1,1,533,445,0.030000," ","int((B*x^2+A)*(e*x^2+d)^3/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, A \,d^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\left(\frac{\sqrt{c \,x^{4}+a}\, x^{5}}{7 c}+\frac{5 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{2}}-\frac{5 \sqrt{c \,x^{4}+a}\, a x}{21 c^{2}}\right) B \,e^{3}+\frac{i \left(3 A \,d^{2} e +B \,d^{3}\right) \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}}+\left(A \,e^{3}+3 B d \,e^{2}\right) \left(\frac{\sqrt{c \,x^{4}+a}\, x^{3}}{5 c}-\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) a^{\frac{3}{2}}}{5 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{\frac{3}{2}}}\right)+\left(3 A d \,e^{2}+3 B \,d^{2} e \right) \left(-\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}\right)"," ",0,"B*e^3*(1/7/c*x^5*(c*x^4+a)^(1/2)-5/21*a/c^2*x*(c*x^4+a)^(1/2)+5/21*a^2/c^2/(I/a^(1/2)*c^(1/2))^(1/2)*(1-I/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*c^(1/2)*x^2)^(1/2)/(c*x^4+a)^(1/2)*EllipticF(x*(I/a^(1/2)*c^(1/2))^(1/2),I))+(A*e^3+3*B*d*e^2)*(1/5/c*x^3*(c*x^4+a)^(1/2)-3/5*I*a^(3/2)/c^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(1-I/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*c^(1/2)*x^2)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF(x*(I/a^(1/2)*c^(1/2))^(1/2),I)-EllipticE(x*(I/a^(1/2)*c^(1/2))^(1/2),I)))+(3*A*d*e^2+3*B*d^2*e)*(1/3/c*x*(c*x^4+a)^(1/2)-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))+I*(3*A*d^2*e+B*d^3)*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(1-I/a^(1/2)*c^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*c^(1/2)*x^2)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF(x*(I/a^(1/2)*c^(1/2))^(1/2),I)-EllipticE(x*(I/a^(1/2)*c^(1/2))^(1/2),I))+A*d^3/(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"
2,1,403,363,0.009000," ","int((B*x^2+A)*(e*x^2+d)^2/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, A \,d^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\left(\frac{\sqrt{c \,x^{4}+a}\, x^{3}}{5 c}-\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) a^{\frac{3}{2}}}{5 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{\frac{3}{2}}}\right) B \,e^{2}+\frac{i \left(2 A d e +B \,d^{2}\right) \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}}+\left(A \,e^{2}+2 B d e \right) \left(-\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}\right)"," ",0,"B*e^2*(1/5*(c*x^4+a)^(1/2)/c*x^3-3/5*I*a^(3/2)/c^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+(A*e^2+2*B*d*e)*(1/3*(c*x^4+a)^(1/2)/c*x-1/3*a/c/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+I*(2*A*d*e+B*d^2)*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+A*d^2/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
3,1,269,285,0.008000," ","int((B*x^2+A)*(e*x^2+d)/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, A d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\left(-\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}\right) B e +\frac{i \left(A e +B d \right) \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,"B*e*(1/3*(c*x^4+a)^(1/2)/c*x-1/3*a/c/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+I*(A*e+B*d)*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))+A*d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)","C"
4,1,169,238,0.005000," ","int((B*x^2+A)/(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)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) B \sqrt{a}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{c}}"," ",0,"I*B*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))+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"
5,1,192,353,0.039000," ","int((B*x^2+A)/(e*x^2+d)/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, B \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, e}+\frac{\left(A e -B d \right) \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d e}"," ",0,"B/e/(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)+(A*e-B*d)/e/d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)*e/d,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))","C"
6,1,679,622,0.035000," ","int((B*x^2+A)/(e*x^2+d)^2/(c*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, B \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d e}+\frac{\left(A e -B d \right) \left(\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\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)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(e \,x^{2}+d \right) d}\right)}{e}"," ",0,"(A*e-B*d)/e*(1/2*e^2/(a*e^2+c*d^2)/d*x*(c*x^4+a)^(1/2)/(e*x^2+d)-1/2*c/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-1/2*I*c^(1/2)*e/d/(a*e^2+c*d^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)+1/2*I*c^(1/2)*e/d/(a*e^2+c*d^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)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2/d^2/(a*e^2+c*d^2)*e^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)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a+3/2/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c)+B/e/d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))","C"
7,1,1591,848,0.036000," ","int((B*x^2+A)/(e*x^2+d)^3/(c*x^4+a)^(1/2),x)","\frac{\left(\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\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)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e^{2} x}{2 \left(a \,e^{2}+c \,d^{2}\right) \left(e \,x^{2}+d \right) d}\right) B}{e}+\frac{\left(A e -B d \right) \left(\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{2} e^{4} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{3}}+\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{c}\, e^{3} \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}-\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{c}\, e^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a c \,e^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}+\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a c \,e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}+\frac{9 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{3}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}-\frac{9 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{3}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}-\frac{7 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{15 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e^{2} x}{4 \left(a \,e^{2}+c \,d^{2}\right) \left(e \,x^{2}+d \right)^{2} d}+\frac{3 \left(a \,e^{2}+3 c \,d^{2}\right) \sqrt{c \,x^{4}+a}\, e^{2} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right) d^{2}}\right)}{e}"," ",0,"B/e*(1/2/(a*e^2+c*d^2)*(c*x^4+a)^(1/2)/(e*x^2+d)/d*e^2*x-1/2*c/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-1/2*I*c^(1/2)*e/d/(a*e^2+c*d^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)+1/2*I*c^(1/2)*e/d/(a*e^2+c*d^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)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2/d^2/(a*e^2+c*d^2)*e^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)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a+3/2/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c)+(A*e-B*d)/e*(1/4*e^2/(a*e^2+c*d^2)/d*x*(c*x^4+a)^(1/2)/(e*x^2+d)^2+3/8*e^2*(a*e^2+3*c*d^2)/d^2/(a*e^2+c*d^2)^2*x*(c*x^4+a)^(1/2)/(e*x^2+d)-1/8*c/d/(a*e^2+c*d^2)^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)*a*e^2-7/8*c^2*d/(a*e^2+c*d^2)^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)-9/8*I*c^(3/2)*e/(a*e^2+c*d^2)^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)+3/8*I*c^(1/2)*e^3/d^2/(a*e^2+c*d^2)^2*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+9/8*I*c^(3/2)*e/(a*e^2+c*d^2)^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)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-3/8*I*c^(1/2)*e^3/d^2/(a*e^2+c*d^2)^2*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+3/8/d^3/(a*e^2+c*d^2)^2*e^4/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a^2+3/4/(a*e^2+c*d^2)^2/d*e^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)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a*c+15/8*d/(a*e^2+c*d^2)^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)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c^2)","C"
8,1,588,946,0.041000," ","int((B*x^2+A)*(e*x^2+d)^3/(c*x^4+a)^(3/2),x)","\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}\right) A \,d^{3}+\left(\frac{a x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, c^{2}}-\frac{5 \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)}{6 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{2}}+\frac{\sqrt{c \,x^{4}+a}\, x}{3 c^{2}}\right) B \,e^{3}+\left(A \,e^{3}+3 B d \,e^{2}\right) \left(-\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, c}+\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{\frac{3}{2}}}\right)+\left(3 A d \,e^{2}+3 B \,d^{2} e \right) \left(-\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, c}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c}\right)+\left(3 A \,d^{2} e +B \,d^{3}\right) \left(\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}\, \sqrt{c}}\right)"," ",0,"B*e^3*(1/2/c^2*a*x/((x^4+a/c)*c)^(1/2)+1/3/c^2*x*(c*x^4+a)^(1/2)-5/6*a/c^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))+(A*e^3+3*B*d*e^2)*(-1/2/c*x^3/((x^4+a/c)*c)^(1/2)+3/2*I/c^(3/2)*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+(3*A*d*e^2+3*B*d^2*e)*(-1/2/c*x/((x^4+a/c)*c)^(1/2)+1/2/c/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+(3*A*d^2*e+B*d^3)*(1/2/a*x^3/((x^4+a/c)*c)^(1/2)-1/2*I/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+A*d^3*(1/2/a*x/((x^4+a/c)*c)^(1/2)+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
9,1,458,725,0.010000," ","int((B*x^2+A)*(e*x^2+d)^2/(c*x^4+a)^(3/2),x)","\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}\right) A \,d^{2}+\left(-\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, c}+\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c^{\frac{3}{2}}}\right) B \,e^{2}+\left(A \,e^{2}+2 B d e \right) \left(-\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, c}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c}\right)+\left(2 A d e +B \,d^{2}\right) \left(\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}\, \sqrt{c}}\right)"," ",0,"B*e^2*(-1/2/((x^4+a/c)*c)^(1/2)/c*x^3+3/2*I/c^(3/2)*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)))+(A*e^2+2*B*d*e)*(-1/2/((x^4+a/c)*c)^(1/2)/c*x+1/2/c/(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))+(2*A*d*e+B*d^2)*(1/2/((x^4+a/c)*c)^(1/2)/a*x^3-1/2*I/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+A*d^2*(1/2/((x^4+a/c)*c)^(1/2)/a*x+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
10,1,320,410,0.004000," ","int((B*x^2+A)*(e*x^2+d)/(c*x^4+a)^(3/2),x)","\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}\right) A d +\left(-\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, c}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, c}\right) B e +\left(A e +B d \right) \left(\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}\, \sqrt{c}}\right)"," ",0,"B*e*(-1/2/((x^4+a/c)*c)^(1/2)/c*x+1/2/c/(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))+(A*e+B*d)*(1/2/((x^4+a/c)*c)^(1/2)/a*x^3-1/2*I/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+A*d*(1/2/((x^4+a/c)*c)^(1/2)/a*x+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
11,1,217,266,0.005000," ","int((B*x^2+A)/(c*x^4+a)^(3/2),x)","\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}\right) A +\left(\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}\, \sqrt{c}}\right) B"," ",0,"B*(1/2/((x^4+a/c)*c)^(1/2)/a*x^3-1/2*I/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)/c^(1/2)*(EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)))+A*(1/2/((x^4+a/c)*c)^(1/2)/a*x+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))","C"
12,1,564,724,0.034000," ","int((B*x^2+A)/(e*x^2+d)/(c*x^4+a)^(3/2),x)","\frac{\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{c}\right) c}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}\right) B}{e}+\frac{\left(A e -B d \right) \left(-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{c}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{c}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{2 \left(\frac{e \,x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right) a}-\frac{d x}{4 \left(a \,e^{2}+c \,d^{2}\right) a}\right) c}{\sqrt{\left(x^{4}+\frac{a}{c}\right) c}}\right)}{e}"," ",0,"B/e*(1/2/((x^4+a/c)*c)^(1/2)/a*x+1/2/a/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I))+(A*e-B*d)/e*(-2*c*(1/4/a*e/(a*e^2+c*d^2)*x^3-1/4/a*d/(a*e^2+c*d^2)*x)/((x^4+a/c)*c)^(1/2)+1/2/a*c*d/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*I/a^(1/2)*c^(1/2)*e/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-1/2*I/a^(1/2)*c^(1/2)*e/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/(a*e^2+c*d^2)*e^2/d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)))","C"
13,1,1384,1467,0.043000," ","int((B*x^2+A)/(e*x^2+d)^2/(c*x^4+a)^(3/2),x)","\frac{\left(-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{c}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{c}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \sqrt{a}}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c d \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, a}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{\left(a \,e^{2}+c \,d^{2}\right) \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}-\frac{2 \left(\frac{e \,x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right) a}-\frac{d x}{4 \left(a \,e^{2}+c \,d^{2}\right) a}\right) c}{\sqrt{\left(x^{4}+\frac{a}{c}\right) c}}\right) B}{e}+\frac{\left(A e -B d \right) \left(\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,e^{4} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e^{3} \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} d}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} d}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{\frac{3}{2}} d e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{\frac{3}{2}} d e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a}}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,e^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{7 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e^{4} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right) d}-\frac{2 \left(\frac{c d e \,x^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{\left(a \,e^{2}-c \,d^{2}\right) x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}\right) c}{\sqrt{\left(x^{4}+\frac{a}{c}\right) c}}\right)}{e}"," ",0,"(A*e-B*d)/e*(1/2*e^4/(a*e^2+c*d^2)^2/d*x*(c*x^4+a)^(1/2)/(e*x^2+d)-2*c*(1/2/a*c*d*e/(a*e^2+c*d^2)^2*x^3+1/4/a*(a*e^2-c*d^2)/(a*e^2+c*d^2)^2*x)/((x^4+a/c)*c)^(1/2)-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)*e^2*c/(a*e^2+c*d^2)^2+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)/a*c^2/(a*e^2+c*d^2)^2*d^2-1/2*I*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*c^(1/2)*e^3/d/(a*e^2+c*d^2)^2*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*I*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*c^(1/2)*e^3/d/(a*e^2+c*d^2)^2*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+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^(3/2)*d*e/(a*e^2+c*d^2)^2*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-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^(3/2)*d*e/(a*e^2+c*d^2)^2*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*e^4/d^2/(a*e^2+c*d^2)^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)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a+7/2*e^2/(a*e^2+c*d^2)^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)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c)+B/e*(-2*(1/4/(a*e^2+c*d^2)/a*e*x^3-1/4/(a*e^2+c*d^2)/a*d*x)/((x^4+a/c)*c)^(1/2)*c+1/2/a*c*d/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*I/a^(1/2)*c^(1/2)*e/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-1/2*I/a^(1/2)*c^(1/2)*e/(a*e^2+c*d^2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/(a*e^2+c*d^2)*e^2/d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)))","C"
14,1,2326,2394,0.048000," ","int((B*x^2+A)/(e*x^2+d)^3/(c*x^4+a)^(3/2),x)","\frac{\left(\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a \,e^{4} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{2}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e^{3} \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} d}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{c}\, e^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} d}-\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{\frac{3}{2}} d e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a}}+\frac{i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{\frac{3}{2}} d e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{a}}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2} a}-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,e^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{2}}+\frac{7 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c \,e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e^{4} x}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right) d}-\frac{2 \left(\frac{c d e \,x^{3}}{2 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}+\frac{\left(a \,e^{2}-c \,d^{2}\right) x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} a}\right) c}{\sqrt{\left(x^{4}+\frac{a}{c}\right) c}}\right) B}{e}+\frac{\left(A e -B d \right) \left(\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{2} e^{6} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d^{3}}+\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{c}\, e^{5} \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3} d^{2}}-\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{c}\, e^{5} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3} d^{2}}-\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a c \,e^{4} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3} d}+\frac{3 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, a c \,e^{4} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, d}+\frac{21 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{3}{2}} e^{3} \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{21 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c^{\frac{3}{2}} e^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3}}-\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{\frac{5}{2}} d^{2} e \EllipticE \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a}}+\frac{3 i \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{\frac{5}{2}} d^{2} e \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{a}}+\frac{\sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{3} d^{3} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3} a}-\frac{27 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d \,e^{2} \EllipticF \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , i\right)}{8 \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}\, \left(a \,e^{2}+c \,d^{2}\right)^{3}}+\frac{63 \sqrt{-\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{c}\, x^{2}}{\sqrt{a}}+1}\, c^{2} d \,e^{2} \EllipticPi \left(\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, x , \frac{i \sqrt{a}\, e}{\sqrt{c}\, d}, \frac{\sqrt{-\frac{i \sqrt{c}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}}\right)}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \sqrt{\frac{i \sqrt{c}}{\sqrt{a}}}\, \sqrt{c \,x^{4}+a}}+\frac{\sqrt{c \,x^{4}+a}\, e^{4} x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{2} \left(e \,x^{2}+d \right)^{2} d}+\frac{\left(3 a \,e^{2}+17 c \,d^{2}\right) \sqrt{c \,x^{4}+a}\, e^{4} x}{8 \left(a \,e^{2}+c \,d^{2}\right)^{3} \left(e \,x^{2}+d \right) d^{2}}-\frac{2 \left(-\frac{\left(a \,e^{2}-3 c \,d^{2}\right) c e \,x^{3}}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} a}+\frac{\left(3 a \,e^{2}-c \,d^{2}\right) c d x}{4 \left(a \,e^{2}+c \,d^{2}\right)^{3} a}\right) c}{\sqrt{\left(x^{4}+\frac{a}{c}\right) c}}\right)}{e}"," ",0,"B/e*(1/2/(a*e^2+c*d^2)^2*(c*x^4+a)^(1/2)/(e*x^2+d)/d*e^4*x-2*(1/2/(a*e^2+c*d^2)^2/a*c*d*e*x^3+1/4*(a*e^2-c*d^2)/(a*e^2+c*d^2)^2/a*x)/((x^4+a/c)*c)^(1/2)*c-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)*e^2*c/(a*e^2+c*d^2)^2+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)/a*c^2/(a*e^2+c*d^2)^2*d^2-1/2*I*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*c^(1/2)*e^3/d/(a*e^2+c*d^2)^2*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*I*a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*c^(1/2)*e^3/d/(a*e^2+c*d^2)^2*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+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^(3/2)*d*e/(a*e^2+c*d^2)^2*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-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^(3/2)*d*e/(a*e^2+c*d^2)^2*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+1/2*e^4/d^2/(a*e^2+c*d^2)^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)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a+7/2*e^2/(a*e^2+c*d^2)^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)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c)+(A*e-B*d)/e*(1/4*e^4/(a*e^2+c*d^2)^2/d*x*(c*x^4+a)^(1/2)/(e*x^2+d)^2+1/8*e^4*(3*a*e^2+17*c*d^2)/d^2/(a*e^2+c*d^2)^3*x*(c*x^4+a)^(1/2)/(e*x^2+d)-2*c*(-1/4*c*e*(a*e^2-3*c*d^2)/a/(a*e^2+c*d^2)^3*x^3+1/4*c*d*(3*a*e^2-c*d^2)/a/(a*e^2+c*d^2)^3*x)/((x^4+a/c)*c)^(1/2)-1/8/(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*e^4/d/(a*e^2+c*d^2)^3*a-27/8/(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^2*e^2*d/(a*e^2+c*d^2)^3+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)*c^3*d^3/a/(a*e^2+c*d^2)^3+3/2*I/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*c^(5/2)*e/(a*e^2+c*d^2)^3*d^2*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+21/8*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^(3/2)*e^3/(a*e^2+c*d^2)^3*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+3/8*I*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*c^(1/2)*e^5/d^2/(a*e^2+c*d^2)^3*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-21/8*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^(3/2)*e^3/(a*e^2+c*d^2)^3*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-3/2*I/a^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*c^(5/2)*e/(a*e^2+c*d^2)^3*d^2*EllipticE((I/a^(1/2)*c^(1/2))^(1/2)*x,I)-3/8*I*a^(3/2)/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*c^(1/2)*e^5/d^2/(a*e^2+c*d^2)^3*EllipticF((I/a^(1/2)*c^(1/2))^(1/2)*x,I)+3/8*e^6/d^3/(a*e^2+c*d^2)^3/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a^2+3/4*e^4/(a*e^2+c*d^2)^3/d/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*a*c+63/8*e^2*d/(a*e^2+c*d^2)^3/(I/a^(1/2)*c^(1/2))^(1/2)*(-I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*c^(1/2)*x^2+1)^(1/2)/(c*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*c^(1/2))^(1/2)*x,I*a^(1/2)/c^(1/2)/d*e,(-I/a^(1/2)*c^(1/2))^(1/2)/(I/a^(1/2)*c^(1/2))^(1/2))*c^2)","C"
15,0,0,141,0.105000," ","int((B*x^2+A)*(e*x^2+d)^q/(c*x^4+a),x)","\int \frac{\left(B \,x^{2}+A \right) \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+a}\, dx"," ",0,"int((B*x^2+A)*(e*x^2+d)^q/(c*x^4+a),x)","F"
16,1,81,67,0.027000," ","int((x^2+2)/(x^2+1)/(x^4+3*x^2+2)^(1/2),x)","\frac{\left(x^{2}+2\right) x}{\sqrt{\left(x^{2}+1\right) \left(x^{2}+2\right)}}-\frac{i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \left(-\EllipticE \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)+\EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"(x^2+2)*x/((x^2+1)*(x^2+2))^(1/2)-1/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*(EllipticF(1/2*I*x*2^(1/2),2^(1/2))-EllipticE(1/2*I*x*2^(1/2),2^(1/2)))","C"
17,1,1708,739,0.019000," ","int((B*x^2+A)*(e*x^2+d)^3/(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}\, A \,d^{3} \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}}+\left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{5}}{7 c}-\frac{6 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b \,x^{3}}{35 c^{2}}-\frac{\left(-\frac{5 a}{7 c}+\frac{24 b^{2}}{35 c^{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}\, 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{18 a b}{35 c^{2}}-\frac{2 \left(-\frac{5 a}{7 c}+\frac{24 b^{2}}{35 c^{2}}\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{5 a}{7 c}+\frac{24 b^{2}}{35 c^{2}}\right) \sqrt{c \,x^{4}+b \,x^{2}+a}\, x}{3 c}\right) B \,e^{3}-\frac{\left(3 A \,d^{2} e +B \,d^{3}\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)}+\left(A \,e^{3}+3 B d \,e^{2}\right) \left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{3}}{5 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 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)}{15 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{\left(-\frac{3 a}{5 c}+\frac{8 b^{2}}{15 c^{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{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b x}{15 c^{2}}\right)+\left(3 A d \,e^{2}+3 B \,d^{2} e \right) \left(\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}\right)"," ",0,"B*e^3*(1/7/c*x^5*(c*x^4+b*x^2+a)^(1/2)-6/35*b/c^2*x^3*(c*x^4+b*x^2+a)^(1/2)+1/3*(-5/7*a/c+24/35*b^2/c^2)/c*x*(c*x^4+b*x^2+a)^(1/2)-1/12*(-5/7*a/c+24/35*b^2/c^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*(18/35*b/c^2*a-2/3*(-5/7*a/c+24/35*b^2/c^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*e^3+3*B*d*e^2)*(1/5*(c*x^4+b*x^2+a)^(1/2)/c*x^3-4/15*(c*x^4+b*x^2+a)^(1/2)*b/c^2*x+1/15*b/c^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))-1/2*(-3/5*a/c+8/15*b^2/c^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))))+(3*A*d*e^2+3*B*d^2*e)*(1/3*(c*x^4+b*x^2+a)^(1/2)/c*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))))-1/2*(3*A*d^2*e+B*d^3)*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)))+1/4*A*d^3*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))","B"
18,1,1201,516,0.011000," ","int((B*x^2+A)*(e*x^2+d)^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}\, A \,d^{2} \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}}+\left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, x^{3}}{5 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 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)}{15 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, c^{2}}-\frac{\left(-\frac{3 a}{5 c}+\frac{8 b^{2}}{15 c^{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{4 \sqrt{c \,x^{4}+b \,x^{2}+a}\, b x}{15 c^{2}}\right) B \,e^{2}-\frac{\left(2 A d e +B \,d^{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)}+\left(A \,e^{2}+2 B d e \right) \left(\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}\right)"," ",0,"B*e^2*(1/5*(c*x^4+b*x^2+a)^(1/2)/c*x^3-4/15*(c*x^4+b*x^2+a)^(1/2)*b/c^2*x+1/15*b/c^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))-1/2*(-3/5*a/c+8/15*b^2/c^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*e^2+2*B*d*e)*(1/3*(c*x^4+b*x^2+a)^(1/2)/c*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))))-1/2*(2*A*d*e+B*d^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)))+1/4*A*d^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))","B"
19,1,759,360,0.007000," ","int((B*x^2+A)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, A d \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}}+\left(\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}\right) B e -\frac{\left(A e +B d \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)}"," ",0,"B*e*(1/3*(c*x^4+b*x^2+a)^(1/2)/c*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))))-1/2*(A*e+B*d)*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)))+1/4*A*d*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))","B"
20,1,362,283,0.000000," ","int((B*x^2+A)/(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}\, 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)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+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}\, \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 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*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)))+1/4*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))","A"
21,1,359,408,0.036000," ","int((B*x^2+A)/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, 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}\, e}+\frac{\left(A e -B d \right) \sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d e}"," ",0,"1/4*B/e*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+(A*e-B*d)/e/d*2^(1/2)/(-1/a*b+1/a*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*x^2*b-1/2/a*x^2*(-4*a*c+b^2)^(1/2))^(1/2)*(1+1/2/a*x^2*b+1/2/a*x^2*(-4*a*c+b^2)^(1/2))^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a*e/d,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))","A"
22,1,1495,745,0.042000," ","int((B*x^2+A)/(e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, B \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d e}+\frac{\left(A e -B d \right) \left(-\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, a c e \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)}{4 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) d}+\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, a c e \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(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, \left(b +\sqrt{-4 a c +b^{2}}\right) d}+\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, a \,e^{2} \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d^{2}}-\frac{\sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, b e \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d}-\frac{\sqrt{2}\, \sqrt{\frac{2 b \,x^{2}}{a}-\frac{2 \sqrt{-4 a c +b^{2}}\, x^{2}}{a}+4}\, \sqrt{\frac{2 b \,x^{2}}{a}+\frac{2 \sqrt{-4 a c +b^{2}}\, 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)}{8 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\frac{3 \sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, c \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}}+\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, e^{2} x}{2 \left(a \,e^{2}-d e b +c \,d^{2}\right) \left(e \,x^{2}+d \right) d}\right)}{e}"," ",0,"(A*e-B*d)/e*(1/2*e^2/(a*e^2-b*d*e+c*d^2)/d*x*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d)-1/8*c/(a*e^2-b*d*e+c*d^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(-4*a*c+b^2)^(1/2)/a*x^2)^(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))+1/4*c*e/(a*e^2-b*d*e+c*d^2)/d*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(-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*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))-1/4*c*e/(a*e^2-b*d*e+c*d^2)/d*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(4+2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2)^(1/2)*(4+2/a*b*x^2+2*(-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))*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))+1/2/(a*e^2-b*d*e+c*d^2)/d^2*e^2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*a-1/(a*e^2-b*d*e+c*d^2)/d*e*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*b+3/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*c)+B/e/d*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))","B"
23,1,4476,1080,0.048000," ","int((B*x^2+A)/(e*x^2+d)^3/(c*x^4+b*x^2+a)^(1/2),x)","\text{output too large to display}"," ",0,"B/e*(1/2/(a*e^2-b*d*e+c*d^2)*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d)/d*e^2*x-1/8*c/(a*e^2-b*d*e+c*d^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))+1/4*c*e/(a*e^2-b*d*e+c*d^2)/d*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))-1/4*c*e/(a*e^2-b*d*e+c*d^2)/d*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*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))+1/2/(a*e^2-b*d*e+c*d^2)/d^2*e^2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*a-1/(a*e^2-b*d*e+c*d^2)/d*e*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*b+3/2/(a*e^2-b*d*e+c*d^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*c)+(A*e-B*d)/e*(1/4*e^2/(a*e^2-b*d*e+c*d^2)/d*x*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d)^2+3/8*e^2*(a*e^2-2*b*d*e+3*c*d^2)/(a*e^2-b*d*e+c*d^2)^2/d^2*x*(c*x^4+b*x^2+a)^(1/2)/(e*x^2+d)+3/16*e^3*c/(a*e^2-b*d*e+c*d^2)^2/d^2*a^2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))+9/16*e*c^2/(a*e^2-b*d*e+c*d^2)^2*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))-3/16*e^3*c/(a*e^2-b*d*e+c*d^2)^2/d^2*a^2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*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))-1/(a*e^2-b*d*e+c*d^2)^2/d^2*e^3*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*a*b+3/4/(a*e^2-b*d*e+c*d^2)^2/d*e^2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*a*c-1/32*c/(a*e^2-b*d*e+c*d^2)^2/d*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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*e^2+1/8*c/(a*e^2-b*d*e+c*d^2)^2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*e*b+1/(a*e^2-b*d*e+c*d^2)^2/d*e^2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*b^2-5/2/(a*e^2-b*d*e+c*d^2)^2*e*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*b*c+3/8/(a*e^2-b*d*e+c*d^2)^2/d^3*e^4*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*a^2-3/8*e^2*c/(a*e^2-b*d*e+c*d^2)^2/d*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*b+3/8*e^2*c/(a*e^2-b*d*e+c*d^2)^2/d*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*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))*b-9/16*e*c^2/(a*e^2-b*d*e+c*d^2)^2*a*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*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))+15/8/(a*e^2-b*d*e+c*d^2)^2*d*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))*c^2-7/32*c^2/(a*e^2-b*d*e+c*d^2)^2*d*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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)))","B"
24,1,2445,841,0.037000," ","int((B*x^2+A)*(e*x^2+d)^3/(c*x^4+b*x^2+a)^(3/2),x)","\left(-\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}}\right) A \,d^{3}+\left(-\frac{\left(-\frac{5 b}{3 c^{2}}-\frac{\left(3 a c -b^{2}\right) b}{\left(4 a c -b^{2}\right) c^{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(3 a c -b^{2}\right) b \,x^{3}}{2 \left(4 a c -b^{2}\right) c^{3}}-\frac{\left(2 a c -b^{2}\right) a x}{2 \left(4 a c -b^{2}\right) c^{3}}\right) c}{\sqrt{\left(x^{4}+\frac{b \,x^{2}}{c}+\frac{a}{c}\right) c}}+\frac{\left(-\frac{\left(2 a c -b^{2}\right) a}{\left(4 a c -b^{2}\right) c^{2}}-\frac{a}{3 c^{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}\, x}{3 c^{2}}\right) B \,e^{3}+\left(A \,e^{3}+3 B d \,e^{2}\right) \left(-\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}}\right)+\left(3 A d \,e^{2}+3 B \,d^{2} e \right) \left(-\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}}\right)+\left(3 A \,d^{2} e +B \,d^{3}\right) \left(\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}}\right)"," ",0,"B*e^3*(-2*c*(-1/2*b/c^3*(3*a*c-b^2)/(4*a*c-b^2)*x^3-1/2*(2*a*c-b^2)*a/c^3/(4*a*c-b^2)*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)+1/3/c^2*x*(c*x^4+b*x^2+a)^(1/2)+1/4*(-1/c^2*(2*a*c-b^2)*a/(4*a*c-b^2)-1/3*a/c^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*(-5/3*b/c^2-b/c^2*(3*a*c-b^2)/(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*e^3+3*B*d*e^2)*(-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+a/c)*c)^(1/2)-1/4/c*a*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))-1/2*(1/c+1/c*(2*a*c-b^2)/(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))))+(3*A*d*e^2+3*B*d^2*e)*(-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/(4*a*c-b^2)*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))))+(3*A*d^2*e+B*d^3)*(-2*(-1/(4*a*c-b^2)*x^3-1/2/(4*a*c-b^2)*b/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c-1/4/(4*a*c-b^2)*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/(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*d^3*(-2*(1/2/(4*a*c-b^2)/a*b*x^3-1/2*(2*a*c-b^2)/(4*a*c-b^2)/a/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c+1/4*(1/a-(2*a*c-b^2)/(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)*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))))","B"
25,1,1891,618,0.012000," ","int((B*x^2+A)*(e*x^2+d)^2/(c*x^4+b*x^2+a)^(3/2),x)","\left(-\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}}\right) A \,d^{2}+\left(-\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}}\right) B \,e^{2}+\left(A \,e^{2}+2 B d e \right) \left(-\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}}\right)+\left(2 A d e +B \,d^{2}\right) \left(\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}}\right)"," ",0,"B*e^2*(-2*(-1/2/(4*a*c-b^2)*a*b/c^2*x+1/2*(2*a*c-b^2)/(4*a*c-b^2)/c^2*x^3)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c-1/4/c*a*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))-1/2*(1/c+(2*a*c-b^2)/(4*a*c-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*e^2+2*B*d*e)*(-2*(1/2/(4*a*c-b^2)*b/c*x^3+1/(4*a*c-b^2)*a/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c+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/(4*a*c-b^2)*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))))+(2*A*d*e+B*d^2)*(-2*(-1/(4*a*c-b^2)*x^3-1/2/(4*a*c-b^2)*b/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c-1/4/(4*a*c-b^2)*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/(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*d^2*(-2*(1/2/(4*a*c-b^2)/a*b*x^3-1/2*(2*a*c-b^2)/(4*a*c-b^2)/a/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c+1/4*(1/a-(2*a*c-b^2)/(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)*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))))","B"
26,1,1390,471,0.009000," ","int((B*x^2+A)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","\left(-\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}}\right) A d +\left(-\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}}\right) B e +\left(A e +B d \right) \left(\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}}\right)"," ",0,"B*e*(-2*(1/2/(4*a*c-b^2)*b/c*x^3+1/(4*a*c-b^2)*a/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c+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/(4*a*c-b^2)*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*e+B*d)*(-2*(-1/(4*a*c-b^2)*x^3-1/2/(4*a*c-b^2)*b/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c-1/4/(4*a*c-b^2)*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/(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*d*(-2*(1/2/(4*a*c-b^2)/a*b*x^3-1/2*(2*a*c-b^2)/(4*a*c-b^2)/a/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c+1/4*(1/a-(2*a*c-b^2)/(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)*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))))","B"
27,1,931,392,0.006000," ","int((B*x^2+A)/(c*x^4+b*x^2+a)^(3/2),x)","\left(-\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}}\right) A +\left(\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}}\right) B"," ",0,"B*(-2*(-1/(4*a*c-b^2)*x^3-1/2/(4*a*c-b^2)*b/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c-1/4/(4*a*c-b^2)*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/(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*(-2*(1/2/(4*a*c-b^2)/a*b*x^3-1/2*(2*a*c-b^2)/(4*a*c-b^2)/a/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c+1/4*(1/a-(2*a*c-b^2)/(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)*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))))","B"
28,1,3241,832,0.036000," ","int((B*x^2+A)/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x)","\text{output too large to display}"," ",0,"B/e*(-2*(1/2/(4*a*c-b^2)/a*b*x^3-1/2*(2*a*c-b^2)/(4*a*c-b^2)/a/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)*c+1/4*(1/a-(2*a*c-b^2)/(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)*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*e-B*d)/e*(-2*c*(1/2*(2*a*c*e-b^2*e+b*c*d)/a/(4*a*c-b^2)/(a*e^2-b*d*e+c*d^2)*x^3+1/2*(3*a*b*c*e-2*a*c^2*d-b^3*e+b^2*c*d)/a/(4*a*c-b^2)/(a*e^2-b*d*e+c*d^2)/c*x)/((x^4+b/c*x^2+a/c)*c)^(1/2)-1/4*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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/(a*e^2-b*d*e+c*d^2)*b*e+1/4*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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/(a*e^2-b*d*e+c*d^2)*c*d+3/4*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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*a*c-b^2)/(a*e^2-b*d*e+c*d^2)*b*c*e-1/2*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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*a*c-b^2)/(a*e^2-b*d*e+c*d^2)*c^2*d-1/4*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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/(4*a*c-b^2)/(a*e^2-b*d*e+c*d^2)*b^3*e+1/4*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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/(4*a*c-b^2)/(a*e^2-b*d*e+c*d^2)*b^2*c*d-c^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*a*e+1/2*c/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*b^2*e-1/2*c^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*b*d+c^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*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*e-1/2*c/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*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))*b^2*e+1/2*c^2/(a*e^2-b*d*e+c*d^2)/(4*a*c-b^2)*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(2/a*b*x^2-2*(-4*a*c+b^2)^(1/2)/a*x^2+4)^(1/2)*(2/a*b*x^2+2*(-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))*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))*b*d+1/(a*e^2-b*d*e+c*d^2)*e^2/d*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)))","B"
29,1,8276,1252,0.059000," ","int((B*x^2+A)/(e*x^2+d)^2/(c*x^4+b*x^2+a)^(3/2),x)","\text{output too large to display}"," ",0,"result too large to display","B"
30,1,365,244,0.102000," ","int((a^(1/2)+x^2*c^(1/2))/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-\frac{2 \left(-b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{\frac{2 \left(b +\sqrt{-4 a c +b^{2}}\right) x^{2}}{a}+4}\, \sqrt{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)}{4 \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, e}+\frac{\left(\sqrt{a}\, e -\sqrt{c}\, d \right) \sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d e}"," ",0,"1/4*c^(1/2)/e*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+(e*a^(1/2)-d*c^(1/2))/e/d*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))","A"
31,1,369,262,0.081000," ","int((1+x^2*(1/a*c)^(1/2))/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x)","\frac{\sqrt{\frac{c}{a}}\, \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}\, e}+\frac{\left(-\sqrt{\frac{c}{a}}\, d +e \right) \sqrt{2}\, \sqrt{\frac{b \,x^{2}}{2 a}-\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \sqrt{\frac{b \,x^{2}}{2 a}+\frac{\sqrt{-4 a c +b^{2}}\, x^{2}}{2 a}+1}\, \EllipticPi \left(\frac{\sqrt{2}\, \sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}\, x}{2}, -\frac{2 a e}{\left(-b +\sqrt{-4 a c +b^{2}}\right) d}, \frac{\sqrt{-\frac{b +\sqrt{-4 a c +b^{2}}}{2 a}}\, \sqrt{2}}{\sqrt{\frac{-b +\sqrt{-4 a c +b^{2}}}{a}}}\right)}{\sqrt{-\frac{b}{a}+\frac{\sqrt{-4 a c +b^{2}}}{a}}\, \sqrt{c \,x^{4}+b \,x^{2}+a}\, d e}"," ",0,"1/4*(1/a*c)^(1/2)/e*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*(-2*(-b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)*(2*(b+(-4*a*c+b^2)^(1/2))/a*x^2+4)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticF(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,1/2*(2*(b+(-4*a*c+b^2)^(1/2))/a*b/c-4)^(1/2))+1/e*(-d*(1/a*c)^(1/2)+e)/d*2^(1/2)/(-1/a*b+(-4*a*c+b^2)^(1/2)/a)^(1/2)*(1/2/a*b*x^2-1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)*(1/2/a*b*x^2+1/2*(-4*a*c+b^2)^(1/2)/a*x^2+1)^(1/2)/(c*x^4+b*x^2+a)^(1/2)*EllipticPi(1/2*2^(1/2)*((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*x,-2/(-b+(-4*a*c+b^2)^(1/2))*a/d*e,(-1/2*(b+(-4*a*c+b^2)^(1/2))/a)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))/a)^(1/2))","A"
32,1,93,133,0.034000," ","int((315*x^2+946)/(5*x^2+7)/(x^4+3*x^2+2)^(1/2),x)","-\frac{63 i \sqrt{2}\, \sqrt{2 x^{2}+4}\, \sqrt{x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)}{2 \sqrt{x^{4}+3 x^{2}+2}}-\frac{505 i \sqrt{2}\, \sqrt{\frac{x^{2}}{2}+1}\, \sqrt{x^{2}+1}\, \EllipticPi \left(\frac{i \sqrt{2}\, x}{2}, \frac{10}{7}, \sqrt{2}\right)}{7 \sqrt{x^{4}+3 x^{2}+2}}"," ",0,"-63/2*I*2^(1/2)*(2*x^2+4)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticF(1/2*I*2^(1/2)*x,2^(1/2))-505/7*I*2^(1/2)*(1+1/2*x^2)^(1/2)*(x^2+1)^(1/2)/(x^4+3*x^2+2)^(1/2)*EllipticPi(1/2*I*2^(1/2)*x,10/7,2^(1/2))","C"
33,0,0,198,0.084000," ","int((B*x^2+A)*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","\int \frac{\left(B \,x^{2}+A \right) \left(e \,x^{2}+d \right)^{q}}{c \,x^{4}+b \,x^{2}+a}\, dx"," ",0,"int((B*x^2+A)*(e*x^2+d)^q/(c*x^4+b*x^2+a),x)","F"
34,1,296,80,0.030000," ","int(x*(2*x^2+1)/(x^4+x^2+1)/(x^2+1)^(1/2),x)","-\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+2}\, \left(\sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+2}\, \sqrt{3}}{2}\right)+\arctan \left(\frac{\sqrt{\frac{2 \left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+2}\, \left(x +1\right)}{\left(\frac{\left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+1\right) \left(-x +1\right)}\right)\right)}{4 \sqrt{\frac{\frac{\left(x +1\right)^{2}}{\left(-x +1\right)^{2}}+1}{\left(\frac{x +1}{-x +1}+1\right)^{2}}}\, \left(\frac{x +1}{-x +1}+1\right)}-\frac{\sqrt{2}\, \sqrt{\frac{2 \left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+2}\, \left(\sqrt{3}\, \arctanh \left(\frac{\sqrt{\frac{2 \left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+2}\, \sqrt{3}}{2}\right)+\arctan \left(\frac{\sqrt{\frac{2 \left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+2}\, \left(x -1\right)}{\left(\frac{\left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+1\right) \left(-x -1\right)}\right)\right)}{4 \sqrt{\frac{\frac{\left(x -1\right)^{2}}{\left(-x -1\right)^{2}}+1}{\left(\frac{x -1}{-x -1}+1\right)^{2}}}\, \left(\frac{x -1}{-x -1}+1\right)}"," ",0,"-1/4*2^(1/2)*(2*(x+1)^2/(1-x)^2+2)^(1/2)*(3^(1/2)*arctanh(1/2*(2*(x+1)^2/(1-x)^2+2)^(1/2)*3^(1/2))+arctan(1/((x+1)^2/(1-x)^2+1)*(2*(x+1)^2/(1-x)^2+2)^(1/2)*(x+1)/(1-x)))/(((x+1)^2/(1-x)^2+1)/((x+1)/(1-x)+1)^2)^(1/2)/((x+1)/(1-x)+1)-1/4*2^(1/2)*(2*(x-1)^2/(-1-x)^2+2)^(1/2)*(3^(1/2)*arctanh(1/2*(2*(x-1)^2/(-1-x)^2+2)^(1/2)*3^(1/2))+arctan(1/((x-1)^2/(-1-x)^2+1)*(2*(x-1)^2/(-1-x)^2+2)^(1/2)*(x-1)/(-1-x)))/(((x-1)^2/(-1-x)^2+1)/((x-1)/(-1-x)+1)^2)^(1/2)/((x-1)/(-1-x)+1)","B"
35,1,238,105,0.042000," ","int((c*x^4+b*x^2+a)^(1/2)/(-c*d*x^4+a*d),x)","-\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}}{\sqrt{-2 b -4 \sqrt{a c}}\, x}\right)}{4 \sqrt{a c}\, \sqrt{-2 b -4 \sqrt{a c}}\, d}+\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}}{\sqrt{-2 b +4 \sqrt{a c}}\, x}\right)}{4 \sqrt{a c}\, \sqrt{-2 b +4 \sqrt{a c}}\, d}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}}{\sqrt{-2 b -4 \sqrt{a c}}\, x}\right)}{2 \sqrt{-2 b -4 \sqrt{a c}}\, d}-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}}{\sqrt{-2 b +4 \sqrt{a c}}\, x}\right)}{2 \sqrt{-2 b +4 \sqrt{a c}}\, d}"," ",0,"-1/2/d*2^(1/2)/(-4*(a*c)^(1/2)-2*b)^(1/2)*arctan((c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x/(-4*(a*c)^(1/2)-2*b)^(1/2))-1/4/d*2^(1/2)/(a*c)^(1/2)/(-4*(a*c)^(1/2)-2*b)^(1/2)*arctan((c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x/(-4*(a*c)^(1/2)-2*b)^(1/2))*b-1/2/d*2^(1/2)/(4*(a*c)^(1/2)-2*b)^(1/2)*arctan((c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x/(4*(a*c)^(1/2)-2*b)^(1/2))+1/4/d*2^(1/2)/(a*c)^(1/2)/(4*(a*c)^(1/2)-2*b)^(1/2)*arctan((c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x/(4*(a*c)^(1/2)-2*b)^(1/2))*b","B"
36,1,568,183,0.108000," ","int((-c*x^4+b*x^2+a)^(1/2)/(c*d*x^4+a*d),x)","\frac{\sqrt{2}\, \arctan \left(\frac{-\frac{2 \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}}{x}+2 \sqrt{b +\sqrt{4 a c +b^{2}}}}{2 \sqrt{-b +\sqrt{4 a c +b^{2}}}}\right)}{4 \sqrt{-b +\sqrt{4 a c +b^{2}}}\, d}-\frac{\sqrt{2}\, \arctan \left(\frac{\frac{2 \sqrt{-c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}}{x}+2 \sqrt{b +\sqrt{4 a c +b^{2}}}}{2 \sqrt{-b +\sqrt{4 a c +b^{2}}}}\right)}{4 \sqrt{-b +\sqrt{4 a c +b^{2}}}\, d}-\frac{\sqrt{2}\, \sqrt{b +\sqrt{4 a c +b^{2}}}\, b \ln \left(\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}\, \sqrt{b +\sqrt{4 a c +b^{2}}}}{x}+\frac{-c \,x^{4}+b \,x^{2}+a}{x^{2}}+\sqrt{4 a c +b^{2}}\right)}{32 a c d}+\frac{\sqrt{2}\, \sqrt{b +\sqrt{4 a c +b^{2}}}\, b \ln \left(\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}\, \sqrt{b +\sqrt{4 a c +b^{2}}}}{x}-\frac{-c \,x^{4}+b \,x^{2}+a}{x^{2}}-\sqrt{4 a c +b^{2}}\right)}{32 a c d}+\frac{\sqrt{2}\, \sqrt{b +\sqrt{4 a c +b^{2}}}\, \sqrt{4 a c +b^{2}}\, \ln \left(\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}\, \sqrt{b +\sqrt{4 a c +b^{2}}}}{x}+\frac{-c \,x^{4}+b \,x^{2}+a}{x^{2}}+\sqrt{4 a c +b^{2}}\right)}{32 a c d}-\frac{\sqrt{2}\, \sqrt{b +\sqrt{4 a c +b^{2}}}\, \sqrt{4 a c +b^{2}}\, \ln \left(\frac{\sqrt{-c \,x^{4}+b \,x^{2}+a}\, \sqrt{2}\, \sqrt{b +\sqrt{4 a c +b^{2}}}}{x}-\frac{-c \,x^{4}+b \,x^{2}+a}{x^{2}}-\sqrt{4 a c +b^{2}}\right)}{32 a c d}"," ",0,"1/32/d*2^(1/2)*(b+(4*a*c+b^2)^(1/2))^(1/2)/a/c*b*ln((-c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x*(b+(4*a*c+b^2)^(1/2))^(1/2)-(-c*x^4+b*x^2+a)/x^2-(4*a*c+b^2)^(1/2))-1/32/d*2^(1/2)*(b+(4*a*c+b^2)^(1/2))^(1/2)/a/c*(4*a*c+b^2)^(1/2)*ln((-c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x*(b+(4*a*c+b^2)^(1/2))^(1/2)-(-c*x^4+b*x^2+a)/x^2-(4*a*c+b^2)^(1/2))+1/4/d*2^(1/2)/(-b+(4*a*c+b^2)^(1/2))^(1/2)*arctan(1/2*(2*(b+(4*a*c+b^2)^(1/2))^(1/2)-2*(-c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x)/(-b+(4*a*c+b^2)^(1/2))^(1/2))-1/32/d*2^(1/2)*(b+(4*a*c+b^2)^(1/2))^(1/2)/a/c*b*ln((-c*x^4+b*x^2+a)/x^2+(-c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x*(b+(4*a*c+b^2)^(1/2))^(1/2)+(4*a*c+b^2)^(1/2))+1/32/d*2^(1/2)*(b+(4*a*c+b^2)^(1/2))^(1/2)/a/c*(4*a*c+b^2)^(1/2)*ln((-c*x^4+b*x^2+a)/x^2+(-c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x*(b+(4*a*c+b^2)^(1/2))^(1/2)+(4*a*c+b^2)^(1/2))-1/4/d*2^(1/2)/(-b+(4*a*c+b^2)^(1/2))^(1/2)*arctan(1/2*(2*(-c*x^4+b*x^2+a)^(1/2)*2^(1/2)/x+2*(b+(4*a*c+b^2)^(1/2))^(1/2))/(-b+(4*a*c+b^2)^(1/2))^(1/2))","B"
37,1,442,243,0.014000," ","int(x*(d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2),x)","\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(-960 a c \,d^{4} e \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+240 a \,d^{3} e^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+720 b \,c^{2} d^{3} e \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-600 b c \,d^{2} e^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+105 b d \,e^{5} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-960 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{9}{2}} e x +720 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{7}{2}} e x +768 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{9}{2}} x^{2}-420 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{5}{2}} e^{3} x -480 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{7}{2}} e^{2}+360 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{5}{2}} e^{2}-672 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{7}{2}} e x -210 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{3}{2}} e^{4}+1280 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{9}{2}}-512 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b c \,d^{\frac{7}{2}}+560 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{5}{2}} e^{2}\right)}{3840 \left(b \,x^{2}+a \right) d^{\frac{11}{2}}}"," ",0,"1/3840*((b*x^2+a)^2)^(1/2)*(768*(d*x^2+e*x+c)^(3/2)*d^(9/2)*x^2*b-672*(d*x^2+e*x+c)^(3/2)*d^(7/2)*x*b*e+1280*(d*x^2+e*x+c)^(3/2)*d^(9/2)*a-512*(d*x^2+e*x+c)^(3/2)*d^(7/2)*b*c+560*(d*x^2+e*x+c)^(3/2)*d^(5/2)*b*e^2-960*(d*x^2+e*x+c)^(1/2)*d^(9/2)*x*a*e+720*(d*x^2+e*x+c)^(1/2)*d^(7/2)*x*b*c*e-420*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x*b*e^3-480*(d*x^2+e*x+c)^(1/2)*d^(7/2)*a*e^2+360*(d*x^2+e*x+c)^(1/2)*d^(5/2)*b*c*e^2-210*(d*x^2+e*x+c)^(1/2)*d^(3/2)*b*e^4-960*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*a*c*d^4*e+240*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*a*d^3*e^3+720*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*b*c^2*d^3*e-600*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*b*c*d^2*e^3+105*ln(1/2*(2*(d*x^2+e*x+c)^(1/2)*d^(1/2)+2*d*x+e)/d^(1/2))*b*d*e^5)/(b*x^2+a)/d^(11/2)","A"
38,1,373,217,0.010000," ","int((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2),x)","\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(192 a c \,d^{4} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-48 a \,d^{3} e^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-48 b \,c^{2} d^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+72 b c \,d^{2} e^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-15 b d \,e^{4} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+192 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{9}{2}} x -48 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{7}{2}} x +60 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{5}{2}} e^{2} x +96 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{7}{2}} e -24 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{5}{2}} e +96 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{7}{2}} x +30 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{3}{2}} e^{3}-80 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{5}{2}} e \right)}{384 \left(b \,x^{2}+a \right) d^{\frac{9}{2}}}"," ",0,"1/384*((b*x^2+a)^2)^(1/2)*(96*d^(7/2)*(d*x^2+e*x+c)^(3/2)*x*b-80*d^(5/2)*(d*x^2+e*x+c)^(3/2)*b*e+192*d^(9/2)*(d*x^2+e*x+c)^(1/2)*x*a-48*d^(7/2)*(d*x^2+e*x+c)^(1/2)*x*b*c+60*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x*b*e^2+96*d^(7/2)*(d*x^2+e*x+c)^(1/2)*a*e-24*d^(5/2)*(d*x^2+e*x+c)^(1/2)*b*c*e+30*d^(3/2)*(d*x^2+e*x+c)^(1/2)*b*e^3+192*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*a*c*d^4-48*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*a*d^3*e^2-48*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*c^2*d^3+72*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*c*d^2*e^2-15*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*d*e^4)/(b*x^2+a)/d^(9/2)","A"
39,1,251,216,0.011000," ","int((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x,x)","-\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(48 a \sqrt{c}\, d^{\frac{7}{2}} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)-24 a \,d^{3} e \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+12 b c \,d^{2} e \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-3 b d \,e^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+12 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{5}{2}} e x -48 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{7}{2}}+6 \sqrt{d \,x^{2}+e x +c}\, b \,d^{\frac{3}{2}} e^{2}-16 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,d^{\frac{5}{2}}\right)}{48 \left(b \,x^{2}+a \right) d^{\frac{7}{2}}}"," ",0,"-1/48*((b*x^2+a)^2)^(1/2)*(48*c^(1/2)*d^(7/2)*ln((2*c+e*x+2*c^(1/2)*(d*x^2+e*x+c)^(1/2))/x)*a-16*d^(5/2)*(d*x^2+e*x+c)^(3/2)*b+12*d^(5/2)*(d*x^2+e*x+c)^(1/2)*x*b*e-48*d^(7/2)*(d*x^2+e*x+c)^(1/2)*a+6*d^(3/2)*(d*x^2+e*x+c)^(1/2)*b*e^2-24*d^3*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*a*e+12*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*c*d^2*e-3*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*b*d*e^3)/(b*x^2+a)/d^(7/2)","A"
40,1,288,224,0.010000," ","int((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^2,x)","-\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(-8 a c \,d^{3} x \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+4 a \sqrt{c}\, d^{\frac{5}{2}} e x \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)-4 b \,c^{2} d^{2} x \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+b c d \,e^{2} x \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-8 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{7}{2}} x^{2}-4 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{5}{2}} x^{2}-8 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}} e x -2 \sqrt{d \,x^{2}+e x +c}\, b c \,d^{\frac{3}{2}} e x +8 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{5}{2}}\right)}{8 \left(b \,x^{2}+a \right) c \,d^{\frac{5}{2}} x}"," ",0,"-1/8*((b*x^2+a)^2)^(1/2)*(-8*(d*x^2+e*x+c)^(1/2)*d^(7/2)*x^2*a-4*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x^2*b*c+4*c^(1/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*d^(5/2)*x*a*e+8*(d*x^2+e*x+c)^(3/2)*d^(5/2)*a-8*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x*a*e-2*(d*x^2+e*x+c)^(1/2)*d^(3/2)*x*b*c*e-8*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*x*a*c*d^3-4*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*x*b*c^2*d^2+ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*x*b*c*d*e^2)/(b*x^2+a)/c/x/d^(5/2)","A"
41,1,329,216,0.010000," ","int((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^3,x)","\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(-4 a \,c^{\frac{3}{2}} d^{\frac{5}{2}} x^{2} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)+a \sqrt{c}\, d^{\frac{3}{2}} e^{2} x^{2} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)-8 b \,c^{\frac{5}{2}} d^{\frac{3}{2}} x^{2} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)+4 b \,c^{2} d e \,x^{2} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)-2 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}} e \,x^{3}+4 \sqrt{d \,x^{2}+e x +c}\, a c \,d^{\frac{5}{2}} x^{2}-2 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{3}{2}} e^{2} x^{2}+8 \sqrt{d \,x^{2}+e x +c}\, b \,c^{2} d^{\frac{3}{2}} x^{2}+2 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{3}{2}} e x -4 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a c \,d^{\frac{3}{2}}\right)}{8 \left(b \,x^{2}+a \right) c^{2} d^{\frac{3}{2}} x^{2}}"," ",0,"1/8*((b*x^2+a)^2)^(1/2)*(-4*d^(5/2)*c^(3/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^2*a-8*d^(3/2)*c^(5/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^2*b-2*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x^3*a*e+4*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x^2*a*c+d^(3/2)*c^(1/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^2*a*e^2+2*(d*x^2+e*x+c)^(3/2)*d^(3/2)*x*a*e-2*(d*x^2+e*x+c)^(1/2)*d^(3/2)*x^2*a*e^2+8*(d*x^2+e*x+c)^(1/2)*d^(3/2)*x^2*b*c^2-4*(d*x^2+e*x+c)^(3/2)*d^(3/2)*a*c+4*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*d*x^2*b*c^2*e)/d^(3/2)/x^2/c^2/(b*x^2+a)","A"
42,1,412,224,0.013000," ","int((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^4,x)","-\frac{\sqrt{\left(b \,x^{2}+a \right)^{2}}\, \left(-12 a \,c^{\frac{3}{2}} d^{\frac{5}{2}} e \,x^{3} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)+3 a \sqrt{c}\, d^{\frac{3}{2}} e^{3} x^{3} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)-48 b \,c^{3} d^{2} x^{3} \ln \left(\frac{2 d x +e +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{d}}{2 \sqrt{d}}\right)+24 b \,c^{\frac{5}{2}} d^{\frac{3}{2}} e \,x^{3} \ln \left(\frac{e x +2 c +2 \sqrt{d \,x^{2}+e x +c}\, \sqrt{c}}{x}\right)-6 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{5}{2}} e^{2} x^{4}-48 \sqrt{d \,x^{2}+e x +c}\, b \,c^{2} d^{\frac{5}{2}} x^{4}+12 \sqrt{d \,x^{2}+e x +c}\, a c \,d^{\frac{5}{2}} e \,x^{3}-6 \sqrt{d \,x^{2}+e x +c}\, a \,d^{\frac{3}{2}} e^{3} x^{3}-48 \sqrt{d \,x^{2}+e x +c}\, b \,c^{2} d^{\frac{3}{2}} e \,x^{3}+6 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,d^{\frac{3}{2}} e^{2} x^{2}+48 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} b \,c^{2} d^{\frac{3}{2}} x^{2}-12 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a c \,d^{\frac{3}{2}} e x +16 \left(d \,x^{2}+e x +c \right)^{\frac{3}{2}} a \,c^{2} d^{\frac{3}{2}}\right)}{48 \left(b \,x^{2}+a \right) c^{3} d^{\frac{3}{2}} x^{3}}"," ",0,"-1/48*((b*x^2+a)^2)^(1/2)*(-12*d^(5/2)*c^(3/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^3*a*e+24*d^(3/2)*c^(5/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^3*b*e-6*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x^4*a*e^2-48*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x^4*b*c^2+12*(d*x^2+e*x+c)^(1/2)*d^(5/2)*x^3*a*c*e+3*d^(3/2)*c^(1/2)*ln((e*x+2*c+2*(d*x^2+e*x+c)^(1/2)*c^(1/2))/x)*x^3*a*e^3+6*(d*x^2+e*x+c)^(3/2)*d^(3/2)*x^2*a*e^2+48*(d*x^2+e*x+c)^(3/2)*d^(3/2)*x^2*b*c^2-6*(d*x^2+e*x+c)^(1/2)*d^(3/2)*x^3*a*e^3-48*(d*x^2+e*x+c)^(1/2)*d^(3/2)*x^3*b*c^2*e-12*(d*x^2+e*x+c)^(3/2)*d^(3/2)*x*a*c*e-48*ln(1/2*(2*d*x+e+2*(d*x^2+e*x+c)^(1/2)*d^(1/2))/d^(1/2))*x^3*b*c^3*d^2+16*(d*x^2+e*x+c)^(3/2)*d^(3/2)*a*c^2)/d^(3/2)/x^3/c^3/(b*x^2+a)","A"