(1/2)/a^2/x^4+5/16*b^2/a^3/x^2*(c*x^4+b*x^2-a)^(1/2)-5/32*b^3/a^3/(-a)^(1/2)*ln((b*x^2-2*a+2*(-a)^(1/2)*(c*x^4+b*x^2-a)^(1/2))/x^2)-3/8*b/a^2*c/(-a)^(1/2)*ln((b*x^2-2*a+2*(-a)^(1/2)*(c*x^4+b*x^2-a)^(1/2))/x^2)+1/3*c/a^2/x^2*(c*x^4+b*x^2-a)^(1/2)","A"
976,1,391,339,0.052000," ","int(x^4/(-c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{3 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right) c}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, c}-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, x}{3 c}"," ",0,"-1/3*x*(-c*x^4+b*x^2+a)^(1/2)/c+1/12/c*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*x*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4-2*b*(b+(4*a*c+b^2)^(1/2))/a/c)^(1/2))-1/3*b/c*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(4-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)*(4+2*(b+(4*a*c+b^2)^(1/2))/a*x^2)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*x*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4-2*b*(b+(4*a*c+b^2)^(1/2))/a/c)^(1/2))-EllipticE(1/2*x*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2),1/2*(-4-2*b*(b+(4*a*c+b^2)^(1/2))/a/c)^(1/2)))","A"
977,1,217,311,0.011000," ","int(x^2/(-c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right)}"," ",0,"-1/2*a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
978,1,145,141,0.007000," ","int(1/(-c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}}"," ",0,"1/4*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))","A"
979,1,241,340,0.013000," ","int(1/x^2/(-c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) c}{2 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right)}-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}}{a x}"," ",0,"-(-c*x^4+b*x^2+a)^(1/2)/a/x+1/2*c*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
980,1,417,371,0.015000," ","int(1/x^4/(-c*x^4+b*x^2+a)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) b c}{3 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{4 a c +b^{2}}\right) a}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) x^{2}}{a}+4}\, c \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{-\frac{2 \left(b +\sqrt{4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{12 \sqrt{\frac{-b +\sqrt{4 a c +b^{2}}}{a}}\, \sqrt{-c \,x^{4}+b \,x^{2}+a}\, a}+\frac{2 \sqrt{-c \,x^{4}+b \,x^{2}+a}\, b}{3 a^{2} x}-\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}}{3 a \,x^{3}}"," ",0,"-1/3*(-c*x^4+b*x^2+a)^(1/2)/a/x^3+2/3*b*(-c*x^4+b*x^2+a)^(1/2)/a^2/x+1/12*c/a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/3*b*c/a*2^(1/2)/((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(-c*x^4+b*x^2+a)^(1/2)/(b+(4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(-2*(b+(4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
981,1,354,172,0.020000," ","int(x^9/(c*x^4+b*x^2+a)^(3/2),x)","\frac{x^{6}}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}-\frac{13 a \,b^{2} x^{2}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}+\frac{15 b^{4} x^{2}}{16 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{3}}-\frac{5 b \,x^{4}}{8 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{13 a \,b^{3}}{8 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{3}}+\frac{3 a \,x^{2}}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}+\frac{15 b^{5}}{32 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{4}}-\frac{15 b^{2} x^{2}}{16 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{3}}-\frac{3 a \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{5}{2}}}+\frac{15 b^{2} \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{16 c^{\frac{7}{2}}}-\frac{13 a b}{8 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{3}}+\frac{15 b^{3}}{32 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{4}}"," ",0,"1/4*x^6/c/(c*x^4+b*x^2+a)^(1/2)-5/8*b/c^2*x^4/(c*x^4+b*x^2+a)^(1/2)-15/16*b^2/c^3*x^2/(c*x^4+b*x^2+a)^(1/2)+15/32*b^3/c^4/(c*x^4+b*x^2+a)^(1/2)+15/16*b^4/c^3/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2+15/32*b^5/c^4/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)+15/16*b^2/c^(7/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))-13/8*b/c^3*a/(c*x^4+b*x^2+a)^(1/2)-13/4*b^2/c^2*a/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2-13/8*b^3/c^3*a/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)+3/4/c^2*a*x^2/(c*x^4+b*x^2+a)^(1/2)-3/4/c^(5/2)*a*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","B"
982,1,264,118,0.015000," ","int(x^7/(c*x^4+b*x^2+a)^(3/2),x)","\frac{2 a b \,x^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}-\frac{3 b^{3} x^{2}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}+\frac{x^{4}}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}+\frac{a \,b^{2}}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{3 b^{4}}{8 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{3}}+\frac{3 b \,x^{2}}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{3 b \ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{4 c^{\frac{5}{2}}}+\frac{a}{\sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{3 b^{2}}{8 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{3}}"," ",0,"1/2*x^4/c/(c*x^4+b*x^2+a)^(1/2)+3/4*b/c^2*x^2/(c*x^4+b*x^2+a)^(1/2)-3/8*b^2/c^3/(c*x^4+b*x^2+a)^(1/2)-3/4*b^3/c^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2-3/8*b^4/c^3/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)-3/4*b/c^(5/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))+1/c^2*a/(c*x^4+b*x^2+a)^(1/2)+2/c*a*b/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2+1/c^2*a*b^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)","B"
983,1,149,101,0.016000," ","int(x^5/(c*x^4+b*x^2+a)^(3/2),x)","\frac{b^{2} x^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}+\frac{b^{3}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{x^{2}}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}+\frac{\ln \left(\frac{c \,x^{2}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c \,x^{4}+b \,x^{2}+a}\right)}{2 c^{\frac{3}{2}}}+\frac{b}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}"," ",0,"-1/2*x^2/c/(c*x^4+b*x^2+a)^(1/2)+1/4*b/c^2/(c*x^4+b*x^2+a)^(1/2)+1/2*b^2/c/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2+1/4*b^3/c^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)+1/2/c^(3/2)*ln((c*x^2+1/2*b)/c^(1/2)+(c*x^4+b*x^2+a)^(1/2))","A"
984,1,38,34,0.006000," ","int(x^3/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{b \,x^{2}+2 a}{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(4 a c -b^{2}\right)}"," ",0,"-(b*x^2+2*a)/(c*x^4+b*x^2+a)^(1/2)/(4*a*c-b^2)","A"
985,1,36,35,0.004000," ","int(x/(c*x^4+b*x^2+a)^(3/2),x)","\frac{2 c \,x^{2}+b}{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(4 a c -b^{2}\right)}"," ",0,"(2*c*x^2+b)/(c*x^4+b*x^2+a)^(1/2)/(4*a*c-b^2)","A"
986,1,99,77,0.014000," ","int(1/x/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{\left(2 c \,x^{2}+b \right) b}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a}-\frac{\ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{2 a^{\frac{3}{2}}}+\frac{1}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a}"," ",0,"1/2/a/(c*x^4+b*x^2+a)^(1/2)-1/2*b/a*(2*c*x^2+b)/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)-1/2/a^(3/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
987,1,195,123,0.015000," ","int(1/x^3/(c*x^4+b*x^2+a)^(3/2),x)","\frac{3 b^{2} c \,x^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2}}+\frac{3 b^{3}}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2}}-\frac{2 \left(2 c \,x^{2}+b \right) c}{\left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a}+\frac{3 b \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4 a^{\frac{5}{2}}}-\frac{3 b}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2}}-\frac{1}{2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{2}}"," ",0,"-1/2/a/x^2/(c*x^4+b*x^2+a)^(1/2)-3/4*b/a^2/(c*x^4+b*x^2+a)^(1/2)+3/2*b^2/a^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2*c+3/4*b^3/a^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)+3/4*b/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)-2*c/a*(2*c*x^2+b)/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)","A"
988,1,314,175,0.018000," ","int(1/x^5/(c*x^4+b*x^2+a)^(3/2),x)","\frac{13 b \,c^{2} x^{2}}{2 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2}}-\frac{15 b^{3} c \,x^{2}}{8 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{3}}+\frac{13 b^{2} c}{4 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2}}-\frac{15 b^{4}}{16 \left(4 a c -b^{2}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{3}}+\frac{3 c \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{4 a^{\frac{5}{2}}}-\frac{15 b^{2} \ln \left(\frac{b \,x^{2}+2 a +2 \sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{a}}{x^{2}}\right)}{16 a^{\frac{7}{2}}}-\frac{3 c}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2}}+\frac{15 b^{2}}{16 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{3}}+\frac{5 b}{8 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a^{2} x^{2}}-\frac{1}{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, a \,x^{4}}"," ",0,"-1/4/a/x^4/(c*x^4+b*x^2+a)^(1/2)+5/8*b/a^2/x^2/(c*x^4+b*x^2+a)^(1/2)+15/16*b^2/a^3/(c*x^4+b*x^2+a)^(1/2)-15/8*b^3/a^3/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2*c-15/16*b^4/a^3/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)-15/16*b^2/a^(7/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)+13/2*b/a^2*c^2/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)*x^2+13/4*b^2/a^2*c/(4*a*c-b^2)/(c*x^4+b*x^2+a)^(1/2)-3/4*c/a^2/(c*x^4+b*x^2+a)^(1/2)+3/4*c/a^(5/2)*ln((b*x^2+2*a+2*(c*x^4+b*x^2+a)^(1/2)*a^(1/2))/x^2)","A"
989,1,482,404,0.024000," ","int(x^6/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c}-\frac{\left(\frac{1}{c}+\frac{2 a c -b^{2}}{\left(4 a c -b^{2}\right) c}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{2 \left(-\frac{a b x}{2 \left(4 a c -b^{2}\right) c^{2}}+\frac{\left(2 a c -b^{2}\right) x^{3}}{2 \left(4 a c -b^{2}\right) c^{2}}\right) c}{\sqrt{\left(x^{4}+\frac{b \,x^{2}}{c}+\frac{a}{c}\right) c}}"," ",0,"-2*c*(1/2/c^2*(2*a*c-b^2)/(4*a*c-b^2)*x^3-1/2*a*b/c^2/(4*a*c-b^2)*x)/((x^4+b/c*x^2+1/c*a)*c)^(1/2)-1/4/(4*a*c-b^2)*a*b/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(1/c+(2*a*c-b^2)/c/(4*a*c-b^2))*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
990,1,450,340,0.015000," ","int(x^4/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a b}{2 \left(4 a c -b^{2}\right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}+\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, a \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{2 \left(4 a c -b^{2}\right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{2 \left(\frac{b \,x^{3}}{2 \left(4 a c -b^{2}\right) c}+\frac{a x}{\left(4 a c -b^{2}\right) c}\right) c}{\sqrt{\left(x^{4}+\frac{b \,x^{2}}{c}+\frac{a}{c}\right) c}}"," ",0,"-2*c*(1/2*b/(4*a*c-b^2)/c*x^3+a/c/(4*a*c-b^2)*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)+1/2*a/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*b/(4*a*c-b^2)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
991,1,446,339,0.014000," ","int(x^2/(c*x^4+b*x^2+a)^(3/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a c}{\left(4 a c -b^{2}\right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, b \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \left(4 a c -b^{2}\right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{2 \left(-\frac{x^{3}}{4 a c -b^{2}}-\frac{b x}{2 \left(4 a c -b^{2}\right) c}\right) c}{\sqrt{\left(x^{4}+\frac{b \,x^{2}}{c}+\frac{a}{c}\right) c}}"," ",0,"-2*c*(-1/(4*a*c-b^2)*x^3-1/2*b/(4*a*c-b^2)/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)-1/4*b/(4*a*c-b^2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+c/(4*a*c-b^2)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
992,1,481,351,0.012000," ","int(1/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) b c}{2 \left(4 a c -b^{2}\right) \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{2 \left(\frac{b \,x^{3}}{2 \left(4 a c -b^{2}\right) a}-\frac{\left(2 a c -b^{2}\right) x}{2 \left(4 a c -b^{2}\right) a c}\right) c}{\sqrt{\left(x^{4}+\frac{b \,x^{2}}{c}+\frac{a}{c}\right) c}}+\frac{\left(\frac{1}{a}-\frac{2 a c -b^{2}}{\left(4 a c -b^{2}\right) a}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}"," ",0,"-2*c*(1/2*b/a/(4*a*c-b^2)*x^3-1/2*(2*a*c-b^2)/a/(4*a*c-b^2)/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)+1/4*(1/a-(2*a*c-b^2)/a/(4*a*c-b^2))*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*b/(4*a*c-b^2)*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
993,1,536,424,0.020000," ","int(1/x^2/(c*x^4+b*x^2+a)^(3/2),x)","-\frac{\left(\frac{\left(2 a c -b^{2}\right) c}{\left(4 a c -b^{2}\right) a^{2}}+\frac{c}{a^{2}}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \left(-\EllipticE \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)+\EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)\right) a}{2 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right)}-\frac{2 \left(\frac{\left(2 a c -b^{2}\right) x^{3}}{2 \left(4 a c -b^{2}\right) a^{2}}+\frac{\left(3 a c -b^{2}\right) b x}{2 \left(4 a c -b^{2}\right) a^{2} c}\right) c}{\sqrt{\left(x^{4}+\frac{b \,x^{2}}{c}+\frac{a}{c}\right) c}}+\frac{\left(-\frac{b}{a^{2}}+\frac{\left(3 a c -b^{2}\right) b}{\left(4 a c -b^{2}\right) a^{2}}\right) \sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \EllipticF \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, \frac{\sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) b}{a c}-4}}{2}\right)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}-\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{a^{2} x}"," ",0,"-2*c*(1/2*(2*a*c-b^2)/(4*a*c-b^2)/a^2*x^3+1/2*b*(3*a*c-b^2)/a^2/(4*a*c-b^2)/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)-1/a^2*(c*x^4+b*x^2+a)^(1/2)/x+1/4*(-1/a^2*b+b*(3*a*c-b^2)/a^2/(4*a*c-b^2))*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-1/2*(c*(2*a*c-b^2)/(4*a*c-b^2)/a^2+c/a^2)*a*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)/(b+(-4*a*c+b^2)^(1/2))*(EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))-EllipticE(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2)))","A"
994,1,37,42,0.005000," ","int(x^4/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-c \,x^{2}+2 b \right) x}{3 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{2}}"," ",0,"-1/3*(c*x^2+b)*(-c*x^2+2*b)*x/c^2/(c*x^4+b*x^2)^(1/2)","A"
995,1,64,46,0.007000," ","int(x^3/(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b}\, \left(-b c \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)+\sqrt{c \,x^{2}+b}\, c^{\frac{3}{2}} x \right) x}{2 \sqrt{c \,x^{4}+b \,x^{2}}\, c^{\frac{5}{2}}}"," ",0,"1/2*x*(c*x^2+b)^(1/2)*(x*(c*x^2+b)^(1/2)*c^(3/2)-b*ln(c^(1/2)*x+(c*x^2+b)^(1/2))*c)/(c*x^4+b*x^2)^(1/2)/c^(5/2)","A"
996,1,26,20,0.005000," ","int(x^2/(c*x^4+b*x^2)^(1/2),x)","\frac{\left(c \,x^{2}+b \right) x}{\sqrt{c \,x^{4}+b \,x^{2}}\, c}"," ",0,"(c*x^2+b)/(c*x^4+b*x^2)^(1/2)/c*x","A"
997,1,44,25,0.003000," ","int(x/(c*x^4+b*x^2)^(1/2),x)","\frac{\sqrt{c \,x^{2}+b}\, x \ln \left(\sqrt{c}\, x +\sqrt{c \,x^{2}+b}\right)}{\sqrt{c \,x^{4}+b \,x^{2}}\, \sqrt{c}}"," ",0,"1/(c*x^4+b*x^2)^(1/2)*x*(c*x^2+b)^(1/2)*ln(c^(1/2)*x+(c*x^2+b)^(1/2))/c^(1/2)","A"
998,1,50,24,0.005000," ","int(1/(c*x^4+b*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b}\, x \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)}{\sqrt{c \,x^{4}+b \,x^{2}}\, \sqrt{b}}"," ",0,"-1/(c*x^4+b*x^2)^(1/2)*x*(c*x^2+b)^(1/2)/b^(1/2)*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)","B"
999,1,26,21,0.004000," ","int(1/x/(c*x^4+b*x^2)^(1/2),x)","-\frac{c \,x^{2}+b}{\sqrt{c \,x^{4}+b \,x^{2}}\, b}"," ",0,"-(c*x^2+b)/b/(c*x^4+b*x^2)^(1/2)","A"
1000,1,73,47,0.008000," ","int(1/x^2/(c*x^4+b*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b}\, \left(-b c \,x^{2} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)+\sqrt{c \,x^{2}+b}\, b^{\frac{3}{2}}\right)}{2 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{\frac{5}{2}} x}"," ",0,"-1/2/x*(c*x^2+b)^(1/2)*(-c*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^2*b+(c*x^2+b)^(1/2)*b^(3/2))/(c*x^4+b*x^2)^(1/2)/b^(5/2)","A"
1001,1,37,44,0.005000," ","int(1/x^3/(c*x^4+b*x^2)^(1/2),x)","-\frac{\left(c \,x^{2}+b \right) \left(-2 c \,x^{2}+b \right)}{3 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{2} x^{2}}"," ",0,"-1/3*(c*x^2+b)*(-2*c*x^2+b)/x^2/b^2/(c*x^4+b*x^2)^(1/2)","A"
1002,1,94,71,0.007000," ","int(1/x^4/(c*x^4+b*x^2)^(1/2),x)","-\frac{\sqrt{c \,x^{2}+b}\, \left(3 b \,c^{2} x^{4} \ln \left(\frac{2 b +2 \sqrt{c \,x^{2}+b}\, \sqrt{b}}{x}\right)-3 \sqrt{c \,x^{2}+b}\, b^{\frac{3}{2}} c \,x^{2}+2 \sqrt{c \,x^{2}+b}\, b^{\frac{5}{2}}\right)}{8 \sqrt{c \,x^{4}+b \,x^{2}}\, b^{\frac{7}{2}} x^{3}}"," ",0,"-1/8*(c*x^2+b)^(1/2)*(3*ln(2*(b+(c*x^2+b)^(1/2)*b^(1/2))/x)*x^4*b*c^2-3*(c*x^2+b)^(1/2)*b^(3/2)*x^2*c+2*(c*x^2+b)^(1/2)*b^(5/2))/x^3/(c*x^4+b*x^2)^(1/2)/b^(7/2)","A"
1003,1,91,115,0.050000," ","int(x^4/(c*x^4+a)^(1/2),x)","-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c}+\frac{\sqrt{c \,x^{4}+a}\, x}{3 c}"," ",0,"1/3*x*(c*x^4+a)^(1/2)/c-1/3*a/c/(I/a^(1/2)*c^(1/2))^(1/2)*(1-I/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*c^(1/2)*x^2)^(1/2)/(c*x^4+a)^(1/2)*EllipticF(x*(I/a^(1/2)*c^(1/2))^(1/2),I)","C"
1004,1,15,14,0.006000," ","int(x^3/(c*x^4+a)^(1/2),x)","\frac{\sqrt{c \,x^{4}+a}}{2 c}"," ",0,"1/2*(c*x^4+a)^(1/2)/c","A"
1005,1,97,226,0.006000," ","int(x^2/(c*x^4+a)^(1/2),x)","\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}"," ",0,"I*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
1006,1,24,22,0.008000," ","int(x/(c*x^4+a)^(1/2),x)","\frac{\ln \left(\sqrt{c}\, x^{2}+\sqrt{c \,x^{4}+a}\right)}{2 \sqrt{c}}"," ",0,"1/2*ln(x^2*c^(1/2)+(c*x^4+a)^(1/2))/c^(1/2)","A"
1007,1,70,99,0.005000," ","int(1/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}"," ",0,"1/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
1008,1,29,19,0.011000," ","int(1/x/(c*x^4+a)^(1/2),x)","-\frac{\ln \left(\frac{2 a +2 \sqrt{c \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{a}}"," ",0,"-1/2/a^(1/2)*ln((2*a+2*a^(1/2)*(c*x^4+a)^(1/2))/x^2)","A"
1009,1,115,246,0.011000," ","int(1/x^2/(c*x^4+a)^(1/2),x)","\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{c}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}}-\frac{\sqrt{c \,x^{4}+a}}{a x}"," ",0,"-(c*x^4+a)^(1/2)/a/x+I*c^(1/2)/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
1010,1,18,17,0.005000," ","int(1/x^3/(c*x^4+a)^(1/2),x)","-\frac{\sqrt{c \,x^{4}+a}}{2 a \,x^{2}}"," ",0,"-1/2*(c*x^4+a)^(1/2)/a/x^2","A"
1011,1,93,117,0.013000," ","int(1/x^4/(c*x^4+a)^(1/2),x)","-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}-\frac{\sqrt{c \,x^{4}+a}}{3 a \,x^{3}}"," ",0,"-1/3*(c*x^4+a)^(1/2)/a/x^3-1/3*c/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
1012,1,59,57,0.007000," ","int(x^4/(b*x^2+a)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, x^{3}}{4 b}+\frac{3 a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{5}{2}}}-\frac{3 \sqrt{b \,x^{2}+a}\, a x}{8 b^{2}}"," ",0,"1/4*x^3*(b*x^2+a)^(1/2)/b-3/8*a*x*(b*x^2+a)^(1/2)/b^2+3/8*a^2/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
1013,1,25,30,0.005000," ","int(x^3/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \left(-b \,x^{2}+2 a \right)}{3 b^{2}}"," ",0,"-1/3*(b*x^2+a)^(1/2)*(-b*x^2+2*a)/b^2","A"
1014,1,39,37,0.006000," ","int(x^2/(b*x^2+a)^(1/2),x)","-\frac{a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{3}{2}}}+\frac{\sqrt{b \,x^{2}+a}\, x}{2 b}"," ",0,"1/2*x*(b*x^2+a)^(1/2)/b-1/2*a/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
1015,1,14,13,0.003000," ","int(x/(b*x^2+a)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}}{b}"," ",0,"(b*x^2+a)^(1/2)/b","A"
1016,1,21,19,0.003000," ","int(1/(b*x^2+a)^(1/2),x)","\frac{\ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\sqrt{b}}"," ",0,"ln(b^(1/2)*x+(b*x^2+a)^(1/2))/b^(1/2)","A"
1017,1,29,19,0.005000," ","int(1/x/(b*x^2+a)^(1/2),x)","-\frac{\ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{\sqrt{a}}"," ",0,"-1/a^(1/2)*ln((2*a+2*a^(1/2)*(b*x^2+a)^(1/2))/x)","A"
1018,1,18,17,0.005000," ","int(1/x^2/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}}{a x}"," ",0,"-(b*x^2+a)^(1/2)/a/x","A"
1019,1,48,38,0.006000," ","int(1/x^3/(b*x^2+a)^(1/2),x)","\frac{b \ln \left(\frac{2 a +2 \sqrt{b \,x^{2}+a}\, \sqrt{a}}{x}\right)}{2 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{2}+a}}{2 a \,x^{2}}"," ",0,"-1/2*(b*x^2+a)^(1/2)/a/x^2+1/2*b/a^(3/2)*ln((2*a+2*(b*x^2+a)^(1/2)*a^(1/2))/x)","A"
1020,1,26,36,0.005000," ","int(1/x^4/(b*x^2+a)^(1/2),x)","-\frac{\sqrt{b \,x^{2}+a}\, \left(-2 b \,x^{2}+a \right)}{3 a^{2} x^{3}}"," ",0,"-1/3*(b*x^2+a)^(1/2)*(-2*b*x^2+a)/a^2/x^3","A"
1021,1,13,12,0.004000," ","int(x^4/(c*x^4)^(1/2),x)","\frac{x^{5}}{3 \sqrt{c \,x^{4}}}"," ",0,"1/3*x^5/(c*x^4)^(1/2)","A"
1022,1,13,12,0.003000," ","int(x^3/(c*x^4)^(1/2),x)","\frac{x^{4}}{2 \sqrt{c \,x^{4}}}"," ",0,"1/2*x^4/(c*x^4)^(1/2)","A"
1023,1,12,11,0.003000," ","int(x^2/(c*x^4)^(1/2),x)","\frac{x^{3}}{\sqrt{c \,x^{4}}}"," ",0,"x^3/(c*x^4)^(1/2)","A"
1024,1,14,13,0.003000," ","int(x/(c*x^4)^(1/2),x)","\frac{x^{2} \ln \left(x \right)}{\sqrt{c \,x^{4}}}"," ",0,"x^2*ln(x)/(c*x^4)^(1/2)","A"
1025,1,11,10,0.002000," ","int(1/(c*x^4)^(1/2),x)","-\frac{x}{\sqrt{c \,x^{4}}}"," ",0,"-x/(c*x^4)^(1/2)","A"
1026,1,10,9,0.002000," ","int(1/x/(c*x^4)^(1/2),x)","-\frac{1}{2 \sqrt{c \,x^{4}}}"," ",0,"-1/2/(c*x^4)^(1/2)","A"
1027,1,13,12,0.002000," ","int(1/x^2/(c*x^4)^(1/2),x)","-\frac{1}{3 \sqrt{c \,x^{4}}\, x}"," ",0,"-1/3/x/(c*x^4)^(1/2)","A"
1028,1,13,12,0.003000," ","int(1/x^3/(c*x^4)^(1/2),x)","-\frac{1}{4 \sqrt{c \,x^{4}}\, x^{2}}"," ",0,"-1/4/x^2/(c*x^4)^(1/2)","A"
1029,1,13,12,0.003000," ","int(1/x^4/(c*x^4)^(1/2),x)","-\frac{1}{5 \sqrt{c \,x^{4}}\, x^{3}}"," ",0,"-1/5/x^3/(c*x^4)^(1/2)","A"
1030,1,9,8,0.001000," ","int(x^4/a^(1/2),x)","\frac{x^{5}}{5 \sqrt{a}}"," ",0,"1/5*x^5/a^(1/2)","A"
1031,1,9,8,0.000000," ","int(x^3/a^(1/2),x)","\frac{x^{4}}{4 \sqrt{a}}"," ",0,"1/4*x^4/a^(1/2)","A"
1032,1,9,8,0.001000," ","int(x^2/a^(1/2),x)","\frac{x^{3}}{3 \sqrt{a}}"," ",0,"1/3*x^3/a^(1/2)","A"
1033,1,9,8,0.000000," ","int(x/a^(1/2),x)","\frac{x^{2}}{2 \sqrt{a}}"," ",0,"1/2*x^2/a^(1/2)","A"
1034,1,6,5,0.000000," ","int(1/a^(1/2),x)","\frac{x}{\sqrt{a}}"," ",0,"x/a^(1/2)","A"
1035,1,7,6,0.001000," ","int(1/x/a^(1/2),x)","\frac{\ln \left(x \right)}{\sqrt{a}}"," ",0,"ln(x)/a^(1/2)","A"
1036,1,9,8,0.000000," ","int(1/x^2/a^(1/2),x)","-\frac{1}{\sqrt{a}\, x}"," ",0,"-1/x/a^(1/2)","A"
1037,1,9,8,0.001000," ","int(1/x^3/a^(1/2),x)","-\frac{1}{2 \sqrt{a}\, x^{2}}"," ",0,"-1/2/x^2/a^(1/2)","A"
1038,1,9,8,0.000000," ","int(1/x^4/a^(1/2),x)","-\frac{1}{3 \sqrt{a}\, x^{3}}"," ",0,"-1/3/x^3/a^(1/2)","A"
1039,1,43,13,0.008000," ","int(1/(-x^4-2*x^2+3)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{3 x^{2}+9}\, \EllipticF \left(x , \frac{i \sqrt{3}}{3}\right)}{3 \sqrt{-x^{4}-2 x^{2}+3}}"," ",0,"1/3*(-x^2+1)^(1/2)*(3*x^2+9)^(1/2)/(-x^4-2*x^2+3)^(1/2)*EllipticF(x,1/3*I*3^(1/2))","B"
1040,1,82,56,0.083000," ","int(1/(-x^4+5*x^2-1)^(1/2),x)","\frac{\sqrt{-\left(\frac{5}{2}-\frac{\sqrt{21}}{2}\right) x^{2}+1}\, \sqrt{-\left(\frac{5}{2}+\frac{\sqrt{21}}{2}\right) x^{2}+1}\, \EllipticF \left(\left(\frac{\sqrt{7}}{2}-\frac{\sqrt{3}}{2}\right) x , \frac{5}{2}+\frac{\sqrt{21}}{2}\right)}{\left(\frac{\sqrt{7}}{2}-\frac{\sqrt{3}}{2}\right) \sqrt{-x^{4}+5 x^{2}-1}}"," ",0,"1/(1/2*7^(1/2)-1/2*3^(1/2))*(1-(5/2-1/2*21^(1/2))*x^2)^(1/2)*(1-(5/2+1/2*21^(1/2))*x^2)^(1/2)/(-x^4+5*x^2-1)^(1/2)*EllipticF(x*(1/2*7^(1/2)-1/2*3^(1/2)),5/2+1/2*21^(1/2))","A"
1041,1,22,19,0.003000," ","int(x^(5/2)*(c*x^4+b*x^2+a),x)","\frac{2 \left(77 c \,x^{4}+105 b \,x^{2}+165 a \right) x^{\frac{7}{2}}}{1155}"," ",0,"2/1155*x^(7/2)*(77*c*x^4+105*b*x^2+165*a)","A"
1042,1,22,19,0.004000," ","int(x^(3/2)*(c*x^4+b*x^2+a),x)","\frac{2 \left(45 c \,x^{4}+65 b \,x^{2}+117 a \right) x^{\frac{5}{2}}}{585}"," ",0,"2/585*x^(5/2)*(45*c*x^4+65*b*x^2+117*a)","A"
1043,1,22,19,0.004000," ","int(x^(1/2)*(c*x^4+b*x^2+a),x)","\frac{2 \left(21 c \,x^{4}+33 b \,x^{2}+77 a \right) x^{\frac{3}{2}}}{231}"," ",0,"2/231*x^(3/2)*(21*c*x^4+33*b*x^2+77*a)","A"
1044,1,22,19,0.005000," ","int((c*x^4+b*x^2+a)/x^(1/2),x)","\frac{2 \left(5 c \,x^{4}+9 b \,x^{2}+45 a \right) \sqrt{x}}{45}"," ",0,"2/45*x^(1/2)*(5*c*x^4+9*b*x^2+45*a)","A"
1045,1,22,19,0.004000," ","int((c*x^4+b*x^2+a)/x^(3/2),x)","-\frac{2 \left(-3 c \,x^{4}-7 b \,x^{2}+21 a \right)}{21 \sqrt{x}}"," ",0,"-2/21*(-3*c*x^4-7*b*x^2+21*a)/x^(1/2)","A"
1046,1,22,19,0.004000," ","int((c*x^4+b*x^2+a)/x^(5/2),x)","-\frac{2 \left(-3 c \,x^{4}-15 b \,x^{2}+5 a \right)}{15 x^{\frac{3}{2}}}"," ",0,"-2/15*(-3*c*x^4-15*b*x^2+5*a)/x^(3/2)","A"
1047,1,22,19,0.004000," ","int((c*x^4+b*x^2+a)/x^(7/2),x)","-\frac{2 \left(-5 c \,x^{4}+15 b \,x^{2}+3 a \right)}{15 x^{\frac{5}{2}}}"," ",0,"-2/15*(-5*c*x^4+15*b*x^2+3*a)/x^(5/2)","A"
1048,1,49,44,0.006000," ","int(x^(5/2)*(c*x^4+b*x^2+a)^2,x)","\frac{2 \left(21945 c^{2} x^{8}+53130 b c \,x^{6}+67298 a c \,x^{4}+33649 b^{2} x^{4}+91770 a b \,x^{2}+72105 a^{2}\right) x^{\frac{7}{2}}}{504735}"," ",0,"2/504735*x^(7/2)*(21945*c^2*x^8+53130*b*c*x^6+67298*a*c*x^4+33649*b^2*x^4+91770*a*b*x^2+72105*a^2)","A"
1049,1,49,44,0.007000," ","int(x^(3/2)*(c*x^4+b*x^2+a)^2,x)","\frac{2 \left(3315 c^{2} x^{8}+8190 b c \,x^{6}+10710 a c \,x^{4}+5355 b^{2} x^{4}+15470 a b \,x^{2}+13923 a^{2}\right) x^{\frac{5}{2}}}{69615}"," ",0,"2/69615*x^(5/2)*(3315*c^2*x^8+8190*b*c*x^6+10710*a*c*x^4+5355*b^2*x^4+15470*a*b*x^2+13923*a^2)","A"
1050,1,49,44,0.006000," ","int(x^(1/2)*(c*x^4+b*x^2+a)^2,x)","\frac{2 \left(1155 c^{2} x^{8}+2926 b c \,x^{6}+3990 a c \,x^{4}+1995 b^{2} x^{4}+6270 a b \,x^{2}+7315 a^{2}\right) x^{\frac{3}{2}}}{21945}"," ",0,"2/21945*x^(3/2)*(1155*c^2*x^8+2926*b*c*x^6+3990*a*c*x^4+1995*b^2*x^4+6270*a*b*x^2+7315*a^2)","A"
1051,1,49,44,0.006000," ","int((c*x^4+b*x^2+a)^2/x^(1/2),x)","\frac{2 \left(585 c^{2} x^{8}+1530 b c \,x^{6}+2210 a c \,x^{4}+1105 b^{2} x^{4}+3978 a b \,x^{2}+9945 a^{2}\right) \sqrt{x}}{9945}"," ",0,"2/9945*x^(1/2)*(585*c^2*x^8+1530*b*c*x^6+2210*a*c*x^4+1105*b^2*x^4+3978*a*b*x^2+9945*a^2)","A"
1052,1,49,44,0.007000," ","int((c*x^4+b*x^2+a)^2/x^(3/2),x)","-\frac{2 \left(-77 c^{2} x^{8}-210 b c \,x^{6}-330 a c \,x^{4}-165 b^{2} x^{4}-770 a b \,x^{2}+1155 a^{2}\right)}{1155 \sqrt{x}}"," ",0,"-2/1155*(-77*c^2*x^8-210*b*c*x^6-330*a*c*x^4-165*b^2*x^4-770*a*b*x^2+1155*a^2)/x^(1/2)","A"
1053,1,49,44,0.007000," ","int((c*x^4+b*x^2+a)^2/x^(5/2),x)","-\frac{2 \left(-45 c^{2} x^{8}-130 b c \,x^{6}-234 a c \,x^{4}-117 b^{2} x^{4}-1170 a b \,x^{2}+195 a^{2}\right)}{585 x^{\frac{3}{2}}}"," ",0,"-2/585*(-45*c^2*x^8-130*b*c*x^6-234*a*c*x^4-117*b^2*x^4-1170*a*b*x^2+195*a^2)/x^(3/2)","A"
1054,1,49,44,0.007000," ","int((c*x^4+b*x^2+a)^2/x^(7/2),x)","-\frac{2 \left(-105 c^{2} x^{8}-330 b c \,x^{6}-770 a c \,x^{4}-385 b^{2} x^{4}+2310 a b \,x^{2}+231 a^{2}\right)}{1155 x^{\frac{5}{2}}}"," ",0,"-2/1155*(-105*c^2*x^8-330*b*c*x^6-770*a*c*x^4-385*b^2*x^4+2310*a*b*x^2+231*a^2)/x^(5/2)","A"
1055,1,90,75,0.008000," ","int(x^(5/2)*(c*x^4+b*x^2+a)^3,x)","\frac{2 \left(1514205 c^{3} x^{12}+5215595 b \,c^{2} x^{10}+6122655 a \,c^{2} x^{8}+6122655 b^{2} c \,x^{8}+14823270 a b c \,x^{6}+2470545 b^{3} x^{6}+9388071 a^{2} c \,x^{4}+9388071 a \,b^{2} x^{4}+12801915 a^{2} b \,x^{2}+6705765 a^{3}\right) x^{\frac{7}{2}}}{46940355}"," ",0,"2/46940355*x^(7/2)*(1514205*c^3*x^12+5215595*b*c^2*x^10+6122655*a*c^2*x^8+6122655*b^2*c*x^8+14823270*a*b*c*x^6+2470545*b^3*x^6+9388071*a^2*c*x^4+9388071*a*b^2*x^4+12801915*a^2*b*x^2+6705765*a^3)","A"
1056,1,90,75,0.007000," ","int(x^(3/2)*(c*x^4+b*x^2+a)^3,x)","\frac{2 \left(116025 c^{3} x^{12}+403767 b \,c^{2} x^{10}+480675 a \,c^{2} x^{8}+480675 b^{2} c \,x^{8}+1187550 a b c \,x^{6}+197925 b^{3} x^{6}+776475 a^{2} c \,x^{4}+776475 a \,b^{2} x^{4}+1121575 a^{2} b \,x^{2}+672945 a^{3}\right) x^{\frac{5}{2}}}{3364725}"," ",0,"2/3364725*x^(5/2)*(116025*c^3*x^12+403767*b*c^2*x^10+480675*a*c^2*x^8+480675*b^2*c*x^8+1187550*a*b*c*x^6+197925*b^3*x^6+776475*a^2*c*x^4+776475*a*b^2*x^4+1121575*a^2*b*x^2+672945*a^3)","A"
1057,1,90,75,0.008000," ","int(x^(1/2)*(c*x^4+b*x^2+a)^3,x)","\frac{2 \left(168245 c^{3} x^{12}+592515 b \,c^{2} x^{10}+717255 a \,c^{2} x^{8}+717255 b^{2} c \,x^{8}+1817046 a b c \,x^{6}+302841 b^{3} x^{6}+1238895 a^{2} c \,x^{4}+1238895 a \,b^{2} x^{4}+1946835 a^{2} b \,x^{2}+1514205 a^{3}\right) x^{\frac{3}{2}}}{4542615}"," ",0,"2/4542615*x^(3/2)*(168245*c^3*x^12+592515*b*c^2*x^10+717255*a*c^2*x^8+717255*b^2*c*x^8+1817046*a*b*c*x^6+302841*b^3*x^6+1238895*a^2*c*x^4+1238895*a*b^2*x^4+1946835*a^2*b*x^2+1514205*a^3)","A"
1058,1,90,75,0.007000," ","int((c*x^4+b*x^2+a)^3/x^(1/2),x)","\frac{2 \left(4641 c^{3} x^{12}+16575 b \,c^{2} x^{10}+20475 a \,c^{2} x^{8}+20475 b^{2} c \,x^{8}+53550 a b c \,x^{6}+8925 b^{3} x^{6}+38675 a^{2} c \,x^{4}+38675 a \,b^{2} x^{4}+69615 a^{2} b \,x^{2}+116025 a^{3}\right) \sqrt{x}}{116025}"," ",0,"2/116025*x^(1/2)*(4641*c^3*x^12+16575*b*c^2*x^10+20475*a*c^2*x^8+20475*b^2*c*x^8+53550*a*b*c*x^6+8925*b^3*x^6+38675*a^2*c*x^4+38675*a*b^2*x^4+69615*a^2*b*x^2+116025*a^3)","A"
1059,1,90,75,0.006000," ","int((c*x^4+b*x^2+a)^3/x^(3/2),x)","-\frac{2 \left(-7315 c^{3} x^{12}-26565 b \,c^{2} x^{10}-33649 a \,c^{2} x^{8}-33649 b^{2} c \,x^{8}-91770 a b c \,x^{6}-15295 b^{3} x^{6}-72105 a^{2} c \,x^{4}-72105 a \,b^{2} x^{4}-168245 a^{2} b \,x^{2}+168245 a^{3}\right)}{168245 \sqrt{x}}"," ",0,"-2/168245*(-7315*c^3*x^12-26565*b*c^2*x^10-33649*a*c^2*x^8-33649*b^2*c*x^8-91770*a*b*c*x^6-15295*b^3*x^6-72105*a^2*c*x^4-72105*a*b^2*x^4-168245*a^2*b*x^2+168245*a^3)/x^(1/2)","A"
1060,1,90,75,0.008000," ","int((c*x^4+b*x^2+a)^3/x^(5/2),x)","-\frac{2 \left(-3315 c^{3} x^{12}-12285 b \,c^{2} x^{10}-16065 a \,c^{2} x^{8}-16065 b^{2} c \,x^{8}-46410 a b c \,x^{6}-7735 b^{3} x^{6}-41769 a^{2} c \,x^{4}-41769 a \,b^{2} x^{4}-208845 a^{2} b \,x^{2}+23205 a^{3}\right)}{69615 x^{\frac{3}{2}}}"," ",0,"-2/69615*(-3315*c^3*x^12-12285*b*c^2*x^10-16065*a*c^2*x^8-16065*b^2*c*x^8-46410*a*b*c*x^6-7735*b^3*x^6-41769*a^2*c*x^4-41769*a*b^2*x^4-208845*a^2*b*x^2+23205*a^3)/x^(3/2)","A"
1061,1,90,75,0.007000," ","int((c*x^4+b*x^2+a)^3/x^(7/2),x)","-\frac{2 \left(-385 c^{3} x^{12}-1463 b \,c^{2} x^{10}-1995 a \,c^{2} x^{8}-1995 b^{2} c \,x^{8}-6270 a b c \,x^{6}-1045 b^{3} x^{6}-7315 a^{2} c \,x^{4}-7315 a \,b^{2} x^{4}+21945 a^{2} b \,x^{2}+1463 a^{3}\right)}{7315 x^{\frac{5}{2}}}"," ",0,"-2/7315*(-385*c^3*x^12-1463*b*c^2*x^10-1995*a*c^2*x^8-1995*b^2*c*x^8-6270*a*b*c*x^6-1045*b^3*x^6-7315*a^2*c*x^4-7315*a*b^2*x^4+21945*a^2*b*x^2+1463*a^3)/x^(5/2)","A"
1062,1,65,309,0.059000," ","int(x^(9/2)/(c*x^4+b*x^2+a),x)","\frac{2 x^{\frac{3}{2}}}{3 c}-\frac{\left(\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} b +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} a \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{2 c \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}"," ",0,"2/3/c*x^(3/2)-1/2/c*sum((_R^6*b+_R^2*a)/(2*_R^7*c+_R^3*b)*ln(x^(1/2)-_R),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1063,1,64,309,0.010000," ","int(x^(7/2)/(c*x^4+b*x^2+a),x)","\frac{\left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} b -a \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{2 c \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{2 \sqrt{x}}{c}"," ",0,"2/c*x^(1/2)+1/2/c*sum((-_R^4*b-a)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1064,1,45,253,0.008000," ","int(x^(5/2)/(c*x^4+b*x^2+a),x)","\frac{\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{4 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b}"," ",0,"1/2*sum(_R^6/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1065,1,45,253,0.008000," ","int(x^(3/2)/(c*x^4+b*x^2+a),x)","\frac{\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{4 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b}"," ",0,"1/2*sum(_R^4/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1066,1,45,251,0.007000," ","int(x^(1/2)/(c*x^4+b*x^2+a),x)","\frac{\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{4 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b}"," ",0,"1/2*sum(_R^2/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1067,1,42,251,0.006000," ","int(1/x^(1/2)/(c*x^4+b*x^2+a),x)","\frac{\ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{4 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b}"," ",0,"1/2*sum(1/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1068,1,65,291,0.010000," ","int(1/x^(3/2)/(c*x^4+b*x^2+a),x)","-\frac{\left(\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{2 a \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}-\frac{2}{a \sqrt{x}}"," ",0,"-1/2/a*sum((_R^6*c+_R^2*b)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))-2/a/x^(1/2)","C"
1069,1,64,291,0.011000," ","int(1/x^(5/2)/(c*x^4+b*x^2+a),x)","\frac{\left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} c -b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{2 a \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}-\frac{2}{3 a \,x^{\frac{3}{2}}}"," ",0,"1/2/a*sum((-_R^4*c-b)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))-2/3/a/x^(3/2)","C"
1070,1,82,330,0.013000," ","int(1/x^(7/2)/(c*x^4+b*x^2+a),x)","\frac{\left(\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} b c +\left(-a c +b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{2 a^{2} \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{2 b}{a^{2} \sqrt{x}}-\frac{2}{5 a \,x^{\frac{5}{2}}}"," ",0,"1/2/a^2*sum((b*c*_R^6+(-a*c+b^2)*_R^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))-2/5/a/x^(5/2)+2*b/a^2/x^(1/2)","C"
1071,1,149,440,0.021000," ","int(x^(13/2)/(c*x^4+b*x^2+a)^2,x)","\frac{\left(\left(14 a c -3 b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6}-3 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} a b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) c \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{\frac{a b \,x^{\frac{3}{2}}}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) x^{\frac{7}{2}}}{2 \left(4 a c -b^{2}\right) c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"2*(-1/4*(2*a*c-b^2)/(4*a*c-b^2)/c*x^(7/2)+1/4/(4*a*c-b^2)*a*b/c*x^(3/2))/(c*x^4+b*x^2+a)+1/8/c/(4*a*c-b^2)*sum(((14*a*c-3*b^2)*_R^6-3*_R^2*a*b)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1072,1,146,424,0.020000," ","int(x^(11/2)/(c*x^4+b*x^2+a)^2,x)","\frac{\left(\left(10 a c -b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4}-a b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) c \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{\frac{a b \sqrt{x}}{2 \left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) x^{\frac{5}{2}}}{2 \left(4 a c -b^{2}\right) c}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"2*(-1/4*(2*a*c-b^2)/(4*a*c-b^2)/c*x^(5/2)+1/4/(4*a*c-b^2)*a*b/c*x^(1/2))/(c*x^4+b*x^2+a)+1/8/c/(4*a*c-b^2)*sum(((10*a*c-b^2)*_R^4-a*b)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1073,1,120,377,0.019000," ","int(x^(9/2)/(c*x^4+b*x^2+a)^2,x)","-\frac{\left(\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} b -6 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} a \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{b \,x^{\frac{7}{2}}}{2 \left(4 a c -b^{2}\right)}-\frac{a \,x^{\frac{3}{2}}}{4 a c -b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"2*(-1/4*b/(4*a*c-b^2)*x^(7/2)-1/2*a/(4*a*c-b^2)*x^(3/2))/(c*x^4+b*x^2+a)-1/8/(4*a*c-b^2)*sum((_R^6*b-6*_R^2*a)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1074,1,118,383,0.020000," ","int(x^(7/2)/(c*x^4+b*x^2+a)^2,x)","\frac{\left(-3 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} b +2 a \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{b \,x^{\frac{5}{2}}}{2 \left(4 a c -b^{2}\right)}-\frac{a \sqrt{x}}{4 a c -b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"2*(-1/4*b/(4*a*c-b^2)*x^(5/2)-1/2*a/(4*a*c-b^2)*x^(1/2))/(c*x^4+b*x^2+a)+1/8/(4*a*c-b^2)*sum((-3*_R^4*b+2*a)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1075,1,121,350,0.019000," ","int(x^(5/2)/(c*x^4+b*x^2+a)^2,x)","\frac{\left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} c -3 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{\frac{2 c \,x^{\frac{7}{2}}}{8 a c -2 b^{2}}+\frac{2 b \,x^{\frac{3}{2}}}{16 a c -4 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"2*(1/2*c/(4*a*c-b^2)*x^(7/2)+1/4*b/(4*a*c-b^2)*x^(3/2))/(c*x^4+b*x^2+a)+1/8/(4*a*c-b^2)*sum((2*_R^6*c-3*_R^2*b)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1076,1,118,350,0.020000," ","int(x^(3/2)/(c*x^4+b*x^2+a)^2,x)","\frac{\left(6 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} c -b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{\frac{2 c \,x^{\frac{5}{2}}}{8 a c -2 b^{2}}+\frac{2 b \sqrt{x}}{16 a c -4 b^{2}}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"2*(1/2*c/(4*a*c-b^2)*x^(5/2)+1/4*b/(4*a*c-b^2)*x^(1/2))/(c*x^4+b*x^2+a)+1/8/(4*a*c-b^2)*sum((6*_R^4*c-b)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1077,1,146,399,0.020000," ","int(x^(1/2)/(c*x^4+b*x^2+a)^2,x)","-\frac{\left(\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} b c +\left(-10 a c +b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) a \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{b c \,x^{\frac{7}{2}}}{2 \left(4 a c -b^{2}\right) a}+\frac{\left(2 a c -b^{2}\right) x^{\frac{3}{2}}}{2 \left(4 a c -b^{2}\right) a}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"2*(-1/4*b/a/(4*a*c-b^2)*c*x^(7/2)+1/4*(2*a*c-b^2)/(4*a*c-b^2)/a*x^(3/2))/(c*x^4+b*x^2+a)-1/8/a/(4*a*c-b^2)*sum((_R^6*b*c+(-10*a*c+b^2)*_R^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1078,1,144,403,0.019000," ","int(1/x^(1/2)/(c*x^4+b*x^2+a)^2,x)","\frac{\left(-3 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} b c +14 a c -3 b^{2}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) a \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{b c \,x^{\frac{5}{2}}}{2 \left(4 a c -b^{2}\right) a}+\frac{\left(2 a c -b^{2}\right) \sqrt{x}}{2 \left(4 a c -b^{2}\right) a}}{c \,x^{4}+b \,x^{2}+a}"," ",0,"2*(-1/4*b/a/(4*a*c-b^2)*c*x^(5/2)+1/4*(2*a*c-b^2)/(4*a*c-b^2)/a*x^(1/2))/(c*x^4+b*x^2+a)+1/8/a/(4*a*c-b^2)*sum((-3*_R^4*b*c+14*a*c-3*b^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1079,1,245,469,0.027000," ","int(1/x^(3/2)/(c*x^4+b*x^2+a)^2,x)","-\frac{c^{2} x^{\frac{7}{2}}}{\left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c \,x^{\frac{7}{2}}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 b c \,x^{\frac{3}{2}}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{3} x^{\frac{3}{2}}}{2 \left(c \,x^{4}+b \,x^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{\left(\left(18 a c -5 b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} c +\left(23 a c -5 b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{8 \left(4 a c -b^{2}\right) a^{2} \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}-\frac{2}{a^{2} \sqrt{x}}"," ",0,"-1/a/(c*x^4+b*x^2+a)*c^2/(4*a*c-b^2)*x^(7/2)+1/2/a^2/(c*x^4+b*x^2+a)*c/(4*a*c-b^2)*x^(7/2)*b^2-3/2/a/(c*x^4+b*x^2+a)*b/(4*a*c-b^2)*x^(3/2)*c+1/2/a^2/(c*x^4+b*x^2+a)*b^3/(4*a*c-b^2)*x^(3/2)-1/8/a^2/(4*a*c-b^2)*sum((c*(18*a*c-5*b^2)*_R^6+b*(23*a*c-5*b^2)*_R^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))-2/a^2/x^(1/2)","C"
1080,1,275,523,0.039000," ","int(x^(15/2)/(c*x^4+b*x^2+a)^3,x)","\frac{3 \left(\left(-28 a c +b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} b +12 a^{2} c +a \,b^{2}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{\left(28 a c -b^{2}\right) b \,x^{\frac{13}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \left(8 a c +b^{2}\right) a b \,x^{\frac{5}{2}}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(68 a^{2} c^{2}+7 a \,b^{2} c +3 b^{4}\right) x^{\frac{9}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{3 \left(12 a c +b^{2}\right) a^{2} \sqrt{x}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(-3/32*a^2*(12*a*c+b^2)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(1/2)-3/16*a/c*b*(8*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(5/2)-1/32*(68*a^2*c^2+7*a*b^2*c+3*b^4)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(9/2)-1/32*b*(28*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(13/2))/(c*x^4+b*x^2+a)^2+3/64/c/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((b*(-28*a*c+b^2)*_R^4+12*a^2*c+a*b^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1081,1,242,467,0.038000," ","int(x^(13/2)/(c*x^4+b*x^2+a)^3,x)","\frac{\left(\left(28 a c +5 b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6}-72 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} a b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{\frac{2 \left(28 a c +5 b^{2}\right) c \,x^{\frac{15}{2}}}{512 a^{2} c^{2}-256 a \,b^{2} c +32 b^{4}}+\frac{9 \left(4 a c +b^{2}\right) b \,x^{\frac{11}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 a^{2} b \,x^{\frac{3}{2}}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(4 a c -37 b^{2}\right) a \,x^{\frac{7}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*b*x^(3/2)-1/32*a*(4*a*c-37*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(7/2)+9/32*b*(4*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(11/2)+1/32*c*(28*a*c+5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(15/2))/(c*x^4+b*x^2+a)^2+1/64/(16*a^2*c^2-8*a*b^2*c+b^4)*sum(((28*a*c+5*b^2)*_R^6-72*_R^2*a*b)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1082,1,241,467,0.036000," ","int(x^(11/2)/(c*x^4+b*x^2+a)^3,x)","\frac{3 \left(\left(20 a c +7 b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4}-8 a b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{\frac{2 \left(20 a c +7 b^{2}\right) c \,x^{\frac{13}{2}}}{512 a^{2} c^{2}-256 a \,b^{2} c +32 b^{4}}+\frac{2 \left(28 a c +11 b^{2}\right) b \,x^{\frac{9}{2}}}{512 a^{2} c^{2}-256 a \,b^{2} c +32 b^{4}}+\frac{3 a^{2} b \sqrt{x}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \left(4 a c -13 b^{2}\right) a \,x^{\frac{5}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(3/4/(16*a^2*c^2-8*a*b^2*c+b^4)*a^2*b*x^(1/2)-3/32*(4*a*c-13*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*a*x^(5/2)+1/32*b*(28*a*c+11*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(9/2)+1/32*c*(20*a*c+7*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(13/2))/(c*x^4+b*x^2+a)^2+3/64/(16*a^2*c^2-8*a*b^2*c+b^4)*sum(((20*a*c+7*b^2)*_R^4-8*a*b)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1083,1,244,429,0.036000," ","int(x^(9/2)/(c*x^4+b*x^2+a)^3,x)","-\frac{3 \left(8 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} b c +\left(-20 a c -7 b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{3 b \,c^{2} x^{\frac{15}{2}}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 \left(4 a c -13 b^{2}\right) c \,x^{\frac{11}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(28 a c +11 b^{2}\right) b \,x^{\frac{7}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(20 a c +7 b^{2}\right) a \,x^{\frac{3}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(-1/32*a*(20*a*c+7*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(3/2)-1/32*b*(28*a*c+11*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(7/2)+3/32*(4*a*c-13*b^2)*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(11/2)-3/4*b*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(15/2))/(c*x^4+b*x^2+a)^2-3/64/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((8*_R^6*b*c+(-20*a*c-7*b^2)*_R^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1084,1,237,429,0.036000," ","int(x^(7/2)/(c*x^4+b*x^2+a)^3,x)","\frac{\left(-72 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} b c +28 a c +5 b^{2}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{3 b \,c^{2} x^{\frac{13}{2}}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{2 \left(4 a c -37 b^{2}\right) c \,x^{\frac{9}{2}}}{512 a^{2} c^{2}-256 a \,b^{2} c +32 b^{4}}-\frac{9 \left(4 a c +b^{2}\right) b \,x^{\frac{5}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(28 a c +5 b^{2}\right) a \sqrt{x}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(-1/32*a*(28*a*c+5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(1/2)-9/32*b*(4*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(5/2)+1/32*c*(4*a*c-37*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(9/2)-3/4*b*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(13/2))/(c*x^4+b*x^2+a)^2+1/64/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((-72*_R^4*b*c+28*a*c+5*b^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1085,1,277,490,0.037000," ","int(x^(5/2)/(c*x^4+b*x^2+a)^3,x)","\frac{3 \left(\left(12 a c +b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} c +\left(-28 a c +b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2} b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{\frac{3 \left(12 a c +b^{2}\right) c^{2} x^{\frac{15}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{3 \left(8 a c +b^{2}\right) b c \,x^{\frac{11}{2}}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(68 a^{2} c^{2}+7 a \,b^{2} c +3 b^{4}\right) x^{\frac{7}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{2 \left(28 a c -b^{2}\right) b \,x^{\frac{3}{2}}}{512 a^{2} c^{2}-256 a \,b^{2} c +32 b^{4}}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(1/32*b*(28*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(3/2)+1/32*(68*a^2*c^2+7*a*b^2*c+3*b^4)/a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(7/2)+3/16/a*c*b*(8*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(11/2)+3/32*c^2*(12*a*c+b^2)/a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(15/2))/(c*x^4+b*x^2+a)^2+3/64/a/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((c*(12*a*c+b^2)*_R^6+b*(-28*a*c+b^2)*_R^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1086,1,270,490,0.037000," ","int(x^(3/2)/(c*x^4+b*x^2+a)^3,x)","\frac{3 \left(\left(44 a c +b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} c -12 a b c +b^{3}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{\frac{\left(44 a c +b^{2}\right) c^{2} x^{\frac{13}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(32 a c +b^{2}\right) b c \,x^{\frac{9}{2}}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(76 a^{2} c^{2}+13 a \,b^{2} c +b^{4}\right) x^{\frac{5}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{3 \left(12 a c -b^{2}\right) b \sqrt{x}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(3/32*b*(12*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(1/2)+1/32*(76*a^2*c^2+13*a*b^2*c+b^4)/a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(5/2)+1/16/a*c*b*(32*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(9/2)+1/32*c^2*(44*a*c+b^2)/a/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(13/2))/(c*x^4+b*x^2+a)^2+3/64/a/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((c*(44*a*c+b^2)*_R^4-12*a*b*c+b^3)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1087,1,321,554,0.053000," ","int(x^(1/2)/(c*x^4+b*x^2+a)^3,x)","-\frac{\left(\left(44 a c -5 b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{6} b c +\left(-260 a^{2} c^{2}+49 a \,b^{2} c -5 b^{4}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{2}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2} \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{\left(44 a c -5 b^{2}\right) b \,c^{2} x^{\frac{15}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{\left(52 a^{2} c^{2}-89 a \,b^{2} c +10 b^{4}\right) c \,x^{\frac{11}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{\left(8 a^{2} c^{2}+36 a \,b^{2} c -5 b^{4}\right) b \,x^{\frac{7}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{3 \left(28 a^{2} c^{2}-23 a \,b^{2} c +3 b^{4}\right) x^{\frac{3}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(3/32*(28*a^2*c^2-23*a*b^2*c+3*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^(3/2)-1/32*b*(8*a^2*c^2+36*a*b^2*c-5*b^4)/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(7/2)+1/32/a^2*c*(52*a^2*c^2-89*a*b^2*c+10*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(11/2)-1/32*c^2*b*(44*a*c-5*b^2)/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(15/2))/(c*x^4+b*x^2+a)^2-1/64/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((b*c*(44*a*c-5*b^2)*_R^6+(-260*a^2*c^2+49*a*b^2*c-5*b^4)*_R^2)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1088,1,316,554,0.038000," ","int(1/x^(1/2)/(c*x^4+b*x^2+a)^3,x)","\frac{3 \left(\left(-52 a c +7 b^{2}\right) \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{4} b c +140 a^{2} c^{2}-59 a \,b^{2} c +7 b^{4}\right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)+\sqrt{x}\right)}{64 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2} \left(2 \RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(c \,\textit{\_Z}^{8}+b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}+\frac{-\frac{\left(52 a c -7 b^{2}\right) b \,c^{2} x^{\frac{13}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{\left(60 a^{2} c^{2}-107 a \,b^{2} c +14 b^{4}\right) c \,x^{\frac{9}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{\left(8 a^{2} c^{2}+44 a \,b^{2} c -7 b^{4}\right) b \,x^{\frac{5}{2}}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{\left(92 a^{2} c^{2}-79 a \,b^{2} c +11 b^{4}\right) \sqrt{x}}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}"," ",0,"2*(1/32*(92*a^2*c^2-79*a*b^2*c+11*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^(1/2)-1/32*b*(8*a^2*c^2+44*a*b^2*c-7*b^4)/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(5/2)+1/32/a^2*c*(60*a^2*c^2-107*a*b^2*c+14*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(9/2)-1/32*c^2*b*(52*a*c-7*b^2)/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^(13/2))/(c*x^4+b*x^2+a)^2+3/64/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*sum((b*c*(-52*a*c+7*b^2)*_R^4+140*a^2*c^2-59*a*b^2*c+7*b^4)/(2*_R^7*c+_R^3*b)*ln(-_R+x^(1/2)),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
1089,0,0,121,0.083000," ","int((d*x)^(3/2)*(c*x^4+b*x^2+a)^(1/2),x)","\int \left(d x \right)^{\frac{3}{2}} \sqrt{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((d*x)^(3/2)*(c*x^4+b*x^2+a)^(1/2),x)","F"
1090,0,0,121,0.057000," ","int((d*x)^(1/2)*(c*x^4+b*x^2+a)^(1/2),x)","\int \sqrt{d x}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((d*x)^(1/2)*(c*x^4+b*x^2+a)^(1/2),x)","F"
1091,0,0,121,0.050000," ","int((c*x^4+b*x^2+a)^(1/2)/(d*x)^(1/2),x)","\int \frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{\sqrt{d x}}\, dx"," ",0,"int((c*x^4+b*x^2+a)^(1/2)/(d*x)^(1/2),x)","F"
1092,0,0,121,0.053000," ","int((c*x^4+b*x^2+a)^(1/2)/(d*x)^(3/2),x)","\int \frac{\sqrt{c \,x^{4}+b \,x^{2}+a}}{\left(d x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*x^4+b*x^2+a)^(1/2)/(d*x)^(3/2),x)","F"
1093,0,0,122,0.062000," ","int((d*x)^(3/2)*(c*x^4+b*x^2+a)^(3/2),x)","\int \left(d x \right)^{\frac{3}{2}} \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}\, dx"," ",0,"int((d*x)^(3/2)*(c*x^4+b*x^2+a)^(3/2),x)","F"
1094,0,0,122,0.061000," ","int((d*x)^(1/2)*(c*x^4+b*x^2+a)^(3/2),x)","\int \sqrt{d x}\, \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}\, dx"," ",0,"int((d*x)^(1/2)*(c*x^4+b*x^2+a)^(3/2),x)","F"
1095,0,0,122,0.057000," ","int((c*x^4+b*x^2+a)^(3/2)/(d*x)^(1/2),x)","\int \frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{\sqrt{d x}}\, dx"," ",0,"int((c*x^4+b*x^2+a)^(3/2)/(d*x)^(1/2),x)","F"
1096,0,0,122,0.058000," ","int((c*x^4+b*x^2+a)^(3/2)/(d*x)^(3/2),x)","\int \frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}{\left(d x \right)^{\frac{3}{2}}}\, dx"," ",0,"int((c*x^4+b*x^2+a)^(3/2)/(d*x)^(3/2),x)","F"
1097,0,0,121,0.028000," ","int((d*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{\left(d x \right)^{\frac{3}{2}}}{\sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int((d*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x)","F"
1098,0,0,121,0.023000," ","int((d*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{\sqrt{d x}}{\sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int((d*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x)","F"
1099,0,0,121,0.024000," ","int(1/(d*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{1}{\sqrt{d x}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int(1/(d*x)^(1/2)/(c*x^4+b*x^2+a)^(1/2),x)","F"
1100,0,0,121,0.055000," ","int(1/(d*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{1}{\left(d x \right)^{\frac{3}{2}} \sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int(1/(d*x)^(3/2)/(c*x^4+b*x^2+a)^(1/2),x)","F"
1101,0,0,124,0.026000," ","int((d*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{\left(d x \right)^{\frac{3}{2}}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x)","F"
1102,0,0,124,0.027000," ","int((d*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{\sqrt{d x}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x)","F"
1103,0,0,124,0.034000," ","int(1/(d*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{1}{\sqrt{d x}\, \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(d*x)^(1/2)/(c*x^4+b*x^2+a)^(3/2),x)","F"
1104,0,0,124,0.123000," ","int(1/(d*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{1}{\left(d x \right)^{\frac{3}{2}} \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(d*x)^(3/2)/(c*x^4+b*x^2+a)^(3/2),x)","F"
1105,1,782,156,0.009000," ","int((d*x)^m*(c*x^4+b*x^2+a)^3,x)","\frac{\left(c^{3} m^{6} x^{12}+36 c^{3} m^{5} x^{12}+3 b \,c^{2} m^{6} x^{10}+505 c^{3} m^{4} x^{12}+114 b \,c^{2} m^{5} x^{10}+3480 c^{3} m^{3} x^{12}+3 a \,c^{2} m^{6} x^{8}+3 b^{2} c \,m^{6} x^{8}+1665 b \,c^{2} m^{4} x^{10}+12139 c^{3} m^{2} x^{12}+120 a \,c^{2} m^{5} x^{8}+120 b^{2} c \,m^{5} x^{8}+11820 b \,c^{2} m^{3} x^{10}+19524 c^{3} m \,x^{12}+6 a b c \,m^{6} x^{6}+1839 a \,c^{2} m^{4} x^{8}+b^{3} m^{6} x^{6}+1839 b^{2} c \,m^{4} x^{8}+42117 b \,c^{2} m^{2} x^{10}+10395 c^{3} x^{12}+252 a b c \,m^{5} x^{6}+13584 a \,c^{2} m^{3} x^{8}+42 b^{3} m^{5} x^{6}+13584 b^{2} c \,m^{3} x^{8}+68706 b \,c^{2} m \,x^{10}+3 a^{2} c \,m^{6} x^{4}+3 a \,b^{2} m^{6} x^{4}+4074 a b c \,m^{4} x^{6}+49881 a \,c^{2} m^{2} x^{8}+679 b^{3} m^{4} x^{6}+49881 b^{2} c \,m^{2} x^{8}+36855 b \,c^{2} x^{10}+132 a^{2} c \,m^{5} x^{4}+132 a \,b^{2} m^{5} x^{4}+31752 a b c \,m^{3} x^{6}+83064 a \,c^{2} m \,x^{8}+5292 b^{3} m^{3} x^{6}+83064 b^{2} c m \,x^{8}+3 a^{2} b \,m^{6} x^{2}+2259 a^{2} c \,m^{4} x^{4}+2259 a \,b^{2} m^{4} x^{4}+122010 a b c \,m^{2} x^{6}+45045 a \,c^{2} x^{8}+20335 b^{3} m^{2} x^{6}+45045 b^{2} c \,x^{8}+138 a^{2} b \,m^{5} x^{2}+18840 a^{2} c \,m^{3} x^{4}+18840 a \,b^{2} m^{3} x^{4}+209916 a b c m \,x^{6}+34986 b^{3} m \,x^{6}+a^{3} m^{6}+2505 a^{2} b \,m^{4} x^{2}+77937 a^{2} c \,m^{2} x^{4}+77937 a \,b^{2} m^{2} x^{4}+115830 a b c \,x^{6}+19305 b^{3} x^{6}+48 a^{3} m^{5}+22620 a^{2} b \,m^{3} x^{2}+142308 a^{2} c m \,x^{4}+142308 a \,b^{2} m \,x^{4}+925 a^{3} m^{4}+104277 a^{2} b \,m^{2} x^{2}+81081 a^{2} c \,x^{4}+81081 a \,b^{2} x^{4}+9120 a^{3} m^{3}+219162 a^{2} b m \,x^{2}+48259 a^{3} m^{2}+135135 a^{2} b \,x^{2}+129072 a^{3} m +135135 a^{3}\right) x \left(d x \right)^{m}}{\left(m +13\right) \left(m +11\right) \left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x*(c^3*m^6*x^12+36*c^3*m^5*x^12+3*b*c^2*m^6*x^10+505*c^3*m^4*x^12+114*b*c^2*m^5*x^10+3480*c^3*m^3*x^12+3*a*c^2*m^6*x^8+3*b^2*c*m^6*x^8+1665*b*c^2*m^4*x^10+12139*c^3*m^2*x^12+120*a*c^2*m^5*x^8+120*b^2*c*m^5*x^8+11820*b*c^2*m^3*x^10+19524*c^3*m*x^12+6*a*b*c*m^6*x^6+1839*a*c^2*m^4*x^8+b^3*m^6*x^6+1839*b^2*c*m^4*x^8+42117*b*c^2*m^2*x^10+10395*c^3*x^12+252*a*b*c*m^5*x^6+13584*a*c^2*m^3*x^8+42*b^3*m^5*x^6+13584*b^2*c*m^3*x^8+68706*b*c^2*m*x^10+3*a^2*c*m^6*x^4+3*a*b^2*m^6*x^4+4074*a*b*c*m^4*x^6+49881*a*c^2*m^2*x^8+679*b^3*m^4*x^6+49881*b^2*c*m^2*x^8+36855*b*c^2*x^10+132*a^2*c*m^5*x^4+132*a*b^2*m^5*x^4+31752*a*b*c*m^3*x^6+83064*a*c^2*m*x^8+5292*b^3*m^3*x^6+83064*b^2*c*m*x^8+3*a^2*b*m^6*x^2+2259*a^2*c*m^4*x^4+2259*a*b^2*m^4*x^4+122010*a*b*c*m^2*x^6+45045*a*c^2*x^8+20335*b^3*m^2*x^6+45045*b^2*c*x^8+138*a^2*b*m^5*x^2+18840*a^2*c*m^3*x^4+18840*a*b^2*m^3*x^4+209916*a*b*c*m*x^6+34986*b^3*m*x^6+a^3*m^6+2505*a^2*b*m^4*x^2+77937*a^2*c*m^2*x^4+77937*a*b^2*m^2*x^4+115830*a*b*c*x^6+19305*b^3*x^6+48*a^3*m^5+22620*a^2*b*m^3*x^2+142308*a^2*c*m*x^4+142308*a*b^2*m*x^4+925*a^3*m^4+104277*a^2*b*m^2*x^2+81081*a^2*c*x^4+81081*a*b^2*x^4+9120*a^3*m^3+219162*a^2*b*m*x^2+48259*a^3*m^2+135135*a^2*b*x^2+129072*a^3*m+135135*a^3)*(d*x)^m/(m+13)/(m+11)/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)","B"
1106,1,301,101,0.008000," ","int((d*x)^m*(c*x^4+b*x^2+a)^2,x)","\frac{\left(c^{2} m^{4} x^{8}+16 c^{2} m^{3} x^{8}+2 b c \,m^{4} x^{6}+86 c^{2} m^{2} x^{8}+36 b c \,m^{3} x^{6}+176 c^{2} m \,x^{8}+2 a c \,m^{4} x^{4}+b^{2} m^{4} x^{4}+208 b c \,m^{2} x^{6}+105 c^{2} x^{8}+40 a c \,m^{3} x^{4}+20 b^{2} m^{3} x^{4}+444 b c m \,x^{6}+2 a b \,m^{4} x^{2}+260 a c \,m^{2} x^{4}+130 b^{2} m^{2} x^{4}+270 b c \,x^{6}+44 a b \,m^{3} x^{2}+600 a c m \,x^{4}+300 b^{2} m \,x^{4}+a^{2} m^{4}+328 a b \,m^{2} x^{2}+378 a c \,x^{4}+189 b^{2} x^{4}+24 a^{2} m^{3}+916 a b m \,x^{2}+206 a^{2} m^{2}+630 a b \,x^{2}+744 a^{2} m +945 a^{2}\right) x \left(d x \right)^{m}}{\left(m +9\right) \left(m +7\right) \left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x*(c^2*m^4*x^8+16*c^2*m^3*x^8+2*b*c*m^4*x^6+86*c^2*m^2*x^8+36*b*c*m^3*x^6+176*c^2*m*x^8+2*a*c*m^4*x^4+b^2*m^4*x^4+208*b*c*m^2*x^6+105*c^2*x^8+40*a*c*m^3*x^4+20*b^2*m^3*x^4+444*b*c*m*x^6+2*a*b*m^4*x^2+260*a*c*m^2*x^4+130*b^2*m^2*x^4+270*b*c*x^6+44*a*b*m^3*x^2+600*a*c*m*x^4+300*b^2*m*x^4+a^2*m^4+328*a*b*m^2*x^2+378*a*c*x^4+189*b^2*x^4+24*a^2*m^3+916*a*b*m*x^2+206*a^2*m^2+630*a*b*x^2+744*a^2*m+945*a^2)*(d*x)^m/(m+9)/(m+7)/(m+5)/(m+3)/(m+1)","B"
1107,1,78,52,0.004000," ","int((d*x)^m*(c*x^4+b*x^2+a),x)","\frac{\left(c \,m^{2} x^{4}+4 c m \,x^{4}+b \,m^{2} x^{2}+3 c \,x^{4}+6 b m \,x^{2}+a \,m^{2}+5 b \,x^{2}+8 a m +15 a \right) x \left(d x \right)^{m}}{\left(m +5\right) \left(m +3\right) \left(m +1\right)}"," ",0,"x*(c*m^2*x^4+4*c*m*x^4+b*m^2*x^2+3*c*x^4+6*b*m*x^2+a*m^2+5*b*x^2+8*a*m+15*a)*(d*x)^m/(m+5)/(m+3)/(m+1)","A"
1108,0,0,157,0.035000," ","int((d*x)^m/(c*x^4+b*x^2+a),x)","\int \frac{\left(d x \right)^{m}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((d*x)^m/(c*x^4+b*x^2+a),x)","F"
1109,0,0,289,0.027000," ","int((d*x)^m/(c*x^4+b*x^2+a)^2,x)","\int \frac{\left(d x \right)^{m}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{2}}\, dx"," ",0,"int((d*x)^m/(c*x^4+b*x^2+a)^2,x)","F"
1110,0,0,136,0.011000," ","int((d*x)^m*(c*x^4+b*x^2+a)^(3/2),x)","\int \left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}} \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(c*x^4+b*x^2+a)^(3/2),x)","F"
1111,0,0,135,0.010000," ","int((d*x)^m*(c*x^4+b*x^2+a)^(1/2),x)","\int \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(c*x^4+b*x^2+a)^(1/2),x)","F"
1112,0,0,135,0.014000," ","int((d*x)^m/(c*x^4+b*x^2+a)^(1/2),x)","\int \frac{\left(d x \right)^{m}}{\sqrt{c \,x^{4}+b \,x^{2}+a}}\, dx"," ",0,"int((d*x)^m/(c*x^4+b*x^2+a)^(1/2),x)","F"
1113,0,0,138,0.011000," ","int((d*x)^m/(c*x^4+b*x^2+a)^(3/2),x)","\int \frac{\left(d x \right)^{m}}{\left(c \,x^{4}+b \,x^{2}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^m/(c*x^4+b*x^2+a)^(3/2),x)","F"
1114,0,0,143,0.074000," ","int((d*x)^m*(c*x^4+b*x^2+a)^p,x)","\int \left(d x \right)^{m} \left(c \,x^{4}+b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((d*x)^m*(c*x^4+b*x^2+a)^p,x)","F"
1115,0,0,242,0.060000," ","int(x^7*(c*x^4+b*x^2+a)^p,x)","\int x^{7} \left(c \,x^{4}+b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^7*(c*x^4+b*x^2+a)^p,x)","F"
1116,0,0,208,0.048000," ","int(x^5*(c*x^4+b*x^2+a)^p,x)","\int x^{5} \left(c \,x^{4}+b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^5*(c*x^4+b*x^2+a)^p,x)","F"
1117,0,0,147,0.035000," ","int(x^3*(c*x^4+b*x^2+a)^p,x)","\int x^{3} \left(c \,x^{4}+b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^3*(c*x^4+b*x^2+a)^p,x)","F"
1118,0,0,115,0.023000," ","int(x*(c*x^4+b*x^2+a)^p,x)","\int x \left(c \,x^{4}+b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x*(c*x^4+b*x^2+a)^p,x)","F"
1119,0,0,144,0.018000," ","int((c*x^4+b*x^2+a)^p/x,x)","\int \frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{p}}{x}\, dx"," ",0,"int((c*x^4+b*x^2+a)^p/x,x)","F"
1120,0,0,156,0.032000," ","int((c*x^4+b*x^2+a)^p/x^3,x)","\int \frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{p}}{x^{3}}\, dx"," ",0,"int((c*x^4+b*x^2+a)^p/x^3,x)","F"
1121,0,0,154,0.042000," ","int((c*x^4+b*x^2+a)^p/x^5,x)","\int \frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{p}}{x^{5}}\, dx"," ",0,"int((c*x^4+b*x^2+a)^p/x^5,x)","F"
1122,0,0,124,0.038000," ","int(x^4*(c*x^4+b*x^2+a)^p,x)","\int x^{4} \left(c \,x^{4}+b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^4*(c*x^4+b*x^2+a)^p,x)","F"
1123,0,0,124,0.029000," ","int(x^2*(c*x^4+b*x^2+a)^p,x)","\int x^{2} \left(c \,x^{4}+b \,x^{2}+a \right)^{p}\, dx"," ",0,"int(x^2*(c*x^4+b*x^2+a)^p,x)","F"
1124,0,0,121,0.016000," ","int((c*x^4+b*x^2+a)^p,x)","\int \left(c \,x^{4}+b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((c*x^4+b*x^2+a)^p,x)","F"
1125,0,0,124,0.030000," ","int((c*x^4+b*x^2+a)^p/x^2,x)","\int \frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{p}}{x^{2}}\, dx"," ",0,"int((c*x^4+b*x^2+a)^p/x^2,x)","F"
1126,0,0,124,0.038000," ","int((c*x^4+b*x^2+a)^p/x^4,x)","\int \frac{\left(c \,x^{4}+b \,x^{2}+a \right)^{p}}{x^{4}}\, dx"," ",0,"int((c*x^4+b*x^2+a)^p/x^4,x)","F"