1,1,200,0,0.403804," ","integrate((B*x+A)*(c*x^2+b*x+a)/(f*x^2+d),x, algorithm=""fricas"")","\left[\frac{B c d f x^{2} + 2 \, {\left(B b + A c\right)} d f x - {\left(A a f - {\left(B b + A c\right)} d\right)} \sqrt{-d f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-d f} x - d}{f x^{2} + d}\right) - {\left(B c d^{2} - {\left(B a + A b\right)} d f\right)} \log\left(f x^{2} + d\right)}{2 \, d f^{2}}, \frac{B c d f x^{2} + 2 \, {\left(B b + A c\right)} d f x + 2 \, {\left(A a f - {\left(B b + A c\right)} d\right)} \sqrt{d f} \arctan\left(\frac{\sqrt{d f} x}{d}\right) - {\left(B c d^{2} - {\left(B a + A b\right)} d f\right)} \log\left(f x^{2} + d\right)}{2 \, d f^{2}}\right]"," ",0,"[1/2*(B*c*d*f*x^2 + 2*(B*b + A*c)*d*f*x - (A*a*f - (B*b + A*c)*d)*sqrt(-d*f)*log((f*x^2 - 2*sqrt(-d*f)*x - d)/(f*x^2 + d)) - (B*c*d^2 - (B*a + A*b)*d*f)*log(f*x^2 + d))/(d*f^2), 1/2*(B*c*d*f*x^2 + 2*(B*b + A*c)*d*f*x + 2*(A*a*f - (B*b + A*c)*d)*sqrt(d*f)*arctan(sqrt(d*f)*x/d) - (B*c*d^2 - (B*a + A*b)*d*f)*log(f*x^2 + d))/(d*f^2)]","A",0
2,1,500,0,0.417821," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(f*x^2+d),x, algorithm=""fricas"")","\left[\frac{3 \, B c^{2} d f^{2} x^{4} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d f^{2} x^{3} - 6 \, {\left(B c^{2} d^{2} f - {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d f^{2}\right)} x^{2} - 6 \, {\left(A a^{2} f^{2} + {\left(2 \, B b c + A c^{2}\right)} d^{2} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d f\right)} \sqrt{-d f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-d f} x - d}{f x^{2} + d}\right) - 12 \, {\left({\left(2 \, B b c + A c^{2}\right)} d^{2} f - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d f^{2}\right)} x + 6 \, {\left(B c^{2} d^{3} - {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} f + {\left(B a^{2} + 2 \, A a b\right)} d f^{2}\right)} \log\left(f x^{2} + d\right)}{12 \, d f^{3}}, \frac{3 \, B c^{2} d f^{2} x^{4} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d f^{2} x^{3} - 6 \, {\left(B c^{2} d^{2} f - {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d f^{2}\right)} x^{2} + 12 \, {\left(A a^{2} f^{2} + {\left(2 \, B b c + A c^{2}\right)} d^{2} - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d f\right)} \sqrt{d f} \arctan\left(\frac{\sqrt{d f} x}{d}\right) - 12 \, {\left({\left(2 \, B b c + A c^{2}\right)} d^{2} f - {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d f^{2}\right)} x + 6 \, {\left(B c^{2} d^{3} - {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} f + {\left(B a^{2} + 2 \, A a b\right)} d f^{2}\right)} \log\left(f x^{2} + d\right)}{12 \, d f^{3}}\right]"," ",0,"[1/12*(3*B*c^2*d*f^2*x^4 + 4*(2*B*b*c + A*c^2)*d*f^2*x^3 - 6*(B*c^2*d^2*f - (B*b^2 + 2*(B*a + A*b)*c)*d*f^2)*x^2 - 6*(A*a^2*f^2 + (2*B*b*c + A*c^2)*d^2 - (2*B*a*b + A*b^2 + 2*A*a*c)*d*f)*sqrt(-d*f)*log((f*x^2 - 2*sqrt(-d*f)*x - d)/(f*x^2 + d)) - 12*((2*B*b*c + A*c^2)*d^2*f - (2*B*a*b + A*b^2 + 2*A*a*c)*d*f^2)*x + 6*(B*c^2*d^3 - (B*b^2 + 2*(B*a + A*b)*c)*d^2*f + (B*a^2 + 2*A*a*b)*d*f^2)*log(f*x^2 + d))/(d*f^3), 1/12*(3*B*c^2*d*f^2*x^4 + 4*(2*B*b*c + A*c^2)*d*f^2*x^3 - 6*(B*c^2*d^2*f - (B*b^2 + 2*(B*a + A*b)*c)*d*f^2)*x^2 + 12*(A*a^2*f^2 + (2*B*b*c + A*c^2)*d^2 - (2*B*a*b + A*b^2 + 2*A*a*c)*d*f)*sqrt(d*f)*arctan(sqrt(d*f)*x/d) - 12*((2*B*b*c + A*c^2)*d^2*f - (2*B*a*b + A*b^2 + 2*A*a*c)*d*f^2)*x + 6*(B*c^2*d^3 - (B*b^2 + 2*(B*a + A*b)*c)*d^2*f + (B*a^2 + 2*A*a*b)*d*f^2)*log(f*x^2 + d))/(d*f^3)]","A",0
3,1,1014,0,0.438197," ","integrate((B*x+A)*(c*x^2+b*x+a)^3/(f*x^2+d),x, algorithm=""fricas"")","\left[\frac{10 \, B c^{3} d f^{3} x^{6} + 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d f^{3} x^{5} - 15 \, {\left(B c^{3} d^{2} f^{2} - 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d f^{3}\right)} x^{4} - 20 \, {\left({\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} f^{2} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d f^{3}\right)} x^{3} + 30 \, {\left(B c^{3} d^{3} f - 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} f^{2} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d f^{3}\right)} x^{2} - 30 \, {\left(A a^{3} f^{3} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} f - 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d f^{2}\right)} \sqrt{-d f} \log\left(\frac{f x^{2} - 2 \, \sqrt{-d f} x - d}{f x^{2} + d}\right) + 60 \, {\left({\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} f - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} f^{2} + 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d f^{3}\right)} x - 30 \, {\left(B c^{3} d^{4} - 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} f + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} f^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d f^{3}\right)} \log\left(f x^{2} + d\right)}{60 \, d f^{4}}, \frac{10 \, B c^{3} d f^{3} x^{6} + 12 \, {\left(3 \, B b c^{2} + A c^{3}\right)} d f^{3} x^{5} - 15 \, {\left(B c^{3} d^{2} f^{2} - 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d f^{3}\right)} x^{4} - 20 \, {\left({\left(3 \, B b c^{2} + A c^{3}\right)} d^{2} f^{2} - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d f^{3}\right)} x^{3} + 30 \, {\left(B c^{3} d^{3} f - 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{2} f^{2} + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d f^{3}\right)} x^{2} + 60 \, {\left(A a^{3} f^{3} - {\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} + {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} f - 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d f^{2}\right)} \sqrt{d f} \arctan\left(\frac{\sqrt{d f} x}{d}\right) + 60 \, {\left({\left(3 \, B b c^{2} + A c^{3}\right)} d^{3} f - {\left(B b^{3} + 3 \, A a c^{2} + 3 \, {\left(2 \, B a b + A b^{2}\right)} c\right)} d^{2} f^{2} + 3 \, {\left(B a^{2} b + A a b^{2} + A a^{2} c\right)} d f^{3}\right)} x - 30 \, {\left(B c^{3} d^{4} - 3 \, {\left(B b^{2} c + {\left(B a + A b\right)} c^{2}\right)} d^{3} f + {\left(3 \, B a b^{2} + A b^{3} + 3 \, {\left(B a^{2} + 2 \, A a b\right)} c\right)} d^{2} f^{2} - {\left(B a^{3} + 3 \, A a^{2} b\right)} d f^{3}\right)} \log\left(f x^{2} + d\right)}{60 \, d f^{4}}\right]"," ",0,"[1/60*(10*B*c^3*d*f^3*x^6 + 12*(3*B*b*c^2 + A*c^3)*d*f^3*x^5 - 15*(B*c^3*d^2*f^2 - 3*(B*b^2*c + (B*a + A*b)*c^2)*d*f^3)*x^4 - 20*((3*B*b*c^2 + A*c^3)*d^2*f^2 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*f^3)*x^3 + 30*(B*c^3*d^3*f - 3*(B*b^2*c + (B*a + A*b)*c^2)*d^2*f^2 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*f^3)*x^2 - 30*(A*a^3*f^3 - (3*B*b*c^2 + A*c^3)*d^3 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*f - 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*f^2)*sqrt(-d*f)*log((f*x^2 - 2*sqrt(-d*f)*x - d)/(f*x^2 + d)) + 60*((3*B*b*c^2 + A*c^3)*d^3*f - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*f^2 + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*f^3)*x - 30*(B*c^3*d^4 - 3*(B*b^2*c + (B*a + A*b)*c^2)*d^3*f + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*f^2 - (B*a^3 + 3*A*a^2*b)*d*f^3)*log(f*x^2 + d))/(d*f^4), 1/60*(10*B*c^3*d*f^3*x^6 + 12*(3*B*b*c^2 + A*c^3)*d*f^3*x^5 - 15*(B*c^3*d^2*f^2 - 3*(B*b^2*c + (B*a + A*b)*c^2)*d*f^3)*x^4 - 20*((3*B*b*c^2 + A*c^3)*d^2*f^2 - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d*f^3)*x^3 + 30*(B*c^3*d^3*f - 3*(B*b^2*c + (B*a + A*b)*c^2)*d^2*f^2 + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d*f^3)*x^2 + 60*(A*a^3*f^3 - (3*B*b*c^2 + A*c^3)*d^3 + (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*f - 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*f^2)*sqrt(d*f)*arctan(sqrt(d*f)*x/d) + 60*((3*B*b*c^2 + A*c^3)*d^3*f - (B*b^3 + 3*A*a*c^2 + 3*(2*B*a*b + A*b^2)*c)*d^2*f^2 + 3*(B*a^2*b + A*a*b^2 + A*a^2*c)*d*f^3)*x - 30*(B*c^3*d^4 - 3*(B*b^2*c + (B*a + A*b)*c^2)*d^3*f + (3*B*a*b^2 + A*b^3 + 3*(B*a^2 + 2*A*a*b)*c)*d^2*f^2 - (B*a^3 + 3*A*a^2*b)*d*f^3)*log(f*x^2 + d))/(d*f^4)]","A",0
4,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)/(f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
5,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
6,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
7,1,6113,0,52.196261," ","integrate((B*x+A)/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{B^{2} c d^{2} + A^{2} a f^{2} + {\left(B^{2} a - 2 \, A B b + A^{2} c\right)} d f + {\left(c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}}} \log\left(-\frac{{\left(B^{4} b^{2} - 2 \, A B^{3} b c\right)} d^{2} - 2 \, {\left(A B^{3} a b - A^{3} B b c\right)} d f + {\left(2 \, A^{3} B a b - A^{4} b^{2}\right)} f^{2} + 2 \, {\left({\left(2 \, A^{3} B a - A^{4} b\right)} c f^{2} + {\left(B^{4} b c - 2 \, A B^{3} c^{2}\right)} d^{2} - 2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d f\right)} x + 2 \, {\left({\left(B^{3} b^{2} - 3 \, A B^{2} b c + 2 \, A^{2} B c^{2}\right)} d^{2} f - {\left(3 \, A B^{2} a b - A^{2} B b^{2} - {\left(4 \, A^{2} B a - A^{3} b\right)} c\right)} d f^{2} + {\left(2 \, A^{2} B a^{2} - A^{3} a b\right)} f^{3} - {\left(B c^{3} d^{4} f - {\left(B b^{2} c - {\left(3 \, B a - A b\right)} c^{2}\right)} d^{3} f^{2} - {\left(B a b^{2} - A b^{3} - {\left(3 \, B a^{2} - 2 \, A a b\right)} c\right)} d^{2} f^{3} + {\left(B a^{3} - A a^{2} b\right)} d f^{4}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{B^{2} c d^{2} + A^{2} a f^{2} + {\left(B^{2} a - 2 \, A B b + A^{2} c\right)} d f + {\left(c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}}} - {\left(2 \, B^{2} a c^{2} d^{3} f - 2 \, A^{2} a^{3} f^{4} - 2 \, {\left(B^{2} a b^{2} - 2 \, B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{2} f^{2} + 2 \, {\left(B^{2} a^{3} + A^{2} a b^{2} - 2 \, A^{2} a^{2} c\right)} d f^{3} + {\left(B^{2} b c^{2} d^{3} f - A^{2} a^{2} b f^{4} - {\left(B^{2} b^{3} - 2 \, B^{2} a b c + A^{2} b c^{2}\right)} d^{2} f^{2} + {\left(B^{2} a^{2} b + A^{2} b^{3} - 2 \, A^{2} a b c\right)} d f^{3}\right)} x\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{\frac{B^{2} c d^{2} + A^{2} a f^{2} + {\left(B^{2} a - 2 \, A B b + A^{2} c\right)} d f + {\left(c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}}} \log\left(-\frac{{\left(B^{4} b^{2} - 2 \, A B^{3} b c\right)} d^{2} - 2 \, {\left(A B^{3} a b - A^{3} B b c\right)} d f + {\left(2 \, A^{3} B a b - A^{4} b^{2}\right)} f^{2} + 2 \, {\left({\left(2 \, A^{3} B a - A^{4} b\right)} c f^{2} + {\left(B^{4} b c - 2 \, A B^{3} c^{2}\right)} d^{2} - 2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d f\right)} x - 2 \, {\left({\left(B^{3} b^{2} - 3 \, A B^{2} b c + 2 \, A^{2} B c^{2}\right)} d^{2} f - {\left(3 \, A B^{2} a b - A^{2} B b^{2} - {\left(4 \, A^{2} B a - A^{3} b\right)} c\right)} d f^{2} + {\left(2 \, A^{2} B a^{2} - A^{3} a b\right)} f^{3} - {\left(B c^{3} d^{4} f - {\left(B b^{2} c - {\left(3 \, B a - A b\right)} c^{2}\right)} d^{3} f^{2} - {\left(B a b^{2} - A b^{3} - {\left(3 \, B a^{2} - 2 \, A a b\right)} c\right)} d^{2} f^{3} + {\left(B a^{3} - A a^{2} b\right)} d f^{4}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{B^{2} c d^{2} + A^{2} a f^{2} + {\left(B^{2} a - 2 \, A B b + A^{2} c\right)} d f + {\left(c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}}} - {\left(2 \, B^{2} a c^{2} d^{3} f - 2 \, A^{2} a^{3} f^{4} - 2 \, {\left(B^{2} a b^{2} - 2 \, B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{2} f^{2} + 2 \, {\left(B^{2} a^{3} + A^{2} a b^{2} - 2 \, A^{2} a^{2} c\right)} d f^{3} + {\left(B^{2} b c^{2} d^{3} f - A^{2} a^{2} b f^{4} - {\left(B^{2} b^{3} - 2 \, B^{2} a b c + A^{2} b c^{2}\right)} d^{2} f^{2} + {\left(B^{2} a^{2} b + A^{2} b^{3} - 2 \, A^{2} a b c\right)} d f^{3}\right)} x\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{\frac{B^{2} c d^{2} + A^{2} a f^{2} + {\left(B^{2} a - 2 \, A B b + A^{2} c\right)} d f - {\left(c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}}} \log\left(-\frac{{\left(B^{4} b^{2} - 2 \, A B^{3} b c\right)} d^{2} - 2 \, {\left(A B^{3} a b - A^{3} B b c\right)} d f + {\left(2 \, A^{3} B a b - A^{4} b^{2}\right)} f^{2} + 2 \, {\left({\left(2 \, A^{3} B a - A^{4} b\right)} c f^{2} + {\left(B^{4} b c - 2 \, A B^{3} c^{2}\right)} d^{2} - 2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d f\right)} x + 2 \, {\left({\left(B^{3} b^{2} - 3 \, A B^{2} b c + 2 \, A^{2} B c^{2}\right)} d^{2} f - {\left(3 \, A B^{2} a b - A^{2} B b^{2} - {\left(4 \, A^{2} B a - A^{3} b\right)} c\right)} d f^{2} + {\left(2 \, A^{2} B a^{2} - A^{3} a b\right)} f^{3} + {\left(B c^{3} d^{4} f - {\left(B b^{2} c - {\left(3 \, B a - A b\right)} c^{2}\right)} d^{3} f^{2} - {\left(B a b^{2} - A b^{3} - {\left(3 \, B a^{2} - 2 \, A a b\right)} c\right)} d^{2} f^{3} + {\left(B a^{3} - A a^{2} b\right)} d f^{4}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{B^{2} c d^{2} + A^{2} a f^{2} + {\left(B^{2} a - 2 \, A B b + A^{2} c\right)} d f - {\left(c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}}} + {\left(2 \, B^{2} a c^{2} d^{3} f - 2 \, A^{2} a^{3} f^{4} - 2 \, {\left(B^{2} a b^{2} - 2 \, B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{2} f^{2} + 2 \, {\left(B^{2} a^{3} + A^{2} a b^{2} - 2 \, A^{2} a^{2} c\right)} d f^{3} + {\left(B^{2} b c^{2} d^{3} f - A^{2} a^{2} b f^{4} - {\left(B^{2} b^{3} - 2 \, B^{2} a b c + A^{2} b c^{2}\right)} d^{2} f^{2} + {\left(B^{2} a^{2} b + A^{2} b^{3} - 2 \, A^{2} a b c\right)} d f^{3}\right)} x\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{\frac{B^{2} c d^{2} + A^{2} a f^{2} + {\left(B^{2} a - 2 \, A B b + A^{2} c\right)} d f - {\left(c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}}} \log\left(-\frac{{\left(B^{4} b^{2} - 2 \, A B^{3} b c\right)} d^{2} - 2 \, {\left(A B^{3} a b - A^{3} B b c\right)} d f + {\left(2 \, A^{3} B a b - A^{4} b^{2}\right)} f^{2} + 2 \, {\left({\left(2 \, A^{3} B a - A^{4} b\right)} c f^{2} + {\left(B^{4} b c - 2 \, A B^{3} c^{2}\right)} d^{2} - 2 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d f\right)} x - 2 \, {\left({\left(B^{3} b^{2} - 3 \, A B^{2} b c + 2 \, A^{2} B c^{2}\right)} d^{2} f - {\left(3 \, A B^{2} a b - A^{2} B b^{2} - {\left(4 \, A^{2} B a - A^{3} b\right)} c\right)} d f^{2} + {\left(2 \, A^{2} B a^{2} - A^{3} a b\right)} f^{3} + {\left(B c^{3} d^{4} f - {\left(B b^{2} c - {\left(3 \, B a - A b\right)} c^{2}\right)} d^{3} f^{2} - {\left(B a b^{2} - A b^{3} - {\left(3 \, B a^{2} - 2 \, A a b\right)} c\right)} d^{2} f^{3} + {\left(B a^{3} - A a^{2} b\right)} d f^{4}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{B^{2} c d^{2} + A^{2} a f^{2} + {\left(B^{2} a - 2 \, A B b + A^{2} c\right)} d f - {\left(c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{c^{2} d^{3} f + a^{2} d f^{3} - {\left(b^{2} - 2 \, a c\right)} d^{2} f^{2}}} + {\left(2 \, B^{2} a c^{2} d^{3} f - 2 \, A^{2} a^{3} f^{4} - 2 \, {\left(B^{2} a b^{2} - 2 \, B^{2} a^{2} c + A^{2} a c^{2}\right)} d^{2} f^{2} + 2 \, {\left(B^{2} a^{3} + A^{2} a b^{2} - 2 \, A^{2} a^{2} c\right)} d f^{3} + {\left(B^{2} b c^{2} d^{3} f - A^{2} a^{2} b f^{4} - {\left(B^{2} b^{3} - 2 \, B^{2} a b c + A^{2} b c^{2}\right)} d^{2} f^{2} + {\left(B^{2} a^{2} b + A^{2} b^{3} - 2 \, A^{2} a b c\right)} d f^{3}\right)} x\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} - 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{c^{4} d^{5} f + a^{4} d f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{4}}}}{x}\right)"," ",0,"1/4*sqrt((B^2*c*d^2 + A^2*a*f^2 + (B^2*a - 2*A*B*b + A^2*c)*d*f + (c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/(c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2))*log(-((B^4*b^2 - 2*A*B^3*b*c)*d^2 - 2*(A*B^3*a*b - A^3*B*b*c)*d*f + (2*A^3*B*a*b - A^4*b^2)*f^2 + 2*((2*A^3*B*a - A^4*b)*c*f^2 + (B^4*b*c - 2*A*B^3*c^2)*d^2 - 2*(A*B^3*a*c - A^3*B*c^2)*d*f)*x + 2*((B^3*b^2 - 3*A*B^2*b*c + 2*A^2*B*c^2)*d^2*f - (3*A*B^2*a*b - A^2*B*b^2 - (4*A^2*B*a - A^3*b)*c)*d*f^2 + (2*A^2*B*a^2 - A^3*a*b)*f^3 - (B*c^3*d^4*f - (B*b^2*c - (3*B*a - A*b)*c^2)*d^3*f^2 - (B*a*b^2 - A*b^3 - (3*B*a^2 - 2*A*a*b)*c)*d^2*f^3 + (B*a^3 - A*a^2*b)*d*f^4)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))*sqrt(c*x^2 + b*x + a)*sqrt((B^2*c*d^2 + A^2*a*f^2 + (B^2*a - 2*A*B*b + A^2*c)*d*f + (c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/(c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)) - (2*B^2*a*c^2*d^3*f - 2*A^2*a^3*f^4 - 2*(B^2*a*b^2 - 2*B^2*a^2*c + A^2*a*c^2)*d^2*f^2 + 2*(B^2*a^3 + A^2*a*b^2 - 2*A^2*a^2*c)*d*f^3 + (B^2*b*c^2*d^3*f - A^2*a^2*b*f^4 - (B^2*b^3 - 2*B^2*a*b*c + A^2*b*c^2)*d^2*f^2 + (B^2*a^2*b + A^2*b^3 - 2*A^2*a*b*c)*d*f^3)*x)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/x) - 1/4*sqrt((B^2*c*d^2 + A^2*a*f^2 + (B^2*a - 2*A*B*b + A^2*c)*d*f + (c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/(c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2))*log(-((B^4*b^2 - 2*A*B^3*b*c)*d^2 - 2*(A*B^3*a*b - A^3*B*b*c)*d*f + (2*A^3*B*a*b - A^4*b^2)*f^2 + 2*((2*A^3*B*a - A^4*b)*c*f^2 + (B^4*b*c - 2*A*B^3*c^2)*d^2 - 2*(A*B^3*a*c - A^3*B*c^2)*d*f)*x - 2*((B^3*b^2 - 3*A*B^2*b*c + 2*A^2*B*c^2)*d^2*f - (3*A*B^2*a*b - A^2*B*b^2 - (4*A^2*B*a - A^3*b)*c)*d*f^2 + (2*A^2*B*a^2 - A^3*a*b)*f^3 - (B*c^3*d^4*f - (B*b^2*c - (3*B*a - A*b)*c^2)*d^3*f^2 - (B*a*b^2 - A*b^3 - (3*B*a^2 - 2*A*a*b)*c)*d^2*f^3 + (B*a^3 - A*a^2*b)*d*f^4)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))*sqrt(c*x^2 + b*x + a)*sqrt((B^2*c*d^2 + A^2*a*f^2 + (B^2*a - 2*A*B*b + A^2*c)*d*f + (c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/(c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)) - (2*B^2*a*c^2*d^3*f - 2*A^2*a^3*f^4 - 2*(B^2*a*b^2 - 2*B^2*a^2*c + A^2*a*c^2)*d^2*f^2 + 2*(B^2*a^3 + A^2*a*b^2 - 2*A^2*a^2*c)*d*f^3 + (B^2*b*c^2*d^3*f - A^2*a^2*b*f^4 - (B^2*b^3 - 2*B^2*a*b*c + A^2*b*c^2)*d^2*f^2 + (B^2*a^2*b + A^2*b^3 - 2*A^2*a*b*c)*d*f^3)*x)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/x) + 1/4*sqrt((B^2*c*d^2 + A^2*a*f^2 + (B^2*a - 2*A*B*b + A^2*c)*d*f - (c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/(c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2))*log(-((B^4*b^2 - 2*A*B^3*b*c)*d^2 - 2*(A*B^3*a*b - A^3*B*b*c)*d*f + (2*A^3*B*a*b - A^4*b^2)*f^2 + 2*((2*A^3*B*a - A^4*b)*c*f^2 + (B^4*b*c - 2*A*B^3*c^2)*d^2 - 2*(A*B^3*a*c - A^3*B*c^2)*d*f)*x + 2*((B^3*b^2 - 3*A*B^2*b*c + 2*A^2*B*c^2)*d^2*f - (3*A*B^2*a*b - A^2*B*b^2 - (4*A^2*B*a - A^3*b)*c)*d*f^2 + (2*A^2*B*a^2 - A^3*a*b)*f^3 + (B*c^3*d^4*f - (B*b^2*c - (3*B*a - A*b)*c^2)*d^3*f^2 - (B*a*b^2 - A*b^3 - (3*B*a^2 - 2*A*a*b)*c)*d^2*f^3 + (B*a^3 - A*a^2*b)*d*f^4)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))*sqrt(c*x^2 + b*x + a)*sqrt((B^2*c*d^2 + A^2*a*f^2 + (B^2*a - 2*A*B*b + A^2*c)*d*f - (c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/(c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)) + (2*B^2*a*c^2*d^3*f - 2*A^2*a^3*f^4 - 2*(B^2*a*b^2 - 2*B^2*a^2*c + A^2*a*c^2)*d^2*f^2 + 2*(B^2*a^3 + A^2*a*b^2 - 2*A^2*a^2*c)*d*f^3 + (B^2*b*c^2*d^3*f - A^2*a^2*b*f^4 - (B^2*b^3 - 2*B^2*a*b*c + A^2*b*c^2)*d^2*f^2 + (B^2*a^2*b + A^2*b^3 - 2*A^2*a*b*c)*d*f^3)*x)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/x) - 1/4*sqrt((B^2*c*d^2 + A^2*a*f^2 + (B^2*a - 2*A*B*b + A^2*c)*d*f - (c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/(c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2))*log(-((B^4*b^2 - 2*A*B^3*b*c)*d^2 - 2*(A*B^3*a*b - A^3*B*b*c)*d*f + (2*A^3*B*a*b - A^4*b^2)*f^2 + 2*((2*A^3*B*a - A^4*b)*c*f^2 + (B^4*b*c - 2*A*B^3*c^2)*d^2 - 2*(A*B^3*a*c - A^3*B*c^2)*d*f)*x - 2*((B^3*b^2 - 3*A*B^2*b*c + 2*A^2*B*c^2)*d^2*f - (3*A*B^2*a*b - A^2*B*b^2 - (4*A^2*B*a - A^3*b)*c)*d*f^2 + (2*A^2*B*a^2 - A^3*a*b)*f^3 + (B*c^3*d^4*f - (B*b^2*c - (3*B*a - A*b)*c^2)*d^3*f^2 - (B*a*b^2 - A*b^3 - (3*B*a^2 - 2*A*a*b)*c)*d^2*f^3 + (B*a^3 - A*a^2*b)*d*f^4)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))*sqrt(c*x^2 + b*x + a)*sqrt((B^2*c*d^2 + A^2*a*f^2 + (B^2*a - 2*A*B*b + A^2*c)*d*f - (c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/(c^2*d^3*f + a^2*d*f^3 - (b^2 - 2*a*c)*d^2*f^2)) + (2*B^2*a*c^2*d^3*f - 2*A^2*a^3*f^4 - 2*(B^2*a*b^2 - 2*B^2*a^2*c + A^2*a*c^2)*d^2*f^2 + 2*(B^2*a^3 + A^2*a*b^2 - 2*A^2*a^2*c)*d*f^3 + (B^2*b*c^2*d^3*f - A^2*a^2*b*f^4 - (B^2*b^3 - 2*B^2*a*b*c + A^2*b*c^2)*d^2*f^2 + (B^2*a^2*b + A^2*b^3 - 2*A^2*a*b*c)*d*f^3)*x)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 - 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/(c^4*d^5*f + a^4*d*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^4)))/x)","B",0
8,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
9,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)^(5/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
10,1,46,0,0.628621," ","integrate((1+2*x)/(x^2-1)/(x^2+x-1)^(1/2),x, algorithm=""fricas"")","\arctan\left(-x + \sqrt{x^{2} + x - 1} - 1\right) - \frac{3}{2} \, \log\left(-x + \sqrt{x^{2} + x - 1} + 2\right) + \frac{3}{2} \, \log\left(-x + \sqrt{x^{2} + x - 1}\right)"," ",0,"arctan(-x + sqrt(x^2 + x - 1) - 1) - 3/2*log(-x + sqrt(x^2 + x - 1) + 2) + 3/2*log(-x + sqrt(x^2 + x - 1))","A",0
11,1,758,0,0.560008," ","integrate((1+2*x)/(x^2+1)/(x^2+x-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{20} \cdot 5^{\frac{1}{4}} \sqrt{4 \, \sqrt{5} + 10} {\left(2 \, \sqrt{5} - 5\right)} \log\left(2 \, x^{2} - 2 \, \sqrt{x^{2} + x - 1} x + \frac{1}{5} \, {\left(5^{\frac{1}{4}} \sqrt{x^{2} + x - 1} {\left(2 \, \sqrt{5} - 5\right)} - 5^{\frac{1}{4}} {\left(\sqrt{5} {\left(2 \, x + 1\right)} - 5 \, x\right)}\right)} \sqrt{4 \, \sqrt{5} + 10} + x + \sqrt{5}\right) - \frac{1}{20} \cdot 5^{\frac{1}{4}} \sqrt{4 \, \sqrt{5} + 10} {\left(2 \, \sqrt{5} - 5\right)} \log\left(2 \, x^{2} - 2 \, \sqrt{x^{2} + x - 1} x - \frac{1}{5} \, {\left(5^{\frac{1}{4}} \sqrt{x^{2} + x - 1} {\left(2 \, \sqrt{5} - 5\right)} - 5^{\frac{1}{4}} {\left(\sqrt{5} {\left(2 \, x + 1\right)} - 5 \, x\right)}\right)} \sqrt{4 \, \sqrt{5} + 10} + x + \sqrt{5}\right) - \frac{1}{5} \cdot 5^{\frac{3}{4}} \sqrt{4 \, \sqrt{5} + 10} \arctan\left(\frac{2}{55} \, \sqrt{5} {\left(\sqrt{5} {\left(2 \, x - 1\right)} + 3 \, x + 4\right)} + \frac{1}{275} \, \sqrt{10 \, x^{2} - 10 \, \sqrt{x^{2} + x - 1} x + {\left(5^{\frac{1}{4}} \sqrt{x^{2} + x - 1} {\left(2 \, \sqrt{5} - 5\right)} - 5^{\frac{1}{4}} {\left(\sqrt{5} {\left(2 \, x + 1\right)} - 5 \, x\right)}\right)} \sqrt{4 \, \sqrt{5} + 10} + 5 \, x + 5 \, \sqrt{5}} {\left({\left(5^{\frac{3}{4}} {\left(2 \, \sqrt{5} + 3\right)} + 2 \cdot 5^{\frac{1}{4}} {\left(4 \, \sqrt{5} - 5\right)}\right)} \sqrt{4 \, \sqrt{5} + 10} + 2 \, \sqrt{5} {\left(3 \, \sqrt{5} + 10\right)} - 20 \, \sqrt{5} + 80\right)} - \frac{2}{55} \, \sqrt{x^{2} + x - 1} {\left(\sqrt{5} {\left(2 \, \sqrt{5} + 3\right)} + 8 \, \sqrt{5} - 10\right)} + \frac{1}{55} \, \sqrt{5} {\left(16 \, x + 3\right)} + \frac{1}{275} \, {\left(5^{\frac{3}{4}} {\left(\sqrt{5} {\left(3 \, x + 4\right)} + 10 \, x - 5\right)} - \sqrt{x^{2} + x - 1} {\left(5^{\frac{3}{4}} {\left(3 \, \sqrt{5} + 10\right)} - 10 \cdot 5^{\frac{1}{4}} {\left(\sqrt{5} - 4\right)}\right)} - 10 \cdot 5^{\frac{1}{4}} {\left(\sqrt{5} {\left(x - 6\right)} - 4 \, x + 13\right)}\right)} \sqrt{4 \, \sqrt{5} + 10} - \frac{4}{11} \, x + \frac{2}{11}\right) - \frac{1}{5} \cdot 5^{\frac{3}{4}} \sqrt{4 \, \sqrt{5} + 10} \arctan\left(-\frac{2}{55} \, \sqrt{5} {\left(\sqrt{5} {\left(2 \, x - 1\right)} + 3 \, x + 4\right)} + \frac{1}{275} \, \sqrt{10 \, x^{2} - 10 \, \sqrt{x^{2} + x - 1} x - {\left(5^{\frac{1}{4}} \sqrt{x^{2} + x - 1} {\left(2 \, \sqrt{5} - 5\right)} - 5^{\frac{1}{4}} {\left(\sqrt{5} {\left(2 \, x + 1\right)} - 5 \, x\right)}\right)} \sqrt{4 \, \sqrt{5} + 10} + 5 \, x + 5 \, \sqrt{5}} {\left({\left(5^{\frac{3}{4}} {\left(2 \, \sqrt{5} + 3\right)} + 2 \cdot 5^{\frac{1}{4}} {\left(4 \, \sqrt{5} - 5\right)}\right)} \sqrt{4 \, \sqrt{5} + 10} - 2 \, \sqrt{5} {\left(3 \, \sqrt{5} + 10\right)} + 20 \, \sqrt{5} - 80\right)} + \frac{2}{55} \, \sqrt{x^{2} + x - 1} {\left(\sqrt{5} {\left(2 \, \sqrt{5} + 3\right)} + 8 \, \sqrt{5} - 10\right)} - \frac{1}{55} \, \sqrt{5} {\left(16 \, x + 3\right)} + \frac{1}{275} \, {\left(5^{\frac{3}{4}} {\left(\sqrt{5} {\left(3 \, x + 4\right)} + 10 \, x - 5\right)} - \sqrt{x^{2} + x - 1} {\left(5^{\frac{3}{4}} {\left(3 \, \sqrt{5} + 10\right)} - 10 \cdot 5^{\frac{1}{4}} {\left(\sqrt{5} - 4\right)}\right)} - 10 \cdot 5^{\frac{1}{4}} {\left(\sqrt{5} {\left(x - 6\right)} - 4 \, x + 13\right)}\right)} \sqrt{4 \, \sqrt{5} + 10} + \frac{4}{11} \, x - \frac{2}{11}\right)"," ",0,"1/20*5^(1/4)*sqrt(4*sqrt(5) + 10)*(2*sqrt(5) - 5)*log(2*x^2 - 2*sqrt(x^2 + x - 1)*x + 1/5*(5^(1/4)*sqrt(x^2 + x - 1)*(2*sqrt(5) - 5) - 5^(1/4)*(sqrt(5)*(2*x + 1) - 5*x))*sqrt(4*sqrt(5) + 10) + x + sqrt(5)) - 1/20*5^(1/4)*sqrt(4*sqrt(5) + 10)*(2*sqrt(5) - 5)*log(2*x^2 - 2*sqrt(x^2 + x - 1)*x - 1/5*(5^(1/4)*sqrt(x^2 + x - 1)*(2*sqrt(5) - 5) - 5^(1/4)*(sqrt(5)*(2*x + 1) - 5*x))*sqrt(4*sqrt(5) + 10) + x + sqrt(5)) - 1/5*5^(3/4)*sqrt(4*sqrt(5) + 10)*arctan(2/55*sqrt(5)*(sqrt(5)*(2*x - 1) + 3*x + 4) + 1/275*sqrt(10*x^2 - 10*sqrt(x^2 + x - 1)*x + (5^(1/4)*sqrt(x^2 + x - 1)*(2*sqrt(5) - 5) - 5^(1/4)*(sqrt(5)*(2*x + 1) - 5*x))*sqrt(4*sqrt(5) + 10) + 5*x + 5*sqrt(5))*((5^(3/4)*(2*sqrt(5) + 3) + 2*5^(1/4)*(4*sqrt(5) - 5))*sqrt(4*sqrt(5) + 10) + 2*sqrt(5)*(3*sqrt(5) + 10) - 20*sqrt(5) + 80) - 2/55*sqrt(x^2 + x - 1)*(sqrt(5)*(2*sqrt(5) + 3) + 8*sqrt(5) - 10) + 1/55*sqrt(5)*(16*x + 3) + 1/275*(5^(3/4)*(sqrt(5)*(3*x + 4) + 10*x - 5) - sqrt(x^2 + x - 1)*(5^(3/4)*(3*sqrt(5) + 10) - 10*5^(1/4)*(sqrt(5) - 4)) - 10*5^(1/4)*(sqrt(5)*(x - 6) - 4*x + 13))*sqrt(4*sqrt(5) + 10) - 4/11*x + 2/11) - 1/5*5^(3/4)*sqrt(4*sqrt(5) + 10)*arctan(-2/55*sqrt(5)*(sqrt(5)*(2*x - 1) + 3*x + 4) + 1/275*sqrt(10*x^2 - 10*sqrt(x^2 + x - 1)*x - (5^(1/4)*sqrt(x^2 + x - 1)*(2*sqrt(5) - 5) - 5^(1/4)*(sqrt(5)*(2*x + 1) - 5*x))*sqrt(4*sqrt(5) + 10) + 5*x + 5*sqrt(5))*((5^(3/4)*(2*sqrt(5) + 3) + 2*5^(1/4)*(4*sqrt(5) - 5))*sqrt(4*sqrt(5) + 10) - 2*sqrt(5)*(3*sqrt(5) + 10) + 20*sqrt(5) - 80) + 2/55*sqrt(x^2 + x - 1)*(sqrt(5)*(2*sqrt(5) + 3) + 8*sqrt(5) - 10) - 1/55*sqrt(5)*(16*x + 3) + 1/275*(5^(3/4)*(sqrt(5)*(3*x + 4) + 10*x - 5) - sqrt(x^2 + x - 1)*(5^(3/4)*(3*sqrt(5) + 10) - 10*5^(1/4)*(sqrt(5) - 4)) - 10*5^(1/4)*(sqrt(5)*(x - 6) - 4*x + 13))*sqrt(4*sqrt(5) + 10) + 4/11*x - 2/11)","B",0
12,-1,0,0,0.000000," ","integrate((b*x+a-c)/(x^2+1)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
13,1,583,0,0.444284," ","integrate((B*x+A)*(c*x^2+b*x+a)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[\frac{{\left(B c e^{2} f^{2} - 4 \, B c d f^{3}\right)} x^{2} - {\left(B c e^{3} - 2 \, A a f^{3} + {\left(2 \, {\left(B b + A c\right)} d + {\left(B a + A b\right)} e\right)} f^{2} - {\left(3 \, B c d e + {\left(B b + A c\right)} e^{2}\right)} f\right)} \sqrt{e^{2} - 4 \, d f} \log\left(\frac{2 \, f^{2} x^{2} + 2 \, e f x + e^{2} - 2 \, d f - \sqrt{e^{2} - 4 \, d f} {\left(2 \, f x + e\right)}}{f x^{2} + e x + d}\right) - 2 \, {\left(B c e^{3} f + 4 \, {\left(B b + A c\right)} d f^{3} - {\left(4 \, B c d e + {\left(B b + A c\right)} e^{2}\right)} f^{2}\right)} x + {\left(B c e^{4} - 4 \, {\left(B a + A b\right)} d f^{3} + {\left(4 \, B c d^{2} + 4 \, {\left(B b + A c\right)} d e + {\left(B a + A b\right)} e^{2}\right)} f^{2} - {\left(5 \, B c d e^{2} + {\left(B b + A c\right)} e^{3}\right)} f\right)} \log\left(f x^{2} + e x + d\right)}{2 \, {\left(e^{2} f^{3} - 4 \, d f^{4}\right)}}, \frac{{\left(B c e^{2} f^{2} - 4 \, B c d f^{3}\right)} x^{2} + 2 \, {\left(B c e^{3} - 2 \, A a f^{3} + {\left(2 \, {\left(B b + A c\right)} d + {\left(B a + A b\right)} e\right)} f^{2} - {\left(3 \, B c d e + {\left(B b + A c\right)} e^{2}\right)} f\right)} \sqrt{-e^{2} + 4 \, d f} \arctan\left(-\frac{\sqrt{-e^{2} + 4 \, d f} {\left(2 \, f x + e\right)}}{e^{2} - 4 \, d f}\right) - 2 \, {\left(B c e^{3} f + 4 \, {\left(B b + A c\right)} d f^{3} - {\left(4 \, B c d e + {\left(B b + A c\right)} e^{2}\right)} f^{2}\right)} x + {\left(B c e^{4} - 4 \, {\left(B a + A b\right)} d f^{3} + {\left(4 \, B c d^{2} + 4 \, {\left(B b + A c\right)} d e + {\left(B a + A b\right)} e^{2}\right)} f^{2} - {\left(5 \, B c d e^{2} + {\left(B b + A c\right)} e^{3}\right)} f\right)} \log\left(f x^{2} + e x + d\right)}{2 \, {\left(e^{2} f^{3} - 4 \, d f^{4}\right)}}\right]"," ",0,"[1/2*((B*c*e^2*f^2 - 4*B*c*d*f^3)*x^2 - (B*c*e^3 - 2*A*a*f^3 + (2*(B*b + A*c)*d + (B*a + A*b)*e)*f^2 - (3*B*c*d*e + (B*b + A*c)*e^2)*f)*sqrt(e^2 - 4*d*f)*log((2*f^2*x^2 + 2*e*f*x + e^2 - 2*d*f - sqrt(e^2 - 4*d*f)*(2*f*x + e))/(f*x^2 + e*x + d)) - 2*(B*c*e^3*f + 4*(B*b + A*c)*d*f^3 - (4*B*c*d*e + (B*b + A*c)*e^2)*f^2)*x + (B*c*e^4 - 4*(B*a + A*b)*d*f^3 + (4*B*c*d^2 + 4*(B*b + A*c)*d*e + (B*a + A*b)*e^2)*f^2 - (5*B*c*d*e^2 + (B*b + A*c)*e^3)*f)*log(f*x^2 + e*x + d))/(e^2*f^3 - 4*d*f^4), 1/2*((B*c*e^2*f^2 - 4*B*c*d*f^3)*x^2 + 2*(B*c*e^3 - 2*A*a*f^3 + (2*(B*b + A*c)*d + (B*a + A*b)*e)*f^2 - (3*B*c*d*e + (B*b + A*c)*e^2)*f)*sqrt(-e^2 + 4*d*f)*arctan(-sqrt(-e^2 + 4*d*f)*(2*f*x + e)/(e^2 - 4*d*f)) - 2*(B*c*e^3*f + 4*(B*b + A*c)*d*f^3 - (4*B*c*d*e + (B*b + A*c)*e^2)*f^2)*x + (B*c*e^4 - 4*(B*a + A*b)*d*f^3 + (4*B*c*d^2 + 4*(B*b + A*c)*d*e + (B*a + A*b)*e^2)*f^2 - (5*B*c*d*e^2 + (B*b + A*c)*e^3)*f)*log(f*x^2 + e*x + d))/(e^2*f^3 - 4*d*f^4)]","A",0
14,1,1837,0,0.609790," ","integrate((B*x+A)*(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(B c^{2} e^{2} f^{4} - 4 \, B c^{2} d f^{5}\right)} x^{4} - 4 \, {\left(B c^{2} e^{3} f^{3} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d f^{5} - {\left(4 \, B c^{2} d e + {\left(2 \, B b c + A c^{2}\right)} e^{2}\right)} f^{4}\right)} x^{3} + 6 \, {\left(B c^{2} e^{4} f^{2} - 4 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d f^{5} + {\left(4 \, B c^{2} d^{2} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d e + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{2}\right)} f^{4} - {\left(5 \, B c^{2} d e^{2} + {\left(2 \, B b c + A c^{2}\right)} e^{3}\right)} f^{3}\right)} x^{2} - 6 \, {\left(B c^{2} e^{5} - 2 \, A a^{2} f^{5} + {\left(2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d + {\left(B a^{2} + 2 \, A a b\right)} e\right)} f^{4} - {\left(2 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{2}\right)} f^{3} + {\left(5 \, B c^{2} d^{2} e + 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{2} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{3}\right)} f^{2} - {\left(5 \, B c^{2} d e^{3} + {\left(2 \, B b c + A c^{2}\right)} e^{4}\right)} f\right)} \sqrt{e^{2} - 4 \, d f} \log\left(\frac{2 \, f^{2} x^{2} + 2 \, e f x + e^{2} - 2 \, d f - \sqrt{e^{2} - 4 \, d f} {\left(2 \, f x + e\right)}}{f x^{2} + e x + d}\right) - 12 \, {\left(B c^{2} e^{5} f + 4 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d f^{5} - {\left(4 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} + 4 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{2}\right)} f^{4} + {\left(8 \, B c^{2} d^{2} e + 5 \, {\left(2 \, B b c + A c^{2}\right)} d e^{2} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{3}\right)} f^{3} - {\left(6 \, B c^{2} d e^{3} + {\left(2 \, B b c + A c^{2}\right)} e^{4}\right)} f^{2}\right)} x + 6 \, {\left(B c^{2} e^{6} - 4 \, {\left(B a^{2} + 2 \, A a b\right)} d f^{5} + {\left(4 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} + 4 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e + {\left(B a^{2} + 2 \, A a b\right)} e^{2}\right)} f^{4} - {\left(4 \, B c^{2} d^{3} + 8 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e + 5 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{2} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{3}\right)} f^{3} + {\left(13 \, B c^{2} d^{2} e^{2} + 6 \, {\left(2 \, B b c + A c^{2}\right)} d e^{3} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{4}\right)} f^{2} - {\left(7 \, B c^{2} d e^{4} + {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} f\right)} \log\left(f x^{2} + e x + d\right)}{12 \, {\left(e^{2} f^{5} - 4 \, d f^{6}\right)}}, \frac{3 \, {\left(B c^{2} e^{2} f^{4} - 4 \, B c^{2} d f^{5}\right)} x^{4} - 4 \, {\left(B c^{2} e^{3} f^{3} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d f^{5} - {\left(4 \, B c^{2} d e + {\left(2 \, B b c + A c^{2}\right)} e^{2}\right)} f^{4}\right)} x^{3} + 6 \, {\left(B c^{2} e^{4} f^{2} - 4 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d f^{5} + {\left(4 \, B c^{2} d^{2} + 4 \, {\left(2 \, B b c + A c^{2}\right)} d e + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{2}\right)} f^{4} - {\left(5 \, B c^{2} d e^{2} + {\left(2 \, B b c + A c^{2}\right)} e^{3}\right)} f^{3}\right)} x^{2} + 12 \, {\left(B c^{2} e^{5} - 2 \, A a^{2} f^{5} + {\left(2 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d + {\left(B a^{2} + 2 \, A a b\right)} e\right)} f^{4} - {\left(2 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} + 3 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{2}\right)} f^{3} + {\left(5 \, B c^{2} d^{2} e + 4 \, {\left(2 \, B b c + A c^{2}\right)} d e^{2} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{3}\right)} f^{2} - {\left(5 \, B c^{2} d e^{3} + {\left(2 \, B b c + A c^{2}\right)} e^{4}\right)} f\right)} \sqrt{-e^{2} + 4 \, d f} \arctan\left(-\frac{\sqrt{-e^{2} + 4 \, d f} {\left(2 \, f x + e\right)}}{e^{2} - 4 \, d f}\right) - 12 \, {\left(B c^{2} e^{5} f + 4 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d f^{5} - {\left(4 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} + 4 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{2}\right)} f^{4} + {\left(8 \, B c^{2} d^{2} e + 5 \, {\left(2 \, B b c + A c^{2}\right)} d e^{2} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{3}\right)} f^{3} - {\left(6 \, B c^{2} d e^{3} + {\left(2 \, B b c + A c^{2}\right)} e^{4}\right)} f^{2}\right)} x + 6 \, {\left(B c^{2} e^{6} - 4 \, {\left(B a^{2} + 2 \, A a b\right)} d f^{5} + {\left(4 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d^{2} + 4 \, {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} d e + {\left(B a^{2} + 2 \, A a b\right)} e^{2}\right)} f^{4} - {\left(4 \, B c^{2} d^{3} + 8 \, {\left(2 \, B b c + A c^{2}\right)} d^{2} e + 5 \, {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} d e^{2} + {\left(2 \, B a b + A b^{2} + 2 \, A a c\right)} e^{3}\right)} f^{3} + {\left(13 \, B c^{2} d^{2} e^{2} + 6 \, {\left(2 \, B b c + A c^{2}\right)} d e^{3} + {\left(B b^{2} + 2 \, {\left(B a + A b\right)} c\right)} e^{4}\right)} f^{2} - {\left(7 \, B c^{2} d e^{4} + {\left(2 \, B b c + A c^{2}\right)} e^{5}\right)} f\right)} \log\left(f x^{2} + e x + d\right)}{12 \, {\left(e^{2} f^{5} - 4 \, d f^{6}\right)}}\right]"," ",0,"[1/12*(3*(B*c^2*e^2*f^4 - 4*B*c^2*d*f^5)*x^4 - 4*(B*c^2*e^3*f^3 + 4*(2*B*b*c + A*c^2)*d*f^5 - (4*B*c^2*d*e + (2*B*b*c + A*c^2)*e^2)*f^4)*x^3 + 6*(B*c^2*e^4*f^2 - 4*(B*b^2 + 2*(B*a + A*b)*c)*d*f^5 + (4*B*c^2*d^2 + 4*(2*B*b*c + A*c^2)*d*e + (B*b^2 + 2*(B*a + A*b)*c)*e^2)*f^4 - (5*B*c^2*d*e^2 + (2*B*b*c + A*c^2)*e^3)*f^3)*x^2 - 6*(B*c^2*e^5 - 2*A*a^2*f^5 + (2*(2*B*a*b + A*b^2 + 2*A*a*c)*d + (B*a^2 + 2*A*a*b)*e)*f^4 - (2*(2*B*b*c + A*c^2)*d^2 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d*e + (2*B*a*b + A*b^2 + 2*A*a*c)*e^2)*f^3 + (5*B*c^2*d^2*e + 4*(2*B*b*c + A*c^2)*d*e^2 + (B*b^2 + 2*(B*a + A*b)*c)*e^3)*f^2 - (5*B*c^2*d*e^3 + (2*B*b*c + A*c^2)*e^4)*f)*sqrt(e^2 - 4*d*f)*log((2*f^2*x^2 + 2*e*f*x + e^2 - 2*d*f - sqrt(e^2 - 4*d*f)*(2*f*x + e))/(f*x^2 + e*x + d)) - 12*(B*c^2*e^5*f + 4*(2*B*a*b + A*b^2 + 2*A*a*c)*d*f^5 - (4*(2*B*b*c + A*c^2)*d^2 + 4*(B*b^2 + 2*(B*a + A*b)*c)*d*e + (2*B*a*b + A*b^2 + 2*A*a*c)*e^2)*f^4 + (8*B*c^2*d^2*e + 5*(2*B*b*c + A*c^2)*d*e^2 + (B*b^2 + 2*(B*a + A*b)*c)*e^3)*f^3 - (6*B*c^2*d*e^3 + (2*B*b*c + A*c^2)*e^4)*f^2)*x + 6*(B*c^2*e^6 - 4*(B*a^2 + 2*A*a*b)*d*f^5 + (4*(B*b^2 + 2*(B*a + A*b)*c)*d^2 + 4*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e + (B*a^2 + 2*A*a*b)*e^2)*f^4 - (4*B*c^2*d^3 + 8*(2*B*b*c + A*c^2)*d^2*e + 5*(B*b^2 + 2*(B*a + A*b)*c)*d*e^2 + (2*B*a*b + A*b^2 + 2*A*a*c)*e^3)*f^3 + (13*B*c^2*d^2*e^2 + 6*(2*B*b*c + A*c^2)*d*e^3 + (B*b^2 + 2*(B*a + A*b)*c)*e^4)*f^2 - (7*B*c^2*d*e^4 + (2*B*b*c + A*c^2)*e^5)*f)*log(f*x^2 + e*x + d))/(e^2*f^5 - 4*d*f^6), 1/12*(3*(B*c^2*e^2*f^4 - 4*B*c^2*d*f^5)*x^4 - 4*(B*c^2*e^3*f^3 + 4*(2*B*b*c + A*c^2)*d*f^5 - (4*B*c^2*d*e + (2*B*b*c + A*c^2)*e^2)*f^4)*x^3 + 6*(B*c^2*e^4*f^2 - 4*(B*b^2 + 2*(B*a + A*b)*c)*d*f^5 + (4*B*c^2*d^2 + 4*(2*B*b*c + A*c^2)*d*e + (B*b^2 + 2*(B*a + A*b)*c)*e^2)*f^4 - (5*B*c^2*d*e^2 + (2*B*b*c + A*c^2)*e^3)*f^3)*x^2 + 12*(B*c^2*e^5 - 2*A*a^2*f^5 + (2*(2*B*a*b + A*b^2 + 2*A*a*c)*d + (B*a^2 + 2*A*a*b)*e)*f^4 - (2*(2*B*b*c + A*c^2)*d^2 + 3*(B*b^2 + 2*(B*a + A*b)*c)*d*e + (2*B*a*b + A*b^2 + 2*A*a*c)*e^2)*f^3 + (5*B*c^2*d^2*e + 4*(2*B*b*c + A*c^2)*d*e^2 + (B*b^2 + 2*(B*a + A*b)*c)*e^3)*f^2 - (5*B*c^2*d*e^3 + (2*B*b*c + A*c^2)*e^4)*f)*sqrt(-e^2 + 4*d*f)*arctan(-sqrt(-e^2 + 4*d*f)*(2*f*x + e)/(e^2 - 4*d*f)) - 12*(B*c^2*e^5*f + 4*(2*B*a*b + A*b^2 + 2*A*a*c)*d*f^5 - (4*(2*B*b*c + A*c^2)*d^2 + 4*(B*b^2 + 2*(B*a + A*b)*c)*d*e + (2*B*a*b + A*b^2 + 2*A*a*c)*e^2)*f^4 + (8*B*c^2*d^2*e + 5*(2*B*b*c + A*c^2)*d*e^2 + (B*b^2 + 2*(B*a + A*b)*c)*e^3)*f^3 - (6*B*c^2*d*e^3 + (2*B*b*c + A*c^2)*e^4)*f^2)*x + 6*(B*c^2*e^6 - 4*(B*a^2 + 2*A*a*b)*d*f^5 + (4*(B*b^2 + 2*(B*a + A*b)*c)*d^2 + 4*(2*B*a*b + A*b^2 + 2*A*a*c)*d*e + (B*a^2 + 2*A*a*b)*e^2)*f^4 - (4*B*c^2*d^3 + 8*(2*B*b*c + A*c^2)*d^2*e + 5*(B*b^2 + 2*(B*a + A*b)*c)*d*e^2 + (2*B*a*b + A*b^2 + 2*A*a*c)*e^3)*f^3 + (13*B*c^2*d^2*e^2 + 6*(2*B*b*c + A*c^2)*d*e^3 + (B*b^2 + 2*(B*a + A*b)*c)*e^4)*f^2 - (7*B*c^2*d*e^4 + (2*B*b*c + A*c^2)*e^5)*f)*log(f*x^2 + e*x + d))/(e^2*f^5 - 4*d*f^6)]","A",0
15,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)^2/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
17,1,1150,0,0.644461," ","integrate((h*x+g)/(c*x^2+b*x+a)/(c*d*x^2+b*d*x+a*d)^2,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} g - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} h\right)} x^{3} + 9 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} h\right)} x^{2} - 6 \, {\left(2 \, a^{2} c^{2} g - a^{2} b c h + {\left(2 \, c^{4} g - b c^{3} h\right)} x^{4} + 2 \, {\left(2 \, b c^{3} g - b^{2} c^{2} h\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} g - {\left(b^{3} c + 2 \, a b c^{2}\right)} h\right)} x^{2} + 2 \, {\left(2 \, a b c^{2} g - a b^{2} c h\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} g - {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} h + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} g - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} h\right)} x}{2 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d^{2} x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d^{2}\right)}}, \frac{6 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} g - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} h\right)} x^{3} + 9 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} h\right)} x^{2} - 12 \, {\left(2 \, a^{2} c^{2} g - a^{2} b c h + {\left(2 \, c^{4} g - b c^{3} h\right)} x^{4} + 2 \, {\left(2 \, b c^{3} g - b^{2} c^{2} h\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} g - {\left(b^{3} c + 2 \, a b c^{2}\right)} h\right)} x^{2} + 2 \, {\left(2 \, a b c^{2} g - a b^{2} c h\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} g - {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} h + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} g - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} h\right)} x}{2 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d^{2} x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d^{2} x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d^{2} x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d^{2} x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d^{2}\right)}}\right]"," ",0,"[1/2*(6*(2*(b^2*c^3 - 4*a*c^4)*g - (b^3*c^2 - 4*a*b*c^3)*h)*x^3 + 9*(2*(b^3*c^2 - 4*a*b*c^3)*g - (b^4*c - 4*a*b^2*c^2)*h)*x^2 - 6*(2*a^2*c^2*g - a^2*b*c*h + (2*c^4*g - b*c^3*h)*x^4 + 2*(2*b*c^3*g - b^2*c^2*h)*x^3 + (2*(b^2*c^2 + 2*a*c^3)*g - (b^3*c + 2*a*b*c^2)*h)*x^2 + 2*(2*a*b*c^2*g - a*b^2*c*h)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*g - (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*h + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*g - (b^5 + a*b^3*c - 20*a^2*b*c^2)*h)*x)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*d^2), 1/2*(6*(2*(b^2*c^3 - 4*a*c^4)*g - (b^3*c^2 - 4*a*b*c^3)*h)*x^3 + 9*(2*(b^3*c^2 - 4*a*b*c^3)*g - (b^4*c - 4*a*b^2*c^2)*h)*x^2 - 12*(2*a^2*c^2*g - a^2*b*c*h + (2*c^4*g - b*c^3*h)*x^4 + 2*(2*b*c^3*g - b^2*c^2*h)*x^3 + (2*(b^2*c^2 + 2*a*c^3)*g - (b^3*c + 2*a*b*c^2)*h)*x^2 + 2*(2*a*b*c^2*g - a*b^2*c*h)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*g - (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*h + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*g - (b^5 + a*b^3*c - 20*a^2*b*c^2)*h)*x)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d^2*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d^2*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d^2*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d^2*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*d^2)]","B",0
18,1,1130,0,0.610761," ","integrate((h*x+g)/(c*x^2+b*x+a)^2/(c*d*x^2+b*d*x+a*d),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} g - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} h\right)} x^{3} + 9 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} h\right)} x^{2} - 6 \, {\left(2 \, a^{2} c^{2} g - a^{2} b c h + {\left(2 \, c^{4} g - b c^{3} h\right)} x^{4} + 2 \, {\left(2 \, b c^{3} g - b^{2} c^{2} h\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} g - {\left(b^{3} c + 2 \, a b c^{2}\right)} h\right)} x^{2} + 2 \, {\left(2 \, a b c^{2} g - a b^{2} c h\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} g - {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} h + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} g - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} h\right)} x}{2 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d\right)}}, \frac{6 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} g - {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} h\right)} x^{3} + 9 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} g - {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} h\right)} x^{2} - 12 \, {\left(2 \, a^{2} c^{2} g - a^{2} b c h + {\left(2 \, c^{4} g - b c^{3} h\right)} x^{4} + 2 \, {\left(2 \, b c^{3} g - b^{2} c^{2} h\right)} x^{3} + {\left(2 \, {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} g - {\left(b^{3} c + 2 \, a b c^{2}\right)} h\right)} x^{2} + 2 \, {\left(2 \, a b c^{2} g - a b^{2} c h\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left(b^{5} - 14 \, a b^{3} c + 40 \, a^{2} b c^{2}\right)} g - {\left(a b^{4} + 4 \, a^{2} b^{2} c - 32 \, a^{3} c^{2}\right)} h + 2 \, {\left(2 \, {\left(b^{4} c + a b^{2} c^{2} - 20 \, a^{2} c^{3}\right)} g - {\left(b^{5} + a b^{3} c - 20 \, a^{2} b c^{2}\right)} h\right)} x}{2 \, {\left({\left(b^{6} c^{2} - 12 \, a b^{4} c^{3} + 48 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d x^{4} + 2 \, {\left(b^{7} c - 12 \, a b^{5} c^{2} + 48 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} d x^{3} + {\left(b^{8} - 10 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 32 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} d x^{2} + 2 \, {\left(a b^{7} - 12 \, a^{2} b^{5} c + 48 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} d x + {\left(a^{2} b^{6} - 12 \, a^{3} b^{4} c + 48 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} d\right)}}\right]"," ",0,"[1/2*(6*(2*(b^2*c^3 - 4*a*c^4)*g - (b^3*c^2 - 4*a*b*c^3)*h)*x^3 + 9*(2*(b^3*c^2 - 4*a*b*c^3)*g - (b^4*c - 4*a*b^2*c^2)*h)*x^2 - 6*(2*a^2*c^2*g - a^2*b*c*h + (2*c^4*g - b*c^3*h)*x^4 + 2*(2*b*c^3*g - b^2*c^2*h)*x^3 + (2*(b^2*c^2 + 2*a*c^3)*g - (b^3*c + 2*a*b*c^2)*h)*x^2 + 2*(2*a*b*c^2*g - a*b^2*c*h)*x)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*g - (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*h + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*g - (b^5 + a*b^3*c - 20*a^2*b*c^2)*h)*x)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*d), 1/2*(6*(2*(b^2*c^3 - 4*a*c^4)*g - (b^3*c^2 - 4*a*b*c^3)*h)*x^3 + 9*(2*(b^3*c^2 - 4*a*b*c^3)*g - (b^4*c - 4*a*b^2*c^2)*h)*x^2 - 12*(2*a^2*c^2*g - a^2*b*c*h + (2*c^4*g - b*c^3*h)*x^4 + 2*(2*b*c^3*g - b^2*c^2*h)*x^3 + (2*(b^2*c^2 + 2*a*c^3)*g - (b^3*c + 2*a*b*c^2)*h)*x^2 + 2*(2*a*b*c^2*g - a*b^2*c*h)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - (b^5 - 14*a*b^3*c + 40*a^2*b*c^2)*g - (a*b^4 + 4*a^2*b^2*c - 32*a^3*c^2)*h + 2*(2*(b^4*c + a*b^2*c^2 - 20*a^2*c^3)*g - (b^5 + a*b^3*c - 20*a^2*b*c^2)*h)*x)/((b^6*c^2 - 12*a*b^4*c^3 + 48*a^2*b^2*c^4 - 64*a^3*c^5)*d*x^4 + 2*(b^7*c - 12*a*b^5*c^2 + 48*a^2*b^3*c^3 - 64*a^3*b*c^4)*d*x^3 + (b^8 - 10*a*b^6*c + 24*a^2*b^4*c^2 + 32*a^3*b^2*c^3 - 128*a^4*c^4)*d*x^2 + 2*(a*b^7 - 12*a^2*b^5*c + 48*a^3*b^3*c^2 - 64*a^4*b*c^3)*d*x + (a^2*b^6 - 12*a^3*b^4*c + 48*a^4*b^2*c^2 - 64*a^5*c^3)*d)]","B",0
19,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,-1,0,0,0.000000," ","integrate((B*x+A)*(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
21,-1,0,0,0.000000," ","integrate((B*x+A)/(c*x^2+b*x+a)/(f*x^2+e*x+d)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
22,1,6861,0,47.866530," ","integrate((B*x+A)/(c*x^2+a)/(f*x^2+e*x+d)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-\frac{2 \, A B a c e - {\left(B^{2} a c - A^{2} c^{2}\right)} d + {\left(B^{2} a^{2} - A^{2} a c\right)} f + {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} \log\left(-\frac{2 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e^{2} - 2 \, {\left(A B^{3} a^{2} + A^{3} B a c\right)} e f - 2 \, {\left(2 \, {\left(A B^{3} a^{2} + A^{3} B a c\right)} f^{2} - {\left(2 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} f\right)} x + 2 \, {\left(2 \, A^{2} B c^{3} d^{2} + 2 \, A^{2} B a^{2} c f^{2} + {\left(3 \, A B^{2} a c^{2} - A^{3} c^{3}\right)} d e + {\left(B^{3} a^{2} c - A^{2} B a c^{2}\right)} e^{2} - {\left(4 \, A^{2} B a c^{2} d + {\left(3 \, A B^{2} a^{2} c - A^{3} a c^{2}\right)} e\right)} f - {\left(B a c^{4} d^{3} - A a c^{4} d^{2} e + B a^{2} c^{3} d e^{2} - A a^{2} c^{3} e^{3} - B a^{4} c f^{3} + {\left(3 \, B a^{3} c^{2} d - A a^{3} c^{2} e\right)} f^{2} - {\left(3 \, B a^{2} c^{3} d^{2} - 2 \, A a^{2} c^{3} d e + B a^{3} c^{2} e^{2}\right)} f\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}\right)} \sqrt{f x^{2} + e x + d} \sqrt{-\frac{2 \, A B a c e - {\left(B^{2} a c - A^{2} c^{2}\right)} d + {\left(B^{2} a^{2} - A^{2} a c\right)} f + {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} - {\left(2 \, {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{3} + 2 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d e^{2} - 4 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{2} f + 2 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d f^{2} + {\left({\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{2} e + {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} e^{3} - 2 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d e f + {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} e f^{2}\right)} x\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{x}\right) + \frac{1}{4} \, \sqrt{-\frac{2 \, A B a c e - {\left(B^{2} a c - A^{2} c^{2}\right)} d + {\left(B^{2} a^{2} - A^{2} a c\right)} f + {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} \log\left(-\frac{2 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e^{2} - 2 \, {\left(A B^{3} a^{2} + A^{3} B a c\right)} e f - 2 \, {\left(2 \, {\left(A B^{3} a^{2} + A^{3} B a c\right)} f^{2} - {\left(2 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} f\right)} x - 2 \, {\left(2 \, A^{2} B c^{3} d^{2} + 2 \, A^{2} B a^{2} c f^{2} + {\left(3 \, A B^{2} a c^{2} - A^{3} c^{3}\right)} d e + {\left(B^{3} a^{2} c - A^{2} B a c^{2}\right)} e^{2} - {\left(4 \, A^{2} B a c^{2} d + {\left(3 \, A B^{2} a^{2} c - A^{3} a c^{2}\right)} e\right)} f - {\left(B a c^{4} d^{3} - A a c^{4} d^{2} e + B a^{2} c^{3} d e^{2} - A a^{2} c^{3} e^{3} - B a^{4} c f^{3} + {\left(3 \, B a^{3} c^{2} d - A a^{3} c^{2} e\right)} f^{2} - {\left(3 \, B a^{2} c^{3} d^{2} - 2 \, A a^{2} c^{3} d e + B a^{3} c^{2} e^{2}\right)} f\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}\right)} \sqrt{f x^{2} + e x + d} \sqrt{-\frac{2 \, A B a c e - {\left(B^{2} a c - A^{2} c^{2}\right)} d + {\left(B^{2} a^{2} - A^{2} a c\right)} f + {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} - {\left(2 \, {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{3} + 2 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d e^{2} - 4 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{2} f + 2 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d f^{2} + {\left({\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{2} e + {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} e^{3} - 2 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d e f + {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} e f^{2}\right)} x\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{x}\right) - \frac{1}{4} \, \sqrt{-\frac{2 \, A B a c e - {\left(B^{2} a c - A^{2} c^{2}\right)} d + {\left(B^{2} a^{2} - A^{2} a c\right)} f - {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} \log\left(-\frac{2 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e^{2} - 2 \, {\left(A B^{3} a^{2} + A^{3} B a c\right)} e f - 2 \, {\left(2 \, {\left(A B^{3} a^{2} + A^{3} B a c\right)} f^{2} - {\left(2 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} f\right)} x + 2 \, {\left(2 \, A^{2} B c^{3} d^{2} + 2 \, A^{2} B a^{2} c f^{2} + {\left(3 \, A B^{2} a c^{2} - A^{3} c^{3}\right)} d e + {\left(B^{3} a^{2} c - A^{2} B a c^{2}\right)} e^{2} - {\left(4 \, A^{2} B a c^{2} d + {\left(3 \, A B^{2} a^{2} c - A^{3} a c^{2}\right)} e\right)} f + {\left(B a c^{4} d^{3} - A a c^{4} d^{2} e + B a^{2} c^{3} d e^{2} - A a^{2} c^{3} e^{3} - B a^{4} c f^{3} + {\left(3 \, B a^{3} c^{2} d - A a^{3} c^{2} e\right)} f^{2} - {\left(3 \, B a^{2} c^{3} d^{2} - 2 \, A a^{2} c^{3} d e + B a^{3} c^{2} e^{2}\right)} f\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}\right)} \sqrt{f x^{2} + e x + d} \sqrt{-\frac{2 \, A B a c e - {\left(B^{2} a c - A^{2} c^{2}\right)} d + {\left(B^{2} a^{2} - A^{2} a c\right)} f - {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} + {\left(2 \, {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{3} + 2 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d e^{2} - 4 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{2} f + 2 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d f^{2} + {\left({\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{2} e + {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} e^{3} - 2 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d e f + {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} e f^{2}\right)} x\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{x}\right) + \frac{1}{4} \, \sqrt{-\frac{2 \, A B a c e - {\left(B^{2} a c - A^{2} c^{2}\right)} d + {\left(B^{2} a^{2} - A^{2} a c\right)} f - {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} \log\left(-\frac{2 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e^{2} - 2 \, {\left(A B^{3} a^{2} + A^{3} B a c\right)} e f - 2 \, {\left(2 \, {\left(A B^{3} a^{2} + A^{3} B a c\right)} f^{2} - {\left(2 \, {\left(A B^{3} a c + A^{3} B c^{2}\right)} d + {\left(B^{4} a^{2} - A^{4} c^{2}\right)} e\right)} f\right)} x - 2 \, {\left(2 \, A^{2} B c^{3} d^{2} + 2 \, A^{2} B a^{2} c f^{2} + {\left(3 \, A B^{2} a c^{2} - A^{3} c^{3}\right)} d e + {\left(B^{3} a^{2} c - A^{2} B a c^{2}\right)} e^{2} - {\left(4 \, A^{2} B a c^{2} d + {\left(3 \, A B^{2} a^{2} c - A^{3} a c^{2}\right)} e\right)} f + {\left(B a c^{4} d^{3} - A a c^{4} d^{2} e + B a^{2} c^{3} d e^{2} - A a^{2} c^{3} e^{3} - B a^{4} c f^{3} + {\left(3 \, B a^{3} c^{2} d - A a^{3} c^{2} e\right)} f^{2} - {\left(3 \, B a^{2} c^{3} d^{2} - 2 \, A a^{2} c^{3} d e + B a^{3} c^{2} e^{2}\right)} f\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}\right)} \sqrt{f x^{2} + e x + d} \sqrt{-\frac{2 \, A B a c e - {\left(B^{2} a c - A^{2} c^{2}\right)} d + {\left(B^{2} a^{2} - A^{2} a c\right)} f - {\left(a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{a c^{3} d^{2} + a^{2} c^{2} e^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} + {\left(2 \, {\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{3} + 2 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d e^{2} - 4 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d^{2} f + 2 \, {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} d f^{2} + {\left({\left(B^{2} a c^{3} + A^{2} c^{4}\right)} d^{2} e + {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} e^{3} - 2 \, {\left(B^{2} a^{2} c^{2} + A^{2} a c^{3}\right)} d e f + {\left(B^{2} a^{3} c + A^{2} a^{2} c^{2}\right)} e f^{2}\right)} x\right)} \sqrt{-\frac{4 \, A^{2} B^{2} c^{2} d^{2} + 4 \, A^{2} B^{2} a^{2} f^{2} + 4 \, {\left(A B^{3} a c - A^{3} B c^{2}\right)} d e + {\left(B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}\right)} e^{2} - 4 \, {\left(2 \, A^{2} B^{2} a c d + {\left(A B^{3} a^{2} - A^{3} B a c\right)} e\right)} f}{a c^{5} d^{4} + 2 \, a^{2} c^{4} d^{2} e^{2} + a^{3} c^{3} e^{4} - 4 \, a^{4} c^{2} d f^{3} + a^{5} c f^{4} + 2 \, {\left(3 \, a^{3} c^{3} d^{2} + a^{4} c^{2} e^{2}\right)} f^{2} - 4 \, {\left(a^{2} c^{4} d^{3} + a^{3} c^{3} d e^{2}\right)} f}}}{x}\right)"," ",0,"-1/4*sqrt(-(2*A*B*a*c*e - (B^2*a*c - A^2*c^2)*d + (B^2*a^2 - A^2*a*c)*f + (a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/(a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2))*log(-(2*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 - A^4*c^2)*e^2 - 2*(A*B^3*a^2 + A^3*B*a*c)*e*f - 2*(2*(A*B^3*a^2 + A^3*B*a*c)*f^2 - (2*(A*B^3*a*c + A^3*B*c^2)*d + (B^4*a^2 - A^4*c^2)*e)*f)*x + 2*(2*A^2*B*c^3*d^2 + 2*A^2*B*a^2*c*f^2 + (3*A*B^2*a*c^2 - A^3*c^3)*d*e + (B^3*a^2*c - A^2*B*a*c^2)*e^2 - (4*A^2*B*a*c^2*d + (3*A*B^2*a^2*c - A^3*a*c^2)*e)*f - (B*a*c^4*d^3 - A*a*c^4*d^2*e + B*a^2*c^3*d*e^2 - A*a^2*c^3*e^3 - B*a^4*c*f^3 + (3*B*a^3*c^2*d - A*a^3*c^2*e)*f^2 - (3*B*a^2*c^3*d^2 - 2*A*a^2*c^3*d*e + B*a^3*c^2*e^2)*f)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))*sqrt(f*x^2 + e*x + d)*sqrt(-(2*A*B*a*c*e - (B^2*a*c - A^2*c^2)*d + (B^2*a^2 - A^2*a*c)*f + (a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/(a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)) - (2*(B^2*a*c^3 + A^2*c^4)*d^3 + 2*(B^2*a^2*c^2 + A^2*a*c^3)*d*e^2 - 4*(B^2*a^2*c^2 + A^2*a*c^3)*d^2*f + 2*(B^2*a^3*c + A^2*a^2*c^2)*d*f^2 + ((B^2*a*c^3 + A^2*c^4)*d^2*e + (B^2*a^2*c^2 + A^2*a*c^3)*e^3 - 2*(B^2*a^2*c^2 + A^2*a*c^3)*d*e*f + (B^2*a^3*c + A^2*a^2*c^2)*e*f^2)*x)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/x) + 1/4*sqrt(-(2*A*B*a*c*e - (B^2*a*c - A^2*c^2)*d + (B^2*a^2 - A^2*a*c)*f + (a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/(a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2))*log(-(2*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 - A^4*c^2)*e^2 - 2*(A*B^3*a^2 + A^3*B*a*c)*e*f - 2*(2*(A*B^3*a^2 + A^3*B*a*c)*f^2 - (2*(A*B^3*a*c + A^3*B*c^2)*d + (B^4*a^2 - A^4*c^2)*e)*f)*x - 2*(2*A^2*B*c^3*d^2 + 2*A^2*B*a^2*c*f^2 + (3*A*B^2*a*c^2 - A^3*c^3)*d*e + (B^3*a^2*c - A^2*B*a*c^2)*e^2 - (4*A^2*B*a*c^2*d + (3*A*B^2*a^2*c - A^3*a*c^2)*e)*f - (B*a*c^4*d^3 - A*a*c^4*d^2*e + B*a^2*c^3*d*e^2 - A*a^2*c^3*e^3 - B*a^4*c*f^3 + (3*B*a^3*c^2*d - A*a^3*c^2*e)*f^2 - (3*B*a^2*c^3*d^2 - 2*A*a^2*c^3*d*e + B*a^3*c^2*e^2)*f)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))*sqrt(f*x^2 + e*x + d)*sqrt(-(2*A*B*a*c*e - (B^2*a*c - A^2*c^2)*d + (B^2*a^2 - A^2*a*c)*f + (a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/(a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)) - (2*(B^2*a*c^3 + A^2*c^4)*d^3 + 2*(B^2*a^2*c^2 + A^2*a*c^3)*d*e^2 - 4*(B^2*a^2*c^2 + A^2*a*c^3)*d^2*f + 2*(B^2*a^3*c + A^2*a^2*c^2)*d*f^2 + ((B^2*a*c^3 + A^2*c^4)*d^2*e + (B^2*a^2*c^2 + A^2*a*c^3)*e^3 - 2*(B^2*a^2*c^2 + A^2*a*c^3)*d*e*f + (B^2*a^3*c + A^2*a^2*c^2)*e*f^2)*x)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/x) - 1/4*sqrt(-(2*A*B*a*c*e - (B^2*a*c - A^2*c^2)*d + (B^2*a^2 - A^2*a*c)*f - (a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/(a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2))*log(-(2*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 - A^4*c^2)*e^2 - 2*(A*B^3*a^2 + A^3*B*a*c)*e*f - 2*(2*(A*B^3*a^2 + A^3*B*a*c)*f^2 - (2*(A*B^3*a*c + A^3*B*c^2)*d + (B^4*a^2 - A^4*c^2)*e)*f)*x + 2*(2*A^2*B*c^3*d^2 + 2*A^2*B*a^2*c*f^2 + (3*A*B^2*a*c^2 - A^3*c^3)*d*e + (B^3*a^2*c - A^2*B*a*c^2)*e^2 - (4*A^2*B*a*c^2*d + (3*A*B^2*a^2*c - A^3*a*c^2)*e)*f + (B*a*c^4*d^3 - A*a*c^4*d^2*e + B*a^2*c^3*d*e^2 - A*a^2*c^3*e^3 - B*a^4*c*f^3 + (3*B*a^3*c^2*d - A*a^3*c^2*e)*f^2 - (3*B*a^2*c^3*d^2 - 2*A*a^2*c^3*d*e + B*a^3*c^2*e^2)*f)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))*sqrt(f*x^2 + e*x + d)*sqrt(-(2*A*B*a*c*e - (B^2*a*c - A^2*c^2)*d + (B^2*a^2 - A^2*a*c)*f - (a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/(a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)) + (2*(B^2*a*c^3 + A^2*c^4)*d^3 + 2*(B^2*a^2*c^2 + A^2*a*c^3)*d*e^2 - 4*(B^2*a^2*c^2 + A^2*a*c^3)*d^2*f + 2*(B^2*a^3*c + A^2*a^2*c^2)*d*f^2 + ((B^2*a*c^3 + A^2*c^4)*d^2*e + (B^2*a^2*c^2 + A^2*a*c^3)*e^3 - 2*(B^2*a^2*c^2 + A^2*a*c^3)*d*e*f + (B^2*a^3*c + A^2*a^2*c^2)*e*f^2)*x)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/x) + 1/4*sqrt(-(2*A*B*a*c*e - (B^2*a*c - A^2*c^2)*d + (B^2*a^2 - A^2*a*c)*f - (a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/(a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2))*log(-(2*(A*B^3*a*c + A^3*B*c^2)*d*e + (B^4*a^2 - A^4*c^2)*e^2 - 2*(A*B^3*a^2 + A^3*B*a*c)*e*f - 2*(2*(A*B^3*a^2 + A^3*B*a*c)*f^2 - (2*(A*B^3*a*c + A^3*B*c^2)*d + (B^4*a^2 - A^4*c^2)*e)*f)*x - 2*(2*A^2*B*c^3*d^2 + 2*A^2*B*a^2*c*f^2 + (3*A*B^2*a*c^2 - A^3*c^3)*d*e + (B^3*a^2*c - A^2*B*a*c^2)*e^2 - (4*A^2*B*a*c^2*d + (3*A*B^2*a^2*c - A^3*a*c^2)*e)*f + (B*a*c^4*d^3 - A*a*c^4*d^2*e + B*a^2*c^3*d*e^2 - A*a^2*c^3*e^3 - B*a^4*c*f^3 + (3*B*a^3*c^2*d - A*a^3*c^2*e)*f^2 - (3*B*a^2*c^3*d^2 - 2*A*a^2*c^3*d*e + B*a^3*c^2*e^2)*f)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))*sqrt(f*x^2 + e*x + d)*sqrt(-(2*A*B*a*c*e - (B^2*a*c - A^2*c^2)*d + (B^2*a^2 - A^2*a*c)*f - (a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/(a*c^3*d^2 + a^2*c^2*e^2 - 2*a^2*c^2*d*f + a^3*c*f^2)) + (2*(B^2*a*c^3 + A^2*c^4)*d^3 + 2*(B^2*a^2*c^2 + A^2*a*c^3)*d*e^2 - 4*(B^2*a^2*c^2 + A^2*a*c^3)*d^2*f + 2*(B^2*a^3*c + A^2*a^2*c^2)*d*f^2 + ((B^2*a*c^3 + A^2*c^4)*d^2*e + (B^2*a^2*c^2 + A^2*a*c^3)*e^3 - 2*(B^2*a^2*c^2 + A^2*a*c^3)*d*e*f + (B^2*a^3*c + A^2*a^2*c^2)*e*f^2)*x)*sqrt(-(4*A^2*B^2*c^2*d^2 + 4*A^2*B^2*a^2*f^2 + 4*(A*B^3*a*c - A^3*B*c^2)*d*e + (B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)*e^2 - 4*(2*A^2*B^2*a*c*d + (A*B^3*a^2 - A^3*B*a*c)*e)*f)/(a*c^5*d^4 + 2*a^2*c^4*d^2*e^2 + a^3*c^3*e^4 - 4*a^4*c^2*d*f^3 + a^5*c*f^4 + 2*(3*a^3*c^3*d^2 + a^4*c^2*e^2)*f^2 - 4*(a^2*c^4*d^3 + a^3*c^3*d*e^2)*f)))/x)","B",0
23,1,8977,0,60.516985," ","integrate((B*x+A)/(c*x^2+b*x+a)/(f*x^2+d)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \sqrt{\frac{{\left(B^{2} b^{2} + 2 \, A^{2} c^{2} - 2 \, {\left(B^{2} a + A B b\right)} c\right)} d + {\left(2 \, B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2} - 2 \, A^{2} a c\right)} f + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}}} \log\left(\frac{2 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 2 \, A^{3} B b c^{2} - {\left(2 \, A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a^{2} b - 3 \, A^{2} B^{2} a b^{2} + A^{3} B b^{3} + {\left(2 \, A^{3} B a b - A^{4} b^{2}\right)} c\right)} d f + \sqrt{2} {\left({\left(B^{3} b^{4} - 8 \, A^{2} B a c^{3} + 2 \, {\left(6 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(4 \, B^{3} a b^{2} + 3 \, A B^{2} b^{3}\right)} c\right)} d^{2} + {\left(3 \, A B^{2} a b^{3} - A^{2} B b^{4} + 4 \, {\left(4 \, A^{2} B a^{2} - A^{3} a b\right)} c^{2} - {\left(12 \, A B^{2} a^{2} b - A^{3} b^{3}\right)} c\right)} d f + {\left(2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3} - 4 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c\right)} f^{2} - {\left({\left(B b^{4} c^{2} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{4} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} + {\left(B b^{6} - 4 \, {\left(6 \, B a^{3} + A a^{2} b\right)} c^{3} + {\left(22 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{2} - {\left(8 \, B a b^{4} + A b^{5}\right)} c\right)} d^{2} f + {\left(3 \, B a^{2} b^{4} - A a b^{5} + 4 \, {\left(6 \, B a^{4} - A a^{3} b\right)} c^{2} - {\left(18 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c\right)} d f^{2} + {\left(2 \, B a^{4} b^{2} - A a^{3} b^{3} - 4 \, {\left(2 \, B a^{5} - A a^{4} b\right)} c\right)} f^{3}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}\right)} \sqrt{f x^{2} + d} \sqrt{\frac{{\left(B^{2} b^{2} + 2 \, A^{2} c^{2} - 2 \, {\left(B^{2} a + A B b\right)} c\right)} d + {\left(2 \, B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2} - 2 \, A^{2} a c\right)} f + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}}} - 4 \, {\left({\left(B^{4} a^{2} b - A B^{3} a b^{2} - 2 \, A^{3} B a c^{2} - {\left(2 \, A B^{3} a^{2} - 3 \, A^{2} B^{2} a b\right)} c\right)} d f + {\left(2 \, A B^{3} a^{3} - 3 \, A^{2} B^{2} a^{2} b + A^{3} B a b^{2} + {\left(2 \, A^{3} B a^{2} - A^{4} a b\right)} c\right)} f^{2}\right)} x + 2 \, {\left({\left(4 \, A^{2} a c^{4} + {\left(4 \, B^{2} a^{2} - 4 \, A B a b - A^{2} b^{2}\right)} c^{3} - {\left(B^{2} a b^{2} - A B b^{3}\right)} c^{2}\right)} d^{3} - {\left(B^{2} a b^{4} - A B b^{5} + 8 \, A^{2} a^{2} c^{3} + 2 \, {\left(4 \, B^{2} a^{3} - 4 \, A B a^{2} b - 3 \, A^{2} a b^{2}\right)} c^{2} - {\left(6 \, B^{2} a^{2} b^{2} - 6 \, A B a b^{3} - A^{2} b^{4}\right)} c\right)} d^{2} f - {\left(B^{2} a^{3} b^{2} - A B a^{2} b^{3} - 4 \, A^{2} a^{3} c^{2} - {\left(4 \, B^{2} a^{4} - 4 \, A B a^{3} b - A^{2} a^{2} b^{2}\right)} c\right)} d f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{{\left(B^{2} b^{2} + 2 \, A^{2} c^{2} - 2 \, {\left(B^{2} a + A B b\right)} c\right)} d + {\left(2 \, B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2} - 2 \, A^{2} a c\right)} f + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}}} \log\left(\frac{2 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 2 \, A^{3} B b c^{2} - {\left(2 \, A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a^{2} b - 3 \, A^{2} B^{2} a b^{2} + A^{3} B b^{3} + {\left(2 \, A^{3} B a b - A^{4} b^{2}\right)} c\right)} d f - \sqrt{2} {\left({\left(B^{3} b^{4} - 8 \, A^{2} B a c^{3} + 2 \, {\left(6 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(4 \, B^{3} a b^{2} + 3 \, A B^{2} b^{3}\right)} c\right)} d^{2} + {\left(3 \, A B^{2} a b^{3} - A^{2} B b^{4} + 4 \, {\left(4 \, A^{2} B a^{2} - A^{3} a b\right)} c^{2} - {\left(12 \, A B^{2} a^{2} b - A^{3} b^{3}\right)} c\right)} d f + {\left(2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3} - 4 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c\right)} f^{2} - {\left({\left(B b^{4} c^{2} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{4} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} + {\left(B b^{6} - 4 \, {\left(6 \, B a^{3} + A a^{2} b\right)} c^{3} + {\left(22 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{2} - {\left(8 \, B a b^{4} + A b^{5}\right)} c\right)} d^{2} f + {\left(3 \, B a^{2} b^{4} - A a b^{5} + 4 \, {\left(6 \, B a^{4} - A a^{3} b\right)} c^{2} - {\left(18 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c\right)} d f^{2} + {\left(2 \, B a^{4} b^{2} - A a^{3} b^{3} - 4 \, {\left(2 \, B a^{5} - A a^{4} b\right)} c\right)} f^{3}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}\right)} \sqrt{f x^{2} + d} \sqrt{\frac{{\left(B^{2} b^{2} + 2 \, A^{2} c^{2} - 2 \, {\left(B^{2} a + A B b\right)} c\right)} d + {\left(2 \, B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2} - 2 \, A^{2} a c\right)} f + {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}}} - 4 \, {\left({\left(B^{4} a^{2} b - A B^{3} a b^{2} - 2 \, A^{3} B a c^{2} - {\left(2 \, A B^{3} a^{2} - 3 \, A^{2} B^{2} a b\right)} c\right)} d f + {\left(2 \, A B^{3} a^{3} - 3 \, A^{2} B^{2} a^{2} b + A^{3} B a b^{2} + {\left(2 \, A^{3} B a^{2} - A^{4} a b\right)} c\right)} f^{2}\right)} x + 2 \, {\left({\left(4 \, A^{2} a c^{4} + {\left(4 \, B^{2} a^{2} - 4 \, A B a b - A^{2} b^{2}\right)} c^{3} - {\left(B^{2} a b^{2} - A B b^{3}\right)} c^{2}\right)} d^{3} - {\left(B^{2} a b^{4} - A B b^{5} + 8 \, A^{2} a^{2} c^{3} + 2 \, {\left(4 \, B^{2} a^{3} - 4 \, A B a^{2} b - 3 \, A^{2} a b^{2}\right)} c^{2} - {\left(6 \, B^{2} a^{2} b^{2} - 6 \, A B a b^{3} - A^{2} b^{4}\right)} c\right)} d^{2} f - {\left(B^{2} a^{3} b^{2} - A B a^{2} b^{3} - 4 \, A^{2} a^{3} c^{2} - {\left(4 \, B^{2} a^{4} - 4 \, A B a^{3} b - A^{2} a^{2} b^{2}\right)} c\right)} d f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{{\left(B^{2} b^{2} + 2 \, A^{2} c^{2} - 2 \, {\left(B^{2} a + A B b\right)} c\right)} d + {\left(2 \, B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2} - 2 \, A^{2} a c\right)} f - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}}} \log\left(\frac{2 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 2 \, A^{3} B b c^{2} - {\left(2 \, A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a^{2} b - 3 \, A^{2} B^{2} a b^{2} + A^{3} B b^{3} + {\left(2 \, A^{3} B a b - A^{4} b^{2}\right)} c\right)} d f + \sqrt{2} {\left({\left(B^{3} b^{4} - 8 \, A^{2} B a c^{3} + 2 \, {\left(6 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(4 \, B^{3} a b^{2} + 3 \, A B^{2} b^{3}\right)} c\right)} d^{2} + {\left(3 \, A B^{2} a b^{3} - A^{2} B b^{4} + 4 \, {\left(4 \, A^{2} B a^{2} - A^{3} a b\right)} c^{2} - {\left(12 \, A B^{2} a^{2} b - A^{3} b^{3}\right)} c\right)} d f + {\left(2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3} - 4 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c\right)} f^{2} + {\left({\left(B b^{4} c^{2} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{4} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} + {\left(B b^{6} - 4 \, {\left(6 \, B a^{3} + A a^{2} b\right)} c^{3} + {\left(22 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{2} - {\left(8 \, B a b^{4} + A b^{5}\right)} c\right)} d^{2} f + {\left(3 \, B a^{2} b^{4} - A a b^{5} + 4 \, {\left(6 \, B a^{4} - A a^{3} b\right)} c^{2} - {\left(18 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c\right)} d f^{2} + {\left(2 \, B a^{4} b^{2} - A a^{3} b^{3} - 4 \, {\left(2 \, B a^{5} - A a^{4} b\right)} c\right)} f^{3}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}\right)} \sqrt{f x^{2} + d} \sqrt{\frac{{\left(B^{2} b^{2} + 2 \, A^{2} c^{2} - 2 \, {\left(B^{2} a + A B b\right)} c\right)} d + {\left(2 \, B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2} - 2 \, A^{2} a c\right)} f - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}}} - 4 \, {\left({\left(B^{4} a^{2} b - A B^{3} a b^{2} - 2 \, A^{3} B a c^{2} - {\left(2 \, A B^{3} a^{2} - 3 \, A^{2} B^{2} a b\right)} c\right)} d f + {\left(2 \, A B^{3} a^{3} - 3 \, A^{2} B^{2} a^{2} b + A^{3} B a b^{2} + {\left(2 \, A^{3} B a^{2} - A^{4} a b\right)} c\right)} f^{2}\right)} x - 2 \, {\left({\left(4 \, A^{2} a c^{4} + {\left(4 \, B^{2} a^{2} - 4 \, A B a b - A^{2} b^{2}\right)} c^{3} - {\left(B^{2} a b^{2} - A B b^{3}\right)} c^{2}\right)} d^{3} - {\left(B^{2} a b^{4} - A B b^{5} + 8 \, A^{2} a^{2} c^{3} + 2 \, {\left(4 \, B^{2} a^{3} - 4 \, A B a^{2} b - 3 \, A^{2} a b^{2}\right)} c^{2} - {\left(6 \, B^{2} a^{2} b^{2} - 6 \, A B a b^{3} - A^{2} b^{4}\right)} c\right)} d^{2} f - {\left(B^{2} a^{3} b^{2} - A B a^{2} b^{3} - 4 \, A^{2} a^{3} c^{2} - {\left(4 \, B^{2} a^{4} - 4 \, A B a^{3} b - A^{2} a^{2} b^{2}\right)} c\right)} d f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{{\left(B^{2} b^{2} + 2 \, A^{2} c^{2} - 2 \, {\left(B^{2} a + A B b\right)} c\right)} d + {\left(2 \, B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2} - 2 \, A^{2} a c\right)} f - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}}} \log\left(\frac{2 \, {\left(B^{4} a b^{2} - A B^{3} b^{3} - 2 \, A^{3} B b c^{2} - {\left(2 \, A B^{3} a b - 3 \, A^{2} B^{2} b^{2}\right)} c\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a^{2} b - 3 \, A^{2} B^{2} a b^{2} + A^{3} B b^{3} + {\left(2 \, A^{3} B a b - A^{4} b^{2}\right)} c\right)} d f - \sqrt{2} {\left({\left(B^{3} b^{4} - 8 \, A^{2} B a c^{3} + 2 \, {\left(6 \, A B^{2} a b + A^{2} B b^{2}\right)} c^{2} - {\left(4 \, B^{3} a b^{2} + 3 \, A B^{2} b^{3}\right)} c\right)} d^{2} + {\left(3 \, A B^{2} a b^{3} - A^{2} B b^{4} + 4 \, {\left(4 \, A^{2} B a^{2} - A^{3} a b\right)} c^{2} - {\left(12 \, A B^{2} a^{2} b - A^{3} b^{3}\right)} c\right)} d f + {\left(2 \, A^{2} B a^{2} b^{2} - A^{3} a b^{3} - 4 \, {\left(2 \, A^{2} B a^{3} - A^{3} a^{2} b\right)} c\right)} f^{2} + {\left({\left(B b^{4} c^{2} + 4 \, {\left(2 \, B a^{2} + A a b\right)} c^{4} - {\left(6 \, B a b^{2} + A b^{3}\right)} c^{3}\right)} d^{3} + {\left(B b^{6} - 4 \, {\left(6 \, B a^{3} + A a^{2} b\right)} c^{3} + {\left(22 \, B a^{2} b^{2} + 5 \, A a b^{3}\right)} c^{2} - {\left(8 \, B a b^{4} + A b^{5}\right)} c\right)} d^{2} f + {\left(3 \, B a^{2} b^{4} - A a b^{5} + 4 \, {\left(6 \, B a^{4} - A a^{3} b\right)} c^{2} - {\left(18 \, B a^{3} b^{2} - 5 \, A a^{2} b^{3}\right)} c\right)} d f^{2} + {\left(2 \, B a^{4} b^{2} - A a^{3} b^{3} - 4 \, {\left(2 \, B a^{5} - A a^{4} b\right)} c\right)} f^{3}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}\right)} \sqrt{f x^{2} + d} \sqrt{\frac{{\left(B^{2} b^{2} + 2 \, A^{2} c^{2} - 2 \, {\left(B^{2} a + A B b\right)} c\right)} d + {\left(2 \, B^{2} a^{2} - 2 \, A B a b + A^{2} b^{2} - 2 \, A^{2} a c\right)} f - {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} + {\left(b^{4} - 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d f + {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} f^{2}}} - 4 \, {\left({\left(B^{4} a^{2} b - A B^{3} a b^{2} - 2 \, A^{3} B a c^{2} - {\left(2 \, A B^{3} a^{2} - 3 \, A^{2} B^{2} a b\right)} c\right)} d f + {\left(2 \, A B^{3} a^{3} - 3 \, A^{2} B^{2} a^{2} b + A^{3} B a b^{2} + {\left(2 \, A^{3} B a^{2} - A^{4} a b\right)} c\right)} f^{2}\right)} x - 2 \, {\left({\left(4 \, A^{2} a c^{4} + {\left(4 \, B^{2} a^{2} - 4 \, A B a b - A^{2} b^{2}\right)} c^{3} - {\left(B^{2} a b^{2} - A B b^{3}\right)} c^{2}\right)} d^{3} - {\left(B^{2} a b^{4} - A B b^{5} + 8 \, A^{2} a^{2} c^{3} + 2 \, {\left(4 \, B^{2} a^{3} - 4 \, A B a^{2} b - 3 \, A^{2} a b^{2}\right)} c^{2} - {\left(6 \, B^{2} a^{2} b^{2} - 6 \, A B a b^{3} - A^{2} b^{4}\right)} c\right)} d^{2} f - {\left(B^{2} a^{3} b^{2} - A B a^{2} b^{3} - 4 \, A^{2} a^{3} c^{2} - {\left(4 \, B^{2} a^{4} - 4 \, A B a^{3} b - A^{2} a^{2} b^{2}\right)} c\right)} d f^{2}\right)} \sqrt{\frac{{\left(B^{4} b^{2} - 4 \, A B^{3} b c + 4 \, A^{2} B^{2} c^{2}\right)} d^{2} + 2 \, {\left(2 \, A B^{3} a b - A^{2} B^{2} b^{2} - 2 \, {\left(2 \, A^{2} B^{2} a - A^{3} B b\right)} c\right)} d f + {\left(4 \, A^{2} B^{2} a^{2} - 4 \, A^{3} B a b + A^{4} b^{2}\right)} f^{2}}{{\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{4} + 2 \, {\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{3} f + {\left(b^{6} - 8 \, a b^{4} c + 22 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{2} f^{2} + 2 \, {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d f^{3} + {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} f^{4}}}}{x}\right)"," ",0,"1/4*sqrt(2)*sqrt(((B^2*b^2 + 2*A^2*c^2 - 2*(B^2*a + A*B*b)*c)*d + (2*B^2*a^2 - 2*A*B*a*b + A^2*b^2 - 2*A^2*a*c)*f + ((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2))*log((2*(B^4*a*b^2 - A*B^3*b^3 - 2*A^3*B*b*c^2 - (2*A*B^3*a*b - 3*A^2*B^2*b^2)*c)*d^2 + 2*(2*A*B^3*a^2*b - 3*A^2*B^2*a*b^2 + A^3*B*b^3 + (2*A^3*B*a*b - A^4*b^2)*c)*d*f + sqrt(2)*((B^3*b^4 - 8*A^2*B*a*c^3 + 2*(6*A*B^2*a*b + A^2*B*b^2)*c^2 - (4*B^3*a*b^2 + 3*A*B^2*b^3)*c)*d^2 + (3*A*B^2*a*b^3 - A^2*B*b^4 + 4*(4*A^2*B*a^2 - A^3*a*b)*c^2 - (12*A*B^2*a^2*b - A^3*b^3)*c)*d*f + (2*A^2*B*a^2*b^2 - A^3*a*b^3 - 4*(2*A^2*B*a^3 - A^3*a^2*b)*c)*f^2 - ((B*b^4*c^2 + 4*(2*B*a^2 + A*a*b)*c^4 - (6*B*a*b^2 + A*b^3)*c^3)*d^3 + (B*b^6 - 4*(6*B*a^3 + A*a^2*b)*c^3 + (22*B*a^2*b^2 + 5*A*a*b^3)*c^2 - (8*B*a*b^4 + A*b^5)*c)*d^2*f + (3*B*a^2*b^4 - A*a*b^5 + 4*(6*B*a^4 - A*a^3*b)*c^2 - (18*B*a^3*b^2 - 5*A*a^2*b^3)*c)*d*f^2 + (2*B*a^4*b^2 - A*a^3*b^3 - 4*(2*B*a^5 - A*a^4*b)*c)*f^3)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))*sqrt(f*x^2 + d)*sqrt(((B^2*b^2 + 2*A^2*c^2 - 2*(B^2*a + A*B*b)*c)*d + (2*B^2*a^2 - 2*A*B*a*b + A^2*b^2 - 2*A^2*a*c)*f + ((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)) - 4*((B^4*a^2*b - A*B^3*a*b^2 - 2*A^3*B*a*c^2 - (2*A*B^3*a^2 - 3*A^2*B^2*a*b)*c)*d*f + (2*A*B^3*a^3 - 3*A^2*B^2*a^2*b + A^3*B*a*b^2 + (2*A^3*B*a^2 - A^4*a*b)*c)*f^2)*x + 2*((4*A^2*a*c^4 + (4*B^2*a^2 - 4*A*B*a*b - A^2*b^2)*c^3 - (B^2*a*b^2 - A*B*b^3)*c^2)*d^3 - (B^2*a*b^4 - A*B*b^5 + 8*A^2*a^2*c^3 + 2*(4*B^2*a^3 - 4*A*B*a^2*b - 3*A^2*a*b^2)*c^2 - (6*B^2*a^2*b^2 - 6*A*B*a*b^3 - A^2*b^4)*c)*d^2*f - (B^2*a^3*b^2 - A*B*a^2*b^3 - 4*A^2*a^3*c^2 - (4*B^2*a^4 - 4*A*B*a^3*b - A^2*a^2*b^2)*c)*d*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/x) - 1/4*sqrt(2)*sqrt(((B^2*b^2 + 2*A^2*c^2 - 2*(B^2*a + A*B*b)*c)*d + (2*B^2*a^2 - 2*A*B*a*b + A^2*b^2 - 2*A^2*a*c)*f + ((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2))*log((2*(B^4*a*b^2 - A*B^3*b^3 - 2*A^3*B*b*c^2 - (2*A*B^3*a*b - 3*A^2*B^2*b^2)*c)*d^2 + 2*(2*A*B^3*a^2*b - 3*A^2*B^2*a*b^2 + A^3*B*b^3 + (2*A^3*B*a*b - A^4*b^2)*c)*d*f - sqrt(2)*((B^3*b^4 - 8*A^2*B*a*c^3 + 2*(6*A*B^2*a*b + A^2*B*b^2)*c^2 - (4*B^3*a*b^2 + 3*A*B^2*b^3)*c)*d^2 + (3*A*B^2*a*b^3 - A^2*B*b^4 + 4*(4*A^2*B*a^2 - A^3*a*b)*c^2 - (12*A*B^2*a^2*b - A^3*b^3)*c)*d*f + (2*A^2*B*a^2*b^2 - A^3*a*b^3 - 4*(2*A^2*B*a^3 - A^3*a^2*b)*c)*f^2 - ((B*b^4*c^2 + 4*(2*B*a^2 + A*a*b)*c^4 - (6*B*a*b^2 + A*b^3)*c^3)*d^3 + (B*b^6 - 4*(6*B*a^3 + A*a^2*b)*c^3 + (22*B*a^2*b^2 + 5*A*a*b^3)*c^2 - (8*B*a*b^4 + A*b^5)*c)*d^2*f + (3*B*a^2*b^4 - A*a*b^5 + 4*(6*B*a^4 - A*a^3*b)*c^2 - (18*B*a^3*b^2 - 5*A*a^2*b^3)*c)*d*f^2 + (2*B*a^4*b^2 - A*a^3*b^3 - 4*(2*B*a^5 - A*a^4*b)*c)*f^3)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))*sqrt(f*x^2 + d)*sqrt(((B^2*b^2 + 2*A^2*c^2 - 2*(B^2*a + A*B*b)*c)*d + (2*B^2*a^2 - 2*A*B*a*b + A^2*b^2 - 2*A^2*a*c)*f + ((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)) - 4*((B^4*a^2*b - A*B^3*a*b^2 - 2*A^3*B*a*c^2 - (2*A*B^3*a^2 - 3*A^2*B^2*a*b)*c)*d*f + (2*A*B^3*a^3 - 3*A^2*B^2*a^2*b + A^3*B*a*b^2 + (2*A^3*B*a^2 - A^4*a*b)*c)*f^2)*x + 2*((4*A^2*a*c^4 + (4*B^2*a^2 - 4*A*B*a*b - A^2*b^2)*c^3 - (B^2*a*b^2 - A*B*b^3)*c^2)*d^3 - (B^2*a*b^4 - A*B*b^5 + 8*A^2*a^2*c^3 + 2*(4*B^2*a^3 - 4*A*B*a^2*b - 3*A^2*a*b^2)*c^2 - (6*B^2*a^2*b^2 - 6*A*B*a*b^3 - A^2*b^4)*c)*d^2*f - (B^2*a^3*b^2 - A*B*a^2*b^3 - 4*A^2*a^3*c^2 - (4*B^2*a^4 - 4*A*B*a^3*b - A^2*a^2*b^2)*c)*d*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/x) + 1/4*sqrt(2)*sqrt(((B^2*b^2 + 2*A^2*c^2 - 2*(B^2*a + A*B*b)*c)*d + (2*B^2*a^2 - 2*A*B*a*b + A^2*b^2 - 2*A^2*a*c)*f - ((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2))*log((2*(B^4*a*b^2 - A*B^3*b^3 - 2*A^3*B*b*c^2 - (2*A*B^3*a*b - 3*A^2*B^2*b^2)*c)*d^2 + 2*(2*A*B^3*a^2*b - 3*A^2*B^2*a*b^2 + A^3*B*b^3 + (2*A^3*B*a*b - A^4*b^2)*c)*d*f + sqrt(2)*((B^3*b^4 - 8*A^2*B*a*c^3 + 2*(6*A*B^2*a*b + A^2*B*b^2)*c^2 - (4*B^3*a*b^2 + 3*A*B^2*b^3)*c)*d^2 + (3*A*B^2*a*b^3 - A^2*B*b^4 + 4*(4*A^2*B*a^2 - A^3*a*b)*c^2 - (12*A*B^2*a^2*b - A^3*b^3)*c)*d*f + (2*A^2*B*a^2*b^2 - A^3*a*b^3 - 4*(2*A^2*B*a^3 - A^3*a^2*b)*c)*f^2 + ((B*b^4*c^2 + 4*(2*B*a^2 + A*a*b)*c^4 - (6*B*a*b^2 + A*b^3)*c^3)*d^3 + (B*b^6 - 4*(6*B*a^3 + A*a^2*b)*c^3 + (22*B*a^2*b^2 + 5*A*a*b^3)*c^2 - (8*B*a*b^4 + A*b^5)*c)*d^2*f + (3*B*a^2*b^4 - A*a*b^5 + 4*(6*B*a^4 - A*a^3*b)*c^2 - (18*B*a^3*b^2 - 5*A*a^2*b^3)*c)*d*f^2 + (2*B*a^4*b^2 - A*a^3*b^3 - 4*(2*B*a^5 - A*a^4*b)*c)*f^3)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))*sqrt(f*x^2 + d)*sqrt(((B^2*b^2 + 2*A^2*c^2 - 2*(B^2*a + A*B*b)*c)*d + (2*B^2*a^2 - 2*A*B*a*b + A^2*b^2 - 2*A^2*a*c)*f - ((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)) - 4*((B^4*a^2*b - A*B^3*a*b^2 - 2*A^3*B*a*c^2 - (2*A*B^3*a^2 - 3*A^2*B^2*a*b)*c)*d*f + (2*A*B^3*a^3 - 3*A^2*B^2*a^2*b + A^3*B*a*b^2 + (2*A^3*B*a^2 - A^4*a*b)*c)*f^2)*x - 2*((4*A^2*a*c^4 + (4*B^2*a^2 - 4*A*B*a*b - A^2*b^2)*c^3 - (B^2*a*b^2 - A*B*b^3)*c^2)*d^3 - (B^2*a*b^4 - A*B*b^5 + 8*A^2*a^2*c^3 + 2*(4*B^2*a^3 - 4*A*B*a^2*b - 3*A^2*a*b^2)*c^2 - (6*B^2*a^2*b^2 - 6*A*B*a*b^3 - A^2*b^4)*c)*d^2*f - (B^2*a^3*b^2 - A*B*a^2*b^3 - 4*A^2*a^3*c^2 - (4*B^2*a^4 - 4*A*B*a^3*b - A^2*a^2*b^2)*c)*d*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/x) - 1/4*sqrt(2)*sqrt(((B^2*b^2 + 2*A^2*c^2 - 2*(B^2*a + A*B*b)*c)*d + (2*B^2*a^2 - 2*A*B*a*b + A^2*b^2 - 2*A^2*a*c)*f - ((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2))*log((2*(B^4*a*b^2 - A*B^3*b^3 - 2*A^3*B*b*c^2 - (2*A*B^3*a*b - 3*A^2*B^2*b^2)*c)*d^2 + 2*(2*A*B^3*a^2*b - 3*A^2*B^2*a*b^2 + A^3*B*b^3 + (2*A^3*B*a*b - A^4*b^2)*c)*d*f - sqrt(2)*((B^3*b^4 - 8*A^2*B*a*c^3 + 2*(6*A*B^2*a*b + A^2*B*b^2)*c^2 - (4*B^3*a*b^2 + 3*A*B^2*b^3)*c)*d^2 + (3*A*B^2*a*b^3 - A^2*B*b^4 + 4*(4*A^2*B*a^2 - A^3*a*b)*c^2 - (12*A*B^2*a^2*b - A^3*b^3)*c)*d*f + (2*A^2*B*a^2*b^2 - A^3*a*b^3 - 4*(2*A^2*B*a^3 - A^3*a^2*b)*c)*f^2 + ((B*b^4*c^2 + 4*(2*B*a^2 + A*a*b)*c^4 - (6*B*a*b^2 + A*b^3)*c^3)*d^3 + (B*b^6 - 4*(6*B*a^3 + A*a^2*b)*c^3 + (22*B*a^2*b^2 + 5*A*a*b^3)*c^2 - (8*B*a*b^4 + A*b^5)*c)*d^2*f + (3*B*a^2*b^4 - A*a*b^5 + 4*(6*B*a^4 - A*a^3*b)*c^2 - (18*B*a^3*b^2 - 5*A*a^2*b^3)*c)*d*f^2 + (2*B*a^4*b^2 - A*a^3*b^3 - 4*(2*B*a^5 - A*a^4*b)*c)*f^3)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))*sqrt(f*x^2 + d)*sqrt(((B^2*b^2 + 2*A^2*c^2 - 2*(B^2*a + A*B*b)*c)*d + (2*B^2*a^2 - 2*A*B*a*b + A^2*b^2 - 2*A^2*a*c)*f - ((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/((b^2*c^2 - 4*a*c^3)*d^2 + (b^4 - 6*a*b^2*c + 8*a^2*c^2)*d*f + (a^2*b^2 - 4*a^3*c)*f^2)) - 4*((B^4*a^2*b - A*B^3*a*b^2 - 2*A^3*B*a*c^2 - (2*A*B^3*a^2 - 3*A^2*B^2*a*b)*c)*d*f + (2*A*B^3*a^3 - 3*A^2*B^2*a^2*b + A^3*B*a*b^2 + (2*A^3*B*a^2 - A^4*a*b)*c)*f^2)*x - 2*((4*A^2*a*c^4 + (4*B^2*a^2 - 4*A*B*a*b - A^2*b^2)*c^3 - (B^2*a*b^2 - A*B*b^3)*c^2)*d^3 - (B^2*a*b^4 - A*B*b^5 + 8*A^2*a^2*c^3 + 2*(4*B^2*a^3 - 4*A*B*a^2*b - 3*A^2*a*b^2)*c^2 - (6*B^2*a^2*b^2 - 6*A*B*a*b^3 - A^2*b^4)*c)*d^2*f - (B^2*a^3*b^2 - A*B*a^2*b^3 - 4*A^2*a^3*c^2 - (4*B^2*a^4 - 4*A*B*a^3*b - A^2*a^2*b^2)*c)*d*f^2)*sqrt(((B^4*b^2 - 4*A*B^3*b*c + 4*A^2*B^2*c^2)*d^2 + 2*(2*A*B^3*a*b - A^2*B^2*b^2 - 2*(2*A^2*B^2*a - A^3*B*b)*c)*d*f + (4*A^2*B^2*a^2 - 4*A^3*B*a*b + A^4*b^2)*f^2)/((b^2*c^4 - 4*a*c^5)*d^4 + 2*(b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^3*f + (b^6 - 8*a*b^4*c + 22*a^2*b^2*c^2 - 24*a^3*c^3)*d^2*f^2 + 2*(a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*f^3 + (a^4*b^2 - 4*a^5*c)*f^4)))/x)","B",0
24,1,1515,0,0.541619," ","integrate((B*x+A)/(c*x^2+a)/(f*x^2+d)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{B^{2} a - A^{2} c + 2 \, {\left(a c^{2} d - a^{2} c f\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}}{a c^{2} d - a^{2} c f}} \log\left(\frac{{\left(A B^{3} a + A^{3} B c\right)} f x + {\left(A^{2} B c^{2} d - A^{2} B a c f + {\left(B a c^{3} d^{2} - 2 \, B a^{2} c^{2} d f + B a^{3} c f^{2}\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}\right)} \sqrt{f x^{2} + d} \sqrt{\frac{B^{2} a - A^{2} c + 2 \, {\left(a c^{2} d - a^{2} c f\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}}{a c^{2} d - a^{2} c f}} + \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} {\left({\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{2} - {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d f\right)}}{x}\right) + \frac{1}{4} \, \sqrt{\frac{B^{2} a - A^{2} c + 2 \, {\left(a c^{2} d - a^{2} c f\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}}{a c^{2} d - a^{2} c f}} \log\left(\frac{{\left(A B^{3} a + A^{3} B c\right)} f x - {\left(A^{2} B c^{2} d - A^{2} B a c f + {\left(B a c^{3} d^{2} - 2 \, B a^{2} c^{2} d f + B a^{3} c f^{2}\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}\right)} \sqrt{f x^{2} + d} \sqrt{\frac{B^{2} a - A^{2} c + 2 \, {\left(a c^{2} d - a^{2} c f\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}}{a c^{2} d - a^{2} c f}} + \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} {\left({\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{2} - {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d f\right)}}{x}\right) - \frac{1}{4} \, \sqrt{\frac{B^{2} a - A^{2} c - 2 \, {\left(a c^{2} d - a^{2} c f\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}}{a c^{2} d - a^{2} c f}} \log\left(\frac{{\left(A B^{3} a + A^{3} B c\right)} f x + {\left(A^{2} B c^{2} d - A^{2} B a c f - {\left(B a c^{3} d^{2} - 2 \, B a^{2} c^{2} d f + B a^{3} c f^{2}\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}\right)} \sqrt{f x^{2} + d} \sqrt{\frac{B^{2} a - A^{2} c - 2 \, {\left(a c^{2} d - a^{2} c f\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}}{a c^{2} d - a^{2} c f}} - \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} {\left({\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{2} - {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d f\right)}}{x}\right) + \frac{1}{4} \, \sqrt{\frac{B^{2} a - A^{2} c - 2 \, {\left(a c^{2} d - a^{2} c f\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}}{a c^{2} d - a^{2} c f}} \log\left(\frac{{\left(A B^{3} a + A^{3} B c\right)} f x - {\left(A^{2} B c^{2} d - A^{2} B a c f - {\left(B a c^{3} d^{2} - 2 \, B a^{2} c^{2} d f + B a^{3} c f^{2}\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}\right)} \sqrt{f x^{2} + d} \sqrt{\frac{B^{2} a - A^{2} c - 2 \, {\left(a c^{2} d - a^{2} c f\right)} \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}}}{a c^{2} d - a^{2} c f}} - \sqrt{-\frac{A^{2} B^{2}}{a c^{3} d^{2} - 2 \, a^{2} c^{2} d f + a^{3} c f^{2}}} {\left({\left(B^{2} a c^{2} + A^{2} c^{3}\right)} d^{2} - {\left(B^{2} a^{2} c + A^{2} a c^{2}\right)} d f\right)}}{x}\right)"," ",0,"-1/4*sqrt((B^2*a - A^2*c + 2*(a*c^2*d - a^2*c*f)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))/(a*c^2*d - a^2*c*f))*log(((A*B^3*a + A^3*B*c)*f*x + (A^2*B*c^2*d - A^2*B*a*c*f + (B*a*c^3*d^2 - 2*B*a^2*c^2*d*f + B*a^3*c*f^2)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))*sqrt(f*x^2 + d)*sqrt((B^2*a - A^2*c + 2*(a*c^2*d - a^2*c*f)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))/(a*c^2*d - a^2*c*f)) + sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2))*((B^2*a*c^2 + A^2*c^3)*d^2 - (B^2*a^2*c + A^2*a*c^2)*d*f))/x) + 1/4*sqrt((B^2*a - A^2*c + 2*(a*c^2*d - a^2*c*f)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))/(a*c^2*d - a^2*c*f))*log(((A*B^3*a + A^3*B*c)*f*x - (A^2*B*c^2*d - A^2*B*a*c*f + (B*a*c^3*d^2 - 2*B*a^2*c^2*d*f + B*a^3*c*f^2)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))*sqrt(f*x^2 + d)*sqrt((B^2*a - A^2*c + 2*(a*c^2*d - a^2*c*f)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))/(a*c^2*d - a^2*c*f)) + sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2))*((B^2*a*c^2 + A^2*c^3)*d^2 - (B^2*a^2*c + A^2*a*c^2)*d*f))/x) - 1/4*sqrt((B^2*a - A^2*c - 2*(a*c^2*d - a^2*c*f)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))/(a*c^2*d - a^2*c*f))*log(((A*B^3*a + A^3*B*c)*f*x + (A^2*B*c^2*d - A^2*B*a*c*f - (B*a*c^3*d^2 - 2*B*a^2*c^2*d*f + B*a^3*c*f^2)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))*sqrt(f*x^2 + d)*sqrt((B^2*a - A^2*c - 2*(a*c^2*d - a^2*c*f)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))/(a*c^2*d - a^2*c*f)) - sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2))*((B^2*a*c^2 + A^2*c^3)*d^2 - (B^2*a^2*c + A^2*a*c^2)*d*f))/x) + 1/4*sqrt((B^2*a - A^2*c - 2*(a*c^2*d - a^2*c*f)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))/(a*c^2*d - a^2*c*f))*log(((A*B^3*a + A^3*B*c)*f*x - (A^2*B*c^2*d - A^2*B*a*c*f - (B*a*c^3*d^2 - 2*B*a^2*c^2*d*f + B*a^3*c*f^2)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))*sqrt(f*x^2 + d)*sqrt((B^2*a - A^2*c - 2*(a*c^2*d - a^2*c*f)*sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2)))/(a*c^2*d - a^2*c*f)) - sqrt(-A^2*B^2/(a*c^3*d^2 - 2*a^2*c^2*d*f + a^3*c*f^2))*((B^2*a*c^2 + A^2*c^3)*d^2 - (B^2*a^2*c + A^2*a*c^2)*d*f))/x)","B",0
25,1,322,0,0.444602," ","integrate((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(1/2),x, algorithm=""fricas"")","\frac{2}{5} \, \sqrt{5} \sqrt{5 \, \sqrt{5} \sqrt{2} - 13} \arctan\left(\frac{\sqrt{2} {\left(2 \, \sqrt{5} x - \sqrt{2} x\right)} \sqrt{5 \, \sqrt{5} \sqrt{2} - 13} \sqrt{\frac{\sqrt{5} \sqrt{2} {\left(3 \, x^{2} + 2 \, x\right)} + 6 \, x^{2} - 2 \, {\left(\sqrt{5} \sqrt{2} x + 2 \, x + 2\right)} \sqrt{-2 \, x^{2} + 3 \, x + 1} + 10 \, x + 4}{x^{2}}} + 2 \, {\left(\sqrt{2} {\left(4 \, x - 1\right)} + \sqrt{5} {\left(x + 2\right)} - \sqrt{-2 \, x^{2} + 3 \, x + 1} {\left(2 \, \sqrt{5} - \sqrt{2}\right)}\right)} \sqrt{5 \, \sqrt{5} \sqrt{2} - 13}}{18 \, x}\right) - \frac{1}{10} \, \sqrt{5} \sqrt{5 \, \sqrt{5} \sqrt{2} + 13} \log\left(\frac{9 \, \sqrt{5} \sqrt{2} x + {\left(4 \, \sqrt{5} x - 7 \, \sqrt{2} x\right)} \sqrt{5 \, \sqrt{5} \sqrt{2} + 13} - 18 \, x + 18 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} - 18}{x}\right) + \frac{1}{10} \, \sqrt{5} \sqrt{5 \, \sqrt{5} \sqrt{2} + 13} \log\left(\frac{9 \, \sqrt{5} \sqrt{2} x - {\left(4 \, \sqrt{5} x - 7 \, \sqrt{2} x\right)} \sqrt{5 \, \sqrt{5} \sqrt{2} + 13} - 18 \, x + 18 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} - 18}{x}\right)"," ",0,"2/5*sqrt(5)*sqrt(5*sqrt(5)*sqrt(2) - 13)*arctan(1/18*(sqrt(2)*(2*sqrt(5)*x - sqrt(2)*x)*sqrt(5*sqrt(5)*sqrt(2) - 13)*sqrt((sqrt(5)*sqrt(2)*(3*x^2 + 2*x) + 6*x^2 - 2*(sqrt(5)*sqrt(2)*x + 2*x + 2)*sqrt(-2*x^2 + 3*x + 1) + 10*x + 4)/x^2) + 2*(sqrt(2)*(4*x - 1) + sqrt(5)*(x + 2) - sqrt(-2*x^2 + 3*x + 1)*(2*sqrt(5) - sqrt(2)))*sqrt(5*sqrt(5)*sqrt(2) - 13))/x) - 1/10*sqrt(5)*sqrt(5*sqrt(5)*sqrt(2) + 13)*log((9*sqrt(5)*sqrt(2)*x + (4*sqrt(5)*x - 7*sqrt(2)*x)*sqrt(5*sqrt(5)*sqrt(2) + 13) - 18*x + 18*sqrt(-2*x^2 + 3*x + 1) - 18)/x) + 1/10*sqrt(5)*sqrt(5*sqrt(5)*sqrt(2) + 13)*log((9*sqrt(5)*sqrt(2)*x - (4*sqrt(5)*x - 7*sqrt(2)*x)*sqrt(5*sqrt(5)*sqrt(2) + 13) - 18*x + 18*sqrt(-2*x^2 + 3*x + 1) - 18)/x)","B",0
26,1,344,0,0.441548," ","integrate((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(3/2),x, algorithm=""fricas"")","-\frac{612 \, \sqrt{5} {\left(2 \, x^{2} - 3 \, x - 1\right)} \sqrt{\sqrt{10} - 3} \arctan\left(\frac{\sqrt{10} \sqrt{5} \sqrt{2} x \sqrt{\sqrt{10} - 3} \sqrt{\frac{6 \, x^{2} + \sqrt{10} {\left(3 \, x^{2} + 2 \, x\right)} - 2 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} {\left(\sqrt{10} x + 2 \, x + 2\right)} + 10 \, x + 4}{x^{2}}} + 2 \, {\left(\sqrt{10} \sqrt{5} {\left(x + 1\right)} - \sqrt{10} \sqrt{5} \sqrt{-2 \, x^{2} + 3 \, x + 1} + 5 \, \sqrt{5} x\right)} \sqrt{\sqrt{10} - 3}}{10 \, x}\right) + 153 \, \sqrt{5} {\left(2 \, x^{2} - 3 \, x - 1\right)} \sqrt{\sqrt{10} + 3} \log\left(\frac{9 \, {\left(5 \, \sqrt{10} x + {\left(3 \, \sqrt{10} \sqrt{5} x - 10 \, \sqrt{5} x\right)} \sqrt{\sqrt{10} + 3} - 10 \, x + 10 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} - 10\right)}}{x}\right) - 153 \, \sqrt{5} {\left(2 \, x^{2} - 3 \, x - 1\right)} \sqrt{\sqrt{10} + 3} \log\left(\frac{9 \, {\left(5 \, \sqrt{10} x - {\left(3 \, \sqrt{10} \sqrt{5} x - 10 \, \sqrt{5} x\right)} \sqrt{\sqrt{10} + 3} - 10 \, x + 10 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} - 10\right)}}{x}\right) + 600 \, x^{2} - 20 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} {\left(14 \, x + 15\right)} - 900 \, x - 300}{170 \, {\left(2 \, x^{2} - 3 \, x - 1\right)}}"," ",0,"-1/170*(612*sqrt(5)*(2*x^2 - 3*x - 1)*sqrt(sqrt(10) - 3)*arctan(1/10*(sqrt(10)*sqrt(5)*sqrt(2)*x*sqrt(sqrt(10) - 3)*sqrt((6*x^2 + sqrt(10)*(3*x^2 + 2*x) - 2*sqrt(-2*x^2 + 3*x + 1)*(sqrt(10)*x + 2*x + 2) + 10*x + 4)/x^2) + 2*(sqrt(10)*sqrt(5)*(x + 1) - sqrt(10)*sqrt(5)*sqrt(-2*x^2 + 3*x + 1) + 5*sqrt(5)*x)*sqrt(sqrt(10) - 3))/x) + 153*sqrt(5)*(2*x^2 - 3*x - 1)*sqrt(sqrt(10) + 3)*log(9*(5*sqrt(10)*x + (3*sqrt(10)*sqrt(5)*x - 10*sqrt(5)*x)*sqrt(sqrt(10) + 3) - 10*x + 10*sqrt(-2*x^2 + 3*x + 1) - 10)/x) - 153*sqrt(5)*(2*x^2 - 3*x - 1)*sqrt(sqrt(10) + 3)*log(9*(5*sqrt(10)*x - (3*sqrt(10)*sqrt(5)*x - 10*sqrt(5)*x)*sqrt(sqrt(10) + 3) - 10*x + 10*sqrt(-2*x^2 + 3*x + 1) - 10)/x) + 600*x^2 - 20*sqrt(-2*x^2 + 3*x + 1)*(14*x + 15) - 900*x - 300)/(2*x^2 - 3*x - 1)","B",0
27,1,439,0,0.441982," ","integrate((2+x)/(-3*x^2+4*x+2)/(-2*x^2+3*x+1)^(5/2),x, algorithm=""fricas"")","-\frac{43680 \, x^{4} - 131040 \, x^{3} - 31212 \, \sqrt{5} {\left(4 \, x^{4} - 12 \, x^{3} + 5 \, x^{2} + 6 \, x + 1\right)} \sqrt{17 \, \sqrt{10} - 53} \arctan\left(\frac{\sqrt{2} {\left(\sqrt{10} \sqrt{5} x + 10 \, \sqrt{5} x\right)} \sqrt{17 \, \sqrt{10} - 53} \sqrt{\frac{6 \, x^{2} + \sqrt{10} {\left(3 \, x^{2} + 2 \, x\right)} - 2 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} {\left(\sqrt{10} x + 2 \, x + 2\right)} + 10 \, x + 4}{x^{2}}} + 2 \, {\left(\sqrt{10} \sqrt{5} {\left(6 \, x + 1\right)} - \sqrt{-2 \, x^{2} + 3 \, x + 1} {\left(\sqrt{10} \sqrt{5} + 10 \, \sqrt{5}\right)} + 5 \, \sqrt{5} {\left(3 \, x + 2\right)}\right)} \sqrt{17 \, \sqrt{10} - 53}}{90 \, x}\right) - 7803 \, \sqrt{5} {\left(4 \, x^{4} - 12 \, x^{3} + 5 \, x^{2} + 6 \, x + 1\right)} \sqrt{17 \, \sqrt{10} + 53} \log\left(\frac{9 \, {\left(45 \, \sqrt{10} x + {\left(13 \, \sqrt{10} \sqrt{5} x - 40 \, \sqrt{5} x\right)} \sqrt{17 \, \sqrt{10} + 53} - 90 \, x + 90 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} - 90\right)}}{x}\right) + 7803 \, \sqrt{5} {\left(4 \, x^{4} - 12 \, x^{3} + 5 \, x^{2} + 6 \, x + 1\right)} \sqrt{17 \, \sqrt{10} + 53} \log\left(\frac{9 \, {\left(45 \, \sqrt{10} x - {\left(13 \, \sqrt{10} \sqrt{5} x - 40 \, \sqrt{5} x\right)} \sqrt{17 \, \sqrt{10} + 53} - 90 \, x + 90 \, \sqrt{-2 \, x^{2} + 3 \, x + 1} - 90\right)}}{x}\right) + 54600 \, x^{2} - 20 \, {\left(9628 \, x^{3} - 13860 \, x^{2} - 5925 \, x - 546\right)} \sqrt{-2 \, x^{2} + 3 \, x + 1} + 65520 \, x + 10920}{8670 \, {\left(4 \, x^{4} - 12 \, x^{3} + 5 \, x^{2} + 6 \, x + 1\right)}}"," ",0,"-1/8670*(43680*x^4 - 131040*x^3 - 31212*sqrt(5)*(4*x^4 - 12*x^3 + 5*x^2 + 6*x + 1)*sqrt(17*sqrt(10) - 53)*arctan(1/90*(sqrt(2)*(sqrt(10)*sqrt(5)*x + 10*sqrt(5)*x)*sqrt(17*sqrt(10) - 53)*sqrt((6*x^2 + sqrt(10)*(3*x^2 + 2*x) - 2*sqrt(-2*x^2 + 3*x + 1)*(sqrt(10)*x + 2*x + 2) + 10*x + 4)/x^2) + 2*(sqrt(10)*sqrt(5)*(6*x + 1) - sqrt(-2*x^2 + 3*x + 1)*(sqrt(10)*sqrt(5) + 10*sqrt(5)) + 5*sqrt(5)*(3*x + 2))*sqrt(17*sqrt(10) - 53))/x) - 7803*sqrt(5)*(4*x^4 - 12*x^3 + 5*x^2 + 6*x + 1)*sqrt(17*sqrt(10) + 53)*log(9*(45*sqrt(10)*x + (13*sqrt(10)*sqrt(5)*x - 40*sqrt(5)*x)*sqrt(17*sqrt(10) + 53) - 90*x + 90*sqrt(-2*x^2 + 3*x + 1) - 90)/x) + 7803*sqrt(5)*(4*x^4 - 12*x^3 + 5*x^2 + 6*x + 1)*sqrt(17*sqrt(10) + 53)*log(9*(45*sqrt(10)*x - (13*sqrt(10)*sqrt(5)*x - 40*sqrt(5)*x)*sqrt(17*sqrt(10) + 53) - 90*x + 90*sqrt(-2*x^2 + 3*x + 1) - 90)/x) + 54600*x^2 - 20*(9628*x^3 - 13860*x^2 - 5925*x - 546)*sqrt(-2*x^2 + 3*x + 1) + 65520*x + 10920)/(4*x^4 - 12*x^3 + 5*x^2 + 6*x + 1)","B",0
28,1,245,0,0.431693," ","integrate((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(1/2),x, algorithm=""fricas"")","\frac{1}{10} \, \sqrt{7 \, \sqrt{10} + 25} \log\left(-\frac{3 \, \sqrt{10} x + {\left(\sqrt{10} x - 4 \, x\right)} \sqrt{7 \, \sqrt{10} + 25} + 6 \, x - 6 \, \sqrt{2 \, x^{2} + 3 \, x + 1} + 6}{x}\right) - \frac{1}{10} \, \sqrt{7 \, \sqrt{10} + 25} \log\left(-\frac{3 \, \sqrt{10} x - {\left(\sqrt{10} x - 4 \, x\right)} \sqrt{7 \, \sqrt{10} + 25} + 6 \, x - 6 \, \sqrt{2 \, x^{2} + 3 \, x + 1} + 6}{x}\right) + \frac{1}{10} \, \sqrt{-7 \, \sqrt{10} + 25} \log\left(\frac{3 \, \sqrt{10} x + {\left(\sqrt{10} x + 4 \, x\right)} \sqrt{-7 \, \sqrt{10} + 25} - 6 \, x + 6 \, \sqrt{2 \, x^{2} + 3 \, x + 1} - 6}{x}\right) - \frac{1}{10} \, \sqrt{-7 \, \sqrt{10} + 25} \log\left(\frac{3 \, \sqrt{10} x - {\left(\sqrt{10} x + 4 \, x\right)} \sqrt{-7 \, \sqrt{10} + 25} - 6 \, x + 6 \, \sqrt{2 \, x^{2} + 3 \, x + 1} - 6}{x}\right)"," ",0,"1/10*sqrt(7*sqrt(10) + 25)*log(-(3*sqrt(10)*x + (sqrt(10)*x - 4*x)*sqrt(7*sqrt(10) + 25) + 6*x - 6*sqrt(2*x^2 + 3*x + 1) + 6)/x) - 1/10*sqrt(7*sqrt(10) + 25)*log(-(3*sqrt(10)*x - (sqrt(10)*x - 4*x)*sqrt(7*sqrt(10) + 25) + 6*x - 6*sqrt(2*x^2 + 3*x + 1) + 6)/x) + 1/10*sqrt(-7*sqrt(10) + 25)*log((3*sqrt(10)*x + (sqrt(10)*x + 4*x)*sqrt(-7*sqrt(10) + 25) - 6*x + 6*sqrt(2*x^2 + 3*x + 1) - 6)/x) - 1/10*sqrt(-7*sqrt(10) + 25)*log((3*sqrt(10)*x - (sqrt(10)*x + 4*x)*sqrt(-7*sqrt(10) + 25) - 6*x + 6*sqrt(2*x^2 + 3*x + 1) - 6)/x)","B",0
29,1,365,0,0.446492," ","integrate((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{5} {\left(2 \, x^{2} + 3 \, x + 1\right)} \sqrt{1959 \, \sqrt{10} + 6195} \log\left(-\frac{45 \, \sqrt{10} x + {\left(41 \, \sqrt{10} \sqrt{5} x - 130 \, \sqrt{5} x\right)} \sqrt{1959 \, \sqrt{10} + 6195} + 90 \, x - 90 \, \sqrt{2 \, x^{2} + 3 \, x + 1} + 90}{x}\right) - \sqrt{5} {\left(2 \, x^{2} + 3 \, x + 1\right)} \sqrt{1959 \, \sqrt{10} + 6195} \log\left(-\frac{45 \, \sqrt{10} x - {\left(41 \, \sqrt{10} \sqrt{5} x - 130 \, \sqrt{5} x\right)} \sqrt{1959 \, \sqrt{10} + 6195} + 90 \, x - 90 \, \sqrt{2 \, x^{2} + 3 \, x + 1} + 90}{x}\right) + \sqrt{5} {\left(2 \, x^{2} + 3 \, x + 1\right)} \sqrt{-1959 \, \sqrt{10} + 6195} \log\left(\frac{45 \, \sqrt{10} x + {\left(41 \, \sqrt{10} \sqrt{5} x + 130 \, \sqrt{5} x\right)} \sqrt{-1959 \, \sqrt{10} + 6195} - 90 \, x + 90 \, \sqrt{2 \, x^{2} + 3 \, x + 1} - 90}{x}\right) - \sqrt{5} {\left(2 \, x^{2} + 3 \, x + 1\right)} \sqrt{-1959 \, \sqrt{10} + 6195} \log\left(\frac{45 \, \sqrt{10} x - {\left(41 \, \sqrt{10} \sqrt{5} x + 130 \, \sqrt{5} x\right)} \sqrt{-1959 \, \sqrt{10} + 6195} - 90 \, x + 90 \, \sqrt{2 \, x^{2} + 3 \, x + 1} - 90}{x}\right) + 840 \, x^{2} + 20 \, \sqrt{2 \, x^{2} + 3 \, x + 1} {\left(22 \, x + 21\right)} + 1260 \, x + 420}{50 \, {\left(2 \, x^{2} + 3 \, x + 1\right)}}"," ",0,"1/50*(sqrt(5)*(2*x^2 + 3*x + 1)*sqrt(1959*sqrt(10) + 6195)*log(-(45*sqrt(10)*x + (41*sqrt(10)*sqrt(5)*x - 130*sqrt(5)*x)*sqrt(1959*sqrt(10) + 6195) + 90*x - 90*sqrt(2*x^2 + 3*x + 1) + 90)/x) - sqrt(5)*(2*x^2 + 3*x + 1)*sqrt(1959*sqrt(10) + 6195)*log(-(45*sqrt(10)*x - (41*sqrt(10)*sqrt(5)*x - 130*sqrt(5)*x)*sqrt(1959*sqrt(10) + 6195) + 90*x - 90*sqrt(2*x^2 + 3*x + 1) + 90)/x) + sqrt(5)*(2*x^2 + 3*x + 1)*sqrt(-1959*sqrt(10) + 6195)*log((45*sqrt(10)*x + (41*sqrt(10)*sqrt(5)*x + 130*sqrt(5)*x)*sqrt(-1959*sqrt(10) + 6195) - 90*x + 90*sqrt(2*x^2 + 3*x + 1) - 90)/x) - sqrt(5)*(2*x^2 + 3*x + 1)*sqrt(-1959*sqrt(10) + 6195)*log((45*sqrt(10)*x - (41*sqrt(10)*sqrt(5)*x + 130*sqrt(5)*x)*sqrt(-1959*sqrt(10) + 6195) - 90*x + 90*sqrt(2*x^2 + 3*x + 1) - 90)/x) + 840*x^2 + 20*sqrt(2*x^2 + 3*x + 1)*(22*x + 21) + 1260*x + 420)/(2*x^2 + 3*x + 1)","B",0
30,1,435,0,0.433371," ","integrate((2+x)/(-3*x^2+4*x+2)/(2*x^2+3*x+1)^(5/2),x, algorithm=""fricas"")","\frac{23520 \, x^{4} + 70560 \, x^{3} + \sqrt{3} {\left(4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right)} \sqrt{1544809 \, \sqrt{10} + 4885115} \log\left(-\frac{243 \, \sqrt{10} x + {\left(893 \, \sqrt{10} \sqrt{3} x - 2824 \, \sqrt{3} x\right)} \sqrt{1544809 \, \sqrt{10} + 4885115} + 486 \, x - 486 \, \sqrt{2 \, x^{2} + 3 \, x + 1} + 486}{x}\right) - \sqrt{3} {\left(4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right)} \sqrt{1544809 \, \sqrt{10} + 4885115} \log\left(-\frac{243 \, \sqrt{10} x - {\left(893 \, \sqrt{10} \sqrt{3} x - 2824 \, \sqrt{3} x\right)} \sqrt{1544809 \, \sqrt{10} + 4885115} + 486 \, x - 486 \, \sqrt{2 \, x^{2} + 3 \, x + 1} + 486}{x}\right) + \sqrt{3} {\left(4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right)} \sqrt{-1544809 \, \sqrt{10} + 4885115} \log\left(\frac{243 \, \sqrt{10} x + {\left(893 \, \sqrt{10} \sqrt{3} x + 2824 \, \sqrt{3} x\right)} \sqrt{-1544809 \, \sqrt{10} + 4885115} - 486 \, x + 486 \, \sqrt{2 \, x^{2} + 3 \, x + 1} - 486}{x}\right) - \sqrt{3} {\left(4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right)} \sqrt{-1544809 \, \sqrt{10} + 4885115} \log\left(\frac{243 \, \sqrt{10} x - {\left(893 \, \sqrt{10} \sqrt{3} x + 2824 \, \sqrt{3} x\right)} \sqrt{-1544809 \, \sqrt{10} + 4885115} - 486 \, x + 486 \, \sqrt{2 \, x^{2} + 3 \, x + 1} - 486}{x}\right) + 76440 \, x^{2} + 20 \, {\left(460 \, x^{3} + 1236 \, x^{2} + 1071 \, x + 294\right)} \sqrt{2 \, x^{2} + 3 \, x + 1} + 35280 \, x + 5880}{150 \, {\left(4 \, x^{4} + 12 \, x^{3} + 13 \, x^{2} + 6 \, x + 1\right)}}"," ",0,"1/150*(23520*x^4 + 70560*x^3 + sqrt(3)*(4*x^4 + 12*x^3 + 13*x^2 + 6*x + 1)*sqrt(1544809*sqrt(10) + 4885115)*log(-(243*sqrt(10)*x + (893*sqrt(10)*sqrt(3)*x - 2824*sqrt(3)*x)*sqrt(1544809*sqrt(10) + 4885115) + 486*x - 486*sqrt(2*x^2 + 3*x + 1) + 486)/x) - sqrt(3)*(4*x^4 + 12*x^3 + 13*x^2 + 6*x + 1)*sqrt(1544809*sqrt(10) + 4885115)*log(-(243*sqrt(10)*x - (893*sqrt(10)*sqrt(3)*x - 2824*sqrt(3)*x)*sqrt(1544809*sqrt(10) + 4885115) + 486*x - 486*sqrt(2*x^2 + 3*x + 1) + 486)/x) + sqrt(3)*(4*x^4 + 12*x^3 + 13*x^2 + 6*x + 1)*sqrt(-1544809*sqrt(10) + 4885115)*log((243*sqrt(10)*x + (893*sqrt(10)*sqrt(3)*x + 2824*sqrt(3)*x)*sqrt(-1544809*sqrt(10) + 4885115) - 486*x + 486*sqrt(2*x^2 + 3*x + 1) - 486)/x) - sqrt(3)*(4*x^4 + 12*x^3 + 13*x^2 + 6*x + 1)*sqrt(-1544809*sqrt(10) + 4885115)*log((243*sqrt(10)*x - (893*sqrt(10)*sqrt(3)*x + 2824*sqrt(3)*x)*sqrt(-1544809*sqrt(10) + 4885115) - 486*x + 486*sqrt(2*x^2 + 3*x + 1) - 486)/x) + 76440*x^2 + 20*(460*x^3 + 1236*x^2 + 1071*x + 294)*sqrt(2*x^2 + 3*x + 1) + 35280*x + 5880)/(4*x^4 + 12*x^3 + 13*x^2 + 6*x + 1)","B",0
31,1,49,0,0.410435," ","integrate((1+x)/(x^2+2*x+4)/(x^2+2*x+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{2} + 2 \, x + 5} {\left(x + 2\right)} + 3 \, x + 6\right) - \frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{2} + 2 \, x + 5} x + x + 4\right)"," ",0,"1/2*log(x^2 - sqrt(x^2 + 2*x + 5)*(x + 2) + 3*x + 6) - 1/2*log(x^2 - sqrt(x^2 + 2*x + 5)*x + x + 4)","B",0
32,1,106,0,0.409602," ","integrate((4+x)/(x^2+2*x+4)/(x^2+2*x+5)^(1/2),x, algorithm=""fricas"")","-\sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} {\left(x + 2\right)} + \frac{1}{3} \, \sqrt{3} \sqrt{x^{2} + 2 \, x + 5}\right) + \sqrt{3} \arctan\left(-\frac{1}{3} \, \sqrt{3} x + \frac{1}{3} \, \sqrt{3} \sqrt{x^{2} + 2 \, x + 5}\right) + \frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{2} + 2 \, x + 5} {\left(x + 2\right)} + 3 \, x + 6\right) - \frac{1}{2} \, \log\left(x^{2} - \sqrt{x^{2} + 2 \, x + 5} x + x + 4\right)"," ",0,"-sqrt(3)*arctan(-1/3*sqrt(3)*(x + 2) + 1/3*sqrt(3)*sqrt(x^2 + 2*x + 5)) + sqrt(3)*arctan(-1/3*sqrt(3)*x + 1/3*sqrt(3)*sqrt(x^2 + 2*x + 5)) + 1/2*log(x^2 - sqrt(x^2 + 2*x + 5)*(x + 2) + 3*x + 6) - 1/2*log(x^2 - sqrt(x^2 + 2*x + 5)*x + x + 4)","B",0
33,1,34,0,0.415533," ","integrate((1+2*x)/(x^2+x+3)/(x^2+x+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(\frac{x^{2} - 2 \, \sqrt{2} \sqrt{x^{2} + x + 5} + x + 7}{x^{2} + x + 3}\right)"," ",0,"1/2*sqrt(2)*log((x^2 - 2*sqrt(2)*sqrt(x^2 + x + 5) + x + 7)/(x^2 + x + 3))","A",0
34,1,307,0,0.453651," ","integrate(x/(x^2+x+3)/(x^2+x+5)^(1/2),x, algorithm=""fricas"")","-\frac{1}{33} \, \sqrt{11} \sqrt{6} \sqrt{3} \arctan\left(\frac{2}{33} \, \sqrt{11} \sqrt{3} \sqrt{\sqrt{6} \sqrt{3} {\left(2 \, x + 1\right)} + 6 \, x^{2} - \sqrt{x^{2} + x + 5} {\left(2 \, \sqrt{6} \sqrt{3} + 6 \, x + 3\right)} + 6 \, x + 30} + \frac{1}{33} \, \sqrt{11} {\left(2 \, \sqrt{6} \sqrt{3} + 6 \, x + 3\right)} - \frac{2}{11} \, \sqrt{11} \sqrt{x^{2} + x + 5}\right) + \frac{1}{33} \, \sqrt{11} \sqrt{6} \sqrt{3} \arctan\left(-\frac{1}{33} \, \sqrt{11} {\left(2 \, \sqrt{6} \sqrt{3} - 6 \, x - 3\right)} + \frac{1}{33} \, \sqrt{11} \sqrt{-12 \, \sqrt{6} \sqrt{3} {\left(2 \, x + 1\right)} + 72 \, x^{2} + 12 \, \sqrt{x^{2} + x + 5} {\left(2 \, \sqrt{6} \sqrt{3} - 6 \, x - 3\right)} + 72 \, x + 360} - \frac{2}{11} \, \sqrt{11} \sqrt{x^{2} + x + 5}\right) + \frac{1}{12} \, \sqrt{6} \sqrt{3} \log\left(12 \, \sqrt{6} \sqrt{3} {\left(2 \, x + 1\right)} + 72 \, x^{2} - 12 \, \sqrt{x^{2} + x + 5} {\left(2 \, \sqrt{6} \sqrt{3} + 6 \, x + 3\right)} + 72 \, x + 360\right) - \frac{1}{12} \, \sqrt{6} \sqrt{3} \log\left(-12 \, \sqrt{6} \sqrt{3} {\left(2 \, x + 1\right)} + 72 \, x^{2} + 12 \, \sqrt{x^{2} + x + 5} {\left(2 \, \sqrt{6} \sqrt{3} - 6 \, x - 3\right)} + 72 \, x + 360\right)"," ",0,"-1/33*sqrt(11)*sqrt(6)*sqrt(3)*arctan(2/33*sqrt(11)*sqrt(3)*sqrt(sqrt(6)*sqrt(3)*(2*x + 1) + 6*x^2 - sqrt(x^2 + x + 5)*(2*sqrt(6)*sqrt(3) + 6*x + 3) + 6*x + 30) + 1/33*sqrt(11)*(2*sqrt(6)*sqrt(3) + 6*x + 3) - 2/11*sqrt(11)*sqrt(x^2 + x + 5)) + 1/33*sqrt(11)*sqrt(6)*sqrt(3)*arctan(-1/33*sqrt(11)*(2*sqrt(6)*sqrt(3) - 6*x - 3) + 1/33*sqrt(11)*sqrt(-12*sqrt(6)*sqrt(3)*(2*x + 1) + 72*x^2 + 12*sqrt(x^2 + x + 5)*(2*sqrt(6)*sqrt(3) - 6*x - 3) + 72*x + 360) - 2/11*sqrt(11)*sqrt(x^2 + x + 5)) + 1/12*sqrt(6)*sqrt(3)*log(12*sqrt(6)*sqrt(3)*(2*x + 1) + 72*x^2 - 12*sqrt(x^2 + x + 5)*(2*sqrt(6)*sqrt(3) + 6*x + 3) + 72*x + 360) - 1/12*sqrt(6)*sqrt(3)*log(-12*sqrt(6)*sqrt(3)*(2*x + 1) + 72*x^2 + 12*sqrt(x^2 + x + 5)*(2*sqrt(6)*sqrt(3) - 6*x - 3) + 72*x + 360)","B",0
35,-1,0,0,0.000000," ","integrate((B*x+A)/(b*f*x^2+b*e*x+a*e)^2/(f*x^2+e*x+d)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
36,1,85,0,0.630442," ","integrate((h*x+g)*(c*x^2+b*x+a)^(1/2)/(c*d*x^2+b*d*x+a*d)^2,x, algorithm=""fricas"")","-\frac{2 \, \sqrt{c x^{2} + b x + a} {\left(b g - 2 \, a h + {\left(2 \, c g - b h\right)} x\right)}}{{\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} x^{2} + {\left(b^{3} - 4 \, a b c\right)} d^{2} x + {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2}}"," ",0,"-2*sqrt(c*x^2 + b*x + a)*(b*g - 2*a*h + (2*c*g - b*h)*x)/((b^2*c - 4*a*c^2)*d^2*x^2 + (b^3 - 4*a*b*c)*d^2*x + (a*b^2 - 4*a^2*c)*d^2)","A",0
37,1,56,0,0.423459," ","integrate((3+2*x)/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) + \frac{1}{4} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right)"," ",0,"-1/4*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) + 1/4*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2)","B",0
38,1,132,0,0.429012," ","integrate((3+4*x)/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} x + 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} x - 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - \frac{1}{4} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) + \frac{1}{4} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*(sqrt(2)*x + 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) + 1/2*sqrt(2)*arctan(-1/2*(sqrt(2)*x - 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 1/4*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) + 1/4*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2)","A",0
39,0,0,0,50.452813," ","integrate((h*x+g)*(c*x^2+b*x+a)^(1/2)/(c*d*x^2+b*d*x+a*d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c d x^{2} + b d x + a d} \sqrt{c x^{2} + b x + a} {\left(h x + g\right)}}{c^{2} d^{2} x^{4} + 2 \, b c d^{2} x^{3} + 2 \, a b d^{2} x + {\left(b^{2} + 2 \, a c\right)} d^{2} x^{2} + a^{2} d^{2}}, x\right)"," ",0,"integral(sqrt(c*d*x^2 + b*d*x + a*d)*sqrt(c*x^2 + b*x + a)*(h*x + g)/(c^2*d^2*x^4 + 2*b*c*d^2*x^3 + 2*a*b*d^2*x + (b^2 + 2*a*c)*d^2*x^2 + a^2*d^2), x)","F",0
40,1,175,0,0.429443," ","integrate(x^2*((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{15 \, a c^{2} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(24 \, b d^{2} x^{4} + 30 \, a d^{2} x^{3} + 8 \, b c d x^{2} + 15 \, a c d x - 16 \, b c^{2}\right)} \sqrt{d x^{2} + c}}{240 \, d^{2}}, \frac{15 \, a c^{2} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(24 \, b d^{2} x^{4} + 30 \, a d^{2} x^{3} + 8 \, b c d x^{2} + 15 \, a c d x - 16 \, b c^{2}\right)} \sqrt{d x^{2} + c}}{120 \, d^{2}}\right]"," ",0,"[1/240*(15*a*c^2*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(24*b*d^2*x^4 + 30*a*d^2*x^3 + 8*b*c*d*x^2 + 15*a*c*d*x - 16*b*c^2)*sqrt(d*x^2 + c))/d^2, 1/120*(15*a*c^2*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (24*b*d^2*x^4 + 30*a*d^2*x^3 + 8*b*c*d*x^2 + 15*a*c*d*x - 16*b*c^2)*sqrt(d*x^2 + c))/d^2]","A",0
41,1,157,0,0.429229," ","integrate(x*((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, b c^{2} \sqrt{d} \log\left(-2 \, d x^{2} + 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(6 \, b d^{2} x^{3} + 8 \, a d^{2} x^{2} + 3 \, b c d x + 8 \, a c d\right)} \sqrt{d x^{2} + c}}{48 \, d^{2}}, \frac{3 \, b c^{2} \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) + {\left(6 \, b d^{2} x^{3} + 8 \, a d^{2} x^{2} + 3 \, b c d x + 8 \, a c d\right)} \sqrt{d x^{2} + c}}{24 \, d^{2}}\right]"," ",0,"[1/48*(3*b*c^2*sqrt(d)*log(-2*d*x^2 + 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(6*b*d^2*x^3 + 8*a*d^2*x^2 + 3*b*c*d*x + 8*a*c*d)*sqrt(d*x^2 + c))/d^2, 1/24*(3*b*c^2*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) + (6*b*d^2*x^3 + 8*a*d^2*x^2 + 3*b*c*d*x + 8*a*c*d)*sqrt(d*x^2 + c))/d^2]","A",0
42,1,128,0,0.429783," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, a c \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(2 \, b d x^{2} + 3 \, a d x + 2 \, b c\right)} \sqrt{d x^{2} + c}}{12 \, d}, -\frac{3 \, a c \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - {\left(2 \, b d x^{2} + 3 \, a d x + 2 \, b c\right)} \sqrt{d x^{2} + c}}{6 \, d}\right]"," ",0,"[1/12*(3*a*c*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(2*b*d*x^2 + 3*a*d*x + 2*b*c)*sqrt(d*x^2 + c))/d, -1/6*(3*a*c*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - (2*b*d*x^2 + 3*a*d*x + 2*b*c)*sqrt(d*x^2 + c))/d]","A",0
43,1,341,0,0.445487," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{b c \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, a \sqrt{c} d \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(b d x + 2 \, a d\right)} \sqrt{d x^{2} + c}}{4 \, d}, -\frac{b c \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - a \sqrt{c} d \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - {\left(b d x + 2 \, a d\right)} \sqrt{d x^{2} + c}}{2 \, d}, \frac{4 \, a \sqrt{-c} d \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + b c \sqrt{d} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, {\left(b d x + 2 \, a d\right)} \sqrt{d x^{2} + c}}{4 \, d}, -\frac{b c \sqrt{-d} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - 2 \, a \sqrt{-c} d \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - {\left(b d x + 2 \, a d\right)} \sqrt{d x^{2} + c}}{2 \, d}\right]"," ",0,"[1/4*(b*c*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*a*sqrt(c)*d*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(b*d*x + 2*a*d)*sqrt(d*x^2 + c))/d, -1/2*(b*c*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - a*sqrt(c)*d*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - (b*d*x + 2*a*d)*sqrt(d*x^2 + c))/d, 1/4*(4*a*sqrt(-c)*d*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + b*c*sqrt(d)*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*(b*d*x + 2*a*d)*sqrt(d*x^2 + c))/d, -1/2*(b*c*sqrt(-d)*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - 2*a*sqrt(-c)*d*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - (b*d*x + 2*a*d)*sqrt(d*x^2 + c))/d]","A",0
44,1,333,0,0.444361," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{a \sqrt{d} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + b \sqrt{c} x \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, \sqrt{d x^{2} + c} {\left(b x - a\right)}}{2 \, x}, -\frac{2 \, a \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - b \sqrt{c} x \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, \sqrt{d x^{2} + c} {\left(b x - a\right)}}{2 \, x}, \frac{2 \, b \sqrt{-c} x \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + a \sqrt{d} x \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + 2 \, \sqrt{d x^{2} + c} {\left(b x - a\right)}}{2 \, x}, -\frac{a \sqrt{-d} x \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - b \sqrt{-c} x \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) - \sqrt{d x^{2} + c} {\left(b x - a\right)}}{x}\right]"," ",0,"[1/2*(a*sqrt(d)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + b*sqrt(c)*x*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*sqrt(d*x^2 + c)*(b*x - a))/x, -1/2*(2*a*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - b*sqrt(c)*x*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*sqrt(d*x^2 + c)*(b*x - a))/x, 1/2*(2*b*sqrt(-c)*x*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + a*sqrt(d)*x*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + 2*sqrt(d*x^2 + c)*(b*x - a))/x, -(a*sqrt(-d)*x*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - b*sqrt(-c)*x*arctan(sqrt(-c)/sqrt(d*x^2 + c)) - sqrt(d*x^2 + c)*(b*x - a))/x]","A",0
45,1,377,0,0.439839," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{2 \, b c \sqrt{d} x^{2} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) + a \sqrt{c} d x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) - 2 \, {\left(2 \, b c x + a c\right)} \sqrt{d x^{2} + c}}{4 \, c x^{2}}, -\frac{4 \, b c \sqrt{-d} x^{2} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - a \sqrt{c} d x^{2} \log\left(-\frac{d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{c} + 2 \, c}{x^{2}}\right) + 2 \, {\left(2 \, b c x + a c\right)} \sqrt{d x^{2} + c}}{4 \, c x^{2}}, \frac{a \sqrt{-c} d x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + b c \sqrt{d} x^{2} \log\left(-2 \, d x^{2} - 2 \, \sqrt{d x^{2} + c} \sqrt{d} x - c\right) - {\left(2 \, b c x + a c\right)} \sqrt{d x^{2} + c}}{2 \, c x^{2}}, -\frac{2 \, b c \sqrt{-d} x^{2} \arctan\left(\frac{\sqrt{-d} x}{\sqrt{d x^{2} + c}}\right) - a \sqrt{-c} d x^{2} \arctan\left(\frac{\sqrt{-c}}{\sqrt{d x^{2} + c}}\right) + {\left(2 \, b c x + a c\right)} \sqrt{d x^{2} + c}}{2 \, c x^{2}}\right]"," ",0,"[1/4*(2*b*c*sqrt(d)*x^2*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) + a*sqrt(c)*d*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) - 2*(2*b*c*x + a*c)*sqrt(d*x^2 + c))/(c*x^2), -1/4*(4*b*c*sqrt(-d)*x^2*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - a*sqrt(c)*d*x^2*log(-(d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(c) + 2*c)/x^2) + 2*(2*b*c*x + a*c)*sqrt(d*x^2 + c))/(c*x^2), 1/2*(a*sqrt(-c)*d*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + b*c*sqrt(d)*x^2*log(-2*d*x^2 - 2*sqrt(d*x^2 + c)*sqrt(d)*x - c) - (2*b*c*x + a*c)*sqrt(d*x^2 + c))/(c*x^2), -1/2*(2*b*c*sqrt(-d)*x^2*arctan(sqrt(-d)*x/sqrt(d*x^2 + c)) - a*sqrt(-c)*d*x^2*arctan(sqrt(-c)/sqrt(d*x^2 + c)) + (2*b*c*x + a*c)*sqrt(d*x^2 + c))/(c*x^2)]","A",0
46,1,517,0,0.469155," ","integrate(x^2*((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(32 \, a c^{2} d^{3} - 48 \, b c^{2} d^{2} e - 48 \, a c d^{2} e^{2} + 40 \, b c d e^{3} + 10 \, a d e^{4} - 7 \, b e^{5}\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} - 256 \, b c^{2} d^{3} - 520 \, a c d^{3} e + 460 \, b c d^{2} e^{2} + 150 \, a d^{2} e^{3} - 105 \, b d e^{4} + 48 \, {\left(10 \, a d^{5} + b d^{4} e\right)} x^{3} + 8 \, {\left(16 \, b c d^{4} + 10 \, a d^{4} e - 7 \, b d^{3} e^{2}\right)} x^{2} + 2 \, {\left(120 \, a c d^{4} - 116 \, b c d^{3} e - 50 \, a d^{3} e^{2} + 35 \, b d^{2} e^{3}\right)} x\right)} \sqrt{d x^{2} + e x + c}}{7680 \, d^{5}}, \frac{15 \, {\left(32 \, a c^{2} d^{3} - 48 \, b c^{2} d^{2} e - 48 \, a c d^{2} e^{2} + 40 \, b c d e^{3} + 10 \, a d e^{4} - 7 \, b e^{5}\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} - 256 \, b c^{2} d^{3} - 520 \, a c d^{3} e + 460 \, b c d^{2} e^{2} + 150 \, a d^{2} e^{3} - 105 \, b d e^{4} + 48 \, {\left(10 \, a d^{5} + b d^{4} e\right)} x^{3} + 8 \, {\left(16 \, b c d^{4} + 10 \, a d^{4} e - 7 \, b d^{3} e^{2}\right)} x^{2} + 2 \, {\left(120 \, a c d^{4} - 116 \, b c d^{3} e - 50 \, a d^{3} e^{2} + 35 \, b d^{2} e^{3}\right)} x\right)} \sqrt{d x^{2} + e x + c}}{3840 \, d^{5}}\right]"," ",0,"[-1/7680*(15*(32*a*c^2*d^3 - 48*b*c^2*d^2*e - 48*a*c*d^2*e^2 + 40*b*c*d*e^3 + 10*a*d*e^4 - 7*b*e^5)*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 - 256*b*c^2*d^3 - 520*a*c*d^3*e + 460*b*c*d^2*e^2 + 150*a*d^2*e^3 - 105*b*d*e^4 + 48*(10*a*d^5 + b*d^4*e)*x^3 + 8*(16*b*c*d^4 + 10*a*d^4*e - 7*b*d^3*e^2)*x^2 + 2*(120*a*c*d^4 - 116*b*c*d^3*e - 50*a*d^3*e^2 + 35*b*d^2*e^3)*x)*sqrt(d*x^2 + e*x + c))/d^5, 1/3840*(15*(32*a*c^2*d^3 - 48*b*c^2*d^2*e - 48*a*c*d^2*e^2 + 40*b*c*d*e^3 + 10*a*d*e^4 - 7*b*e^5)*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 - 256*b*c^2*d^3 - 520*a*c*d^3*e + 460*b*c*d^2*e^2 + 150*a*d^2*e^3 - 105*b*d*e^4 + 48*(10*a*d^5 + b*d^4*e)*x^3 + 8*(16*b*c*d^4 + 10*a*d^4*e - 7*b*d^3*e^2)*x^2 + 2*(120*a*c*d^4 - 116*b*c*d^3*e - 50*a*d^3*e^2 + 35*b*d^2*e^3)*x)*sqrt(d*x^2 + e*x + c))/d^5]","A",0
47,1,391,0,0.451577," ","integrate(x*((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, b c^{2} d^{2} + 32 \, a c d^{2} e - 24 \, b c d e^{2} - 8 \, a d e^{3} + 5 \, b e^{4}\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} + 64 \, a c d^{3} - 52 \, b c d^{2} e - 24 \, a d^{2} e^{2} + 15 \, b d e^{3} + 8 \, {\left(8 \, a d^{4} + b d^{3} e\right)} x^{2} + 2 \, {\left(12 \, b c d^{3} + 8 \, a d^{3} e - 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} + 32 \, a c d^{2} e - 24 \, b c d e^{2} - 8 \, a d e^{3} + 5 \, b e^{4}\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} + 64 \, a c d^{3} - 52 \, b c d^{2} e - 24 \, a d^{2} e^{2} + 15 \, b d e^{3} + 8 \, {\left(8 \, a d^{4} + b d^{3} e\right)} x^{2} + 2 \, {\left(12 \, b c d^{3} + 8 \, a d^{3} e - 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 + 32*a*c*d^2*e - 24*b*c*d*e^2 - 8*a*d*e^3 + 5*b*e^4)*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 + 64*a*c*d^3 - 52*b*c*d^2*e - 24*a*d^2*e^2 + 15*b*d*e^3 + 8*(8*a*d^4 + b*d^3*e)*x^2 + 2*(12*b*c*d^3 + 8*a*d^3*e - 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 + 32*a*c*d^2*e - 24*b*c*d*e^2 - 8*a*d*e^3 + 5*b*e^4)*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 + 64*a*c*d^3 - 52*b*c*d^2*e - 24*a*d^2*e^2 + 15*b*d*e^3 + 8*(8*a*d^4 + b*d^3*e)*x^2 + 2*(12*b*c*d^3 + 8*a*d^3*e - 5*b*d^2*e^2)*x)*sqrt(d*x^2 + e*x + c))/d^4]","A",0
48,1,287,0,0.452512," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(8 \, a c d^{2} - 4 \, b c d e - 2 \, a d e^{2} + b e^{3}\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} + 8 \, b c d^{2} + 6 \, a d^{2} e - 3 \, b d e^{2} + 2 \, {\left(6 \, a d^{3} + b d^{2} e\right)} x\right)} \sqrt{d x^{2} + e x + c}}{96 \, d^{3}}, -\frac{3 \, {\left(8 \, a c d^{2} - 4 \, b c d e - 2 \, a d e^{2} + b e^{3}\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} + 8 \, b c d^{2} + 6 \, a d^{2} e - 3 \, b d e^{2} + 2 \, {\left(6 \, a d^{3} + b d^{2} e\right)} x\right)} \sqrt{d x^{2} + e x + c}}{48 \, d^{3}}\right]"," ",0,"[1/96*(3*(8*a*c*d^2 - 4*b*c*d*e - 2*a*d*e^2 + b*e^3)*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 + 8*b*c*d^2 + 6*a*d^2*e - 3*b*d*e^2 + 2*(6*a*d^3 + b*d^2*e)*x)*sqrt(d*x^2 + e*x + c))/d^3, -1/48*(3*(8*a*c*d^2 - 4*b*c*d*e - 2*a*d*e^2 + b*e^3)*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 + 8*b*c*d^2 + 6*a*d^2*e - 3*b*d*e^2 + 2*(6*a*d^3 + b*d^2*e)*x)*sqrt(d*x^2 + e*x + c))/d^3]","A",0
49,1,651,0,1.144934," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x,x, algorithm=""fricas"")","\left[\frac{8 \, a \sqrt{c} d^{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) - {\left(4 \, b c d + 4 \, a d e - b 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(2 \, b d^{2} x + 4 \, a d^{2} + b d e\right)} \sqrt{d x^{2} + e x + c}}{16 \, d^{2}}, \frac{4 \, a \sqrt{c} d^{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) - {\left(4 \, b c d + 4 \, a d e - b 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(2 \, b d^{2} x + 4 \, a d^{2} + b d e\right)} \sqrt{d x^{2} + e x + c}}{8 \, d^{2}}, \frac{16 \, a \sqrt{-c} d^{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) - {\left(4 \, b c d + 4 \, a d e - b 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(2 \, b d^{2} x + 4 \, a d^{2} + b d e\right)} \sqrt{d x^{2} + e x + c}}{16 \, d^{2}}, \frac{8 \, a \sqrt{-c} d^{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) - {\left(4 \, b c d + 4 \, a d e - b 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(2 \, b d^{2} x + 4 \, a d^{2} + b d e\right)} \sqrt{d x^{2} + e x + c}}{8 \, d^{2}}\right]"," ",0,"[1/16*(8*a*sqrt(c)*d^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*b*c*d + 4*a*d*e - b*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*(2*b*d^2*x + 4*a*d^2 + b*d*e)*sqrt(d*x^2 + e*x + c))/d^2, 1/8*(4*a*sqrt(c)*d^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*b*c*d + 4*a*d*e - b*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*(2*b*d^2*x + 4*a*d^2 + b*d*e)*sqrt(d*x^2 + e*x + c))/d^2, 1/16*(16*a*sqrt(-c)*d^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)) - (4*b*c*d + 4*a*d*e - b*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*(2*b*d^2*x + 4*a*d^2 + b*d*e)*sqrt(d*x^2 + e*x + c))/d^2, 1/8*(8*a*sqrt(-c)*d^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)) - (4*b*c*d + 4*a*d*e - b*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*(2*b*d^2*x + 4*a*d^2 + b*d*e)*sqrt(d*x^2 + e*x + c))/d^2]","A",0
50,1,647,0,0.685072," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x^2,x, algorithm=""fricas"")","\left[\frac{{\left(2 \, a c d + b c e\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) + {\left(2 \, b c d + a d e\right)} \sqrt{c} 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) + 4 \, {\left(b c d x - a c d\right)} \sqrt{d x^{2} + e x + c}}{4 \, c d x}, -\frac{2 \, {\left(2 \, a c d + b c e\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) - {\left(2 \, b c d + a d e\right)} \sqrt{c} 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) - 4 \, {\left(b c d x - a c d\right)} \sqrt{d x^{2} + e x + c}}{4 \, c d x}, \frac{2 \, {\left(2 \, b c d + a d e\right)} \sqrt{-c} 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(2 \, a c d + b c e\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(b c d x - a c d\right)} \sqrt{d x^{2} + e x + c}}{4 \, c d x}, \frac{{\left(2 \, b c d + a d e\right)} \sqrt{-c} 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(2 \, a c d + b c e\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(b c d x - a c d\right)} \sqrt{d x^{2} + e x + c}}{2 \, c d x}\right]"," ",0,"[1/4*((2*a*c*d + b*c*e)*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) + (2*b*c*d + a*d*e)*sqrt(c)*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*d*x - a*c*d)*sqrt(d*x^2 + e*x + c))/(c*d*x), -1/4*(2*(2*a*c*d + b*c*e)*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*b*c*d + a*d*e)*sqrt(c)*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*d*x - a*c*d)*sqrt(d*x^2 + e*x + c))/(c*d*x), 1/4*(2*(2*b*c*d + a*d*e)*sqrt(-c)*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)) + (2*a*c*d + b*c*e)*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*(b*c*d*x - a*c*d)*sqrt(d*x^2 + e*x + c))/(c*d*x), 1/2*((2*b*c*d + a*d*e)*sqrt(-c)*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)) - (2*a*c*d + b*c*e)*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*(b*c*d*x - a*c*d)*sqrt(d*x^2 + e*x + c))/(c*d*x)]","A",0
51,1,693,0,0.859482," ","integrate(((b*x+a)^2)^(1/2)*(d*x^2+e*x+c)^(1/2)/x^3,x, algorithm=""fricas"")","\left[\frac{8 \, b c^{2} \sqrt{d} 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(4 \, a c d + 4 \, b c e - a 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(2 \, a c^{2} + {\left(4 \, b c^{2} + a c e\right)} x\right)} \sqrt{d x^{2} + e x + c}}{16 \, c^{2} x^{2}}, -\frac{16 \, b c^{2} \sqrt{-d} 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(4 \, a c d + 4 \, b c e - a 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(2 \, a c^{2} + {\left(4 \, b c^{2} + a c e\right)} x\right)} \sqrt{d x^{2} + e x + c}}{16 \, c^{2} x^{2}}, \frac{4 \, b c^{2} \sqrt{d} 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(4 \, a c d + 4 \, b c e - a 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(2 \, a c^{2} + {\left(4 \, b c^{2} + a c e\right)} x\right)} \sqrt{d x^{2} + e x + c}}{8 \, c^{2} x^{2}}, -\frac{8 \, b c^{2} \sqrt{-d} 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(4 \, a c d + 4 \, b c e - a 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(2 \, a c^{2} + {\left(4 \, b c^{2} + a c e\right)} x\right)} \sqrt{d x^{2} + e x + c}}{8 \, c^{2} x^{2}}\right]"," ",0,"[1/16*(8*b*c^2*sqrt(d)*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) - (4*a*c*d + 4*b*c*e - a*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*(2*a*c^2 + (4*b*c^2 + a*c*e)*x)*sqrt(d*x^2 + e*x + c))/(c^2*x^2), -1/16*(16*b*c^2*sqrt(-d)*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)) + (4*a*c*d + 4*b*c*e - a*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*(2*a*c^2 + (4*b*c^2 + a*c*e)*x)*sqrt(d*x^2 + e*x + c))/(c^2*x^2), 1/8*(4*b*c^2*sqrt(d)*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) + (4*a*c*d + 4*b*c*e - a*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*(2*a*c^2 + (4*b*c^2 + a*c*e)*x)*sqrt(d*x^2 + e*x + c))/(c^2*x^2), -1/8*(8*b*c^2*sqrt(-d)*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)) - (4*a*c*d + 4*b*c*e - a*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*(2*a*c^2 + (4*b*c^2 + a*c*e)*x)*sqrt(d*x^2 + e*x + c))/(c^2*x^2)]","A",0
52,-1,0,0,0.000000," ","integrate(x^2*(c*x^2+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,-1,0,0,0.000000," ","integrate(x*(c*x^2+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
54,-1,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
55,1,2266,0,38.141248," ","integrate((c*x^2+a)^(1/2)/x/(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} d \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} \log\left(\frac{2 \, a c d e x - a^{2} e^{2} + \sqrt{2} {\left(d^{3} e^{2} - 4 \, d^{4} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} - {\left(a d^{2} e^{2} - 4 \, a d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{x}\right) - \sqrt{2} d \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} \log\left(\frac{2 \, a c d e x - a^{2} e^{2} - \sqrt{2} {\left(d^{3} e^{2} - 4 \, d^{4} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} - {\left(a d^{2} e^{2} - 4 \, a d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{x}\right) - \sqrt{2} d \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} \log\left(\frac{2 \, a c d e x - a^{2} e^{2} + \sqrt{2} {\left(d^{3} e^{2} - 4 \, d^{4} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} + {\left(a d^{2} e^{2} - 4 \, a d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{x}\right) + \sqrt{2} d \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} \log\left(\frac{2 \, a c d e x - a^{2} e^{2} - \sqrt{2} {\left(d^{3} e^{2} - 4 \, d^{4} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} + {\left(a d^{2} e^{2} - 4 \, a d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{x}\right) - 2 \, \sqrt{a} \log\left(-\frac{c x^{2} - 2 \, \sqrt{c x^{2} + a} \sqrt{a} + 2 \, a}{x^{2}}\right)}{4 \, d}, -\frac{\sqrt{2} d \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} \log\left(\frac{2 \, a c d e x - a^{2} e^{2} + \sqrt{2} {\left(d^{3} e^{2} - 4 \, d^{4} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} - {\left(a d^{2} e^{2} - 4 \, a d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{x}\right) - \sqrt{2} d \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} \log\left(\frac{2 \, a c d e x - a^{2} e^{2} - \sqrt{2} {\left(d^{3} e^{2} - 4 \, d^{4} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} - {\left(a d^{2} e^{2} - 4 \, a d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{x}\right) - \sqrt{2} d \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} \log\left(\frac{2 \, a c d e x - a^{2} e^{2} + \sqrt{2} {\left(d^{3} e^{2} - 4 \, d^{4} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} + {\left(a d^{2} e^{2} - 4 \, a d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{x}\right) + \sqrt{2} d \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} \log\left(\frac{2 \, a c d e x - a^{2} e^{2} - \sqrt{2} {\left(d^{3} e^{2} - 4 \, d^{4} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(d^{2} e^{2} - 4 \, d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{d^{2} e^{2} - 4 \, d^{3} f}} + {\left(a d^{2} e^{2} - 4 \, a d^{3} f\right)} \sqrt{\frac{a^{2} e^{2}}{d^{4} e^{2} - 4 \, d^{5} f}}}{x}\right) - 4 \, \sqrt{-a} \arctan\left(\frac{\sqrt{-a}}{\sqrt{c x^{2} + a}}\right)}{4 \, d}\right]"," ",0,"[-1/4*(sqrt(2)*d*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f))*log((2*a*c*d*e*x - a^2*e^2 + sqrt(2)*(d^3*e^2 - 4*d^4*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f)) - (a*d^2*e^2 - 4*a*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/x) - sqrt(2)*d*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f))*log((2*a*c*d*e*x - a^2*e^2 - sqrt(2)*(d^3*e^2 - 4*d^4*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f)) - (a*d^2*e^2 - 4*a*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/x) - sqrt(2)*d*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f))*log((2*a*c*d*e*x - a^2*e^2 + sqrt(2)*(d^3*e^2 - 4*d^4*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f)) + (a*d^2*e^2 - 4*a*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/x) + sqrt(2)*d*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f))*log((2*a*c*d*e*x - a^2*e^2 - sqrt(2)*(d^3*e^2 - 4*d^4*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f)) + (a*d^2*e^2 - 4*a*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/x) - 2*sqrt(a)*log(-(c*x^2 - 2*sqrt(c*x^2 + a)*sqrt(a) + 2*a)/x^2))/d, -1/4*(sqrt(2)*d*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f))*log((2*a*c*d*e*x - a^2*e^2 + sqrt(2)*(d^3*e^2 - 4*d^4*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f)) - (a*d^2*e^2 - 4*a*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/x) - sqrt(2)*d*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f))*log((2*a*c*d*e*x - a^2*e^2 - sqrt(2)*(d^3*e^2 - 4*d^4*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f)) - (a*d^2*e^2 - 4*a*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/x) - sqrt(2)*d*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f))*log((2*a*c*d*e*x - a^2*e^2 + sqrt(2)*(d^3*e^2 - 4*d^4*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f)) + (a*d^2*e^2 - 4*a*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/x) + sqrt(2)*d*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f))*log((2*a*c*d*e*x - a^2*e^2 - sqrt(2)*(d^3*e^2 - 4*d^4*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (d^2*e^2 - 4*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/(d^2*e^2 - 4*d^3*f)) + (a*d^2*e^2 - 4*a*d^3*f)*sqrt(a^2*e^2/(d^4*e^2 - 4*d^5*f)))/x) - 4*sqrt(-a)*arctan(sqrt(-a)/sqrt(c*x^2 + a)))/d]","B",0
56,-1,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/x^2/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
57,-1,0,0,0.000000," ","integrate((c*x^2+a)^(1/2)/x^3/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
58,-1,0,0,0.000000," ","integrate(x^2*(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate(x*(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/x/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/x^2/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
63,-1,0,0,0.000000," ","integrate((c*x^2+a)^(3/2)/x^3/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
64,-1,0,0,0.000000," ","integrate(x^3/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
65,-1,0,0,0.000000," ","integrate(x^2/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,1,5085,0,1.645405," ","integrate(x/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} \log\left(\frac{4 \, a c d^{2} e x - 2 \, a^{2} d e^{2} + \sqrt{2} {\left(a^{2} e^{4} - 4 \, a^{2} d e^{2} f - {\left(2 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6} + 8 \, a^{3} d^{2} f^{4} - 6 \, {\left(4 \, a^{2} c d^{3} + a^{3} d e^{2}\right)} f^{3} + {\left(24 \, a c^{2} d^{4} + 22 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} f^{2} - 2 \, {\left(4 \, c^{3} d^{5} + 9 \, a c^{2} d^{3} e^{2} + 4 \, a^{2} c d e^{4}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} + 2 \, {\left(a c^{2} d^{3} e^{2} + a^{2} c d e^{4} - 4 \, a^{3} d^{2} f^{3} + {\left(8 \, a^{2} c d^{3} + a^{3} d e^{2}\right)} f^{2} - 2 \, {\left(2 \, a c^{2} d^{4} + 3 \, a^{2} c d^{2} e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{x}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} \log\left(\frac{4 \, a c d^{2} e x - 2 \, a^{2} d e^{2} - \sqrt{2} {\left(a^{2} e^{4} - 4 \, a^{2} d e^{2} f - {\left(2 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6} + 8 \, a^{3} d^{2} f^{4} - 6 \, {\left(4 \, a^{2} c d^{3} + a^{3} d e^{2}\right)} f^{3} + {\left(24 \, a c^{2} d^{4} + 22 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} f^{2} - 2 \, {\left(4 \, c^{3} d^{5} + 9 \, a c^{2} d^{3} e^{2} + 4 \, a^{2} c d e^{4}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f + {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} + 2 \, {\left(a c^{2} d^{3} e^{2} + a^{2} c d e^{4} - 4 \, a^{3} d^{2} f^{3} + {\left(8 \, a^{2} c d^{3} + a^{3} d e^{2}\right)} f^{2} - 2 \, {\left(2 \, a c^{2} d^{4} + 3 \, a^{2} c d^{2} e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} \log\left(\frac{4 \, a c d^{2} e x - 2 \, a^{2} d e^{2} + \sqrt{2} {\left(a^{2} e^{4} - 4 \, a^{2} d e^{2} f + {\left(2 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6} + 8 \, a^{3} d^{2} f^{4} - 6 \, {\left(4 \, a^{2} c d^{3} + a^{3} d e^{2}\right)} f^{3} + {\left(24 \, a c^{2} d^{4} + 22 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} f^{2} - 2 \, {\left(4 \, c^{3} d^{5} + 9 \, a c^{2} d^{3} e^{2} + 4 \, a^{2} c d e^{4}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} - 2 \, {\left(a c^{2} d^{3} e^{2} + a^{2} c d e^{4} - 4 \, a^{3} d^{2} f^{3} + {\left(8 \, a^{2} c d^{3} + a^{3} d e^{2}\right)} f^{2} - 2 \, {\left(2 \, a c^{2} d^{4} + 3 \, a^{2} c d^{2} e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{x}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} \log\left(\frac{4 \, a c d^{2} e x - 2 \, a^{2} d e^{2} - \sqrt{2} {\left(a^{2} e^{4} - 4 \, a^{2} d e^{2} f + {\left(2 \, c^{3} d^{4} e^{2} + 3 \, a c^{2} d^{2} e^{4} + a^{2} c e^{6} + 8 \, a^{3} d^{2} f^{4} - 6 \, {\left(4 \, a^{2} c d^{3} + a^{3} d e^{2}\right)} f^{3} + {\left(24 \, a c^{2} d^{4} + 22 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} f^{2} - 2 \, {\left(4 \, c^{3} d^{5} + 9 \, a c^{2} d^{3} e^{2} + 4 \, a^{2} c d e^{4}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + a} \sqrt{\frac{2 \, c d^{2} + a e^{2} - 2 \, a d f - {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} - 2 \, {\left(a c^{2} d^{3} e^{2} + a^{2} c d e^{4} - 4 \, a^{3} d^{2} f^{3} + {\left(8 \, a^{2} c d^{3} + a^{3} d e^{2}\right)} f^{2} - 2 \, {\left(2 \, a c^{2} d^{4} + 3 \, a^{2} c d^{2} e^{2}\right)} f\right)} \sqrt{\frac{a^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{x}\right)"," ",0,"-1/4*sqrt(2)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f))*log((4*a*c*d^2*e*x - 2*a^2*d*e^2 + sqrt(2)*(a^2*e^4 - 4*a^2*d*e^2*f - (2*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4 + a^2*c*e^6 + 8*a^3*d^2*f^4 - 6*(4*a^2*c*d^3 + a^3*d*e^2)*f^3 + (24*a*c^2*d^4 + 22*a^2*c*d^2*e^2 + a^3*e^4)*f^2 - 2*(4*c^3*d^5 + 9*a*c^2*d^3*e^2 + 4*a^2*c*d*e^4)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)) + 2*(a*c^2*d^3*e^2 + a^2*c*d*e^4 - 4*a^3*d^2*f^3 + (8*a^2*c*d^3 + a^3*d*e^2)*f^2 - 2*(2*a*c^2*d^4 + 3*a^2*c*d^2*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/x) + 1/4*sqrt(2)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f))*log((4*a*c*d^2*e*x - 2*a^2*d*e^2 - sqrt(2)*(a^2*e^4 - 4*a^2*d*e^2*f - (2*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4 + a^2*c*e^6 + 8*a^3*d^2*f^4 - 6*(4*a^2*c*d^3 + a^3*d*e^2)*f^3 + (24*a*c^2*d^4 + 22*a^2*c*d^2*e^2 + a^3*e^4)*f^2 - 2*(4*c^3*d^5 + 9*a*c^2*d^3*e^2 + 4*a^2*c*d*e^4)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f + (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)) + 2*(a*c^2*d^3*e^2 + a^2*c*d*e^4 - 4*a^3*d^2*f^3 + (8*a^2*c*d^3 + a^3*d*e^2)*f^2 - 2*(2*a*c^2*d^4 + 3*a^2*c*d^2*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/x) - 1/4*sqrt(2)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f))*log((4*a*c*d^2*e*x - 2*a^2*d*e^2 + sqrt(2)*(a^2*e^4 - 4*a^2*d*e^2*f + (2*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4 + a^2*c*e^6 + 8*a^3*d^2*f^4 - 6*(4*a^2*c*d^3 + a^3*d*e^2)*f^3 + (24*a*c^2*d^4 + 22*a^2*c*d^2*e^2 + a^3*e^4)*f^2 - 2*(4*c^3*d^5 + 9*a*c^2*d^3*e^2 + 4*a^2*c*d*e^4)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)) - 2*(a*c^2*d^3*e^2 + a^2*c*d*e^4 - 4*a^3*d^2*f^3 + (8*a^2*c*d^3 + a^3*d*e^2)*f^2 - 2*(2*a*c^2*d^4 + 3*a^2*c*d^2*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/x) + 1/4*sqrt(2)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f))*log((4*a*c*d^2*e*x - 2*a^2*d*e^2 - sqrt(2)*(a^2*e^4 - 4*a^2*d*e^2*f + (2*c^3*d^4*e^2 + 3*a*c^2*d^2*e^4 + a^2*c*e^6 + 8*a^3*d^2*f^4 - 6*(4*a^2*c*d^3 + a^3*d*e^2)*f^3 + (24*a*c^2*d^4 + 22*a^2*c*d^2*e^2 + a^3*e^4)*f^2 - 2*(4*c^3*d^5 + 9*a*c^2*d^3*e^2 + 4*a^2*c*d*e^4)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))*sqrt(c*x^2 + a)*sqrt((2*c*d^2 + a*e^2 - 2*a*d*f - (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)) - 2*(a*c^2*d^3*e^2 + a^2*c*d*e^4 - 4*a^3*d^2*f^3 + (8*a^2*c*d^3 + a^3*d*e^2)*f^2 - 2*(2*a*c^2*d^4 + 3*a^2*c*d^2*e^2)*f)*sqrt(a^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/x)","B",0
67,1,5073,0,1.621593," ","integrate(1/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \sqrt{\frac{c e^{2} - 2 \, c d f + 2 \, a f^{2} + {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} \log\left(\frac{4 \, c^{2} d e f x - 2 \, a c e^{2} f + \sqrt{2} {\left(c^{2} d e^{3} + 4 \, a c d e f^{2} - {\left(4 \, c^{2} d^{2} e + a c e^{3}\right)} f - {\left(c^{3} d^{3} e^{3} + a c^{2} d e^{5} - 4 \, a^{3} d e f^{4} + {\left(4 \, a^{2} c d^{2} e + a^{3} e^{3}\right)} f^{3} + {\left(4 \, a c^{2} d^{3} e - 5 \, a^{2} c d e^{3}\right)} f^{2} - {\left(4 \, c^{3} d^{4} e + 5 \, a c^{2} d^{2} e^{3} - a^{2} c e^{5}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + a} \sqrt{\frac{c e^{2} - 2 \, c d f + 2 \, a f^{2} + {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} + 2 \, {\left(4 \, a^{3} d f^{4} - {\left(8 \, a^{2} c d^{2} + a^{3} e^{2}\right)} f^{3} + 2 \, {\left(2 \, a c^{2} d^{3} + 3 \, a^{2} c d e^{2}\right)} f^{2} - {\left(a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{x}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{c e^{2} - 2 \, c d f + 2 \, a f^{2} + {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} \log\left(\frac{4 \, c^{2} d e f x - 2 \, a c e^{2} f - \sqrt{2} {\left(c^{2} d e^{3} + 4 \, a c d e f^{2} - {\left(4 \, c^{2} d^{2} e + a c e^{3}\right)} f - {\left(c^{3} d^{3} e^{3} + a c^{2} d e^{5} - 4 \, a^{3} d e f^{4} + {\left(4 \, a^{2} c d^{2} e + a^{3} e^{3}\right)} f^{3} + {\left(4 \, a c^{2} d^{3} e - 5 \, a^{2} c d e^{3}\right)} f^{2} - {\left(4 \, c^{3} d^{4} e + 5 \, a c^{2} d^{2} e^{3} - a^{2} c e^{5}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + a} \sqrt{\frac{c e^{2} - 2 \, c d f + 2 \, a f^{2} + {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} + 2 \, {\left(4 \, a^{3} d f^{4} - {\left(8 \, a^{2} c d^{2} + a^{3} e^{2}\right)} f^{3} + 2 \, {\left(2 \, a c^{2} d^{3} + 3 \, a^{2} c d e^{2}\right)} f^{2} - {\left(a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{c e^{2} - 2 \, c d f + 2 \, a f^{2} - {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} \log\left(\frac{4 \, c^{2} d e f x - 2 \, a c e^{2} f + \sqrt{2} {\left(c^{2} d e^{3} + 4 \, a c d e f^{2} - {\left(4 \, c^{2} d^{2} e + a c e^{3}\right)} f + {\left(c^{3} d^{3} e^{3} + a c^{2} d e^{5} - 4 \, a^{3} d e f^{4} + {\left(4 \, a^{2} c d^{2} e + a^{3} e^{3}\right)} f^{3} + {\left(4 \, a c^{2} d^{3} e - 5 \, a^{2} c d e^{3}\right)} f^{2} - {\left(4 \, c^{3} d^{4} e + 5 \, a c^{2} d^{2} e^{3} - a^{2} c e^{5}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + a} \sqrt{\frac{c e^{2} - 2 \, c d f + 2 \, a f^{2} - {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} - 2 \, {\left(4 \, a^{3} d f^{4} - {\left(8 \, a^{2} c d^{2} + a^{3} e^{2}\right)} f^{3} + 2 \, {\left(2 \, a c^{2} d^{3} + 3 \, a^{2} c d e^{2}\right)} f^{2} - {\left(a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{x}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{c e^{2} - 2 \, c d f + 2 \, a f^{2} - {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} \log\left(\frac{4 \, c^{2} d e f x - 2 \, a c e^{2} f - \sqrt{2} {\left(c^{2} d e^{3} + 4 \, a c d e f^{2} - {\left(4 \, c^{2} d^{2} e + a c e^{3}\right)} f + {\left(c^{3} d^{3} e^{3} + a c^{2} d e^{5} - 4 \, a^{3} d e f^{4} + {\left(4 \, a^{2} c d^{2} e + a^{3} e^{3}\right)} f^{3} + {\left(4 \, a c^{2} d^{3} e - 5 \, a^{2} c d e^{3}\right)} f^{2} - {\left(4 \, c^{3} d^{4} e + 5 \, a c^{2} d^{2} e^{3} - a^{2} c e^{5}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + a} \sqrt{\frac{c e^{2} - 2 \, c d f + 2 \, a f^{2} - {\left(c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(8 \, a c d^{2} + a^{2} e^{2}\right)} f^{2} - 2 \, {\left(2 \, c^{2} d^{3} + 3 \, a c d e^{2}\right)} f}} - 2 \, {\left(4 \, a^{3} d f^{4} - {\left(8 \, a^{2} c d^{2} + a^{3} e^{2}\right)} f^{3} + 2 \, {\left(2 \, a c^{2} d^{3} + 3 \, a^{2} c d e^{2}\right)} f^{2} - {\left(a c^{2} d^{2} e^{2} + a^{2} c e^{4}\right)} f\right)} \sqrt{\frac{c^{2} e^{2}}{c^{4} d^{4} e^{2} + 2 \, a c^{3} d^{2} e^{4} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(16 \, a^{3} c d^{2} + a^{4} e^{2}\right)} f^{4} - 12 \, {\left(2 \, a^{2} c^{2} d^{3} + a^{3} c d e^{2}\right)} f^{3} + 2 \, {\left(8 \, a c^{3} d^{4} + 11 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} f^{2} - 4 \, {\left(c^{4} d^{5} + 3 \, a c^{3} d^{3} e^{2} + 2 \, a^{2} c^{2} d e^{4}\right)} f}}}{x}\right)"," ",0,"-1/4*sqrt(2)*sqrt((c*e^2 - 2*c*d*f + 2*a*f^2 + (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f))*log((4*c^2*d*e*f*x - 2*a*c*e^2*f + sqrt(2)*(c^2*d*e^3 + 4*a*c*d*e*f^2 - (4*c^2*d^2*e + a*c*e^3)*f - (c^3*d^3*e^3 + a*c^2*d*e^5 - 4*a^3*d*e*f^4 + (4*a^2*c*d^2*e + a^3*e^3)*f^3 + (4*a*c^2*d^3*e - 5*a^2*c*d*e^3)*f^2 - (4*c^3*d^4*e + 5*a*c^2*d^2*e^3 - a^2*c*e^5)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))*sqrt(c*x^2 + a)*sqrt((c*e^2 - 2*c*d*f + 2*a*f^2 + (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)) + 2*(4*a^3*d*f^4 - (8*a^2*c*d^2 + a^3*e^2)*f^3 + 2*(2*a*c^2*d^3 + 3*a^2*c*d*e^2)*f^2 - (a*c^2*d^2*e^2 + a^2*c*e^4)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/x) + 1/4*sqrt(2)*sqrt((c*e^2 - 2*c*d*f + 2*a*f^2 + (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f))*log((4*c^2*d*e*f*x - 2*a*c*e^2*f - sqrt(2)*(c^2*d*e^3 + 4*a*c*d*e*f^2 - (4*c^2*d^2*e + a*c*e^3)*f - (c^3*d^3*e^3 + a*c^2*d*e^5 - 4*a^3*d*e*f^4 + (4*a^2*c*d^2*e + a^3*e^3)*f^3 + (4*a*c^2*d^3*e - 5*a^2*c*d*e^3)*f^2 - (4*c^3*d^4*e + 5*a*c^2*d^2*e^3 - a^2*c*e^5)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))*sqrt(c*x^2 + a)*sqrt((c*e^2 - 2*c*d*f + 2*a*f^2 + (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)) + 2*(4*a^3*d*f^4 - (8*a^2*c*d^2 + a^3*e^2)*f^3 + 2*(2*a*c^2*d^3 + 3*a^2*c*d*e^2)*f^2 - (a*c^2*d^2*e^2 + a^2*c*e^4)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/x) - 1/4*sqrt(2)*sqrt((c*e^2 - 2*c*d*f + 2*a*f^2 - (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f))*log((4*c^2*d*e*f*x - 2*a*c*e^2*f + sqrt(2)*(c^2*d*e^3 + 4*a*c*d*e*f^2 - (4*c^2*d^2*e + a*c*e^3)*f + (c^3*d^3*e^3 + a*c^2*d*e^5 - 4*a^3*d*e*f^4 + (4*a^2*c*d^2*e + a^3*e^3)*f^3 + (4*a*c^2*d^3*e - 5*a^2*c*d*e^3)*f^2 - (4*c^3*d^4*e + 5*a*c^2*d^2*e^3 - a^2*c*e^5)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))*sqrt(c*x^2 + a)*sqrt((c*e^2 - 2*c*d*f + 2*a*f^2 - (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)) - 2*(4*a^3*d*f^4 - (8*a^2*c*d^2 + a^3*e^2)*f^3 + 2*(2*a*c^2*d^3 + 3*a^2*c*d*e^2)*f^2 - (a*c^2*d^2*e^2 + a^2*c*e^4)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/x) + 1/4*sqrt(2)*sqrt((c*e^2 - 2*c*d*f + 2*a*f^2 - (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f))*log((4*c^2*d*e*f*x - 2*a*c*e^2*f - sqrt(2)*(c^2*d*e^3 + 4*a*c*d*e*f^2 - (4*c^2*d^2*e + a*c*e^3)*f + (c^3*d^3*e^3 + a*c^2*d*e^5 - 4*a^3*d*e*f^4 + (4*a^2*c*d^2*e + a^3*e^3)*f^3 + (4*a*c^2*d^3*e - 5*a^2*c*d*e^3)*f^2 - (4*c^3*d^4*e + 5*a*c^2*d^2*e^3 - a^2*c*e^5)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))*sqrt(c*x^2 + a)*sqrt((c*e^2 - 2*c*d*f + 2*a*f^2 - (c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/(c^2*d^2*e^2 + a*c*e^4 - 4*a^2*d*f^3 + (8*a*c*d^2 + a^2*e^2)*f^2 - 2*(2*c^2*d^3 + 3*a*c*d*e^2)*f)) - 2*(4*a^3*d*f^4 - (8*a^2*c*d^2 + a^3*e^2)*f^3 + 2*(2*a*c^2*d^3 + 3*a^2*c*d*e^2)*f^2 - (a*c^2*d^2*e^2 + a^2*c*e^4)*f)*sqrt(c^2*e^2/(c^4*d^4*e^2 + 2*a*c^3*d^2*e^4 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (16*a^3*c*d^2 + a^4*e^2)*f^4 - 12*(2*a^2*c^2*d^3 + a^3*c*d*e^2)*f^3 + 2*(8*a*c^3*d^4 + 11*a^2*c^2*d^2*e^2 + a^3*c*e^4)*f^2 - 4*(c^4*d^5 + 3*a*c^3*d^3*e^2 + 2*a^2*c^2*d*e^4)*f)))/x)","B",0
68,-1,0,0,0.000000," ","integrate(1/x/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate(1/x^2/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate(1/x^3/(f*x^2+e*x+d)/(c*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,-1,0,0,0.000000," ","integrate(x^3/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
72,-1,0,0,0.000000," ","integrate(x^2/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
73,-1,0,0,0.000000," ","integrate(x/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(1/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,-1,0,0,0.000000," ","integrate(1/x/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
76,-1,0,0,0.000000," ","integrate(1/x^2/(c*x^2+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(x^3*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(x^2*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,-1,0,0,0.000000," ","integrate(x*(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,1,1139,0,98.756203," ","integrate((c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\left[\frac{f \sqrt{\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} + c d + a f}{d f^{2}}} \log\left(\frac{2 \, b c x + 2 \, \sqrt{c x^{2} + b x + a} b f \sqrt{\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} + c d + a f}{d f^{2}}} + b^{2} + {\left(b f^{2} x + 2 \, a f^{2}\right)} \sqrt{\frac{b^{2}}{d f^{3}}}}{x}\right) - f \sqrt{\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} + c d + a f}{d f^{2}}} \log\left(\frac{2 \, b c x - 2 \, \sqrt{c x^{2} + b x + a} b f \sqrt{\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} + c d + a f}{d f^{2}}} + b^{2} + {\left(b f^{2} x + 2 \, a f^{2}\right)} \sqrt{\frac{b^{2}}{d f^{3}}}}{x}\right) + f \sqrt{-\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} - c d - a f}{d f^{2}}} \log\left(\frac{2 \, b c x + 2 \, \sqrt{c x^{2} + b x + a} b f \sqrt{-\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} - c d - a f}{d f^{2}}} + b^{2} - {\left(b f^{2} x + 2 \, a f^{2}\right)} \sqrt{\frac{b^{2}}{d f^{3}}}}{x}\right) - f \sqrt{-\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} - c d - a f}{d f^{2}}} \log\left(\frac{2 \, b c x - 2 \, \sqrt{c x^{2} + b x + a} b f \sqrt{-\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} - c d - a f}{d f^{2}}} + b^{2} - {\left(b f^{2} x + 2 \, a f^{2}\right)} \sqrt{\frac{b^{2}}{d f^{3}}}}{x}\right) + 2 \, \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right)}{4 \, f}, \frac{f \sqrt{\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} + c d + a f}{d f^{2}}} \log\left(\frac{2 \, b c x + 2 \, \sqrt{c x^{2} + b x + a} b f \sqrt{\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} + c d + a f}{d f^{2}}} + b^{2} + {\left(b f^{2} x + 2 \, a f^{2}\right)} \sqrt{\frac{b^{2}}{d f^{3}}}}{x}\right) - f \sqrt{\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} + c d + a f}{d f^{2}}} \log\left(\frac{2 \, b c x - 2 \, \sqrt{c x^{2} + b x + a} b f \sqrt{\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} + c d + a f}{d f^{2}}} + b^{2} + {\left(b f^{2} x + 2 \, a f^{2}\right)} \sqrt{\frac{b^{2}}{d f^{3}}}}{x}\right) + f \sqrt{-\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} - c d - a f}{d f^{2}}} \log\left(\frac{2 \, b c x + 2 \, \sqrt{c x^{2} + b x + a} b f \sqrt{-\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} - c d - a f}{d f^{2}}} + b^{2} - {\left(b f^{2} x + 2 \, a f^{2}\right)} \sqrt{\frac{b^{2}}{d f^{3}}}}{x}\right) - f \sqrt{-\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} - c d - a f}{d f^{2}}} \log\left(\frac{2 \, b c x - 2 \, \sqrt{c x^{2} + b x + a} b f \sqrt{-\frac{d f^{2} \sqrt{\frac{b^{2}}{d f^{3}}} - c d - a f}{d f^{2}}} + b^{2} - {\left(b f^{2} x + 2 \, a f^{2}\right)} \sqrt{\frac{b^{2}}{d f^{3}}}}{x}\right) + 4 \, \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right)}{4 \, f}\right]"," ",0,"[1/4*(f*sqrt((d*f^2*sqrt(b^2/(d*f^3)) + c*d + a*f)/(d*f^2))*log((2*b*c*x + 2*sqrt(c*x^2 + b*x + a)*b*f*sqrt((d*f^2*sqrt(b^2/(d*f^3)) + c*d + a*f)/(d*f^2)) + b^2 + (b*f^2*x + 2*a*f^2)*sqrt(b^2/(d*f^3)))/x) - f*sqrt((d*f^2*sqrt(b^2/(d*f^3)) + c*d + a*f)/(d*f^2))*log((2*b*c*x - 2*sqrt(c*x^2 + b*x + a)*b*f*sqrt((d*f^2*sqrt(b^2/(d*f^3)) + c*d + a*f)/(d*f^2)) + b^2 + (b*f^2*x + 2*a*f^2)*sqrt(b^2/(d*f^3)))/x) + f*sqrt(-(d*f^2*sqrt(b^2/(d*f^3)) - c*d - a*f)/(d*f^2))*log((2*b*c*x + 2*sqrt(c*x^2 + b*x + a)*b*f*sqrt(-(d*f^2*sqrt(b^2/(d*f^3)) - c*d - a*f)/(d*f^2)) + b^2 - (b*f^2*x + 2*a*f^2)*sqrt(b^2/(d*f^3)))/x) - f*sqrt(-(d*f^2*sqrt(b^2/(d*f^3)) - c*d - a*f)/(d*f^2))*log((2*b*c*x - 2*sqrt(c*x^2 + b*x + a)*b*f*sqrt(-(d*f^2*sqrt(b^2/(d*f^3)) - c*d - a*f)/(d*f^2)) + b^2 - (b*f^2*x + 2*a*f^2)*sqrt(b^2/(d*f^3)))/x) + 2*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c))/f, 1/4*(f*sqrt((d*f^2*sqrt(b^2/(d*f^3)) + c*d + a*f)/(d*f^2))*log((2*b*c*x + 2*sqrt(c*x^2 + b*x + a)*b*f*sqrt((d*f^2*sqrt(b^2/(d*f^3)) + c*d + a*f)/(d*f^2)) + b^2 + (b*f^2*x + 2*a*f^2)*sqrt(b^2/(d*f^3)))/x) - f*sqrt((d*f^2*sqrt(b^2/(d*f^3)) + c*d + a*f)/(d*f^2))*log((2*b*c*x - 2*sqrt(c*x^2 + b*x + a)*b*f*sqrt((d*f^2*sqrt(b^2/(d*f^3)) + c*d + a*f)/(d*f^2)) + b^2 + (b*f^2*x + 2*a*f^2)*sqrt(b^2/(d*f^3)))/x) + f*sqrt(-(d*f^2*sqrt(b^2/(d*f^3)) - c*d - a*f)/(d*f^2))*log((2*b*c*x + 2*sqrt(c*x^2 + b*x + a)*b*f*sqrt(-(d*f^2*sqrt(b^2/(d*f^3)) - c*d - a*f)/(d*f^2)) + b^2 - (b*f^2*x + 2*a*f^2)*sqrt(b^2/(d*f^3)))/x) - f*sqrt(-(d*f^2*sqrt(b^2/(d*f^3)) - c*d - a*f)/(d*f^2))*log((2*b*c*x - 2*sqrt(c*x^2 + b*x + a)*b*f*sqrt(-(d*f^2*sqrt(b^2/(d*f^3)) - c*d - a*f)/(d*f^2)) + b^2 - (b*f^2*x + 2*a*f^2)*sqrt(b^2/(d*f^3)))/x) + 4*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)))/f]","B",0
81,1,1253,0,17.018222," ","integrate((c*x^2+b*x+a)^(1/2)/x/(-f*x^2+d),x, algorithm=""fricas"")","\left[\frac{d \sqrt{\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} + c d + a f}{d^{2} f}} \log\left(\frac{2 \, \sqrt{c x^{2} + b x + a} d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} \sqrt{\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} + c d + a f}{d^{2} f}} + 2 \, b c x + b^{2} + {\left(b d f x + 2 \, a d f\right)} \sqrt{\frac{b^{2}}{d^{3} f}}}{x}\right) - d \sqrt{\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} + c d + a f}{d^{2} f}} \log\left(-\frac{2 \, \sqrt{c x^{2} + b x + a} d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} \sqrt{\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} + c d + a f}{d^{2} f}} - 2 \, b c x - b^{2} - {\left(b d f x + 2 \, a d f\right)} \sqrt{\frac{b^{2}}{d^{3} f}}}{x}\right) - d \sqrt{-\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} - c d - a f}{d^{2} f}} \log\left(\frac{2 \, \sqrt{c x^{2} + b x + a} d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} \sqrt{-\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} - c d - a f}{d^{2} f}} + 2 \, b c x + b^{2} - {\left(b d f x + 2 \, a d f\right)} \sqrt{\frac{b^{2}}{d^{3} f}}}{x}\right) + d \sqrt{-\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} - c d - a f}{d^{2} f}} \log\left(-\frac{2 \, \sqrt{c x^{2} + b x + a} d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} \sqrt{-\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} - c d - a f}{d^{2} f}} - 2 \, b c x - b^{2} + {\left(b d f x + 2 \, a d f\right)} \sqrt{\frac{b^{2}}{d^{3} f}}}{x}\right) + 2 \, \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right)}{4 \, d}, \frac{d \sqrt{\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} + c d + a f}{d^{2} f}} \log\left(\frac{2 \, \sqrt{c x^{2} + b x + a} d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} \sqrt{\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} + c d + a f}{d^{2} f}} + 2 \, b c x + b^{2} + {\left(b d f x + 2 \, a d f\right)} \sqrt{\frac{b^{2}}{d^{3} f}}}{x}\right) - d \sqrt{\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} + c d + a f}{d^{2} f}} \log\left(-\frac{2 \, \sqrt{c x^{2} + b x + a} d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} \sqrt{\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} + c d + a f}{d^{2} f}} - 2 \, b c x - b^{2} - {\left(b d f x + 2 \, a d f\right)} \sqrt{\frac{b^{2}}{d^{3} f}}}{x}\right) - d \sqrt{-\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} - c d - a f}{d^{2} f}} \log\left(\frac{2 \, \sqrt{c x^{2} + b x + a} d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} \sqrt{-\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} - c d - a f}{d^{2} f}} + 2 \, b c x + b^{2} - {\left(b d f x + 2 \, a d f\right)} \sqrt{\frac{b^{2}}{d^{3} f}}}{x}\right) + d \sqrt{-\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} - c d - a f}{d^{2} f}} \log\left(-\frac{2 \, \sqrt{c x^{2} + b x + a} d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} \sqrt{-\frac{d^{2} f \sqrt{\frac{b^{2}}{d^{3} f}} - c d - a f}{d^{2} f}} - 2 \, b c x - b^{2} + {\left(b d f x + 2 \, a d f\right)} \sqrt{\frac{b^{2}}{d^{3} f}}}{x}\right) + 4 \, \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right)}{4 \, d}\right]"," ",0,"[1/4*(d*sqrt((d^2*f*sqrt(b^2/(d^3*f)) + c*d + a*f)/(d^2*f))*log((2*sqrt(c*x^2 + b*x + a)*d^2*f*sqrt(b^2/(d^3*f))*sqrt((d^2*f*sqrt(b^2/(d^3*f)) + c*d + a*f)/(d^2*f)) + 2*b*c*x + b^2 + (b*d*f*x + 2*a*d*f)*sqrt(b^2/(d^3*f)))/x) - d*sqrt((d^2*f*sqrt(b^2/(d^3*f)) + c*d + a*f)/(d^2*f))*log(-(2*sqrt(c*x^2 + b*x + a)*d^2*f*sqrt(b^2/(d^3*f))*sqrt((d^2*f*sqrt(b^2/(d^3*f)) + c*d + a*f)/(d^2*f)) - 2*b*c*x - b^2 - (b*d*f*x + 2*a*d*f)*sqrt(b^2/(d^3*f)))/x) - d*sqrt(-(d^2*f*sqrt(b^2/(d^3*f)) - c*d - a*f)/(d^2*f))*log((2*sqrt(c*x^2 + b*x + a)*d^2*f*sqrt(b^2/(d^3*f))*sqrt(-(d^2*f*sqrt(b^2/(d^3*f)) - c*d - a*f)/(d^2*f)) + 2*b*c*x + b^2 - (b*d*f*x + 2*a*d*f)*sqrt(b^2/(d^3*f)))/x) + d*sqrt(-(d^2*f*sqrt(b^2/(d^3*f)) - c*d - a*f)/(d^2*f))*log(-(2*sqrt(c*x^2 + b*x + a)*d^2*f*sqrt(b^2/(d^3*f))*sqrt(-(d^2*f*sqrt(b^2/(d^3*f)) - c*d - a*f)/(d^2*f)) - 2*b*c*x - b^2 + (b*d*f*x + 2*a*d*f)*sqrt(b^2/(d^3*f)))/x) + 2*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2))/d, 1/4*(d*sqrt((d^2*f*sqrt(b^2/(d^3*f)) + c*d + a*f)/(d^2*f))*log((2*sqrt(c*x^2 + b*x + a)*d^2*f*sqrt(b^2/(d^3*f))*sqrt((d^2*f*sqrt(b^2/(d^3*f)) + c*d + a*f)/(d^2*f)) + 2*b*c*x + b^2 + (b*d*f*x + 2*a*d*f)*sqrt(b^2/(d^3*f)))/x) - d*sqrt((d^2*f*sqrt(b^2/(d^3*f)) + c*d + a*f)/(d^2*f))*log(-(2*sqrt(c*x^2 + b*x + a)*d^2*f*sqrt(b^2/(d^3*f))*sqrt((d^2*f*sqrt(b^2/(d^3*f)) + c*d + a*f)/(d^2*f)) - 2*b*c*x - b^2 - (b*d*f*x + 2*a*d*f)*sqrt(b^2/(d^3*f)))/x) - d*sqrt(-(d^2*f*sqrt(b^2/(d^3*f)) - c*d - a*f)/(d^2*f))*log((2*sqrt(c*x^2 + b*x + a)*d^2*f*sqrt(b^2/(d^3*f))*sqrt(-(d^2*f*sqrt(b^2/(d^3*f)) - c*d - a*f)/(d^2*f)) + 2*b*c*x + b^2 - (b*d*f*x + 2*a*d*f)*sqrt(b^2/(d^3*f)))/x) + d*sqrt(-(d^2*f*sqrt(b^2/(d^3*f)) - c*d - a*f)/(d^2*f))*log(-(2*sqrt(c*x^2 + b*x + a)*d^2*f*sqrt(b^2/(d^3*f))*sqrt(-(d^2*f*sqrt(b^2/(d^3*f)) - c*d - a*f)/(d^2*f)) - 2*b*c*x - b^2 + (b*d*f*x + 2*a*d*f)*sqrt(b^2/(d^3*f)))/x) + 4*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)))/d]","B",0
82,1,1094,0,24.594960," ","integrate((c*x^2+b*x+a)^(1/2)/x^2/(-f*x^2+d),x, algorithm=""fricas"")","\left[\frac{a d x \sqrt{\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} + c d + a f}{d^{3}}} \log\left(\frac{2 \, b c x + 2 \, \sqrt{c x^{2} + b x + a} b d \sqrt{\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} + c d + a f}{d^{3}}} + b^{2} + {\left(b d^{2} x + 2 \, a d^{2}\right)} \sqrt{\frac{b^{2} f}{d^{5}}}}{x}\right) - a d x \sqrt{\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} + c d + a f}{d^{3}}} \log\left(\frac{2 \, b c x - 2 \, \sqrt{c x^{2} + b x + a} b d \sqrt{\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} + c d + a f}{d^{3}}} + b^{2} + {\left(b d^{2} x + 2 \, a d^{2}\right)} \sqrt{\frac{b^{2} f}{d^{5}}}}{x}\right) + a d x \sqrt{-\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} - c d - a f}{d^{3}}} \log\left(\frac{2 \, b c x + 2 \, \sqrt{c x^{2} + b x + a} b d \sqrt{-\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} - c d - a f}{d^{3}}} + b^{2} - {\left(b d^{2} x + 2 \, a d^{2}\right)} \sqrt{\frac{b^{2} f}{d^{5}}}}{x}\right) - a d x \sqrt{-\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} - c d - a f}{d^{3}}} \log\left(\frac{2 \, b c x - 2 \, \sqrt{c x^{2} + b x + a} b d \sqrt{-\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} - c d - a f}{d^{3}}} + b^{2} - {\left(b d^{2} x + 2 \, a d^{2}\right)} \sqrt{\frac{b^{2} f}{d^{5}}}}{x}\right) + \sqrt{a} b x \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, \sqrt{c x^{2} + b x + a} a}{4 \, a d x}, \frac{a d x \sqrt{\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} + c d + a f}{d^{3}}} \log\left(\frac{2 \, b c x + 2 \, \sqrt{c x^{2} + b x + a} b d \sqrt{\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} + c d + a f}{d^{3}}} + b^{2} + {\left(b d^{2} x + 2 \, a d^{2}\right)} \sqrt{\frac{b^{2} f}{d^{5}}}}{x}\right) - a d x \sqrt{\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} + c d + a f}{d^{3}}} \log\left(\frac{2 \, b c x - 2 \, \sqrt{c x^{2} + b x + a} b d \sqrt{\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} + c d + a f}{d^{3}}} + b^{2} + {\left(b d^{2} x + 2 \, a d^{2}\right)} \sqrt{\frac{b^{2} f}{d^{5}}}}{x}\right) + a d x \sqrt{-\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} - c d - a f}{d^{3}}} \log\left(\frac{2 \, b c x + 2 \, \sqrt{c x^{2} + b x + a} b d \sqrt{-\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} - c d - a f}{d^{3}}} + b^{2} - {\left(b d^{2} x + 2 \, a d^{2}\right)} \sqrt{\frac{b^{2} f}{d^{5}}}}{x}\right) - a d x \sqrt{-\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} - c d - a f}{d^{3}}} \log\left(\frac{2 \, b c x - 2 \, \sqrt{c x^{2} + b x + a} b d \sqrt{-\frac{d^{3} \sqrt{\frac{b^{2} f}{d^{5}}} - c d - a f}{d^{3}}} + b^{2} - {\left(b d^{2} x + 2 \, a d^{2}\right)} \sqrt{\frac{b^{2} f}{d^{5}}}}{x}\right) + 2 \, \sqrt{-a} b x \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 4 \, \sqrt{c x^{2} + b x + a} a}{4 \, a d x}\right]"," ",0,"[1/4*(a*d*x*sqrt((d^3*sqrt(b^2*f/d^5) + c*d + a*f)/d^3)*log((2*b*c*x + 2*sqrt(c*x^2 + b*x + a)*b*d*sqrt((d^3*sqrt(b^2*f/d^5) + c*d + a*f)/d^3) + b^2 + (b*d^2*x + 2*a*d^2)*sqrt(b^2*f/d^5))/x) - a*d*x*sqrt((d^3*sqrt(b^2*f/d^5) + c*d + a*f)/d^3)*log((2*b*c*x - 2*sqrt(c*x^2 + b*x + a)*b*d*sqrt((d^3*sqrt(b^2*f/d^5) + c*d + a*f)/d^3) + b^2 + (b*d^2*x + 2*a*d^2)*sqrt(b^2*f/d^5))/x) + a*d*x*sqrt(-(d^3*sqrt(b^2*f/d^5) - c*d - a*f)/d^3)*log((2*b*c*x + 2*sqrt(c*x^2 + b*x + a)*b*d*sqrt(-(d^3*sqrt(b^2*f/d^5) - c*d - a*f)/d^3) + b^2 - (b*d^2*x + 2*a*d^2)*sqrt(b^2*f/d^5))/x) - a*d*x*sqrt(-(d^3*sqrt(b^2*f/d^5) - c*d - a*f)/d^3)*log((2*b*c*x - 2*sqrt(c*x^2 + b*x + a)*b*d*sqrt(-(d^3*sqrt(b^2*f/d^5) - c*d - a*f)/d^3) + b^2 - (b*d^2*x + 2*a*d^2)*sqrt(b^2*f/d^5))/x) + sqrt(a)*b*x*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*sqrt(c*x^2 + b*x + a)*a)/(a*d*x), 1/4*(a*d*x*sqrt((d^3*sqrt(b^2*f/d^5) + c*d + a*f)/d^3)*log((2*b*c*x + 2*sqrt(c*x^2 + b*x + a)*b*d*sqrt((d^3*sqrt(b^2*f/d^5) + c*d + a*f)/d^3) + b^2 + (b*d^2*x + 2*a*d^2)*sqrt(b^2*f/d^5))/x) - a*d*x*sqrt((d^3*sqrt(b^2*f/d^5) + c*d + a*f)/d^3)*log((2*b*c*x - 2*sqrt(c*x^2 + b*x + a)*b*d*sqrt((d^3*sqrt(b^2*f/d^5) + c*d + a*f)/d^3) + b^2 + (b*d^2*x + 2*a*d^2)*sqrt(b^2*f/d^5))/x) + a*d*x*sqrt(-(d^3*sqrt(b^2*f/d^5) - c*d - a*f)/d^3)*log((2*b*c*x + 2*sqrt(c*x^2 + b*x + a)*b*d*sqrt(-(d^3*sqrt(b^2*f/d^5) - c*d - a*f)/d^3) + b^2 - (b*d^2*x + 2*a*d^2)*sqrt(b^2*f/d^5))/x) - a*d*x*sqrt(-(d^3*sqrt(b^2*f/d^5) - c*d - a*f)/d^3)*log((2*b*c*x - 2*sqrt(c*x^2 + b*x + a)*b*d*sqrt(-(d^3*sqrt(b^2*f/d^5) - c*d - a*f)/d^3) + b^2 - (b*d^2*x + 2*a*d^2)*sqrt(b^2*f/d^5))/x) + 2*sqrt(-a)*b*x*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 4*sqrt(c*x^2 + b*x + a)*a)/(a*d*x)]","B",0
83,1,1485,0,133.831085," ","integrate((c*x^2+b*x+a)^(1/2)/x^3/(-f*x^2+d),x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} d^{2} x^{2} \sqrt{\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} + c d f + a f^{2}}{d^{4}}} \log\left(\frac{2 \, \sqrt{c x^{2} + b x + a} d^{5} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} \sqrt{\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} + c d f + a f^{2}}{d^{4}}} + 2 \, b c f^{2} x + b^{2} f^{2} + {\left(b d^{3} f x + 2 \, a d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{d^{7}}}}{x}\right) - 4 \, a^{2} d^{2} x^{2} \sqrt{\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} + c d f + a f^{2}}{d^{4}}} \log\left(-\frac{2 \, \sqrt{c x^{2} + b x + a} d^{5} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} \sqrt{\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} + c d f + a f^{2}}{d^{4}}} - 2 \, b c f^{2} x - b^{2} f^{2} - {\left(b d^{3} f x + 2 \, a d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{d^{7}}}}{x}\right) - 4 \, a^{2} d^{2} x^{2} \sqrt{-\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} - c d f - a f^{2}}{d^{4}}} \log\left(\frac{2 \, \sqrt{c x^{2} + b x + a} d^{5} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} \sqrt{-\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} - c d f - a f^{2}}{d^{4}}} + 2 \, b c f^{2} x + b^{2} f^{2} - {\left(b d^{3} f x + 2 \, a d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{d^{7}}}}{x}\right) + 4 \, a^{2} d^{2} x^{2} \sqrt{-\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} - c d f - a f^{2}}{d^{4}}} \log\left(-\frac{2 \, \sqrt{c x^{2} + b x + a} d^{5} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} \sqrt{-\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} - c d f - a f^{2}}{d^{4}}} - 2 \, b c f^{2} x - b^{2} f^{2} + {\left(b d^{3} f x + 2 \, a d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{d^{7}}}}{x}\right) + {\left(8 \, a^{2} f - {\left(b^{2} - 4 \, a c\right)} d\right)} \sqrt{a} x^{2} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right) - 4 \, {\left(a b d x + 2 \, a^{2} d\right)} \sqrt{c x^{2} + b x + a}}{16 \, a^{2} d^{2} x^{2}}, \frac{2 \, a^{2} d^{2} x^{2} \sqrt{\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} + c d f + a f^{2}}{d^{4}}} \log\left(\frac{2 \, \sqrt{c x^{2} + b x + a} d^{5} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} \sqrt{\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} + c d f + a f^{2}}{d^{4}}} + 2 \, b c f^{2} x + b^{2} f^{2} + {\left(b d^{3} f x + 2 \, a d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{d^{7}}}}{x}\right) - 2 \, a^{2} d^{2} x^{2} \sqrt{\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} + c d f + a f^{2}}{d^{4}}} \log\left(-\frac{2 \, \sqrt{c x^{2} + b x + a} d^{5} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} \sqrt{\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} + c d f + a f^{2}}{d^{4}}} - 2 \, b c f^{2} x - b^{2} f^{2} - {\left(b d^{3} f x + 2 \, a d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{d^{7}}}}{x}\right) - 2 \, a^{2} d^{2} x^{2} \sqrt{-\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} - c d f - a f^{2}}{d^{4}}} \log\left(\frac{2 \, \sqrt{c x^{2} + b x + a} d^{5} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} \sqrt{-\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} - c d f - a f^{2}}{d^{4}}} + 2 \, b c f^{2} x + b^{2} f^{2} - {\left(b d^{3} f x + 2 \, a d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{d^{7}}}}{x}\right) + 2 \, a^{2} d^{2} x^{2} \sqrt{-\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} - c d f - a f^{2}}{d^{4}}} \log\left(-\frac{2 \, \sqrt{c x^{2} + b x + a} d^{5} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} \sqrt{-\frac{d^{4} \sqrt{\frac{b^{2} f^{3}}{d^{7}}} - c d f - a f^{2}}{d^{4}}} - 2 \, b c f^{2} x - b^{2} f^{2} + {\left(b d^{3} f x + 2 \, a d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{d^{7}}}}{x}\right) + {\left(8 \, a^{2} f - {\left(b^{2} - 4 \, a c\right)} d\right)} \sqrt{-a} x^{2} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right) - 2 \, {\left(a b d x + 2 \, a^{2} d\right)} \sqrt{c x^{2} + b x + a}}{8 \, a^{2} d^{2} x^{2}}\right]"," ",0,"[1/16*(4*a^2*d^2*x^2*sqrt((d^4*sqrt(b^2*f^3/d^7) + c*d*f + a*f^2)/d^4)*log((2*sqrt(c*x^2 + b*x + a)*d^5*sqrt(b^2*f^3/d^7)*sqrt((d^4*sqrt(b^2*f^3/d^7) + c*d*f + a*f^2)/d^4) + 2*b*c*f^2*x + b^2*f^2 + (b*d^3*f*x + 2*a*d^3*f)*sqrt(b^2*f^3/d^7))/x) - 4*a^2*d^2*x^2*sqrt((d^4*sqrt(b^2*f^3/d^7) + c*d*f + a*f^2)/d^4)*log(-(2*sqrt(c*x^2 + b*x + a)*d^5*sqrt(b^2*f^3/d^7)*sqrt((d^4*sqrt(b^2*f^3/d^7) + c*d*f + a*f^2)/d^4) - 2*b*c*f^2*x - b^2*f^2 - (b*d^3*f*x + 2*a*d^3*f)*sqrt(b^2*f^3/d^7))/x) - 4*a^2*d^2*x^2*sqrt(-(d^4*sqrt(b^2*f^3/d^7) - c*d*f - a*f^2)/d^4)*log((2*sqrt(c*x^2 + b*x + a)*d^5*sqrt(b^2*f^3/d^7)*sqrt(-(d^4*sqrt(b^2*f^3/d^7) - c*d*f - a*f^2)/d^4) + 2*b*c*f^2*x + b^2*f^2 - (b*d^3*f*x + 2*a*d^3*f)*sqrt(b^2*f^3/d^7))/x) + 4*a^2*d^2*x^2*sqrt(-(d^4*sqrt(b^2*f^3/d^7) - c*d*f - a*f^2)/d^4)*log(-(2*sqrt(c*x^2 + b*x + a)*d^5*sqrt(b^2*f^3/d^7)*sqrt(-(d^4*sqrt(b^2*f^3/d^7) - c*d*f - a*f^2)/d^4) - 2*b*c*f^2*x - b^2*f^2 + (b*d^3*f*x + 2*a*d^3*f)*sqrt(b^2*f^3/d^7))/x) + (8*a^2*f - (b^2 - 4*a*c)*d)*sqrt(a)*x^2*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2) - 4*(a*b*d*x + 2*a^2*d)*sqrt(c*x^2 + b*x + a))/(a^2*d^2*x^2), 1/8*(2*a^2*d^2*x^2*sqrt((d^4*sqrt(b^2*f^3/d^7) + c*d*f + a*f^2)/d^4)*log((2*sqrt(c*x^2 + b*x + a)*d^5*sqrt(b^2*f^3/d^7)*sqrt((d^4*sqrt(b^2*f^3/d^7) + c*d*f + a*f^2)/d^4) + 2*b*c*f^2*x + b^2*f^2 + (b*d^3*f*x + 2*a*d^3*f)*sqrt(b^2*f^3/d^7))/x) - 2*a^2*d^2*x^2*sqrt((d^4*sqrt(b^2*f^3/d^7) + c*d*f + a*f^2)/d^4)*log(-(2*sqrt(c*x^2 + b*x + a)*d^5*sqrt(b^2*f^3/d^7)*sqrt((d^4*sqrt(b^2*f^3/d^7) + c*d*f + a*f^2)/d^4) - 2*b*c*f^2*x - b^2*f^2 - (b*d^3*f*x + 2*a*d^3*f)*sqrt(b^2*f^3/d^7))/x) - 2*a^2*d^2*x^2*sqrt(-(d^4*sqrt(b^2*f^3/d^7) - c*d*f - a*f^2)/d^4)*log((2*sqrt(c*x^2 + b*x + a)*d^5*sqrt(b^2*f^3/d^7)*sqrt(-(d^4*sqrt(b^2*f^3/d^7) - c*d*f - a*f^2)/d^4) + 2*b*c*f^2*x + b^2*f^2 - (b*d^3*f*x + 2*a*d^3*f)*sqrt(b^2*f^3/d^7))/x) + 2*a^2*d^2*x^2*sqrt(-(d^4*sqrt(b^2*f^3/d^7) - c*d*f - a*f^2)/d^4)*log(-(2*sqrt(c*x^2 + b*x + a)*d^5*sqrt(b^2*f^3/d^7)*sqrt(-(d^4*sqrt(b^2*f^3/d^7) - c*d*f - a*f^2)/d^4) - 2*b*c*f^2*x - b^2*f^2 + (b*d^3*f*x + 2*a*d^3*f)*sqrt(b^2*f^3/d^7))/x) + (8*a^2*f - (b^2 - 4*a*c)*d)*sqrt(-a)*x^2*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)) - 2*(a*b*d*x + 2*a^2*d)*sqrt(c*x^2 + b*x + a))/(a^2*d^2*x^2)]","B",0
84,-1,0,0,0.000000," ","integrate(x^3*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate(x^2*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,-1,0,0,0.000000," ","integrate(x*(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
87,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
88,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/x/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/x^2/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
90,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/x^3/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
91,1,2579,0,164.298632," ","integrate((c*x^2+b*x+a)^(3/2)/(-x^2+1),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, b^{2} + 12 \, a c + 8 \, c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{a - b + c} \log\left(-\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b - 2 \, c\right)} x + 2 \, a - b\right)} \sqrt{a - b + c} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} x}{x^{2} + 2 \, x + 1}\right) + 4 \, {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{a + b + c} \log\left(-\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b + 2 \, c\right)} x + 2 \, a + b\right)} \sqrt{a + b + c} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c + 2 \, {\left(4 \, a b + 3 \, b^{2} + 4 \, {\left(a + b\right)} c\right)} x}{x^{2} - 2 \, x + 1}\right) - 4 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x + a}}{16 \, c}, -\frac{8 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{-a + b - c} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left({\left(b - 2 \, c\right)} x + 2 \, a - b\right)} \sqrt{-a + b - c}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} x^{2} + a^{2} - a b + a c + {\left(a b - b^{2} + b c\right)} x\right)}}\right) - {\left(3 \, b^{2} + 12 \, a c + 8 \, c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{a + b + c} \log\left(-\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b + 2 \, c\right)} x + 2 \, a + b\right)} \sqrt{a + b + c} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c + 2 \, {\left(4 \, a b + 3 \, b^{2} + 4 \, {\left(a + b\right)} c\right)} x}{x^{2} - 2 \, x + 1}\right) + 4 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x + a}}{16 \, c}, -\frac{8 \, {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left({\left(b + 2 \, c\right)} x + 2 \, a + b\right)} \sqrt{-a - b - c}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} x^{2} + a^{2} + a b + a c + {\left(a b + b^{2} + b c\right)} x\right)}}\right) - {\left(3 \, b^{2} + 12 \, a c + 8 \, c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) - 4 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{a - b + c} \log\left(-\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b - 2 \, c\right)} x + 2 \, a - b\right)} \sqrt{a - b + c} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} x}{x^{2} + 2 \, x + 1}\right) + 4 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x + a}}{16 \, c}, -\frac{8 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{-a + b - c} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left({\left(b - 2 \, c\right)} x + 2 \, a - b\right)} \sqrt{-a + b - c}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} x^{2} + a^{2} - a b + a c + {\left(a b - b^{2} + b c\right)} x\right)}}\right) + 8 \, {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left({\left(b + 2 \, c\right)} x + 2 \, a + b\right)} \sqrt{-a - b - c}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} x^{2} + a^{2} + a b + a c + {\left(a b + b^{2} + b c\right)} x\right)}}\right) - {\left(3 \, b^{2} + 12 \, a c + 8 \, c^{2}\right)} \sqrt{c} \log\left(-8 \, c^{2} x^{2} - 8 \, b c x - b^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{c} - 4 \, a c\right) + 4 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x + a}}{16 \, c}, \frac{{\left(3 \, b^{2} + 12 \, a c + 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{a - b + c} \log\left(-\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b - 2 \, c\right)} x + 2 \, a - b\right)} \sqrt{a - b + c} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} x}{x^{2} + 2 \, x + 1}\right) + 2 \, {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{a + b + c} \log\left(-\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b + 2 \, c\right)} x + 2 \, a + b\right)} \sqrt{a + b + c} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c + 2 \, {\left(4 \, a b + 3 \, b^{2} + 4 \, {\left(a + b\right)} c\right)} x}{x^{2} - 2 \, x + 1}\right) - 2 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x + a}}{8 \, c}, -\frac{4 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{-a + b - c} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left({\left(b - 2 \, c\right)} x + 2 \, a - b\right)} \sqrt{-a + b - c}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} x^{2} + a^{2} - a b + a c + {\left(a b - b^{2} + b c\right)} x\right)}}\right) - {\left(3 \, b^{2} + 12 \, a c + 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{a + b + c} \log\left(-\frac{{\left(b^{2} + 4 \, {\left(a + 2 \, b\right)} c + 8 \, c^{2}\right)} x^{2} + 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b + 2 \, c\right)} x + 2 \, a + b\right)} \sqrt{a + b + c} + 8 \, a^{2} + 8 \, a b + b^{2} + 4 \, a c + 2 \, {\left(4 \, a b + 3 \, b^{2} + 4 \, {\left(a + b\right)} c\right)} x}{x^{2} - 2 \, x + 1}\right) + 2 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x + a}}{8 \, c}, -\frac{4 \, {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left({\left(b + 2 \, c\right)} x + 2 \, a + b\right)} \sqrt{-a - b - c}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} x^{2} + a^{2} + a b + a c + {\left(a b + b^{2} + b c\right)} x\right)}}\right) - {\left(3 \, b^{2} + 12 \, a c + 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) - 2 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{a - b + c} \log\left(-\frac{{\left(b^{2} + 4 \, {\left(a - 2 \, b\right)} c + 8 \, c^{2}\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left({\left(b - 2 \, c\right)} x + 2 \, a - b\right)} \sqrt{a - b + c} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, a c + 2 \, {\left(4 \, a b - 3 \, b^{2} - 4 \, {\left(a - b\right)} c\right)} x}{x^{2} + 2 \, x + 1}\right) + 2 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x + a}}{8 \, c}, -\frac{4 \, {\left({\left(a - b\right)} c + c^{2}\right)} \sqrt{-a + b - c} \arctan\left(-\frac{\sqrt{c x^{2} + b x + a} {\left({\left(b - 2 \, c\right)} x + 2 \, a - b\right)} \sqrt{-a + b - c}}{2 \, {\left({\left({\left(a - b\right)} c + c^{2}\right)} x^{2} + a^{2} - a b + a c + {\left(a b - b^{2} + b c\right)} x\right)}}\right) + 4 \, {\left({\left(a + b\right)} c + c^{2}\right)} \sqrt{-a - b - c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left({\left(b + 2 \, c\right)} x + 2 \, a + b\right)} \sqrt{-a - b - c}}{2 \, {\left({\left({\left(a + b\right)} c + c^{2}\right)} x^{2} + a^{2} + a b + a c + {\left(a b + b^{2} + b c\right)} x\right)}}\right) - {\left(3 \, b^{2} + 12 \, a c + 8 \, c^{2}\right)} \sqrt{-c} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(2 \, c x + b\right)} \sqrt{-c}}{2 \, {\left(c^{2} x^{2} + b c x + a c\right)}}\right) + 2 \, {\left(2 \, c^{2} x + 5 \, b c\right)} \sqrt{c x^{2} + b x + a}}{8 \, c}\right]"," ",0,"[1/16*((3*b^2 + 12*a*c + 8*c^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*((a - b)*c + c^2)*sqrt(a - b + c)*log(-((b^2 + 4*(a - 2*b)*c + 8*c^2)*x^2 - 4*sqrt(c*x^2 + b*x + a)*((b - 2*c)*x + 2*a - b)*sqrt(a - b + c) + 8*a^2 - 8*a*b + b^2 + 4*a*c + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*x)/(x^2 + 2*x + 1)) + 4*((a + b)*c + c^2)*sqrt(a + b + c)*log(-((b^2 + 4*(a + 2*b)*c + 8*c^2)*x^2 + 4*sqrt(c*x^2 + b*x + a)*((b + 2*c)*x + 2*a + b)*sqrt(a + b + c) + 8*a^2 + 8*a*b + b^2 + 4*a*c + 2*(4*a*b + 3*b^2 + 4*(a + b)*c)*x)/(x^2 - 2*x + 1)) - 4*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x + a))/c, -1/16*(8*((a - b)*c + c^2)*sqrt(-a + b - c)*arctan(-1/2*sqrt(c*x^2 + b*x + a)*((b - 2*c)*x + 2*a - b)*sqrt(-a + b - c)/(((a - b)*c + c^2)*x^2 + a^2 - a*b + a*c + (a*b - b^2 + b*c)*x)) - (3*b^2 + 12*a*c + 8*c^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*((a + b)*c + c^2)*sqrt(a + b + c)*log(-((b^2 + 4*(a + 2*b)*c + 8*c^2)*x^2 + 4*sqrt(c*x^2 + b*x + a)*((b + 2*c)*x + 2*a + b)*sqrt(a + b + c) + 8*a^2 + 8*a*b + b^2 + 4*a*c + 2*(4*a*b + 3*b^2 + 4*(a + b)*c)*x)/(x^2 - 2*x + 1)) + 4*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x + a))/c, -1/16*(8*((a + b)*c + c^2)*sqrt(-a - b - c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*((b + 2*c)*x + 2*a + b)*sqrt(-a - b - c)/(((a + b)*c + c^2)*x^2 + a^2 + a*b + a*c + (a*b + b^2 + b*c)*x)) - (3*b^2 + 12*a*c + 8*c^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) - 4*((a - b)*c + c^2)*sqrt(a - b + c)*log(-((b^2 + 4*(a - 2*b)*c + 8*c^2)*x^2 - 4*sqrt(c*x^2 + b*x + a)*((b - 2*c)*x + 2*a - b)*sqrt(a - b + c) + 8*a^2 - 8*a*b + b^2 + 4*a*c + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*x)/(x^2 + 2*x + 1)) + 4*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x + a))/c, -1/16*(8*((a - b)*c + c^2)*sqrt(-a + b - c)*arctan(-1/2*sqrt(c*x^2 + b*x + a)*((b - 2*c)*x + 2*a - b)*sqrt(-a + b - c)/(((a - b)*c + c^2)*x^2 + a^2 - a*b + a*c + (a*b - b^2 + b*c)*x)) + 8*((a + b)*c + c^2)*sqrt(-a - b - c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*((b + 2*c)*x + 2*a + b)*sqrt(-a - b - c)/(((a + b)*c + c^2)*x^2 + a^2 + a*b + a*c + (a*b + b^2 + b*c)*x)) - (3*b^2 + 12*a*c + 8*c^2)*sqrt(c)*log(-8*c^2*x^2 - 8*b*c*x - b^2 + 4*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(c) - 4*a*c) + 4*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x + a))/c, 1/8*((3*b^2 + 12*a*c + 8*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*((a - b)*c + c^2)*sqrt(a - b + c)*log(-((b^2 + 4*(a - 2*b)*c + 8*c^2)*x^2 - 4*sqrt(c*x^2 + b*x + a)*((b - 2*c)*x + 2*a - b)*sqrt(a - b + c) + 8*a^2 - 8*a*b + b^2 + 4*a*c + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*x)/(x^2 + 2*x + 1)) + 2*((a + b)*c + c^2)*sqrt(a + b + c)*log(-((b^2 + 4*(a + 2*b)*c + 8*c^2)*x^2 + 4*sqrt(c*x^2 + b*x + a)*((b + 2*c)*x + 2*a + b)*sqrt(a + b + c) + 8*a^2 + 8*a*b + b^2 + 4*a*c + 2*(4*a*b + 3*b^2 + 4*(a + b)*c)*x)/(x^2 - 2*x + 1)) - 2*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x + a))/c, -1/8*(4*((a - b)*c + c^2)*sqrt(-a + b - c)*arctan(-1/2*sqrt(c*x^2 + b*x + a)*((b - 2*c)*x + 2*a - b)*sqrt(-a + b - c)/(((a - b)*c + c^2)*x^2 + a^2 - a*b + a*c + (a*b - b^2 + b*c)*x)) - (3*b^2 + 12*a*c + 8*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*((a + b)*c + c^2)*sqrt(a + b + c)*log(-((b^2 + 4*(a + 2*b)*c + 8*c^2)*x^2 + 4*sqrt(c*x^2 + b*x + a)*((b + 2*c)*x + 2*a + b)*sqrt(a + b + c) + 8*a^2 + 8*a*b + b^2 + 4*a*c + 2*(4*a*b + 3*b^2 + 4*(a + b)*c)*x)/(x^2 - 2*x + 1)) + 2*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x + a))/c, -1/8*(4*((a + b)*c + c^2)*sqrt(-a - b - c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*((b + 2*c)*x + 2*a + b)*sqrt(-a - b - c)/(((a + b)*c + c^2)*x^2 + a^2 + a*b + a*c + (a*b + b^2 + b*c)*x)) - (3*b^2 + 12*a*c + 8*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) - 2*((a - b)*c + c^2)*sqrt(a - b + c)*log(-((b^2 + 4*(a - 2*b)*c + 8*c^2)*x^2 - 4*sqrt(c*x^2 + b*x + a)*((b - 2*c)*x + 2*a - b)*sqrt(a - b + c) + 8*a^2 - 8*a*b + b^2 + 4*a*c + 2*(4*a*b - 3*b^2 - 4*(a - b)*c)*x)/(x^2 + 2*x + 1)) + 2*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x + a))/c, -1/8*(4*((a - b)*c + c^2)*sqrt(-a + b - c)*arctan(-1/2*sqrt(c*x^2 + b*x + a)*((b - 2*c)*x + 2*a - b)*sqrt(-a + b - c)/(((a - b)*c + c^2)*x^2 + a^2 - a*b + a*c + (a*b - b^2 + b*c)*x)) + 4*((a + b)*c + c^2)*sqrt(-a - b - c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*((b + 2*c)*x + 2*a + b)*sqrt(-a - b - c)/(((a + b)*c + c^2)*x^2 + a^2 + a*b + a*c + (a*b + b^2 + b*c)*x)) - (3*b^2 + 12*a*c + 8*c^2)*sqrt(-c)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(2*c*x + b)*sqrt(-c)/(c^2*x^2 + b*c*x + a*c)) + 2*(2*c^2*x + 5*b*c)*sqrt(c*x^2 + b*x + a))/c]","A",0
92,1,70,0,0.415665," ","integrate((x^2-x-1)^(1/2)/(-x^2+1),x, algorithm=""fricas"")","\arctan\left(-x + \sqrt{x^{2} - x - 1} + 1\right) - \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} - x - 1}\right) + \frac{1}{2} \, \log\left(-x + \sqrt{x^{2} - x - 1} - 2\right) + \log\left(-2 \, x + 2 \, \sqrt{x^{2} - x - 1} + 1\right)"," ",0,"arctan(-x + sqrt(x^2 - x - 1) + 1) - 1/2*log(-x + sqrt(x^2 - x - 1)) + 1/2*log(-x + sqrt(x^2 - x - 1) - 2) + log(-2*x + 2*sqrt(x^2 - x - 1) + 1)","A",0
93,1,777,0,0.460227," ","integrate((x^2+x)^(3/2)/(x^2+1),x, algorithm=""fricas"")","-\frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(8 \, x^{2} - 8 \, \sqrt{x^{2} + x} x + 2 \, {\left(8^{\frac{1}{4}} \sqrt{x^{2} + x} {\left(\sqrt{2} - 1\right)} - 8^{\frac{1}{4}} {\left(\sqrt{2} x - x - 1\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) + \frac{1}{8} \cdot 8^{\frac{1}{4}} \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} \log\left(8 \, x^{2} - 8 \, \sqrt{x^{2} + x} x - 2 \, {\left(8^{\frac{1}{4}} \sqrt{x^{2} + x} {\left(\sqrt{2} - 1\right)} - 8^{\frac{1}{4}} {\left(\sqrt{2} x - x - 1\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4\right) + \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{7} \, \sqrt{2} {\left(\sqrt{2} {\left(5 \, x + 1\right)} + 6 \, x + 4\right)} + \frac{1}{112} \, \sqrt{8 \, x^{2} - 8 \, \sqrt{x^{2} + x} x - 2 \, {\left(8^{\frac{1}{4}} \sqrt{x^{2} + x} {\left(\sqrt{2} - 1\right)} - 8^{\frac{1}{4}} {\left(\sqrt{2} x - x - 1\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} {\left(8 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + {\left(8^{\frac{3}{4}} {\left(5 \, \sqrt{2} + 6\right)} + 8 \cdot 8^{\frac{1}{4}} {\left(2 \, \sqrt{2} + 1\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 64 \, \sqrt{2} + 32\right)} - \frac{1}{7} \, \sqrt{x^{2} + x} {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} + \frac{1}{7} \, \sqrt{2} {\left(8 \, x + 3\right)} + \frac{1}{56} \, {\left(8^{\frac{3}{4}} {\left(\sqrt{2} {\left(5 \, x + 1\right)} + 6 \, x + 4\right)} - \sqrt{x^{2} + x} {\left(8^{\frac{3}{4}} {\left(5 \, \sqrt{2} + 6\right)} + 8 \cdot 8^{\frac{1}{4}} {\left(2 \, \sqrt{2} + 1\right)}\right)} + 8 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} {\left(2 \, x - 1\right)} + x + 3\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + \frac{4}{7} \, x + \frac{5}{7}\right) + \frac{1}{2} \cdot 8^{\frac{1}{4}} \sqrt{2} \sqrt{2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{7} \, \sqrt{2} {\left(\sqrt{2} {\left(5 \, x + 1\right)} + 6 \, x + 4\right)} - \frac{1}{112} \, \sqrt{8 \, x^{2} - 8 \, \sqrt{x^{2} + x} x + 2 \, {\left(8^{\frac{1}{4}} \sqrt{x^{2} + x} {\left(\sqrt{2} - 1\right)} - 8^{\frac{1}{4}} {\left(\sqrt{2} x - x - 1\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 4 \, x + 4 \, \sqrt{2} + 4} {\left(8 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} - {\left(8^{\frac{3}{4}} {\left(5 \, \sqrt{2} + 6\right)} + 8 \cdot 8^{\frac{1}{4}} {\left(2 \, \sqrt{2} + 1\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} + 64 \, \sqrt{2} + 32\right)} + \frac{1}{7} \, \sqrt{x^{2} + x} {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} - \frac{1}{7} \, \sqrt{2} {\left(8 \, x + 3\right)} + \frac{1}{56} \, {\left(8^{\frac{3}{4}} {\left(\sqrt{2} {\left(5 \, x + 1\right)} + 6 \, x + 4\right)} - \sqrt{x^{2} + x} {\left(8^{\frac{3}{4}} {\left(5 \, \sqrt{2} + 6\right)} + 8 \cdot 8^{\frac{1}{4}} {\left(2 \, \sqrt{2} + 1\right)}\right)} + 8 \cdot 8^{\frac{1}{4}} {\left(\sqrt{2} {\left(2 \, x - 1\right)} + x + 3\right)}\right)} \sqrt{2 \, \sqrt{2} + 4} - \frac{4}{7} \, x - \frac{5}{7}\right) + \frac{1}{4} \, \sqrt{x^{2} + x} {\left(2 \, x + 5\right)} + \frac{5}{8} \, \log\left(-2 \, x + 2 \, \sqrt{x^{2} + x} - 1\right)"," ",0,"-1/8*8^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(8*x^2 - 8*sqrt(x^2 + x)*x + 2*(8^(1/4)*sqrt(x^2 + x)*(sqrt(2) - 1) - 8^(1/4)*(sqrt(2)*x - x - 1))*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) + 1/8*8^(1/4)*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2)*log(8*x^2 - 8*sqrt(x^2 + x)*x - 2*(8^(1/4)*sqrt(x^2 + x)*(sqrt(2) - 1) - 8^(1/4)*(sqrt(2)*x - x - 1))*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4) + 1/2*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2) + 4)*arctan(1/7*sqrt(2)*(sqrt(2)*(5*x + 1) + 6*x + 4) + 1/112*sqrt(8*x^2 - 8*sqrt(x^2 + x)*x - 2*(8^(1/4)*sqrt(x^2 + x)*(sqrt(2) - 1) - 8^(1/4)*(sqrt(2)*x - x - 1))*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*(8*sqrt(2)*(5*sqrt(2) + 6) + (8^(3/4)*(5*sqrt(2) + 6) + 8*8^(1/4)*(2*sqrt(2) + 1))*sqrt(2*sqrt(2) + 4) + 64*sqrt(2) + 32) - 1/7*sqrt(x^2 + x)*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4) + 1/7*sqrt(2)*(8*x + 3) + 1/56*(8^(3/4)*(sqrt(2)*(5*x + 1) + 6*x + 4) - sqrt(x^2 + x)*(8^(3/4)*(5*sqrt(2) + 6) + 8*8^(1/4)*(2*sqrt(2) + 1)) + 8*8^(1/4)*(sqrt(2)*(2*x - 1) + x + 3))*sqrt(2*sqrt(2) + 4) + 4/7*x + 5/7) + 1/2*8^(1/4)*sqrt(2)*sqrt(2*sqrt(2) + 4)*arctan(-1/7*sqrt(2)*(sqrt(2)*(5*x + 1) + 6*x + 4) - 1/112*sqrt(8*x^2 - 8*sqrt(x^2 + x)*x + 2*(8^(1/4)*sqrt(x^2 + x)*(sqrt(2) - 1) - 8^(1/4)*(sqrt(2)*x - x - 1))*sqrt(2*sqrt(2) + 4) + 4*x + 4*sqrt(2) + 4)*(8*sqrt(2)*(5*sqrt(2) + 6) - (8^(3/4)*(5*sqrt(2) + 6) + 8*8^(1/4)*(2*sqrt(2) + 1))*sqrt(2*sqrt(2) + 4) + 64*sqrt(2) + 32) + 1/7*sqrt(x^2 + x)*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4) - 1/7*sqrt(2)*(8*x + 3) + 1/56*(8^(3/4)*(sqrt(2)*(5*x + 1) + 6*x + 4) - sqrt(x^2 + x)*(8^(3/4)*(5*sqrt(2) + 6) + 8*8^(1/4)*(2*sqrt(2) + 1)) + 8*8^(1/4)*(sqrt(2)*(2*x - 1) + x + 3))*sqrt(2*sqrt(2) + 4) - 4/7*x - 5/7) + 1/4*sqrt(x^2 + x)*(2*x + 5) + 5/8*log(-2*x + 2*sqrt(x^2 + x) - 1)","B",0
94,-1,0,0,0.000000," ","integrate(x^4/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
95,-1,0,0,0.000000," ","integrate(x^3/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
96,-1,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,1,2753,0,1.051131," ","integrate(x/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{c d + a f + {\left(c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}}} \log\left(\frac{2 \, b c d x + b^{2} d + 2 \, {\left(b^{2} d f - {\left(c^{3} d^{3} f + a^{3} f^{4} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{2} f^{2} - {\left(a b^{2} - 3 \, a^{2} c\right)} d f^{3}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d + a f + {\left(c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}}} - {\left(2 \, a c^{2} d^{2} f + 2 \, a^{3} f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d f^{2} + {\left(b c^{2} d^{2} f + a^{2} b f^{3} - {\left(b^{3} - 2 \, a b c\right)} d f^{2}\right)} x\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{\frac{c d + a f + {\left(c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}}} \log\left(\frac{2 \, b c d x + b^{2} d - 2 \, {\left(b^{2} d f - {\left(c^{3} d^{3} f + a^{3} f^{4} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{2} f^{2} - {\left(a b^{2} - 3 \, a^{2} c\right)} d f^{3}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d + a f + {\left(c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}}} - {\left(2 \, a c^{2} d^{2} f + 2 \, a^{3} f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d f^{2} + {\left(b c^{2} d^{2} f + a^{2} b f^{3} - {\left(b^{3} - 2 \, a b c\right)} d f^{2}\right)} x\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{x}\right) + \frac{1}{4} \, \sqrt{\frac{c d + a f - {\left(c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}}} \log\left(\frac{2 \, b c d x + b^{2} d + 2 \, {\left(b^{2} d f + {\left(c^{3} d^{3} f + a^{3} f^{4} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{2} f^{2} - {\left(a b^{2} - 3 \, a^{2} c\right)} d f^{3}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d + a f - {\left(c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}}} + {\left(2 \, a c^{2} d^{2} f + 2 \, a^{3} f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d f^{2} + {\left(b c^{2} d^{2} f + a^{2} b f^{3} - {\left(b^{3} - 2 \, a b c\right)} d f^{2}\right)} x\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{x}\right) - \frac{1}{4} \, \sqrt{\frac{c d + a f - {\left(c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}}} \log\left(\frac{2 \, b c d x + b^{2} d - 2 \, {\left(b^{2} d f + {\left(c^{3} d^{3} f + a^{3} f^{4} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{2} f^{2} - {\left(a b^{2} - 3 \, a^{2} c\right)} d f^{3}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d + a f - {\left(c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{c^{2} d^{2} f + a^{2} f^{3} - {\left(b^{2} - 2 \, a c\right)} d f^{2}}} + {\left(2 \, a c^{2} d^{2} f + 2 \, a^{3} f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d f^{2} + {\left(b c^{2} d^{2} f + a^{2} b f^{3} - {\left(b^{3} - 2 \, a b c\right)} d f^{2}\right)} x\right)} \sqrt{\frac{b^{2} d}{c^{4} d^{4} f + a^{4} f^{5} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{3} f^{2} + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{2} f^{3} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d f^{4}}}}{x}\right)"," ",0,"1/4*sqrt((c*d + a*f + (c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/(c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2))*log((2*b*c*d*x + b^2*d + 2*(b^2*d*f - (c^3*d^3*f + a^3*f^4 - (b^2*c - 3*a*c^2)*d^2*f^2 - (a*b^2 - 3*a^2*c)*d*f^3)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d + a*f + (c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/(c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)) - (2*a*c^2*d^2*f + 2*a^3*f^3 - 2*(a*b^2 - 2*a^2*c)*d*f^2 + (b*c^2*d^2*f + a^2*b*f^3 - (b^3 - 2*a*b*c)*d*f^2)*x)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/x) - 1/4*sqrt((c*d + a*f + (c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/(c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2))*log((2*b*c*d*x + b^2*d - 2*(b^2*d*f - (c^3*d^3*f + a^3*f^4 - (b^2*c - 3*a*c^2)*d^2*f^2 - (a*b^2 - 3*a^2*c)*d*f^3)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d + a*f + (c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/(c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)) - (2*a*c^2*d^2*f + 2*a^3*f^3 - 2*(a*b^2 - 2*a^2*c)*d*f^2 + (b*c^2*d^2*f + a^2*b*f^3 - (b^3 - 2*a*b*c)*d*f^2)*x)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/x) + 1/4*sqrt((c*d + a*f - (c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/(c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2))*log((2*b*c*d*x + b^2*d + 2*(b^2*d*f + (c^3*d^3*f + a^3*f^4 - (b^2*c - 3*a*c^2)*d^2*f^2 - (a*b^2 - 3*a^2*c)*d*f^3)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d + a*f - (c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/(c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)) + (2*a*c^2*d^2*f + 2*a^3*f^3 - 2*(a*b^2 - 2*a^2*c)*d*f^2 + (b*c^2*d^2*f + a^2*b*f^3 - (b^3 - 2*a*b*c)*d*f^2)*x)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/x) - 1/4*sqrt((c*d + a*f - (c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/(c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2))*log((2*b*c*d*x + b^2*d - 2*(b^2*d*f + (c^3*d^3*f + a^3*f^4 - (b^2*c - 3*a*c^2)*d^2*f^2 - (a*b^2 - 3*a^2*c)*d*f^3)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d + a*f - (c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/(c^2*d^2*f + a^2*f^3 - (b^2 - 2*a*c)*d*f^2)) + (2*a*c^2*d^2*f + 2*a^3*f^3 - 2*(a*b^2 - 2*a^2*c)*d*f^2 + (b*c^2*d^2*f + a^2*b*f^3 - (b^3 - 2*a*b*c)*d*f^2)*x)*sqrt(b^2*d/(c^4*d^4*f + a^4*f^5 - 2*(b^2*c^2 - 2*a*c^3)*d^3*f^2 + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^2*f^3 - 2*(a^2*b^2 - 2*a^3*c)*d*f^4)))/x)","B",0
98,1,2641,0,1.241873," ","integrate(1/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{c d + a f + {\left(c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f}} \log\left(\frac{2 \, b c x + b^{2} + 2 \, {\left(b c d + a b f - {\left(b c^{2} d^{3} + a^{2} b d f^{2} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d + a f + {\left(c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f}} - {\left(2 \, a c^{2} d^{2} + 2 \, a^{3} f^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d f + {\left(b c^{2} d^{2} + a^{2} b f^{2} - {\left(b^{3} - 2 \, a b c\right)} d f\right)} x\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{x}\right) - \frac{1}{4} \, \sqrt{\frac{c d + a f + {\left(c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f}} \log\left(\frac{2 \, b c x + b^{2} - 2 \, {\left(b c d + a b f - {\left(b c^{2} d^{3} + a^{2} b d f^{2} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d + a f + {\left(c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f}} - {\left(2 \, a c^{2} d^{2} + 2 \, a^{3} f^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d f + {\left(b c^{2} d^{2} + a^{2} b f^{2} - {\left(b^{3} - 2 \, a b c\right)} d f\right)} x\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{x}\right) + \frac{1}{4} \, \sqrt{\frac{c d + a f - {\left(c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f}} \log\left(\frac{2 \, b c x + b^{2} + 2 \, {\left(b c d + a b f + {\left(b c^{2} d^{3} + a^{2} b d f^{2} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d + a f - {\left(c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f}} + {\left(2 \, a c^{2} d^{2} + 2 \, a^{3} f^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d f + {\left(b c^{2} d^{2} + a^{2} b f^{2} - {\left(b^{3} - 2 \, a b c\right)} d f\right)} x\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{x}\right) - \frac{1}{4} \, \sqrt{\frac{c d + a f - {\left(c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f}} \log\left(\frac{2 \, b c x + b^{2} - 2 \, {\left(b c d + a b f + {\left(b c^{2} d^{3} + a^{2} b d f^{2} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d + a f - {\left(c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{c^{2} d^{3} + a^{2} d f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2} f}} + {\left(2 \, a c^{2} d^{2} + 2 \, a^{3} f^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d f + {\left(b c^{2} d^{2} + a^{2} b f^{2} - {\left(b^{3} - 2 \, a b c\right)} d f\right)} x\right)} \sqrt{\frac{b^{2} f}{c^{4} d^{5} + a^{4} d f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2} f^{3}}}}{x}\right)"," ",0,"1/4*sqrt((c*d + a*f + (c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/(c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f))*log((2*b*c*x + b^2 + 2*(b*c*d + a*b*f - (b*c^2*d^3 + a^2*b*d*f^2 - (b^3 - 2*a*b*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d + a*f + (c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/(c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)) - (2*a*c^2*d^2 + 2*a^3*f^2 - 2*(a*b^2 - 2*a^2*c)*d*f + (b*c^2*d^2 + a^2*b*f^2 - (b^3 - 2*a*b*c)*d*f)*x)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/x) - 1/4*sqrt((c*d + a*f + (c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/(c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f))*log((2*b*c*x + b^2 - 2*(b*c*d + a*b*f - (b*c^2*d^3 + a^2*b*d*f^2 - (b^3 - 2*a*b*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d + a*f + (c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/(c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)) - (2*a*c^2*d^2 + 2*a^3*f^2 - 2*(a*b^2 - 2*a^2*c)*d*f + (b*c^2*d^2 + a^2*b*f^2 - (b^3 - 2*a*b*c)*d*f)*x)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/x) + 1/4*sqrt((c*d + a*f - (c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/(c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f))*log((2*b*c*x + b^2 + 2*(b*c*d + a*b*f + (b*c^2*d^3 + a^2*b*d*f^2 - (b^3 - 2*a*b*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d + a*f - (c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/(c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)) + (2*a*c^2*d^2 + 2*a^3*f^2 - 2*(a*b^2 - 2*a^2*c)*d*f + (b*c^2*d^2 + a^2*b*f^2 - (b^3 - 2*a*b*c)*d*f)*x)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/x) - 1/4*sqrt((c*d + a*f - (c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/(c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f))*log((2*b*c*x + b^2 - 2*(b*c*d + a*b*f + (b*c^2*d^3 + a^2*b*d*f^2 - (b^3 - 2*a*b*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d + a*f - (c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/(c^2*d^3 + a^2*d*f^2 - (b^2 - 2*a*c)*d^2*f)) + (2*a*c^2*d^2 + 2*a^3*f^2 - 2*(a*b^2 - 2*a^2*c)*d*f + (b*c^2*d^2 + a^2*b*f^2 - (b^3 - 2*a*b*c)*d*f)*x)*sqrt(b^2*f/(c^4*d^5 + a^4*d*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^4*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^2*f^3)))/x)","B",0
99,1,5995,0,70.192646," ","integrate(1/x/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\left[\frac{a d \sqrt{\frac{c d f + a f^{2} + {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} \log\left(\frac{2 \, b c f^{2} x + b^{2} f^{2} + 2 \, {\left(b^{2} d f^{2} - {\left(c^{3} d^{5} + a^{3} d^{2} f^{3} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} f - {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3} f^{2}\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d f + a f^{2} + {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} - {\left(2 \, a c^{2} d^{3} f + 2 \, a^{3} d f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} f^{2} + {\left(b c^{2} d^{3} f + a^{2} b d f^{3} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f^{2}\right)} x\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{x}\right) - a d \sqrt{\frac{c d f + a f^{2} + {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} \log\left(\frac{2 \, b c f^{2} x + b^{2} f^{2} - 2 \, {\left(b^{2} d f^{2} - {\left(c^{3} d^{5} + a^{3} d^{2} f^{3} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} f - {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3} f^{2}\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d f + a f^{2} + {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} - {\left(2 \, a c^{2} d^{3} f + 2 \, a^{3} d f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} f^{2} + {\left(b c^{2} d^{3} f + a^{2} b d f^{3} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f^{2}\right)} x\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{x}\right) + a d \sqrt{\frac{c d f + a f^{2} - {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} \log\left(\frac{2 \, b c f^{2} x + b^{2} f^{2} + 2 \, {\left(b^{2} d f^{2} + {\left(c^{3} d^{5} + a^{3} d^{2} f^{3} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} f - {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3} f^{2}\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d f + a f^{2} - {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} + {\left(2 \, a c^{2} d^{3} f + 2 \, a^{3} d f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} f^{2} + {\left(b c^{2} d^{3} f + a^{2} b d f^{3} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f^{2}\right)} x\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{x}\right) - a d \sqrt{\frac{c d f + a f^{2} - {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} \log\left(\frac{2 \, b c f^{2} x + b^{2} f^{2} - 2 \, {\left(b^{2} d f^{2} + {\left(c^{3} d^{5} + a^{3} d^{2} f^{3} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} f - {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3} f^{2}\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d f + a f^{2} - {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} + {\left(2 \, a c^{2} d^{3} f + 2 \, a^{3} d f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} f^{2} + {\left(b c^{2} d^{3} f + a^{2} b d f^{3} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f^{2}\right)} x\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{x}\right) + 2 \, \sqrt{a} \log\left(-\frac{8 \, a b x + {\left(b^{2} + 4 \, a c\right)} x^{2} - 4 \, \sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{a} + 8 \, a^{2}}{x^{2}}\right)}{4 \, a d}, \frac{a d \sqrt{\frac{c d f + a f^{2} + {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} \log\left(\frac{2 \, b c f^{2} x + b^{2} f^{2} + 2 \, {\left(b^{2} d f^{2} - {\left(c^{3} d^{5} + a^{3} d^{2} f^{3} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} f - {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3} f^{2}\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d f + a f^{2} + {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} - {\left(2 \, a c^{2} d^{3} f + 2 \, a^{3} d f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} f^{2} + {\left(b c^{2} d^{3} f + a^{2} b d f^{3} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f^{2}\right)} x\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{x}\right) - a d \sqrt{\frac{c d f + a f^{2} + {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} \log\left(\frac{2 \, b c f^{2} x + b^{2} f^{2} - 2 \, {\left(b^{2} d f^{2} - {\left(c^{3} d^{5} + a^{3} d^{2} f^{3} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} f - {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3} f^{2}\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d f + a f^{2} + {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} - {\left(2 \, a c^{2} d^{3} f + 2 \, a^{3} d f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} f^{2} + {\left(b c^{2} d^{3} f + a^{2} b d f^{3} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f^{2}\right)} x\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{x}\right) + a d \sqrt{\frac{c d f + a f^{2} - {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} \log\left(\frac{2 \, b c f^{2} x + b^{2} f^{2} + 2 \, {\left(b^{2} d f^{2} + {\left(c^{3} d^{5} + a^{3} d^{2} f^{3} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} f - {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3} f^{2}\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d f + a f^{2} - {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} + {\left(2 \, a c^{2} d^{3} f + 2 \, a^{3} d f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} f^{2} + {\left(b c^{2} d^{3} f + a^{2} b d f^{3} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f^{2}\right)} x\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{x}\right) - a d \sqrt{\frac{c d f + a f^{2} - {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} \log\left(\frac{2 \, b c f^{2} x + b^{2} f^{2} - 2 \, {\left(b^{2} d f^{2} + {\left(c^{3} d^{5} + a^{3} d^{2} f^{3} - {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} f - {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3} f^{2}\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c d f + a f^{2} - {\left(c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{c^{2} d^{4} + a^{2} d^{2} f^{2} - {\left(b^{2} - 2 \, a c\right)} d^{3} f}} + {\left(2 \, a c^{2} d^{3} f + 2 \, a^{3} d f^{3} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2} f^{2} + {\left(b c^{2} d^{3} f + a^{2} b d f^{3} - {\left(b^{3} - 2 \, a b c\right)} d^{2} f^{2}\right)} x\right)} \sqrt{\frac{b^{2} f^{3}}{c^{4} d^{7} + a^{4} d^{3} f^{4} - 2 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{6} f + {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{5} f^{2} - 2 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{4} f^{3}}}}{x}\right) + 4 \, \sqrt{-a} \arctan\left(\frac{\sqrt{c x^{2} + b x + a} {\left(b x + 2 \, a\right)} \sqrt{-a}}{2 \, {\left(a c x^{2} + a b x + a^{2}\right)}}\right)}{4 \, a d}\right]"," ",0,"[1/4*(a*d*sqrt((c*d*f + a*f^2 + (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f))*log((2*b*c*f^2*x + b^2*f^2 + 2*(b^2*d*f^2 - (c^3*d^5 + a^3*d^2*f^3 - (b^2*c - 3*a*c^2)*d^4*f - (a*b^2 - 3*a^2*c)*d^3*f^2)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d*f + a*f^2 + (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)) - (2*a*c^2*d^3*f + 2*a^3*d*f^3 - 2*(a*b^2 - 2*a^2*c)*d^2*f^2 + (b*c^2*d^3*f + a^2*b*d*f^3 - (b^3 - 2*a*b*c)*d^2*f^2)*x)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/x) - a*d*sqrt((c*d*f + a*f^2 + (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f))*log((2*b*c*f^2*x + b^2*f^2 - 2*(b^2*d*f^2 - (c^3*d^5 + a^3*d^2*f^3 - (b^2*c - 3*a*c^2)*d^4*f - (a*b^2 - 3*a^2*c)*d^3*f^2)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d*f + a*f^2 + (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)) - (2*a*c^2*d^3*f + 2*a^3*d*f^3 - 2*(a*b^2 - 2*a^2*c)*d^2*f^2 + (b*c^2*d^3*f + a^2*b*d*f^3 - (b^3 - 2*a*b*c)*d^2*f^2)*x)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/x) + a*d*sqrt((c*d*f + a*f^2 - (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f))*log((2*b*c*f^2*x + b^2*f^2 + 2*(b^2*d*f^2 + (c^3*d^5 + a^3*d^2*f^3 - (b^2*c - 3*a*c^2)*d^4*f - (a*b^2 - 3*a^2*c)*d^3*f^2)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d*f + a*f^2 - (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)) + (2*a*c^2*d^3*f + 2*a^3*d*f^3 - 2*(a*b^2 - 2*a^2*c)*d^2*f^2 + (b*c^2*d^3*f + a^2*b*d*f^3 - (b^3 - 2*a*b*c)*d^2*f^2)*x)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/x) - a*d*sqrt((c*d*f + a*f^2 - (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f))*log((2*b*c*f^2*x + b^2*f^2 - 2*(b^2*d*f^2 + (c^3*d^5 + a^3*d^2*f^3 - (b^2*c - 3*a*c^2)*d^4*f - (a*b^2 - 3*a^2*c)*d^3*f^2)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d*f + a*f^2 - (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)) + (2*a*c^2*d^3*f + 2*a^3*d*f^3 - 2*(a*b^2 - 2*a^2*c)*d^2*f^2 + (b*c^2*d^3*f + a^2*b*d*f^3 - (b^3 - 2*a*b*c)*d^2*f^2)*x)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/x) + 2*sqrt(a)*log(-(8*a*b*x + (b^2 + 4*a*c)*x^2 - 4*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(a) + 8*a^2)/x^2))/(a*d), 1/4*(a*d*sqrt((c*d*f + a*f^2 + (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f))*log((2*b*c*f^2*x + b^2*f^2 + 2*(b^2*d*f^2 - (c^3*d^5 + a^3*d^2*f^3 - (b^2*c - 3*a*c^2)*d^4*f - (a*b^2 - 3*a^2*c)*d^3*f^2)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d*f + a*f^2 + (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)) - (2*a*c^2*d^3*f + 2*a^3*d*f^3 - 2*(a*b^2 - 2*a^2*c)*d^2*f^2 + (b*c^2*d^3*f + a^2*b*d*f^3 - (b^3 - 2*a*b*c)*d^2*f^2)*x)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/x) - a*d*sqrt((c*d*f + a*f^2 + (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f))*log((2*b*c*f^2*x + b^2*f^2 - 2*(b^2*d*f^2 - (c^3*d^5 + a^3*d^2*f^3 - (b^2*c - 3*a*c^2)*d^4*f - (a*b^2 - 3*a^2*c)*d^3*f^2)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d*f + a*f^2 + (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)) - (2*a*c^2*d^3*f + 2*a^3*d*f^3 - 2*(a*b^2 - 2*a^2*c)*d^2*f^2 + (b*c^2*d^3*f + a^2*b*d*f^3 - (b^3 - 2*a*b*c)*d^2*f^2)*x)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/x) + a*d*sqrt((c*d*f + a*f^2 - (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f))*log((2*b*c*f^2*x + b^2*f^2 + 2*(b^2*d*f^2 + (c^3*d^5 + a^3*d^2*f^3 - (b^2*c - 3*a*c^2)*d^4*f - (a*b^2 - 3*a^2*c)*d^3*f^2)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d*f + a*f^2 - (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)) + (2*a*c^2*d^3*f + 2*a^3*d*f^3 - 2*(a*b^2 - 2*a^2*c)*d^2*f^2 + (b*c^2*d^3*f + a^2*b*d*f^3 - (b^3 - 2*a*b*c)*d^2*f^2)*x)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/x) - a*d*sqrt((c*d*f + a*f^2 - (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f))*log((2*b*c*f^2*x + b^2*f^2 - 2*(b^2*d*f^2 + (c^3*d^5 + a^3*d^2*f^3 - (b^2*c - 3*a*c^2)*d^4*f - (a*b^2 - 3*a^2*c)*d^3*f^2)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))*sqrt(c*x^2 + b*x + a)*sqrt((c*d*f + a*f^2 - (c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/(c^2*d^4 + a^2*d^2*f^2 - (b^2 - 2*a*c)*d^3*f)) + (2*a*c^2*d^3*f + 2*a^3*d*f^3 - 2*(a*b^2 - 2*a^2*c)*d^2*f^2 + (b*c^2*d^3*f + a^2*b*d*f^3 - (b^3 - 2*a*b*c)*d^2*f^2)*x)*sqrt(b^2*f^3/(c^4*d^7 + a^4*d^3*f^4 - 2*(b^2*c^2 - 2*a*c^3)*d^6*f + (b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^5*f^2 - 2*(a^2*b^2 - 2*a^3*c)*d^4*f^3)))/x) + 4*sqrt(-a)*arctan(1/2*sqrt(c*x^2 + b*x + a)*(b*x + 2*a)*sqrt(-a)/(a*c*x^2 + a*b*x + a^2)))/(a*d)]","B",0
100,-1,0,0,0.000000," ","integrate(1/x^2/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
101,-1,0,0,0.000000," ","integrate(1/x^3/(c*x^2+b*x+a)^(1/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
102,-1,0,0,0.000000," ","integrate(x^4/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
103,-1,0,0,0.000000," ","integrate(x^3/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,-1,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,-1,0,0,0.000000," ","integrate(x/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
106,-1,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
107,-1,0,0,0.000000," ","integrate(1/x/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate(1/x^2/(c*x^2+b*x+a)^(3/2)/(-f*x^2+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,-1,0,0,0.000000," ","integrate(x^2*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
110,-1,0,0,0.000000," ","integrate(x*(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
111,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
112,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/x/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
113,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/x^2/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,-1,0,0,0.000000," ","integrate(x^3/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
115,-1,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
116,1,11311,0,14.498570," ","integrate(x/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \sqrt{\frac{2 \, c d^{2} - b d e + a e^{2} - 2 \, a d f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} \log\left(-\frac{2 \, b^{2} d^{3} - 4 \, a b d^{2} e + 2 \, a^{2} d e^{2} + \sqrt{2} {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4} - 4 \, {\left(b^{2} d^{3} - 2 \, a b d^{2} e + a^{2} d e^{2}\right)} f - {\left(2 \, c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} - 2 \, a b c d e^{5} + a^{2} c e^{6} + 8 \, a^{3} d^{2} f^{4} + {\left(b^{2} c + 3 \, a c^{2}\right)} d^{2} e^{4} - 2 \, {\left(2 \, a^{2} b d^{2} e + 3 \, a^{3} d e^{2} - 4 \, {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3}\right)} f^{3} + {\left(5 \, a^{2} b d e^{3} + a^{3} e^{4} - 8 \, {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} + 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{3} e - 2 \, {\left(5 \, a b^{2} - 11 \, a^{2} c\right)} d^{2} e^{2}\right)} f^{2} - {\left(8 \, c^{3} d^{5} - 12 \, b c^{2} d^{4} e + a^{2} b e^{5} + 2 \, {\left(b^{2} c + 9 \, a c^{2}\right)} d^{3} e^{2} + {\left(b^{3} - 10 \, a b c\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{4}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{2 \, c d^{2} - b d e + a e^{2} - 2 \, a d f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} + {\left(4 \, b c d^{3} + a b d e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} e\right)} x - {\left(2 \, a c^{2} d^{3} e^{2} - 2 \, a b c d^{2} e^{3} + 2 \, a^{2} c d e^{4} - 8 \, a^{3} d^{2} f^{3} + 2 \, {\left(4 \, a^{2} b d^{2} e + a^{3} d e^{2} - 4 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{3}\right)} f^{2} - 2 \, {\left(4 \, a c^{2} d^{4} - 4 \, a b c d^{3} e + a^{2} b d e^{3} - {\left(a b^{2} - 6 \, a^{2} c\right)} d^{2} e^{2}\right)} f + {\left(b c^{2} d^{3} e^{2} - b^{2} c d^{2} e^{3} + a b c d e^{4} - 4 \, a^{2} b d^{2} f^{3} + {\left(4 \, a b^{2} d^{2} e + a^{2} b d e^{2} - 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{3}\right)} f^{2} - {\left(4 \, b c^{2} d^{4} - 4 \, b^{2} c d^{3} e + a b^{2} d e^{3} - {\left(b^{3} - 6 \, a b c\right)} d^{2} e^{2}\right)} f\right)} x\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{2 \, c d^{2} - b d e + a e^{2} - 2 \, a d f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} \log\left(-\frac{2 \, b^{2} d^{3} - 4 \, a b d^{2} e + 2 \, a^{2} d e^{2} - \sqrt{2} {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4} - 4 \, {\left(b^{2} d^{3} - 2 \, a b d^{2} e + a^{2} d e^{2}\right)} f - {\left(2 \, c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} - 2 \, a b c d e^{5} + a^{2} c e^{6} + 8 \, a^{3} d^{2} f^{4} + {\left(b^{2} c + 3 \, a c^{2}\right)} d^{2} e^{4} - 2 \, {\left(2 \, a^{2} b d^{2} e + 3 \, a^{3} d e^{2} - 4 \, {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3}\right)} f^{3} + {\left(5 \, a^{2} b d e^{3} + a^{3} e^{4} - 8 \, {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} + 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{3} e - 2 \, {\left(5 \, a b^{2} - 11 \, a^{2} c\right)} d^{2} e^{2}\right)} f^{2} - {\left(8 \, c^{3} d^{5} - 12 \, b c^{2} d^{4} e + a^{2} b e^{5} + 2 \, {\left(b^{2} c + 9 \, a c^{2}\right)} d^{3} e^{2} + {\left(b^{3} - 10 \, a b c\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{4}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{2 \, c d^{2} - b d e + a e^{2} - 2 \, a d f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} + {\left(4 \, b c d^{3} + a b d e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} e\right)} x - {\left(2 \, a c^{2} d^{3} e^{2} - 2 \, a b c d^{2} e^{3} + 2 \, a^{2} c d e^{4} - 8 \, a^{3} d^{2} f^{3} + 2 \, {\left(4 \, a^{2} b d^{2} e + a^{3} d e^{2} - 4 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{3}\right)} f^{2} - 2 \, {\left(4 \, a c^{2} d^{4} - 4 \, a b c d^{3} e + a^{2} b d e^{3} - {\left(a b^{2} - 6 \, a^{2} c\right)} d^{2} e^{2}\right)} f + {\left(b c^{2} d^{3} e^{2} - b^{2} c d^{2} e^{3} + a b c d e^{4} - 4 \, a^{2} b d^{2} f^{3} + {\left(4 \, a b^{2} d^{2} e + a^{2} b d e^{2} - 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{3}\right)} f^{2} - {\left(4 \, b c^{2} d^{4} - 4 \, b^{2} c d^{3} e + a b^{2} d e^{3} - {\left(b^{3} - 6 \, a b c\right)} d^{2} e^{2}\right)} f\right)} x\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{x}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{2 \, c d^{2} - b d e + a e^{2} - 2 \, a d f - {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} \log\left(-\frac{2 \, b^{2} d^{3} - 4 \, a b d^{2} e + 2 \, a^{2} d e^{2} + \sqrt{2} {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4} - 4 \, {\left(b^{2} d^{3} - 2 \, a b d^{2} e + a^{2} d e^{2}\right)} f + {\left(2 \, c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} - 2 \, a b c d e^{5} + a^{2} c e^{6} + 8 \, a^{3} d^{2} f^{4} + {\left(b^{2} c + 3 \, a c^{2}\right)} d^{2} e^{4} - 2 \, {\left(2 \, a^{2} b d^{2} e + 3 \, a^{3} d e^{2} - 4 \, {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3}\right)} f^{3} + {\left(5 \, a^{2} b d e^{3} + a^{3} e^{4} - 8 \, {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} + 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{3} e - 2 \, {\left(5 \, a b^{2} - 11 \, a^{2} c\right)} d^{2} e^{2}\right)} f^{2} - {\left(8 \, c^{3} d^{5} - 12 \, b c^{2} d^{4} e + a^{2} b e^{5} + 2 \, {\left(b^{2} c + 9 \, a c^{2}\right)} d^{3} e^{2} + {\left(b^{3} - 10 \, a b c\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{4}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{2 \, c d^{2} - b d e + a e^{2} - 2 \, a d f - {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} + {\left(4 \, b c d^{3} + a b d e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} e\right)} x + {\left(2 \, a c^{2} d^{3} e^{2} - 2 \, a b c d^{2} e^{3} + 2 \, a^{2} c d e^{4} - 8 \, a^{3} d^{2} f^{3} + 2 \, {\left(4 \, a^{2} b d^{2} e + a^{3} d e^{2} - 4 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{3}\right)} f^{2} - 2 \, {\left(4 \, a c^{2} d^{4} - 4 \, a b c d^{3} e + a^{2} b d e^{3} - {\left(a b^{2} - 6 \, a^{2} c\right)} d^{2} e^{2}\right)} f + {\left(b c^{2} d^{3} e^{2} - b^{2} c d^{2} e^{3} + a b c d e^{4} - 4 \, a^{2} b d^{2} f^{3} + {\left(4 \, a b^{2} d^{2} e + a^{2} b d e^{2} - 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{3}\right)} f^{2} - {\left(4 \, b c^{2} d^{4} - 4 \, b^{2} c d^{3} e + a b^{2} d e^{3} - {\left(b^{3} - 6 \, a b c\right)} d^{2} e^{2}\right)} f\right)} x\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{2 \, c d^{2} - b d e + a e^{2} - 2 \, a d f - {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} \log\left(-\frac{2 \, b^{2} d^{3} - 4 \, a b d^{2} e + 2 \, a^{2} d e^{2} - \sqrt{2} {\left(b^{2} d^{2} e^{2} - 2 \, a b d e^{3} + a^{2} e^{4} - 4 \, {\left(b^{2} d^{3} - 2 \, a b d^{2} e + a^{2} d e^{2}\right)} f + {\left(2 \, c^{3} d^{4} e^{2} - 3 \, b c^{2} d^{3} e^{3} - 2 \, a b c d e^{5} + a^{2} c e^{6} + 8 \, a^{3} d^{2} f^{4} + {\left(b^{2} c + 3 \, a c^{2}\right)} d^{2} e^{4} - 2 \, {\left(2 \, a^{2} b d^{2} e + 3 \, a^{3} d e^{2} - 4 \, {\left(a b^{2} - 3 \, a^{2} c\right)} d^{3}\right)} f^{3} + {\left(5 \, a^{2} b d e^{3} + a^{3} e^{4} - 8 \, {\left(b^{2} c - 3 \, a c^{2}\right)} d^{4} + 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{3} e - 2 \, {\left(5 \, a b^{2} - 11 \, a^{2} c\right)} d^{2} e^{2}\right)} f^{2} - {\left(8 \, c^{3} d^{5} - 12 \, b c^{2} d^{4} e + a^{2} b e^{5} + 2 \, {\left(b^{2} c + 9 \, a c^{2}\right)} d^{3} e^{2} + {\left(b^{3} - 10 \, a b c\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{4}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{2 \, c d^{2} - b d e + a e^{2} - 2 \, a d f - {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} + {\left(4 \, b c d^{3} + a b d e^{2} - {\left(b^{2} + 4 \, a c\right)} d^{2} e\right)} x + {\left(2 \, a c^{2} d^{3} e^{2} - 2 \, a b c d^{2} e^{3} + 2 \, a^{2} c d e^{4} - 8 \, a^{3} d^{2} f^{3} + 2 \, {\left(4 \, a^{2} b d^{2} e + a^{3} d e^{2} - 4 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{3}\right)} f^{2} - 2 \, {\left(4 \, a c^{2} d^{4} - 4 \, a b c d^{3} e + a^{2} b d e^{3} - {\left(a b^{2} - 6 \, a^{2} c\right)} d^{2} e^{2}\right)} f + {\left(b c^{2} d^{3} e^{2} - b^{2} c d^{2} e^{3} + a b c d e^{4} - 4 \, a^{2} b d^{2} f^{3} + {\left(4 \, a b^{2} d^{2} e + a^{2} b d e^{2} - 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{3}\right)} f^{2} - {\left(4 \, b c^{2} d^{4} - 4 \, b^{2} c d^{3} e + a b^{2} d e^{3} - {\left(b^{3} - 6 \, a b c\right)} d^{2} e^{2}\right)} f\right)} x\right)} \sqrt{\frac{b^{2} d^{2} - 2 \, a b d e + a^{2} e^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{x}\right)"," ",0,"1/4*sqrt(2)*sqrt((2*c*d^2 - b*d*e + a*e^2 - 2*a*d*f + (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f))*log(-(2*b^2*d^3 - 4*a*b*d^2*e + 2*a^2*d*e^2 + sqrt(2)*(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4 - 4*(b^2*d^3 - 2*a*b*d^2*e + a^2*d*e^2)*f - (2*c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 - 2*a*b*c*d*e^5 + a^2*c*e^6 + 8*a^3*d^2*f^4 + (b^2*c + 3*a*c^2)*d^2*e^4 - 2*(2*a^2*b*d^2*e + 3*a^3*d*e^2 - 4*(a*b^2 - 3*a^2*c)*d^3)*f^3 + (5*a^2*b*d*e^3 + a^3*e^4 - 8*(b^2*c - 3*a*c^2)*d^4 + 4*(b^3 - 2*a*b*c)*d^3*e - 2*(5*a*b^2 - 11*a^2*c)*d^2*e^2)*f^2 - (8*c^3*d^5 - 12*b*c^2*d^4*e + a^2*b*e^5 + 2*(b^2*c + 9*a*c^2)*d^3*e^2 + (b^3 - 10*a*b*c)*d^2*e^3 - 2*(a*b^2 - 4*a^2*c)*d*e^4)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))*sqrt(c*x^2 + b*x + a)*sqrt((2*c*d^2 - b*d*e + a*e^2 - 2*a*d*f + (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)) + (4*b*c*d^3 + a*b*d*e^2 - (b^2 + 4*a*c)*d^2*e)*x - (2*a*c^2*d^3*e^2 - 2*a*b*c*d^2*e^3 + 2*a^2*c*d*e^4 - 8*a^3*d^2*f^3 + 2*(4*a^2*b*d^2*e + a^3*d*e^2 - 4*(a*b^2 - 2*a^2*c)*d^3)*f^2 - 2*(4*a*c^2*d^4 - 4*a*b*c*d^3*e + a^2*b*d*e^3 - (a*b^2 - 6*a^2*c)*d^2*e^2)*f + (b*c^2*d^3*e^2 - b^2*c*d^2*e^3 + a*b*c*d*e^4 - 4*a^2*b*d^2*f^3 + (4*a*b^2*d^2*e + a^2*b*d*e^2 - 4*(b^3 - 2*a*b*c)*d^3)*f^2 - (4*b*c^2*d^4 - 4*b^2*c*d^3*e + a*b^2*d*e^3 - (b^3 - 6*a*b*c)*d^2*e^2)*f)*x)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/x) - 1/4*sqrt(2)*sqrt((2*c*d^2 - b*d*e + a*e^2 - 2*a*d*f + (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f))*log(-(2*b^2*d^3 - 4*a*b*d^2*e + 2*a^2*d*e^2 - sqrt(2)*(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4 - 4*(b^2*d^3 - 2*a*b*d^2*e + a^2*d*e^2)*f - (2*c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 - 2*a*b*c*d*e^5 + a^2*c*e^6 + 8*a^3*d^2*f^4 + (b^2*c + 3*a*c^2)*d^2*e^4 - 2*(2*a^2*b*d^2*e + 3*a^3*d*e^2 - 4*(a*b^2 - 3*a^2*c)*d^3)*f^3 + (5*a^2*b*d*e^3 + a^3*e^4 - 8*(b^2*c - 3*a*c^2)*d^4 + 4*(b^3 - 2*a*b*c)*d^3*e - 2*(5*a*b^2 - 11*a^2*c)*d^2*e^2)*f^2 - (8*c^3*d^5 - 12*b*c^2*d^4*e + a^2*b*e^5 + 2*(b^2*c + 9*a*c^2)*d^3*e^2 + (b^3 - 10*a*b*c)*d^2*e^3 - 2*(a*b^2 - 4*a^2*c)*d*e^4)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))*sqrt(c*x^2 + b*x + a)*sqrt((2*c*d^2 - b*d*e + a*e^2 - 2*a*d*f + (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)) + (4*b*c*d^3 + a*b*d*e^2 - (b^2 + 4*a*c)*d^2*e)*x - (2*a*c^2*d^3*e^2 - 2*a*b*c*d^2*e^3 + 2*a^2*c*d*e^4 - 8*a^3*d^2*f^3 + 2*(4*a^2*b*d^2*e + a^3*d*e^2 - 4*(a*b^2 - 2*a^2*c)*d^3)*f^2 - 2*(4*a*c^2*d^4 - 4*a*b*c*d^3*e + a^2*b*d*e^3 - (a*b^2 - 6*a^2*c)*d^2*e^2)*f + (b*c^2*d^3*e^2 - b^2*c*d^2*e^3 + a*b*c*d*e^4 - 4*a^2*b*d^2*f^3 + (4*a*b^2*d^2*e + a^2*b*d*e^2 - 4*(b^3 - 2*a*b*c)*d^3)*f^2 - (4*b*c^2*d^4 - 4*b^2*c*d^3*e + a*b^2*d*e^3 - (b^3 - 6*a*b*c)*d^2*e^2)*f)*x)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/x) + 1/4*sqrt(2)*sqrt((2*c*d^2 - b*d*e + a*e^2 - 2*a*d*f - (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f))*log(-(2*b^2*d^3 - 4*a*b*d^2*e + 2*a^2*d*e^2 + sqrt(2)*(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4 - 4*(b^2*d^3 - 2*a*b*d^2*e + a^2*d*e^2)*f + (2*c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 - 2*a*b*c*d*e^5 + a^2*c*e^6 + 8*a^3*d^2*f^4 + (b^2*c + 3*a*c^2)*d^2*e^4 - 2*(2*a^2*b*d^2*e + 3*a^3*d*e^2 - 4*(a*b^2 - 3*a^2*c)*d^3)*f^3 + (5*a^2*b*d*e^3 + a^3*e^4 - 8*(b^2*c - 3*a*c^2)*d^4 + 4*(b^3 - 2*a*b*c)*d^3*e - 2*(5*a*b^2 - 11*a^2*c)*d^2*e^2)*f^2 - (8*c^3*d^5 - 12*b*c^2*d^4*e + a^2*b*e^5 + 2*(b^2*c + 9*a*c^2)*d^3*e^2 + (b^3 - 10*a*b*c)*d^2*e^3 - 2*(a*b^2 - 4*a^2*c)*d*e^4)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))*sqrt(c*x^2 + b*x + a)*sqrt((2*c*d^2 - b*d*e + a*e^2 - 2*a*d*f - (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)) + (4*b*c*d^3 + a*b*d*e^2 - (b^2 + 4*a*c)*d^2*e)*x + (2*a*c^2*d^3*e^2 - 2*a*b*c*d^2*e^3 + 2*a^2*c*d*e^4 - 8*a^3*d^2*f^3 + 2*(4*a^2*b*d^2*e + a^3*d*e^2 - 4*(a*b^2 - 2*a^2*c)*d^3)*f^2 - 2*(4*a*c^2*d^4 - 4*a*b*c*d^3*e + a^2*b*d*e^3 - (a*b^2 - 6*a^2*c)*d^2*e^2)*f + (b*c^2*d^3*e^2 - b^2*c*d^2*e^3 + a*b*c*d*e^4 - 4*a^2*b*d^2*f^3 + (4*a*b^2*d^2*e + a^2*b*d*e^2 - 4*(b^3 - 2*a*b*c)*d^3)*f^2 - (4*b*c^2*d^4 - 4*b^2*c*d^3*e + a*b^2*d*e^3 - (b^3 - 6*a*b*c)*d^2*e^2)*f)*x)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/x) - 1/4*sqrt(2)*sqrt((2*c*d^2 - b*d*e + a*e^2 - 2*a*d*f - (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f))*log(-(2*b^2*d^3 - 4*a*b*d^2*e + 2*a^2*d*e^2 - sqrt(2)*(b^2*d^2*e^2 - 2*a*b*d*e^3 + a^2*e^4 - 4*(b^2*d^3 - 2*a*b*d^2*e + a^2*d*e^2)*f + (2*c^3*d^4*e^2 - 3*b*c^2*d^3*e^3 - 2*a*b*c*d*e^5 + a^2*c*e^6 + 8*a^3*d^2*f^4 + (b^2*c + 3*a*c^2)*d^2*e^4 - 2*(2*a^2*b*d^2*e + 3*a^3*d*e^2 - 4*(a*b^2 - 3*a^2*c)*d^3)*f^3 + (5*a^2*b*d*e^3 + a^3*e^4 - 8*(b^2*c - 3*a*c^2)*d^4 + 4*(b^3 - 2*a*b*c)*d^3*e - 2*(5*a*b^2 - 11*a^2*c)*d^2*e^2)*f^2 - (8*c^3*d^5 - 12*b*c^2*d^4*e + a^2*b*e^5 + 2*(b^2*c + 9*a*c^2)*d^3*e^2 + (b^3 - 10*a*b*c)*d^2*e^3 - 2*(a*b^2 - 4*a^2*c)*d*e^4)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))*sqrt(c*x^2 + b*x + a)*sqrt((2*c*d^2 - b*d*e + a*e^2 - 2*a*d*f - (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)) + (4*b*c*d^3 + a*b*d*e^2 - (b^2 + 4*a*c)*d^2*e)*x + (2*a*c^2*d^3*e^2 - 2*a*b*c*d^2*e^3 + 2*a^2*c*d*e^4 - 8*a^3*d^2*f^3 + 2*(4*a^2*b*d^2*e + a^3*d*e^2 - 4*(a*b^2 - 2*a^2*c)*d^3)*f^2 - 2*(4*a*c^2*d^4 - 4*a*b*c*d^3*e + a^2*b*d*e^3 - (a*b^2 - 6*a^2*c)*d^2*e^2)*f + (b*c^2*d^3*e^2 - b^2*c*d^2*e^3 + a*b*c*d*e^4 - 4*a^2*b*d^2*f^3 + (4*a*b^2*d^2*e + a^2*b*d*e^2 - 4*(b^3 - 2*a*b*c)*d^3)*f^2 - (4*b*c^2*d^4 - 4*b^2*c*d^3*e + a*b^2*d*e^3 - (b^3 - 6*a*b*c)*d^2*e^2)*f)*x)*sqrt((b^2*d^2 - 2*a*b*d*e + a^2*e^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/x)","B",0
117,1,11287,0,17.214732," ","integrate(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \sqrt{\frac{c e^{2} + 2 \, a f^{2} - {\left(2 \, c d + b e\right)} f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} \log\left(\frac{2 \, {\left(b^{2} d - a b e\right)} f^{2} + \sqrt{2} {\left(c^{2} d e^{3} - 4 \, a b d f^{3} + {\left(4 \, b c d^{2} + 4 \, a c d e + a b e^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{2} e + b c d e^{2} + a c e^{3}\right)} f - {\left(c^{3} d^{3} e^{3} - b c^{2} d^{2} e^{4} + a c^{2} d e^{5} + 4 \, {\left(2 \, a^{2} b d^{2} - a^{3} d e\right)} f^{4} + {\left(2 \, a^{2} b d e^{2} + a^{3} e^{3} + 8 \, {\left(b^{3} - 2 \, a b c\right)} d^{3} - 4 \, {\left(3 \, a b^{2} - a^{2} c\right)} d^{2} e\right)} f^{3} + {\left(8 \, b c^{2} d^{4} - a^{2} b e^{4} - 4 \, {\left(3 \, b^{2} c - a c^{2}\right)} d^{3} e - 2 \, {\left(b^{3} - 10 \, a b c\right)} d^{2} e^{2} + {\left(3 \, a b^{2} - 5 \, a^{2} c\right)} d e^{3}\right)} f^{2} - {\left(4 \, c^{3} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + 4 \, a b c d e^{4} - a^{2} c e^{5} - {\left(3 \, b^{2} c - 5 \, a c^{2}\right)} d^{2} e^{3}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c e^{2} + 2 \, a f^{2} - {\left(2 \, c d + b e\right)} f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} - 2 \, {\left(b c d e - a c e^{2}\right)} f + {\left({\left(4 \, b c d - b^{2} e\right)} f^{2} - {\left(4 \, c^{2} d e - b c e^{2}\right)} f\right)} x - {\left(8 \, a^{3} d f^{4} - 2 \, {\left(4 \, a^{2} b d e + a^{3} e^{2} - 4 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2}\right)} f^{3} + 2 \, {\left(4 \, a c^{2} d^{3} - 4 \, a b c d^{2} e + a^{2} b e^{3} - {\left(a b^{2} - 6 \, a^{2} c\right)} d e^{2}\right)} f^{2} - 2 \, {\left(a c^{2} d^{2} e^{2} - a b c d e^{3} + a^{2} c e^{4}\right)} f + {\left(4 \, a^{2} b d f^{4} - {\left(4 \, a b^{2} d e + a^{2} b e^{2} - 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{2}\right)} f^{3} + {\left(4 \, b c^{2} d^{3} - 4 \, b^{2} c d^{2} e + a b^{2} e^{3} - {\left(b^{3} - 6 \, a b c\right)} d e^{2}\right)} f^{2} - {\left(b c^{2} d^{2} e^{2} - b^{2} c d e^{3} + a b c e^{4}\right)} f\right)} x\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{c e^{2} + 2 \, a f^{2} - {\left(2 \, c d + b e\right)} f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} \log\left(\frac{2 \, {\left(b^{2} d - a b e\right)} f^{2} - \sqrt{2} {\left(c^{2} d e^{3} - 4 \, a b d f^{3} + {\left(4 \, b c d^{2} + 4 \, a c d e + a b e^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{2} e + b c d e^{2} + a c e^{3}\right)} f - {\left(c^{3} d^{3} e^{3} - b c^{2} d^{2} e^{4} + a c^{2} d e^{5} + 4 \, {\left(2 \, a^{2} b d^{2} - a^{3} d e\right)} f^{4} + {\left(2 \, a^{2} b d e^{2} + a^{3} e^{3} + 8 \, {\left(b^{3} - 2 \, a b c\right)} d^{3} - 4 \, {\left(3 \, a b^{2} - a^{2} c\right)} d^{2} e\right)} f^{3} + {\left(8 \, b c^{2} d^{4} - a^{2} b e^{4} - 4 \, {\left(3 \, b^{2} c - a c^{2}\right)} d^{3} e - 2 \, {\left(b^{3} - 10 \, a b c\right)} d^{2} e^{2} + {\left(3 \, a b^{2} - 5 \, a^{2} c\right)} d e^{3}\right)} f^{2} - {\left(4 \, c^{3} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + 4 \, a b c d e^{4} - a^{2} c e^{5} - {\left(3 \, b^{2} c - 5 \, a c^{2}\right)} d^{2} e^{3}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c e^{2} + 2 \, a f^{2} - {\left(2 \, c d + b e\right)} f + {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} - 2 \, {\left(b c d e - a c e^{2}\right)} f + {\left({\left(4 \, b c d - b^{2} e\right)} f^{2} - {\left(4 \, c^{2} d e - b c e^{2}\right)} f\right)} x - {\left(8 \, a^{3} d f^{4} - 2 \, {\left(4 \, a^{2} b d e + a^{3} e^{2} - 4 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2}\right)} f^{3} + 2 \, {\left(4 \, a c^{2} d^{3} - 4 \, a b c d^{2} e + a^{2} b e^{3} - {\left(a b^{2} - 6 \, a^{2} c\right)} d e^{2}\right)} f^{2} - 2 \, {\left(a c^{2} d^{2} e^{2} - a b c d e^{3} + a^{2} c e^{4}\right)} f + {\left(4 \, a^{2} b d f^{4} - {\left(4 \, a b^{2} d e + a^{2} b e^{2} - 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{2}\right)} f^{3} + {\left(4 \, b c^{2} d^{3} - 4 \, b^{2} c d^{2} e + a b^{2} e^{3} - {\left(b^{3} - 6 \, a b c\right)} d e^{2}\right)} f^{2} - {\left(b c^{2} d^{2} e^{2} - b^{2} c d e^{3} + a b c e^{4}\right)} f\right)} x\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{x}\right) + \frac{1}{4} \, \sqrt{2} \sqrt{\frac{c e^{2} + 2 \, a f^{2} - {\left(2 \, c d + b e\right)} f - {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} \log\left(\frac{2 \, {\left(b^{2} d - a b e\right)} f^{2} + \sqrt{2} {\left(c^{2} d e^{3} - 4 \, a b d f^{3} + {\left(4 \, b c d^{2} + 4 \, a c d e + a b e^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{2} e + b c d e^{2} + a c e^{3}\right)} f + {\left(c^{3} d^{3} e^{3} - b c^{2} d^{2} e^{4} + a c^{2} d e^{5} + 4 \, {\left(2 \, a^{2} b d^{2} - a^{3} d e\right)} f^{4} + {\left(2 \, a^{2} b d e^{2} + a^{3} e^{3} + 8 \, {\left(b^{3} - 2 \, a b c\right)} d^{3} - 4 \, {\left(3 \, a b^{2} - a^{2} c\right)} d^{2} e\right)} f^{3} + {\left(8 \, b c^{2} d^{4} - a^{2} b e^{4} - 4 \, {\left(3 \, b^{2} c - a c^{2}\right)} d^{3} e - 2 \, {\left(b^{3} - 10 \, a b c\right)} d^{2} e^{2} + {\left(3 \, a b^{2} - 5 \, a^{2} c\right)} d e^{3}\right)} f^{2} - {\left(4 \, c^{3} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + 4 \, a b c d e^{4} - a^{2} c e^{5} - {\left(3 \, b^{2} c - 5 \, a c^{2}\right)} d^{2} e^{3}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c e^{2} + 2 \, a f^{2} - {\left(2 \, c d + b e\right)} f - {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} - 2 \, {\left(b c d e - a c e^{2}\right)} f + {\left({\left(4 \, b c d - b^{2} e\right)} f^{2} - {\left(4 \, c^{2} d e - b c e^{2}\right)} f\right)} x + {\left(8 \, a^{3} d f^{4} - 2 \, {\left(4 \, a^{2} b d e + a^{3} e^{2} - 4 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2}\right)} f^{3} + 2 \, {\left(4 \, a c^{2} d^{3} - 4 \, a b c d^{2} e + a^{2} b e^{3} - {\left(a b^{2} - 6 \, a^{2} c\right)} d e^{2}\right)} f^{2} - 2 \, {\left(a c^{2} d^{2} e^{2} - a b c d e^{3} + a^{2} c e^{4}\right)} f + {\left(4 \, a^{2} b d f^{4} - {\left(4 \, a b^{2} d e + a^{2} b e^{2} - 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{2}\right)} f^{3} + {\left(4 \, b c^{2} d^{3} - 4 \, b^{2} c d^{2} e + a b^{2} e^{3} - {\left(b^{3} - 6 \, a b c\right)} d e^{2}\right)} f^{2} - {\left(b c^{2} d^{2} e^{2} - b^{2} c d e^{3} + a b c e^{4}\right)} f\right)} x\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{x}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\frac{c e^{2} + 2 \, a f^{2} - {\left(2 \, c d + b e\right)} f - {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} \log\left(\frac{2 \, {\left(b^{2} d - a b e\right)} f^{2} - \sqrt{2} {\left(c^{2} d e^{3} - 4 \, a b d f^{3} + {\left(4 \, b c d^{2} + 4 \, a c d e + a b e^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{2} e + b c d e^{2} + a c e^{3}\right)} f + {\left(c^{3} d^{3} e^{3} - b c^{2} d^{2} e^{4} + a c^{2} d e^{5} + 4 \, {\left(2 \, a^{2} b d^{2} - a^{3} d e\right)} f^{4} + {\left(2 \, a^{2} b d e^{2} + a^{3} e^{3} + 8 \, {\left(b^{3} - 2 \, a b c\right)} d^{3} - 4 \, {\left(3 \, a b^{2} - a^{2} c\right)} d^{2} e\right)} f^{3} + {\left(8 \, b c^{2} d^{4} - a^{2} b e^{4} - 4 \, {\left(3 \, b^{2} c - a c^{2}\right)} d^{3} e - 2 \, {\left(b^{3} - 10 \, a b c\right)} d^{2} e^{2} + {\left(3 \, a b^{2} - 5 \, a^{2} c\right)} d e^{3}\right)} f^{2} - {\left(4 \, c^{3} d^{4} e - 2 \, b c^{2} d^{3} e^{2} + 4 \, a b c d e^{4} - a^{2} c e^{5} - {\left(3 \, b^{2} c - 5 \, a c^{2}\right)} d^{2} e^{3}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}\right)} \sqrt{c x^{2} + b x + a} \sqrt{\frac{c e^{2} + 2 \, a f^{2} - {\left(2 \, c d + b e\right)} f - {\left(c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{c^{2} d^{2} e^{2} - b c d e^{3} + a c e^{4} - 4 \, a^{2} d f^{3} + {\left(4 \, a b d e + a^{2} e^{2} - 4 \, {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} f^{2} - {\left(4 \, c^{2} d^{3} - 4 \, b c d^{2} e + a b e^{3} - {\left(b^{2} - 6 \, a c\right)} d e^{2}\right)} f}} - 2 \, {\left(b c d e - a c e^{2}\right)} f + {\left({\left(4 \, b c d - b^{2} e\right)} f^{2} - {\left(4 \, c^{2} d e - b c e^{2}\right)} f\right)} x + {\left(8 \, a^{3} d f^{4} - 2 \, {\left(4 \, a^{2} b d e + a^{3} e^{2} - 4 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d^{2}\right)} f^{3} + 2 \, {\left(4 \, a c^{2} d^{3} - 4 \, a b c d^{2} e + a^{2} b e^{3} - {\left(a b^{2} - 6 \, a^{2} c\right)} d e^{2}\right)} f^{2} - 2 \, {\left(a c^{2} d^{2} e^{2} - a b c d e^{3} + a^{2} c e^{4}\right)} f + {\left(4 \, a^{2} b d f^{4} - {\left(4 \, a b^{2} d e + a^{2} b e^{2} - 4 \, {\left(b^{3} - 2 \, a b c\right)} d^{2}\right)} f^{3} + {\left(4 \, b c^{2} d^{3} - 4 \, b^{2} c d^{2} e + a b^{2} e^{3} - {\left(b^{3} - 6 \, a b c\right)} d e^{2}\right)} f^{2} - {\left(b c^{2} d^{2} e^{2} - b^{2} c d e^{3} + a b c e^{4}\right)} f\right)} x\right)} \sqrt{\frac{c^{2} e^{2} - 2 \, b c e f + b^{2} f^{2}}{c^{4} d^{4} e^{2} - 2 \, b c^{3} d^{3} e^{3} - 2 \, a b c^{2} d e^{5} + a^{2} c^{2} e^{6} - 4 \, a^{4} d f^{5} + {\left(b^{2} c^{2} + 2 \, a c^{3}\right)} d^{2} e^{4} + {\left(8 \, a^{3} b d e + a^{4} e^{2} - 8 \, {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} d^{2}\right)} f^{4} - 2 \, {\left(a^{3} b e^{3} + 2 \, {\left(b^{4} - 4 \, a b^{2} c + 6 \, a^{2} c^{2}\right)} d^{3} - 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{2} e + {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{2}\right)} f^{3} - {\left(8 \, {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{4} - 8 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - {\left(b^{4} - 20 \, a b^{2} c + 22 \, a^{2} c^{2}\right)} d^{2} e^{2} + 2 \, {\left(a b^{3} - 5 \, a^{2} b c\right)} d e^{3} - {\left(a^{2} b^{2} + 2 \, a^{3} c\right)} e^{4}\right)} f^{2} - 2 \, {\left(2 \, c^{4} d^{5} - 4 \, b c^{3} d^{4} e + a^{2} b c e^{5} + {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{3} e^{2} + {\left(b^{3} c - 5 \, a b c^{2}\right)} d^{2} e^{3} - 2 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{4}\right)} f}}}{x}\right)"," ",0,"1/4*sqrt(2)*sqrt((c*e^2 + 2*a*f^2 - (2*c*d + b*e)*f + (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f))*log((2*(b^2*d - a*b*e)*f^2 + sqrt(2)*(c^2*d*e^3 - 4*a*b*d*f^3 + (4*b*c*d^2 + 4*a*c*d*e + a*b*e^2)*f^2 - (4*c^2*d^2*e + b*c*d*e^2 + a*c*e^3)*f - (c^3*d^3*e^3 - b*c^2*d^2*e^4 + a*c^2*d*e^5 + 4*(2*a^2*b*d^2 - a^3*d*e)*f^4 + (2*a^2*b*d*e^2 + a^3*e^3 + 8*(b^3 - 2*a*b*c)*d^3 - 4*(3*a*b^2 - a^2*c)*d^2*e)*f^3 + (8*b*c^2*d^4 - a^2*b*e^4 - 4*(3*b^2*c - a*c^2)*d^3*e - 2*(b^3 - 10*a*b*c)*d^2*e^2 + (3*a*b^2 - 5*a^2*c)*d*e^3)*f^2 - (4*c^3*d^4*e - 2*b*c^2*d^3*e^2 + 4*a*b*c*d*e^4 - a^2*c*e^5 - (3*b^2*c - 5*a*c^2)*d^2*e^3)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))*sqrt(c*x^2 + b*x + a)*sqrt((c*e^2 + 2*a*f^2 - (2*c*d + b*e)*f + (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)) - 2*(b*c*d*e - a*c*e^2)*f + ((4*b*c*d - b^2*e)*f^2 - (4*c^2*d*e - b*c*e^2)*f)*x - (8*a^3*d*f^4 - 2*(4*a^2*b*d*e + a^3*e^2 - 4*(a*b^2 - 2*a^2*c)*d^2)*f^3 + 2*(4*a*c^2*d^3 - 4*a*b*c*d^2*e + a^2*b*e^3 - (a*b^2 - 6*a^2*c)*d*e^2)*f^2 - 2*(a*c^2*d^2*e^2 - a*b*c*d*e^3 + a^2*c*e^4)*f + (4*a^2*b*d*f^4 - (4*a*b^2*d*e + a^2*b*e^2 - 4*(b^3 - 2*a*b*c)*d^2)*f^3 + (4*b*c^2*d^3 - 4*b^2*c*d^2*e + a*b^2*e^3 - (b^3 - 6*a*b*c)*d*e^2)*f^2 - (b*c^2*d^2*e^2 - b^2*c*d*e^3 + a*b*c*e^4)*f)*x)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/x) - 1/4*sqrt(2)*sqrt((c*e^2 + 2*a*f^2 - (2*c*d + b*e)*f + (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f))*log((2*(b^2*d - a*b*e)*f^2 - sqrt(2)*(c^2*d*e^3 - 4*a*b*d*f^3 + (4*b*c*d^2 + 4*a*c*d*e + a*b*e^2)*f^2 - (4*c^2*d^2*e + b*c*d*e^2 + a*c*e^3)*f - (c^3*d^3*e^3 - b*c^2*d^2*e^4 + a*c^2*d*e^5 + 4*(2*a^2*b*d^2 - a^3*d*e)*f^4 + (2*a^2*b*d*e^2 + a^3*e^3 + 8*(b^3 - 2*a*b*c)*d^3 - 4*(3*a*b^2 - a^2*c)*d^2*e)*f^3 + (8*b*c^2*d^4 - a^2*b*e^4 - 4*(3*b^2*c - a*c^2)*d^3*e - 2*(b^3 - 10*a*b*c)*d^2*e^2 + (3*a*b^2 - 5*a^2*c)*d*e^3)*f^2 - (4*c^3*d^4*e - 2*b*c^2*d^3*e^2 + 4*a*b*c*d*e^4 - a^2*c*e^5 - (3*b^2*c - 5*a*c^2)*d^2*e^3)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))*sqrt(c*x^2 + b*x + a)*sqrt((c*e^2 + 2*a*f^2 - (2*c*d + b*e)*f + (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)) - 2*(b*c*d*e - a*c*e^2)*f + ((4*b*c*d - b^2*e)*f^2 - (4*c^2*d*e - b*c*e^2)*f)*x - (8*a^3*d*f^4 - 2*(4*a^2*b*d*e + a^3*e^2 - 4*(a*b^2 - 2*a^2*c)*d^2)*f^3 + 2*(4*a*c^2*d^3 - 4*a*b*c*d^2*e + a^2*b*e^3 - (a*b^2 - 6*a^2*c)*d*e^2)*f^2 - 2*(a*c^2*d^2*e^2 - a*b*c*d*e^3 + a^2*c*e^4)*f + (4*a^2*b*d*f^4 - (4*a*b^2*d*e + a^2*b*e^2 - 4*(b^3 - 2*a*b*c)*d^2)*f^3 + (4*b*c^2*d^3 - 4*b^2*c*d^2*e + a*b^2*e^3 - (b^3 - 6*a*b*c)*d*e^2)*f^2 - (b*c^2*d^2*e^2 - b^2*c*d*e^3 + a*b*c*e^4)*f)*x)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/x) + 1/4*sqrt(2)*sqrt((c*e^2 + 2*a*f^2 - (2*c*d + b*e)*f - (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f))*log((2*(b^2*d - a*b*e)*f^2 + sqrt(2)*(c^2*d*e^3 - 4*a*b*d*f^3 + (4*b*c*d^2 + 4*a*c*d*e + a*b*e^2)*f^2 - (4*c^2*d^2*e + b*c*d*e^2 + a*c*e^3)*f + (c^3*d^3*e^3 - b*c^2*d^2*e^4 + a*c^2*d*e^5 + 4*(2*a^2*b*d^2 - a^3*d*e)*f^4 + (2*a^2*b*d*e^2 + a^3*e^3 + 8*(b^3 - 2*a*b*c)*d^3 - 4*(3*a*b^2 - a^2*c)*d^2*e)*f^3 + (8*b*c^2*d^4 - a^2*b*e^4 - 4*(3*b^2*c - a*c^2)*d^3*e - 2*(b^3 - 10*a*b*c)*d^2*e^2 + (3*a*b^2 - 5*a^2*c)*d*e^3)*f^2 - (4*c^3*d^4*e - 2*b*c^2*d^3*e^2 + 4*a*b*c*d*e^4 - a^2*c*e^5 - (3*b^2*c - 5*a*c^2)*d^2*e^3)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))*sqrt(c*x^2 + b*x + a)*sqrt((c*e^2 + 2*a*f^2 - (2*c*d + b*e)*f - (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)) - 2*(b*c*d*e - a*c*e^2)*f + ((4*b*c*d - b^2*e)*f^2 - (4*c^2*d*e - b*c*e^2)*f)*x + (8*a^3*d*f^4 - 2*(4*a^2*b*d*e + a^3*e^2 - 4*(a*b^2 - 2*a^2*c)*d^2)*f^3 + 2*(4*a*c^2*d^3 - 4*a*b*c*d^2*e + a^2*b*e^3 - (a*b^2 - 6*a^2*c)*d*e^2)*f^2 - 2*(a*c^2*d^2*e^2 - a*b*c*d*e^3 + a^2*c*e^4)*f + (4*a^2*b*d*f^4 - (4*a*b^2*d*e + a^2*b*e^2 - 4*(b^3 - 2*a*b*c)*d^2)*f^3 + (4*b*c^2*d^3 - 4*b^2*c*d^2*e + a*b^2*e^3 - (b^3 - 6*a*b*c)*d*e^2)*f^2 - (b*c^2*d^2*e^2 - b^2*c*d*e^3 + a*b*c*e^4)*f)*x)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/x) - 1/4*sqrt(2)*sqrt((c*e^2 + 2*a*f^2 - (2*c*d + b*e)*f - (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f))*log((2*(b^2*d - a*b*e)*f^2 - sqrt(2)*(c^2*d*e^3 - 4*a*b*d*f^3 + (4*b*c*d^2 + 4*a*c*d*e + a*b*e^2)*f^2 - (4*c^2*d^2*e + b*c*d*e^2 + a*c*e^3)*f + (c^3*d^3*e^3 - b*c^2*d^2*e^4 + a*c^2*d*e^5 + 4*(2*a^2*b*d^2 - a^3*d*e)*f^4 + (2*a^2*b*d*e^2 + a^3*e^3 + 8*(b^3 - 2*a*b*c)*d^3 - 4*(3*a*b^2 - a^2*c)*d^2*e)*f^3 + (8*b*c^2*d^4 - a^2*b*e^4 - 4*(3*b^2*c - a*c^2)*d^3*e - 2*(b^3 - 10*a*b*c)*d^2*e^2 + (3*a*b^2 - 5*a^2*c)*d*e^3)*f^2 - (4*c^3*d^4*e - 2*b*c^2*d^3*e^2 + 4*a*b*c*d*e^4 - a^2*c*e^5 - (3*b^2*c - 5*a*c^2)*d^2*e^3)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))*sqrt(c*x^2 + b*x + a)*sqrt((c*e^2 + 2*a*f^2 - (2*c*d + b*e)*f - (c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/(c^2*d^2*e^2 - b*c*d*e^3 + a*c*e^4 - 4*a^2*d*f^3 + (4*a*b*d*e + a^2*e^2 - 4*(b^2 - 2*a*c)*d^2)*f^2 - (4*c^2*d^3 - 4*b*c*d^2*e + a*b*e^3 - (b^2 - 6*a*c)*d*e^2)*f)) - 2*(b*c*d*e - a*c*e^2)*f + ((4*b*c*d - b^2*e)*f^2 - (4*c^2*d*e - b*c*e^2)*f)*x + (8*a^3*d*f^4 - 2*(4*a^2*b*d*e + a^3*e^2 - 4*(a*b^2 - 2*a^2*c)*d^2)*f^3 + 2*(4*a*c^2*d^3 - 4*a*b*c*d^2*e + a^2*b*e^3 - (a*b^2 - 6*a^2*c)*d*e^2)*f^2 - 2*(a*c^2*d^2*e^2 - a*b*c*d*e^3 + a^2*c*e^4)*f + (4*a^2*b*d*f^4 - (4*a*b^2*d*e + a^2*b*e^2 - 4*(b^3 - 2*a*b*c)*d^2)*f^3 + (4*b*c^2*d^3 - 4*b^2*c*d^2*e + a*b^2*e^3 - (b^3 - 6*a*b*c)*d*e^2)*f^2 - (b*c^2*d^2*e^2 - b^2*c*d*e^3 + a*b*c*e^4)*f)*x)*sqrt((c^2*e^2 - 2*b*c*e*f + b^2*f^2)/(c^4*d^4*e^2 - 2*b*c^3*d^3*e^3 - 2*a*b*c^2*d*e^5 + a^2*c^2*e^6 - 4*a^4*d*f^5 + (b^2*c^2 + 2*a*c^3)*d^2*e^4 + (8*a^3*b*d*e + a^4*e^2 - 8*(a^2*b^2 - 2*a^3*c)*d^2)*f^4 - 2*(a^3*b*e^3 + 2*(b^4 - 4*a*b^2*c + 6*a^2*c^2)*d^3 - 4*(a*b^3 - a^2*b*c)*d^2*e + (a^2*b^2 + 6*a^3*c)*d*e^2)*f^3 - (8*(b^2*c^2 - 2*a*c^3)*d^4 - 8*(b^3*c - a*b*c^2)*d^3*e - (b^4 - 20*a*b^2*c + 22*a^2*c^2)*d^2*e^2 + 2*(a*b^3 - 5*a^2*b*c)*d*e^3 - (a^2*b^2 + 2*a^3*c)*e^4)*f^2 - 2*(2*c^4*d^5 - 4*b*c^3*d^4*e + a^2*b*c*e^5 + (b^2*c^2 + 6*a*c^3)*d^3*e^2 + (b^3*c - 5*a*b*c^2)*d^2*e^3 - 2*(a*b^2*c - 2*a^2*c^2)*d*e^4)*f)))/x)","B",0
118,-1,0,0,0.000000," ","integrate(1/x/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
119,-1,0,0,0.000000," ","integrate(1/x^2/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
120,-1,0,0,0.000000," ","integrate(1/x^3/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
121,-1,0,0,0.000000," ","integrate(x^3/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
122,-1,0,0,0.000000," ","integrate(x^2/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
123,-1,0,0,0.000000," ","integrate(x/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
124,-1,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
125,-1,0,0,0.000000," ","integrate(1/x/(c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
126,1,178,0,1.277648," ","integrate(x^4/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-x^{2} - 4 \, x - 3} {\left(x - 10\right)} + \frac{1}{8} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} x + 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} x - 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - \frac{11}{2} \, \arctan\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} {\left(x + 2\right)}}{x^{2} + 4 \, x + 3}\right) + \frac{5}{16} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) - \frac{5}{16} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right)"," ",0,"-1/4*sqrt(-x^2 - 4*x - 3)*(x - 10) + 1/8*sqrt(2)*arctan(1/2*(sqrt(2)*x + 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) + 1/8*sqrt(2)*arctan(-1/2*(sqrt(2)*x - 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 11/2*arctan(sqrt(-x^2 - 4*x - 3)*(x + 2)/(x^2 + 4*x + 3)) + 5/16*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) - 5/16*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2)","A",0
127,1,175,0,1.396815," ","integrate(x^3/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} x + 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) + \frac{1}{8} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} x - 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - \frac{1}{2} \, \sqrt{-x^{2} - 4 \, x - 3} + 2 \, \arctan\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} {\left(x + 2\right)}}{x^{2} + 4 \, x + 3}\right) - \frac{1}{4} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) + \frac{1}{4} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right)"," ",0,"1/8*sqrt(2)*arctan(1/2*(sqrt(2)*x + 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) + 1/8*sqrt(2)*arctan(-1/2*(sqrt(2)*x - 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 1/2*sqrt(-x^2 - 4*x - 3) + 2*arctan(sqrt(-x^2 - 4*x - 3)*(x + 2)/(x^2 + 4*x + 3)) - 1/4*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) + 1/4*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2)","A",0
128,1,161,0,1.036435," ","integrate(x^2/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} x + 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} x - 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - \frac{1}{2} \, \arctan\left(\frac{\sqrt{-x^{2} - 4 \, x - 3} {\left(x + 2\right)}}{x^{2} + 4 \, x + 3}\right) + \frac{1}{8} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) - \frac{1}{8} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right)"," ",0,"-1/4*sqrt(2)*arctan(1/2*(sqrt(2)*x + 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 1/4*sqrt(2)*arctan(-1/2*(sqrt(2)*x - 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 1/2*arctan(sqrt(-x^2 - 4*x - 3)*(x + 2)/(x^2 + 4*x + 3)) + 1/8*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) - 1/8*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2)","A",0
129,1,50,0,0.874691," ","integrate(x/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} {\left(6 \, x^{2} + 20 \, x + 15\right)} \sqrt{-x^{2} - 4 \, x - 3}}{4 \, {\left(2 \, x^{3} + 11 \, x^{2} + 18 \, x + 9\right)}}\right)"," ",0,"1/4*sqrt(2)*arctan(1/4*sqrt(2)*(6*x^2 + 20*x + 15)*sqrt(-x^2 - 4*x - 3)/(2*x^3 + 11*x^2 + 18*x + 9))","A",0
130,1,132,0,0.784624," ","integrate(1/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} x + 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - \frac{1}{6} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} x - 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - \frac{1}{12} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) + \frac{1}{12} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right)"," ",0,"-1/6*sqrt(2)*arctan(1/2*(sqrt(2)*x + 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 1/6*sqrt(2)*arctan(-1/2*(sqrt(2)*x - 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 1/12*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) + 1/12*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2)","A",0
131,1,170,0,1.054967," ","integrate(1/x/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{\sqrt{3} \sqrt{-x^{2} - 4 \, x - 3} {\left(2 \, x + 3\right)}}{3 \, {\left(x^{2} + 4 \, x + 3\right)}}\right) + \frac{1}{18} \, \sqrt{2} \arctan\left(\frac{\sqrt{2} x + 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) + \frac{1}{18} \, \sqrt{2} \arctan\left(-\frac{\sqrt{2} x - 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) + \frac{1}{9} \, \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) - \frac{1}{9} \, \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(-x^2 - 4*x - 3)*(2*x + 3)/(x^2 + 4*x + 3)) + 1/18*sqrt(2)*arctan(1/2*(sqrt(2)*x + 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) + 1/18*sqrt(2)*arctan(-1/2*(sqrt(2)*x - 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) + 1/9*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) - 1/9*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2)","A",0
132,1,194,0,1.090491," ","integrate(1/x^2/(2*x^2+4*x+3)/(-x^2-4*x-3)^(1/2),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{3} x \arctan\left(\frac{\sqrt{3} \sqrt{-x^{2} - 4 \, x - 3} {\left(2 \, x + 3\right)}}{3 \, {\left(x^{2} + 4 \, x + 3\right)}}\right) - 2 \, \sqrt{2} x \arctan\left(\frac{\sqrt{2} x + 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) - 2 \, \sqrt{2} x \arctan\left(-\frac{\sqrt{2} x - 3 \, \sqrt{2} \sqrt{-x^{2} - 4 \, x - 3}}{2 \, {\left(2 \, x + 3\right)}}\right) + 5 \, x \log\left(-\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x + 4 \, x + 3}{x^{2}}\right) - 5 \, x \log\left(\frac{2 \, \sqrt{-x^{2} - 4 \, x - 3} x - 4 \, x - 3}{x^{2}}\right) - 6 \, \sqrt{-x^{2} - 4 \, x - 3}}{54 \, x}"," ",0,"-1/54*(12*sqrt(3)*x*arctan(1/3*sqrt(3)*sqrt(-x^2 - 4*x - 3)*(2*x + 3)/(x^2 + 4*x + 3)) - 2*sqrt(2)*x*arctan(1/2*(sqrt(2)*x + 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) - 2*sqrt(2)*x*arctan(-1/2*(sqrt(2)*x - 3*sqrt(2)*sqrt(-x^2 - 4*x - 3))/(2*x + 3)) + 5*x*log(-(2*sqrt(-x^2 - 4*x - 3)*x + 4*x + 3)/x^2) - 5*x*log((2*sqrt(-x^2 - 4*x - 3)*x - 4*x - 3)/x^2) - 6*sqrt(-x^2 - 4*x - 3))/x","A",0
133,1,88,0,0.954606," ","integrate((2+3*x)^2*(-12*x^2+31*x+30)^2*(12*x^2+17*x+6)^(1/2),x, algorithm=""fricas"")","\frac{1}{1056964608} \, {\left(171228266496 \, x^{7} - 732816211968 \, x^{6} - 1190083166208 \, x^{5} + 3438453030912 \, x^{4} + 8974844476416 \, x^{3} + 7899203409792 \, x^{2} + 3132157281976 \, x + 474999091769\right)} \sqrt{12 \, x^{2} + 17 \, x + 6} + \frac{125455}{3623878656} \, \sqrt{3} \log\left(-8 \, \sqrt{3} \sqrt{12 \, x^{2} + 17 \, x + 6} {\left(24 \, x + 17\right)} + 1152 \, x^{2} + 1632 \, x + 577\right)"," ",0,"1/1056964608*(171228266496*x^7 - 732816211968*x^6 - 1190083166208*x^5 + 3438453030912*x^4 + 8974844476416*x^3 + 7899203409792*x^2 + 3132157281976*x + 474999091769)*sqrt(12*x^2 + 17*x + 6) + 125455/3623878656*sqrt(3)*log(-8*sqrt(3)*sqrt(12*x^2 + 17*x + 6)*(24*x + 17) + 1152*x^2 + 1632*x + 577)","A",0
134,1,73,0,0.873686," ","integrate((2+3*x)*(-12*x^2+31*x+30)*(12*x^2+17*x+6)^(1/2),x, algorithm=""fricas"")","-\frac{1}{122880} \, {\left(884736 \, x^{4} - 1963008 \, x^{3} - 6837888 \, x^{2} - 5455144 \, x - 1353611\right)} \sqrt{12 \, x^{2} + 17 \, x + 6} + \frac{97}{589824} \, \sqrt{3} \log\left(8 \, \sqrt{3} \sqrt{12 \, x^{2} + 17 \, x + 6} {\left(24 \, x + 17\right)} + 1152 \, x^{2} + 1632 \, x + 577\right)"," ",0,"-1/122880*(884736*x^4 - 1963008*x^3 - 6837888*x^2 - 5455144*x - 1353611)*sqrt(12*x^2 + 17*x + 6) + 97/589824*sqrt(3)*log(8*sqrt(3)*sqrt(12*x^2 + 17*x + 6)*(24*x + 17) + 1152*x^2 + 1632*x + 577)","A",0
135,1,53,0,0.631377," ","integrate((12*x^2+17*x+6)^(1/2)/(2+3*x)/(-12*x^2+31*x+30),x, algorithm=""fricas"")","\frac{1}{84} \, \log\left(\frac{291 \, x + 84 \, \sqrt{12 \, x^{2} + 17 \, x + 6} + 206}{x}\right) - \frac{1}{84} \, \log\left(\frac{291 \, x - 84 \, \sqrt{12 \, x^{2} + 17 \, x + 6} + 206}{x}\right)"," ",0,"1/84*log((291*x + 84*sqrt(12*x^2 + 17*x + 6) + 206)/x) - 1/84*log((291*x - 84*sqrt(12*x^2 + 17*x + 6) + 206)/x)","B",0
136,1,126,0,0.980966," ","integrate((12*x^2+17*x+6)^(1/2)/(2+3*x)^2/(-12*x^2+31*x+30)^2,x, algorithm=""fricas"")","\frac{97 \, {\left(36 \, x^{3} - 69 \, x^{2} - 152 \, x - 60\right)} \log\left(\frac{291 \, x + 84 \, \sqrt{12 \, x^{2} + 17 \, x + 6} + 206}{x}\right) - 97 \, {\left(36 \, x^{3} - 69 \, x^{2} - 152 \, x - 60\right)} \log\left(\frac{291 \, x - 84 \, \sqrt{12 \, x^{2} + 17 \, x + 6} + 206}{x}\right) - 168 \, {\left(37644 \, x^{2} - 98767 \, x - 88978\right)} \sqrt{12 \, x^{2} + 17 \, x + 6}}{6453888 \, {\left(36 \, x^{3} - 69 \, x^{2} - 152 \, x - 60\right)}}"," ",0,"1/6453888*(97*(36*x^3 - 69*x^2 - 152*x - 60)*log((291*x + 84*sqrt(12*x^2 + 17*x + 6) + 206)/x) - 97*(36*x^3 - 69*x^2 - 152*x - 60)*log((291*x - 84*sqrt(12*x^2 + 17*x + 6) + 206)/x) - 168*(37644*x^2 - 98767*x - 88978)*sqrt(12*x^2 + 17*x + 6))/(36*x^3 - 69*x^2 - 152*x - 60)","A",0
137,1,186,0,1.736397," ","integrate((12*x^2+17*x+6)^(1/2)/(2+3*x)^3/(-12*x^2+31*x+30)^3,x, algorithm=""fricas"")","\frac{40325 \, {\left(1296 \, x^{6} - 4968 \, x^{5} - 6183 \, x^{4} + 16656 \, x^{3} + 31384 \, x^{2} + 18240 \, x + 3600\right)} \log\left(\frac{291 \, x + 84 \, \sqrt{12 \, x^{2} + 17 \, x + 6} + 206}{x}\right) - 40325 \, {\left(1296 \, x^{6} - 4968 \, x^{5} - 6183 \, x^{4} + 16656 \, x^{3} + 31384 \, x^{2} + 18240 \, x + 3600\right)} \log\left(\frac{291 \, x - 84 \, \sqrt{12 \, x^{2} + 17 \, x + 6} + 206}{x}\right) + 168 \, {\left(706089565584 \, x^{5} - 3206824169544 \, x^{4} - 1096520427663 \, x^{3} + 9848047480070 \, x^{2} + 10124325497244 \, x + 2773753482408\right)} \sqrt{12 \, x^{2} + 17 \, x + 6}}{1275081744384 \, {\left(1296 \, x^{6} - 4968 \, x^{5} - 6183 \, x^{4} + 16656 \, x^{3} + 31384 \, x^{2} + 18240 \, x + 3600\right)}}"," ",0,"1/1275081744384*(40325*(1296*x^6 - 4968*x^5 - 6183*x^4 + 16656*x^3 + 31384*x^2 + 18240*x + 3600)*log((291*x + 84*sqrt(12*x^2 + 17*x + 6) + 206)/x) - 40325*(1296*x^6 - 4968*x^5 - 6183*x^4 + 16656*x^3 + 31384*x^2 + 18240*x + 3600)*log((291*x - 84*sqrt(12*x^2 + 17*x + 6) + 206)/x) + 168*(706089565584*x^5 - 3206824169544*x^4 - 1096520427663*x^3 + 9848047480070*x^2 + 10124325497244*x + 2773753482408)*sqrt(12*x^2 + 17*x + 6))/(1296*x^6 - 4968*x^5 - 6183*x^4 + 16656*x^3 + 31384*x^2 + 18240*x + 3600)","A",0
138,1,11,0,0.597068," ","integrate((-3+2*x)*(x^2-3*x)^(2/3),x, algorithm=""fricas"")","\frac{3}{5} \, {\left(x^{2} - 3 \, x\right)}^{\frac{5}{3}}"," ",0,"3/5*(x^2 - 3*x)^(5/3)","A",0
139,1,11,0,0.667546," ","integrate(((-3+x)*x)^(2/3)*(-3+2*x),x, algorithm=""fricas"")","\frac{3}{5} \, {\left(x^{2} - 3 \, x\right)}^{\frac{5}{3}}"," ",0,"3/5*(x^2 - 3*x)^(5/3)","A",0
140,1,11,0,0.986634," ","integrate(x*(2*x^2-9*x+9)/(x^2-3*x)^(1/3),x, algorithm=""fricas"")","\frac{3}{5} \, {\left(x^{2} - 3 \, x\right)}^{\frac{5}{3}}"," ",0,"3/5*(x^2 - 3*x)^(5/3)","A",0
141,1,11,0,1.024684," ","integrate(x*(2*x^2-9*x+9)/((-3+x)*x)^(1/3),x, algorithm=""fricas"")","\frac{3}{5} \, {\left(x^{2} - 3 \, x\right)}^{\frac{5}{3}}"," ",0,"3/5*(x^2 - 3*x)^(5/3)","A",0
142,-1,0,0,0.000000," ","integrate((h*x+g)/(-c*g^2/h^2+9*c*x^2)^(1/3)/(3*h^2*x^2+g^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
143,-1,0,0,0.000000," ","integrate((h*x+g)/(1/9*(2*b^2*h^2+b*c*g*h-c^2*g^2)/c/h^2+b*x+c*x^2)^(1/3)/(f*(b^2+1/3*(-2*b^2*h^2-b*c*g*h+c^2*g^2)/h^2)/c^2+b*f*x/c+f*x^2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
