1,0,0,0,0.966246," ","integrate((B*x^2+A)*(e*x^2+d)^3/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B e^{3} x^{8} + {\left(3 \, B d e^{2} + A e^{3}\right)} x^{6} + 3 \, {\left(B d^{2} e + A d e^{2}\right)} x^{4} + A d^{3} + {\left(B d^{3} + 3 \, A d^{2} e\right)} x^{2}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((B*e^3*x^8 + (3*B*d*e^2 + A*e^3)*x^6 + 3*(B*d^2*e + A*d*e^2)*x^4 + A*d^3 + (B*d^3 + 3*A*d^2*e)*x^2)/sqrt(c*x^4 + a), x)","F",0
2,0,0,0,1.285016," ","integrate((B*x^2+A)*(e*x^2+d)^2/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B e^{2} x^{6} + {\left(2 \, B d e + A e^{2}\right)} x^{4} + A d^{2} + {\left(B d^{2} + 2 \, A d e\right)} x^{2}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((B*e^2*x^6 + (2*B*d*e + A*e^2)*x^4 + A*d^2 + (B*d^2 + 2*A*d*e)*x^2)/sqrt(c*x^4 + a), x)","F",0
3,0,0,0,1.385129," ","integrate((B*x^2+A)*(e*x^2+d)/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B e x^{4} + {\left(B d + A e\right)} x^{2} + A d}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((B*e*x^4 + (B*d + A*e)*x^2 + A*d)/sqrt(c*x^4 + a), x)","F",0
4,0,0,0,1.309979," ","integrate((B*x^2+A)/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{2} + A}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((B*x^2 + A)/sqrt(c*x^4 + a), x)","F",0
5,0,0,0,114.225468," ","integrate((B*x^2+A)/(e*x^2+d)/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a} {\left(B x^{2} + A\right)}}{c e x^{6} + c d x^{4} + a e x^{2} + a d}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)*(B*x^2 + A)/(c*e*x^6 + c*d*x^4 + a*e*x^2 + a*d), x)","F",0
6,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)^2/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)^3/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
8,0,0,0,1.770903," ","integrate((B*x^2+A)*(e*x^2+d)^3/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{8} + {\left(3 \, B d e^{2} + A e^{3}\right)} x^{6} + 3 \, {\left(B d^{2} e + A d e^{2}\right)} x^{4} + A d^{3} + {\left(B d^{3} + 3 \, A d^{2} e\right)} x^{2}\right)} \sqrt{c x^{4} + a}}{c^{2} x^{8} + 2 \, a c x^{4} + a^{2}}, x\right)"," ",0,"integral((B*e^3*x^8 + (3*B*d*e^2 + A*e^3)*x^6 + 3*(B*d^2*e + A*d*e^2)*x^4 + A*d^3 + (B*d^3 + 3*A*d^2*e)*x^2)*sqrt(c*x^4 + a)/(c^2*x^8 + 2*a*c*x^4 + a^2), x)","F",0
9,0,0,0,1.352323," ","integrate((B*x^2+A)*(e*x^2+d)^2/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{6} + {\left(2 \, B d e + A e^{2}\right)} x^{4} + A d^{2} + {\left(B d^{2} + 2 \, A d e\right)} x^{2}\right)} \sqrt{c x^{4} + a}}{c^{2} x^{8} + 2 \, a c x^{4} + a^{2}}, x\right)"," ",0,"integral((B*e^2*x^6 + (2*B*d*e + A*e^2)*x^4 + A*d^2 + (B*d^2 + 2*A*d*e)*x^2)*sqrt(c*x^4 + a)/(c^2*x^8 + 2*a*c*x^4 + a^2), x)","F",0
10,0,0,0,1.339812," ","integrate((B*x^2+A)*(e*x^2+d)/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{4} + {\left(B d + A e\right)} x^{2} + A d\right)} \sqrt{c x^{4} + a}}{c^{2} x^{8} + 2 \, a c x^{4} + a^{2}}, x\right)"," ",0,"integral((B*e*x^4 + (B*d + A*e)*x^2 + A*d)*sqrt(c*x^4 + a)/(c^2*x^8 + 2*a*c*x^4 + a^2), x)","F",0
11,0,0,0,1.289534," ","integrate((B*x^2+A)/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a} {\left(B x^{2} + A\right)}}{c^{2} x^{8} + 2 \, a c x^{4} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)*(B*x^2 + A)/(c^2*x^8 + 2*a*c*x^4 + a^2), x)","F",0
12,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
13,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)^2/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
14,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)^3/(c*x^4+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,0,0,0,1.803691," ","integrate((B*x^2+A)*(e*x^2+d)^q/(c*x^4+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} {\left(e x^{2} + d\right)}^{q}}{c x^{4} + a}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x^2 + d)^q/(c*x^4 + a), x)","F",0
16,0,0,0,1.732741," ","integrate((x^2+2)/(x^2+1)/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{x^{4} + 2 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(x^4 + 2*x^2 + 1), x)","F",0
17,0,0,0,1.798621," ","integrate((B*x^2+A)*(e*x^2+d)^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B e^{3} x^{8} + {\left(3 \, B d e^{2} + A e^{3}\right)} x^{6} + 3 \, {\left(B d^{2} e + A d e^{2}\right)} x^{4} + A d^{3} + {\left(B d^{3} + 3 \, A d^{2} e\right)} x^{2}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((B*e^3*x^8 + (3*B*d*e^2 + A*e^3)*x^6 + 3*(B*d^2*e + A*d*e^2)*x^4 + A*d^3 + (B*d^3 + 3*A*d^2*e)*x^2)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
18,0,0,0,1.782931," ","integrate((B*x^2+A)*(e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B e^{2} x^{6} + {\left(2 \, B d e + A e^{2}\right)} x^{4} + A d^{2} + {\left(B d^{2} + 2 \, A d e\right)} x^{2}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((B*e^2*x^6 + (2*B*d*e + A*e^2)*x^4 + A*d^2 + (B*d^2 + 2*A*d*e)*x^2)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
19,0,0,0,1.772367," ","integrate((B*x^2+A)*(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B e x^{4} + {\left(B d + A e\right)} x^{2} + A d}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((B*e*x^4 + (B*d + A*e)*x^2 + A*d)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
20,0,0,0,1.145970," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{B x^{2} + A}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((B*x^2 + A)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
21,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
23,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
24,0,0,0,1.294493," ","integrate((B*x^2+A)*(e*x^2+d)^3/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{3} x^{8} + {\left(3 \, B d e^{2} + A e^{3}\right)} x^{6} + 3 \, {\left(B d^{2} e + A d e^{2}\right)} x^{4} + A d^{3} + {\left(B d^{3} + 3 \, A d^{2} e\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e^3*x^8 + (3*B*d*e^2 + A*e^3)*x^6 + 3*(B*d^2*e + A*d*e^2)*x^4 + A*d^3 + (B*d^3 + 3*A*d^2*e)*x^2)*sqrt(c*x^4 + b*x^2 + a)/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
25,0,0,0,0.915001," ","integrate((B*x^2+A)*(e*x^2+d)^2/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e^{2} x^{6} + {\left(2 \, B d e + A e^{2}\right)} x^{4} + A d^{2} + {\left(B d^{2} + 2 \, A d e\right)} x^{2}\right)} \sqrt{c x^{4} + b x^{2} + a}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e^2*x^6 + (2*B*d*e + A*e^2)*x^4 + A*d^2 + (B*d^2 + 2*A*d*e)*x^2)*sqrt(c*x^4 + b*x^2 + a)/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
26,0,0,0,0.971429," ","integrate((B*x^2+A)*(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B e x^{4} + {\left(B d + A e\right)} x^{2} + A d\right)} \sqrt{c x^{4} + b x^{2} + a}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral((B*e*x^4 + (B*d + A*e)*x^2 + A*d)*sqrt(c*x^4 + b*x^2 + a)/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
27,0,0,0,1.159716," ","integrate((B*x^2+A)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(B x^{2} + A\right)}}{c^{2} x^{8} + 2 \, b c x^{6} + {\left(b^{2} + 2 \, a c\right)} x^{4} + 2 \, a b x^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)*(B*x^2 + A)/(c^2*x^8 + 2*b*c*x^6 + (b^2 + 2*a*c)*x^4 + 2*a*b*x^2 + a^2), x)","F",0
28,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
29,-1,0,0,0.000000," ","integrate((B*x^2+A)/(e*x^2+d)^2/(c*x^4+b*x^2+a)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
30,-1,0,0,0.000000," ","integrate((a^(1/2)+x^2*c^(1/2))/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
31,-1,0,0,0.000000," ","integrate((1+x^2*(c/a)^(1/2))/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
32,0,0,0,1.325583," ","integrate((315*x^2+946)/(5*x^2+7)/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2} {\left(315 \, x^{2} + 946\right)}}{5 \, x^{6} + 22 \, x^{4} + 31 \, x^{2} + 14}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)*(315*x^2 + 946)/(5*x^6 + 22*x^4 + 31*x^2 + 14), x)","F",0
33,0,0,0,1.813372," ","integrate((B*x^2+A)*(e*x^2+d)^q/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(B x^{2} + A\right)} {\left(e x^{2} + d\right)}^{q}}{c x^{4} + b x^{2} + a}, x\right)"," ",0,"integral((B*x^2 + A)*(e*x^2 + d)^q/(c*x^4 + b*x^2 + a), x)","F",0
34,1,279,0,1.191240," ","integrate(x*(2*x^2+1)/(x^4+x^2+1)/(x^2+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{3} \log\left(32 \, x^{4} + 80 \, x^{2} + 32 \, \sqrt{3} {\left(x^{3} + x\right)} - 16 \, {\left(2 \, x^{3} + \sqrt{3} {\left(2 \, x^{2} + 1\right)} + 4 \, x\right)} \sqrt{x^{2} + 1} + 32\right) - \frac{1}{4} \, \sqrt{3} \log\left(32 \, x^{4} + 80 \, x^{2} - 32 \, \sqrt{3} {\left(x^{3} + x\right)} - 16 \, {\left(2 \, x^{3} - \sqrt{3} {\left(2 \, x^{2} + 1\right)} + 4 \, x\right)} \sqrt{x^{2} + 1} + 32\right) - \arctan\left(2 \, \sqrt{2 \, x^{4} + 5 \, x^{2} + 2 \, \sqrt{3} {\left(x^{3} + x\right)} - {\left(2 \, x^{3} + \sqrt{3} {\left(2 \, x^{2} + 1\right)} + 4 \, x\right)} \sqrt{x^{2} + 1} + 2} {\left(x + \sqrt{x^{2} + 1}\right)} + \sqrt{3} - 2 \, \sqrt{x^{2} + 1}\right) - \arctan\left(2 \, \sqrt{2 \, x^{4} + 5 \, x^{2} - 2 \, \sqrt{3} {\left(x^{3} + x\right)} - {\left(2 \, x^{3} - \sqrt{3} {\left(2 \, x^{2} + 1\right)} + 4 \, x\right)} \sqrt{x^{2} + 1} + 2} {\left(x + \sqrt{x^{2} + 1}\right)} - \sqrt{3} - 2 \, \sqrt{x^{2} + 1}\right)"," ",0,"1/4*sqrt(3)*log(32*x^4 + 80*x^2 + 32*sqrt(3)*(x^3 + x) - 16*(2*x^3 + sqrt(3)*(2*x^2 + 1) + 4*x)*sqrt(x^2 + 1) + 32) - 1/4*sqrt(3)*log(32*x^4 + 80*x^2 - 32*sqrt(3)*(x^3 + x) - 16*(2*x^3 - sqrt(3)*(2*x^2 + 1) + 4*x)*sqrt(x^2 + 1) + 32) - arctan(2*sqrt(2*x^4 + 5*x^2 + 2*sqrt(3)*(x^3 + x) - (2*x^3 + sqrt(3)*(2*x^2 + 1) + 4*x)*sqrt(x^2 + 1) + 2)*(x + sqrt(x^2 + 1)) + sqrt(3) - 2*sqrt(x^2 + 1)) - arctan(2*sqrt(2*x^4 + 5*x^2 - 2*sqrt(3)*(x^3 + x) - (2*x^3 - sqrt(3)*(2*x^2 + 1) + 4*x)*sqrt(x^2 + 1) + 2)*(x + sqrt(x^2 + 1)) - sqrt(3) - 2*sqrt(x^2 + 1))","B",0
35,1,603,0,9.585155," ","integrate((c*x^4+b*x^2+a)^(1/2)/(-c*d*x^4+a*d),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{\frac{2 \, a c d^{2} \sqrt{\frac{1}{a c d^{4}}} + b}{a c d^{2}}} \log\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(a d^{2} \sqrt{\frac{1}{a c d^{4}}} + x^{2}\right)} + {\left(a c d^{3} x^{3} \sqrt{\frac{1}{a c d^{4}}} + a d x\right)} \sqrt{\frac{2 \, a c d^{2} \sqrt{\frac{1}{a c d^{4}}} + b}{a c d^{2}}}}{c x^{4} - a}\right) - \frac{1}{8} \, \sqrt{\frac{2 \, a c d^{2} \sqrt{\frac{1}{a c d^{4}}} + b}{a c d^{2}}} \log\left(\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(a d^{2} \sqrt{\frac{1}{a c d^{4}}} + x^{2}\right)} - {\left(a c d^{3} x^{3} \sqrt{\frac{1}{a c d^{4}}} + a d x\right)} \sqrt{\frac{2 \, a c d^{2} \sqrt{\frac{1}{a c d^{4}}} + b}{a c d^{2}}}}{c x^{4} - a}\right) + \frac{1}{8} \, \sqrt{-\frac{2 \, a c d^{2} \sqrt{\frac{1}{a c d^{4}}} - b}{a c d^{2}}} \log\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(a d^{2} \sqrt{\frac{1}{a c d^{4}}} - x^{2}\right)} + {\left(a c d^{3} x^{3} \sqrt{\frac{1}{a c d^{4}}} - a d x\right)} \sqrt{-\frac{2 \, a c d^{2} \sqrt{\frac{1}{a c d^{4}}} - b}{a c d^{2}}}}{c x^{4} - a}\right) - \frac{1}{8} \, \sqrt{-\frac{2 \, a c d^{2} \sqrt{\frac{1}{a c d^{4}}} - b}{a c d^{2}}} \log\left(-\frac{\sqrt{c x^{4} + b x^{2} + a} {\left(a d^{2} \sqrt{\frac{1}{a c d^{4}}} - x^{2}\right)} - {\left(a c d^{3} x^{3} \sqrt{\frac{1}{a c d^{4}}} - a d x\right)} \sqrt{-\frac{2 \, a c d^{2} \sqrt{\frac{1}{a c d^{4}}} - b}{a c d^{2}}}}{c x^{4} - a}\right)"," ",0,"1/8*sqrt((2*a*c*d^2*sqrt(1/(a*c*d^4)) + b)/(a*c*d^2))*log((sqrt(c*x^4 + b*x^2 + a)*(a*d^2*sqrt(1/(a*c*d^4)) + x^2) + (a*c*d^3*x^3*sqrt(1/(a*c*d^4)) + a*d*x)*sqrt((2*a*c*d^2*sqrt(1/(a*c*d^4)) + b)/(a*c*d^2)))/(c*x^4 - a)) - 1/8*sqrt((2*a*c*d^2*sqrt(1/(a*c*d^4)) + b)/(a*c*d^2))*log((sqrt(c*x^4 + b*x^2 + a)*(a*d^2*sqrt(1/(a*c*d^4)) + x^2) - (a*c*d^3*x^3*sqrt(1/(a*c*d^4)) + a*d*x)*sqrt((2*a*c*d^2*sqrt(1/(a*c*d^4)) + b)/(a*c*d^2)))/(c*x^4 - a)) + 1/8*sqrt(-(2*a*c*d^2*sqrt(1/(a*c*d^4)) - b)/(a*c*d^2))*log(-(sqrt(c*x^4 + b*x^2 + a)*(a*d^2*sqrt(1/(a*c*d^4)) - x^2) + (a*c*d^3*x^3*sqrt(1/(a*c*d^4)) - a*d*x)*sqrt(-(2*a*c*d^2*sqrt(1/(a*c*d^4)) - b)/(a*c*d^2)))/(c*x^4 - a)) - 1/8*sqrt(-(2*a*c*d^2*sqrt(1/(a*c*d^4)) - b)/(a*c*d^2))*log(-(sqrt(c*x^4 + b*x^2 + a)*(a*d^2*sqrt(1/(a*c*d^4)) - x^2) - (a*c*d^3*x^3*sqrt(1/(a*c*d^4)) - a*d*x)*sqrt(-(2*a*c*d^2*sqrt(1/(a*c*d^4)) - b)/(a*c*d^2)))/(c*x^4 - a))","B",0
36,1,669,0,9.521695," ","integrate((-c*x^4+b*x^2+a)^(1/2)/(c*d*x^4+a*d),x, algorithm=""fricas"")","-\frac{1}{8} \, \sqrt{\frac{2 \, a c d^{2} \sqrt{-\frac{1}{a c d^{4}}} - b}{a c d^{2}}} \log\left(-\frac{\sqrt{-c x^{4} + b x^{2} + a} a d^{2} \sqrt{-\frac{1}{a c d^{4}}} + \sqrt{-c x^{4} + b x^{2} + a} x^{2} + {\left(a c d^{3} x^{3} \sqrt{-\frac{1}{a c d^{4}}} - a d x\right)} \sqrt{\frac{2 \, a c d^{2} \sqrt{-\frac{1}{a c d^{4}}} - b}{a c d^{2}}}}{c x^{4} + a}\right) + \frac{1}{8} \, \sqrt{\frac{2 \, a c d^{2} \sqrt{-\frac{1}{a c d^{4}}} - b}{a c d^{2}}} \log\left(-\frac{\sqrt{-c x^{4} + b x^{2} + a} a d^{2} \sqrt{-\frac{1}{a c d^{4}}} + \sqrt{-c x^{4} + b x^{2} + a} x^{2} - {\left(a c d^{3} x^{3} \sqrt{-\frac{1}{a c d^{4}}} - a d x\right)} \sqrt{\frac{2 \, a c d^{2} \sqrt{-\frac{1}{a c d^{4}}} - b}{a c d^{2}}}}{c x^{4} + a}\right) - \frac{1}{8} \, \sqrt{-\frac{2 \, a c d^{2} \sqrt{-\frac{1}{a c d^{4}}} + b}{a c d^{2}}} \log\left(\frac{\sqrt{-c x^{4} + b x^{2} + a} a d^{2} \sqrt{-\frac{1}{a c d^{4}}} - \sqrt{-c x^{4} + b x^{2} + a} x^{2} + {\left(a c d^{3} x^{3} \sqrt{-\frac{1}{a c d^{4}}} + a d x\right)} \sqrt{-\frac{2 \, a c d^{2} \sqrt{-\frac{1}{a c d^{4}}} + b}{a c d^{2}}}}{c x^{4} + a}\right) + \frac{1}{8} \, \sqrt{-\frac{2 \, a c d^{2} \sqrt{-\frac{1}{a c d^{4}}} + b}{a c d^{2}}} \log\left(\frac{\sqrt{-c x^{4} + b x^{2} + a} a d^{2} \sqrt{-\frac{1}{a c d^{4}}} - \sqrt{-c x^{4} + b x^{2} + a} x^{2} - {\left(a c d^{3} x^{3} \sqrt{-\frac{1}{a c d^{4}}} + a d x\right)} \sqrt{-\frac{2 \, a c d^{2} \sqrt{-\frac{1}{a c d^{4}}} + b}{a c d^{2}}}}{c x^{4} + a}\right)"," ",0,"-1/8*sqrt((2*a*c*d^2*sqrt(-1/(a*c*d^4)) - b)/(a*c*d^2))*log(-(sqrt(-c*x^4 + b*x^2 + a)*a*d^2*sqrt(-1/(a*c*d^4)) + sqrt(-c*x^4 + b*x^2 + a)*x^2 + (a*c*d^3*x^3*sqrt(-1/(a*c*d^4)) - a*d*x)*sqrt((2*a*c*d^2*sqrt(-1/(a*c*d^4)) - b)/(a*c*d^2)))/(c*x^4 + a)) + 1/8*sqrt((2*a*c*d^2*sqrt(-1/(a*c*d^4)) - b)/(a*c*d^2))*log(-(sqrt(-c*x^4 + b*x^2 + a)*a*d^2*sqrt(-1/(a*c*d^4)) + sqrt(-c*x^4 + b*x^2 + a)*x^2 - (a*c*d^3*x^3*sqrt(-1/(a*c*d^4)) - a*d*x)*sqrt((2*a*c*d^2*sqrt(-1/(a*c*d^4)) - b)/(a*c*d^2)))/(c*x^4 + a)) - 1/8*sqrt(-(2*a*c*d^2*sqrt(-1/(a*c*d^4)) + b)/(a*c*d^2))*log((sqrt(-c*x^4 + b*x^2 + a)*a*d^2*sqrt(-1/(a*c*d^4)) - sqrt(-c*x^4 + b*x^2 + a)*x^2 + (a*c*d^3*x^3*sqrt(-1/(a*c*d^4)) + a*d*x)*sqrt(-(2*a*c*d^2*sqrt(-1/(a*c*d^4)) + b)/(a*c*d^2)))/(c*x^4 + a)) + 1/8*sqrt(-(2*a*c*d^2*sqrt(-1/(a*c*d^4)) + b)/(a*c*d^2))*log((sqrt(-c*x^4 + b*x^2 + a)*a*d^2*sqrt(-1/(a*c*d^4)) - sqrt(-c*x^4 + b*x^2 + a)*x^2 - (a*c*d^3*x^3*sqrt(-1/(a*c*d^4)) + a*d*x)*sqrt(-(2*a*c*d^2*sqrt(-1/(a*c*d^4)) + b)/(a*c*d^2)))/(c*x^4 + a))","B",0
37,1,469,0,1.961197," ","integrate(x*(d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(7 \, b e^{5} - 8 \, {\left(5 \, b c d - 2 \, a d^{2}\right)} e^{3} + 16 \, {\left(3 \, b c^{2} d^{2} - 4 \, a c d^{3}\right)} e\right)} \sqrt{d} \log\left(8 \, d^{2} x^{2} + 8 \, d e x + 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + 4 \, {\left(384 \, b d^{5} x^{4} + 48 \, b d^{4} e x^{3} - 256 \, b c^{2} d^{3} + 640 \, a c d^{4} - 105 \, b d e^{4} + 20 \, {\left(23 \, b c d^{2} - 12 \, a d^{3}\right)} e^{2} + 8 \, {\left(16 \, b c d^{4} + 80 \, a d^{5} - 7 \, b d^{3} e^{2}\right)} x^{2} + 2 \, {\left(35 \, b d^{2} e^{3} - 4 \, {\left(29 \, b c d^{3} - 20 \, a d^{4}\right)} e\right)} x\right)} \sqrt{d x^{2} + e x + c}}{7680 \, d^{5}}, -\frac{15 \, {\left(7 \, b e^{5} - 8 \, {\left(5 \, b c d - 2 \, a d^{2}\right)} e^{3} + 16 \, {\left(3 \, b c^{2} d^{2} - 4 \, a c d^{3}\right)} e\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) - 2 \, {\left(384 \, b d^{5} x^{4} + 48 \, b d^{4} e x^{3} - 256 \, b c^{2} d^{3} + 640 \, a c d^{4} - 105 \, b d e^{4} + 20 \, {\left(23 \, b c d^{2} - 12 \, a d^{3}\right)} e^{2} + 8 \, {\left(16 \, b c d^{4} + 80 \, a d^{5} - 7 \, b d^{3} e^{2}\right)} x^{2} + 2 \, {\left(35 \, b d^{2} e^{3} - 4 \, {\left(29 \, b c d^{3} - 20 \, a d^{4}\right)} e\right)} x\right)} \sqrt{d x^{2} + e x + c}}{3840 \, d^{5}}\right]"," ",0,"[1/7680*(15*(7*b*e^5 - 8*(5*b*c*d - 2*a*d^2)*e^3 + 16*(3*b*c^2*d^2 - 4*a*c*d^3)*e)*sqrt(d)*log(8*d^2*x^2 + 8*d*e*x + 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + 4*(384*b*d^5*x^4 + 48*b*d^4*e*x^3 - 256*b*c^2*d^3 + 640*a*c*d^4 - 105*b*d*e^4 + 20*(23*b*c*d^2 - 12*a*d^3)*e^2 + 8*(16*b*c*d^4 + 80*a*d^5 - 7*b*d^3*e^2)*x^2 + 2*(35*b*d^2*e^3 - 4*(29*b*c*d^3 - 20*a*d^4)*e)*x)*sqrt(d*x^2 + e*x + c))/d^5, -1/3840*(15*(7*b*e^5 - 8*(5*b*c*d - 2*a*d^2)*e^3 + 16*(3*b*c^2*d^2 - 4*a*c*d^3)*e)*sqrt(-d)*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) - 2*(384*b*d^5*x^4 + 48*b*d^4*e*x^3 - 256*b*c^2*d^3 + 640*a*c*d^4 - 105*b*d*e^4 + 20*(23*b*c*d^2 - 12*a*d^3)*e^2 + 8*(16*b*c*d^4 + 80*a*d^5 - 7*b*d^3*e^2)*x^2 + 2*(35*b*d^2*e^3 - 4*(29*b*c*d^3 - 20*a*d^4)*e)*x)*sqrt(d*x^2 + e*x + c))/d^5]","A",0
38,1,361,0,1.485363," ","integrate((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, b c^{2} d^{2} - 64 \, a c d^{3} + 5 \, b e^{4} - 8 \, {\left(3 \, b c d - 2 \, a d^{2}\right)} e^{2}\right)} \sqrt{d} \log\left(8 \, d^{2} x^{2} + 8 \, d e x - 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + 4 \, {\left(48 \, b d^{4} x^{3} + 8 \, b d^{3} e x^{2} + 15 \, b d e^{3} - 4 \, {\left(13 \, b c d^{2} - 12 \, a d^{3}\right)} e + 2 \, {\left(12 \, b c d^{3} + 48 \, a d^{4} - 5 \, b d^{2} e^{2}\right)} x\right)} \sqrt{d x^{2} + e x + c}}{768 \, d^{4}}, \frac{3 \, {\left(16 \, b c^{2} d^{2} - 64 \, a c d^{3} + 5 \, b e^{4} - 8 \, {\left(3 \, b c d - 2 \, a d^{2}\right)} e^{2}\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) + 2 \, {\left(48 \, b d^{4} x^{3} + 8 \, b d^{3} e x^{2} + 15 \, b d e^{3} - 4 \, {\left(13 \, b c d^{2} - 12 \, a d^{3}\right)} e + 2 \, {\left(12 \, b c d^{3} + 48 \, a d^{4} - 5 \, b d^{2} e^{2}\right)} x\right)} \sqrt{d x^{2} + e x + c}}{384 \, d^{4}}\right]"," ",0,"[1/768*(3*(16*b*c^2*d^2 - 64*a*c*d^3 + 5*b*e^4 - 8*(3*b*c*d - 2*a*d^2)*e^2)*sqrt(d)*log(8*d^2*x^2 + 8*d*e*x - 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + 4*(48*b*d^4*x^3 + 8*b*d^3*e*x^2 + 15*b*d*e^3 - 4*(13*b*c*d^2 - 12*a*d^3)*e + 2*(12*b*c*d^3 + 48*a*d^4 - 5*b*d^2*e^2)*x)*sqrt(d*x^2 + e*x + c))/d^4, 1/384*(3*(16*b*c^2*d^2 - 64*a*c*d^3 + 5*b*e^4 - 8*(3*b*c*d - 2*a*d^2)*e^2)*sqrt(-d)*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) + 2*(48*b*d^4*x^3 + 8*b*d^3*e*x^2 + 15*b*d*e^3 - 4*(13*b*c*d^2 - 12*a*d^3)*e + 2*(12*b*c*d^3 + 48*a*d^4 - 5*b*d^2*e^2)*x)*sqrt(d*x^2 + e*x + c))/d^4]","A",0
39,1,743,0,3.735374," ","integrate((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{48 \, a \sqrt{c} d^{3} \log\left(\frac{8 \, c e x + {\left(4 \, c d + e^{2}\right)} x^{2} - 4 \, \sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{c} + 8 \, c^{2}}{x^{2}}\right) + 3 \, {\left(b e^{3} - 4 \, {\left(b c d - 2 \, a d^{2}\right)} e\right)} \sqrt{d} \log\left(8 \, d^{2} x^{2} + 8 \, d e x + 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + 4 \, {\left(8 \, b d^{3} x^{2} + 2 \, b d^{2} e x + 8 \, b c d^{2} + 24 \, a d^{3} - 3 \, b d e^{2}\right)} \sqrt{d x^{2} + e x + c}}{96 \, d^{3}}, \frac{24 \, a \sqrt{c} d^{3} \log\left(\frac{8 \, c e x + {\left(4 \, c d + e^{2}\right)} x^{2} - 4 \, \sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{c} + 8 \, c^{2}}{x^{2}}\right) - 3 \, {\left(b e^{3} - 4 \, {\left(b c d - 2 \, a d^{2}\right)} e\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) + 2 \, {\left(8 \, b d^{3} x^{2} + 2 \, b d^{2} e x + 8 \, b c d^{2} + 24 \, a d^{3} - 3 \, b d e^{2}\right)} \sqrt{d x^{2} + e x + c}}{48 \, d^{3}}, \frac{96 \, a \sqrt{-c} d^{3} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{-c}}{2 \, {\left(c d x^{2} + c e x + c^{2}\right)}}\right) + 3 \, {\left(b e^{3} - 4 \, {\left(b c d - 2 \, a d^{2}\right)} e\right)} \sqrt{d} \log\left(8 \, d^{2} x^{2} + 8 \, d e x + 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + 4 \, {\left(8 \, b d^{3} x^{2} + 2 \, b d^{2} e x + 8 \, b c d^{2} + 24 \, a d^{3} - 3 \, b d e^{2}\right)} \sqrt{d x^{2} + e x + c}}{96 \, d^{3}}, \frac{48 \, a \sqrt{-c} d^{3} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{-c}}{2 \, {\left(c d x^{2} + c e x + c^{2}\right)}}\right) - 3 \, {\left(b e^{3} - 4 \, {\left(b c d - 2 \, a d^{2}\right)} e\right)} \sqrt{-d} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) + 2 \, {\left(8 \, b d^{3} x^{2} + 2 \, b d^{2} e x + 8 \, b c d^{2} + 24 \, a d^{3} - 3 \, b d e^{2}\right)} \sqrt{d x^{2} + e x + c}}{48 \, d^{3}}\right]"," ",0,"[1/96*(48*a*sqrt(c)*d^3*log((8*c*e*x + (4*c*d + e^2)*x^2 - 4*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(c) + 8*c^2)/x^2) + 3*(b*e^3 - 4*(b*c*d - 2*a*d^2)*e)*sqrt(d)*log(8*d^2*x^2 + 8*d*e*x + 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + 4*(8*b*d^3*x^2 + 2*b*d^2*e*x + 8*b*c*d^2 + 24*a*d^3 - 3*b*d*e^2)*sqrt(d*x^2 + e*x + c))/d^3, 1/48*(24*a*sqrt(c)*d^3*log((8*c*e*x + (4*c*d + e^2)*x^2 - 4*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(c) + 8*c^2)/x^2) - 3*(b*e^3 - 4*(b*c*d - 2*a*d^2)*e)*sqrt(-d)*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) + 2*(8*b*d^3*x^2 + 2*b*d^2*e*x + 8*b*c*d^2 + 24*a*d^3 - 3*b*d*e^2)*sqrt(d*x^2 + e*x + c))/d^3, 1/96*(96*a*sqrt(-c)*d^3*arctan(1/2*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(-c)/(c*d*x^2 + c*e*x + c^2)) + 3*(b*e^3 - 4*(b*c*d - 2*a*d^2)*e)*sqrt(d)*log(8*d^2*x^2 + 8*d*e*x + 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + 4*(8*b*d^3*x^2 + 2*b*d^2*e*x + 8*b*c*d^2 + 24*a*d^3 - 3*b*d*e^2)*sqrt(d*x^2 + e*x + c))/d^3, 1/48*(48*a*sqrt(-c)*d^3*arctan(1/2*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(-c)/(c*d*x^2 + c*e*x + c^2)) - 3*(b*e^3 - 4*(b*c*d - 2*a*d^2)*e)*sqrt(-d)*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) + 2*(8*b*d^3*x^2 + 2*b*d^2*e*x + 8*b*c*d^2 + 24*a*d^3 - 3*b*d*e^2)*sqrt(d*x^2 + e*x + c))/d^3]","A",0
40,1,731,0,3.704834," ","integrate((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{4 \, a \sqrt{c} d^{2} e x \log\left(\frac{8 \, c e x + {\left(4 \, c d + e^{2}\right)} x^{2} - 4 \, \sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{c} + 8 \, c^{2}}{x^{2}}\right) - {\left(4 \, b c^{2} d + 8 \, a c d^{2} - b c e^{2}\right)} \sqrt{d} x \log\left(8 \, d^{2} x^{2} + 8 \, d e x - 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + 4 \, {\left(2 \, b c d^{2} x^{2} + b c d e x - 4 \, a c d^{2}\right)} \sqrt{d x^{2} + e x + c}}{16 \, c d^{2} x}, \frac{2 \, a \sqrt{c} d^{2} e x \log\left(\frac{8 \, c e x + {\left(4 \, c d + e^{2}\right)} x^{2} - 4 \, \sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{c} + 8 \, c^{2}}{x^{2}}\right) - {\left(4 \, b c^{2} d + 8 \, a c d^{2} - b c e^{2}\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) + 2 \, {\left(2 \, b c d^{2} x^{2} + b c d e x - 4 \, a c d^{2}\right)} \sqrt{d x^{2} + e x + c}}{8 \, c d^{2} x}, \frac{8 \, a \sqrt{-c} d^{2} e x \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{-c}}{2 \, {\left(c d x^{2} + c e x + c^{2}\right)}}\right) - {\left(4 \, b c^{2} d + 8 \, a c d^{2} - b c e^{2}\right)} \sqrt{d} x \log\left(8 \, d^{2} x^{2} + 8 \, d e x - 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + 4 \, {\left(2 \, b c d^{2} x^{2} + b c d e x - 4 \, a c d^{2}\right)} \sqrt{d x^{2} + e x + c}}{16 \, c d^{2} x}, \frac{4 \, a \sqrt{-c} d^{2} e x \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{-c}}{2 \, {\left(c d x^{2} + c e x + c^{2}\right)}}\right) - {\left(4 \, b c^{2} d + 8 \, a c d^{2} - b c e^{2}\right)} \sqrt{-d} x \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) + 2 \, {\left(2 \, b c d^{2} x^{2} + b c d e x - 4 \, a c d^{2}\right)} \sqrt{d x^{2} + e x + c}}{8 \, c d^{2} x}\right]"," ",0,"[1/16*(4*a*sqrt(c)*d^2*e*x*log((8*c*e*x + (4*c*d + e^2)*x^2 - 4*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(c) + 8*c^2)/x^2) - (4*b*c^2*d + 8*a*c*d^2 - b*c*e^2)*sqrt(d)*x*log(8*d^2*x^2 + 8*d*e*x - 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + 4*(2*b*c*d^2*x^2 + b*c*d*e*x - 4*a*c*d^2)*sqrt(d*x^2 + e*x + c))/(c*d^2*x), 1/8*(2*a*sqrt(c)*d^2*e*x*log((8*c*e*x + (4*c*d + e^2)*x^2 - 4*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(c) + 8*c^2)/x^2) - (4*b*c^2*d + 8*a*c*d^2 - b*c*e^2)*sqrt(-d)*x*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) + 2*(2*b*c*d^2*x^2 + b*c*d*e*x - 4*a*c*d^2)*sqrt(d*x^2 + e*x + c))/(c*d^2*x), 1/16*(8*a*sqrt(-c)*d^2*e*x*arctan(1/2*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(-c)/(c*d*x^2 + c*e*x + c^2)) - (4*b*c^2*d + 8*a*c*d^2 - b*c*e^2)*sqrt(d)*x*log(8*d^2*x^2 + 8*d*e*x - 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + 4*(2*b*c*d^2*x^2 + b*c*d*e*x - 4*a*c*d^2)*sqrt(d*x^2 + e*x + c))/(c*d^2*x), 1/8*(4*a*sqrt(-c)*d^2*e*x*arctan(1/2*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(-c)/(c*d*x^2 + c*e*x + c^2)) - (4*b*c^2*d + 8*a*c*d^2 - b*c*e^2)*sqrt(-d)*x*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) + 2*(2*b*c*d^2*x^2 + b*c*d*e*x - 4*a*c*d^2)*sqrt(d*x^2 + e*x + c))/(c*d^2*x)]","A",0
41,1,749,0,3.422556," ","integrate((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{4 \, b c^{2} \sqrt{d} e x^{2} \log\left(8 \, d^{2} x^{2} + 8 \, d e x + 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) - {\left(8 \, b c^{2} d + 4 \, a c d^{2} - a d e^{2}\right)} \sqrt{c} x^{2} \log\left(\frac{8 \, c e x + {\left(4 \, c d + e^{2}\right)} x^{2} + 4 \, \sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{c} + 8 \, c^{2}}{x^{2}}\right) + 4 \, {\left(4 \, b c^{2} d x^{2} - a c d e x - 2 \, a c^{2} d\right)} \sqrt{d x^{2} + e x + c}}{16 \, c^{2} d x^{2}}, -\frac{8 \, b c^{2} \sqrt{-d} e x^{2} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) + {\left(8 \, b c^{2} d + 4 \, a c d^{2} - a d e^{2}\right)} \sqrt{c} x^{2} \log\left(\frac{8 \, c e x + {\left(4 \, c d + e^{2}\right)} x^{2} + 4 \, \sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{c} + 8 \, c^{2}}{x^{2}}\right) - 4 \, {\left(4 \, b c^{2} d x^{2} - a c d e x - 2 \, a c^{2} d\right)} \sqrt{d x^{2} + e x + c}}{16 \, c^{2} d x^{2}}, \frac{2 \, b c^{2} \sqrt{d} e x^{2} \log\left(8 \, d^{2} x^{2} + 8 \, d e x + 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + {\left(8 \, b c^{2} d + 4 \, a c d^{2} - a d e^{2}\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{-c}}{2 \, {\left(c d x^{2} + c e x + c^{2}\right)}}\right) + 2 \, {\left(4 \, b c^{2} d x^{2} - a c d e x - 2 \, a c^{2} d\right)} \sqrt{d x^{2} + e x + c}}{8 \, c^{2} d x^{2}}, -\frac{4 \, b c^{2} \sqrt{-d} e x^{2} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) - {\left(8 \, b c^{2} d + 4 \, a c d^{2} - a d e^{2}\right)} \sqrt{-c} x^{2} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{-c}}{2 \, {\left(c d x^{2} + c e x + c^{2}\right)}}\right) - 2 \, {\left(4 \, b c^{2} d x^{2} - a c d e x - 2 \, a c^{2} d\right)} \sqrt{d x^{2} + e x + c}}{8 \, c^{2} d x^{2}}\right]"," ",0,"[1/16*(4*b*c^2*sqrt(d)*e*x^2*log(8*d^2*x^2 + 8*d*e*x + 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) - (8*b*c^2*d + 4*a*c*d^2 - a*d*e^2)*sqrt(c)*x^2*log((8*c*e*x + (4*c*d + e^2)*x^2 + 4*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(c) + 8*c^2)/x^2) + 4*(4*b*c^2*d*x^2 - a*c*d*e*x - 2*a*c^2*d)*sqrt(d*x^2 + e*x + c))/(c^2*d*x^2), -1/16*(8*b*c^2*sqrt(-d)*e*x^2*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) + (8*b*c^2*d + 4*a*c*d^2 - a*d*e^2)*sqrt(c)*x^2*log((8*c*e*x + (4*c*d + e^2)*x^2 + 4*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(c) + 8*c^2)/x^2) - 4*(4*b*c^2*d*x^2 - a*c*d*e*x - 2*a*c^2*d)*sqrt(d*x^2 + e*x + c))/(c^2*d*x^2), 1/8*(2*b*c^2*sqrt(d)*e*x^2*log(8*d^2*x^2 + 8*d*e*x + 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + (8*b*c^2*d + 4*a*c*d^2 - a*d*e^2)*sqrt(-c)*x^2*arctan(1/2*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(-c)/(c*d*x^2 + c*e*x + c^2)) + 2*(4*b*c^2*d*x^2 - a*c*d*e*x - 2*a*c^2*d)*sqrt(d*x^2 + e*x + c))/(c^2*d*x^2), -1/8*(4*b*c^2*sqrt(-d)*e*x^2*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) - (8*b*c^2*d + 4*a*c*d^2 - a*d*e^2)*sqrt(-c)*x^2*arctan(1/2*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(-c)/(c*d*x^2 + c*e*x + c^2)) - 2*(4*b*c^2*d*x^2 - a*c*d*e*x - 2*a*c^2*d)*sqrt(d*x^2 + e*x + c))/(c^2*d*x^2)]","A",0
42,1,791,0,3.480505," ","integrate((d*x^2+e*x+c)^(1/2)*((b*x^2+a)^2)^(1/2)/x^4,x, algorithm=""fricas"")","\left[\frac{48 \, b c^{3} \sqrt{d} x^{3} \log\left(8 \, d^{2} x^{2} + 8 \, d e x + 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + 3 \, {\left(a e^{3} + 4 \, {\left(2 \, b c^{2} - a c d\right)} e\right)} \sqrt{c} x^{3} \log\left(\frac{8 \, c e x + {\left(4 \, c d + e^{2}\right)} x^{2} - 4 \, \sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{c} + 8 \, c^{2}}{x^{2}}\right) - 4 \, {\left(2 \, a c^{2} e x + 8 \, a c^{3} + {\left(24 \, b c^{3} + 8 \, a c^{2} d - 3 \, a c e^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + e x + c}}{96 \, c^{3} x^{3}}, -\frac{96 \, b c^{3} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) - 3 \, {\left(a e^{3} + 4 \, {\left(2 \, b c^{2} - a c d\right)} e\right)} \sqrt{c} x^{3} \log\left(\frac{8 \, c e x + {\left(4 \, c d + e^{2}\right)} x^{2} - 4 \, \sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{c} + 8 \, c^{2}}{x^{2}}\right) + 4 \, {\left(2 \, a c^{2} e x + 8 \, a c^{3} + {\left(24 \, b c^{3} + 8 \, a c^{2} d - 3 \, a c e^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + e x + c}}{96 \, c^{3} x^{3}}, \frac{24 \, b c^{3} \sqrt{d} x^{3} \log\left(8 \, d^{2} x^{2} + 8 \, d e x + 4 \, \sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{d} + 4 \, c d + e^{2}\right) + 3 \, {\left(a e^{3} + 4 \, {\left(2 \, b c^{2} - a c d\right)} e\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{-c}}{2 \, {\left(c d x^{2} + c e x + c^{2}\right)}}\right) - 2 \, {\left(2 \, a c^{2} e x + 8 \, a c^{3} + {\left(24 \, b c^{3} + 8 \, a c^{2} d - 3 \, a c e^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + e x + c}}{48 \, c^{3} x^{3}}, -\frac{48 \, b c^{3} \sqrt{-d} x^{3} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(2 \, d x + e\right)} \sqrt{-d}}{2 \, {\left(d^{2} x^{2} + d e x + c d\right)}}\right) - 3 \, {\left(a e^{3} + 4 \, {\left(2 \, b c^{2} - a c d\right)} e\right)} \sqrt{-c} x^{3} \arctan\left(\frac{\sqrt{d x^{2} + e x + c} {\left(e x + 2 \, c\right)} \sqrt{-c}}{2 \, {\left(c d x^{2} + c e x + c^{2}\right)}}\right) + 2 \, {\left(2 \, a c^{2} e x + 8 \, a c^{3} + {\left(24 \, b c^{3} + 8 \, a c^{2} d - 3 \, a c e^{2}\right)} x^{2}\right)} \sqrt{d x^{2} + e x + c}}{48 \, c^{3} x^{3}}\right]"," ",0,"[1/96*(48*b*c^3*sqrt(d)*x^3*log(8*d^2*x^2 + 8*d*e*x + 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + 3*(a*e^3 + 4*(2*b*c^2 - a*c*d)*e)*sqrt(c)*x^3*log((8*c*e*x + (4*c*d + e^2)*x^2 - 4*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(c) + 8*c^2)/x^2) - 4*(2*a*c^2*e*x + 8*a*c^3 + (24*b*c^3 + 8*a*c^2*d - 3*a*c*e^2)*x^2)*sqrt(d*x^2 + e*x + c))/(c^3*x^3), -1/96*(96*b*c^3*sqrt(-d)*x^3*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) - 3*(a*e^3 + 4*(2*b*c^2 - a*c*d)*e)*sqrt(c)*x^3*log((8*c*e*x + (4*c*d + e^2)*x^2 - 4*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(c) + 8*c^2)/x^2) + 4*(2*a*c^2*e*x + 8*a*c^3 + (24*b*c^3 + 8*a*c^2*d - 3*a*c*e^2)*x^2)*sqrt(d*x^2 + e*x + c))/(c^3*x^3), 1/48*(24*b*c^3*sqrt(d)*x^3*log(8*d^2*x^2 + 8*d*e*x + 4*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(d) + 4*c*d + e^2) + 3*(a*e^3 + 4*(2*b*c^2 - a*c*d)*e)*sqrt(-c)*x^3*arctan(1/2*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(-c)/(c*d*x^2 + c*e*x + c^2)) - 2*(2*a*c^2*e*x + 8*a*c^3 + (24*b*c^3 + 8*a*c^2*d - 3*a*c*e^2)*x^2)*sqrt(d*x^2 + e*x + c))/(c^3*x^3), -1/48*(48*b*c^3*sqrt(-d)*x^3*arctan(1/2*sqrt(d*x^2 + e*x + c)*(2*d*x + e)*sqrt(-d)/(d^2*x^2 + d*e*x + c*d)) - 3*(a*e^3 + 4*(2*b*c^2 - a*c*d)*e)*sqrt(-c)*x^3*arctan(1/2*sqrt(d*x^2 + e*x + c)*(e*x + 2*c)*sqrt(-c)/(c*d*x^2 + c*e*x + c^2)) + 2*(2*a*c^2*e*x + 8*a*c^3 + (24*b*c^3 + 8*a*c^2*d - 3*a*c*e^2)*x^2)*sqrt(d*x^2 + e*x + c))/(c^3*x^3)]","A",0
