1,1,205,0,0.430253," ","integrate((a+b*x+b*f*x^2/e)/(f*x^2+e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b e^{2} + 4 \, {\left(b d - 2 \, a e\right)} f\right)} \sqrt{f} \log\left(-8 \, f^{2} x^{2} - 8 \, e f x - e^{2} - 4 \, \sqrt{f x^{2} + e x + d} {\left(2 \, f x + e\right)} \sqrt{f} - 4 \, d f\right) - 4 \, {\left(2 \, b f^{2} x + b e f\right)} \sqrt{f x^{2} + e x + d}}{16 \, e f^{2}}, \frac{{\left(b e^{2} + 4 \, {\left(b d - 2 \, a e\right)} f\right)} \sqrt{-f} \arctan\left(\frac{\sqrt{f x^{2} + e x + d} {\left(2 \, f x + e\right)} \sqrt{-f}}{2 \, {\left(f^{2} x^{2} + e f x + d f\right)}}\right) + 2 \, {\left(2 \, b f^{2} x + b e f\right)} \sqrt{f x^{2} + e x + d}}{8 \, e f^{2}}\right]"," ",0,"[-1/16*((b*e^2 + 4*(b*d - 2*a*e)*f)*sqrt(f)*log(-8*f^2*x^2 - 8*e*f*x - e^2 - 4*sqrt(f*x^2 + e*x + d)*(2*f*x + e)*sqrt(f) - 4*d*f) - 4*(2*b*f^2*x + b*e*f)*sqrt(f*x^2 + e*x + d))/(e*f^2), 1/8*((b*e^2 + 4*(b*d - 2*a*e)*f)*sqrt(-f)*arctan(1/2*sqrt(f*x^2 + e*x + d)*(2*f*x + e)*sqrt(-f)/(f^2*x^2 + e*f*x + d*f)) + 2*(2*b*f^2*x + b*e*f)*sqrt(f*x^2 + e*x + d))/(e*f^2)]","A",0
2,1,1079,0,0.662454," ","integrate(1/(a+b*x+b*f*x^2/e)/(f*x^2+e*x+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{e}{b^{2} d e - a b e^{2} - 4 \, {\left(a b d - a^{2} e\right)} f}} \log\left(\frac{8 \, b^{2} d^{2} e^{4} - 8 \, a b d e^{5} + a^{2} e^{6} + 16 \, a^{2} d^{2} e^{2} f^{2} + {\left(b^{2} e^{4} f^{2} + 16 \, {\left(b^{2} d^{2} - 8 \, a b d e + 8 \, a^{2} e^{2}\right)} f^{4} + 8 \, {\left(3 \, b^{2} d e^{2} - 4 \, a b e^{3}\right)} f^{3}\right)} x^{4} + 2 \, {\left(b^{2} e^{5} f + 16 \, {\left(b^{2} d^{2} e - 8 \, a b d e^{2} + 8 \, a^{2} e^{3}\right)} f^{3} + 8 \, {\left(3 \, b^{2} d e^{3} - 4 \, a b e^{4}\right)} f^{2}\right)} x^{3} + {\left(b^{2} e^{6} - 32 \, {\left(3 \, a b d^{2} e - 4 \, a^{2} d e^{2}\right)} f^{3} + 16 \, {\left(3 \, b^{2} d^{2} e^{2} - 13 \, a b d e^{3} + 10 \, a^{2} e^{4}\right)} f^{2} + 2 \, {\left(16 \, b^{2} d e^{4} - 19 \, a b e^{5}\right)} f\right)} x^{2} - 8 \, {\left(4 \, a b d^{2} e^{3} - 3 \, a^{2} d e^{4}\right)} f + 2 \, {\left(4 \, b^{2} d e^{5} - 3 \, a b e^{6} - 16 \, {\left(3 \, a b d^{2} e^{2} - 4 \, a^{2} d e^{3}\right)} f^{2} + 8 \, {\left(2 \, b^{2} d^{2} e^{3} - 5 \, a b d e^{4} + 2 \, a^{2} e^{5}\right)} f\right)} x - 4 \, {\left(2 \, b^{3} d^{2} e^{4} - 3 \, a b^{2} d e^{5} + a^{2} b e^{6} - 2 \, {\left(16 \, {\left(a b^{2} d^{2} - 3 \, a^{2} b d e + 2 \, a^{3} e^{2}\right)} f^{4} - 4 \, {\left(b^{3} d^{2} e - 4 \, a b^{2} d e^{2} + 3 \, a^{2} b e^{3}\right)} f^{3} - {\left(b^{3} d e^{3} - a b^{2} e^{4}\right)} f^{2}\right)} x^{3} + 16 \, {\left(a^{2} b d^{2} e^{2} - a^{3} d e^{3}\right)} f^{2} - 3 \, {\left(16 \, {\left(a b^{2} d^{2} e - 3 \, a^{2} b d e^{2} + 2 \, a^{3} e^{3}\right)} f^{3} - 4 \, {\left(b^{3} d^{2} e^{2} - 4 \, a b^{2} d e^{3} + 3 \, a^{2} b e^{4}\right)} f^{2} - {\left(b^{3} d e^{4} - a b^{2} e^{5}\right)} f\right)} x^{2} - 4 \, {\left(3 \, a b^{2} d^{2} e^{3} - 4 \, a^{2} b d e^{4} + a^{3} e^{5}\right)} f + {\left(b^{3} d e^{5} - a b^{2} e^{6} + 32 \, {\left(a^{2} b d^{2} e - a^{3} d e^{2}\right)} f^{3} - 40 \, {\left(a b^{2} d^{2} e^{2} - 2 \, a^{2} b d e^{3} + a^{3} e^{4}\right)} f^{2} + 2 \, {\left(4 \, b^{3} d^{2} e^{3} - 11 \, a b^{2} d e^{4} + 7 \, a^{2} b e^{5}\right)} f\right)} x\right)} \sqrt{f x^{2} + e x + d} \sqrt{\frac{e}{b^{2} d e - a b e^{2} - 4 \, {\left(a b d - a^{2} e\right)} f}}}{b^{2} f^{2} x^{4} + 2 \, b^{2} e f x^{3} + 2 \, a b e^{2} x + a^{2} e^{2} + {\left(b^{2} e^{2} + 2 \, a b e f\right)} x^{2}}\right), -\sqrt{-\frac{e}{b^{2} d e - a b e^{2} - 4 \, {\left(a b d - a^{2} e\right)} f}} \arctan\left(-\frac{{\left(2 \, b d e^{2} - a e^{3} - 4 \, a d e f + {\left(b e^{2} f + 4 \, {\left(b d - 2 \, a e\right)} f^{2}\right)} x^{2} + {\left(b e^{3} + 4 \, {\left(b d e - 2 \, a e^{2}\right)} f\right)} x\right)} \sqrt{f x^{2} + e x + d} \sqrt{-\frac{e}{b^{2} d e - a b e^{2} - 4 \, {\left(a b d - a^{2} e\right)} f}}}{2 \, {\left(2 \, e f^{2} x^{3} + 3 \, e^{2} f x^{2} + d e^{2} + {\left(e^{3} + 2 \, d e f\right)} x\right)}}\right)\right]"," ",0,"[1/2*sqrt(e/(b^2*d*e - a*b*e^2 - 4*(a*b*d - a^2*e)*f))*log((8*b^2*d^2*e^4 - 8*a*b*d*e^5 + a^2*e^6 + 16*a^2*d^2*e^2*f^2 + (b^2*e^4*f^2 + 16*(b^2*d^2 - 8*a*b*d*e + 8*a^2*e^2)*f^4 + 8*(3*b^2*d*e^2 - 4*a*b*e^3)*f^3)*x^4 + 2*(b^2*e^5*f + 16*(b^2*d^2*e - 8*a*b*d*e^2 + 8*a^2*e^3)*f^3 + 8*(3*b^2*d*e^3 - 4*a*b*e^4)*f^2)*x^3 + (b^2*e^6 - 32*(3*a*b*d^2*e - 4*a^2*d*e^2)*f^3 + 16*(3*b^2*d^2*e^2 - 13*a*b*d*e^3 + 10*a^2*e^4)*f^2 + 2*(16*b^2*d*e^4 - 19*a*b*e^5)*f)*x^2 - 8*(4*a*b*d^2*e^3 - 3*a^2*d*e^4)*f + 2*(4*b^2*d*e^5 - 3*a*b*e^6 - 16*(3*a*b*d^2*e^2 - 4*a^2*d*e^3)*f^2 + 8*(2*b^2*d^2*e^3 - 5*a*b*d*e^4 + 2*a^2*e^5)*f)*x - 4*(2*b^3*d^2*e^4 - 3*a*b^2*d*e^5 + a^2*b*e^6 - 2*(16*(a*b^2*d^2 - 3*a^2*b*d*e + 2*a^3*e^2)*f^4 - 4*(b^3*d^2*e - 4*a*b^2*d*e^2 + 3*a^2*b*e^3)*f^3 - (b^3*d*e^3 - a*b^2*e^4)*f^2)*x^3 + 16*(a^2*b*d^2*e^2 - a^3*d*e^3)*f^2 - 3*(16*(a*b^2*d^2*e - 3*a^2*b*d*e^2 + 2*a^3*e^3)*f^3 - 4*(b^3*d^2*e^2 - 4*a*b^2*d*e^3 + 3*a^2*b*e^4)*f^2 - (b^3*d*e^4 - a*b^2*e^5)*f)*x^2 - 4*(3*a*b^2*d^2*e^3 - 4*a^2*b*d*e^4 + a^3*e^5)*f + (b^3*d*e^5 - a*b^2*e^6 + 32*(a^2*b*d^2*e - a^3*d*e^2)*f^3 - 40*(a*b^2*d^2*e^2 - 2*a^2*b*d*e^3 + a^3*e^4)*f^2 + 2*(4*b^3*d^2*e^3 - 11*a*b^2*d*e^4 + 7*a^2*b*e^5)*f)*x)*sqrt(f*x^2 + e*x + d)*sqrt(e/(b^2*d*e - a*b*e^2 - 4*(a*b*d - a^2*e)*f)))/(b^2*f^2*x^4 + 2*b^2*e*f*x^3 + 2*a*b*e^2*x + a^2*e^2 + (b^2*e^2 + 2*a*b*e*f)*x^2)), -sqrt(-e/(b^2*d*e - a*b*e^2 - 4*(a*b*d - a^2*e)*f))*arctan(-1/2*(2*b*d*e^2 - a*e^3 - 4*a*d*e*f + (b*e^2*f + 4*(b*d - 2*a*e)*f^2)*x^2 + (b*e^3 + 4*(b*d*e - 2*a*e^2)*f)*x)*sqrt(f*x^2 + e*x + d)*sqrt(-e/(b^2*d*e - a*b*e^2 - 4*(a*b*d - a^2*e)*f))/(2*e*f^2*x^3 + 3*e^2*f*x^2 + d*e^2 + (e^3 + 2*d*e*f)*x))]","B",0
3,1,813,0,0.515934," ","integrate(1/(c*x^2+b*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{8 \, a^{2} b^{4} + {\left(b^{4} c^{2} + 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4} + 128 \, c^{4} d^{2} - 32 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d\right)} x^{4} + 2 \, {\left(b^{5} c + 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 128 \, b c^{3} d^{2} - 32 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d\right)} x^{3} + {\left(b^{4} + 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} + {\left(b^{6} + 32 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 32 \, {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} - 2 \, {\left(19 \, b^{4} c + 104 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} d\right)} x^{2} - 4 \, {\left(2 \, a b^{3} + 2 \, {\left(b^{2} c^{2} + 4 \, a c^{3} - 8 \, c^{3} d\right)} x^{3} + 3 \, {\left(b^{3} c + 4 \, a b c^{2} - 8 \, b c^{2} d\right)} x^{2} - {\left(b^{3} + 4 \, a b c\right)} d + {\left(b^{4} + 8 \, a b^{2} c - 2 \, {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d\right)} x\right)} \sqrt{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d} \sqrt{c x^{2} + b x + a} - 8 \, {\left(a b^{4} + 4 \, a^{2} b^{2} c\right)} d + 2 \, {\left(4 \, a b^{5} + 16 \, a^{2} b^{3} c + 16 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{2} - {\left(3 \, b^{5} + 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d\right)} x}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, b d x + {\left(b^{2} + 2 \, c d\right)} x^{2} + d^{2}}\right)}{2 \, \sqrt{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d}}, -\frac{\sqrt{-a b^{2} - 4 \, c d^{2} + {\left(b^{2} + 4 \, a c\right)} d} \arctan\left(-\frac{{\left(2 \, a b^{2} + {\left(b^{2} c + 4 \, a c^{2} - 8 \, c^{2} d\right)} x^{2} - {\left(b^{2} + 4 \, a c\right)} d + {\left(b^{3} + 4 \, a b c - 8 \, b c d\right)} x\right)} \sqrt{-a b^{2} - 4 \, c d^{2} + {\left(b^{2} + 4 \, a c\right)} d} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a^{2} b^{3} + 4 \, a b c d^{2} + 2 \, {\left(a b^{2} c^{2} + 4 \, c^{3} d^{2} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d\right)} x^{3} + 3 \, {\left(a b^{3} c + 4 \, b c^{2} d^{2} - {\left(b^{3} c + 4 \, a b c^{2}\right)} d\right)} x^{2} - {\left(a b^{3} + 4 \, a^{2} b c\right)} d + {\left(a b^{4} + 2 \, a^{2} b^{2} c + 4 \, {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} - {\left(b^{4} + 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d\right)} x\right)}}\right)}{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d}\right]"," ",0,"[1/2*log((8*a^2*b^4 + (b^4*c^2 + 24*a*b^2*c^3 + 16*a^2*c^4 + 128*c^4*d^2 - 32*(b^2*c^3 + 4*a*c^4)*d)*x^4 + 2*(b^5*c + 24*a*b^3*c^2 + 16*a^2*b*c^3 + 128*b*c^3*d^2 - 32*(b^3*c^2 + 4*a*b*c^3)*d)*x^3 + (b^4 + 24*a*b^2*c + 16*a^2*c^2)*d^2 + (b^6 + 32*a*b^4*c + 48*a^2*b^2*c^2 + 32*(5*b^2*c^2 + 4*a*c^3)*d^2 - 2*(19*b^4*c + 104*a*b^2*c^2 + 48*a^2*c^3)*d)*x^2 - 4*(2*a*b^3 + 2*(b^2*c^2 + 4*a*c^3 - 8*c^3*d)*x^3 + 3*(b^3*c + 4*a*b*c^2 - 8*b*c^2*d)*x^2 - (b^3 + 4*a*b*c)*d + (b^4 + 8*a*b^2*c - 2*(5*b^2*c + 4*a*c^2)*d)*x)*sqrt(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d)*sqrt(c*x^2 + b*x + a) - 8*(a*b^4 + 4*a^2*b^2*c)*d + 2*(4*a*b^5 + 16*a^2*b^3*c + 16*(b^3*c + 4*a*b*c^2)*d^2 - (3*b^5 + 40*a*b^3*c + 48*a^2*b*c^2)*d)*x)/(c^2*x^4 + 2*b*c*x^3 + 2*b*d*x + (b^2 + 2*c*d)*x^2 + d^2))/sqrt(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d), -sqrt(-a*b^2 - 4*c*d^2 + (b^2 + 4*a*c)*d)*arctan(-1/2*(2*a*b^2 + (b^2*c + 4*a*c^2 - 8*c^2*d)*x^2 - (b^2 + 4*a*c)*d + (b^3 + 4*a*b*c - 8*b*c*d)*x)*sqrt(-a*b^2 - 4*c*d^2 + (b^2 + 4*a*c)*d)*sqrt(c*x^2 + b*x + a)/(a^2*b^3 + 4*a*b*c*d^2 + 2*(a*b^2*c^2 + 4*c^3*d^2 - (b^2*c^2 + 4*a*c^3)*d)*x^3 + 3*(a*b^3*c + 4*b*c^2*d^2 - (b^3*c + 4*a*b*c^2)*d)*x^2 - (a*b^3 + 4*a^2*b*c)*d + (a*b^4 + 2*a^2*b^2*c + 4*(b^2*c + 2*a*c^2)*d^2 - (b^4 + 6*a*b^2*c + 8*a^2*c^2)*d)*x))/(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d)]","B",0
4,1,1544,0,0.842538," ","integrate(1/(c*x^2+b*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d} {\left(8 \, c d^{2} - {\left(b^{2} c + 4 \, a c^{2} - 8 \, c^{2} d\right)} x^{2} - {\left(b^{2} + 4 \, a c\right)} d - {\left(b^{3} + 4 \, a b c - 8 \, b c d\right)} x\right)} \log\left(\frac{8 \, a^{2} b^{4} + {\left(b^{4} c^{2} + 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4} + 128 \, c^{4} d^{2} - 32 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d\right)} x^{4} + 2 \, {\left(b^{5} c + 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 128 \, b c^{3} d^{2} - 32 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d\right)} x^{3} + {\left(b^{4} + 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} + {\left(b^{6} + 32 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 32 \, {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} - 2 \, {\left(19 \, b^{4} c + 104 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} d\right)} x^{2} - 4 \, {\left(2 \, a b^{3} + 2 \, {\left(b^{2} c^{2} + 4 \, a c^{3} - 8 \, c^{3} d\right)} x^{3} + 3 \, {\left(b^{3} c + 4 \, a b c^{2} - 8 \, b c^{2} d\right)} x^{2} - {\left(b^{3} + 4 \, a b c\right)} d + {\left(b^{4} + 8 \, a b^{2} c - 2 \, {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d\right)} x\right)} \sqrt{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d} \sqrt{c x^{2} + b x + a} - 8 \, {\left(a b^{4} + 4 \, a^{2} b^{2} c\right)} d + 2 \, {\left(4 \, a b^{5} + 16 \, a^{2} b^{3} c + 16 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{2} - {\left(3 \, b^{5} + 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d\right)} x}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, b d x + {\left(b^{2} + 2 \, c d\right)} x^{2} + d^{2}}\right) - 4 \, {\left(a b^{3} + 4 \, b c d^{2} - {\left(b^{3} + 4 \, a b c\right)} d + 2 \, {\left(a b^{2} c + 4 \, c^{2} d^{2} - {\left(b^{2} c + 4 \, a c^{2}\right)} d\right)} x\right)} \sqrt{c x^{2} + b x + a}}{4 \, {\left(a^{2} b^{4} d + 16 \, c^{2} d^{5} - 8 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{4} + {\left(b^{4} + 16 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{4} + 4 \, a^{2} b^{2} c\right)} d^{2} + {\left(a^{2} b^{4} c + 16 \, c^{3} d^{4} - 8 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{3} + {\left(b^{4} c + 16 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} - 2 \, {\left(a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d\right)} x^{2} + {\left(a^{2} b^{5} + 16 \, b c^{2} d^{4} - 8 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{3} + {\left(b^{5} + 16 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} + 4 \, a^{2} b^{3} c\right)} d\right)} x\right)}}, -\frac{\sqrt{-a b^{2} - 4 \, c d^{2} + {\left(b^{2} + 4 \, a c\right)} d} {\left(8 \, c d^{2} - {\left(b^{2} c + 4 \, a c^{2} - 8 \, c^{2} d\right)} x^{2} - {\left(b^{2} + 4 \, a c\right)} d - {\left(b^{3} + 4 \, a b c - 8 \, b c d\right)} x\right)} \arctan\left(-\frac{{\left(2 \, a b^{2} + {\left(b^{2} c + 4 \, a c^{2} - 8 \, c^{2} d\right)} x^{2} - {\left(b^{2} + 4 \, a c\right)} d + {\left(b^{3} + 4 \, a b c - 8 \, b c d\right)} x\right)} \sqrt{-a b^{2} - 4 \, c d^{2} + {\left(b^{2} + 4 \, a c\right)} d} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a^{2} b^{3} + 4 \, a b c d^{2} + 2 \, {\left(a b^{2} c^{2} + 4 \, c^{3} d^{2} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d\right)} x^{3} + 3 \, {\left(a b^{3} c + 4 \, b c^{2} d^{2} - {\left(b^{3} c + 4 \, a b c^{2}\right)} d\right)} x^{2} - {\left(a b^{3} + 4 \, a^{2} b c\right)} d + {\left(a b^{4} + 2 \, a^{2} b^{2} c + 4 \, {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} - {\left(b^{4} + 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d\right)} x\right)}}\right) + 2 \, {\left(a b^{3} + 4 \, b c d^{2} - {\left(b^{3} + 4 \, a b c\right)} d + 2 \, {\left(a b^{2} c + 4 \, c^{2} d^{2} - {\left(b^{2} c + 4 \, a c^{2}\right)} d\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a^{2} b^{4} d + 16 \, c^{2} d^{5} - 8 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{4} + {\left(b^{4} + 16 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(a b^{4} + 4 \, a^{2} b^{2} c\right)} d^{2} + {\left(a^{2} b^{4} c + 16 \, c^{3} d^{4} - 8 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{3} + {\left(b^{4} c + 16 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{2} - 2 \, {\left(a b^{4} c + 4 \, a^{2} b^{2} c^{2}\right)} d\right)} x^{2} + {\left(a^{2} b^{5} + 16 \, b c^{2} d^{4} - 8 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{3} + {\left(b^{5} + 16 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} - 2 \, {\left(a b^{5} + 4 \, a^{2} b^{3} c\right)} d\right)} x\right)}}\right]"," ",0,"[1/4*(sqrt(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d)*(8*c*d^2 - (b^2*c + 4*a*c^2 - 8*c^2*d)*x^2 - (b^2 + 4*a*c)*d - (b^3 + 4*a*b*c - 8*b*c*d)*x)*log((8*a^2*b^4 + (b^4*c^2 + 24*a*b^2*c^3 + 16*a^2*c^4 + 128*c^4*d^2 - 32*(b^2*c^3 + 4*a*c^4)*d)*x^4 + 2*(b^5*c + 24*a*b^3*c^2 + 16*a^2*b*c^3 + 128*b*c^3*d^2 - 32*(b^3*c^2 + 4*a*b*c^3)*d)*x^3 + (b^4 + 24*a*b^2*c + 16*a^2*c^2)*d^2 + (b^6 + 32*a*b^4*c + 48*a^2*b^2*c^2 + 32*(5*b^2*c^2 + 4*a*c^3)*d^2 - 2*(19*b^4*c + 104*a*b^2*c^2 + 48*a^2*c^3)*d)*x^2 - 4*(2*a*b^3 + 2*(b^2*c^2 + 4*a*c^3 - 8*c^3*d)*x^3 + 3*(b^3*c + 4*a*b*c^2 - 8*b*c^2*d)*x^2 - (b^3 + 4*a*b*c)*d + (b^4 + 8*a*b^2*c - 2*(5*b^2*c + 4*a*c^2)*d)*x)*sqrt(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d)*sqrt(c*x^2 + b*x + a) - 8*(a*b^4 + 4*a^2*b^2*c)*d + 2*(4*a*b^5 + 16*a^2*b^3*c + 16*(b^3*c + 4*a*b*c^2)*d^2 - (3*b^5 + 40*a*b^3*c + 48*a^2*b*c^2)*d)*x)/(c^2*x^4 + 2*b*c*x^3 + 2*b*d*x + (b^2 + 2*c*d)*x^2 + d^2)) - 4*(a*b^3 + 4*b*c*d^2 - (b^3 + 4*a*b*c)*d + 2*(a*b^2*c + 4*c^2*d^2 - (b^2*c + 4*a*c^2)*d)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*d + 16*c^2*d^5 - 8*(b^2*c + 4*a*c^2)*d^4 + (b^4 + 16*a*b^2*c + 16*a^2*c^2)*d^3 - 2*(a*b^4 + 4*a^2*b^2*c)*d^2 + (a^2*b^4*c + 16*c^3*d^4 - 8*(b^2*c^2 + 4*a*c^3)*d^3 + (b^4*c + 16*a*b^2*c^2 + 16*a^2*c^3)*d^2 - 2*(a*b^4*c + 4*a^2*b^2*c^2)*d)*x^2 + (a^2*b^5 + 16*b*c^2*d^4 - 8*(b^3*c + 4*a*b*c^2)*d^3 + (b^5 + 16*a*b^3*c + 16*a^2*b*c^2)*d^2 - 2*(a*b^5 + 4*a^2*b^3*c)*d)*x), -1/2*(sqrt(-a*b^2 - 4*c*d^2 + (b^2 + 4*a*c)*d)*(8*c*d^2 - (b^2*c + 4*a*c^2 - 8*c^2*d)*x^2 - (b^2 + 4*a*c)*d - (b^3 + 4*a*b*c - 8*b*c*d)*x)*arctan(-1/2*(2*a*b^2 + (b^2*c + 4*a*c^2 - 8*c^2*d)*x^2 - (b^2 + 4*a*c)*d + (b^3 + 4*a*b*c - 8*b*c*d)*x)*sqrt(-a*b^2 - 4*c*d^2 + (b^2 + 4*a*c)*d)*sqrt(c*x^2 + b*x + a)/(a^2*b^3 + 4*a*b*c*d^2 + 2*(a*b^2*c^2 + 4*c^3*d^2 - (b^2*c^2 + 4*a*c^3)*d)*x^3 + 3*(a*b^3*c + 4*b*c^2*d^2 - (b^3*c + 4*a*b*c^2)*d)*x^2 - (a*b^3 + 4*a^2*b*c)*d + (a*b^4 + 2*a^2*b^2*c + 4*(b^2*c + 2*a*c^2)*d^2 - (b^4 + 6*a*b^2*c + 8*a^2*c^2)*d)*x)) + 2*(a*b^3 + 4*b*c*d^2 - (b^3 + 4*a*b*c)*d + 2*(a*b^2*c + 4*c^2*d^2 - (b^2*c + 4*a*c^2)*d)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*d + 16*c^2*d^5 - 8*(b^2*c + 4*a*c^2)*d^4 + (b^4 + 16*a*b^2*c + 16*a^2*c^2)*d^3 - 2*(a*b^4 + 4*a^2*b^2*c)*d^2 + (a^2*b^4*c + 16*c^3*d^4 - 8*(b^2*c^2 + 4*a*c^3)*d^3 + (b^4*c + 16*a*b^2*c^2 + 16*a^2*c^3)*d^2 - 2*(a*b^4*c + 4*a^2*b^2*c^2)*d)*x^2 + (a^2*b^5 + 16*b*c^2*d^4 - 8*(b^3*c + 4*a*b*c^2)*d^3 + (b^5 + 16*a*b^3*c + 16*a^2*b*c^2)*d^2 - 2*(a*b^5 + 4*a^2*b^3*c)*d)*x)]","B",0
5,1,3818,0,4.819814," ","integrate(1/(c*x^2+b*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(128 \, c^{2} d^{4} + {\left(3 \, b^{4} c^{2} + 8 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} + 128 \, c^{4} d^{2} - 32 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d\right)} x^{4} - 32 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{3} + 2 \, {\left(3 \, b^{5} c + 8 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3} + 128 \, b c^{3} d^{2} - 32 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d\right)} x^{3} + {\left(3 \, b^{4} + 8 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} d^{2} + {\left(3 \, b^{6} + 8 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 256 \, c^{3} d^{3} + 64 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} - 2 \, {\left(13 \, b^{4} c + 56 \, a b^{2} c^{2} - 48 \, a^{2} c^{3}\right)} d\right)} x^{2} + 2 \, {\left(128 \, b c^{2} d^{3} - 32 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{2} + {\left(3 \, b^{5} + 8 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d\right)} x\right)} \sqrt{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d} \log\left(\frac{8 \, a^{2} b^{4} + {\left(b^{4} c^{2} + 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4} + 128 \, c^{4} d^{2} - 32 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d\right)} x^{4} + 2 \, {\left(b^{5} c + 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 128 \, b c^{3} d^{2} - 32 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d\right)} x^{3} + {\left(b^{4} + 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} + {\left(b^{6} + 32 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 32 \, {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} - 2 \, {\left(19 \, b^{4} c + 104 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} d\right)} x^{2} - 4 \, {\left(2 \, a b^{3} + 2 \, {\left(b^{2} c^{2} + 4 \, a c^{3} - 8 \, c^{3} d\right)} x^{3} + 3 \, {\left(b^{3} c + 4 \, a b c^{2} - 8 \, b c^{2} d\right)} x^{2} - {\left(b^{3} + 4 \, a b c\right)} d + {\left(b^{4} + 8 \, a b^{2} c - 2 \, {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d\right)} x\right)} \sqrt{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d} \sqrt{c x^{2} + b x + a} - 8 \, {\left(a b^{4} + 4 \, a^{2} b^{2} c\right)} d + 2 \, {\left(4 \, a b^{5} + 16 \, a^{2} b^{3} c + 16 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{2} - {\left(3 \, b^{5} + 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d\right)} x}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, b d x + {\left(b^{2} + 2 \, c d\right)} x^{2} + d^{2}}\right) - 4 \, {\left(2 \, a^{2} b^{5} + 128 \, b c^{2} d^{4} - 52 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{3} - 6 \, {\left(a b^{4} c^{2} + 4 \, a^{2} b^{2} c^{3} - 32 \, c^{4} d^{3} + 12 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d^{2} - {\left(b^{4} c^{2} + 16 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d\right)} x^{3} + 5 \, {\left(b^{5} + 16 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} - 9 \, {\left(a b^{5} c + 4 \, a^{2} b^{3} c^{2} - 32 \, b c^{3} d^{3} + 12 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d^{2} - {\left(b^{5} c + 16 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} x^{2} - 7 \, {\left(a b^{5} + 4 \, a^{2} b^{3} c\right)} d - {\left(3 \, a b^{6} + 8 \, a^{2} b^{4} c - 256 \, c^{3} d^{4} + 8 \, {\left(b^{2} c^{2} + 52 \, a c^{3}\right)} d^{3} + 2 \, {\left(13 \, b^{4} c - 8 \, a b^{2} c^{2} - 80 \, a^{2} c^{3}\right)} d^{2} - {\left(3 \, b^{6} + 34 \, a b^{4} c - 8 \, a^{2} b^{2} c^{2}\right)} d\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(a^{3} b^{6} d^{2} + 64 \, c^{3} d^{8} - 48 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{7} + 12 \, {\left(b^{4} c + 12 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{6} - {\left(b^{6} + 36 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3}\right)} d^{5} + 3 \, {\left(a b^{6} + 12 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d^{4} + {\left(a^{3} b^{6} c^{2} + 64 \, c^{5} d^{6} - 48 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{5} + 12 \, {\left(b^{4} c^{3} + 12 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} - {\left(b^{6} c^{2} + 36 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} + 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(a b^{6} c^{2} + 12 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4}\right)} d^{2} - 3 \, {\left(a^{2} b^{6} c^{2} + 4 \, a^{3} b^{4} c^{3}\right)} d\right)} x^{4} - 3 \, {\left(a^{2} b^{6} + 4 \, a^{3} b^{4} c\right)} d^{3} + 2 \, {\left(a^{3} b^{7} c + 64 \, b c^{4} d^{6} - 48 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{5} + 12 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} - {\left(b^{7} c + 36 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} + 64 \, a^{3} b c^{4}\right)} d^{3} + 3 \, {\left(a b^{7} c + 12 \, a^{2} b^{5} c^{2} + 16 \, a^{3} b^{3} c^{3}\right)} d^{2} - 3 \, {\left(a^{2} b^{7} c + 4 \, a^{3} b^{5} c^{2}\right)} d\right)} x^{3} + {\left(a^{3} b^{8} + 128 \, c^{4} d^{7} - 32 \, {\left(b^{2} c^{3} + 12 \, a c^{4}\right)} d^{6} - 24 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} - 16 \, a^{2} c^{4}\right)} d^{5} + 2 \, {\left(5 \, b^{6} c + 36 \, a b^{4} c^{2} - 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{4} - {\left(b^{8} + 30 \, a b^{6} c + 72 \, a^{2} b^{4} c^{2} - 32 \, a^{3} b^{2} c^{3}\right)} d^{3} + 3 \, {\left(a b^{8} + 10 \, a^{2} b^{6} c + 8 \, a^{3} b^{4} c^{2}\right)} d^{2} - {\left(3 \, a^{2} b^{8} + 10 \, a^{3} b^{6} c\right)} d\right)} x^{2} + 2 \, {\left(a^{3} b^{7} d + 64 \, b c^{3} d^{7} - 48 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d^{6} + 12 \, {\left(b^{5} c + 12 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} - {\left(b^{7} + 36 \, a b^{5} c + 144 \, a^{2} b^{3} c^{2} + 64 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{7} + 12 \, a^{2} b^{5} c + 16 \, a^{3} b^{3} c^{2}\right)} d^{3} - 3 \, {\left(a^{2} b^{7} + 4 \, a^{3} b^{5} c\right)} d^{2}\right)} x\right)}}, -\frac{{\left(128 \, c^{2} d^{4} + {\left(3 \, b^{4} c^{2} + 8 \, a b^{2} c^{3} + 48 \, a^{2} c^{4} + 128 \, c^{4} d^{2} - 32 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d\right)} x^{4} - 32 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d^{3} + 2 \, {\left(3 \, b^{5} c + 8 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3} + 128 \, b c^{3} d^{2} - 32 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d\right)} x^{3} + {\left(3 \, b^{4} + 8 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} d^{2} + {\left(3 \, b^{6} + 8 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 256 \, c^{3} d^{3} + 64 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d^{2} - 2 \, {\left(13 \, b^{4} c + 56 \, a b^{2} c^{2} - 48 \, a^{2} c^{3}\right)} d\right)} x^{2} + 2 \, {\left(128 \, b c^{2} d^{3} - 32 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{2} + {\left(3 \, b^{5} + 8 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d\right)} x\right)} \sqrt{-a b^{2} - 4 \, c d^{2} + {\left(b^{2} + 4 \, a c\right)} d} \arctan\left(-\frac{{\left(2 \, a b^{2} + {\left(b^{2} c + 4 \, a c^{2} - 8 \, c^{2} d\right)} x^{2} - {\left(b^{2} + 4 \, a c\right)} d + {\left(b^{3} + 4 \, a b c - 8 \, b c d\right)} x\right)} \sqrt{-a b^{2} - 4 \, c d^{2} + {\left(b^{2} + 4 \, a c\right)} d} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a^{2} b^{3} + 4 \, a b c d^{2} + 2 \, {\left(a b^{2} c^{2} + 4 \, c^{3} d^{2} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d\right)} x^{3} + 3 \, {\left(a b^{3} c + 4 \, b c^{2} d^{2} - {\left(b^{3} c + 4 \, a b c^{2}\right)} d\right)} x^{2} - {\left(a b^{3} + 4 \, a^{2} b c\right)} d + {\left(a b^{4} + 2 \, a^{2} b^{2} c + 4 \, {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} - {\left(b^{4} + 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d\right)} x\right)}}\right) + 2 \, {\left(2 \, a^{2} b^{5} + 128 \, b c^{2} d^{4} - 52 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{3} - 6 \, {\left(a b^{4} c^{2} + 4 \, a^{2} b^{2} c^{3} - 32 \, c^{4} d^{3} + 12 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d^{2} - {\left(b^{4} c^{2} + 16 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d\right)} x^{3} + 5 \, {\left(b^{5} + 16 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} d^{2} - 9 \, {\left(a b^{5} c + 4 \, a^{2} b^{3} c^{2} - 32 \, b c^{3} d^{3} + 12 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d^{2} - {\left(b^{5} c + 16 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d\right)} x^{2} - 7 \, {\left(a b^{5} + 4 \, a^{2} b^{3} c\right)} d - {\left(3 \, a b^{6} + 8 \, a^{2} b^{4} c - 256 \, c^{3} d^{4} + 8 \, {\left(b^{2} c^{2} + 52 \, a c^{3}\right)} d^{3} + 2 \, {\left(13 \, b^{4} c - 8 \, a b^{2} c^{2} - 80 \, a^{2} c^{3}\right)} d^{2} - {\left(3 \, b^{6} + 34 \, a b^{4} c - 8 \, a^{2} b^{2} c^{2}\right)} d\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(a^{3} b^{6} d^{2} + 64 \, c^{3} d^{8} - 48 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{7} + 12 \, {\left(b^{4} c + 12 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} d^{6} - {\left(b^{6} + 36 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} + 64 \, a^{3} c^{3}\right)} d^{5} + 3 \, {\left(a b^{6} + 12 \, a^{2} b^{4} c + 16 \, a^{3} b^{2} c^{2}\right)} d^{4} + {\left(a^{3} b^{6} c^{2} + 64 \, c^{5} d^{6} - 48 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{5} + 12 \, {\left(b^{4} c^{3} + 12 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d^{4} - {\left(b^{6} c^{2} + 36 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} + 64 \, a^{3} c^{5}\right)} d^{3} + 3 \, {\left(a b^{6} c^{2} + 12 \, a^{2} b^{4} c^{3} + 16 \, a^{3} b^{2} c^{4}\right)} d^{2} - 3 \, {\left(a^{2} b^{6} c^{2} + 4 \, a^{3} b^{4} c^{3}\right)} d\right)} x^{4} - 3 \, {\left(a^{2} b^{6} + 4 \, a^{3} b^{4} c\right)} d^{3} + 2 \, {\left(a^{3} b^{7} c + 64 \, b c^{4} d^{6} - 48 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{5} + 12 \, {\left(b^{5} c^{2} + 12 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d^{4} - {\left(b^{7} c + 36 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} + 64 \, a^{3} b c^{4}\right)} d^{3} + 3 \, {\left(a b^{7} c + 12 \, a^{2} b^{5} c^{2} + 16 \, a^{3} b^{3} c^{3}\right)} d^{2} - 3 \, {\left(a^{2} b^{7} c + 4 \, a^{3} b^{5} c^{2}\right)} d\right)} x^{3} + {\left(a^{3} b^{8} + 128 \, c^{4} d^{7} - 32 \, {\left(b^{2} c^{3} + 12 \, a c^{4}\right)} d^{6} - 24 \, {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} - 16 \, a^{2} c^{4}\right)} d^{5} + 2 \, {\left(5 \, b^{6} c + 36 \, a b^{4} c^{2} - 48 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} d^{4} - {\left(b^{8} + 30 \, a b^{6} c + 72 \, a^{2} b^{4} c^{2} - 32 \, a^{3} b^{2} c^{3}\right)} d^{3} + 3 \, {\left(a b^{8} + 10 \, a^{2} b^{6} c + 8 \, a^{3} b^{4} c^{2}\right)} d^{2} - {\left(3 \, a^{2} b^{8} + 10 \, a^{3} b^{6} c\right)} d\right)} x^{2} + 2 \, {\left(a^{3} b^{7} d + 64 \, b c^{3} d^{7} - 48 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d^{6} + 12 \, {\left(b^{5} c + 12 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{5} - {\left(b^{7} + 36 \, a b^{5} c + 144 \, a^{2} b^{3} c^{2} + 64 \, a^{3} b c^{3}\right)} d^{4} + 3 \, {\left(a b^{7} + 12 \, a^{2} b^{5} c + 16 \, a^{3} b^{3} c^{2}\right)} d^{3} - 3 \, {\left(a^{2} b^{7} + 4 \, a^{3} b^{5} c\right)} d^{2}\right)} x\right)}}\right]"," ",0,"[1/16*((128*c^2*d^4 + (3*b^4*c^2 + 8*a*b^2*c^3 + 48*a^2*c^4 + 128*c^4*d^2 - 32*(b^2*c^3 + 4*a*c^4)*d)*x^4 - 32*(b^2*c + 4*a*c^2)*d^3 + 2*(3*b^5*c + 8*a*b^3*c^2 + 48*a^2*b*c^3 + 128*b*c^3*d^2 - 32*(b^3*c^2 + 4*a*b*c^3)*d)*x^3 + (3*b^4 + 8*a*b^2*c + 48*a^2*c^2)*d^2 + (3*b^6 + 8*a*b^4*c + 48*a^2*b^2*c^2 + 256*c^3*d^3 + 64*(b^2*c^2 - 4*a*c^3)*d^2 - 2*(13*b^4*c + 56*a*b^2*c^2 - 48*a^2*c^3)*d)*x^2 + 2*(128*b*c^2*d^3 - 32*(b^3*c + 4*a*b*c^2)*d^2 + (3*b^5 + 8*a*b^3*c + 48*a^2*b*c^2)*d)*x)*sqrt(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d)*log((8*a^2*b^4 + (b^4*c^2 + 24*a*b^2*c^3 + 16*a^2*c^4 + 128*c^4*d^2 - 32*(b^2*c^3 + 4*a*c^4)*d)*x^4 + 2*(b^5*c + 24*a*b^3*c^2 + 16*a^2*b*c^3 + 128*b*c^3*d^2 - 32*(b^3*c^2 + 4*a*b*c^3)*d)*x^3 + (b^4 + 24*a*b^2*c + 16*a^2*c^2)*d^2 + (b^6 + 32*a*b^4*c + 48*a^2*b^2*c^2 + 32*(5*b^2*c^2 + 4*a*c^3)*d^2 - 2*(19*b^4*c + 104*a*b^2*c^2 + 48*a^2*c^3)*d)*x^2 - 4*(2*a*b^3 + 2*(b^2*c^2 + 4*a*c^3 - 8*c^3*d)*x^3 + 3*(b^3*c + 4*a*b*c^2 - 8*b*c^2*d)*x^2 - (b^3 + 4*a*b*c)*d + (b^4 + 8*a*b^2*c - 2*(5*b^2*c + 4*a*c^2)*d)*x)*sqrt(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d)*sqrt(c*x^2 + b*x + a) - 8*(a*b^4 + 4*a^2*b^2*c)*d + 2*(4*a*b^5 + 16*a^2*b^3*c + 16*(b^3*c + 4*a*b*c^2)*d^2 - (3*b^5 + 40*a*b^3*c + 48*a^2*b*c^2)*d)*x)/(c^2*x^4 + 2*b*c*x^3 + 2*b*d*x + (b^2 + 2*c*d)*x^2 + d^2)) - 4*(2*a^2*b^5 + 128*b*c^2*d^4 - 52*(b^3*c + 4*a*b*c^2)*d^3 - 6*(a*b^4*c^2 + 4*a^2*b^2*c^3 - 32*c^4*d^3 + 12*(b^2*c^3 + 4*a*c^4)*d^2 - (b^4*c^2 + 16*a*b^2*c^3 + 16*a^2*c^4)*d)*x^3 + 5*(b^5 + 16*a*b^3*c + 16*a^2*b*c^2)*d^2 - 9*(a*b^5*c + 4*a^2*b^3*c^2 - 32*b*c^3*d^3 + 12*(b^3*c^2 + 4*a*b*c^3)*d^2 - (b^5*c + 16*a*b^3*c^2 + 16*a^2*b*c^3)*d)*x^2 - 7*(a*b^5 + 4*a^2*b^3*c)*d - (3*a*b^6 + 8*a^2*b^4*c - 256*c^3*d^4 + 8*(b^2*c^2 + 52*a*c^3)*d^3 + 2*(13*b^4*c - 8*a*b^2*c^2 - 80*a^2*c^3)*d^2 - (3*b^6 + 34*a*b^4*c - 8*a^2*b^2*c^2)*d)*x)*sqrt(c*x^2 + b*x + a))/(a^3*b^6*d^2 + 64*c^3*d^8 - 48*(b^2*c^2 + 4*a*c^3)*d^7 + 12*(b^4*c + 12*a*b^2*c^2 + 16*a^2*c^3)*d^6 - (b^6 + 36*a*b^4*c + 144*a^2*b^2*c^2 + 64*a^3*c^3)*d^5 + 3*(a*b^6 + 12*a^2*b^4*c + 16*a^3*b^2*c^2)*d^4 + (a^3*b^6*c^2 + 64*c^5*d^6 - 48*(b^2*c^4 + 4*a*c^5)*d^5 + 12*(b^4*c^3 + 12*a*b^2*c^4 + 16*a^2*c^5)*d^4 - (b^6*c^2 + 36*a*b^4*c^3 + 144*a^2*b^2*c^4 + 64*a^3*c^5)*d^3 + 3*(a*b^6*c^2 + 12*a^2*b^4*c^3 + 16*a^3*b^2*c^4)*d^2 - 3*(a^2*b^6*c^2 + 4*a^3*b^4*c^3)*d)*x^4 - 3*(a^2*b^6 + 4*a^3*b^4*c)*d^3 + 2*(a^3*b^7*c + 64*b*c^4*d^6 - 48*(b^3*c^3 + 4*a*b*c^4)*d^5 + 12*(b^5*c^2 + 12*a*b^3*c^3 + 16*a^2*b*c^4)*d^4 - (b^7*c + 36*a*b^5*c^2 + 144*a^2*b^3*c^3 + 64*a^3*b*c^4)*d^3 + 3*(a*b^7*c + 12*a^2*b^5*c^2 + 16*a^3*b^3*c^3)*d^2 - 3*(a^2*b^7*c + 4*a^3*b^5*c^2)*d)*x^3 + (a^3*b^8 + 128*c^4*d^7 - 32*(b^2*c^3 + 12*a*c^4)*d^6 - 24*(b^4*c^2 - 4*a*b^2*c^3 - 16*a^2*c^4)*d^5 + 2*(5*b^6*c + 36*a*b^4*c^2 - 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^4 - (b^8 + 30*a*b^6*c + 72*a^2*b^4*c^2 - 32*a^3*b^2*c^3)*d^3 + 3*(a*b^8 + 10*a^2*b^6*c + 8*a^3*b^4*c^2)*d^2 - (3*a^2*b^8 + 10*a^3*b^6*c)*d)*x^2 + 2*(a^3*b^7*d + 64*b*c^3*d^7 - 48*(b^3*c^2 + 4*a*b*c^3)*d^6 + 12*(b^5*c + 12*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 - (b^7 + 36*a*b^5*c + 144*a^2*b^3*c^2 + 64*a^3*b*c^3)*d^4 + 3*(a*b^7 + 12*a^2*b^5*c + 16*a^3*b^3*c^2)*d^3 - 3*(a^2*b^7 + 4*a^3*b^5*c)*d^2)*x), -1/8*((128*c^2*d^4 + (3*b^4*c^2 + 8*a*b^2*c^3 + 48*a^2*c^4 + 128*c^4*d^2 - 32*(b^2*c^3 + 4*a*c^4)*d)*x^4 - 32*(b^2*c + 4*a*c^2)*d^3 + 2*(3*b^5*c + 8*a*b^3*c^2 + 48*a^2*b*c^3 + 128*b*c^3*d^2 - 32*(b^3*c^2 + 4*a*b*c^3)*d)*x^3 + (3*b^4 + 8*a*b^2*c + 48*a^2*c^2)*d^2 + (3*b^6 + 8*a*b^4*c + 48*a^2*b^2*c^2 + 256*c^3*d^3 + 64*(b^2*c^2 - 4*a*c^3)*d^2 - 2*(13*b^4*c + 56*a*b^2*c^2 - 48*a^2*c^3)*d)*x^2 + 2*(128*b*c^2*d^3 - 32*(b^3*c + 4*a*b*c^2)*d^2 + (3*b^5 + 8*a*b^3*c + 48*a^2*b*c^2)*d)*x)*sqrt(-a*b^2 - 4*c*d^2 + (b^2 + 4*a*c)*d)*arctan(-1/2*(2*a*b^2 + (b^2*c + 4*a*c^2 - 8*c^2*d)*x^2 - (b^2 + 4*a*c)*d + (b^3 + 4*a*b*c - 8*b*c*d)*x)*sqrt(-a*b^2 - 4*c*d^2 + (b^2 + 4*a*c)*d)*sqrt(c*x^2 + b*x + a)/(a^2*b^3 + 4*a*b*c*d^2 + 2*(a*b^2*c^2 + 4*c^3*d^2 - (b^2*c^2 + 4*a*c^3)*d)*x^3 + 3*(a*b^3*c + 4*b*c^2*d^2 - (b^3*c + 4*a*b*c^2)*d)*x^2 - (a*b^3 + 4*a^2*b*c)*d + (a*b^4 + 2*a^2*b^2*c + 4*(b^2*c + 2*a*c^2)*d^2 - (b^4 + 6*a*b^2*c + 8*a^2*c^2)*d)*x)) + 2*(2*a^2*b^5 + 128*b*c^2*d^4 - 52*(b^3*c + 4*a*b*c^2)*d^3 - 6*(a*b^4*c^2 + 4*a^2*b^2*c^3 - 32*c^4*d^3 + 12*(b^2*c^3 + 4*a*c^4)*d^2 - (b^4*c^2 + 16*a*b^2*c^3 + 16*a^2*c^4)*d)*x^3 + 5*(b^5 + 16*a*b^3*c + 16*a^2*b*c^2)*d^2 - 9*(a*b^5*c + 4*a^2*b^3*c^2 - 32*b*c^3*d^3 + 12*(b^3*c^2 + 4*a*b*c^3)*d^2 - (b^5*c + 16*a*b^3*c^2 + 16*a^2*b*c^3)*d)*x^2 - 7*(a*b^5 + 4*a^2*b^3*c)*d - (3*a*b^6 + 8*a^2*b^4*c - 256*c^3*d^4 + 8*(b^2*c^2 + 52*a*c^3)*d^3 + 2*(13*b^4*c - 8*a*b^2*c^2 - 80*a^2*c^3)*d^2 - (3*b^6 + 34*a*b^4*c - 8*a^2*b^2*c^2)*d)*x)*sqrt(c*x^2 + b*x + a))/(a^3*b^6*d^2 + 64*c^3*d^8 - 48*(b^2*c^2 + 4*a*c^3)*d^7 + 12*(b^4*c + 12*a*b^2*c^2 + 16*a^2*c^3)*d^6 - (b^6 + 36*a*b^4*c + 144*a^2*b^2*c^2 + 64*a^3*c^3)*d^5 + 3*(a*b^6 + 12*a^2*b^4*c + 16*a^3*b^2*c^2)*d^4 + (a^3*b^6*c^2 + 64*c^5*d^6 - 48*(b^2*c^4 + 4*a*c^5)*d^5 + 12*(b^4*c^3 + 12*a*b^2*c^4 + 16*a^2*c^5)*d^4 - (b^6*c^2 + 36*a*b^4*c^3 + 144*a^2*b^2*c^4 + 64*a^3*c^5)*d^3 + 3*(a*b^6*c^2 + 12*a^2*b^4*c^3 + 16*a^3*b^2*c^4)*d^2 - 3*(a^2*b^6*c^2 + 4*a^3*b^4*c^3)*d)*x^4 - 3*(a^2*b^6 + 4*a^3*b^4*c)*d^3 + 2*(a^3*b^7*c + 64*b*c^4*d^6 - 48*(b^3*c^3 + 4*a*b*c^4)*d^5 + 12*(b^5*c^2 + 12*a*b^3*c^3 + 16*a^2*b*c^4)*d^4 - (b^7*c + 36*a*b^5*c^2 + 144*a^2*b^3*c^3 + 64*a^3*b*c^4)*d^3 + 3*(a*b^7*c + 12*a^2*b^5*c^2 + 16*a^3*b^3*c^3)*d^2 - 3*(a^2*b^7*c + 4*a^3*b^5*c^2)*d)*x^3 + (a^3*b^8 + 128*c^4*d^7 - 32*(b^2*c^3 + 12*a*c^4)*d^6 - 24*(b^4*c^2 - 4*a*b^2*c^3 - 16*a^2*c^4)*d^5 + 2*(5*b^6*c + 36*a*b^4*c^2 - 48*a^2*b^2*c^3 - 64*a^3*c^4)*d^4 - (b^8 + 30*a*b^6*c + 72*a^2*b^4*c^2 - 32*a^3*b^2*c^3)*d^3 + 3*(a*b^8 + 10*a^2*b^6*c + 8*a^3*b^4*c^2)*d^2 - (3*a^2*b^8 + 10*a^3*b^6*c)*d)*x^2 + 2*(a^3*b^7*d + 64*b*c^3*d^7 - 48*(b^3*c^2 + 4*a*b*c^3)*d^6 + 12*(b^5*c + 12*a*b^3*c^2 + 16*a^2*b*c^3)*d^5 - (b^7 + 36*a*b^5*c + 144*a^2*b^3*c^2 + 64*a^3*b*c^3)*d^4 + 3*(a*b^7 + 12*a^2*b^5*c + 16*a^3*b^3*c^2)*d^3 - 3*(a^2*b^7 + 4*a^3*b^5*c)*d^2)*x)]","B",0
6,1,8134,0,20.448978," ","integrate(1/(c*x^2+b*x+d)^4/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(1024 \, c^{3} d^{6} - {\left(5 \, b^{6} c^{3} + 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} + 320 \, a^{3} c^{6} - 1024 \, c^{6} d^{3} + 384 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{2} - 24 \, {\left(3 \, b^{4} c^{4} + 8 \, a b^{2} c^{5} + 48 \, a^{2} c^{6}\right)} d\right)} x^{6} - 384 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} - 3 \, {\left(5 \, b^{7} c^{2} + 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} + 320 \, a^{3} b c^{5} - 1024 \, b c^{5} d^{3} + 384 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d^{2} - 24 \, {\left(3 \, b^{5} c^{3} + 8 \, a b^{3} c^{4} + 48 \, a^{2} b c^{5}\right)} d\right)} x^{5} + 24 \, {\left(3 \, b^{4} c + 8 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} d^{4} - 3 \, {\left(5 \, b^{8} c + 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} + 320 \, a^{3} b^{2} c^{4} - 1024 \, c^{5} d^{4} - 128 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} d^{3} + 24 \, {\left(13 \, b^{4} c^{3} + 56 \, a b^{2} c^{4} - 48 \, a^{2} c^{5}\right)} d^{2} - {\left(67 \, b^{6} c^{2} + 180 \, a b^{4} c^{3} + 1104 \, a^{2} b^{2} c^{4} - 320 \, a^{3} c^{5}\right)} d\right)} x^{4} - {\left(5 \, b^{6} + 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 320 \, a^{3} c^{3}\right)} d^{3} - {\left(5 \, b^{9} + 12 \, a b^{7} c + 48 \, a^{2} b^{5} c^{2} + 320 \, a^{3} b^{3} c^{3} - 6144 \, b c^{4} d^{4} + 256 \, {\left(5 \, b^{3} c^{3} + 36 \, a b c^{4}\right)} d^{3} - 48 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 144 \, a^{2} b c^{4}\right)} d^{2} - 6 \, {\left(7 \, b^{7} c + 20 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} - 320 \, a^{3} b c^{4}\right)} d\right)} x^{3} + 3 \, {\left(1024 \, c^{4} d^{5} + 128 \, {\left(5 \, b^{2} c^{3} - 12 \, a c^{4}\right)} d^{4} - 24 \, {\left(13 \, b^{4} c^{2} + 56 \, a b^{2} c^{3} - 48 \, a^{2} c^{4}\right)} d^{3} + {\left(67 \, b^{6} c + 180 \, a b^{4} c^{2} + 1104 \, a^{2} b^{2} c^{3} - 320 \, a^{3} c^{4}\right)} d^{2} - {\left(5 \, b^{8} + 12 \, a b^{6} c + 48 \, a^{2} b^{4} c^{2} + 320 \, a^{3} b^{2} c^{3}\right)} d\right)} x^{2} + 3 \, {\left(1024 \, b c^{3} d^{5} - 384 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d^{4} + 24 \, {\left(3 \, b^{5} c + 8 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} d^{3} - {\left(5 \, b^{7} + 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} + 320 \, a^{3} b c^{3}\right)} d^{2}\right)} x\right)} \sqrt{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d} \log\left(\frac{8 \, a^{2} b^{4} + {\left(b^{4} c^{2} + 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4} + 128 \, c^{4} d^{2} - 32 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d\right)} x^{4} + 2 \, {\left(b^{5} c + 24 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3} + 128 \, b c^{3} d^{2} - 32 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d\right)} x^{3} + {\left(b^{4} + 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} d^{2} + {\left(b^{6} + 32 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 32 \, {\left(5 \, b^{2} c^{2} + 4 \, a c^{3}\right)} d^{2} - 2 \, {\left(19 \, b^{4} c + 104 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} d\right)} x^{2} - 4 \, {\left(2 \, a b^{3} + 2 \, {\left(b^{2} c^{2} + 4 \, a c^{3} - 8 \, c^{3} d\right)} x^{3} + 3 \, {\left(b^{3} c + 4 \, a b c^{2} - 8 \, b c^{2} d\right)} x^{2} - {\left(b^{3} + 4 \, a b c\right)} d + {\left(b^{4} + 8 \, a b^{2} c - 2 \, {\left(5 \, b^{2} c + 4 \, a c^{2}\right)} d\right)} x\right)} \sqrt{a b^{2} + 4 \, c d^{2} - {\left(b^{2} + 4 \, a c\right)} d} \sqrt{c x^{2} + b x + a} - 8 \, {\left(a b^{4} + 4 \, a^{2} b^{2} c\right)} d + 2 \, {\left(4 \, a b^{5} + 16 \, a^{2} b^{3} c + 16 \, {\left(b^{3} c + 4 \, a b c^{2}\right)} d^{2} - {\left(3 \, b^{5} + 40 \, a b^{3} c + 48 \, a^{2} b c^{2}\right)} d\right)} x}{c^{2} x^{4} + 2 \, b c x^{3} + 2 \, b d x + {\left(b^{2} + 2 \, c d\right)} x^{2} + d^{2}}\right) - 4 \, {\left(8 \, a^{3} b^{7} + 4608 \, b c^{3} d^{6} - 2592 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d^{5} + 2 \, {\left(15 \, a b^{6} c^{3} + 56 \, a^{2} b^{4} c^{4} + 240 \, a^{3} b^{2} c^{5} + 2816 \, c^{6} d^{4} - 1408 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{3} + 4 \, {\left(59 \, b^{4} c^{4} + 584 \, a b^{2} c^{5} + 944 \, a^{2} c^{6}\right)} d^{2} - {\left(15 \, b^{6} c^{3} + 292 \, a b^{4} c^{4} + 1168 \, a^{2} b^{2} c^{5} + 960 \, a^{3} c^{6}\right)} d\right)} x^{5} + 4 \, {\left(123 \, b^{5} c + 1352 \, a b^{3} c^{2} + 1968 \, a^{2} b c^{3}\right)} d^{4} + 5 \, {\left(15 \, a b^{7} c^{2} + 56 \, a^{2} b^{5} c^{3} + 240 \, a^{3} b^{3} c^{4} + 2816 \, b c^{5} d^{4} - 1408 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d^{3} + 4 \, {\left(59 \, b^{5} c^{3} + 584 \, a b^{3} c^{4} + 944 \, a^{2} b c^{5}\right)} d^{2} - {\left(15 \, b^{7} c^{2} + 292 \, a b^{5} c^{3} + 1168 \, a^{2} b^{3} c^{4} + 960 \, a^{3} b c^{5}\right)} d\right)} x^{4} - {\left(33 \, b^{7} + 940 \, a b^{5} c + 3760 \, a^{2} b^{3} c^{2} + 2112 \, a^{3} b c^{3}\right)} d^{3} + 4 \, {\left(15 \, a b^{8} c + 51 \, a^{2} b^{6} c^{2} + 220 \, a^{3} b^{4} c^{3} + 3456 \, c^{5} d^{5} + 16 \, {\left(63 \, b^{2} c^{4} - 452 \, a c^{5}\right)} d^{4} - 4 \, {\left(273 \, b^{4} c^{3} + 584 \, a b^{2} c^{4} - 1264 \, a^{2} c^{5}\right)} d^{3} + 8 \, {\left(27 \, b^{6} c^{2} + 233 \, a b^{4} c^{3} + 236 \, a^{2} b^{2} c^{4} - 160 \, a^{3} c^{5}\right)} d^{2} - {\left(15 \, b^{8} c + 267 \, a b^{6} c^{2} + 992 \, a^{2} b^{4} c^{3} + 560 \, a^{3} b^{2} c^{4}\right)} d\right)} x^{3} + {\left(59 \, a b^{7} + 584 \, a^{2} b^{5} c + 944 \, a^{3} b^{3} c^{2}\right)} d^{2} + {\left(15 \, a b^{9} + 26 \, a^{2} b^{7} c + 120 \, a^{3} b^{5} c^{2} + 20736 \, b c^{4} d^{5} - 32 \, {\left(251 \, b^{3} c^{3} + 1356 \, a b c^{4}\right)} d^{4} + 8 \, {\left(61 \, b^{5} c^{2} + 1768 \, a b^{3} c^{3} + 3792 \, a^{2} b c^{4}\right)} d^{3} + 4 \, {\left(29 \, b^{7} c - 124 \, a b^{5} c^{2} - 1888 \, a^{2} b^{3} c^{3} - 1920 \, a^{3} b c^{4}\right)} d^{2} - {\left(15 \, b^{9} + 142 \, a b^{7} c + 112 \, a^{2} b^{5} c^{2} - 1440 \, a^{3} b^{3} c^{3}\right)} d\right)} x^{2} - 34 \, {\left(a^{2} b^{7} + 4 \, a^{3} b^{5} c\right)} d - 2 \, {\left(5 \, a^{2} b^{8} + 12 \, a^{3} b^{6} c - 4608 \, c^{4} d^{6} - 864 \, {\left(b^{2} c^{3} - 12 \, a c^{4}\right)} d^{5} + 4 \, {\left(329 \, b^{4} c^{2} + 456 \, a b^{2} c^{3} - 1968 \, a^{2} c^{4}\right)} d^{4} - {\left(283 \, b^{6} c + 2356 \, a b^{4} c^{2} + 1296 \, a^{2} b^{2} c^{3} - 2112 \, a^{3} c^{4}\right)} d^{3} + {\left(20 \, b^{8} + 413 \, a b^{6} c + 1304 \, a^{2} b^{4} c^{2} + 336 \, a^{3} b^{2} c^{3}\right)} d^{2} - {\left(25 \, a b^{8} + 142 \, a^{2} b^{6} c + 264 \, a^{3} b^{4} c^{2}\right)} d\right)} x\right)} \sqrt{c x^{2} + b x + a}}{96 \, {\left(a^{4} b^{8} d^{3} + 256 \, c^{4} d^{11} - 256 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d^{10} + 32 \, {\left(3 \, b^{4} c^{2} + 32 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{9} - 16 \, {\left(b^{6} c + 24 \, a b^{4} c^{2} + 96 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{8} + {\left(b^{8} + 64 \, a b^{6} c + 576 \, a^{2} b^{4} c^{2} + 1024 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} d^{7} - 4 \, {\left(a b^{8} + 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} + 64 \, a^{4} b^{2} c^{3}\right)} d^{6} + {\left(a^{4} b^{8} c^{3} + 256 \, c^{7} d^{8} - 256 \, {\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d^{7} + 32 \, {\left(3 \, b^{4} c^{5} + 32 \, a b^{2} c^{6} + 48 \, a^{2} c^{7}\right)} d^{6} - 16 \, {\left(b^{6} c^{4} + 24 \, a b^{4} c^{5} + 96 \, a^{2} b^{2} c^{6} + 64 \, a^{3} c^{7}\right)} d^{5} + {\left(b^{8} c^{3} + 64 \, a b^{6} c^{4} + 576 \, a^{2} b^{4} c^{5} + 1024 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} d^{4} - 4 \, {\left(a b^{8} c^{3} + 24 \, a^{2} b^{6} c^{4} + 96 \, a^{3} b^{4} c^{5} + 64 \, a^{4} b^{2} c^{6}\right)} d^{3} + 2 \, {\left(3 \, a^{2} b^{8} c^{3} + 32 \, a^{3} b^{6} c^{4} + 48 \, a^{4} b^{4} c^{5}\right)} d^{2} - 4 \, {\left(a^{3} b^{8} c^{3} + 4 \, a^{4} b^{6} c^{4}\right)} d\right)} x^{6} + 2 \, {\left(3 \, a^{2} b^{8} + 32 \, a^{3} b^{6} c + 48 \, a^{4} b^{4} c^{2}\right)} d^{5} + 3 \, {\left(a^{4} b^{9} c^{2} + 256 \, b c^{6} d^{8} - 256 \, {\left(b^{3} c^{5} + 4 \, a b c^{6}\right)} d^{7} + 32 \, {\left(3 \, b^{5} c^{4} + 32 \, a b^{3} c^{5} + 48 \, a^{2} b c^{6}\right)} d^{6} - 16 \, {\left(b^{7} c^{3} + 24 \, a b^{5} c^{4} + 96 \, a^{2} b^{3} c^{5} + 64 \, a^{3} b c^{6}\right)} d^{5} + {\left(b^{9} c^{2} + 64 \, a b^{7} c^{3} + 576 \, a^{2} b^{5} c^{4} + 1024 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} d^{4} - 4 \, {\left(a b^{9} c^{2} + 24 \, a^{2} b^{7} c^{3} + 96 \, a^{3} b^{5} c^{4} + 64 \, a^{4} b^{3} c^{5}\right)} d^{3} + 2 \, {\left(3 \, a^{2} b^{9} c^{2} + 32 \, a^{3} b^{7} c^{3} + 48 \, a^{4} b^{5} c^{4}\right)} d^{2} - 4 \, {\left(a^{3} b^{9} c^{2} + 4 \, a^{4} b^{7} c^{3}\right)} d\right)} x^{5} - 4 \, {\left(a^{3} b^{8} + 4 \, a^{4} b^{6} c\right)} d^{4} + 3 \, {\left(a^{4} b^{10} c - 1024 \, a c^{6} d^{8} + 256 \, c^{6} d^{9} - 32 \, {\left(5 \, b^{4} c^{4} - 48 \, a^{2} c^{6}\right)} d^{7} + 16 \, {\left(5 \, b^{6} c^{3} + 40 \, a b^{4} c^{4} - 64 \, a^{3} c^{6}\right)} d^{6} - {\left(15 \, b^{8} c^{2} + 320 \, a b^{6} c^{3} + 960 \, a^{2} b^{4} c^{4} - 256 \, a^{4} c^{6}\right)} d^{5} + {\left(b^{10} c + 60 \, a b^{8} c^{2} + 480 \, a^{2} b^{6} c^{3} + 640 \, a^{3} b^{4} c^{4}\right)} d^{4} - 2 \, {\left(2 \, a b^{10} c + 45 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} + 80 \, a^{4} b^{4} c^{4}\right)} d^{3} + 2 \, {\left(3 \, a^{2} b^{10} c + 30 \, a^{3} b^{8} c^{2} + 40 \, a^{4} b^{6} c^{3}\right)} d^{2} - {\left(4 \, a^{3} b^{10} c + 15 \, a^{4} b^{8} c^{2}\right)} d\right)} x^{4} + {\left(a^{4} b^{11} + 1536 \, b c^{5} d^{9} - 256 \, {\left(5 \, b^{3} c^{4} + 24 \, a b c^{5}\right)} d^{8} + 64 \, {\left(5 \, b^{5} c^{3} + 80 \, a b^{3} c^{4} + 144 \, a^{2} b c^{5}\right)} d^{7} - 256 \, {\left(5 \, a b^{5} c^{3} + 30 \, a^{2} b^{3} c^{4} + 24 \, a^{3} b c^{5}\right)} d^{6} - 2 \, {\left(5 \, b^{9} c - 960 \, a^{2} b^{5} c^{3} - 2560 \, a^{3} b^{3} c^{4} - 768 \, a^{4} b c^{5}\right)} d^{5} + {\left(b^{11} + 40 \, a b^{9} c - 1280 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4}\right)} d^{4} - 4 \, {\left(a b^{11} + 15 \, a^{2} b^{9} c - 80 \, a^{4} b^{5} c^{3}\right)} d^{3} + 2 \, {\left(3 \, a^{2} b^{11} + 20 \, a^{3} b^{9} c\right)} d^{2} - 2 \, {\left(2 \, a^{3} b^{11} + 5 \, a^{4} b^{9} c\right)} d\right)} x^{3} + 3 \, {\left(a^{4} b^{10} d - 1024 \, a c^{5} d^{9} + 256 \, c^{5} d^{10} - 32 \, {\left(5 \, b^{4} c^{3} - 48 \, a^{2} c^{5}\right)} d^{8} + 16 \, {\left(5 \, b^{6} c^{2} + 40 \, a b^{4} c^{3} - 64 \, a^{3} c^{5}\right)} d^{7} - {\left(15 \, b^{8} c + 320 \, a b^{6} c^{2} + 960 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{6} + {\left(b^{10} + 60 \, a b^{8} c + 480 \, a^{2} b^{6} c^{2} + 640 \, a^{3} b^{4} c^{3}\right)} d^{5} - 2 \, {\left(2 \, a b^{10} + 45 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} + 80 \, a^{4} b^{4} c^{3}\right)} d^{4} + 2 \, {\left(3 \, a^{2} b^{10} + 30 \, a^{3} b^{8} c + 40 \, a^{4} b^{6} c^{2}\right)} d^{3} - {\left(4 \, a^{3} b^{10} + 15 \, a^{4} b^{8} c\right)} d^{2}\right)} x^{2} + 3 \, {\left(a^{4} b^{9} d^{2} + 256 \, b c^{4} d^{10} - 256 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{9} + 32 \, {\left(3 \, b^{5} c^{2} + 32 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} d^{8} - 16 \, {\left(b^{7} c + 24 \, a b^{5} c^{2} + 96 \, a^{2} b^{3} c^{3} + 64 \, a^{3} b c^{4}\right)} d^{7} + {\left(b^{9} + 64 \, a b^{7} c + 576 \, a^{2} b^{5} c^{2} + 1024 \, a^{3} b^{3} c^{3} + 256 \, a^{4} b c^{4}\right)} d^{6} - 4 \, {\left(a b^{9} + 24 \, a^{2} b^{7} c + 96 \, a^{3} b^{5} c^{2} + 64 \, a^{4} b^{3} c^{3}\right)} d^{5} + 2 \, {\left(3 \, a^{2} b^{9} + 32 \, a^{3} b^{7} c + 48 \, a^{4} b^{5} c^{2}\right)} d^{4} - 4 \, {\left(a^{3} b^{9} + 4 \, a^{4} b^{7} c\right)} d^{3}\right)} x\right)}}, -\frac{3 \, {\left(1024 \, c^{3} d^{6} - {\left(5 \, b^{6} c^{3} + 12 \, a b^{4} c^{4} + 48 \, a^{2} b^{2} c^{5} + 320 \, a^{3} c^{6} - 1024 \, c^{6} d^{3} + 384 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{2} - 24 \, {\left(3 \, b^{4} c^{4} + 8 \, a b^{2} c^{5} + 48 \, a^{2} c^{6}\right)} d\right)} x^{6} - 384 \, {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d^{5} - 3 \, {\left(5 \, b^{7} c^{2} + 12 \, a b^{5} c^{3} + 48 \, a^{2} b^{3} c^{4} + 320 \, a^{3} b c^{5} - 1024 \, b c^{5} d^{3} + 384 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d^{2} - 24 \, {\left(3 \, b^{5} c^{3} + 8 \, a b^{3} c^{4} + 48 \, a^{2} b c^{5}\right)} d\right)} x^{5} + 24 \, {\left(3 \, b^{4} c + 8 \, a b^{2} c^{2} + 48 \, a^{2} c^{3}\right)} d^{4} - 3 \, {\left(5 \, b^{8} c + 12 \, a b^{6} c^{2} + 48 \, a^{2} b^{4} c^{3} + 320 \, a^{3} b^{2} c^{4} - 1024 \, c^{5} d^{4} - 128 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} d^{3} + 24 \, {\left(13 \, b^{4} c^{3} + 56 \, a b^{2} c^{4} - 48 \, a^{2} c^{5}\right)} d^{2} - {\left(67 \, b^{6} c^{2} + 180 \, a b^{4} c^{3} + 1104 \, a^{2} b^{2} c^{4} - 320 \, a^{3} c^{5}\right)} d\right)} x^{4} - {\left(5 \, b^{6} + 12 \, a b^{4} c + 48 \, a^{2} b^{2} c^{2} + 320 \, a^{3} c^{3}\right)} d^{3} - {\left(5 \, b^{9} + 12 \, a b^{7} c + 48 \, a^{2} b^{5} c^{2} + 320 \, a^{3} b^{3} c^{3} - 6144 \, b c^{4} d^{4} + 256 \, {\left(5 \, b^{3} c^{3} + 36 \, a b c^{4}\right)} d^{3} - 48 \, {\left(b^{5} c^{2} - 8 \, a b^{3} c^{3} + 144 \, a^{2} b c^{4}\right)} d^{2} - 6 \, {\left(7 \, b^{7} c + 20 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} - 320 \, a^{3} b c^{4}\right)} d\right)} x^{3} + 3 \, {\left(1024 \, c^{4} d^{5} + 128 \, {\left(5 \, b^{2} c^{3} - 12 \, a c^{4}\right)} d^{4} - 24 \, {\left(13 \, b^{4} c^{2} + 56 \, a b^{2} c^{3} - 48 \, a^{2} c^{4}\right)} d^{3} + {\left(67 \, b^{6} c + 180 \, a b^{4} c^{2} + 1104 \, a^{2} b^{2} c^{3} - 320 \, a^{3} c^{4}\right)} d^{2} - {\left(5 \, b^{8} + 12 \, a b^{6} c + 48 \, a^{2} b^{4} c^{2} + 320 \, a^{3} b^{2} c^{3}\right)} d\right)} x^{2} + 3 \, {\left(1024 \, b c^{3} d^{5} - 384 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d^{4} + 24 \, {\left(3 \, b^{5} c + 8 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} d^{3} - {\left(5 \, b^{7} + 12 \, a b^{5} c + 48 \, a^{2} b^{3} c^{2} + 320 \, a^{3} b c^{3}\right)} d^{2}\right)} x\right)} \sqrt{-a b^{2} - 4 \, c d^{2} + {\left(b^{2} + 4 \, a c\right)} d} \arctan\left(-\frac{{\left(2 \, a b^{2} + {\left(b^{2} c + 4 \, a c^{2} - 8 \, c^{2} d\right)} x^{2} - {\left(b^{2} + 4 \, a c\right)} d + {\left(b^{3} + 4 \, a b c - 8 \, b c d\right)} x\right)} \sqrt{-a b^{2} - 4 \, c d^{2} + {\left(b^{2} + 4 \, a c\right)} d} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a^{2} b^{3} + 4 \, a b c d^{2} + 2 \, {\left(a b^{2} c^{2} + 4 \, c^{3} d^{2} - {\left(b^{2} c^{2} + 4 \, a c^{3}\right)} d\right)} x^{3} + 3 \, {\left(a b^{3} c + 4 \, b c^{2} d^{2} - {\left(b^{3} c + 4 \, a b c^{2}\right)} d\right)} x^{2} - {\left(a b^{3} + 4 \, a^{2} b c\right)} d + {\left(a b^{4} + 2 \, a^{2} b^{2} c + 4 \, {\left(b^{2} c + 2 \, a c^{2}\right)} d^{2} - {\left(b^{4} + 6 \, a b^{2} c + 8 \, a^{2} c^{2}\right)} d\right)} x\right)}}\right) + 2 \, {\left(8 \, a^{3} b^{7} + 4608 \, b c^{3} d^{6} - 2592 \, {\left(b^{3} c^{2} + 4 \, a b c^{3}\right)} d^{5} + 2 \, {\left(15 \, a b^{6} c^{3} + 56 \, a^{2} b^{4} c^{4} + 240 \, a^{3} b^{2} c^{5} + 2816 \, c^{6} d^{4} - 1408 \, {\left(b^{2} c^{5} + 4 \, a c^{6}\right)} d^{3} + 4 \, {\left(59 \, b^{4} c^{4} + 584 \, a b^{2} c^{5} + 944 \, a^{2} c^{6}\right)} d^{2} - {\left(15 \, b^{6} c^{3} + 292 \, a b^{4} c^{4} + 1168 \, a^{2} b^{2} c^{5} + 960 \, a^{3} c^{6}\right)} d\right)} x^{5} + 4 \, {\left(123 \, b^{5} c + 1352 \, a b^{3} c^{2} + 1968 \, a^{2} b c^{3}\right)} d^{4} + 5 \, {\left(15 \, a b^{7} c^{2} + 56 \, a^{2} b^{5} c^{3} + 240 \, a^{3} b^{3} c^{4} + 2816 \, b c^{5} d^{4} - 1408 \, {\left(b^{3} c^{4} + 4 \, a b c^{5}\right)} d^{3} + 4 \, {\left(59 \, b^{5} c^{3} + 584 \, a b^{3} c^{4} + 944 \, a^{2} b c^{5}\right)} d^{2} - {\left(15 \, b^{7} c^{2} + 292 \, a b^{5} c^{3} + 1168 \, a^{2} b^{3} c^{4} + 960 \, a^{3} b c^{5}\right)} d\right)} x^{4} - {\left(33 \, b^{7} + 940 \, a b^{5} c + 3760 \, a^{2} b^{3} c^{2} + 2112 \, a^{3} b c^{3}\right)} d^{3} + 4 \, {\left(15 \, a b^{8} c + 51 \, a^{2} b^{6} c^{2} + 220 \, a^{3} b^{4} c^{3} + 3456 \, c^{5} d^{5} + 16 \, {\left(63 \, b^{2} c^{4} - 452 \, a c^{5}\right)} d^{4} - 4 \, {\left(273 \, b^{4} c^{3} + 584 \, a b^{2} c^{4} - 1264 \, a^{2} c^{5}\right)} d^{3} + 8 \, {\left(27 \, b^{6} c^{2} + 233 \, a b^{4} c^{3} + 236 \, a^{2} b^{2} c^{4} - 160 \, a^{3} c^{5}\right)} d^{2} - {\left(15 \, b^{8} c + 267 \, a b^{6} c^{2} + 992 \, a^{2} b^{4} c^{3} + 560 \, a^{3} b^{2} c^{4}\right)} d\right)} x^{3} + {\left(59 \, a b^{7} + 584 \, a^{2} b^{5} c + 944 \, a^{3} b^{3} c^{2}\right)} d^{2} + {\left(15 \, a b^{9} + 26 \, a^{2} b^{7} c + 120 \, a^{3} b^{5} c^{2} + 20736 \, b c^{4} d^{5} - 32 \, {\left(251 \, b^{3} c^{3} + 1356 \, a b c^{4}\right)} d^{4} + 8 \, {\left(61 \, b^{5} c^{2} + 1768 \, a b^{3} c^{3} + 3792 \, a^{2} b c^{4}\right)} d^{3} + 4 \, {\left(29 \, b^{7} c - 124 \, a b^{5} c^{2} - 1888 \, a^{2} b^{3} c^{3} - 1920 \, a^{3} b c^{4}\right)} d^{2} - {\left(15 \, b^{9} + 142 \, a b^{7} c + 112 \, a^{2} b^{5} c^{2} - 1440 \, a^{3} b^{3} c^{3}\right)} d\right)} x^{2} - 34 \, {\left(a^{2} b^{7} + 4 \, a^{3} b^{5} c\right)} d - 2 \, {\left(5 \, a^{2} b^{8} + 12 \, a^{3} b^{6} c - 4608 \, c^{4} d^{6} - 864 \, {\left(b^{2} c^{3} - 12 \, a c^{4}\right)} d^{5} + 4 \, {\left(329 \, b^{4} c^{2} + 456 \, a b^{2} c^{3} - 1968 \, a^{2} c^{4}\right)} d^{4} - {\left(283 \, b^{6} c + 2356 \, a b^{4} c^{2} + 1296 \, a^{2} b^{2} c^{3} - 2112 \, a^{3} c^{4}\right)} d^{3} + {\left(20 \, b^{8} + 413 \, a b^{6} c + 1304 \, a^{2} b^{4} c^{2} + 336 \, a^{3} b^{2} c^{3}\right)} d^{2} - {\left(25 \, a b^{8} + 142 \, a^{2} b^{6} c + 264 \, a^{3} b^{4} c^{2}\right)} d\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(a^{4} b^{8} d^{3} + 256 \, c^{4} d^{11} - 256 \, {\left(b^{2} c^{3} + 4 \, a c^{4}\right)} d^{10} + 32 \, {\left(3 \, b^{4} c^{2} + 32 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d^{9} - 16 \, {\left(b^{6} c + 24 \, a b^{4} c^{2} + 96 \, a^{2} b^{2} c^{3} + 64 \, a^{3} c^{4}\right)} d^{8} + {\left(b^{8} + 64 \, a b^{6} c + 576 \, a^{2} b^{4} c^{2} + 1024 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} d^{7} - 4 \, {\left(a b^{8} + 24 \, a^{2} b^{6} c + 96 \, a^{3} b^{4} c^{2} + 64 \, a^{4} b^{2} c^{3}\right)} d^{6} + {\left(a^{4} b^{8} c^{3} + 256 \, c^{7} d^{8} - 256 \, {\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d^{7} + 32 \, {\left(3 \, b^{4} c^{5} + 32 \, a b^{2} c^{6} + 48 \, a^{2} c^{7}\right)} d^{6} - 16 \, {\left(b^{6} c^{4} + 24 \, a b^{4} c^{5} + 96 \, a^{2} b^{2} c^{6} + 64 \, a^{3} c^{7}\right)} d^{5} + {\left(b^{8} c^{3} + 64 \, a b^{6} c^{4} + 576 \, a^{2} b^{4} c^{5} + 1024 \, a^{3} b^{2} c^{6} + 256 \, a^{4} c^{7}\right)} d^{4} - 4 \, {\left(a b^{8} c^{3} + 24 \, a^{2} b^{6} c^{4} + 96 \, a^{3} b^{4} c^{5} + 64 \, a^{4} b^{2} c^{6}\right)} d^{3} + 2 \, {\left(3 \, a^{2} b^{8} c^{3} + 32 \, a^{3} b^{6} c^{4} + 48 \, a^{4} b^{4} c^{5}\right)} d^{2} - 4 \, {\left(a^{3} b^{8} c^{3} + 4 \, a^{4} b^{6} c^{4}\right)} d\right)} x^{6} + 2 \, {\left(3 \, a^{2} b^{8} + 32 \, a^{3} b^{6} c + 48 \, a^{4} b^{4} c^{2}\right)} d^{5} + 3 \, {\left(a^{4} b^{9} c^{2} + 256 \, b c^{6} d^{8} - 256 \, {\left(b^{3} c^{5} + 4 \, a b c^{6}\right)} d^{7} + 32 \, {\left(3 \, b^{5} c^{4} + 32 \, a b^{3} c^{5} + 48 \, a^{2} b c^{6}\right)} d^{6} - 16 \, {\left(b^{7} c^{3} + 24 \, a b^{5} c^{4} + 96 \, a^{2} b^{3} c^{5} + 64 \, a^{3} b c^{6}\right)} d^{5} + {\left(b^{9} c^{2} + 64 \, a b^{7} c^{3} + 576 \, a^{2} b^{5} c^{4} + 1024 \, a^{3} b^{3} c^{5} + 256 \, a^{4} b c^{6}\right)} d^{4} - 4 \, {\left(a b^{9} c^{2} + 24 \, a^{2} b^{7} c^{3} + 96 \, a^{3} b^{5} c^{4} + 64 \, a^{4} b^{3} c^{5}\right)} d^{3} + 2 \, {\left(3 \, a^{2} b^{9} c^{2} + 32 \, a^{3} b^{7} c^{3} + 48 \, a^{4} b^{5} c^{4}\right)} d^{2} - 4 \, {\left(a^{3} b^{9} c^{2} + 4 \, a^{4} b^{7} c^{3}\right)} d\right)} x^{5} - 4 \, {\left(a^{3} b^{8} + 4 \, a^{4} b^{6} c\right)} d^{4} + 3 \, {\left(a^{4} b^{10} c - 1024 \, a c^{6} d^{8} + 256 \, c^{6} d^{9} - 32 \, {\left(5 \, b^{4} c^{4} - 48 \, a^{2} c^{6}\right)} d^{7} + 16 \, {\left(5 \, b^{6} c^{3} + 40 \, a b^{4} c^{4} - 64 \, a^{3} c^{6}\right)} d^{6} - {\left(15 \, b^{8} c^{2} + 320 \, a b^{6} c^{3} + 960 \, a^{2} b^{4} c^{4} - 256 \, a^{4} c^{6}\right)} d^{5} + {\left(b^{10} c + 60 \, a b^{8} c^{2} + 480 \, a^{2} b^{6} c^{3} + 640 \, a^{3} b^{4} c^{4}\right)} d^{4} - 2 \, {\left(2 \, a b^{10} c + 45 \, a^{2} b^{8} c^{2} + 160 \, a^{3} b^{6} c^{3} + 80 \, a^{4} b^{4} c^{4}\right)} d^{3} + 2 \, {\left(3 \, a^{2} b^{10} c + 30 \, a^{3} b^{8} c^{2} + 40 \, a^{4} b^{6} c^{3}\right)} d^{2} - {\left(4 \, a^{3} b^{10} c + 15 \, a^{4} b^{8} c^{2}\right)} d\right)} x^{4} + {\left(a^{4} b^{11} + 1536 \, b c^{5} d^{9} - 256 \, {\left(5 \, b^{3} c^{4} + 24 \, a b c^{5}\right)} d^{8} + 64 \, {\left(5 \, b^{5} c^{3} + 80 \, a b^{3} c^{4} + 144 \, a^{2} b c^{5}\right)} d^{7} - 256 \, {\left(5 \, a b^{5} c^{3} + 30 \, a^{2} b^{3} c^{4} + 24 \, a^{3} b c^{5}\right)} d^{6} - 2 \, {\left(5 \, b^{9} c - 960 \, a^{2} b^{5} c^{3} - 2560 \, a^{3} b^{3} c^{4} - 768 \, a^{4} b c^{5}\right)} d^{5} + {\left(b^{11} + 40 \, a b^{9} c - 1280 \, a^{3} b^{5} c^{3} - 1280 \, a^{4} b^{3} c^{4}\right)} d^{4} - 4 \, {\left(a b^{11} + 15 \, a^{2} b^{9} c - 80 \, a^{4} b^{5} c^{3}\right)} d^{3} + 2 \, {\left(3 \, a^{2} b^{11} + 20 \, a^{3} b^{9} c\right)} d^{2} - 2 \, {\left(2 \, a^{3} b^{11} + 5 \, a^{4} b^{9} c\right)} d\right)} x^{3} + 3 \, {\left(a^{4} b^{10} d - 1024 \, a c^{5} d^{9} + 256 \, c^{5} d^{10} - 32 \, {\left(5 \, b^{4} c^{3} - 48 \, a^{2} c^{5}\right)} d^{8} + 16 \, {\left(5 \, b^{6} c^{2} + 40 \, a b^{4} c^{3} - 64 \, a^{3} c^{5}\right)} d^{7} - {\left(15 \, b^{8} c + 320 \, a b^{6} c^{2} + 960 \, a^{2} b^{4} c^{3} - 256 \, a^{4} c^{5}\right)} d^{6} + {\left(b^{10} + 60 \, a b^{8} c + 480 \, a^{2} b^{6} c^{2} + 640 \, a^{3} b^{4} c^{3}\right)} d^{5} - 2 \, {\left(2 \, a b^{10} + 45 \, a^{2} b^{8} c + 160 \, a^{3} b^{6} c^{2} + 80 \, a^{4} b^{4} c^{3}\right)} d^{4} + 2 \, {\left(3 \, a^{2} b^{10} + 30 \, a^{3} b^{8} c + 40 \, a^{4} b^{6} c^{2}\right)} d^{3} - {\left(4 \, a^{3} b^{10} + 15 \, a^{4} b^{8} c\right)} d^{2}\right)} x^{2} + 3 \, {\left(a^{4} b^{9} d^{2} + 256 \, b c^{4} d^{10} - 256 \, {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d^{9} + 32 \, {\left(3 \, b^{5} c^{2} + 32 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} d^{8} - 16 \, {\left(b^{7} c + 24 \, a b^{5} c^{2} + 96 \, a^{2} b^{3} c^{3} + 64 \, a^{3} b c^{4}\right)} d^{7} + {\left(b^{9} + 64 \, a b^{7} c + 576 \, a^{2} b^{5} c^{2} + 1024 \, a^{3} b^{3} c^{3} + 256 \, a^{4} b c^{4}\right)} d^{6} - 4 \, {\left(a b^{9} + 24 \, a^{2} b^{7} c + 96 \, a^{3} b^{5} c^{2} + 64 \, a^{4} b^{3} c^{3}\right)} d^{5} + 2 \, {\left(3 \, a^{2} b^{9} + 32 \, a^{3} b^{7} c + 48 \, a^{4} b^{5} c^{2}\right)} d^{4} - 4 \, {\left(a^{3} b^{9} + 4 \, a^{4} b^{7} c\right)} d^{3}\right)} x\right)}}\right]"," ",0,"[1/96*(3*(1024*c^3*d^6 - (5*b^6*c^3 + 12*a*b^4*c^4 + 48*a^2*b^2*c^5 + 320*a^3*c^6 - 1024*c^6*d^3 + 384*(b^2*c^5 + 4*a*c^6)*d^2 - 24*(3*b^4*c^4 + 8*a*b^2*c^5 + 48*a^2*c^6)*d)*x^6 - 384*(b^2*c^2 + 4*a*c^3)*d^5 - 3*(5*b^7*c^2 + 12*a*b^5*c^3 + 48*a^2*b^3*c^4 + 320*a^3*b*c^5 - 1024*b*c^5*d^3 + 384*(b^3*c^4 + 4*a*b*c^5)*d^2 - 24*(3*b^5*c^3 + 8*a*b^3*c^4 + 48*a^2*b*c^5)*d)*x^5 + 24*(3*b^4*c + 8*a*b^2*c^2 + 48*a^2*c^3)*d^4 - 3*(5*b^8*c + 12*a*b^6*c^2 + 48*a^2*b^4*c^3 + 320*a^3*b^2*c^4 - 1024*c^5*d^4 - 128*(5*b^2*c^4 - 12*a*c^5)*d^3 + 24*(13*b^4*c^3 + 56*a*b^2*c^4 - 48*a^2*c^5)*d^2 - (67*b^6*c^2 + 180*a*b^4*c^3 + 1104*a^2*b^2*c^4 - 320*a^3*c^5)*d)*x^4 - (5*b^6 + 12*a*b^4*c + 48*a^2*b^2*c^2 + 320*a^3*c^3)*d^3 - (5*b^9 + 12*a*b^7*c + 48*a^2*b^5*c^2 + 320*a^3*b^3*c^3 - 6144*b*c^4*d^4 + 256*(5*b^3*c^3 + 36*a*b*c^4)*d^3 - 48*(b^5*c^2 - 8*a*b^3*c^3 + 144*a^2*b*c^4)*d^2 - 6*(7*b^7*c + 20*a*b^5*c^2 + 144*a^2*b^3*c^3 - 320*a^3*b*c^4)*d)*x^3 + 3*(1024*c^4*d^5 + 128*(5*b^2*c^3 - 12*a*c^4)*d^4 - 24*(13*b^4*c^2 + 56*a*b^2*c^3 - 48*a^2*c^4)*d^3 + (67*b^6*c + 180*a*b^4*c^2 + 1104*a^2*b^2*c^3 - 320*a^3*c^4)*d^2 - (5*b^8 + 12*a*b^6*c + 48*a^2*b^4*c^2 + 320*a^3*b^2*c^3)*d)*x^2 + 3*(1024*b*c^3*d^5 - 384*(b^3*c^2 + 4*a*b*c^3)*d^4 + 24*(3*b^5*c + 8*a*b^3*c^2 + 48*a^2*b*c^3)*d^3 - (5*b^7 + 12*a*b^5*c + 48*a^2*b^3*c^2 + 320*a^3*b*c^3)*d^2)*x)*sqrt(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d)*log((8*a^2*b^4 + (b^4*c^2 + 24*a*b^2*c^3 + 16*a^2*c^4 + 128*c^4*d^2 - 32*(b^2*c^3 + 4*a*c^4)*d)*x^4 + 2*(b^5*c + 24*a*b^3*c^2 + 16*a^2*b*c^3 + 128*b*c^3*d^2 - 32*(b^3*c^2 + 4*a*b*c^3)*d)*x^3 + (b^4 + 24*a*b^2*c + 16*a^2*c^2)*d^2 + (b^6 + 32*a*b^4*c + 48*a^2*b^2*c^2 + 32*(5*b^2*c^2 + 4*a*c^3)*d^2 - 2*(19*b^4*c + 104*a*b^2*c^2 + 48*a^2*c^3)*d)*x^2 - 4*(2*a*b^3 + 2*(b^2*c^2 + 4*a*c^3 - 8*c^3*d)*x^3 + 3*(b^3*c + 4*a*b*c^2 - 8*b*c^2*d)*x^2 - (b^3 + 4*a*b*c)*d + (b^4 + 8*a*b^2*c - 2*(5*b^2*c + 4*a*c^2)*d)*x)*sqrt(a*b^2 + 4*c*d^2 - (b^2 + 4*a*c)*d)*sqrt(c*x^2 + b*x + a) - 8*(a*b^4 + 4*a^2*b^2*c)*d + 2*(4*a*b^5 + 16*a^2*b^3*c + 16*(b^3*c + 4*a*b*c^2)*d^2 - (3*b^5 + 40*a*b^3*c + 48*a^2*b*c^2)*d)*x)/(c^2*x^4 + 2*b*c*x^3 + 2*b*d*x + (b^2 + 2*c*d)*x^2 + d^2)) - 4*(8*a^3*b^7 + 4608*b*c^3*d^6 - 2592*(b^3*c^2 + 4*a*b*c^3)*d^5 + 2*(15*a*b^6*c^3 + 56*a^2*b^4*c^4 + 240*a^3*b^2*c^5 + 2816*c^6*d^4 - 1408*(b^2*c^5 + 4*a*c^6)*d^3 + 4*(59*b^4*c^4 + 584*a*b^2*c^5 + 944*a^2*c^6)*d^2 - (15*b^6*c^3 + 292*a*b^4*c^4 + 1168*a^2*b^2*c^5 + 960*a^3*c^6)*d)*x^5 + 4*(123*b^5*c + 1352*a*b^3*c^2 + 1968*a^2*b*c^3)*d^4 + 5*(15*a*b^7*c^2 + 56*a^2*b^5*c^3 + 240*a^3*b^3*c^4 + 2816*b*c^5*d^4 - 1408*(b^3*c^4 + 4*a*b*c^5)*d^3 + 4*(59*b^5*c^3 + 584*a*b^3*c^4 + 944*a^2*b*c^5)*d^2 - (15*b^7*c^2 + 292*a*b^5*c^3 + 1168*a^2*b^3*c^4 + 960*a^3*b*c^5)*d)*x^4 - (33*b^7 + 940*a*b^5*c + 3760*a^2*b^3*c^2 + 2112*a^3*b*c^3)*d^3 + 4*(15*a*b^8*c + 51*a^2*b^6*c^2 + 220*a^3*b^4*c^3 + 3456*c^5*d^5 + 16*(63*b^2*c^4 - 452*a*c^5)*d^4 - 4*(273*b^4*c^3 + 584*a*b^2*c^4 - 1264*a^2*c^5)*d^3 + 8*(27*b^6*c^2 + 233*a*b^4*c^3 + 236*a^2*b^2*c^4 - 160*a^3*c^5)*d^2 - (15*b^8*c + 267*a*b^6*c^2 + 992*a^2*b^4*c^3 + 560*a^3*b^2*c^4)*d)*x^3 + (59*a*b^7 + 584*a^2*b^5*c + 944*a^3*b^3*c^2)*d^2 + (15*a*b^9 + 26*a^2*b^7*c + 120*a^3*b^5*c^2 + 20736*b*c^4*d^5 - 32*(251*b^3*c^3 + 1356*a*b*c^4)*d^4 + 8*(61*b^5*c^2 + 1768*a*b^3*c^3 + 3792*a^2*b*c^4)*d^3 + 4*(29*b^7*c - 124*a*b^5*c^2 - 1888*a^2*b^3*c^3 - 1920*a^3*b*c^4)*d^2 - (15*b^9 + 142*a*b^7*c + 112*a^2*b^5*c^2 - 1440*a^3*b^3*c^3)*d)*x^2 - 34*(a^2*b^7 + 4*a^3*b^5*c)*d - 2*(5*a^2*b^8 + 12*a^3*b^6*c - 4608*c^4*d^6 - 864*(b^2*c^3 - 12*a*c^4)*d^5 + 4*(329*b^4*c^2 + 456*a*b^2*c^3 - 1968*a^2*c^4)*d^4 - (283*b^6*c + 2356*a*b^4*c^2 + 1296*a^2*b^2*c^3 - 2112*a^3*c^4)*d^3 + (20*b^8 + 413*a*b^6*c + 1304*a^2*b^4*c^2 + 336*a^3*b^2*c^3)*d^2 - (25*a*b^8 + 142*a^2*b^6*c + 264*a^3*b^4*c^2)*d)*x)*sqrt(c*x^2 + b*x + a))/(a^4*b^8*d^3 + 256*c^4*d^11 - 256*(b^2*c^3 + 4*a*c^4)*d^10 + 32*(3*b^4*c^2 + 32*a*b^2*c^3 + 48*a^2*c^4)*d^9 - 16*(b^6*c + 24*a*b^4*c^2 + 96*a^2*b^2*c^3 + 64*a^3*c^4)*d^8 + (b^8 + 64*a*b^6*c + 576*a^2*b^4*c^2 + 1024*a^3*b^2*c^3 + 256*a^4*c^4)*d^7 - 4*(a*b^8 + 24*a^2*b^6*c + 96*a^3*b^4*c^2 + 64*a^4*b^2*c^3)*d^6 + (a^4*b^8*c^3 + 256*c^7*d^8 - 256*(b^2*c^6 + 4*a*c^7)*d^7 + 32*(3*b^4*c^5 + 32*a*b^2*c^6 + 48*a^2*c^7)*d^6 - 16*(b^6*c^4 + 24*a*b^4*c^5 + 96*a^2*b^2*c^6 + 64*a^3*c^7)*d^5 + (b^8*c^3 + 64*a*b^6*c^4 + 576*a^2*b^4*c^5 + 1024*a^3*b^2*c^6 + 256*a^4*c^7)*d^4 - 4*(a*b^8*c^3 + 24*a^2*b^6*c^4 + 96*a^3*b^4*c^5 + 64*a^4*b^2*c^6)*d^3 + 2*(3*a^2*b^8*c^3 + 32*a^3*b^6*c^4 + 48*a^4*b^4*c^5)*d^2 - 4*(a^3*b^8*c^3 + 4*a^4*b^6*c^4)*d)*x^6 + 2*(3*a^2*b^8 + 32*a^3*b^6*c + 48*a^4*b^4*c^2)*d^5 + 3*(a^4*b^9*c^2 + 256*b*c^6*d^8 - 256*(b^3*c^5 + 4*a*b*c^6)*d^7 + 32*(3*b^5*c^4 + 32*a*b^3*c^5 + 48*a^2*b*c^6)*d^6 - 16*(b^7*c^3 + 24*a*b^5*c^4 + 96*a^2*b^3*c^5 + 64*a^3*b*c^6)*d^5 + (b^9*c^2 + 64*a*b^7*c^3 + 576*a^2*b^5*c^4 + 1024*a^3*b^3*c^5 + 256*a^4*b*c^6)*d^4 - 4*(a*b^9*c^2 + 24*a^2*b^7*c^3 + 96*a^3*b^5*c^4 + 64*a^4*b^3*c^5)*d^3 + 2*(3*a^2*b^9*c^2 + 32*a^3*b^7*c^3 + 48*a^4*b^5*c^4)*d^2 - 4*(a^3*b^9*c^2 + 4*a^4*b^7*c^3)*d)*x^5 - 4*(a^3*b^8 + 4*a^4*b^6*c)*d^4 + 3*(a^4*b^10*c - 1024*a*c^6*d^8 + 256*c^6*d^9 - 32*(5*b^4*c^4 - 48*a^2*c^6)*d^7 + 16*(5*b^6*c^3 + 40*a*b^4*c^4 - 64*a^3*c^6)*d^6 - (15*b^8*c^2 + 320*a*b^6*c^3 + 960*a^2*b^4*c^4 - 256*a^4*c^6)*d^5 + (b^10*c + 60*a*b^8*c^2 + 480*a^2*b^6*c^3 + 640*a^3*b^4*c^4)*d^4 - 2*(2*a*b^10*c + 45*a^2*b^8*c^2 + 160*a^3*b^6*c^3 + 80*a^4*b^4*c^4)*d^3 + 2*(3*a^2*b^10*c + 30*a^3*b^8*c^2 + 40*a^4*b^6*c^3)*d^2 - (4*a^3*b^10*c + 15*a^4*b^8*c^2)*d)*x^4 + (a^4*b^11 + 1536*b*c^5*d^9 - 256*(5*b^3*c^4 + 24*a*b*c^5)*d^8 + 64*(5*b^5*c^3 + 80*a*b^3*c^4 + 144*a^2*b*c^5)*d^7 - 256*(5*a*b^5*c^3 + 30*a^2*b^3*c^4 + 24*a^3*b*c^5)*d^6 - 2*(5*b^9*c - 960*a^2*b^5*c^3 - 2560*a^3*b^3*c^4 - 768*a^4*b*c^5)*d^5 + (b^11 + 40*a*b^9*c - 1280*a^3*b^5*c^3 - 1280*a^4*b^3*c^4)*d^4 - 4*(a*b^11 + 15*a^2*b^9*c - 80*a^4*b^5*c^3)*d^3 + 2*(3*a^2*b^11 + 20*a^3*b^9*c)*d^2 - 2*(2*a^3*b^11 + 5*a^4*b^9*c)*d)*x^3 + 3*(a^4*b^10*d - 1024*a*c^5*d^9 + 256*c^5*d^10 - 32*(5*b^4*c^3 - 48*a^2*c^5)*d^8 + 16*(5*b^6*c^2 + 40*a*b^4*c^3 - 64*a^3*c^5)*d^7 - (15*b^8*c + 320*a*b^6*c^2 + 960*a^2*b^4*c^3 - 256*a^4*c^5)*d^6 + (b^10 + 60*a*b^8*c + 480*a^2*b^6*c^2 + 640*a^3*b^4*c^3)*d^5 - 2*(2*a*b^10 + 45*a^2*b^8*c + 160*a^3*b^6*c^2 + 80*a^4*b^4*c^3)*d^4 + 2*(3*a^2*b^10 + 30*a^3*b^8*c + 40*a^4*b^6*c^2)*d^3 - (4*a^3*b^10 + 15*a^4*b^8*c)*d^2)*x^2 + 3*(a^4*b^9*d^2 + 256*b*c^4*d^10 - 256*(b^3*c^3 + 4*a*b*c^4)*d^9 + 32*(3*b^5*c^2 + 32*a*b^3*c^3 + 48*a^2*b*c^4)*d^8 - 16*(b^7*c + 24*a*b^5*c^2 + 96*a^2*b^3*c^3 + 64*a^3*b*c^4)*d^7 + (b^9 + 64*a*b^7*c + 576*a^2*b^5*c^2 + 1024*a^3*b^3*c^3 + 256*a^4*b*c^4)*d^6 - 4*(a*b^9 + 24*a^2*b^7*c + 96*a^3*b^5*c^2 + 64*a^4*b^3*c^3)*d^5 + 2*(3*a^2*b^9 + 32*a^3*b^7*c + 48*a^4*b^5*c^2)*d^4 - 4*(a^3*b^9 + 4*a^4*b^7*c)*d^3)*x), -1/48*(3*(1024*c^3*d^6 - (5*b^6*c^3 + 12*a*b^4*c^4 + 48*a^2*b^2*c^5 + 320*a^3*c^6 - 1024*c^6*d^3 + 384*(b^2*c^5 + 4*a*c^6)*d^2 - 24*(3*b^4*c^4 + 8*a*b^2*c^5 + 48*a^2*c^6)*d)*x^6 - 384*(b^2*c^2 + 4*a*c^3)*d^5 - 3*(5*b^7*c^2 + 12*a*b^5*c^3 + 48*a^2*b^3*c^4 + 320*a^3*b*c^5 - 1024*b*c^5*d^3 + 384*(b^3*c^4 + 4*a*b*c^5)*d^2 - 24*(3*b^5*c^3 + 8*a*b^3*c^4 + 48*a^2*b*c^5)*d)*x^5 + 24*(3*b^4*c + 8*a*b^2*c^2 + 48*a^2*c^3)*d^4 - 3*(5*b^8*c + 12*a*b^6*c^2 + 48*a^2*b^4*c^3 + 320*a^3*b^2*c^4 - 1024*c^5*d^4 - 128*(5*b^2*c^4 - 12*a*c^5)*d^3 + 24*(13*b^4*c^3 + 56*a*b^2*c^4 - 48*a^2*c^5)*d^2 - (67*b^6*c^2 + 180*a*b^4*c^3 + 1104*a^2*b^2*c^4 - 320*a^3*c^5)*d)*x^4 - (5*b^6 + 12*a*b^4*c + 48*a^2*b^2*c^2 + 320*a^3*c^3)*d^3 - (5*b^9 + 12*a*b^7*c + 48*a^2*b^5*c^2 + 320*a^3*b^3*c^3 - 6144*b*c^4*d^4 + 256*(5*b^3*c^3 + 36*a*b*c^4)*d^3 - 48*(b^5*c^2 - 8*a*b^3*c^3 + 144*a^2*b*c^4)*d^2 - 6*(7*b^7*c + 20*a*b^5*c^2 + 144*a^2*b^3*c^3 - 320*a^3*b*c^4)*d)*x^3 + 3*(1024*c^4*d^5 + 128*(5*b^2*c^3 - 12*a*c^4)*d^4 - 24*(13*b^4*c^2 + 56*a*b^2*c^3 - 48*a^2*c^4)*d^3 + (67*b^6*c + 180*a*b^4*c^2 + 1104*a^2*b^2*c^3 - 320*a^3*c^4)*d^2 - (5*b^8 + 12*a*b^6*c + 48*a^2*b^4*c^2 + 320*a^3*b^2*c^3)*d)*x^2 + 3*(1024*b*c^3*d^5 - 384*(b^3*c^2 + 4*a*b*c^3)*d^4 + 24*(3*b^5*c + 8*a*b^3*c^2 + 48*a^2*b*c^3)*d^3 - (5*b^7 + 12*a*b^5*c + 48*a^2*b^3*c^2 + 320*a^3*b*c^3)*d^2)*x)*sqrt(-a*b^2 - 4*c*d^2 + (b^2 + 4*a*c)*d)*arctan(-1/2*(2*a*b^2 + (b^2*c + 4*a*c^2 - 8*c^2*d)*x^2 - (b^2 + 4*a*c)*d + (b^3 + 4*a*b*c - 8*b*c*d)*x)*sqrt(-a*b^2 - 4*c*d^2 + (b^2 + 4*a*c)*d)*sqrt(c*x^2 + b*x + a)/(a^2*b^3 + 4*a*b*c*d^2 + 2*(a*b^2*c^2 + 4*c^3*d^2 - (b^2*c^2 + 4*a*c^3)*d)*x^3 + 3*(a*b^3*c + 4*b*c^2*d^2 - (b^3*c + 4*a*b*c^2)*d)*x^2 - (a*b^3 + 4*a^2*b*c)*d + (a*b^4 + 2*a^2*b^2*c + 4*(b^2*c + 2*a*c^2)*d^2 - (b^4 + 6*a*b^2*c + 8*a^2*c^2)*d)*x)) + 2*(8*a^3*b^7 + 4608*b*c^3*d^6 - 2592*(b^3*c^2 + 4*a*b*c^3)*d^5 + 2*(15*a*b^6*c^3 + 56*a^2*b^4*c^4 + 240*a^3*b^2*c^5 + 2816*c^6*d^4 - 1408*(b^2*c^5 + 4*a*c^6)*d^3 + 4*(59*b^4*c^4 + 584*a*b^2*c^5 + 944*a^2*c^6)*d^2 - (15*b^6*c^3 + 292*a*b^4*c^4 + 1168*a^2*b^2*c^5 + 960*a^3*c^6)*d)*x^5 + 4*(123*b^5*c + 1352*a*b^3*c^2 + 1968*a^2*b*c^3)*d^4 + 5*(15*a*b^7*c^2 + 56*a^2*b^5*c^3 + 240*a^3*b^3*c^4 + 2816*b*c^5*d^4 - 1408*(b^3*c^4 + 4*a*b*c^5)*d^3 + 4*(59*b^5*c^3 + 584*a*b^3*c^4 + 944*a^2*b*c^5)*d^2 - (15*b^7*c^2 + 292*a*b^5*c^3 + 1168*a^2*b^3*c^4 + 960*a^3*b*c^5)*d)*x^4 - (33*b^7 + 940*a*b^5*c + 3760*a^2*b^3*c^2 + 2112*a^3*b*c^3)*d^3 + 4*(15*a*b^8*c + 51*a^2*b^6*c^2 + 220*a^3*b^4*c^3 + 3456*c^5*d^5 + 16*(63*b^2*c^4 - 452*a*c^5)*d^4 - 4*(273*b^4*c^3 + 584*a*b^2*c^4 - 1264*a^2*c^5)*d^3 + 8*(27*b^6*c^2 + 233*a*b^4*c^3 + 236*a^2*b^2*c^4 - 160*a^3*c^5)*d^2 - (15*b^8*c + 267*a*b^6*c^2 + 992*a^2*b^4*c^3 + 560*a^3*b^2*c^4)*d)*x^3 + (59*a*b^7 + 584*a^2*b^5*c + 944*a^3*b^3*c^2)*d^2 + (15*a*b^9 + 26*a^2*b^7*c + 120*a^3*b^5*c^2 + 20736*b*c^4*d^5 - 32*(251*b^3*c^3 + 1356*a*b*c^4)*d^4 + 8*(61*b^5*c^2 + 1768*a*b^3*c^3 + 3792*a^2*b*c^4)*d^3 + 4*(29*b^7*c - 124*a*b^5*c^2 - 1888*a^2*b^3*c^3 - 1920*a^3*b*c^4)*d^2 - (15*b^9 + 142*a*b^7*c + 112*a^2*b^5*c^2 - 1440*a^3*b^3*c^3)*d)*x^2 - 34*(a^2*b^7 + 4*a^3*b^5*c)*d - 2*(5*a^2*b^8 + 12*a^3*b^6*c - 4608*c^4*d^6 - 864*(b^2*c^3 - 12*a*c^4)*d^5 + 4*(329*b^4*c^2 + 456*a*b^2*c^3 - 1968*a^2*c^4)*d^4 - (283*b^6*c + 2356*a*b^4*c^2 + 1296*a^2*b^2*c^3 - 2112*a^3*c^4)*d^3 + (20*b^8 + 413*a*b^6*c + 1304*a^2*b^4*c^2 + 336*a^3*b^2*c^3)*d^2 - (25*a*b^8 + 142*a^2*b^6*c + 264*a^3*b^4*c^2)*d)*x)*sqrt(c*x^2 + b*x + a))/(a^4*b^8*d^3 + 256*c^4*d^11 - 256*(b^2*c^3 + 4*a*c^4)*d^10 + 32*(3*b^4*c^2 + 32*a*b^2*c^3 + 48*a^2*c^4)*d^9 - 16*(b^6*c + 24*a*b^4*c^2 + 96*a^2*b^2*c^3 + 64*a^3*c^4)*d^8 + (b^8 + 64*a*b^6*c + 576*a^2*b^4*c^2 + 1024*a^3*b^2*c^3 + 256*a^4*c^4)*d^7 - 4*(a*b^8 + 24*a^2*b^6*c + 96*a^3*b^4*c^2 + 64*a^4*b^2*c^3)*d^6 + (a^4*b^8*c^3 + 256*c^7*d^8 - 256*(b^2*c^6 + 4*a*c^7)*d^7 + 32*(3*b^4*c^5 + 32*a*b^2*c^6 + 48*a^2*c^7)*d^6 - 16*(b^6*c^4 + 24*a*b^4*c^5 + 96*a^2*b^2*c^6 + 64*a^3*c^7)*d^5 + (b^8*c^3 + 64*a*b^6*c^4 + 576*a^2*b^4*c^5 + 1024*a^3*b^2*c^6 + 256*a^4*c^7)*d^4 - 4*(a*b^8*c^3 + 24*a^2*b^6*c^4 + 96*a^3*b^4*c^5 + 64*a^4*b^2*c^6)*d^3 + 2*(3*a^2*b^8*c^3 + 32*a^3*b^6*c^4 + 48*a^4*b^4*c^5)*d^2 - 4*(a^3*b^8*c^3 + 4*a^4*b^6*c^4)*d)*x^6 + 2*(3*a^2*b^8 + 32*a^3*b^6*c + 48*a^4*b^4*c^2)*d^5 + 3*(a^4*b^9*c^2 + 256*b*c^6*d^8 - 256*(b^3*c^5 + 4*a*b*c^6)*d^7 + 32*(3*b^5*c^4 + 32*a*b^3*c^5 + 48*a^2*b*c^6)*d^6 - 16*(b^7*c^3 + 24*a*b^5*c^4 + 96*a^2*b^3*c^5 + 64*a^3*b*c^6)*d^5 + (b^9*c^2 + 64*a*b^7*c^3 + 576*a^2*b^5*c^4 + 1024*a^3*b^3*c^5 + 256*a^4*b*c^6)*d^4 - 4*(a*b^9*c^2 + 24*a^2*b^7*c^3 + 96*a^3*b^5*c^4 + 64*a^4*b^3*c^5)*d^3 + 2*(3*a^2*b^9*c^2 + 32*a^3*b^7*c^3 + 48*a^4*b^5*c^4)*d^2 - 4*(a^3*b^9*c^2 + 4*a^4*b^7*c^3)*d)*x^5 - 4*(a^3*b^8 + 4*a^4*b^6*c)*d^4 + 3*(a^4*b^10*c - 1024*a*c^6*d^8 + 256*c^6*d^9 - 32*(5*b^4*c^4 - 48*a^2*c^6)*d^7 + 16*(5*b^6*c^3 + 40*a*b^4*c^4 - 64*a^3*c^6)*d^6 - (15*b^8*c^2 + 320*a*b^6*c^3 + 960*a^2*b^4*c^4 - 256*a^4*c^6)*d^5 + (b^10*c + 60*a*b^8*c^2 + 480*a^2*b^6*c^3 + 640*a^3*b^4*c^4)*d^4 - 2*(2*a*b^10*c + 45*a^2*b^8*c^2 + 160*a^3*b^6*c^3 + 80*a^4*b^4*c^4)*d^3 + 2*(3*a^2*b^10*c + 30*a^3*b^8*c^2 + 40*a^4*b^6*c^3)*d^2 - (4*a^3*b^10*c + 15*a^4*b^8*c^2)*d)*x^4 + (a^4*b^11 + 1536*b*c^5*d^9 - 256*(5*b^3*c^4 + 24*a*b*c^5)*d^8 + 64*(5*b^5*c^3 + 80*a*b^3*c^4 + 144*a^2*b*c^5)*d^7 - 256*(5*a*b^5*c^3 + 30*a^2*b^3*c^4 + 24*a^3*b*c^5)*d^6 - 2*(5*b^9*c - 960*a^2*b^5*c^3 - 2560*a^3*b^3*c^4 - 768*a^4*b*c^5)*d^5 + (b^11 + 40*a*b^9*c - 1280*a^3*b^5*c^3 - 1280*a^4*b^3*c^4)*d^4 - 4*(a*b^11 + 15*a^2*b^9*c - 80*a^4*b^5*c^3)*d^3 + 2*(3*a^2*b^11 + 20*a^3*b^9*c)*d^2 - 2*(2*a^3*b^11 + 5*a^4*b^9*c)*d)*x^3 + 3*(a^4*b^10*d - 1024*a*c^5*d^9 + 256*c^5*d^10 - 32*(5*b^4*c^3 - 48*a^2*c^5)*d^8 + 16*(5*b^6*c^2 + 40*a*b^4*c^3 - 64*a^3*c^5)*d^7 - (15*b^8*c + 320*a*b^6*c^2 + 960*a^2*b^4*c^3 - 256*a^4*c^5)*d^6 + (b^10 + 60*a*b^8*c + 480*a^2*b^6*c^2 + 640*a^3*b^4*c^3)*d^5 - 2*(2*a*b^10 + 45*a^2*b^8*c + 160*a^3*b^6*c^2 + 80*a^4*b^4*c^3)*d^4 + 2*(3*a^2*b^10 + 30*a^3*b^8*c + 40*a^4*b^6*c^2)*d^3 - (4*a^3*b^10 + 15*a^4*b^8*c)*d^2)*x^2 + 3*(a^4*b^9*d^2 + 256*b*c^4*d^10 - 256*(b^3*c^3 + 4*a*b*c^4)*d^9 + 32*(3*b^5*c^2 + 32*a*b^3*c^3 + 48*a^2*b*c^4)*d^8 - 16*(b^7*c + 24*a*b^5*c^2 + 96*a^2*b^3*c^3 + 64*a^3*b*c^4)*d^7 + (b^9 + 64*a*b^7*c + 576*a^2*b^5*c^2 + 1024*a^3*b^3*c^3 + 256*a^4*b*c^4)*d^6 - 4*(a*b^9 + 24*a^2*b^7*c + 96*a^3*b^5*c^2 + 64*a^4*b^3*c^3)*d^5 + 2*(3*a^2*b^9 + 32*a^3*b^7*c + 48*a^4*b^5*c^2)*d^4 - 4*(a^3*b^9 + 4*a^4*b^7*c)*d^3)*x)]","B",0
7,1,2005,0,1.573285," ","integrate(1/(b*f*x^2+b*e*x+a*e)^2/(f*x^2+e*x+d)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{b^{2} d e^{2} - a b e^{3} - 4 \, {\left(a b d e - a^{2} e^{2}\right)} f} {\left(a b e^{3} + {\left(b^{2} e^{2} f + 4 \, {\left(b^{2} d - 2 \, a b e\right)} f^{2}\right)} x^{2} + 4 \, {\left(a b d e - 2 \, a^{2} e^{2}\right)} f + {\left(b^{2} e^{3} + 4 \, {\left(b^{2} d e - 2 \, a b e^{2}\right)} f\right)} x\right)} \log\left(\frac{8 \, b^{2} d^{2} e^{4} - 8 \, a b d e^{5} + a^{2} e^{6} + 16 \, a^{2} d^{2} e^{2} f^{2} + {\left(b^{2} e^{4} f^{2} + 16 \, {\left(b^{2} d^{2} - 8 \, a b d e + 8 \, a^{2} e^{2}\right)} f^{4} + 8 \, {\left(3 \, b^{2} d e^{2} - 4 \, a b e^{3}\right)} f^{3}\right)} x^{4} + 2 \, {\left(b^{2} e^{5} f + 16 \, {\left(b^{2} d^{2} e - 8 \, a b d e^{2} + 8 \, a^{2} e^{3}\right)} f^{3} + 8 \, {\left(3 \, b^{2} d e^{3} - 4 \, a b e^{4}\right)} f^{2}\right)} x^{3} + {\left(b^{2} e^{6} - 32 \, {\left(3 \, a b d^{2} e - 4 \, a^{2} d e^{2}\right)} f^{3} + 16 \, {\left(3 \, b^{2} d^{2} e^{2} - 13 \, a b d e^{3} + 10 \, a^{2} e^{4}\right)} f^{2} + 2 \, {\left(16 \, b^{2} d e^{4} - 19 \, a b e^{5}\right)} f\right)} x^{2} - 4 \, \sqrt{b^{2} d e^{2} - a b e^{3} - 4 \, {\left(a b d e - a^{2} e^{2}\right)} f} {\left(2 \, b d e^{3} - a e^{4} - 4 \, a d e^{2} f + 2 \, {\left(b e^{2} f^{2} + 4 \, {\left(b d - 2 \, a e\right)} f^{3}\right)} x^{3} + 3 \, {\left(b e^{3} f + 4 \, {\left(b d e - 2 \, a e^{2}\right)} f^{2}\right)} x^{2} + {\left(b e^{4} - 8 \, a d e f^{2} + 2 \, {\left(4 \, b d e^{2} - 5 \, a e^{3}\right)} f\right)} x\right)} \sqrt{f x^{2} + e x + d} - 8 \, {\left(4 \, a b d^{2} e^{3} - 3 \, a^{2} d e^{4}\right)} f + 2 \, {\left(4 \, b^{2} d e^{5} - 3 \, a b e^{6} - 16 \, {\left(3 \, a b d^{2} e^{2} - 4 \, a^{2} d e^{3}\right)} f^{2} + 8 \, {\left(2 \, b^{2} d^{2} e^{3} - 5 \, a b d e^{4} + 2 \, a^{2} e^{5}\right)} f\right)} x}{b^{2} f^{2} x^{4} + 2 \, b^{2} e f x^{3} + 2 \, a b e^{2} x + a^{2} e^{2} + {\left(b^{2} e^{2} + 2 \, a b e f\right)} x^{2}}\right) + 4 \, {\left(b^{3} d e^{3} - a b^{2} e^{4} - 4 \, {\left(a b^{2} d e^{2} - a^{2} b e^{3}\right)} f - 2 \, {\left(4 \, {\left(a b^{2} d e - a^{2} b e^{2}\right)} f^{2} - {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} f\right)} x\right)} \sqrt{f x^{2} + e x + d}}{4 \, {\left(a b^{4} d^{2} e^{5} - 2 \, a^{2} b^{3} d e^{6} + a^{3} b^{2} e^{7} + 16 \, {\left(a^{3} b^{2} d^{2} e^{3} - 2 \, a^{4} b d e^{4} + a^{5} e^{5}\right)} f^{2} + {\left(16 \, {\left(a^{2} b^{3} d^{2} e^{2} - 2 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}\right)} f^{3} - 8 \, {\left(a b^{4} d^{2} e^{3} - 2 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} f^{2} + {\left(b^{5} d^{2} e^{4} - 2 \, a b^{4} d e^{5} + a^{2} b^{3} e^{6}\right)} f\right)} x^{2} - 8 \, {\left(a^{2} b^{3} d^{2} e^{4} - 2 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} f + {\left(b^{5} d^{2} e^{5} - 2 \, a b^{4} d e^{6} + a^{2} b^{3} e^{7} + 16 \, {\left(a^{2} b^{3} d^{2} e^{3} - 2 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} f^{2} - 8 \, {\left(a b^{4} d^{2} e^{4} - 2 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} f\right)} x\right)}}, \frac{\sqrt{-b^{2} d e^{2} + a b e^{3} + 4 \, {\left(a b d e - a^{2} e^{2}\right)} f} {\left(a b e^{3} + {\left(b^{2} e^{2} f + 4 \, {\left(b^{2} d - 2 \, a b e\right)} f^{2}\right)} x^{2} + 4 \, {\left(a b d e - 2 \, a^{2} e^{2}\right)} f + {\left(b^{2} e^{3} + 4 \, {\left(b^{2} d e - 2 \, a b e^{2}\right)} f\right)} x\right)} \arctan\left(-\frac{\sqrt{-b^{2} d e^{2} + a b e^{3} + 4 \, {\left(a b d e - a^{2} e^{2}\right)} f} {\left(2 \, b d e^{2} - a e^{3} - 4 \, a d e f + {\left(b e^{2} f + 4 \, {\left(b d - 2 \, a e\right)} f^{2}\right)} x^{2} + {\left(b e^{3} + 4 \, {\left(b d e - 2 \, a e^{2}\right)} f\right)} x\right)} \sqrt{f x^{2} + e x + d}}{2 \, {\left(b^{2} d^{2} e^{3} - a b d e^{4} - 2 \, {\left(4 \, {\left(a b d e - a^{2} e^{2}\right)} f^{3} - {\left(b^{2} d e^{2} - a b e^{3}\right)} f^{2}\right)} x^{3} - 3 \, {\left(4 \, {\left(a b d e^{2} - a^{2} e^{3}\right)} f^{2} - {\left(b^{2} d e^{3} - a b e^{4}\right)} f\right)} x^{2} - 4 \, {\left(a b d^{2} e^{2} - a^{2} d e^{3}\right)} f + {\left(b^{2} d e^{4} - a b e^{5} - 8 \, {\left(a b d^{2} e - a^{2} d e^{2}\right)} f^{2} + 2 \, {\left(b^{2} d^{2} e^{2} - 3 \, a b d e^{3} + 2 \, a^{2} e^{4}\right)} f\right)} x\right)}}\right) - 2 \, {\left(b^{3} d e^{3} - a b^{2} e^{4} - 4 \, {\left(a b^{2} d e^{2} - a^{2} b e^{3}\right)} f - 2 \, {\left(4 \, {\left(a b^{2} d e - a^{2} b e^{2}\right)} f^{2} - {\left(b^{3} d e^{2} - a b^{2} e^{3}\right)} f\right)} x\right)} \sqrt{f x^{2} + e x + d}}{2 \, {\left(a b^{4} d^{2} e^{5} - 2 \, a^{2} b^{3} d e^{6} + a^{3} b^{2} e^{7} + 16 \, {\left(a^{3} b^{2} d^{2} e^{3} - 2 \, a^{4} b d e^{4} + a^{5} e^{5}\right)} f^{2} + {\left(16 \, {\left(a^{2} b^{3} d^{2} e^{2} - 2 \, a^{3} b^{2} d e^{3} + a^{4} b e^{4}\right)} f^{3} - 8 \, {\left(a b^{4} d^{2} e^{3} - 2 \, a^{2} b^{3} d e^{4} + a^{3} b^{2} e^{5}\right)} f^{2} + {\left(b^{5} d^{2} e^{4} - 2 \, a b^{4} d e^{5} + a^{2} b^{3} e^{6}\right)} f\right)} x^{2} - 8 \, {\left(a^{2} b^{3} d^{2} e^{4} - 2 \, a^{3} b^{2} d e^{5} + a^{4} b e^{6}\right)} f + {\left(b^{5} d^{2} e^{5} - 2 \, a b^{4} d e^{6} + a^{2} b^{3} e^{7} + 16 \, {\left(a^{2} b^{3} d^{2} e^{3} - 2 \, a^{3} b^{2} d e^{4} + a^{4} b e^{5}\right)} f^{2} - 8 \, {\left(a b^{4} d^{2} e^{4} - 2 \, a^{2} b^{3} d e^{5} + a^{3} b^{2} e^{6}\right)} f\right)} x\right)}}\right]"," ",0,"[-1/4*(sqrt(b^2*d*e^2 - a*b*e^3 - 4*(a*b*d*e - a^2*e^2)*f)*(a*b*e^3 + (b^2*e^2*f + 4*(b^2*d - 2*a*b*e)*f^2)*x^2 + 4*(a*b*d*e - 2*a^2*e^2)*f + (b^2*e^3 + 4*(b^2*d*e - 2*a*b*e^2)*f)*x)*log((8*b^2*d^2*e^4 - 8*a*b*d*e^5 + a^2*e^6 + 16*a^2*d^2*e^2*f^2 + (b^2*e^4*f^2 + 16*(b^2*d^2 - 8*a*b*d*e + 8*a^2*e^2)*f^4 + 8*(3*b^2*d*e^2 - 4*a*b*e^3)*f^3)*x^4 + 2*(b^2*e^5*f + 16*(b^2*d^2*e - 8*a*b*d*e^2 + 8*a^2*e^3)*f^3 + 8*(3*b^2*d*e^3 - 4*a*b*e^4)*f^2)*x^3 + (b^2*e^6 - 32*(3*a*b*d^2*e - 4*a^2*d*e^2)*f^3 + 16*(3*b^2*d^2*e^2 - 13*a*b*d*e^3 + 10*a^2*e^4)*f^2 + 2*(16*b^2*d*e^4 - 19*a*b*e^5)*f)*x^2 - 4*sqrt(b^2*d*e^2 - a*b*e^3 - 4*(a*b*d*e - a^2*e^2)*f)*(2*b*d*e^3 - a*e^4 - 4*a*d*e^2*f + 2*(b*e^2*f^2 + 4*(b*d - 2*a*e)*f^3)*x^3 + 3*(b*e^3*f + 4*(b*d*e - 2*a*e^2)*f^2)*x^2 + (b*e^4 - 8*a*d*e*f^2 + 2*(4*b*d*e^2 - 5*a*e^3)*f)*x)*sqrt(f*x^2 + e*x + d) - 8*(4*a*b*d^2*e^3 - 3*a^2*d*e^4)*f + 2*(4*b^2*d*e^5 - 3*a*b*e^6 - 16*(3*a*b*d^2*e^2 - 4*a^2*d*e^3)*f^2 + 8*(2*b^2*d^2*e^3 - 5*a*b*d*e^4 + 2*a^2*e^5)*f)*x)/(b^2*f^2*x^4 + 2*b^2*e*f*x^3 + 2*a*b*e^2*x + a^2*e^2 + (b^2*e^2 + 2*a*b*e*f)*x^2)) + 4*(b^3*d*e^3 - a*b^2*e^4 - 4*(a*b^2*d*e^2 - a^2*b*e^3)*f - 2*(4*(a*b^2*d*e - a^2*b*e^2)*f^2 - (b^3*d*e^2 - a*b^2*e^3)*f)*x)*sqrt(f*x^2 + e*x + d))/(a*b^4*d^2*e^5 - 2*a^2*b^3*d*e^6 + a^3*b^2*e^7 + 16*(a^3*b^2*d^2*e^3 - 2*a^4*b*d*e^4 + a^5*e^5)*f^2 + (16*(a^2*b^3*d^2*e^2 - 2*a^3*b^2*d*e^3 + a^4*b*e^4)*f^3 - 8*(a*b^4*d^2*e^3 - 2*a^2*b^3*d*e^4 + a^3*b^2*e^5)*f^2 + (b^5*d^2*e^4 - 2*a*b^4*d*e^5 + a^2*b^3*e^6)*f)*x^2 - 8*(a^2*b^3*d^2*e^4 - 2*a^3*b^2*d*e^5 + a^4*b*e^6)*f + (b^5*d^2*e^5 - 2*a*b^4*d*e^6 + a^2*b^3*e^7 + 16*(a^2*b^3*d^2*e^3 - 2*a^3*b^2*d*e^4 + a^4*b*e^5)*f^2 - 8*(a*b^4*d^2*e^4 - 2*a^2*b^3*d*e^5 + a^3*b^2*e^6)*f)*x), 1/2*(sqrt(-b^2*d*e^2 + a*b*e^3 + 4*(a*b*d*e - a^2*e^2)*f)*(a*b*e^3 + (b^2*e^2*f + 4*(b^2*d - 2*a*b*e)*f^2)*x^2 + 4*(a*b*d*e - 2*a^2*e^2)*f + (b^2*e^3 + 4*(b^2*d*e - 2*a*b*e^2)*f)*x)*arctan(-1/2*sqrt(-b^2*d*e^2 + a*b*e^3 + 4*(a*b*d*e - a^2*e^2)*f)*(2*b*d*e^2 - a*e^3 - 4*a*d*e*f + (b*e^2*f + 4*(b*d - 2*a*e)*f^2)*x^2 + (b*e^3 + 4*(b*d*e - 2*a*e^2)*f)*x)*sqrt(f*x^2 + e*x + d)/(b^2*d^2*e^3 - a*b*d*e^4 - 2*(4*(a*b*d*e - a^2*e^2)*f^3 - (b^2*d*e^2 - a*b*e^3)*f^2)*x^3 - 3*(4*(a*b*d*e^2 - a^2*e^3)*f^2 - (b^2*d*e^3 - a*b*e^4)*f)*x^2 - 4*(a*b*d^2*e^2 - a^2*d*e^3)*f + (b^2*d*e^4 - a*b*e^5 - 8*(a*b*d^2*e - a^2*d*e^2)*f^2 + 2*(b^2*d^2*e^2 - 3*a*b*d*e^3 + 2*a^2*e^4)*f)*x)) - 2*(b^3*d*e^3 - a*b^2*e^4 - 4*(a*b^2*d*e^2 - a^2*b*e^3)*f - 2*(4*(a*b^2*d*e - a^2*b*e^2)*f^2 - (b^3*d*e^2 - a*b^2*e^3)*f)*x)*sqrt(f*x^2 + e*x + d))/(a*b^4*d^2*e^5 - 2*a^2*b^3*d*e^6 + a^3*b^2*e^7 + 16*(a^3*b^2*d^2*e^3 - 2*a^4*b*d*e^4 + a^5*e^5)*f^2 + (16*(a^2*b^3*d^2*e^2 - 2*a^3*b^2*d*e^3 + a^4*b*e^4)*f^3 - 8*(a*b^4*d^2*e^3 - 2*a^2*b^3*d*e^4 + a^3*b^2*e^5)*f^2 + (b^5*d^2*e^4 - 2*a*b^4*d*e^5 + a^2*b^3*e^6)*f)*x^2 - 8*(a^2*b^3*d^2*e^4 - 2*a^3*b^2*d*e^5 + a^4*b*e^6)*f + (b^5*d^2*e^5 - 2*a*b^4*d*e^6 + a^2*b^3*e^7 + 16*(a^2*b^3*d^2*e^3 - 2*a^3*b^2*d*e^4 + a^4*b*e^5)*f^2 - 8*(a*b^4*d^2*e^4 - 2*a^2*b^3*d*e^5 + a^3*b^2*e^6)*f)*x)]","B",0
8,1,38,0,0.397583," ","integrate(1/(x^2+2*x+4)/(x^2+2*x+5)^(1/2),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} \sqrt{x^{2} + 2 \, x + 5} {\left(x + 1\right)} - \frac{1}{3} \, \sqrt{3} {\left(x^{2} + 2 \, x + 4\right)}\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*sqrt(x^2 + 2*x + 5)*(x + 1) - 1/3*sqrt(3)*(x^2 + 2*x + 4))","A",0
9,0,0,0,0.430589," ","integrate((a+1/2*e*x+c*x^2)^p*(2*c*x^2+e*x+2*a)^q,x, algorithm=""fricas"")","{\rm integral}\left({\left(2 \, c x^{2} + e x + 2 \, a\right)}^{q} {\left(c x^{2} + \frac{1}{2} \, e x + a\right)}^{p}, x\right)"," ",0,"integral((2*c*x^2 + e*x + 2*a)^q*(c*x^2 + 1/2*e*x + a)^p, x)","F",0
10,0,0,0,0.424184," ","integrate((a+c*e*x/f+c*x^2)^p*(a*f/c+e*x+f*x^2)^q,x, algorithm=""fricas"")","{\rm integral}\left(\left(\frac{c f x^{2} + c e x + a f}{c}\right)^{q} \left(\frac{c f x^{2} + c e x + a f}{f}\right)^{p}, x\right)"," ",0,"integral(((c*f*x^2 + c*e*x + a*f)/c)^q*((c*f*x^2 + c*e*x + a*f)/f)^p, x)","F",0
11,1,22,0,0.403667," ","integrate(((1+x)^2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""fricas"")","\sqrt{x^{2} + 1} - \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"sqrt(x^2 + 1) - log(-x + sqrt(x^2 + 1))","A",0
12,1,82,0,0.412727," ","integrate(1/(x^2-1)^2/(x^2+x-1)^(1/2),x, algorithm=""fricas"")","\frac{2 \, {\left(x^{2} - 1\right)} \arctan\left(-x + \sqrt{x^{2} + x - 1} - 1\right) + 5 \, {\left(x^{2} - 1\right)} \log\left(-x + \sqrt{x^{2} + x - 1} + 2\right) - 5 \, {\left(x^{2} - 1\right)} \log\left(-x + \sqrt{x^{2} + x - 1}\right) - 4 \, \sqrt{x^{2} + x - 1}}{8 \, {\left(x^{2} - 1\right)}}"," ",0,"1/8*(2*(x^2 - 1)*arctan(-x + sqrt(x^2 + x - 1) - 1) + 5*(x^2 - 1)*log(-x + sqrt(x^2 + x - 1) + 2) - 5*(x^2 - 1)*log(-x + sqrt(x^2 + x - 1)) - 4*sqrt(x^2 + x - 1))/(x^2 - 1)","A",0
13,0,0,0,0.419318," ","integrate(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{f x^{2} + d}}{c f x^{4} + b f x^{3} + b d x + {\left(c d + a f\right)} x^{2} + a d}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(f*x^2 + d)/(c*f*x^4 + b*f*x^3 + b*d*x + (c*d + a*f)*x^2 + a*d), x)","F",0
14,1,161,0,0.423658," ","integrate((-x^2-4*x-3)^(1/2)/(2*x^2+4*x+3),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
15,1,54,0,0.336809," ","integrate((2*x^2-x+3)*(5*x^2+3*x+2)^4,x, algorithm=""fricas"")","\frac{1250}{11} x^{11} + \frac{475}{2} x^{10} + \frac{5075}{9} x^{9} + \frac{3415}{4} x^{8} + 1176 x^{7} + \frac{2377}{2} x^{6} + \frac{5099}{5} x^{5} + 656 x^{4} + \frac{1064}{3} x^{3} + 136 x^{2} + 48 x"," ",0,"1250/11*x^11 + 475/2*x^10 + 5075/9*x^9 + 3415/4*x^8 + 1176*x^7 + 2377/2*x^6 + 5099/5*x^5 + 656*x^4 + 1064/3*x^3 + 136*x^2 + 48*x","A",0
16,1,44,0,0.341893," ","integrate((2*x^2-x+3)*(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{250}{9} x^{9} + \frac{325}{8} x^{8} + \frac{720}{7} x^{7} + 134 x^{6} + \frac{876}{5} x^{5} + \frac{579}{4} x^{4} + \frac{322}{3} x^{3} + 50 x^{2} + 24 x"," ",0,"250/9*x^9 + 325/8*x^8 + 720/7*x^7 + 134*x^6 + 876/5*x^5 + 579/4*x^4 + 322/3*x^3 + 50*x^2 + 24*x","A",0
17,1,34,0,0.340752," ","integrate((2*x^2-x+3)*(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{50}{7} x^{7} + \frac{35}{6} x^{6} + \frac{103}{5} x^{5} + \frac{85}{4} x^{4} + \frac{83}{3} x^{3} + 16 x^{2} + 12 x"," ",0,"50/7*x^7 + 35/6*x^6 + 103/5*x^5 + 85/4*x^4 + 83/3*x^3 + 16*x^2 + 12*x","A",0
18,1,24,0,0.340586," ","integrate((2*x^2-x+3)*(5*x^2+3*x+2),x, algorithm=""fricas"")","2 x^{5} + \frac{1}{4} x^{4} + \frac{16}{3} x^{3} + \frac{7}{2} x^{2} + 6 x"," ",0,"2*x^5 + 1/4*x^4 + 16/3*x^3 + 7/2*x^2 + 6*x","A",0
19,1,33,0,0.392966," ","integrate((2*x^2-x+3)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{143}{775} \, \sqrt{31} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + \frac{2}{5} \, x - \frac{11}{50} \, \log\left(5 \, x^{2} + 3 \, x + 2\right)"," ",0,"143/775*sqrt(31)*arctan(1/31*sqrt(31)*(10*x + 3)) + 2/5*x - 11/50*log(5*x^2 + 3*x + 2)","A",0
20,1,45,0,0.387589," ","integrate((2*x^2-x+3)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{410 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 4433 \, x + 2387}{4805 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/4805*(410*sqrt(31)*(5*x^2 + 3*x + 2)*arctan(1/31*sqrt(31)*(10*x + 3)) + 4433*x + 2387)/(5*x^2 + 3*x + 2)","A",0
21,1,75,0,0.389996," ","integrate((2*x^2-x+3)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{171430 \, x^{3} + 2212 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 154287 \, x^{2} + 126914 \, x + 35371}{59582 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/59582*(171430*x^3 + 2212*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*arctan(1/31*sqrt(31)*(10*x + 3)) + 154287*x^2 + 126914*x + 35371)/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","A",0
22,1,64,0,0.345165," ","integrate((2*x^2-x+3)^2*(5*x^2+3*x+2)^4,x, algorithm=""fricas"")","\frac{2500}{13} x^{13} + \frac{875}{3} x^{12} + \frac{11525}{11} x^{11} + 1571 x^{10} + \frac{24859}{9} x^{9} + 3315 x^{8} + \frac{27763}{7} x^{7} + \frac{10771}{3} x^{6} + \frac{14801}{5} x^{5} + 1838 x^{4} + \frac{3016}{3} x^{3} + 384 x^{2} + 144 x"," ",0,"2500/13*x^13 + 875/3*x^12 + 11525/11*x^11 + 1571*x^10 + 24859/9*x^9 + 3315*x^8 + 27763/7*x^7 + 10771/3*x^6 + 14801/5*x^5 + 1838*x^4 + 3016/3*x^3 + 384*x^2 + 144*x","A",0
23,1,54,0,0.337981," ","integrate((2*x^2-x+3)^2*(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{500}{11} x^{11} + 40 x^{10} + \frac{1865}{9} x^{9} + \frac{1863}{8} x^{8} + 444 x^{7} + 449 x^{6} + \frac{2693}{5} x^{5} + \frac{1615}{4} x^{4} + \frac{914}{3} x^{3} + 138 x^{2} + 72 x"," ",0,"500/11*x^11 + 40*x^10 + 1865/9*x^9 + 1863/8*x^8 + 444*x^7 + 449*x^6 + 2693/5*x^5 + 1615/4*x^4 + 914/3*x^3 + 138*x^2 + 72*x","A",0
24,1,44,0,0.331852," ","integrate((2*x^2-x+3)^2*(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{100}{9} x^{9} + \frac{5}{2} x^{8} + \frac{321}{7} x^{7} + \frac{86}{3} x^{6} + 78 x^{5} + 59 x^{4} + \frac{241}{3} x^{3} + 42 x^{2} + 36 x"," ",0,"100/9*x^9 + 5/2*x^8 + 321/7*x^7 + 86/3*x^6 + 78*x^5 + 59*x^4 + 241/3*x^3 + 42*x^2 + 36*x","A",0
25,1,34,0,0.337219," ","integrate((2*x^2-x+3)^2*(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{20}{7} x^{7} - \frac{4}{3} x^{6} + \frac{61}{5} x^{5} + \frac{1}{4} x^{4} + \frac{53}{3} x^{3} + \frac{15}{2} x^{2} + 18 x"," ",0,"20/7*x^7 - 4/3*x^6 + 61/5*x^5 + 1/4*x^4 + 53/3*x^3 + 15/2*x^2 + 18*x","A",0
26,1,43,0,0.392088," ","integrate((2*x^2-x+3)^2/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{4}{15} \, x^{3} - \frac{16}{25} \, x^{2} + \frac{8349}{19375} \, \sqrt{31} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + \frac{381}{125} \, x - \frac{1573}{1250} \, \log\left(5 \, x^{2} + 3 \, x + 2\right)"," ",0,"4/15*x^3 - 16/25*x^2 + 8349/19375*sqrt(31)*arctan(1/31*sqrt(31)*(10*x + 3)) + 381/125*x - 1573/1250*log(5*x^2 + 3*x + 2)","A",0
27,1,78,0,0.396394," ","integrate((2*x^2-x+3)^2/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{96100 \, x^{3} + 41932 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 57660 \, x^{2} - 21142 \, {\left(5 \, x^{2} + 3 \, x + 2\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 297259 \, x + 228811}{120125 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/120125*(96100*x^3 + 41932*sqrt(31)*(5*x^2 + 3*x + 2)*arctan(1/31*sqrt(31)*(10*x + 3)) + 57660*x^2 - 21142*(5*x^2 + 3*x + 2)*log(5*x^2 + 3*x + 2) + 297259*x + 228811)/(5*x^2 + 3*x + 2)","A",0
28,1,75,0,0.383206," ","integrate((2*x^2-x+3)^2/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{15587110 \, x^{3} + 216500 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 15339203 \, x^{2} + 11431684 \, x + 3813403}{1489550 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/1489550*(15587110*x^3 + 216500*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*arctan(1/31*sqrt(31)*(10*x + 3)) + 15339203*x^2 + 11431684*x + 3813403)/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","A",0
29,1,105,0,0.376897," ","integrate((2*x^2-x+3)^2/(5*x^2+3*x+2)^4,x, algorithm=""fricas"")","\frac{387996000 \, x^{5} + 581994000 \, x^{4} + 666245676 \, x^{3} + 1001280 \, \sqrt{31} {\left(125 \, x^{6} + 225 \, x^{5} + 285 \, x^{4} + 207 \, x^{3} + 114 \, x^{2} + 36 \, x + 8\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 396198507 \, x^{2} + 175922148 \, x + 39036409}{13852815 \, {\left(125 \, x^{6} + 225 \, x^{5} + 285 \, x^{4} + 207 \, x^{3} + 114 \, x^{2} + 36 \, x + 8\right)}}"," ",0,"1/13852815*(387996000*x^5 + 581994000*x^4 + 666245676*x^3 + 1001280*sqrt(31)*(125*x^6 + 225*x^5 + 285*x^4 + 207*x^3 + 114*x^2 + 36*x + 8)*arctan(1/31*sqrt(31)*(10*x + 3)) + 396198507*x^2 + 175922148*x + 39036409)/(125*x^6 + 225*x^5 + 285*x^4 + 207*x^3 + 114*x^2 + 36*x + 8)","A",0
30,1,74,0,0.338892," ","integrate((2*x^2-x+3)^3*(5*x^2+3*x+2)^4,x, algorithm=""fricas"")","\frac{1000}{3} x^{15} + \frac{2250}{7} x^{14} + \frac{27050}{13} x^{13} + \frac{30395}{12} x^{12} + \frac{68583}{11} x^{11} + \frac{75311}{10} x^{10} + \frac{103583}{9} x^{9} + \frac{94881}{8} x^{8} + \frac{91349}{7} x^{7} + \frac{64529}{6} x^{6} + \frac{43083}{5} x^{5} + 5144 x^{4} + 2856 x^{3} + 1080 x^{2} + 432 x"," ",0,"1000/3*x^15 + 2250/7*x^14 + 27050/13*x^13 + 30395/12*x^12 + 68583/11*x^11 + 75311/10*x^10 + 103583/9*x^9 + 94881/8*x^8 + 91349/7*x^7 + 64529/6*x^6 + 43083/5*x^5 + 5144*x^4 + 2856*x^3 + 1080*x^2 + 432*x","A",0
31,1,64,0,0.329134," ","integrate((2*x^2-x+3)^3*(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{1000}{13} x^{13} + 25 x^{12} + \frac{4830}{11} x^{11} + \frac{3061}{10} x^{10} + \frac{3316}{3} x^{9} + \frac{7869}{8} x^{8} + \frac{12016}{7} x^{7} + \frac{2873}{2} x^{6} + \frac{8292}{5} x^{5} + \frac{4483}{4} x^{4} + 870 x^{3} + 378 x^{2} + 216 x"," ",0,"1000/13*x^13 + 25*x^12 + 4830/11*x^11 + 3061/10*x^10 + 3316/3*x^9 + 7869/8*x^8 + 12016/7*x^7 + 2873/2*x^6 + 8292/5*x^5 + 4483/4*x^4 + 870*x^3 + 378*x^2 + 216*x","A",0
32,1,54,0,0.337255," ","integrate((2*x^2-x+3)^3*(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{200}{11} x^{11} - 6 x^{10} + \frac{922}{9} x^{9} + \frac{83}{8} x^{8} + \frac{1571}{7} x^{7} + \frac{299}{3} x^{6} + \frac{1416}{5} x^{5} + \frac{635}{4} x^{4} + 237 x^{3} + 108 x^{2} + 108 x"," ",0,"200/11*x^11 - 6*x^10 + 922/9*x^9 + 83/8*x^8 + 1571/7*x^7 + 299/3*x^6 + 1416/5*x^5 + 635/4*x^4 + 237*x^3 + 108*x^2 + 108*x","A",0
33,1,44,0,0.332473," ","integrate((2*x^2-x+3)^3*(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{40}{9} x^{9} - \frac{9}{2} x^{8} + \frac{190}{7} x^{7} - \frac{83}{6} x^{6} + \frac{288}{5} x^{5} - 5 x^{4} + 60 x^{3} + \frac{27}{2} x^{2} + 54 x"," ",0,"40/9*x^9 - 9/2*x^8 + 190/7*x^7 - 83/6*x^6 + 288/5*x^5 - 5*x^4 + 60*x^3 + 27/2*x^2 + 54*x","A",0
34,1,53,0,0.408389," ","integrate((2*x^2-x+3)^3/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{8}{25} \, x^{5} - \frac{21}{25} \, x^{4} + \frac{1222}{375} \, x^{3} - \frac{7451}{1250} \, x^{2} + \frac{328757}{484375} \, \sqrt{31} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + \frac{49508}{3125} \, x - \frac{158389}{31250} \, \log\left(5 \, x^{2} + 3 \, x + 2\right)"," ",0,"8/25*x^5 - 21/25*x^4 + 1222/375*x^3 - 7451/1250*x^2 + 328757/484375*sqrt(31)*arctan(1/31*sqrt(31)*(10*x + 3)) + 49508/3125*x - 158389/31250*log(5*x^2 + 3*x + 2)","A",0
35,1,88,0,0.408174," ","integrate((2*x^2-x+3)^3/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{9610000 \, x^{5} - 33154500 \, x^{4} + 191815600 \, x^{3} + 22917642 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 111226140 \, x^{2} - 31047027 \, {\left(5 \, x^{2} + 3 \, x + 2\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 145678362 \, x + 109671738}{18018750 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/18018750*(9610000*x^5 - 33154500*x^4 + 191815600*x^3 + 22917642*sqrt(31)*(5*x^2 + 3*x + 2)*arctan(1/31*sqrt(31)*(10*x + 3)) + 111226140*x^2 - 31047027*(5*x^2 + 3*x + 2)*log(5*x^2 + 3*x + 2) + 145678362*x + 109671738)/(5*x^2 + 3*x + 2)","A",0
36,1,118,0,0.392807," ","integrate((2*x^2-x+3)^3/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{59582000 \, x^{5} + 71498400 \, x^{4} + 1355107960 \, x^{3} + 22682352 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 1506812195 \, x^{2} - 3932412 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 1011087630 \, x + 395974315}{37238750 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/37238750*(59582000*x^5 + 71498400*x^4 + 1355107960*x^3 + 22682352*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*arctan(1/31*sqrt(31)*(10*x + 3)) + 1506812195*x^2 - 3932412*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*log(5*x^2 + 3*x + 2) + 1011087630*x + 395974315)/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","A",0
37,1,63,0,0.396946," ","integrate((5*x^2+3*x+2)^4/(2*x^2-x+3),x, algorithm=""fricas"")","\frac{625}{14} \, x^{7} + \frac{3625}{24} \, x^{6} + \frac{1855}{8} \, x^{5} + \frac{6245}{64} \, x^{4} - \frac{21229}{96} \, x^{3} - \frac{28747}{128} \, x^{2} - \frac{1156639}{5888} \, \sqrt{23} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + \frac{122691}{128} \, x + \frac{307461}{512} \, \log\left(2 \, x^{2} - x + 3\right)"," ",0,"625/14*x^7 + 3625/24*x^6 + 1855/8*x^5 + 6245/64*x^4 - 21229/96*x^3 - 28747/128*x^2 - 1156639/5888*sqrt(23)*arctan(1/23*sqrt(23)*(4*x - 1)) + 122691/128*x + 307461/512*log(2*x^2 - x + 3)","A",0
38,1,53,0,0.413578," ","integrate((5*x^2+3*x+2)^3/(2*x^2-x+3),x, algorithm=""fricas"")","\frac{25}{2} \, x^{5} + \frac{575}{16} \, x^{4} + \frac{965}{24} \, x^{3} - \frac{829}{32} \, x^{2} + \frac{59895}{1472} \, \sqrt{23} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - \frac{4795}{32} \, x + \frac{1331}{128} \, \log\left(2 \, x^{2} - x + 3\right)"," ",0,"25/2*x^5 + 575/16*x^4 + 965/24*x^3 - 829/32*x^2 + 59895/1472*sqrt(23)*arctan(1/23*sqrt(23)*(4*x - 1)) - 4795/32*x + 1331/128*log(2*x^2 - x + 3)","A",0
39,1,43,0,0.434112," ","integrate((5*x^2+3*x+2)^2/(2*x^2-x+3),x, algorithm=""fricas"")","\frac{25}{6} \, x^{3} + \frac{85}{8} \, x^{2} - \frac{847}{368} \, \sqrt{23} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + \frac{51}{8} \, x - \frac{363}{32} \, \log\left(2 \, x^{2} - x + 3\right)"," ",0,"25/6*x^3 + 85/8*x^2 - 847/368*sqrt(23)*arctan(1/23*sqrt(23)*(4*x - 1)) + 51/8*x - 363/32*log(2*x^2 - x + 3)","A",0
40,1,33,0,0.394802," ","integrate((5*x^2+3*x+2)/(2*x^2-x+3),x, algorithm=""fricas"")","-\frac{33}{92} \, \sqrt{23} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + \frac{5}{2} \, x + \frac{11}{8} \, \log\left(2 \, x^{2} - x + 3\right)"," ",0,"-33/92*sqrt(23)*arctan(1/23*sqrt(23)*(4*x - 1)) + 5/2*x + 11/8*log(2*x^2 - x + 3)","A",0
41,1,59,0,0.406875," ","integrate(1/(2*x^2-x+3)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{13}{682} \, \sqrt{31} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) - \frac{3}{506} \, \sqrt{23} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + \frac{1}{44} \, \log\left(5 \, x^{2} + 3 \, x + 2\right) - \frac{1}{44} \, \log\left(2 \, x^{2} - x + 3\right)"," ",0,"13/682*sqrt(31)*arctan(1/31*sqrt(31)*(10*x + 3)) - 3/506*sqrt(23)*arctan(1/23*sqrt(23)*(4*x - 1)) + 1/44*log(5*x^2 + 3*x + 2) - 1/44*log(2*x^2 - x + 3)","A",0
42,1,117,0,0.411756," ","integrate(1/(2*x^2-x+3)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{132986 \, \sqrt{31} {\left(5 \, x^{2} + 3 \, x + 2\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) - 13454 \, \sqrt{23} {\left(5 \, x^{2} + 3 \, x + 2\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - 66309 \, {\left(5 \, x^{2} + 3 \, x + 2\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 66309 \, {\left(5 \, x^{2} + 3 \, x + 2\right)} \log\left(2 \, x^{2} - x + 3\right) + 2039180 \, x + 125488}{21395704 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/21395704*(132986*sqrt(31)*(5*x^2 + 3*x + 2)*arctan(1/31*sqrt(31)*(10*x + 3)) - 13454*sqrt(23)*(5*x^2 + 3*x + 2)*arctan(1/23*sqrt(23)*(4*x - 1)) - 66309*(5*x^2 + 3*x + 2)*log(5*x^2 + 3*x + 2) + 66309*(5*x^2 + 3*x + 2)*log(2*x^2 - x + 3) + 2039180*x + 125488)/(5*x^2 + 3*x + 2)","A",0
43,1,177,0,0.402477," ","integrate(1/(2*x^2-x+3)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{3388960300 \, x^{3} + 38998478 \, \sqrt{31} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 2681190 \, \sqrt{23} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 3276177960 \, x^{2} + 685193 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) - 685193 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \log\left(2 \, x^{2} - x + 3\right) + 2796625568 \, x + 539912120}{14591870128 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/14591870128*(3388960300*x^3 + 38998478*sqrt(31)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*arctan(1/31*sqrt(31)*(10*x + 3)) + 2681190*sqrt(23)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*arctan(1/23*sqrt(23)*(4*x - 1)) + 3276177960*x^2 + 685193*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*log(5*x^2 + 3*x + 2) - 685193*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*log(2*x^2 - x + 3) + 2796625568*x + 539912120)/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","A",0
44,1,98,0,0.393463," ","integrate((5*x^2+3*x+2)^4/(2*x^2-x+3)^2,x, algorithm=""fricas"")","\frac{12696000 \, x^{7} + 47610000 \, x^{6} + 74800600 \, x^{5} - 20609840 \, x^{4} - 413058012 \, x^{3} + 79756182 \, \sqrt{23} {\left(2 \, x^{2} - x + 3\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 193356906 \, x^{2} - 48582831 \, {\left(2 \, x^{2} - x + 3\right)} \log\left(2 \, x^{2} - x + 3\right) - 930684489 \, x - 102033129}{203136 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/203136*(12696000*x^7 + 47610000*x^6 + 74800600*x^5 - 20609840*x^4 - 413058012*x^3 + 79756182*sqrt(23)*(2*x^2 - x + 3)*arctan(1/23*sqrt(23)*(4*x - 1)) + 193356906*x^2 - 48582831*(2*x^2 - x + 3)*log(2*x^2 - x + 3) - 930684489*x - 102033129)/(2*x^2 - x + 3)","A",0
45,1,88,0,0.431863," ","integrate((5*x^2+3*x+2)^3/(2*x^2-x+3)^2,x, algorithm=""fricas"")","\frac{1058000 \, x^{5} + 3914600 \, x^{4} + 5173620 \, x^{3} - 1343826 \, \sqrt{23} {\left(2 \, x^{2} - x + 3\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 3761190 \, x^{2} - 3264459 \, {\left(2 \, x^{2} - x + 3\right)} \log\left(2 \, x^{2} - x + 3\right) + 12845385 \, x - 1561263}{50784 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/50784*(1058000*x^5 + 3914600*x^4 + 5173620*x^3 - 1343826*sqrt(23)*(2*x^2 - x + 3)*arctan(1/23*sqrt(23)*(4*x - 1)) + 3761190*x^2 - 3264459*(2*x^2 - x + 3)*log(2*x^2 - x + 3) + 12845385*x - 1561263)/(2*x^2 - x + 3)","A",0
46,1,78,0,0.407427," ","integrate((5*x^2+3*x+2)^2/(2*x^2-x+3)^2,x, algorithm=""fricas"")","\frac{52900 \, x^{3} - 3718 \, \sqrt{23} {\left(2 \, x^{2} - x + 3\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - 26450 \, x^{2} + 29095 \, {\left(2 \, x^{2} - x + 3\right)} \log\left(2 \, x^{2} - x + 3\right) + 59869 \, x + 52877}{4232 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/4232*(52900*x^3 - 3718*sqrt(23)*(2*x^2 - x + 3)*arctan(1/23*sqrt(23)*(4*x - 1)) - 26450*x^2 + 29095*(2*x^2 - x + 3)*log(2*x^2 - x + 3) + 59869*x + 52877)/(2*x^2 - x + 3)","A",0
47,1,45,0,0.400873," ","integrate((5*x^2+3*x+2)/(2*x^2-x+3)^2,x, algorithm=""fricas"")","\frac{164 \, \sqrt{23} {\left(2 \, x^{2} - x + 3\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - 759 \, x - 1265}{1058 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/1058*(164*sqrt(23)*(2*x^2 - x + 3)*arctan(1/23*sqrt(23)*(4*x - 1)) - 759*x - 1265)/(2*x^2 - x + 3)","A",0
48,1,117,0,0.414143," ","integrate(1/(2*x^2-x+3)^2/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{73002 \, \sqrt{31} {\left(2 \, x^{2} - x + 3\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) - 14942 \, \sqrt{23} {\left(2 \, x^{2} - x + 3\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 213187 \, {\left(2 \, x^{2} - x + 3\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) - 213187 \, {\left(2 \, x^{2} - x + 3\right)} \log\left(2 \, x^{2} - x + 3\right) - 188232 \, x + 407836}{15874232 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/15874232*(73002*sqrt(31)*(2*x^2 - x + 3)*arctan(1/31*sqrt(31)*(10*x + 3)) - 14942*sqrt(23)*(2*x^2 - x + 3)*arctan(1/23*sqrt(23)*(4*x - 1)) + 213187*(2*x^2 - x + 3)*log(5*x^2 + 3*x + 2) - 213187*(2*x^2 - x + 3)*log(2*x^2 - x + 3) - 188232*x + 407836)/(2*x^2 - x + 3)","A",0
49,1,167,0,0.433857," ","integrate(1/(2*x^2-x+3)^2/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{214898200 \, x^{3} + 13376294 \, \sqrt{31} {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) - 5322018 \, \sqrt{23} {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - 290975300 \, x^{2} - 9659011 \, {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 9659011 \, {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)} \log\left(2 \, x^{2} - x + 3\right) + 349923288 \, x - 136217224}{5413113112 \, {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)}}"," ",0,"1/5413113112*(214898200*x^3 + 13376294*sqrt(31)*(10*x^4 + x^3 + 16*x^2 + 7*x + 6)*arctan(1/31*sqrt(31)*(10*x + 3)) - 5322018*sqrt(23)*(10*x^4 + x^3 + 16*x^2 + 7*x + 6)*arctan(1/23*sqrt(23)*(4*x - 1)) - 290975300*x^2 - 9659011*(10*x^4 + x^3 + 16*x^2 + 7*x + 6)*log(5*x^2 + 3*x + 2) + 9659011*(10*x^4 + x^3 + 16*x^2 + 7*x + 6)*log(2*x^2 - x + 3) + 349923288*x - 136217224)/(10*x^4 + x^3 + 16*x^2 + 7*x + 6)","A",0
50,1,237,0,0.408773," ","integrate(1/(2*x^2-x+3)^2/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{1253927859800 \, x^{5} + 679296504260 \, x^{4} + 2185021181068 \, x^{3} + 4722995582 \, \sqrt{31} {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 1522737174 \, \sqrt{23} {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 1500218514344 \, x^{2} - 1528665583 \, {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 1528665583 \, {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)} \log\left(2 \, x^{2} - x + 3\right) + 1338609358240 \, x + 218880812656}{7383486284768 \, {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)}}"," ",0,"1/7383486284768*(1253927859800*x^5 + 679296504260*x^4 + 2185021181068*x^3 + 4722995582*sqrt(31)*(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12)*arctan(1/31*sqrt(31)*(10*x + 3)) + 1522737174*sqrt(23)*(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12)*arctan(1/23*sqrt(23)*(4*x - 1)) + 1500218514344*x^2 - 1528665583*(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12)*log(5*x^2 + 3*x + 2) + 1528665583*(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12)*log(2*x^2 - x + 3) + 1338609358240*x + 218880812656)/(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12)","A",0
51,1,128,0,0.411057," ","integrate((5*x^2+3*x+2)^4/(2*x^2-x+3)^3,x, algorithm=""fricas"")","\frac{486680000 \, x^{7} + 2360398000 \, x^{6} + 5100406400 \, x^{5} + 2157209100 \, x^{4} + 24531516180 \, x^{3} - 765597492 \, \sqrt{23} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - 6171678159 \, x^{2} - 1015822830 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x^{2} - x + 3\right) + 23692590858 \, x - 453041787}{4672128 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/4672128*(486680000*x^7 + 2360398000*x^6 + 5100406400*x^5 + 2157209100*x^4 + 24531516180*x^3 - 765597492*sqrt(23)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*arctan(1/23*sqrt(23)*(4*x - 1)) - 6171678159*x^2 - 1015822830*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(2*x^2 - x + 3) + 23692590858*x - 453041787)/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
52,1,118,0,0.394127," ","integrate((5*x^2+3*x+2)^3/(2*x^2-x+3)^3,x, algorithm=""fricas"")","\frac{24334000 \, x^{5} - 24334000 \, x^{4} + 43385176 \, x^{3} - 330198 \, \sqrt{23} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 40329281 \, x^{2} + 10037775 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x^{2} - x + 3\right) - 12446818 \, x + 82485337}{389344 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/389344*(24334000*x^5 - 24334000*x^4 + 43385176*x^3 - 330198*sqrt(23)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*arctan(1/23*sqrt(23)*(4*x - 1)) + 40329281*x^2 + 10037775*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(2*x^2 - x + 3) - 12446818*x + 82485337)/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
53,1,75,0,0.387120," ","integrate((5*x^2+3*x+2)^2/(2*x^2-x+3)^3,x, algorithm=""fricas"")","-\frac{419980 \, x^{3} - 34640 \, \sqrt{23} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 1023385 \, x^{2} + 237314 \, x + 1241977}{97336 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/97336*(419980*x^3 - 34640*sqrt(23)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*arctan(1/23*sqrt(23)*(4*x - 1)) + 1023385*x^2 + 237314*x + 1241977)/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
54,1,75,0,0.417642," ","integrate((5*x^2+3*x+2)/(2*x^2-x+3)^3,x, algorithm=""fricas"")","\frac{12052 \, x^{3} + 524 \, \sqrt{23} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - 9039 \, x^{2} + 10856 \, x - 19067}{24334 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/24334*(12052*x^3 + 524*sqrt(23)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*arctan(1/23*sqrt(23)*(4*x - 1)) - 9039*x^2 + 10856*x - 19067)/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
55,1,177,0,0.431066," ","integrate(1/(2*x^2-x+3)^3/(5*x^2+3*x+2),x, algorithm=""fricas"")","-\frac{46807024 \, x^{3} - 6010498 \, \sqrt{31} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) - 3310986 \, \sqrt{23} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) - 250850512 \, x^{2} - 44884063 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 44884063 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(2 \, x^{2} - x + 3\right) + 231556732 \, x - 444353008}{8032361392 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"-1/8032361392*(46807024*x^3 - 6010498*sqrt(31)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*arctan(1/31*sqrt(31)*(10*x + 3)) - 3310986*sqrt(23)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*arctan(1/23*sqrt(23)*(4*x - 1)) - 250850512*x^2 - 44884063*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(5*x^2 + 3*x + 2) + 44884063*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(2*x^2 - x + 3) + 231556732*x - 444353008)/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
56,1,227,0,0.426254," ","integrate(1/(2*x^2-x+3)^3/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","-\frac{31725248720 \, x^{5} + 260524883872 \, x^{4} - 158204886268 \, x^{3} - 6004584838 \, \sqrt{31} {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 3917991234 \, \sqrt{23} {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 679966484692 \, x^{2} + 2116340147 \, {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) - 2116340147 \, {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)} \log\left(2 \, x^{2} - x + 3\right) - 184712689040 \, x + 277008109136}{5478070469344 \, {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)}}"," ",0,"-1/5478070469344*(31725248720*x^5 + 260524883872*x^4 - 158204886268*x^3 - 6004584838*sqrt(31)*(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18)*arctan(1/31*sqrt(31)*(10*x + 3)) + 3917991234*sqrt(23)*(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18)*arctan(1/23*sqrt(23)*(4*x - 1)) + 679966484692*x^2 + 2116340147*(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18)*log(5*x^2 + 3*x + 2) - 2116340147*(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18)*log(2*x^2 - x + 3) - 184712689040*x + 277008109136)/(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18)","A",0
57,1,297,0,0.427593," ","integrate(1/(2*x^2-x+3)^3/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{67202918046000 \, x^{7} - 2238718468800 \, x^{6} + 186872434930060 \, x^{5} + 62827256425340 \, x^{4} + 173919793526820 \, x^{3} + 67376830890 \, \sqrt{31} {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)} \arctan\left(\frac{1}{31} \, \sqrt{31} {\left(10 \, x + 3\right)}\right) + 52466419650 \, \sqrt{23} {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)} \arctan\left(\frac{1}{23} \, \sqrt{23} {\left(4 \, x - 1\right)}\right) + 73595926401690 \, x^{2} - 146799174285 \, {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)} \log\left(5 \, x^{2} + 3 \, x + 2\right) + 146799174285 \, {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)} \log\left(2 \, x^{2} - x + 3\right) + 78707350628632 \, x + 7381223830244}{467005507511576 \, {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)}}"," ",0,"1/467005507511576*(67202918046000*x^7 - 2238718468800*x^6 + 186872434930060*x^5 + 62827256425340*x^4 + 173919793526820*x^3 + 67376830890*sqrt(31)*(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36)*arctan(1/31*sqrt(31)*(10*x + 3)) + 52466419650*sqrt(23)*(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36)*arctan(1/23*sqrt(23)*(4*x - 1)) + 73595926401690*x^2 - 146799174285*(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36)*log(5*x^2 + 3*x + 2) + 146799174285*(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36)*log(2*x^2 - x + 3) + 78707350628632*x + 7381223830244)/(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36)","A",0
58,1,98,0,0.436847," ","integrate((5*x^2+3*x+2)^4*(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{21139292160} \, {\left(1321205760000 \, x^{9} + 3486515200000 \, x^{8} + 6327795712000 \, x^{7} + 7725962035200 \, x^{6} + 7612808028160 \, x^{5} + 5354741991424 \, x^{4} + 2211683657856 \, x^{3} - 174418077792 \, x^{2} + 537752185764 \, x + 3801512106459\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{8267844569}{536870912} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/21139292160*(1321205760000*x^9 + 3486515200000*x^8 + 6327795712000*x^7 + 7725962035200*x^6 + 7612808028160*x^5 + 5354741991424*x^4 + 2211683657856*x^3 - 174418077792*x^2 + 537752185764*x + 3801512106459)*sqrt(2*x^2 - x + 3) + 8267844569/536870912*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
59,1,88,0,0.433646," ","integrate((5*x^2+3*x+2)^3*(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{220200960} \, {\left(3440640000 \, x^{7} + 6955008000 \, x^{6} + 10958233600 \, x^{5} + 11212171264 \, x^{4} + 9872163456 \, x^{3} + 4583812128 \, x^{2} - 1621307916 \, x - 3957369321\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{155620231}{16777216} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/220200960*(3440640000*x^7 + 6955008000*x^6 + 10958233600*x^5 + 11212171264*x^4 + 9872163456*x^3 + 4583812128*x^2 - 1621307916*x - 3957369321)*sqrt(2*x^2 - x + 3) + 155620231/16777216*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
60,1,78,0,0.418890," ","integrate((5*x^2+3*x+2)^2*(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{49152} \, {\left(204800 \, x^{5} + 284672 \, x^{4} + 408960 \, x^{3} + 365536 \, x^{2} + 328204 \, x - 64023\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{284533}{131072} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/49152*(204800*x^5 + 284672*x^4 + 408960*x^3 + 365536*x^2 + 328204*x - 64023)*sqrt(2*x^2 - x + 3) + 284533/131072*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
61,1,68,0,0.410868," ","integrate((5*x^2+3*x+2)*(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{1536} \, {\left(1920 \, x^{3} + 1376 \, x^{2} + 2684 \, x + 3261\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{1863}{4096} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/1536*(1920*x^3 + 1376*x^2 + 2684*x + 3261)*sqrt(2*x^2 - x + 3) + 1863/4096*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
62,1,2016,0,0.993876," ","integrate((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{1}{1550} \cdot 6050^{\frac{1}{4}} \sqrt{31} \sqrt{5} \sqrt{2} \sqrt{13 \, \sqrt{2} + 20} \arctan\left(\frac{460 \, \sqrt{5} {\left(4 \cdot 6050^{\frac{3}{4}} \sqrt{31} {\left(4702 \, x^{7} - 19541 \, x^{6} + 40352 \, x^{5} - 68777 \, x^{4} + 35480 \, x^{3} - 19080 \, x^{2} - \sqrt{2} {\left(4028 \, x^{7} - 14488 \, x^{6} + 30919 \, x^{5} - 46671 \, x^{4} + 22688 \, x^{3} - 9144 \, x^{2} - 27648 \, x + 17280\right)} - 34560 \, x + 27648\right)} + 5 \cdot 6050^{\frac{1}{4}} \sqrt{31} {\left(22836 \, x^{7} - 355266 \, x^{6} + 1914360 \, x^{5} - 4475096 \, x^{4} + 5840640 \, x^{3} - 4011840 \, x^{2} - \sqrt{2} {\left(18463 \, x^{7} - 280047 \, x^{6} + 1453472 \, x^{5} - 3238500 \, x^{4} + 4140576 \, x^{3} - 2378592 \, x^{2} - 3068928 \, x + 1990656\right)} - 3981312 \, x + 3068928\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{13 \, \sqrt{2} + 20} + 253000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{10} {\left(\sqrt{5} {\left(4 \cdot 6050^{\frac{3}{4}} \sqrt{31} {\left(15454 \, x^{7} - 22399 \, x^{6} + 73509 \, x^{5} - 37360 \, x^{4} + 52200 \, x^{3} + 13824 \, x^{2} - \sqrt{2} {\left(15438 \, x^{7} - 22007 \, x^{6} + 69837 \, x^{5} - 21232 \, x^{4} + 19368 \, x^{3} + 44928 \, x^{2} - 44928 \, x\right)} - 13824 \, x\right)} + 5 \cdot 6050^{\frac{1}{4}} \sqrt{31} {\left(77254 \, x^{7} - 1000024 \, x^{6} + 3868360 \, x^{5} - 5120640 \, x^{4} + 7012800 \, x^{3} + 2405376 \, x^{2} - \sqrt{2} {\left(69479 \, x^{7} - 898236 \, x^{6} + 3454740 \, x^{5} - 4394304 \, x^{4} + 5347296 \, x^{3} + 4478976 \, x^{2} - 4478976 \, x\right)} - 2405376 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{13 \, \sqrt{2} + 20} + 550 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 25 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{6050^{\frac{1}{4}} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(3 \, x + 5\right)} - 8 \, x + 2\right)} \sqrt{13 \, \sqrt{2} + 20} - 245 \, x^{2} - 220 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 755 \, x - 1000}{x^{2}}} + 2875 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{89125 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + \frac{1}{1550} \cdot 6050^{\frac{1}{4}} \sqrt{31} \sqrt{5} \sqrt{2} \sqrt{13 \, \sqrt{2} + 20} \arctan\left(\frac{460 \, \sqrt{5} {\left(4 \cdot 6050^{\frac{3}{4}} \sqrt{31} {\left(4702 \, x^{7} - 19541 \, x^{6} + 40352 \, x^{5} - 68777 \, x^{4} + 35480 \, x^{3} - 19080 \, x^{2} - \sqrt{2} {\left(4028 \, x^{7} - 14488 \, x^{6} + 30919 \, x^{5} - 46671 \, x^{4} + 22688 \, x^{3} - 9144 \, x^{2} - 27648 \, x + 17280\right)} - 34560 \, x + 27648\right)} + 5 \cdot 6050^{\frac{1}{4}} \sqrt{31} {\left(22836 \, x^{7} - 355266 \, x^{6} + 1914360 \, x^{5} - 4475096 \, x^{4} + 5840640 \, x^{3} - 4011840 \, x^{2} - \sqrt{2} {\left(18463 \, x^{7} - 280047 \, x^{6} + 1453472 \, x^{5} - 3238500 \, x^{4} + 4140576 \, x^{3} - 2378592 \, x^{2} - 3068928 \, x + 1990656\right)} - 3981312 \, x + 3068928\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{13 \, \sqrt{2} + 20} - 253000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{10} {\left(\sqrt{5} {\left(4 \cdot 6050^{\frac{3}{4}} \sqrt{31} {\left(15454 \, x^{7} - 22399 \, x^{6} + 73509 \, x^{5} - 37360 \, x^{4} + 52200 \, x^{3} + 13824 \, x^{2} - \sqrt{2} {\left(15438 \, x^{7} - 22007 \, x^{6} + 69837 \, x^{5} - 21232 \, x^{4} + 19368 \, x^{3} + 44928 \, x^{2} - 44928 \, x\right)} - 13824 \, x\right)} + 5 \cdot 6050^{\frac{1}{4}} \sqrt{31} {\left(77254 \, x^{7} - 1000024 \, x^{6} + 3868360 \, x^{5} - 5120640 \, x^{4} + 7012800 \, x^{3} + 2405376 \, x^{2} - \sqrt{2} {\left(69479 \, x^{7} - 898236 \, x^{6} + 3454740 \, x^{5} - 4394304 \, x^{4} + 5347296 \, x^{3} + 4478976 \, x^{2} - 4478976 \, x\right)} - 2405376 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{13 \, \sqrt{2} + 20} - 550 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 25 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{6050^{\frac{1}{4}} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(3 \, x + 5\right)} - 8 \, x + 2\right)} \sqrt{13 \, \sqrt{2} + 20} + 245 \, x^{2} + 220 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 755 \, x + 1000}{x^{2}}} - 2875 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{89125 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) - \frac{1}{6200} \cdot 6050^{\frac{1}{4}} \sqrt{5} \sqrt{13 \, \sqrt{2} + 20} {\left(13 \, \sqrt{2} - 20\right)} \log\left(\frac{40 \, {\left(6050^{\frac{1}{4}} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(3 \, x + 5\right)} - 8 \, x + 2\right)} \sqrt{13 \, \sqrt{2} + 20} + 245 \, x^{2} + 220 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 755 \, x + 1000\right)}}{x^{2}}\right) + \frac{1}{6200} \cdot 6050^{\frac{1}{4}} \sqrt{5} \sqrt{13 \, \sqrt{2} + 20} {\left(13 \, \sqrt{2} - 20\right)} \log\left(-\frac{40 \, {\left(6050^{\frac{1}{4}} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(3 \, x + 5\right)} - 8 \, x + 2\right)} \sqrt{13 \, \sqrt{2} + 20} - 245 \, x^{2} - 220 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 755 \, x - 1000\right)}}{x^{2}}\right) + \frac{1}{10} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/1550*6050^(1/4)*sqrt(31)*sqrt(5)*sqrt(2)*sqrt(13*sqrt(2) + 20)*arctan(1/89125*(460*sqrt(5)*(4*6050^(3/4)*sqrt(31)*(4702*x^7 - 19541*x^6 + 40352*x^5 - 68777*x^4 + 35480*x^3 - 19080*x^2 - sqrt(2)*(4028*x^7 - 14488*x^6 + 30919*x^5 - 46671*x^4 + 22688*x^3 - 9144*x^2 - 27648*x + 17280) - 34560*x + 27648) + 5*6050^(1/4)*sqrt(31)*(22836*x^7 - 355266*x^6 + 1914360*x^5 - 4475096*x^4 + 5840640*x^3 - 4011840*x^2 - sqrt(2)*(18463*x^7 - 280047*x^6 + 1453472*x^5 - 3238500*x^4 + 4140576*x^3 - 2378592*x^2 - 3068928*x + 1990656) - 3981312*x + 3068928))*sqrt(2*x^2 - x + 3)*sqrt(13*sqrt(2) + 20) + 253000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(10)*(sqrt(5)*(4*6050^(3/4)*sqrt(31)*(15454*x^7 - 22399*x^6 + 73509*x^5 - 37360*x^4 + 52200*x^3 + 13824*x^2 - sqrt(2)*(15438*x^7 - 22007*x^6 + 69837*x^5 - 21232*x^4 + 19368*x^3 + 44928*x^2 - 44928*x) - 13824*x) + 5*6050^(1/4)*sqrt(31)*(77254*x^7 - 1000024*x^6 + 3868360*x^5 - 5120640*x^4 + 7012800*x^3 + 2405376*x^2 - sqrt(2)*(69479*x^7 - 898236*x^6 + 3454740*x^5 - 4394304*x^4 + 5347296*x^3 + 4478976*x^2 - 4478976*x) - 2405376*x))*sqrt(2*x^2 - x + 3)*sqrt(13*sqrt(2) + 20) + 550*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 25*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(6050^(1/4)*sqrt(5)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(3*x + 5) - 8*x + 2)*sqrt(13*sqrt(2) + 20) - 245*x^2 - 220*sqrt(2)*(2*x^2 - x + 3) + 755*x - 1000)/x^2) + 2875*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 1/1550*6050^(1/4)*sqrt(31)*sqrt(5)*sqrt(2)*sqrt(13*sqrt(2) + 20)*arctan(1/89125*(460*sqrt(5)*(4*6050^(3/4)*sqrt(31)*(4702*x^7 - 19541*x^6 + 40352*x^5 - 68777*x^4 + 35480*x^3 - 19080*x^2 - sqrt(2)*(4028*x^7 - 14488*x^6 + 30919*x^5 - 46671*x^4 + 22688*x^3 - 9144*x^2 - 27648*x + 17280) - 34560*x + 27648) + 5*6050^(1/4)*sqrt(31)*(22836*x^7 - 355266*x^6 + 1914360*x^5 - 4475096*x^4 + 5840640*x^3 - 4011840*x^2 - sqrt(2)*(18463*x^7 - 280047*x^6 + 1453472*x^5 - 3238500*x^4 + 4140576*x^3 - 2378592*x^2 - 3068928*x + 1990656) - 3981312*x + 3068928))*sqrt(2*x^2 - x + 3)*sqrt(13*sqrt(2) + 20) - 253000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(10)*(sqrt(5)*(4*6050^(3/4)*sqrt(31)*(15454*x^7 - 22399*x^6 + 73509*x^5 - 37360*x^4 + 52200*x^3 + 13824*x^2 - sqrt(2)*(15438*x^7 - 22007*x^6 + 69837*x^5 - 21232*x^4 + 19368*x^3 + 44928*x^2 - 44928*x) - 13824*x) + 5*6050^(1/4)*sqrt(31)*(77254*x^7 - 1000024*x^6 + 3868360*x^5 - 5120640*x^4 + 7012800*x^3 + 2405376*x^2 - sqrt(2)*(69479*x^7 - 898236*x^6 + 3454740*x^5 - 4394304*x^4 + 5347296*x^3 + 4478976*x^2 - 4478976*x) - 2405376*x))*sqrt(2*x^2 - x + 3)*sqrt(13*sqrt(2) + 20) - 550*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 25*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((6050^(1/4)*sqrt(5)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(3*x + 5) - 8*x + 2)*sqrt(13*sqrt(2) + 20) + 245*x^2 + 220*sqrt(2)*(2*x^2 - x + 3) - 755*x + 1000)/x^2) - 2875*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) - 1/6200*6050^(1/4)*sqrt(5)*sqrt(13*sqrt(2) + 20)*(13*sqrt(2) - 20)*log(40*(6050^(1/4)*sqrt(5)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(3*x + 5) - 8*x + 2)*sqrt(13*sqrt(2) + 20) + 245*x^2 + 220*sqrt(2)*(2*x^2 - x + 3) - 755*x + 1000)/x^2) + 1/6200*6050^(1/4)*sqrt(5)*sqrt(13*sqrt(2) + 20)*(13*sqrt(2) - 20)*log(-40*(6050^(1/4)*sqrt(5)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(3*x + 5) - 8*x + 2)*sqrt(13*sqrt(2) + 20) - 245*x^2 - 220*sqrt(2)*(2*x^2 - x + 3) + 755*x - 1000)/x^2) + 1/10*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","B",0
63,1,2102,0,1.193999," ","integrate((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","-\frac{88412 \cdot 4988406728^{\frac{1}{4}} \sqrt{24971} \sqrt{341} \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{70517 \, \sqrt{2} + 99884} \arctan\left(\frac{3096404 \, \sqrt{24971} {\left(11 \cdot 4988406728^{\frac{3}{4}} \sqrt{341} {\left(537184 \, x^{7} - 2047820 \, x^{6} + 4310846 \, x^{5} - 6853210 \, x^{4} + 3421536 \, x^{3} - 1589328 \, x^{2} - \sqrt{2} {\left(370014 \, x^{7} - 1438653 \, x^{6} + 3014868 \, x^{5} - 4873381 \, x^{4} + 2452952 \, x^{3} - 1184616 \, x^{2} - 2633472 \, x + 1893888\right)} - 3787776 \, x + 2633472\right)} + 774101 \cdot 4988406728^{\frac{1}{4}} \sqrt{341} {\left(40625 \, x^{7} - 622509 \, x^{6} + 3280912 \, x^{5} - 7459052 \, x^{4} + 9621216 \, x^{3} - 5992992 \, x^{2} - \sqrt{2} {\left(28204 \, x^{7} - 433677 \, x^{6} + 2297444 \, x^{5} - 5257628 \, x^{4} + 6800832 \, x^{3} - 4341024 \, x^{2} - 4810752 \, x + 3442176\right)} - 6884352 \, x + 4810752\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{70517 \, \sqrt{2} + 99884} + 30285984782473634104 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{49942} {\left(\sqrt{24971} {\left(11 \cdot 4988406728^{\frac{3}{4}} \sqrt{341} {\left(84604 \, x^{7} - 121310 \, x^{6} + 389610 \, x^{5} - 147168 \, x^{4} + 168912 \, x^{3} + 186624 \, x^{2} - \sqrt{2} {\left(57082 \, x^{7} - 82029 \, x^{6} + 264639 \, x^{5} - 107216 \, x^{4} + 130104 \, x^{3} + 110592 \, x^{2} - 110592 \, x\right)} - 186624 \, x\right)} + 774101 \cdot 4988406728^{\frac{1}{4}} \sqrt{341} {\left(6379 \, x^{7} - 82508 \, x^{6} + 318020 \, x^{5} - 410688 \, x^{4} + 523872 \, x^{3} + 331776 \, x^{2} - \sqrt{2} {\left(4365 \, x^{7} - 56468 \, x^{6} + 217820 \, x^{5} - 282816 \, x^{4} + 366624 \, x^{3} + 207360 \, x^{2} - 207360 \, x\right)} - 331776 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{70517 \, \sqrt{2} + 99884} + 425261673562 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 19330076071 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{4988406728^{\frac{1}{4}} \sqrt{24971} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(10 \, x + 3\right)} - 13 \, x - 7\right)} \sqrt{70517 \, \sqrt{2} + 99884} - 1175859419 \, x^{2} - 1055873764 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 3623566781 \, x - 4799426200}{x^{2}}} + 344158917982654933 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{10668926457462302923 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 88412 \cdot 4988406728^{\frac{1}{4}} \sqrt{24971} \sqrt{341} \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{70517 \, \sqrt{2} + 99884} \arctan\left(\frac{3096404 \, \sqrt{24971} {\left(11 \cdot 4988406728^{\frac{3}{4}} \sqrt{341} {\left(537184 \, x^{7} - 2047820 \, x^{6} + 4310846 \, x^{5} - 6853210 \, x^{4} + 3421536 \, x^{3} - 1589328 \, x^{2} - \sqrt{2} {\left(370014 \, x^{7} - 1438653 \, x^{6} + 3014868 \, x^{5} - 4873381 \, x^{4} + 2452952 \, x^{3} - 1184616 \, x^{2} - 2633472 \, x + 1893888\right)} - 3787776 \, x + 2633472\right)} + 774101 \cdot 4988406728^{\frac{1}{4}} \sqrt{341} {\left(40625 \, x^{7} - 622509 \, x^{6} + 3280912 \, x^{5} - 7459052 \, x^{4} + 9621216 \, x^{3} - 5992992 \, x^{2} - \sqrt{2} {\left(28204 \, x^{7} - 433677 \, x^{6} + 2297444 \, x^{5} - 5257628 \, x^{4} + 6800832 \, x^{3} - 4341024 \, x^{2} - 4810752 \, x + 3442176\right)} - 6884352 \, x + 4810752\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{70517 \, \sqrt{2} + 99884} - 30285984782473634104 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{49942} {\left(\sqrt{24971} {\left(11 \cdot 4988406728^{\frac{3}{4}} \sqrt{341} {\left(84604 \, x^{7} - 121310 \, x^{6} + 389610 \, x^{5} - 147168 \, x^{4} + 168912 \, x^{3} + 186624 \, x^{2} - \sqrt{2} {\left(57082 \, x^{7} - 82029 \, x^{6} + 264639 \, x^{5} - 107216 \, x^{4} + 130104 \, x^{3} + 110592 \, x^{2} - 110592 \, x\right)} - 186624 \, x\right)} + 774101 \cdot 4988406728^{\frac{1}{4}} \sqrt{341} {\left(6379 \, x^{7} - 82508 \, x^{6} + 318020 \, x^{5} - 410688 \, x^{4} + 523872 \, x^{3} + 331776 \, x^{2} - \sqrt{2} {\left(4365 \, x^{7} - 56468 \, x^{6} + 217820 \, x^{5} - 282816 \, x^{4} + 366624 \, x^{3} + 207360 \, x^{2} - 207360 \, x\right)} - 331776 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{70517 \, \sqrt{2} + 99884} - 425261673562 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 19330076071 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{4988406728^{\frac{1}{4}} \sqrt{24971} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(10 \, x + 3\right)} - 13 \, x - 7\right)} \sqrt{70517 \, \sqrt{2} + 99884} + 1175859419 \, x^{2} + 1055873764 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 3623566781 \, x + 4799426200}{x^{2}}} - 344158917982654933 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{10668926457462302923 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) - 4988406728^{\frac{1}{4}} \sqrt{24971} \sqrt{341} \sqrt{31} {\left(499420 \, x^{2} - 70517 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 299652 \, x + 199768\right)} \sqrt{70517 \, \sqrt{2} + 99884} \log\left(\frac{199768 \, {\left(4988406728^{\frac{1}{4}} \sqrt{24971} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(10 \, x + 3\right)} - 13 \, x - 7\right)} \sqrt{70517 \, \sqrt{2} + 99884} + 1175859419 \, x^{2} + 1055873764 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 3623566781 \, x + 4799426200\right)}}{x^{2}}\right) + 4988406728^{\frac{1}{4}} \sqrt{24971} \sqrt{341} \sqrt{31} {\left(499420 \, x^{2} - 70517 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 299652 \, x + 199768\right)} \sqrt{70517 \, \sqrt{2} + 99884} \log\left(-\frac{199768 \, {\left(4988406728^{\frac{1}{4}} \sqrt{24971} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(10 \, x + 3\right)} - 13 \, x - 7\right)} \sqrt{70517 \, \sqrt{2} + 99884} - 1175859419 \, x^{2} - 1055873764 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 3623566781 \, x - 4799426200\right)}}{x^{2}}\right) - 6022703949856 \, \sqrt{2 \, x^{2} - x + 3} {\left(10 \, x + 3\right)}}{186703822445536 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"-1/186703822445536*(88412*4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(70517*sqrt(2) + 99884)*arctan(1/10668926457462302923*(3096404*sqrt(24971)*(11*4988406728^(3/4)*sqrt(341)*(537184*x^7 - 2047820*x^6 + 4310846*x^5 - 6853210*x^4 + 3421536*x^3 - 1589328*x^2 - sqrt(2)*(370014*x^7 - 1438653*x^6 + 3014868*x^5 - 4873381*x^4 + 2452952*x^3 - 1184616*x^2 - 2633472*x + 1893888) - 3787776*x + 2633472) + 774101*4988406728^(1/4)*sqrt(341)*(40625*x^7 - 622509*x^6 + 3280912*x^5 - 7459052*x^4 + 9621216*x^3 - 5992992*x^2 - sqrt(2)*(28204*x^7 - 433677*x^6 + 2297444*x^5 - 5257628*x^4 + 6800832*x^3 - 4341024*x^2 - 4810752*x + 3442176) - 6884352*x + 4810752))*sqrt(2*x^2 - x + 3)*sqrt(70517*sqrt(2) + 99884) + 30285984782473634104*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(49942)*(sqrt(24971)*(11*4988406728^(3/4)*sqrt(341)*(84604*x^7 - 121310*x^6 + 389610*x^5 - 147168*x^4 + 168912*x^3 + 186624*x^2 - sqrt(2)*(57082*x^7 - 82029*x^6 + 264639*x^5 - 107216*x^4 + 130104*x^3 + 110592*x^2 - 110592*x) - 186624*x) + 774101*4988406728^(1/4)*sqrt(341)*(6379*x^7 - 82508*x^6 + 318020*x^5 - 410688*x^4 + 523872*x^3 + 331776*x^2 - sqrt(2)*(4365*x^7 - 56468*x^6 + 217820*x^5 - 282816*x^4 + 366624*x^3 + 207360*x^2 - 207360*x) - 331776*x))*sqrt(2*x^2 - x + 3)*sqrt(70517*sqrt(2) + 99884) + 425261673562*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 19330076071*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(10*x + 3) - 13*x - 7)*sqrt(70517*sqrt(2) + 99884) - 1175859419*x^2 - 1055873764*sqrt(2)*(2*x^2 - x + 3) + 3623566781*x - 4799426200)/x^2) + 344158917982654933*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 88412*4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(70517*sqrt(2) + 99884)*arctan(1/10668926457462302923*(3096404*sqrt(24971)*(11*4988406728^(3/4)*sqrt(341)*(537184*x^7 - 2047820*x^6 + 4310846*x^5 - 6853210*x^4 + 3421536*x^3 - 1589328*x^2 - sqrt(2)*(370014*x^7 - 1438653*x^6 + 3014868*x^5 - 4873381*x^4 + 2452952*x^3 - 1184616*x^2 - 2633472*x + 1893888) - 3787776*x + 2633472) + 774101*4988406728^(1/4)*sqrt(341)*(40625*x^7 - 622509*x^6 + 3280912*x^5 - 7459052*x^4 + 9621216*x^3 - 5992992*x^2 - sqrt(2)*(28204*x^7 - 433677*x^6 + 2297444*x^5 - 5257628*x^4 + 6800832*x^3 - 4341024*x^2 - 4810752*x + 3442176) - 6884352*x + 4810752))*sqrt(2*x^2 - x + 3)*sqrt(70517*sqrt(2) + 99884) - 30285984782473634104*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(49942)*(sqrt(24971)*(11*4988406728^(3/4)*sqrt(341)*(84604*x^7 - 121310*x^6 + 389610*x^5 - 147168*x^4 + 168912*x^3 + 186624*x^2 - sqrt(2)*(57082*x^7 - 82029*x^6 + 264639*x^5 - 107216*x^4 + 130104*x^3 + 110592*x^2 - 110592*x) - 186624*x) + 774101*4988406728^(1/4)*sqrt(341)*(6379*x^7 - 82508*x^6 + 318020*x^5 - 410688*x^4 + 523872*x^3 + 331776*x^2 - sqrt(2)*(4365*x^7 - 56468*x^6 + 217820*x^5 - 282816*x^4 + 366624*x^3 + 207360*x^2 - 207360*x) - 331776*x))*sqrt(2*x^2 - x + 3)*sqrt(70517*sqrt(2) + 99884) - 425261673562*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 19330076071*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(10*x + 3) - 13*x - 7)*sqrt(70517*sqrt(2) + 99884) + 1175859419*x^2 + 1055873764*sqrt(2)*(2*x^2 - x + 3) - 3623566781*x + 4799426200)/x^2) - 344158917982654933*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) - 4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*(499420*x^2 - 70517*sqrt(2)*(5*x^2 + 3*x + 2) + 299652*x + 199768)*sqrt(70517*sqrt(2) + 99884)*log(199768*(4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(10*x + 3) - 13*x - 7)*sqrt(70517*sqrt(2) + 99884) + 1175859419*x^2 + 1055873764*sqrt(2)*(2*x^2 - x + 3) - 3623566781*x + 4799426200)/x^2) + 4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*(499420*x^2 - 70517*sqrt(2)*(5*x^2 + 3*x + 2) + 299652*x + 199768)*sqrt(70517*sqrt(2) + 99884)*log(-199768*(4988406728^(1/4)*sqrt(24971)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(10*x + 3) - 13*x - 7)*sqrt(70517*sqrt(2) + 99884) - 1175859419*x^2 - 1055873764*sqrt(2)*(2*x^2 - x + 3) + 3623566781*x - 4799426200)/x^2) - 6022703949856*sqrt(2*x^2 - x + 3)*(10*x + 3))/(5*x^2 + 3*x + 2)","B",0
64,1,2182,0,1.437047," ","integrate((2*x^2-x+3)^(1/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{14205421276 \cdot 788032707736935368450^{\frac{1}{4}} \sqrt{39699690370} \sqrt{341} \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{112285869463 \, \sqrt{2} + 158798761480} \arctan\left(\frac{2461380802940 \, \sqrt{39699690370} {\left(22 \cdot 788032707736935368450^{\frac{3}{4}} \sqrt{341} {\left(667937076 \, x^{7} - 2573871186 \, x^{6} + 5404850058 \, x^{5} - 8671430212 \, x^{4} + 4348809776 \, x^{3} - 2064441888 \, x^{2} - \sqrt{2} {\left(473555282 \, x^{7} - 1821195871 \, x^{6} + 3826055542 \, x^{5} - 6128133137 \, x^{4} + 3070797960 \, x^{3} - 1452037320 \, x^{2} - 3352976640 \, x + 2366869248\right)} - 4733738496 \, x + 3352976640\right)} + 615345200735 \cdot 788032707736935368450^{\frac{1}{4}} \sqrt{341} {\left(50730703 \, x^{7} - 778833417 \, x^{6} + 4116367112 \, x^{5} - 9392273180 \, x^{4} + 12133646496 \, x^{3} - 7660912032 \, x^{2} - \sqrt{2} {\left(35938543 \, x^{7} - 551546778 \, x^{6} + 2913578540 \, x^{5} - 6643469608 \, x^{4} + 8580088800 \, x^{3} - 5403919680 \, x^{2} - 6107913216 \, x + 4313793024\right)} - 8627586048 \, x + 6107913216\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{112285869463 \, \sqrt{2} + 158798761480} + 2444264331446112042193970130340819353377000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{39699690370}{160673}} {\left(\sqrt{39699690370} {\left(22 \cdot 788032707736935368450^{\frac{3}{4}} \sqrt{341} {\left(104024992 \, x^{7} - 149335248 \, x^{6} + 480784368 \, x^{5} - 188730368 \, x^{4} + 223535232 \, x^{3} + 214417152 \, x^{2} - \sqrt{2} {\left(73906058 \, x^{7} - 106073653 \, x^{6} + 341348823 \, x^{5} - 133050960 \, x^{4} + 156704760 \, x^{3} + 154338048 \, x^{2} - 154338048 \, x\right)} - 214417152 \, x\right)} + 615345200735 \cdot 788032707736935368450^{\frac{1}{4}} \sqrt{341} {\left(7903323 \, x^{7} - 102233612 \, x^{6} + 394216580 \, x^{5} - 510585408 \, x^{4} + 657060192 \, x^{3} + 391744512 \, x^{2} - 4 \, \sqrt{2} {\left(1401761 \, x^{7} - 18132196 \, x^{6} + 69912940 \, x^{5} - 90501120 \, x^{4} + 116274240 \, x^{3} + 70118784 \, x^{2} - 70118784 \, x\right)} - 391744512 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{112285869463 \, \sqrt{2} + 158798761480} + 43175912524323866211143695850 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 1962541478378357555051986175 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{788032707736935368450^{\frac{1}{4}} \sqrt{39699690370} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(12053 \, x + 5138\right)} - 17191 \, x - 6915\right)} \sqrt{112285869463 \, \sqrt{2} + 158798761480} - 150182556985858180945 \, x^{2} - 134857806273015509420 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 462807471527848680055 \, x - 612990028513706861000}{x^{2}}} + 27775731039160364115840569662963856288375 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{861047662213971287591057659551879544939625 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 14205421276 \cdot 788032707736935368450^{\frac{1}{4}} \sqrt{39699690370} \sqrt{341} \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{112285869463 \, \sqrt{2} + 158798761480} \arctan\left(\frac{2461380802940 \, \sqrt{39699690370} {\left(22 \cdot 788032707736935368450^{\frac{3}{4}} \sqrt{341} {\left(667937076 \, x^{7} - 2573871186 \, x^{6} + 5404850058 \, x^{5} - 8671430212 \, x^{4} + 4348809776 \, x^{3} - 2064441888 \, x^{2} - \sqrt{2} {\left(473555282 \, x^{7} - 1821195871 \, x^{6} + 3826055542 \, x^{5} - 6128133137 \, x^{4} + 3070797960 \, x^{3} - 1452037320 \, x^{2} - 3352976640 \, x + 2366869248\right)} - 4733738496 \, x + 3352976640\right)} + 615345200735 \cdot 788032707736935368450^{\frac{1}{4}} \sqrt{341} {\left(50730703 \, x^{7} - 778833417 \, x^{6} + 4116367112 \, x^{5} - 9392273180 \, x^{4} + 12133646496 \, x^{3} - 7660912032 \, x^{2} - \sqrt{2} {\left(35938543 \, x^{7} - 551546778 \, x^{6} + 2913578540 \, x^{5} - 6643469608 \, x^{4} + 8580088800 \, x^{3} - 5403919680 \, x^{2} - 6107913216 \, x + 4313793024\right)} - 8627586048 \, x + 6107913216\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{112285869463 \, \sqrt{2} + 158798761480} - 2444264331446112042193970130340819353377000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{39699690370}{160673}} {\left(\sqrt{39699690370} {\left(22 \cdot 788032707736935368450^{\frac{3}{4}} \sqrt{341} {\left(104024992 \, x^{7} - 149335248 \, x^{6} + 480784368 \, x^{5} - 188730368 \, x^{4} + 223535232 \, x^{3} + 214417152 \, x^{2} - \sqrt{2} {\left(73906058 \, x^{7} - 106073653 \, x^{6} + 341348823 \, x^{5} - 133050960 \, x^{4} + 156704760 \, x^{3} + 154338048 \, x^{2} - 154338048 \, x\right)} - 214417152 \, x\right)} + 615345200735 \cdot 788032707736935368450^{\frac{1}{4}} \sqrt{341} {\left(7903323 \, x^{7} - 102233612 \, x^{6} + 394216580 \, x^{5} - 510585408 \, x^{4} + 657060192 \, x^{3} + 391744512 \, x^{2} - 4 \, \sqrt{2} {\left(1401761 \, x^{7} - 18132196 \, x^{6} + 69912940 \, x^{5} - 90501120 \, x^{4} + 116274240 \, x^{3} + 70118784 \, x^{2} - 70118784 \, x\right)} - 391744512 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{112285869463 \, \sqrt{2} + 158798761480} - 43175912524323866211143695850 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 1962541478378357555051986175 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{788032707736935368450^{\frac{1}{4}} \sqrt{39699690370} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(12053 \, x + 5138\right)} - 17191 \, x - 6915\right)} \sqrt{112285869463 \, \sqrt{2} + 158798761480} + 150182556985858180945 \, x^{2} + 134857806273015509420 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 462807471527848680055 \, x + 612990028513706861000}{x^{2}}} - 27775731039160364115840569662963856288375 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{861047662213971287591057659551879544939625 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 788032707736935368450^{\frac{1}{4}} \sqrt{39699690370} \sqrt{341} \sqrt{31} {\left(3969969037000 \, x^{4} + 4763962844400 \, x^{3} + 4605164082920 \, x^{2} - 112285869463 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} + 1905585137760 \, x + 635195045920\right)} \sqrt{112285869463 \, \sqrt{2} + 158798761480} \log\left(\frac{635195045920 \, {\left(788032707736935368450^{\frac{1}{4}} \sqrt{39699690370} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(12053 \, x + 5138\right)} - 17191 \, x - 6915\right)} \sqrt{112285869463 \, \sqrt{2} + 158798761480} + 150182556985858180945 \, x^{2} + 134857806273015509420 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 462807471527848680055 \, x + 612990028513706861000\right)}}{160673 \, x^{2}}\right) - 788032707736935368450^{\frac{1}{4}} \sqrt{39699690370} \sqrt{341} \sqrt{31} {\left(3969969037000 \, x^{4} + 4763962844400 \, x^{3} + 4605164082920 \, x^{2} - 112285869463 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} + 1905585137760 \, x + 635195045920\right)} \sqrt{112285869463 \, \sqrt{2} + 158798761480} \log\left(-\frac{635195045920 \, {\left(788032707736935368450^{\frac{1}{4}} \sqrt{39699690370} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(12053 \, x + 5138\right)} - 17191 \, x - 6915\right)} \sqrt{112285869463 \, \sqrt{2} + 158798761480} - 150182556985858180945 \, x^{2} - 134857806273015509420 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 462807471527848680055 \, x - 612990028513706861000\right)}}{160673 \, x^{2}}\right) + 769228926981280465731680 \, {\left(68325 \, x^{3} + 58315 \, x^{2} + 51362 \, x + 11020\right)} \sqrt{2 \, x^{2} - x + 3}}{65052151896952926425996714240 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/65052151896952926425996714240*(14205421276*788032707736935368450^(1/4)*sqrt(39699690370)*sqrt(341)*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(112285869463*sqrt(2) + 158798761480)*arctan(1/861047662213971287591057659551879544939625*(2461380802940*sqrt(39699690370)*(22*788032707736935368450^(3/4)*sqrt(341)*(667937076*x^7 - 2573871186*x^6 + 5404850058*x^5 - 8671430212*x^4 + 4348809776*x^3 - 2064441888*x^2 - sqrt(2)*(473555282*x^7 - 1821195871*x^6 + 3826055542*x^5 - 6128133137*x^4 + 3070797960*x^3 - 1452037320*x^2 - 3352976640*x + 2366869248) - 4733738496*x + 3352976640) + 615345200735*788032707736935368450^(1/4)*sqrt(341)*(50730703*x^7 - 778833417*x^6 + 4116367112*x^5 - 9392273180*x^4 + 12133646496*x^3 - 7660912032*x^2 - sqrt(2)*(35938543*x^7 - 551546778*x^6 + 2913578540*x^5 - 6643469608*x^4 + 8580088800*x^3 - 5403919680*x^2 - 6107913216*x + 4313793024) - 8627586048*x + 6107913216))*sqrt(2*x^2 - x + 3)*sqrt(112285869463*sqrt(2) + 158798761480) + 2444264331446112042193970130340819353377000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(39699690370/160673)*(sqrt(39699690370)*(22*788032707736935368450^(3/4)*sqrt(341)*(104024992*x^7 - 149335248*x^6 + 480784368*x^5 - 188730368*x^4 + 223535232*x^3 + 214417152*x^2 - sqrt(2)*(73906058*x^7 - 106073653*x^6 + 341348823*x^5 - 133050960*x^4 + 156704760*x^3 + 154338048*x^2 - 154338048*x) - 214417152*x) + 615345200735*788032707736935368450^(1/4)*sqrt(341)*(7903323*x^7 - 102233612*x^6 + 394216580*x^5 - 510585408*x^4 + 657060192*x^3 + 391744512*x^2 - 4*sqrt(2)*(1401761*x^7 - 18132196*x^6 + 69912940*x^5 - 90501120*x^4 + 116274240*x^3 + 70118784*x^2 - 70118784*x) - 391744512*x))*sqrt(2*x^2 - x + 3)*sqrt(112285869463*sqrt(2) + 158798761480) + 43175912524323866211143695850*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 1962541478378357555051986175*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(788032707736935368450^(1/4)*sqrt(39699690370)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(12053*x + 5138) - 17191*x - 6915)*sqrt(112285869463*sqrt(2) + 158798761480) - 150182556985858180945*x^2 - 134857806273015509420*sqrt(2)*(2*x^2 - x + 3) + 462807471527848680055*x - 612990028513706861000)/x^2) + 27775731039160364115840569662963856288375*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 14205421276*788032707736935368450^(1/4)*sqrt(39699690370)*sqrt(341)*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(112285869463*sqrt(2) + 158798761480)*arctan(1/861047662213971287591057659551879544939625*(2461380802940*sqrt(39699690370)*(22*788032707736935368450^(3/4)*sqrt(341)*(667937076*x^7 - 2573871186*x^6 + 5404850058*x^5 - 8671430212*x^4 + 4348809776*x^3 - 2064441888*x^2 - sqrt(2)*(473555282*x^7 - 1821195871*x^6 + 3826055542*x^5 - 6128133137*x^4 + 3070797960*x^3 - 1452037320*x^2 - 3352976640*x + 2366869248) - 4733738496*x + 3352976640) + 615345200735*788032707736935368450^(1/4)*sqrt(341)*(50730703*x^7 - 778833417*x^6 + 4116367112*x^5 - 9392273180*x^4 + 12133646496*x^3 - 7660912032*x^2 - sqrt(2)*(35938543*x^7 - 551546778*x^6 + 2913578540*x^5 - 6643469608*x^4 + 8580088800*x^3 - 5403919680*x^2 - 6107913216*x + 4313793024) - 8627586048*x + 6107913216))*sqrt(2*x^2 - x + 3)*sqrt(112285869463*sqrt(2) + 158798761480) - 2444264331446112042193970130340819353377000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(39699690370/160673)*(sqrt(39699690370)*(22*788032707736935368450^(3/4)*sqrt(341)*(104024992*x^7 - 149335248*x^6 + 480784368*x^5 - 188730368*x^4 + 223535232*x^3 + 214417152*x^2 - sqrt(2)*(73906058*x^7 - 106073653*x^6 + 341348823*x^5 - 133050960*x^4 + 156704760*x^3 + 154338048*x^2 - 154338048*x) - 214417152*x) + 615345200735*788032707736935368450^(1/4)*sqrt(341)*(7903323*x^7 - 102233612*x^6 + 394216580*x^5 - 510585408*x^4 + 657060192*x^3 + 391744512*x^2 - 4*sqrt(2)*(1401761*x^7 - 18132196*x^6 + 69912940*x^5 - 90501120*x^4 + 116274240*x^3 + 70118784*x^2 - 70118784*x) - 391744512*x))*sqrt(2*x^2 - x + 3)*sqrt(112285869463*sqrt(2) + 158798761480) - 43175912524323866211143695850*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 1962541478378357555051986175*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((788032707736935368450^(1/4)*sqrt(39699690370)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(12053*x + 5138) - 17191*x - 6915)*sqrt(112285869463*sqrt(2) + 158798761480) + 150182556985858180945*x^2 + 134857806273015509420*sqrt(2)*(2*x^2 - x + 3) - 462807471527848680055*x + 612990028513706861000)/x^2) - 27775731039160364115840569662963856288375*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 788032707736935368450^(1/4)*sqrt(39699690370)*sqrt(341)*sqrt(31)*(3969969037000*x^4 + 4763962844400*x^3 + 4605164082920*x^2 - 112285869463*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) + 1905585137760*x + 635195045920)*sqrt(112285869463*sqrt(2) + 158798761480)*log(635195045920/160673*(788032707736935368450^(1/4)*sqrt(39699690370)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(12053*x + 5138) - 17191*x - 6915)*sqrt(112285869463*sqrt(2) + 158798761480) + 150182556985858180945*x^2 + 134857806273015509420*sqrt(2)*(2*x^2 - x + 3) - 462807471527848680055*x + 612990028513706861000)/x^2) - 788032707736935368450^(1/4)*sqrt(39699690370)*sqrt(341)*sqrt(31)*(3969969037000*x^4 + 4763962844400*x^3 + 4605164082920*x^2 - 112285869463*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) + 1905585137760*x + 635195045920)*sqrt(112285869463*sqrt(2) + 158798761480)*log(-635195045920/160673*(788032707736935368450^(1/4)*sqrt(39699690370)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(12053*x + 5138) - 17191*x - 6915)*sqrt(112285869463*sqrt(2) + 158798761480) - 150182556985858180945*x^2 - 134857806273015509420*sqrt(2)*(2*x^2 - x + 3) + 462807471527848680055*x - 612990028513706861000)/x^2) + 769228926981280465731680*(68325*x^3 + 58315*x^2 + 51362*x + 11020)*sqrt(2*x^2 - x + 3))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
65,1,108,0,0.479057," ","integrate((2*x^2-x+3)^(3/2)*(5*x^2+3*x+2)^4,x, algorithm=""fricas"")","\frac{1}{676457349120} \, {\left(70464307200000 \, x^{11} + 144451829760000 \, x^{10} + 349379651174400 \, x^{9} + 534038708224000 \, x^{8} + 745133229998080 \, x^{7} + 765087080448000 \, x^{6} + 675479464714240 \, x^{5} + 451581382260736 \, x^{4} + 239021184223104 \, x^{3} + 65151998063712 \, x^{2} + 12971175524316 \, x + 74032009514181\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{606427533063}{17179869184} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/676457349120*(70464307200000*x^11 + 144451829760000*x^10 + 349379651174400*x^9 + 534038708224000*x^8 + 745133229998080*x^7 + 765087080448000*x^6 + 675479464714240*x^5 + 451581382260736*x^4 + 239021184223104*x^3 + 65151998063712*x^2 + 12971175524316*x + 74032009514181)*sqrt(2*x^2 - x + 3) + 606427533063/17179869184*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
66,1,98,0,0.460318," ","integrate((2*x^2-x+3)^(3/2)*(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{1}{3523215360} \, {\left(88080384000 \, x^{9} + 124780544000 \, x^{8} + 328328806400 \, x^{7} + 430820229120 \, x^{6} + 571298324480 \, x^{5} + 487891884032 \, x^{4} + 389257196928 \, x^{3} + 199615064544 \, x^{2} + 53985432012 \, x - 72152399943\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{1059790665}{268435456} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/3523215360*(88080384000*x^9 + 124780544000*x^8 + 328328806400*x^7 + 430820229120*x^6 + 571298324480*x^5 + 487891884032*x^4 + 389257196928*x^3 + 199615064544*x^2 + 53985432012*x - 72152399943)*sqrt(2*x^2 - x + 3) + 1059790665/268435456*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
67,1,88,0,0.454796," ","integrate((2*x^2-x+3)^(3/2)*(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{1}{110100480} \, {\left(688128000 \, x^{7} + 525926400 \, x^{6} + 2025840640 \, x^{5} + 2061273088 \, x^{4} + 2728413312 \, x^{3} + 1799647136 \, x^{2} + 1619403428 \, x + 439831323\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{12850997}{8388608} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/110100480*(688128000*x^7 + 525926400*x^6 + 2025840640*x^5 + 2061273088*x^4 + 2728413312*x^3 + 1799647136*x^2 + 1619403428*x + 439831323)*sqrt(2*x^2 - x + 3) + 12850997/8388608*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
68,1,78,0,0.409895," ","integrate((2*x^2-x+3)^(3/2)*(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{1}{122880} \, {\left(204800 \, x^{5} + 14336 \, x^{4} + 561024 \, x^{3} + 319072 \, x^{2} + 565276 \, x + 388341\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{94691}{65536} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/122880*(204800*x^5 + 14336*x^4 + 561024*x^3 + 319072*x^2 + 565276*x + 388341)*sqrt(2*x^2 - x + 3) + 94691/65536*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
69,1,2027,0,0.994488," ","integrate((2*x^2-x+3)^(3/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{11}{77500} \cdot 24200^{\frac{1}{4}} \sqrt{31} \sqrt{10} \sqrt{2} \sqrt{247 \, \sqrt{2} + 1000} \arctan\left(\frac{230 \, \sqrt{10} {\left(2 \cdot 24200^{\frac{3}{4}} \sqrt{31} {\left(20846 \, x^{7} - 109153 \, x^{6} + 215386 \, x^{5} - 427391 \, x^{4} + 234360 \, x^{3} - 156600 \, x^{2} - \sqrt{2} {\left(28854 \, x^{7} - 90639 \, x^{6} + 200187 \, x^{5} - 262838 \, x^{4} + 117544 \, x^{3} - 23472 \, x^{2} - 186624 \, x + 86400\right)} - 172800 \, x + 186624\right)} + 5 \cdot 24200^{\frac{1}{4}} \sqrt{31} {\left(112238 \, x^{7} - 1817988 \, x^{6} + 10351960 \, x^{5} - 25791248 \, x^{4} + 34522560 \, x^{3} - 28368000 \, x^{2} - \sqrt{2} {\left(125839 \, x^{7} - 1864281 \, x^{6} + 9323336 \, x^{5} - 19725020 \, x^{4} + 24624288 \, x^{3} - 10862496 \, x^{2} - 19989504 \, x + 10533888\right)} - 21067776 \, x + 19989504\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{247 \, \sqrt{2} + 1000} + 30107000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{5}{119}} {\left(\sqrt{10} {\left(2 \cdot 24200^{\frac{3}{4}} \sqrt{31} {\left(46522 \, x^{7} - 71117 \, x^{6} + 257247 \, x^{5} - 273360 \, x^{4} + 484920 \, x^{3} - 269568 \, x^{2} - 16 \, \sqrt{2} {\left(7714 \, x^{7} - 10881 \, x^{6} + 33771 \, x^{5} - 5576 \, x^{4} - 576 \, x^{3} + 32184 \, x^{2} - 32184 \, x\right)} + 269568 \, x\right)} + 5 \cdot 24200^{\frac{1}{4}} \sqrt{31} {\left(309512 \, x^{7} - 4017952 \, x^{6} + 15741280 \, x^{5} - 22625280 \, x^{4} + 37693440 \, x^{3} - 13519872 \, x^{2} - \sqrt{2} {\left(516957 \, x^{7} - 6676948 \, x^{6} + 25569820 \, x^{5} - 31522752 \, x^{4} + 34450848 \, x^{3} + 46199808 \, x^{2} - 46199808 \, x\right)} + 13519872 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{247 \, \sqrt{2} + 1000} + 130900 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 5950 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{24200^{\frac{1}{4}} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(x - 75\right)} + 74 \, x - 76\right)} \sqrt{247 \, \sqrt{2} + 1000} + 58310 \, x^{2} + 52360 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 179690 \, x + 238000}{x^{2}}} + 342125 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{10605875 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + \frac{11}{77500} \cdot 24200^{\frac{1}{4}} \sqrt{31} \sqrt{10} \sqrt{2} \sqrt{247 \, \sqrt{2} + 1000} \arctan\left(\frac{230 \, \sqrt{10} {\left(2 \cdot 24200^{\frac{3}{4}} \sqrt{31} {\left(20846 \, x^{7} - 109153 \, x^{6} + 215386 \, x^{5} - 427391 \, x^{4} + 234360 \, x^{3} - 156600 \, x^{2} - \sqrt{2} {\left(28854 \, x^{7} - 90639 \, x^{6} + 200187 \, x^{5} - 262838 \, x^{4} + 117544 \, x^{3} - 23472 \, x^{2} - 186624 \, x + 86400\right)} - 172800 \, x + 186624\right)} + 5 \cdot 24200^{\frac{1}{4}} \sqrt{31} {\left(112238 \, x^{7} - 1817988 \, x^{6} + 10351960 \, x^{5} - 25791248 \, x^{4} + 34522560 \, x^{3} - 28368000 \, x^{2} - \sqrt{2} {\left(125839 \, x^{7} - 1864281 \, x^{6} + 9323336 \, x^{5} - 19725020 \, x^{4} + 24624288 \, x^{3} - 10862496 \, x^{2} - 19989504 \, x + 10533888\right)} - 21067776 \, x + 19989504\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{247 \, \sqrt{2} + 1000} - 30107000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{5}{119}} {\left(\sqrt{10} {\left(2 \cdot 24200^{\frac{3}{4}} \sqrt{31} {\left(46522 \, x^{7} - 71117 \, x^{6} + 257247 \, x^{5} - 273360 \, x^{4} + 484920 \, x^{3} - 269568 \, x^{2} - 16 \, \sqrt{2} {\left(7714 \, x^{7} - 10881 \, x^{6} + 33771 \, x^{5} - 5576 \, x^{4} - 576 \, x^{3} + 32184 \, x^{2} - 32184 \, x\right)} + 269568 \, x\right)} + 5 \cdot 24200^{\frac{1}{4}} \sqrt{31} {\left(309512 \, x^{7} - 4017952 \, x^{6} + 15741280 \, x^{5} - 22625280 \, x^{4} + 37693440 \, x^{3} - 13519872 \, x^{2} - \sqrt{2} {\left(516957 \, x^{7} - 6676948 \, x^{6} + 25569820 \, x^{5} - 31522752 \, x^{4} + 34450848 \, x^{3} + 46199808 \, x^{2} - 46199808 \, x\right)} + 13519872 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{247 \, \sqrt{2} + 1000} - 130900 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 5950 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{24200^{\frac{1}{4}} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(x - 75\right)} + 74 \, x - 76\right)} \sqrt{247 \, \sqrt{2} + 1000} - 58310 \, x^{2} - 52360 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 179690 \, x - 238000}{x^{2}}} - 342125 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{10605875 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + \frac{11}{36890000} \cdot 24200^{\frac{1}{4}} \sqrt{10} \sqrt{247 \, \sqrt{2} + 1000} {\left(247 \, \sqrt{2} - 1000\right)} \log\left(\frac{1512500 \, {\left(24200^{\frac{1}{4}} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(x - 75\right)} + 74 \, x - 76\right)} \sqrt{247 \, \sqrt{2} + 1000} + 58310 \, x^{2} + 52360 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 179690 \, x + 238000\right)}}{119 \, x^{2}}\right) - \frac{11}{36890000} \cdot 24200^{\frac{1}{4}} \sqrt{10} \sqrt{247 \, \sqrt{2} + 1000} {\left(247 \, \sqrt{2} - 1000\right)} \log\left(-\frac{1512500 \, {\left(24200^{\frac{1}{4}} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(x - 75\right)} + 74 \, x - 76\right)} \sqrt{247 \, \sqrt{2} + 1000} - 58310 \, x^{2} - 52360 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 179690 \, x - 238000\right)}}{119 \, x^{2}}\right) + \frac{1}{100} \, \sqrt{2 \, x^{2} - x + 3} {\left(20 \, x - 49\right)} + \frac{2203}{4000} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"11/77500*24200^(1/4)*sqrt(31)*sqrt(10)*sqrt(2)*sqrt(247*sqrt(2) + 1000)*arctan(1/10605875*(230*sqrt(10)*(2*24200^(3/4)*sqrt(31)*(20846*x^7 - 109153*x^6 + 215386*x^5 - 427391*x^4 + 234360*x^3 - 156600*x^2 - sqrt(2)*(28854*x^7 - 90639*x^6 + 200187*x^5 - 262838*x^4 + 117544*x^3 - 23472*x^2 - 186624*x + 86400) - 172800*x + 186624) + 5*24200^(1/4)*sqrt(31)*(112238*x^7 - 1817988*x^6 + 10351960*x^5 - 25791248*x^4 + 34522560*x^3 - 28368000*x^2 - sqrt(2)*(125839*x^7 - 1864281*x^6 + 9323336*x^5 - 19725020*x^4 + 24624288*x^3 - 10862496*x^2 - 19989504*x + 10533888) - 21067776*x + 19989504))*sqrt(2*x^2 - x + 3)*sqrt(247*sqrt(2) + 1000) + 30107000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(5/119)*(sqrt(10)*(2*24200^(3/4)*sqrt(31)*(46522*x^7 - 71117*x^6 + 257247*x^5 - 273360*x^4 + 484920*x^3 - 269568*x^2 - 16*sqrt(2)*(7714*x^7 - 10881*x^6 + 33771*x^5 - 5576*x^4 - 576*x^3 + 32184*x^2 - 32184*x) + 269568*x) + 5*24200^(1/4)*sqrt(31)*(309512*x^7 - 4017952*x^6 + 15741280*x^5 - 22625280*x^4 + 37693440*x^3 - 13519872*x^2 - sqrt(2)*(516957*x^7 - 6676948*x^6 + 25569820*x^5 - 31522752*x^4 + 34450848*x^3 + 46199808*x^2 - 46199808*x) + 13519872*x))*sqrt(2*x^2 - x + 3)*sqrt(247*sqrt(2) + 1000) + 130900*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 5950*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((24200^(1/4)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(x - 75) + 74*x - 76)*sqrt(247*sqrt(2) + 1000) + 58310*x^2 + 52360*sqrt(2)*(2*x^2 - x + 3) - 179690*x + 238000)/x^2) + 342125*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 11/77500*24200^(1/4)*sqrt(31)*sqrt(10)*sqrt(2)*sqrt(247*sqrt(2) + 1000)*arctan(1/10605875*(230*sqrt(10)*(2*24200^(3/4)*sqrt(31)*(20846*x^7 - 109153*x^6 + 215386*x^5 - 427391*x^4 + 234360*x^3 - 156600*x^2 - sqrt(2)*(28854*x^7 - 90639*x^6 + 200187*x^5 - 262838*x^4 + 117544*x^3 - 23472*x^2 - 186624*x + 86400) - 172800*x + 186624) + 5*24200^(1/4)*sqrt(31)*(112238*x^7 - 1817988*x^6 + 10351960*x^5 - 25791248*x^4 + 34522560*x^3 - 28368000*x^2 - sqrt(2)*(125839*x^7 - 1864281*x^6 + 9323336*x^5 - 19725020*x^4 + 24624288*x^3 - 10862496*x^2 - 19989504*x + 10533888) - 21067776*x + 19989504))*sqrt(2*x^2 - x + 3)*sqrt(247*sqrt(2) + 1000) - 30107000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(5/119)*(sqrt(10)*(2*24200^(3/4)*sqrt(31)*(46522*x^7 - 71117*x^6 + 257247*x^5 - 273360*x^4 + 484920*x^3 - 269568*x^2 - 16*sqrt(2)*(7714*x^7 - 10881*x^6 + 33771*x^5 - 5576*x^4 - 576*x^3 + 32184*x^2 - 32184*x) + 269568*x) + 5*24200^(1/4)*sqrt(31)*(309512*x^7 - 4017952*x^6 + 15741280*x^5 - 22625280*x^4 + 37693440*x^3 - 13519872*x^2 - sqrt(2)*(516957*x^7 - 6676948*x^6 + 25569820*x^5 - 31522752*x^4 + 34450848*x^3 + 46199808*x^2 - 46199808*x) + 13519872*x))*sqrt(2*x^2 - x + 3)*sqrt(247*sqrt(2) + 1000) - 130900*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 5950*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(24200^(1/4)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(x - 75) + 74*x - 76)*sqrt(247*sqrt(2) + 1000) - 58310*x^2 - 52360*sqrt(2)*(2*x^2 - x + 3) + 179690*x - 238000)/x^2) - 342125*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 11/36890000*24200^(1/4)*sqrt(10)*sqrt(247*sqrt(2) + 1000)*(247*sqrt(2) - 1000)*log(1512500/119*(24200^(1/4)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(x - 75) + 74*x - 76)*sqrt(247*sqrt(2) + 1000) + 58310*x^2 + 52360*sqrt(2)*(2*x^2 - x + 3) - 179690*x + 238000)/x^2) - 11/36890000*24200^(1/4)*sqrt(10)*sqrt(247*sqrt(2) + 1000)*(247*sqrt(2) - 1000)*log(-1512500/119*(24200^(1/4)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(x - 75) + 74*x - 76)*sqrt(247*sqrt(2) + 1000) - 58310*x^2 - 52360*sqrt(2)*(2*x^2 - x + 3) + 179690*x - 238000)/x^2) + 1/100*sqrt(2*x^2 - x + 3)*(20*x - 49) + 2203/4000*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","B",0
70,1,2150,0,1.290855," ","integrate((2*x^2-x+3)^(3/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{10421084 \cdot 1987037073032^{\frac{1}{4}} \sqrt{45307} \sqrt{62} \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{3169333 \, \sqrt{2} + 4530700} \arctan\left(\frac{64607782 \, \sqrt{45307} {\left(2 \cdot 1987037073032^{\frac{3}{4}} \sqrt{62} {\left(2433118 \, x^{7} - 9616349 \, x^{6} + 20077988 \, x^{5} - 32895253 \, x^{4} + 16664280 \, x^{3} - 8289000 \, x^{2} - \sqrt{2} {\left(1842432 \, x^{7} - 6916062 \, x^{6} + 14611071 \, x^{5} - 22920229 \, x^{4} + 11367152 \, x^{3} - 5107176 \, x^{2} - 12897792 \, x + 8726400\right)} - 17452800 \, x + 12897792\right)} + 1404517 \cdot 1987037073032^{\frac{1}{4}} \sqrt{62} {\left(373384 \, x^{7} - 5757834 \, x^{6} + 30631880 \, x^{5} - 70476664 \, x^{4} + 91370880 \, x^{3} - 59457600 \, x^{2} - \sqrt{2} {\left(276977 \, x^{7} - 4232733 \, x^{6} + 22218448 \, x^{5} - 50249260 \, x^{4} + 64668384 \, x^{3} - 39479328 \, x^{2} - 46697472 \, x + 32016384\right)} - 64032768 \, x + 46697472\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{3169333 \, \sqrt{2} + 4530700} + 490410017080486186043272 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{45307}{2711}} {\left(\sqrt{45307} {\left(2 \cdot 1987037073032^{\frac{3}{4}} \sqrt{62} {\left(8480726 \, x^{7} - 12210811 \, x^{6} + 39548601 \, x^{5} - 16962480 \, x^{4} + 21434760 \, x^{3} + 14432256 \, x^{2} - \sqrt{2} {\left(6779042 \, x^{7} - 9704193 \, x^{6} + 31062363 \, x^{5} - 11094928 \, x^{4} + 12114072 \, x^{3} + 16301952 \, x^{2} - 16301952 \, x\right)} - 14432256 \, x\right)} + 1404517 \cdot 1987037073032^{\frac{1}{4}} \sqrt{62} {\left(1312966 \, x^{7} - 16987736 \, x^{6} + 65572040 \, x^{5} - 85530240 \, x^{4} + 112374720 \, x^{3} + 57314304 \, x^{2} - \sqrt{2} {\left(1011501 \, x^{7} - 13081364 \, x^{6} + 50391260 \, x^{5} - 64806336 \, x^{4} + 81634464 \, x^{3} + 56070144 \, x^{2} - 56070144 \, x\right)} - 57314304 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{3169333 \, \sqrt{2} + 4530700} + 7590571938849196 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 345025997220418 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{1987037073032^{\frac{1}{4}} \sqrt{45307} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(1867 \, x + 1425\right)} - 3292 \, x - 442\right)} \sqrt{3169333 \, \sqrt{2} + 4530700} - 11567627293306 \, x^{2} - 10387257161336 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 35647177985494 \, x - 47214805278800}{x^{2}}} + 5572841103187343023219 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{172758074198807633719789 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 10421084 \cdot 1987037073032^{\frac{1}{4}} \sqrt{45307} \sqrt{62} \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{3169333 \, \sqrt{2} + 4530700} \arctan\left(\frac{64607782 \, \sqrt{45307} {\left(2 \cdot 1987037073032^{\frac{3}{4}} \sqrt{62} {\left(2433118 \, x^{7} - 9616349 \, x^{6} + 20077988 \, x^{5} - 32895253 \, x^{4} + 16664280 \, x^{3} - 8289000 \, x^{2} - \sqrt{2} {\left(1842432 \, x^{7} - 6916062 \, x^{6} + 14611071 \, x^{5} - 22920229 \, x^{4} + 11367152 \, x^{3} - 5107176 \, x^{2} - 12897792 \, x + 8726400\right)} - 17452800 \, x + 12897792\right)} + 1404517 \cdot 1987037073032^{\frac{1}{4}} \sqrt{62} {\left(373384 \, x^{7} - 5757834 \, x^{6} + 30631880 \, x^{5} - 70476664 \, x^{4} + 91370880 \, x^{3} - 59457600 \, x^{2} - \sqrt{2} {\left(276977 \, x^{7} - 4232733 \, x^{6} + 22218448 \, x^{5} - 50249260 \, x^{4} + 64668384 \, x^{3} - 39479328 \, x^{2} - 46697472 \, x + 32016384\right)} - 64032768 \, x + 46697472\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{3169333 \, \sqrt{2} + 4530700} - 490410017080486186043272 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{45307}{2711}} {\left(\sqrt{45307} {\left(2 \cdot 1987037073032^{\frac{3}{4}} \sqrt{62} {\left(8480726 \, x^{7} - 12210811 \, x^{6} + 39548601 \, x^{5} - 16962480 \, x^{4} + 21434760 \, x^{3} + 14432256 \, x^{2} - \sqrt{2} {\left(6779042 \, x^{7} - 9704193 \, x^{6} + 31062363 \, x^{5} - 11094928 \, x^{4} + 12114072 \, x^{3} + 16301952 \, x^{2} - 16301952 \, x\right)} - 14432256 \, x\right)} + 1404517 \cdot 1987037073032^{\frac{1}{4}} \sqrt{62} {\left(1312966 \, x^{7} - 16987736 \, x^{6} + 65572040 \, x^{5} - 85530240 \, x^{4} + 112374720 \, x^{3} + 57314304 \, x^{2} - \sqrt{2} {\left(1011501 \, x^{7} - 13081364 \, x^{6} + 50391260 \, x^{5} - 64806336 \, x^{4} + 81634464 \, x^{3} + 56070144 \, x^{2} - 56070144 \, x\right)} - 57314304 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{3169333 \, \sqrt{2} + 4530700} - 7590571938849196 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 345025997220418 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{1987037073032^{\frac{1}{4}} \sqrt{45307} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(1867 \, x + 1425\right)} - 3292 \, x - 442\right)} \sqrt{3169333 \, \sqrt{2} + 4530700} + 11567627293306 \, x^{2} + 10387257161336 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 35647177985494 \, x + 47214805278800}{x^{2}}} - 5572841103187343023219 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{172758074198807633719789 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 1987037073032^{\frac{1}{4}} \sqrt{45307} \sqrt{62} \sqrt{31} {\left(22653500 \, x^{2} - 3169333 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 13592100 \, x + 9061400\right)} \sqrt{3169333 \, \sqrt{2} + 4530700} \log\left(\frac{113267500 \, {\left(1987037073032^{\frac{1}{4}} \sqrt{45307} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(1867 \, x + 1425\right)} - 3292 \, x - 442\right)} \sqrt{3169333 \, \sqrt{2} + 4530700} + 11567627293306 \, x^{2} + 10387257161336 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 35647177985494 \, x + 47214805278800\right)}}{2711 \, x^{2}}\right) - 1987037073032^{\frac{1}{4}} \sqrt{45307} \sqrt{62} \sqrt{31} {\left(22653500 \, x^{2} - 3169333 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 13592100 \, x + 9061400\right)} \sqrt{3169333 \, \sqrt{2} + 4530700} \log\left(-\frac{113267500 \, {\left(1987037073032^{\frac{1}{4}} \sqrt{45307} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(1867 \, x + 1425\right)} - 3292 \, x - 442\right)} \sqrt{3169333 \, \sqrt{2} + 4530700} - 11567627293306 \, x^{2} - 10387257161336 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 35647177985494 \, x - 47214805278800\right)}}{2711 \, x^{2}}\right) + 3629874229834144 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 6440099440028320 \, \sqrt{2 \, x^{2} - x + 3} {\left(13 \, x + 7\right)}}{90746855745853600 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/90746855745853600*(10421084*1987037073032^(1/4)*sqrt(45307)*sqrt(62)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(3169333*sqrt(2) + 4530700)*arctan(1/172758074198807633719789*(64607782*sqrt(45307)*(2*1987037073032^(3/4)*sqrt(62)*(2433118*x^7 - 9616349*x^6 + 20077988*x^5 - 32895253*x^4 + 16664280*x^3 - 8289000*x^2 - sqrt(2)*(1842432*x^7 - 6916062*x^6 + 14611071*x^5 - 22920229*x^4 + 11367152*x^3 - 5107176*x^2 - 12897792*x + 8726400) - 17452800*x + 12897792) + 1404517*1987037073032^(1/4)*sqrt(62)*(373384*x^7 - 5757834*x^6 + 30631880*x^5 - 70476664*x^4 + 91370880*x^3 - 59457600*x^2 - sqrt(2)*(276977*x^7 - 4232733*x^6 + 22218448*x^5 - 50249260*x^4 + 64668384*x^3 - 39479328*x^2 - 46697472*x + 32016384) - 64032768*x + 46697472))*sqrt(2*x^2 - x + 3)*sqrt(3169333*sqrt(2) + 4530700) + 490410017080486186043272*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(45307/2711)*(sqrt(45307)*(2*1987037073032^(3/4)*sqrt(62)*(8480726*x^7 - 12210811*x^6 + 39548601*x^5 - 16962480*x^4 + 21434760*x^3 + 14432256*x^2 - sqrt(2)*(6779042*x^7 - 9704193*x^6 + 31062363*x^5 - 11094928*x^4 + 12114072*x^3 + 16301952*x^2 - 16301952*x) - 14432256*x) + 1404517*1987037073032^(1/4)*sqrt(62)*(1312966*x^7 - 16987736*x^6 + 65572040*x^5 - 85530240*x^4 + 112374720*x^3 + 57314304*x^2 - sqrt(2)*(1011501*x^7 - 13081364*x^6 + 50391260*x^5 - 64806336*x^4 + 81634464*x^3 + 56070144*x^2 - 56070144*x) - 57314304*x))*sqrt(2*x^2 - x + 3)*sqrt(3169333*sqrt(2) + 4530700) + 7590571938849196*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 345025997220418*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(1987037073032^(1/4)*sqrt(45307)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(1867*x + 1425) - 3292*x - 442)*sqrt(3169333*sqrt(2) + 4530700) - 11567627293306*x^2 - 10387257161336*sqrt(2)*(2*x^2 - x + 3) + 35647177985494*x - 47214805278800)/x^2) + 5572841103187343023219*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 10421084*1987037073032^(1/4)*sqrt(45307)*sqrt(62)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(3169333*sqrt(2) + 4530700)*arctan(1/172758074198807633719789*(64607782*sqrt(45307)*(2*1987037073032^(3/4)*sqrt(62)*(2433118*x^7 - 9616349*x^6 + 20077988*x^5 - 32895253*x^4 + 16664280*x^3 - 8289000*x^2 - sqrt(2)*(1842432*x^7 - 6916062*x^6 + 14611071*x^5 - 22920229*x^4 + 11367152*x^3 - 5107176*x^2 - 12897792*x + 8726400) - 17452800*x + 12897792) + 1404517*1987037073032^(1/4)*sqrt(62)*(373384*x^7 - 5757834*x^6 + 30631880*x^5 - 70476664*x^4 + 91370880*x^3 - 59457600*x^2 - sqrt(2)*(276977*x^7 - 4232733*x^6 + 22218448*x^5 - 50249260*x^4 + 64668384*x^3 - 39479328*x^2 - 46697472*x + 32016384) - 64032768*x + 46697472))*sqrt(2*x^2 - x + 3)*sqrt(3169333*sqrt(2) + 4530700) - 490410017080486186043272*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(45307/2711)*(sqrt(45307)*(2*1987037073032^(3/4)*sqrt(62)*(8480726*x^7 - 12210811*x^6 + 39548601*x^5 - 16962480*x^4 + 21434760*x^3 + 14432256*x^2 - sqrt(2)*(6779042*x^7 - 9704193*x^6 + 31062363*x^5 - 11094928*x^4 + 12114072*x^3 + 16301952*x^2 - 16301952*x) - 14432256*x) + 1404517*1987037073032^(1/4)*sqrt(62)*(1312966*x^7 - 16987736*x^6 + 65572040*x^5 - 85530240*x^4 + 112374720*x^3 + 57314304*x^2 - sqrt(2)*(1011501*x^7 - 13081364*x^6 + 50391260*x^5 - 64806336*x^4 + 81634464*x^3 + 56070144*x^2 - 56070144*x) - 57314304*x))*sqrt(2*x^2 - x + 3)*sqrt(3169333*sqrt(2) + 4530700) - 7590571938849196*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 345025997220418*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((1987037073032^(1/4)*sqrt(45307)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(1867*x + 1425) - 3292*x - 442)*sqrt(3169333*sqrt(2) + 4530700) + 11567627293306*x^2 + 10387257161336*sqrt(2)*(2*x^2 - x + 3) - 35647177985494*x + 47214805278800)/x^2) - 5572841103187343023219*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 1987037073032^(1/4)*sqrt(45307)*sqrt(62)*sqrt(31)*(22653500*x^2 - 3169333*sqrt(2)*(5*x^2 + 3*x + 2) + 13592100*x + 9061400)*sqrt(3169333*sqrt(2) + 4530700)*log(113267500/2711*(1987037073032^(1/4)*sqrt(45307)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(1867*x + 1425) - 3292*x - 442)*sqrt(3169333*sqrt(2) + 4530700) + 11567627293306*x^2 + 10387257161336*sqrt(2)*(2*x^2 - x + 3) - 35647177985494*x + 47214805278800)/x^2) - 1987037073032^(1/4)*sqrt(45307)*sqrt(62)*sqrt(31)*(22653500*x^2 - 3169333*sqrt(2)*(5*x^2 + 3*x + 2) + 13592100*x + 9061400)*sqrt(3169333*sqrt(2) + 4530700)*log(-113267500/2711*(1987037073032^(1/4)*sqrt(45307)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(1867*x + 1425) - 3292*x - 442)*sqrt(3169333*sqrt(2) + 4530700) - 11567627293306*x^2 - 10387257161336*sqrt(2)*(2*x^2 - x + 3) + 35647177985494*x - 47214805278800)/x^2) + 3629874229834144*sqrt(2)*(5*x^2 + 3*x + 2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 6440099440028320*sqrt(2*x^2 - x + 3)*(13*x + 7))/(5*x^2 + 3*x + 2)","B",0
71,1,2183,0,1.270287," ","integrate((2*x^2-x+3)^(3/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","-\frac{189113268 \cdot 134689869150937352^{\frac{1}{4}} \sqrt{129754513} \sqrt{341} \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{366990269 \, \sqrt{2} + 519018052} \arctan\left(\frac{16089559612 \, \sqrt{129754513} {\left(11 \cdot 134689869150937352^{\frac{3}{4}} \sqrt{341} {\left(38305160 \, x^{7} - 147261352 \, x^{6} + 309398878 \, x^{5} - 495410374 \, x^{4} + 248212864 \, x^{3} - 117285552 \, x^{2} - \sqrt{2} {\left(26988622 \, x^{7} - 104036813 \, x^{6} + 218448200 \, x^{5} - 350579241 \, x^{4} + 175844824 \, x^{3} - 83534472 \, x^{2} - 191303424 \, x + 135585792\right)} - 271171584 \, x + 191303424\right)} + 4022389903 \cdot 134689869150937352^{\frac{1}{4}} \sqrt{341} {\left(2906601 \, x^{7} - 44604657 \, x^{6} + 235604928 \, x^{5} - 537156764 \, x^{4} + 693706464 \, x^{3} - 436717728 \, x^{2} - \sqrt{2} {\left(2050114 \, x^{7} - 31475955 \, x^{6} + 166375268 \, x^{5} - 379661892 \, x^{4} + 490500864 \, x^{3} - 309827808 \, x^{2} - 348696576 \, x + 246965760\right)} - 493931520 \, x + 348696576\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{366990269 \, \sqrt{2} + 519018052} + 3029638713748420756426308089806504 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{259509026}{713}} {\left(\sqrt{129754513} {\left(11 \cdot 134689869150937352^{\frac{3}{4}} \sqrt{341} {\left(5980372 \, x^{7} - 8582986 \, x^{6} + 27618126 \, x^{5} - 10751392 \, x^{4} + 12649968 \, x^{3} + 12517632 \, x^{2} - \sqrt{2} {\left(4201650 \, x^{7} - 6032009 \, x^{6} + 19421619 \, x^{5} - 7633552 \, x^{4} + 9050328 \, x^{3} + 8640000 \, x^{2} - 8640000 \, x\right)} - 12517632 \, x\right)} + 4022389903 \cdot 134689869150937352^{\frac{1}{4}} \sqrt{341} {\left(453599 \, x^{7} - 5867420 \, x^{6} + 22622900 \, x^{5} - 29282112 \, x^{4} + 37610208 \, x^{3} + 22726656 \, x^{2} - \sqrt{2} {\left(319303 \, x^{7} - 4130364 \, x^{6} + 15927060 \, x^{5} - 20630592 \, x^{4} + 26556768 \, x^{3} + 15800832 \, x^{2} - 15800832 \, x\right)} - 22726656 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{366990269 \, \sqrt{2} + 519018052} + 8186887989068712800954 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 372131272230396036407 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{134689869150937352^{\frac{1}{4}} \sqrt{129754513} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(696 \, x + 277\right)} - 973 \, x - 419\right)} \sqrt{366990269 \, \sqrt{2} + 519018052} - 4356437317274441 \, x^{2} - 3911902897144396 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 13424939487927359 \, x - 17781376805201800}{x^{2}}} + 34427712656232054050298955565983 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{1067259092343193675559267622545473 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 189113268 \cdot 134689869150937352^{\frac{1}{4}} \sqrt{129754513} \sqrt{341} \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{366990269 \, \sqrt{2} + 519018052} \arctan\left(\frac{16089559612 \, \sqrt{129754513} {\left(11 \cdot 134689869150937352^{\frac{3}{4}} \sqrt{341} {\left(38305160 \, x^{7} - 147261352 \, x^{6} + 309398878 \, x^{5} - 495410374 \, x^{4} + 248212864 \, x^{3} - 117285552 \, x^{2} - \sqrt{2} {\left(26988622 \, x^{7} - 104036813 \, x^{6} + 218448200 \, x^{5} - 350579241 \, x^{4} + 175844824 \, x^{3} - 83534472 \, x^{2} - 191303424 \, x + 135585792\right)} - 271171584 \, x + 191303424\right)} + 4022389903 \cdot 134689869150937352^{\frac{1}{4}} \sqrt{341} {\left(2906601 \, x^{7} - 44604657 \, x^{6} + 235604928 \, x^{5} - 537156764 \, x^{4} + 693706464 \, x^{3} - 436717728 \, x^{2} - \sqrt{2} {\left(2050114 \, x^{7} - 31475955 \, x^{6} + 166375268 \, x^{5} - 379661892 \, x^{4} + 490500864 \, x^{3} - 309827808 \, x^{2} - 348696576 \, x + 246965760\right)} - 493931520 \, x + 348696576\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{366990269 \, \sqrt{2} + 519018052} - 3029638713748420756426308089806504 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{259509026}{713}} {\left(\sqrt{129754513} {\left(11 \cdot 134689869150937352^{\frac{3}{4}} \sqrt{341} {\left(5980372 \, x^{7} - 8582986 \, x^{6} + 27618126 \, x^{5} - 10751392 \, x^{4} + 12649968 \, x^{3} + 12517632 \, x^{2} - \sqrt{2} {\left(4201650 \, x^{7} - 6032009 \, x^{6} + 19421619 \, x^{5} - 7633552 \, x^{4} + 9050328 \, x^{3} + 8640000 \, x^{2} - 8640000 \, x\right)} - 12517632 \, x\right)} + 4022389903 \cdot 134689869150937352^{\frac{1}{4}} \sqrt{341} {\left(453599 \, x^{7} - 5867420 \, x^{6} + 22622900 \, x^{5} - 29282112 \, x^{4} + 37610208 \, x^{3} + 22726656 \, x^{2} - \sqrt{2} {\left(319303 \, x^{7} - 4130364 \, x^{6} + 15927060 \, x^{5} - 20630592 \, x^{4} + 26556768 \, x^{3} + 15800832 \, x^{2} - 15800832 \, x\right)} - 22726656 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{366990269 \, \sqrt{2} + 519018052} - 8186887989068712800954 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 372131272230396036407 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{134689869150937352^{\frac{1}{4}} \sqrt{129754513} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(696 \, x + 277\right)} - 973 \, x - 419\right)} \sqrt{366990269 \, \sqrt{2} + 519018052} + 4356437317274441 \, x^{2} + 3911902897144396 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 13424939487927359 \, x + 17781376805201800}{x^{2}}} - 34427712656232054050298955565983 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{1067259092343193675559267622545473 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) - 3 \cdot 134689869150937352^{\frac{1}{4}} \sqrt{129754513} \sqrt{341} \sqrt{31} {\left(12975451300 \, x^{4} + 15570541560 \, x^{3} + 15051523508 \, x^{2} - 366990269 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} + 6228216624 \, x + 2076072208\right)} \sqrt{366990269 \, \sqrt{2} + 519018052} \log\left(\frac{9342324936 \, {\left(134689869150937352^{\frac{1}{4}} \sqrt{129754513} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(696 \, x + 277\right)} - 973 \, x - 419\right)} \sqrt{366990269 \, \sqrt{2} + 519018052} + 4356437317274441 \, x^{2} + 3911902897144396 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 13424939487927359 \, x + 17781376805201800\right)}}{713 \, x^{2}}\right) + 3 \cdot 134689869150937352^{\frac{1}{4}} \sqrt{129754513} \sqrt{341} \sqrt{31} {\left(12975451300 \, x^{4} + 15570541560 \, x^{3} + 15051523508 \, x^{2} - 366990269 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} + 6228216624 \, x + 2076072208\right)} \sqrt{366990269 \, \sqrt{2} + 519018052} \log\left(-\frac{9342324936 \, {\left(134689869150937352^{\frac{1}{4}} \sqrt{129754513} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(696 \, x + 277\right)} - 973 \, x - 419\right)} \sqrt{366990269 \, \sqrt{2} + 519018052} - 4356437317274441 \, x^{2} - 3911902897144396 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 13424939487927359 \, x - 17781376805201800\right)}}{713 \, x^{2}}\right) - 22313494125311634784 \, {\left(11680 \, x^{3} + 10171 \, x^{2} + 8343 \, x + 2220\right)} \sqrt{2 \, x^{2} - x + 3}}{85773071417697924109696 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/85773071417697924109696*(189113268*134689869150937352^(1/4)*sqrt(129754513)*sqrt(341)*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(366990269*sqrt(2) + 519018052)*arctan(1/1067259092343193675559267622545473*(16089559612*sqrt(129754513)*(11*134689869150937352^(3/4)*sqrt(341)*(38305160*x^7 - 147261352*x^6 + 309398878*x^5 - 495410374*x^4 + 248212864*x^3 - 117285552*x^2 - sqrt(2)*(26988622*x^7 - 104036813*x^6 + 218448200*x^5 - 350579241*x^4 + 175844824*x^3 - 83534472*x^2 - 191303424*x + 135585792) - 271171584*x + 191303424) + 4022389903*134689869150937352^(1/4)*sqrt(341)*(2906601*x^7 - 44604657*x^6 + 235604928*x^5 - 537156764*x^4 + 693706464*x^3 - 436717728*x^2 - sqrt(2)*(2050114*x^7 - 31475955*x^6 + 166375268*x^5 - 379661892*x^4 + 490500864*x^3 - 309827808*x^2 - 348696576*x + 246965760) - 493931520*x + 348696576))*sqrt(2*x^2 - x + 3)*sqrt(366990269*sqrt(2) + 519018052) + 3029638713748420756426308089806504*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(259509026/713)*(sqrt(129754513)*(11*134689869150937352^(3/4)*sqrt(341)*(5980372*x^7 - 8582986*x^6 + 27618126*x^5 - 10751392*x^4 + 12649968*x^3 + 12517632*x^2 - sqrt(2)*(4201650*x^7 - 6032009*x^6 + 19421619*x^5 - 7633552*x^4 + 9050328*x^3 + 8640000*x^2 - 8640000*x) - 12517632*x) + 4022389903*134689869150937352^(1/4)*sqrt(341)*(453599*x^7 - 5867420*x^6 + 22622900*x^5 - 29282112*x^4 + 37610208*x^3 + 22726656*x^2 - sqrt(2)*(319303*x^7 - 4130364*x^6 + 15927060*x^5 - 20630592*x^4 + 26556768*x^3 + 15800832*x^2 - 15800832*x) - 22726656*x))*sqrt(2*x^2 - x + 3)*sqrt(366990269*sqrt(2) + 519018052) + 8186887989068712800954*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 372131272230396036407*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(134689869150937352^(1/4)*sqrt(129754513)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(696*x + 277) - 973*x - 419)*sqrt(366990269*sqrt(2) + 519018052) - 4356437317274441*x^2 - 3911902897144396*sqrt(2)*(2*x^2 - x + 3) + 13424939487927359*x - 17781376805201800)/x^2) + 34427712656232054050298955565983*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 189113268*134689869150937352^(1/4)*sqrt(129754513)*sqrt(341)*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(366990269*sqrt(2) + 519018052)*arctan(1/1067259092343193675559267622545473*(16089559612*sqrt(129754513)*(11*134689869150937352^(3/4)*sqrt(341)*(38305160*x^7 - 147261352*x^6 + 309398878*x^5 - 495410374*x^4 + 248212864*x^3 - 117285552*x^2 - sqrt(2)*(26988622*x^7 - 104036813*x^6 + 218448200*x^5 - 350579241*x^4 + 175844824*x^3 - 83534472*x^2 - 191303424*x + 135585792) - 271171584*x + 191303424) + 4022389903*134689869150937352^(1/4)*sqrt(341)*(2906601*x^7 - 44604657*x^6 + 235604928*x^5 - 537156764*x^4 + 693706464*x^3 - 436717728*x^2 - sqrt(2)*(2050114*x^7 - 31475955*x^6 + 166375268*x^5 - 379661892*x^4 + 490500864*x^3 - 309827808*x^2 - 348696576*x + 246965760) - 493931520*x + 348696576))*sqrt(2*x^2 - x + 3)*sqrt(366990269*sqrt(2) + 519018052) - 3029638713748420756426308089806504*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(259509026/713)*(sqrt(129754513)*(11*134689869150937352^(3/4)*sqrt(341)*(5980372*x^7 - 8582986*x^6 + 27618126*x^5 - 10751392*x^4 + 12649968*x^3 + 12517632*x^2 - sqrt(2)*(4201650*x^7 - 6032009*x^6 + 19421619*x^5 - 7633552*x^4 + 9050328*x^3 + 8640000*x^2 - 8640000*x) - 12517632*x) + 4022389903*134689869150937352^(1/4)*sqrt(341)*(453599*x^7 - 5867420*x^6 + 22622900*x^5 - 29282112*x^4 + 37610208*x^3 + 22726656*x^2 - sqrt(2)*(319303*x^7 - 4130364*x^6 + 15927060*x^5 - 20630592*x^4 + 26556768*x^3 + 15800832*x^2 - 15800832*x) - 22726656*x))*sqrt(2*x^2 - x + 3)*sqrt(366990269*sqrt(2) + 519018052) - 8186887989068712800954*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 372131272230396036407*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((134689869150937352^(1/4)*sqrt(129754513)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(696*x + 277) - 973*x - 419)*sqrt(366990269*sqrt(2) + 519018052) + 4356437317274441*x^2 + 3911902897144396*sqrt(2)*(2*x^2 - x + 3) - 13424939487927359*x + 17781376805201800)/x^2) - 34427712656232054050298955565983*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) - 3*134689869150937352^(1/4)*sqrt(129754513)*sqrt(341)*sqrt(31)*(12975451300*x^4 + 15570541560*x^3 + 15051523508*x^2 - 366990269*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) + 6228216624*x + 2076072208)*sqrt(366990269*sqrt(2) + 519018052)*log(9342324936/713*(134689869150937352^(1/4)*sqrt(129754513)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(696*x + 277) - 973*x - 419)*sqrt(366990269*sqrt(2) + 519018052) + 4356437317274441*x^2 + 3911902897144396*sqrt(2)*(2*x^2 - x + 3) - 13424939487927359*x + 17781376805201800)/x^2) + 3*134689869150937352^(1/4)*sqrt(129754513)*sqrt(341)*sqrt(31)*(12975451300*x^4 + 15570541560*x^3 + 15051523508*x^2 - 366990269*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) + 6228216624*x + 2076072208)*sqrt(366990269*sqrt(2) + 519018052)*log(-9342324936/713*(134689869150937352^(1/4)*sqrt(129754513)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(696*x + 277) - 973*x - 419)*sqrt(366990269*sqrt(2) + 519018052) - 4356437317274441*x^2 - 3911902897144396*sqrt(2)*(2*x^2 - x + 3) + 13424939487927359*x - 17781376805201800)/x^2) - 22313494125311634784*(11680*x^3 + 10171*x^2 + 8343*x + 2220)*sqrt(2*x^2 - x + 3))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
72,1,118,0,0.419348," ","integrate((2*x^2-x+3)^(5/2)*(5*x^2+3*x+2)^4,x, algorithm=""fricas"")","\frac{1}{140703128616960} \, {\left(25125558681600000 \, x^{13} + 37398427729920000 \, x^{12} + 137233466130432000 \, x^{11} + 204932411660697600 \, x^{10} + 363646430503501824 \, x^{9} + 439064558846345216 \, x^{8} + 530502956133122048 \, x^{7} + 485091164642279424 \, x^{6} + 405468382284161024 \, x^{5} + 257786732552566784 \, x^{4} + 142490931553577856 \, x^{3} + 50064174038215008 \, x^{2} + 12071614275862524 \, x + 10820567498568669\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{14641852251147}{274877906944} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/140703128616960*(25125558681600000*x^13 + 37398427729920000*x^12 + 137233466130432000*x^11 + 204932411660697600*x^10 + 363646430503501824*x^9 + 439064558846345216*x^8 + 530502956133122048*x^7 + 485091164642279424*x^6 + 405468382284161024*x^5 + 257786732552566784*x^4 + 142490931553577856*x^3 + 50064174038215008*x^2 + 12071614275862524*x + 10820567498568669)*sqrt(2*x^2 - x + 3) + 14641852251147/274877906944*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
73,1,108,0,0.417071," ","integrate((2*x^2-x+3)^(5/2)*(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{1}{67645734912} \, {\left(2818572288000 \, x^{11} + 2395786444800 \, x^{10} + 12943588589568 \, x^{9} + 14341894045696 \, x^{8} + 27835561148416 \, x^{7} + 28347538538496 \, x^{6} + 34378613923840 \, x^{5} + 26186527209472 \, x^{4} + 20384824684416 \, x^{3} + 10060731582048 \, x^{2} + 4560943728924 \, x - 1191399152715\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{10569777075}{8589934592} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/67645734912*(2818572288000*x^11 + 2395786444800*x^10 + 12943588589568*x^9 + 14341894045696*x^8 + 27835561148416*x^7 + 28347538538496*x^6 + 34378613923840*x^5 + 26186527209472*x^4 + 20384824684416*x^3 + 10060731582048*x^2 + 4560943728924*x - 1191399152715)*sqrt(2*x^2 - x + 3) + 10569777075/8589934592*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
74,1,98,0,0.414693," ","integrate((2*x^2-x+3)^(5/2)*(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{1}{1056964608} \, {\left(10569646080 \, x^{9} + 2055208960 \, x^{8} + 44163137536 \, x^{7} + 26401898496 \, x^{6} + 75389820928 \, x^{5} + 57147467776 \, x^{4} + 77872272000 \, x^{3} + 42992644128 \, x^{2} + 39533249652 \, x + 14824182519\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{94111745}{134217728} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/1056964608*(10569646080*x^9 + 2055208960*x^8 + 44163137536*x^7 + 26401898496*x^6 + 75389820928*x^5 + 57147467776*x^4 + 77872272000*x^3 + 42992644128*x^2 + 39533249652*x + 14824182519)*sqrt(2*x^2 - x + 3) + 94111745/134217728*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
75,1,88,0,0.410787," ","integrate((2*x^2-x+3)^(5/2)*(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{1}{11010048} \, {\left(27525120 \, x^{7} - 13565952 \, x^{6} + 118808576 \, x^{5} - 1619968 \, x^{4} + 172684416 \, x^{3} + 67272352 \, x^{2} + 148957444 \, x + 58536675\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{16851295}{4194304} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/11010048*(27525120*x^7 - 13565952*x^6 + 118808576*x^5 - 1619968*x^4 + 172684416*x^3 + 67272352*x^2 + 148957444*x + 58536675)*sqrt(2*x^2 - x + 3) + 16851295/4194304*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
76,1,2010,0,1.039827," ","integrate((2*x^2-x+3)^(5/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{121}{96875000} \cdot 6050^{\frac{1}{4}} \sqrt{31} \sqrt{2} \sqrt{-772850000 \, \sqrt{2} + 2500000000} \arctan\left(\frac{722441500000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} + 2300 \, {\left(4 \cdot 6050^{\frac{3}{4}} \sqrt{31} {\left(35898 \, x^{7} - 441939 \, x^{6} + 782418 \, x^{5} - 2117233 \, x^{4} + 1272680 \, x^{3} - 1081800 \, x^{2} - \sqrt{2} {\left(173702 \, x^{7} - 453907 \, x^{6} + 1056481 \, x^{5} - 1083344 \, x^{4} + 393672 \, x^{3} + 152064 \, x^{2} - 1043712 \, x + 259200\right)} - 518400 \, x + 1043712\right)} + 5 \cdot 6050^{\frac{1}{4}} \sqrt{31} {\left(317294 \, x^{7} - 5870544 \, x^{6} + 38857480 \, x^{5} - 111531424 \, x^{4} + 156761280 \, x^{3} - 168192000 \, x^{2} - \sqrt{2} {\left(712757 \, x^{7} - 10233303 \, x^{6} + 48529768 \, x^{5} - 94500260 \, x^{4} + 113086944 \, x^{3} - 22282848 \, x^{2} - 106417152 \, x + 37407744\right)} - 74815488 \, x + 106417152\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{-772850000 \, \sqrt{2} + 2500000000} - \sqrt{\frac{10}{5711}} {\left(314105000 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - {\left(4 \cdot 6050^{\frac{3}{4}} \sqrt{31} {\left(167914 \, x^{7} - 195429 \, x^{6} + 331239 \, x^{5} + 1685680 \, x^{4} - 3693960 \, x^{3} + 4195584 \, x^{2} + 22 \, \sqrt{2} {\left(37846 \, x^{7} - 52859 \, x^{6} + 160569 \, x^{5} - 4464 \, x^{4} - 49464 \, x^{3} + 202176 \, x^{2} - 202176 \, x\right)} - 4195584 \, x\right)} - 5 \cdot 6050^{\frac{1}{4}} \sqrt{31} {\left(160956 \, x^{7} - 2232176 \, x^{6} + 11218640 \, x^{5} - 38096640 \, x^{4} + 139374720 \, x^{3} - 296027136 \, x^{2} - \sqrt{2} {\left(3246491 \, x^{7} - 41888524 \, x^{6} + 159670660 \, x^{5} - 190080576 \, x^{4} + 180496224 \, x^{3} + 376648704 \, x^{2} - 376648704 \, x\right)} + 296027136 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{-772850000 \, \sqrt{2} + 2500000000} + 14277500 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{6050^{\frac{1}{4}} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(163 \, x - 725\right)} + 562 \, x - 888\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} + 139919500 \, x^{2} + 125642000 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 431180500 \, x + 571100000}{x^{2}}} + 8209562500 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{254496437500 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + \frac{121}{96875000} \cdot 6050^{\frac{1}{4}} \sqrt{31} \sqrt{2} \sqrt{-772850000 \, \sqrt{2} + 2500000000} \arctan\left(-\frac{722441500000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2300 \, {\left(4 \cdot 6050^{\frac{3}{4}} \sqrt{31} {\left(35898 \, x^{7} - 441939 \, x^{6} + 782418 \, x^{5} - 2117233 \, x^{4} + 1272680 \, x^{3} - 1081800 \, x^{2} - \sqrt{2} {\left(173702 \, x^{7} - 453907 \, x^{6} + 1056481 \, x^{5} - 1083344 \, x^{4} + 393672 \, x^{3} + 152064 \, x^{2} - 1043712 \, x + 259200\right)} - 518400 \, x + 1043712\right)} + 5 \cdot 6050^{\frac{1}{4}} \sqrt{31} {\left(317294 \, x^{7} - 5870544 \, x^{6} + 38857480 \, x^{5} - 111531424 \, x^{4} + 156761280 \, x^{3} - 168192000 \, x^{2} - \sqrt{2} {\left(712757 \, x^{7} - 10233303 \, x^{6} + 48529768 \, x^{5} - 94500260 \, x^{4} + 113086944 \, x^{3} - 22282848 \, x^{2} - 106417152 \, x + 37407744\right)} - 74815488 \, x + 106417152\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{-772850000 \, \sqrt{2} + 2500000000} - \sqrt{\frac{10}{5711}} {\left(314105000 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + {\left(4 \cdot 6050^{\frac{3}{4}} \sqrt{31} {\left(167914 \, x^{7} - 195429 \, x^{6} + 331239 \, x^{5} + 1685680 \, x^{4} - 3693960 \, x^{3} + 4195584 \, x^{2} + 22 \, \sqrt{2} {\left(37846 \, x^{7} - 52859 \, x^{6} + 160569 \, x^{5} - 4464 \, x^{4} - 49464 \, x^{3} + 202176 \, x^{2} - 202176 \, x\right)} - 4195584 \, x\right)} - 5 \cdot 6050^{\frac{1}{4}} \sqrt{31} {\left(160956 \, x^{7} - 2232176 \, x^{6} + 11218640 \, x^{5} - 38096640 \, x^{4} + 139374720 \, x^{3} - 296027136 \, x^{2} - \sqrt{2} {\left(3246491 \, x^{7} - 41888524 \, x^{6} + 159670660 \, x^{5} - 190080576 \, x^{4} + 180496224 \, x^{3} + 376648704 \, x^{2} - 376648704 \, x\right)} + 296027136 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{-772850000 \, \sqrt{2} + 2500000000} + 14277500 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{6050^{\frac{1}{4}} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(163 \, x - 725\right)} + 562 \, x - 888\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} - 139919500 \, x^{2} - 125642000 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 431180500 \, x - 571100000}{x^{2}}} + 8209562500 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{254496437500 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) - \frac{121}{2213012500000} \cdot 6050^{\frac{1}{4}} {\left(15457 \, \sqrt{2} + 50000\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} \log\left(\frac{9150625000 \, {\left(6050^{\frac{1}{4}} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(163 \, x - 725\right)} + 562 \, x - 888\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} + 139919500 \, x^{2} + 125642000 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 431180500 \, x + 571100000\right)}}{5711 \, x^{2}}\right) + \frac{121}{2213012500000} \cdot 6050^{\frac{1}{4}} {\left(15457 \, \sqrt{2} + 50000\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} \log\left(-\frac{9150625000 \, {\left(6050^{\frac{1}{4}} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(163 \, x - 725\right)} + 562 \, x - 888\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} - 139919500 \, x^{2} - 125642000 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 431180500 \, x - 571100000\right)}}{5711 \, x^{2}}\right) + \frac{1}{240000} \, {\left(48000 \, x^{3} - 106400 \, x^{2} + 412060 \, x - 802347\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{7216203}{3200000} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"121/96875000*6050^(1/4)*sqrt(31)*sqrt(2)*sqrt(-772850000*sqrt(2) + 2500000000)*arctan(1/254496437500*(722441500000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) + 2300*(4*6050^(3/4)*sqrt(31)*(35898*x^7 - 441939*x^6 + 782418*x^5 - 2117233*x^4 + 1272680*x^3 - 1081800*x^2 - sqrt(2)*(173702*x^7 - 453907*x^6 + 1056481*x^5 - 1083344*x^4 + 393672*x^3 + 152064*x^2 - 1043712*x + 259200) - 518400*x + 1043712) + 5*6050^(1/4)*sqrt(31)*(317294*x^7 - 5870544*x^6 + 38857480*x^5 - 111531424*x^4 + 156761280*x^3 - 168192000*x^2 - sqrt(2)*(712757*x^7 - 10233303*x^6 + 48529768*x^5 - 94500260*x^4 + 113086944*x^3 - 22282848*x^2 - 106417152*x + 37407744) - 74815488*x + 106417152))*sqrt(2*x^2 - x + 3)*sqrt(-772850000*sqrt(2) + 2500000000) - sqrt(10/5711)*(314105000*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - (4*6050^(3/4)*sqrt(31)*(167914*x^7 - 195429*x^6 + 331239*x^5 + 1685680*x^4 - 3693960*x^3 + 4195584*x^2 + 22*sqrt(2)*(37846*x^7 - 52859*x^6 + 160569*x^5 - 4464*x^4 - 49464*x^3 + 202176*x^2 - 202176*x) - 4195584*x) - 5*6050^(1/4)*sqrt(31)*(160956*x^7 - 2232176*x^6 + 11218640*x^5 - 38096640*x^4 + 139374720*x^3 - 296027136*x^2 - sqrt(2)*(3246491*x^7 - 41888524*x^6 + 159670660*x^5 - 190080576*x^4 + 180496224*x^3 + 376648704*x^2 - 376648704*x) + 296027136*x))*sqrt(2*x^2 - x + 3)*sqrt(-772850000*sqrt(2) + 2500000000) + 14277500*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((6050^(1/4)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(163*x - 725) + 562*x - 888)*sqrt(-772850000*sqrt(2) + 2500000000) + 139919500*x^2 + 125642000*sqrt(2)*(2*x^2 - x + 3) - 431180500*x + 571100000)/x^2) + 8209562500*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 121/96875000*6050^(1/4)*sqrt(31)*sqrt(2)*sqrt(-772850000*sqrt(2) + 2500000000)*arctan(-1/254496437500*(722441500000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2300*(4*6050^(3/4)*sqrt(31)*(35898*x^7 - 441939*x^6 + 782418*x^5 - 2117233*x^4 + 1272680*x^3 - 1081800*x^2 - sqrt(2)*(173702*x^7 - 453907*x^6 + 1056481*x^5 - 1083344*x^4 + 393672*x^3 + 152064*x^2 - 1043712*x + 259200) - 518400*x + 1043712) + 5*6050^(1/4)*sqrt(31)*(317294*x^7 - 5870544*x^6 + 38857480*x^5 - 111531424*x^4 + 156761280*x^3 - 168192000*x^2 - sqrt(2)*(712757*x^7 - 10233303*x^6 + 48529768*x^5 - 94500260*x^4 + 113086944*x^3 - 22282848*x^2 - 106417152*x + 37407744) - 74815488*x + 106417152))*sqrt(2*x^2 - x + 3)*sqrt(-772850000*sqrt(2) + 2500000000) - sqrt(10/5711)*(314105000*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + (4*6050^(3/4)*sqrt(31)*(167914*x^7 - 195429*x^6 + 331239*x^5 + 1685680*x^4 - 3693960*x^3 + 4195584*x^2 + 22*sqrt(2)*(37846*x^7 - 52859*x^6 + 160569*x^5 - 4464*x^4 - 49464*x^3 + 202176*x^2 - 202176*x) - 4195584*x) - 5*6050^(1/4)*sqrt(31)*(160956*x^7 - 2232176*x^6 + 11218640*x^5 - 38096640*x^4 + 139374720*x^3 - 296027136*x^2 - sqrt(2)*(3246491*x^7 - 41888524*x^6 + 159670660*x^5 - 190080576*x^4 + 180496224*x^3 + 376648704*x^2 - 376648704*x) + 296027136*x))*sqrt(2*x^2 - x + 3)*sqrt(-772850000*sqrt(2) + 2500000000) + 14277500*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(6050^(1/4)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(163*x - 725) + 562*x - 888)*sqrt(-772850000*sqrt(2) + 2500000000) - 139919500*x^2 - 125642000*sqrt(2)*(2*x^2 - x + 3) + 431180500*x - 571100000)/x^2) + 8209562500*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) - 121/2213012500000*6050^(1/4)*(15457*sqrt(2) + 50000)*sqrt(-772850000*sqrt(2) + 2500000000)*log(9150625000/5711*(6050^(1/4)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(163*x - 725) + 562*x - 888)*sqrt(-772850000*sqrt(2) + 2500000000) + 139919500*x^2 + 125642000*sqrt(2)*(2*x^2 - x + 3) - 431180500*x + 571100000)/x^2) + 121/2213012500000*6050^(1/4)*(15457*sqrt(2) + 50000)*sqrt(-772850000*sqrt(2) + 2500000000)*log(-9150625000/5711*(6050^(1/4)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(163*x - 725) + 562*x - 888)*sqrt(-772850000*sqrt(2) + 2500000000) - 139919500*x^2 - 125642000*sqrt(2)*(2*x^2 - x + 3) + 431180500*x - 571100000)/x^2) + 1/240000*(48000*x^3 - 106400*x^2 + 412060*x - 802347)*sqrt(2*x^2 - x + 3) + 7216203/3200000*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","B",0
77,1,2161,0,1.316871," ","integrate((2*x^2-x+3)^(5/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{38925001324 \cdot 1464599010050^{\frac{1}{4}} \sqrt{155590} \sqrt{62} \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{224510383 \, \sqrt{2} + 388975000} \arctan\left(\frac{110935670 \, \sqrt{155590} {\left(4 \cdot 1464599010050^{\frac{3}{4}} \sqrt{62} {\left(18997882 \, x^{7} - 82713851 \, x^{6} + 169131062 \, x^{5} - 298338397 \, x^{4} + 156222120 \, x^{3} - 89116200 \, x^{2} - \sqrt{2} {\left(18111018 \, x^{7} - 62947113 \, x^{6} + 135463929 \, x^{5} - 197908246 \, x^{4} + 94500248 \, x^{3} - 34095024 \, x^{2} - 122404608 \, x + 71452800\right)} - 142905600 \, x + 122404608\right)} + 2411645 \cdot 1464599010050^{\frac{1}{4}} \sqrt{62} {\left(3035566 \, x^{7} - 47612316 \, x^{6} + 259553720 \, x^{5} - 615321136 \, x^{4} + 807721920 \, x^{3} - 579888000 \, x^{2} - \sqrt{2} {\left(2643323 \, x^{7} - 39854517 \, x^{6} + 204950152 \, x^{5} - 451004140 \, x^{4} + 573424416 \, x^{3} - 311722272 \, x^{2} - 434377728 \, x + 268655616\right)} - 537311232 \, x + 434377728\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{224510383 \, \sqrt{2} + 388975000} + 843027075536136774714827000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{77795}{920561}} {\left(\sqrt{155590} {\left(4 \cdot 1464599010050^{\frac{3}{4}} \sqrt{62} {\left(58767374 \, x^{7} - 85793239 \, x^{6} + 285539949 \, x^{5} - 168939120 \, x^{4} + 253241640 \, x^{3} + 601344 \, x^{2} - 4 \, \sqrt{2} {\left(17889302 \, x^{7} - 25424283 \, x^{6} + 80174553 \, x^{5} - 21241168 \, x^{4} + 15593832 \, x^{3} + 58564512 \, x^{2} - 58564512 \, x\right)} - 601344 \, x\right)} + 2411645 \cdot 1464599010050^{\frac{1}{4}} \sqrt{62} {\left(9891184 \, x^{7} - 128099264 \, x^{6} + 496592960 \, x^{5} - 666984960 \, x^{4} + 949582080 \, x^{3} + 183223296 \, x^{2} - \sqrt{2} {\left(10181049 \, x^{7} - 131588036 \, x^{6} + 505509740 \, x^{5} - 637596864 \, x^{4} + 754818336 \, x^{3} + 725677056 \, x^{2} - 725677056 \, x\right)} - 183223296 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{224510383 \, \sqrt{2} + 388975000} + 7599242656001778100 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 345420120727353550 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{1464599010050^{\frac{1}{4}} \sqrt{155590} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(9733 \, x + 29025\right)} - 38758 \, x + 19292\right)} \sqrt{224510383 \, \sqrt{2} + 388975000} - 6744561519183110 \, x^{2} - 6056340956001160 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 20784261008094890 \, x - 27528822527278000}{x^{2}}} + 9579853131092463349032125 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{296975447063866363819995875 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 38925001324 \cdot 1464599010050^{\frac{1}{4}} \sqrt{155590} \sqrt{62} \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{224510383 \, \sqrt{2} + 388975000} \arctan\left(\frac{110935670 \, \sqrt{155590} {\left(4 \cdot 1464599010050^{\frac{3}{4}} \sqrt{62} {\left(18997882 \, x^{7} - 82713851 \, x^{6} + 169131062 \, x^{5} - 298338397 \, x^{4} + 156222120 \, x^{3} - 89116200 \, x^{2} - \sqrt{2} {\left(18111018 \, x^{7} - 62947113 \, x^{6} + 135463929 \, x^{5} - 197908246 \, x^{4} + 94500248 \, x^{3} - 34095024 \, x^{2} - 122404608 \, x + 71452800\right)} - 142905600 \, x + 122404608\right)} + 2411645 \cdot 1464599010050^{\frac{1}{4}} \sqrt{62} {\left(3035566 \, x^{7} - 47612316 \, x^{6} + 259553720 \, x^{5} - 615321136 \, x^{4} + 807721920 \, x^{3} - 579888000 \, x^{2} - \sqrt{2} {\left(2643323 \, x^{7} - 39854517 \, x^{6} + 204950152 \, x^{5} - 451004140 \, x^{4} + 573424416 \, x^{3} - 311722272 \, x^{2} - 434377728 \, x + 268655616\right)} - 537311232 \, x + 434377728\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{224510383 \, \sqrt{2} + 388975000} - 843027075536136774714827000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{77795}{920561}} {\left(\sqrt{155590} {\left(4 \cdot 1464599010050^{\frac{3}{4}} \sqrt{62} {\left(58767374 \, x^{7} - 85793239 \, x^{6} + 285539949 \, x^{5} - 168939120 \, x^{4} + 253241640 \, x^{3} + 601344 \, x^{2} - 4 \, \sqrt{2} {\left(17889302 \, x^{7} - 25424283 \, x^{6} + 80174553 \, x^{5} - 21241168 \, x^{4} + 15593832 \, x^{3} + 58564512 \, x^{2} - 58564512 \, x\right)} - 601344 \, x\right)} + 2411645 \cdot 1464599010050^{\frac{1}{4}} \sqrt{62} {\left(9891184 \, x^{7} - 128099264 \, x^{6} + 496592960 \, x^{5} - 666984960 \, x^{4} + 949582080 \, x^{3} + 183223296 \, x^{2} - \sqrt{2} {\left(10181049 \, x^{7} - 131588036 \, x^{6} + 505509740 \, x^{5} - 637596864 \, x^{4} + 754818336 \, x^{3} + 725677056 \, x^{2} - 725677056 \, x\right)} - 183223296 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{224510383 \, \sqrt{2} + 388975000} - 7599242656001778100 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 345420120727353550 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{1464599010050^{\frac{1}{4}} \sqrt{155590} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(9733 \, x + 29025\right)} - 38758 \, x + 19292\right)} \sqrt{224510383 \, \sqrt{2} + 388975000} + 6744561519183110 \, x^{2} + 6056340956001160 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 20784261008094890 \, x + 27528822527278000}{x^{2}}} - 9579853131092463349032125 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{296975447063866363819995875 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 11 \cdot 1464599010050^{\frac{1}{4}} \sqrt{155590} \sqrt{62} \sqrt{31} {\left(1944875000 \, x^{2} - 224510383 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 1166925000 \, x + 777950000\right)} \sqrt{224510383 \, \sqrt{2} + 388975000} \log\left(\frac{14708117187500 \, {\left(1464599010050^{\frac{1}{4}} \sqrt{155590} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(9733 \, x + 29025\right)} - 38758 \, x + 19292\right)} \sqrt{224510383 \, \sqrt{2} + 388975000} + 6744561519183110 \, x^{2} + 6056340956001160 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 20784261008094890 \, x + 27528822527278000\right)}}{920561 \, x^{2}}\right) - 11 \cdot 1464599010050^{\frac{1}{4}} \sqrt{155590} \sqrt{62} \sqrt{31} {\left(1944875000 \, x^{2} - 224510383 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 1166925000 \, x + 777950000\right)} \sqrt{224510383 \, \sqrt{2} + 388975000} \log\left(-\frac{14708117187500 \, {\left(1464599010050^{\frac{1}{4}} \sqrt{155590} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(9733 \, x + 29025\right)} - 38758 \, x + 19292\right)} \sqrt{224510383 \, \sqrt{2} + 388975000} - 6744561519183110 \, x^{2} - 6056340956001160 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 20784261008094890 \, x - 27528822527278000\right)}}{920561 \, x^{2}}\right) + 634792486776896221210 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 170678699669123600 \, {\left(3100 \, x^{3} - 12555 \, x^{2} + 9289 \, x + 8996\right)} \sqrt{2 \, x^{2} - x + 3}}{1322759922435707900000 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/1322759922435707900000*(38925001324*1464599010050^(1/4)*sqrt(155590)*sqrt(62)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(224510383*sqrt(2) + 388975000)*arctan(1/296975447063866363819995875*(110935670*sqrt(155590)*(4*1464599010050^(3/4)*sqrt(62)*(18997882*x^7 - 82713851*x^6 + 169131062*x^5 - 298338397*x^4 + 156222120*x^3 - 89116200*x^2 - sqrt(2)*(18111018*x^7 - 62947113*x^6 + 135463929*x^5 - 197908246*x^4 + 94500248*x^3 - 34095024*x^2 - 122404608*x + 71452800) - 142905600*x + 122404608) + 2411645*1464599010050^(1/4)*sqrt(62)*(3035566*x^7 - 47612316*x^6 + 259553720*x^5 - 615321136*x^4 + 807721920*x^3 - 579888000*x^2 - sqrt(2)*(2643323*x^7 - 39854517*x^6 + 204950152*x^5 - 451004140*x^4 + 573424416*x^3 - 311722272*x^2 - 434377728*x + 268655616) - 537311232*x + 434377728))*sqrt(2*x^2 - x + 3)*sqrt(224510383*sqrt(2) + 388975000) + 843027075536136774714827000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(77795/920561)*(sqrt(155590)*(4*1464599010050^(3/4)*sqrt(62)*(58767374*x^7 - 85793239*x^6 + 285539949*x^5 - 168939120*x^4 + 253241640*x^3 + 601344*x^2 - 4*sqrt(2)*(17889302*x^7 - 25424283*x^6 + 80174553*x^5 - 21241168*x^4 + 15593832*x^3 + 58564512*x^2 - 58564512*x) - 601344*x) + 2411645*1464599010050^(1/4)*sqrt(62)*(9891184*x^7 - 128099264*x^6 + 496592960*x^5 - 666984960*x^4 + 949582080*x^3 + 183223296*x^2 - sqrt(2)*(10181049*x^7 - 131588036*x^6 + 505509740*x^5 - 637596864*x^4 + 754818336*x^3 + 725677056*x^2 - 725677056*x) - 183223296*x))*sqrt(2*x^2 - x + 3)*sqrt(224510383*sqrt(2) + 388975000) + 7599242656001778100*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 345420120727353550*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(1464599010050^(1/4)*sqrt(155590)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(9733*x + 29025) - 38758*x + 19292)*sqrt(224510383*sqrt(2) + 388975000) - 6744561519183110*x^2 - 6056340956001160*sqrt(2)*(2*x^2 - x + 3) + 20784261008094890*x - 27528822527278000)/x^2) + 9579853131092463349032125*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 38925001324*1464599010050^(1/4)*sqrt(155590)*sqrt(62)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(224510383*sqrt(2) + 388975000)*arctan(1/296975447063866363819995875*(110935670*sqrt(155590)*(4*1464599010050^(3/4)*sqrt(62)*(18997882*x^7 - 82713851*x^6 + 169131062*x^5 - 298338397*x^4 + 156222120*x^3 - 89116200*x^2 - sqrt(2)*(18111018*x^7 - 62947113*x^6 + 135463929*x^5 - 197908246*x^4 + 94500248*x^3 - 34095024*x^2 - 122404608*x + 71452800) - 142905600*x + 122404608) + 2411645*1464599010050^(1/4)*sqrt(62)*(3035566*x^7 - 47612316*x^6 + 259553720*x^5 - 615321136*x^4 + 807721920*x^3 - 579888000*x^2 - sqrt(2)*(2643323*x^7 - 39854517*x^6 + 204950152*x^5 - 451004140*x^4 + 573424416*x^3 - 311722272*x^2 - 434377728*x + 268655616) - 537311232*x + 434377728))*sqrt(2*x^2 - x + 3)*sqrt(224510383*sqrt(2) + 388975000) - 843027075536136774714827000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(77795/920561)*(sqrt(155590)*(4*1464599010050^(3/4)*sqrt(62)*(58767374*x^7 - 85793239*x^6 + 285539949*x^5 - 168939120*x^4 + 253241640*x^3 + 601344*x^2 - 4*sqrt(2)*(17889302*x^7 - 25424283*x^6 + 80174553*x^5 - 21241168*x^4 + 15593832*x^3 + 58564512*x^2 - 58564512*x) - 601344*x) + 2411645*1464599010050^(1/4)*sqrt(62)*(9891184*x^7 - 128099264*x^6 + 496592960*x^5 - 666984960*x^4 + 949582080*x^3 + 183223296*x^2 - sqrt(2)*(10181049*x^7 - 131588036*x^6 + 505509740*x^5 - 637596864*x^4 + 754818336*x^3 + 725677056*x^2 - 725677056*x) - 183223296*x))*sqrt(2*x^2 - x + 3)*sqrt(224510383*sqrt(2) + 388975000) - 7599242656001778100*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 345420120727353550*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((1464599010050^(1/4)*sqrt(155590)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(9733*x + 29025) - 38758*x + 19292)*sqrt(224510383*sqrt(2) + 388975000) + 6744561519183110*x^2 + 6056340956001160*sqrt(2)*(2*x^2 - x + 3) - 20784261008094890*x + 27528822527278000)/x^2) - 9579853131092463349032125*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 11*1464599010050^(1/4)*sqrt(155590)*sqrt(62)*sqrt(31)*(1944875000*x^2 - 224510383*sqrt(2)*(5*x^2 + 3*x + 2) + 1166925000*x + 777950000)*sqrt(224510383*sqrt(2) + 388975000)*log(14708117187500/920561*(1464599010050^(1/4)*sqrt(155590)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(9733*x + 29025) - 38758*x + 19292)*sqrt(224510383*sqrt(2) + 388975000) + 6744561519183110*x^2 + 6056340956001160*sqrt(2)*(2*x^2 - x + 3) - 20784261008094890*x + 27528822527278000)/x^2) - 11*1464599010050^(1/4)*sqrt(155590)*sqrt(62)*sqrt(31)*(1944875000*x^2 - 224510383*sqrt(2)*(5*x^2 + 3*x + 2) + 1166925000*x + 777950000)*sqrt(224510383*sqrt(2) + 388975000)*log(-14708117187500/920561*(1464599010050^(1/4)*sqrt(155590)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(9733*x + 29025) - 38758*x + 19292)*sqrt(224510383*sqrt(2) + 388975000) - 6744561519183110*x^2 - 6056340956001160*sqrt(2)*(2*x^2 - x + 3) + 20784261008094890*x - 27528822527278000)/x^2) + 634792486776896221210*sqrt(2)*(5*x^2 + 3*x + 2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 170678699669123600*(3100*x^3 - 12555*x^2 + 9289*x + 8996)*sqrt(2*x^2 - x + 3))/(5*x^2 + 3*x + 2)","B",0
78,1,2240,0,1.479016," ","integrate((2*x^2-x+3)^(5/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{3184949732636 \cdot 3868444992270541948232^{\frac{1}{4}} \sqrt{1999081657} \sqrt{62} \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} \arctan\left(\frac{2850690442882 \, \sqrt{1999081657} {\left(2 \cdot 3868444992270541948232^{\frac{3}{4}} \sqrt{62} {\left(2627559914 \, x^{7} - 10187615527 \, x^{6} + 21362956024 \, x^{5} - 34451465819 \, x^{4} + 17321103240 \, x^{3} - 8320757400 \, x^{2} - \sqrt{2} {\left(1893366636 \, x^{7} - 7237484076 \, x^{6} + 15226003533 \, x^{5} - 24262105817 \, x^{4} + 12127036096 \, x^{3} - 5664787848 \, x^{2} - 13367586816 \, x + 9338025600\right)} - 18676051200 \, x + 13367586816\right)} + 61971531367 \cdot 3868444992270541948232^{\frac{1}{4}} \sqrt{62} {\left(400116332 \, x^{7} - 6149336082 \, x^{6} + 32552996440 \, x^{5} - 74427496472 \, x^{4} + 96235107840 \, x^{3} - 61219656000 \, x^{2} - \sqrt{2} {\left(286685371 \, x^{7} - 4395067059 \, x^{6} + 23180544704 \, x^{5} - 52748573780 \, x^{4} + 68065744032 \, x^{3} - 42544702944 \, x^{2} - 48625837056 \, x + 34092306432\right)} - 68184612864 \, x + 48625837056\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} + 12874924822431853972621854418491567805329688 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{1999081657}{828550919}} {\left(\sqrt{1999081657} {\left(2 \cdot 3868444992270541948232^{\frac{3}{4}} \sqrt{62} {\left(9351066298 \, x^{7} - 13433496653 \, x^{6} + 43310345823 \, x^{5} - 17374572240 \, x^{4} + 20927636280 \, x^{3} + 18483199488 \, x^{2} - \sqrt{2} {\left(6839273266 \, x^{7} - 9809465289 \, x^{6} + 31524099699 \, x^{5} - 12024617744 \, x^{4} + 13914887256 \, x^{3} + 14839341696 \, x^{2} - 14839341696 \, x\right)} - 18483199488 \, x\right)} + 61971531367 \cdot 3868444992270541948232^{\frac{1}{4}} \sqrt{62} {\left(1427210918 \, x^{7} - 18462714328 \, x^{6} + 71210222920 \, x^{5} - 92387041920 \, x^{4} + 119489780160 \, x^{3} + 68726817792 \, x^{2} - \sqrt{2} {\left(1033310523 \, x^{7} - 13365477772 \, x^{6} + 51521534980 \, x^{5} - 66583614528 \, x^{4} + 85122955872 \, x^{3} + 53108877312 \, x^{2} - 53108877312 \, x\right)} - 68726817792 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} + 4516423329856721284677540671884 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 205291969538941876576251848722 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{3868444992270541948232^{\frac{1}{4}} \sqrt{1999081657} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(2141441 \, x + 1076175\right)} - 3217616 \, x - 1065266\right)} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} - 155990877430002205517374 \, x^{2} - 140073440957553000872744 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 480706581467965980267826 \, x - 636697458897968185785200}{x^{2}}} + 146305963891271067870702891119222361424201 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{4535484880629403103991789624695893204150231 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 3184949732636 \cdot 3868444992270541948232^{\frac{1}{4}} \sqrt{1999081657} \sqrt{62} \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} \arctan\left(\frac{2850690442882 \, \sqrt{1999081657} {\left(2 \cdot 3868444992270541948232^{\frac{3}{4}} \sqrt{62} {\left(2627559914 \, x^{7} - 10187615527 \, x^{6} + 21362956024 \, x^{5} - 34451465819 \, x^{4} + 17321103240 \, x^{3} - 8320757400 \, x^{2} - \sqrt{2} {\left(1893366636 \, x^{7} - 7237484076 \, x^{6} + 15226003533 \, x^{5} - 24262105817 \, x^{4} + 12127036096 \, x^{3} - 5664787848 \, x^{2} - 13367586816 \, x + 9338025600\right)} - 18676051200 \, x + 13367586816\right)} + 61971531367 \cdot 3868444992270541948232^{\frac{1}{4}} \sqrt{62} {\left(400116332 \, x^{7} - 6149336082 \, x^{6} + 32552996440 \, x^{5} - 74427496472 \, x^{4} + 96235107840 \, x^{3} - 61219656000 \, x^{2} - \sqrt{2} {\left(286685371 \, x^{7} - 4395067059 \, x^{6} + 23180544704 \, x^{5} - 52748573780 \, x^{4} + 68065744032 \, x^{3} - 42544702944 \, x^{2} - 48625837056 \, x + 34092306432\right)} - 68184612864 \, x + 48625837056\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} - 12874924822431853972621854418491567805329688 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{1999081657}{828550919}} {\left(\sqrt{1999081657} {\left(2 \cdot 3868444992270541948232^{\frac{3}{4}} \sqrt{62} {\left(9351066298 \, x^{7} - 13433496653 \, x^{6} + 43310345823 \, x^{5} - 17374572240 \, x^{4} + 20927636280 \, x^{3} + 18483199488 \, x^{2} - \sqrt{2} {\left(6839273266 \, x^{7} - 9809465289 \, x^{6} + 31524099699 \, x^{5} - 12024617744 \, x^{4} + 13914887256 \, x^{3} + 14839341696 \, x^{2} - 14839341696 \, x\right)} - 18483199488 \, x\right)} + 61971531367 \cdot 3868444992270541948232^{\frac{1}{4}} \sqrt{62} {\left(1427210918 \, x^{7} - 18462714328 \, x^{6} + 71210222920 \, x^{5} - 92387041920 \, x^{4} + 119489780160 \, x^{3} + 68726817792 \, x^{2} - \sqrt{2} {\left(1033310523 \, x^{7} - 13365477772 \, x^{6} + 51521534980 \, x^{5} - 66583614528 \, x^{4} + 85122955872 \, x^{3} + 53108877312 \, x^{2} - 53108877312 \, x\right)} - 68726817792 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} - 4516423329856721284677540671884 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 205291969538941876576251848722 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{3868444992270541948232^{\frac{1}{4}} \sqrt{1999081657} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(2141441 \, x + 1076175\right)} - 3217616 \, x - 1065266\right)} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} + 155990877430002205517374 \, x^{2} + 140073440957553000872744 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 480706581467965980267826 \, x + 636697458897968185785200}{x^{2}}} - 146305963891271067870702891119222361424201 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{4535484880629403103991789624695893204150231 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 3868444992270541948232^{\frac{1}{4}} \sqrt{1999081657} \sqrt{62} \sqrt{31} {\left(124942603562500 \, x^{4} + 149931124275000 \, x^{3} + 144933420132500 \, x^{2} - 3531015707557 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} + 59972449710000 \, x + 19990816570000\right)} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} \log\left(\frac{3123565089062500 \, {\left(3868444992270541948232^{\frac{1}{4}} \sqrt{1999081657} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(2141441 \, x + 1076175\right)} - 3217616 \, x - 1065266\right)} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} + 155990877430002205517374 \, x^{2} + 140073440957553000872744 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 480706581467965980267826 \, x + 636697458897968185785200\right)}}{828550919 \, x^{2}}\right) - 3868444992270541948232^{\frac{1}{4}} \sqrt{1999081657} \sqrt{62} \sqrt{31} {\left(124942603562500 \, x^{4} + 149931124275000 \, x^{3} + 144933420132500 \, x^{2} - 3531015707557 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} + 59972449710000 \, x + 19990816570000\right)} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} \log\left(-\frac{3123565089062500 \, {\left(3868444992270541948232^{\frac{1}{4}} \sqrt{1999081657} \sqrt{62} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(2141441 \, x + 1076175\right)} - 3217616 \, x - 1065266\right)} \sqrt{3531015707557 \, \sqrt{2} + 4997704142500} - 155990877430002205517374 \, x^{2} - 140073440957553000872744 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 480706581467965980267826 \, x - 636697458897968185785200\right)}}{828550919 \, x^{2}}\right) + 12139426558738796942545211648 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 86845533393682860541101280 \, {\left(97155 \, x^{3} + 93872 \, x^{2} + 69621 \, x + 22552\right)} \sqrt{2 \, x^{2} - x + 3}}{758714159921174808909075728000 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"1/758714159921174808909075728000*(3184949732636*3868444992270541948232^(1/4)*sqrt(1999081657)*sqrt(62)*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(3531015707557*sqrt(2) + 4997704142500)*arctan(1/4535484880629403103991789624695893204150231*(2850690442882*sqrt(1999081657)*(2*3868444992270541948232^(3/4)*sqrt(62)*(2627559914*x^7 - 10187615527*x^6 + 21362956024*x^5 - 34451465819*x^4 + 17321103240*x^3 - 8320757400*x^2 - sqrt(2)*(1893366636*x^7 - 7237484076*x^6 + 15226003533*x^5 - 24262105817*x^4 + 12127036096*x^3 - 5664787848*x^2 - 13367586816*x + 9338025600) - 18676051200*x + 13367586816) + 61971531367*3868444992270541948232^(1/4)*sqrt(62)*(400116332*x^7 - 6149336082*x^6 + 32552996440*x^5 - 74427496472*x^4 + 96235107840*x^3 - 61219656000*x^2 - sqrt(2)*(286685371*x^7 - 4395067059*x^6 + 23180544704*x^5 - 52748573780*x^4 + 68065744032*x^3 - 42544702944*x^2 - 48625837056*x + 34092306432) - 68184612864*x + 48625837056))*sqrt(2*x^2 - x + 3)*sqrt(3531015707557*sqrt(2) + 4997704142500) + 12874924822431853972621854418491567805329688*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(1999081657/828550919)*(sqrt(1999081657)*(2*3868444992270541948232^(3/4)*sqrt(62)*(9351066298*x^7 - 13433496653*x^6 + 43310345823*x^5 - 17374572240*x^4 + 20927636280*x^3 + 18483199488*x^2 - sqrt(2)*(6839273266*x^7 - 9809465289*x^6 + 31524099699*x^5 - 12024617744*x^4 + 13914887256*x^3 + 14839341696*x^2 - 14839341696*x) - 18483199488*x) + 61971531367*3868444992270541948232^(1/4)*sqrt(62)*(1427210918*x^7 - 18462714328*x^6 + 71210222920*x^5 - 92387041920*x^4 + 119489780160*x^3 + 68726817792*x^2 - sqrt(2)*(1033310523*x^7 - 13365477772*x^6 + 51521534980*x^5 - 66583614528*x^4 + 85122955872*x^3 + 53108877312*x^2 - 53108877312*x) - 68726817792*x))*sqrt(2*x^2 - x + 3)*sqrt(3531015707557*sqrt(2) + 4997704142500) + 4516423329856721284677540671884*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 205291969538941876576251848722*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(3868444992270541948232^(1/4)*sqrt(1999081657)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(2141441*x + 1076175) - 3217616*x - 1065266)*sqrt(3531015707557*sqrt(2) + 4997704142500) - 155990877430002205517374*x^2 - 140073440957553000872744*sqrt(2)*(2*x^2 - x + 3) + 480706581467965980267826*x - 636697458897968185785200)/x^2) + 146305963891271067870702891119222361424201*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 3184949732636*3868444992270541948232^(1/4)*sqrt(1999081657)*sqrt(62)*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(3531015707557*sqrt(2) + 4997704142500)*arctan(1/4535484880629403103991789624695893204150231*(2850690442882*sqrt(1999081657)*(2*3868444992270541948232^(3/4)*sqrt(62)*(2627559914*x^7 - 10187615527*x^6 + 21362956024*x^5 - 34451465819*x^4 + 17321103240*x^3 - 8320757400*x^2 - sqrt(2)*(1893366636*x^7 - 7237484076*x^6 + 15226003533*x^5 - 24262105817*x^4 + 12127036096*x^3 - 5664787848*x^2 - 13367586816*x + 9338025600) - 18676051200*x + 13367586816) + 61971531367*3868444992270541948232^(1/4)*sqrt(62)*(400116332*x^7 - 6149336082*x^6 + 32552996440*x^5 - 74427496472*x^4 + 96235107840*x^3 - 61219656000*x^2 - sqrt(2)*(286685371*x^7 - 4395067059*x^6 + 23180544704*x^5 - 52748573780*x^4 + 68065744032*x^3 - 42544702944*x^2 - 48625837056*x + 34092306432) - 68184612864*x + 48625837056))*sqrt(2*x^2 - x + 3)*sqrt(3531015707557*sqrt(2) + 4997704142500) - 12874924822431853972621854418491567805329688*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(1999081657/828550919)*(sqrt(1999081657)*(2*3868444992270541948232^(3/4)*sqrt(62)*(9351066298*x^7 - 13433496653*x^6 + 43310345823*x^5 - 17374572240*x^4 + 20927636280*x^3 + 18483199488*x^2 - sqrt(2)*(6839273266*x^7 - 9809465289*x^6 + 31524099699*x^5 - 12024617744*x^4 + 13914887256*x^3 + 14839341696*x^2 - 14839341696*x) - 18483199488*x) + 61971531367*3868444992270541948232^(1/4)*sqrt(62)*(1427210918*x^7 - 18462714328*x^6 + 71210222920*x^5 - 92387041920*x^4 + 119489780160*x^3 + 68726817792*x^2 - sqrt(2)*(1033310523*x^7 - 13365477772*x^6 + 51521534980*x^5 - 66583614528*x^4 + 85122955872*x^3 + 53108877312*x^2 - 53108877312*x) - 68726817792*x))*sqrt(2*x^2 - x + 3)*sqrt(3531015707557*sqrt(2) + 4997704142500) - 4516423329856721284677540671884*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 205291969538941876576251848722*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((3868444992270541948232^(1/4)*sqrt(1999081657)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(2141441*x + 1076175) - 3217616*x - 1065266)*sqrt(3531015707557*sqrt(2) + 4997704142500) + 155990877430002205517374*x^2 + 140073440957553000872744*sqrt(2)*(2*x^2 - x + 3) - 480706581467965980267826*x + 636697458897968185785200)/x^2) - 146305963891271067870702891119222361424201*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 3868444992270541948232^(1/4)*sqrt(1999081657)*sqrt(62)*sqrt(31)*(124942603562500*x^4 + 149931124275000*x^3 + 144933420132500*x^2 - 3531015707557*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) + 59972449710000*x + 19990816570000)*sqrt(3531015707557*sqrt(2) + 4997704142500)*log(3123565089062500/828550919*(3868444992270541948232^(1/4)*sqrt(1999081657)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(2141441*x + 1076175) - 3217616*x - 1065266)*sqrt(3531015707557*sqrt(2) + 4997704142500) + 155990877430002205517374*x^2 + 140073440957553000872744*sqrt(2)*(2*x^2 - x + 3) - 480706581467965980267826*x + 636697458897968185785200)/x^2) - 3868444992270541948232^(1/4)*sqrt(1999081657)*sqrt(62)*sqrt(31)*(124942603562500*x^4 + 149931124275000*x^3 + 144933420132500*x^2 - 3531015707557*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) + 59972449710000*x + 19990816570000)*sqrt(3531015707557*sqrt(2) + 4997704142500)*log(-3123565089062500/828550919*(3868444992270541948232^(1/4)*sqrt(1999081657)*sqrt(62)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(2141441*x + 1076175) - 3217616*x - 1065266)*sqrt(3531015707557*sqrt(2) + 4997704142500) - 155990877430002205517374*x^2 - 140073440957553000872744*sqrt(2)*(2*x^2 - x + 3) + 480706581467965980267826*x - 636697458897968185785200)/x^2) + 12139426558738796942545211648*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 86845533393682860541101280*(97155*x^3 + 93872*x^2 + 69621*x + 22552)*sqrt(2*x^2 - x + 3))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
79,1,88,0,0.432626," ","integrate((5*x^2+3*x+2)^4/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{88080384} \, {\left(3440640000 \, x^{7} + 11280384000 \, x^{6} + 17338163200 \, x^{5} + 9842108416 \, x^{4} - 7584175488 \, x^{3} - 10367779296 \, x^{2} + 18864088884 \, x + 49479262983\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{2899366573}{33554432} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/88080384*(3440640000*x^7 + 11280384000*x^6 + 17338163200*x^5 + 9842108416*x^4 - 7584175488*x^3 - 10367779296*x^2 + 18864088884*x + 49479262983)*sqrt(2*x^2 - x + 3) + 2899366573/33554432*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
80,1,78,0,0.406934," ","integrate((5*x^2+3*x+2)^3/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{98304} \, {\left(1024000 \, x^{5} + 2775040 \, x^{4} + 3143040 \, x^{3} - 325152 \, x^{2} - 4473396 \, x - 610119\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{9267707}{262144} \, \sqrt{2} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/98304*(1024000*x^5 + 2775040*x^4 + 3143040*x^3 - 325152*x^2 - 4473396*x - 610119)*sqrt(2*x^2 - x + 3) + 9267707/262144*sqrt(2)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
81,1,68,0,0.408083," ","integrate((5*x^2+3*x+2)^2/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{3072} \, {\left(9600 \, x^{3} + 20960 \, x^{2} + 13772 \, x - 34119\right)} \sqrt{2 \, x^{2} - x + 3} + \frac{30725}{8192} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/3072*(9600*x^3 + 20960*x^2 + 13772*x - 34119)*sqrt(2*x^2 - x + 3) + 30725/8192*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
82,1,58,0,0.414864," ","integrate((5*x^2+3*x+2)/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{1}{16} \, \sqrt{2 \, x^{2} - x + 3} {\left(20 \, x + 39\right)} + \frac{17}{128} \, \sqrt{2} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right)"," ",0,"1/16*sqrt(2*x^2 - x + 3)*(20*x + 39) + 17/128*sqrt(2)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25)","A",0
83,1,2002,0,1.132212," ","integrate(1/(5*x^2+3*x+2)/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","-\frac{1}{845680} \, \sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{5} \sqrt{13 \, \sqrt{2} + 20} {\left(13 \, \sqrt{2} - 20\right)} \log\left(\frac{1240 \, {\left(\sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(4 \, x - 1\right)} - 3 \, x - 5\right)} \sqrt{13 \, \sqrt{2} + 20} + 7595 \, x^{2} + 6820 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 23405 \, x + 31000\right)}}{x^{2}}\right) + \frac{1}{845680} \, \sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{5} \sqrt{13 \, \sqrt{2} + 20} {\left(13 \, \sqrt{2} - 20\right)} \log\left(-\frac{1240 \, {\left(\sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(4 \, x - 1\right)} - 3 \, x - 5\right)} \sqrt{13 \, \sqrt{2} + 20} - 7595 \, x^{2} - 6820 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 23405 \, x - 31000\right)}}{x^{2}}\right) - \frac{1}{6820} \, \sqrt{341} 200^{\frac{1}{4}} \sqrt{5} \sqrt{2} \sqrt{13 \, \sqrt{2} + 20} \arctan\left(\frac{14260 \, \sqrt{341} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(11 \cdot 200^{\frac{3}{4}} {\left(8056 \, x^{7} - 28976 \, x^{6} + 61838 \, x^{5} - 93342 \, x^{4} + 45376 \, x^{3} - 18288 \, x^{2} - \sqrt{2} {\left(4702 \, x^{7} - 19541 \, x^{6} + 40352 \, x^{5} - 68777 \, x^{4} + 35480 \, x^{3} - 19080 \, x^{2} - 34560 \, x + 27648\right)} - 55296 \, x + 34560\right)} + 5 \cdot 200^{\frac{1}{4}} {\left(18463 \, x^{7} - 280047 \, x^{6} + 1453472 \, x^{5} - 3238500 \, x^{4} + 4140576 \, x^{3} - 2378592 \, x^{2} - \sqrt{2} {\left(11418 \, x^{7} - 177633 \, x^{6} + 957180 \, x^{5} - 2237548 \, x^{4} + 2920320 \, x^{3} - 2005920 \, x^{2} - 1990656 \, x + 1534464\right)} - 3068928 \, x + 1990656\right)}\right)} \sqrt{13 \, \sqrt{2} + 20} + 7843000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{310} {\left(\sqrt{341} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(11 \cdot 200^{\frac{3}{4}} {\left(30876 \, x^{7} - 44014 \, x^{6} + 139674 \, x^{5} - 42464 \, x^{4} + 38736 \, x^{3} + 89856 \, x^{2} - \sqrt{2} {\left(15454 \, x^{7} - 22399 \, x^{6} + 73509 \, x^{5} - 37360 \, x^{4} + 52200 \, x^{3} + 13824 \, x^{2} - 13824 \, x\right)} - 89856 \, x\right)} + 5 \cdot 200^{\frac{1}{4}} {\left(69479 \, x^{7} - 898236 \, x^{6} + 3454740 \, x^{5} - 4394304 \, x^{4} + 5347296 \, x^{3} + 4478976 \, x^{2} - \sqrt{2} {\left(38627 \, x^{7} - 500012 \, x^{6} + 1934180 \, x^{5} - 2560320 \, x^{4} + 3506400 \, x^{3} + 1202688 \, x^{2} - 1202688 \, x\right)} - 4478976 \, x\right)}\right)} \sqrt{13 \, \sqrt{2} + 20} + 550 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 25 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{\sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(4 \, x - 1\right)} - 3 \, x - 5\right)} \sqrt{13 \, \sqrt{2} + 20} - 7595 \, x^{2} - 6820 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 23405 \, x - 31000}{x^{2}}} + 89125 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{2762875 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) - \frac{1}{6820} \, \sqrt{341} 200^{\frac{1}{4}} \sqrt{5} \sqrt{2} \sqrt{13 \, \sqrt{2} + 20} \arctan\left(\frac{14260 \, \sqrt{341} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(11 \cdot 200^{\frac{3}{4}} {\left(8056 \, x^{7} - 28976 \, x^{6} + 61838 \, x^{5} - 93342 \, x^{4} + 45376 \, x^{3} - 18288 \, x^{2} - \sqrt{2} {\left(4702 \, x^{7} - 19541 \, x^{6} + 40352 \, x^{5} - 68777 \, x^{4} + 35480 \, x^{3} - 19080 \, x^{2} - 34560 \, x + 27648\right)} - 55296 \, x + 34560\right)} + 5 \cdot 200^{\frac{1}{4}} {\left(18463 \, x^{7} - 280047 \, x^{6} + 1453472 \, x^{5} - 3238500 \, x^{4} + 4140576 \, x^{3} - 2378592 \, x^{2} - \sqrt{2} {\left(11418 \, x^{7} - 177633 \, x^{6} + 957180 \, x^{5} - 2237548 \, x^{4} + 2920320 \, x^{3} - 2005920 \, x^{2} - 1990656 \, x + 1534464\right)} - 3068928 \, x + 1990656\right)}\right)} \sqrt{13 \, \sqrt{2} + 20} - 7843000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{310} {\left(\sqrt{341} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(11 \cdot 200^{\frac{3}{4}} {\left(30876 \, x^{7} - 44014 \, x^{6} + 139674 \, x^{5} - 42464 \, x^{4} + 38736 \, x^{3} + 89856 \, x^{2} - \sqrt{2} {\left(15454 \, x^{7} - 22399 \, x^{6} + 73509 \, x^{5} - 37360 \, x^{4} + 52200 \, x^{3} + 13824 \, x^{2} - 13824 \, x\right)} - 89856 \, x\right)} + 5 \cdot 200^{\frac{1}{4}} {\left(69479 \, x^{7} - 898236 \, x^{6} + 3454740 \, x^{5} - 4394304 \, x^{4} + 5347296 \, x^{3} + 4478976 \, x^{2} - \sqrt{2} {\left(38627 \, x^{7} - 500012 \, x^{6} + 1934180 \, x^{5} - 2560320 \, x^{4} + 3506400 \, x^{3} + 1202688 \, x^{2} - 1202688 \, x\right)} - 4478976 \, x\right)}\right)} \sqrt{13 \, \sqrt{2} + 20} - 550 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 25 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{\sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{5} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(4 \, x - 1\right)} - 3 \, x - 5\right)} \sqrt{13 \, \sqrt{2} + 20} + 7595 \, x^{2} + 6820 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 23405 \, x + 31000}{x^{2}}} - 89125 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{2762875 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right)"," ",0,"-1/845680*sqrt(341)*200^(1/4)*sqrt(31)*sqrt(5)*sqrt(13*sqrt(2) + 20)*(13*sqrt(2) - 20)*log(1240*(sqrt(341)*200^(1/4)*sqrt(31)*sqrt(5)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(4*x - 1) - 3*x - 5)*sqrt(13*sqrt(2) + 20) + 7595*x^2 + 6820*sqrt(2)*(2*x^2 - x + 3) - 23405*x + 31000)/x^2) + 1/845680*sqrt(341)*200^(1/4)*sqrt(31)*sqrt(5)*sqrt(13*sqrt(2) + 20)*(13*sqrt(2) - 20)*log(-1240*(sqrt(341)*200^(1/4)*sqrt(31)*sqrt(5)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(4*x - 1) - 3*x - 5)*sqrt(13*sqrt(2) + 20) - 7595*x^2 - 6820*sqrt(2)*(2*x^2 - x + 3) + 23405*x - 31000)/x^2) - 1/6820*sqrt(341)*200^(1/4)*sqrt(5)*sqrt(2)*sqrt(13*sqrt(2) + 20)*arctan(1/2762875*(14260*sqrt(341)*sqrt(5)*sqrt(2*x^2 - x + 3)*(11*200^(3/4)*(8056*x^7 - 28976*x^6 + 61838*x^5 - 93342*x^4 + 45376*x^3 - 18288*x^2 - sqrt(2)*(4702*x^7 - 19541*x^6 + 40352*x^5 - 68777*x^4 + 35480*x^3 - 19080*x^2 - 34560*x + 27648) - 55296*x + 34560) + 5*200^(1/4)*(18463*x^7 - 280047*x^6 + 1453472*x^5 - 3238500*x^4 + 4140576*x^3 - 2378592*x^2 - sqrt(2)*(11418*x^7 - 177633*x^6 + 957180*x^5 - 2237548*x^4 + 2920320*x^3 - 2005920*x^2 - 1990656*x + 1534464) - 3068928*x + 1990656))*sqrt(13*sqrt(2) + 20) + 7843000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(310)*(sqrt(341)*sqrt(5)*sqrt(2*x^2 - x + 3)*(11*200^(3/4)*(30876*x^7 - 44014*x^6 + 139674*x^5 - 42464*x^4 + 38736*x^3 + 89856*x^2 - sqrt(2)*(15454*x^7 - 22399*x^6 + 73509*x^5 - 37360*x^4 + 52200*x^3 + 13824*x^2 - 13824*x) - 89856*x) + 5*200^(1/4)*(69479*x^7 - 898236*x^6 + 3454740*x^5 - 4394304*x^4 + 5347296*x^3 + 4478976*x^2 - sqrt(2)*(38627*x^7 - 500012*x^6 + 1934180*x^5 - 2560320*x^4 + 3506400*x^3 + 1202688*x^2 - 1202688*x) - 4478976*x))*sqrt(13*sqrt(2) + 20) + 550*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 25*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(sqrt(341)*200^(1/4)*sqrt(31)*sqrt(5)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(4*x - 1) - 3*x - 5)*sqrt(13*sqrt(2) + 20) - 7595*x^2 - 6820*sqrt(2)*(2*x^2 - x + 3) + 23405*x - 31000)/x^2) + 89125*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) - 1/6820*sqrt(341)*200^(1/4)*sqrt(5)*sqrt(2)*sqrt(13*sqrt(2) + 20)*arctan(1/2762875*(14260*sqrt(341)*sqrt(5)*sqrt(2*x^2 - x + 3)*(11*200^(3/4)*(8056*x^7 - 28976*x^6 + 61838*x^5 - 93342*x^4 + 45376*x^3 - 18288*x^2 - sqrt(2)*(4702*x^7 - 19541*x^6 + 40352*x^5 - 68777*x^4 + 35480*x^3 - 19080*x^2 - 34560*x + 27648) - 55296*x + 34560) + 5*200^(1/4)*(18463*x^7 - 280047*x^6 + 1453472*x^5 - 3238500*x^4 + 4140576*x^3 - 2378592*x^2 - sqrt(2)*(11418*x^7 - 177633*x^6 + 957180*x^5 - 2237548*x^4 + 2920320*x^3 - 2005920*x^2 - 1990656*x + 1534464) - 3068928*x + 1990656))*sqrt(13*sqrt(2) + 20) - 7843000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(310)*(sqrt(341)*sqrt(5)*sqrt(2*x^2 - x + 3)*(11*200^(3/4)*(30876*x^7 - 44014*x^6 + 139674*x^5 - 42464*x^4 + 38736*x^3 + 89856*x^2 - sqrt(2)*(15454*x^7 - 22399*x^6 + 73509*x^5 - 37360*x^4 + 52200*x^3 + 13824*x^2 - 13824*x) - 89856*x) + 5*200^(1/4)*(69479*x^7 - 898236*x^6 + 3454740*x^5 - 4394304*x^4 + 5347296*x^3 + 4478976*x^2 - sqrt(2)*(38627*x^7 - 500012*x^6 + 1934180*x^5 - 2560320*x^4 + 3506400*x^3 + 1202688*x^2 - 1202688*x) - 4478976*x))*sqrt(13*sqrt(2) + 20) - 550*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 25*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((sqrt(341)*200^(1/4)*sqrt(31)*sqrt(5)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(4*x - 1) - 3*x - 5)*sqrt(13*sqrt(2) + 20) + 7595*x^2 + 6820*sqrt(2)*(2*x^2 - x + 3) - 23405*x + 31000)/x^2) - 89125*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456))","B",0
84,1,2102,0,1.250165," ","integrate(1/(5*x^2+3*x+2)^2/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","\frac{8422204 \cdot 563606738^{\frac{1}{4}} \sqrt{33574} \sqrt{341} \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{2343727 \, \sqrt{2} + 3357400} \arctan\left(\frac{47876524 \, \sqrt{33574} {\left(22 \cdot 563606738^{\frac{3}{4}} \sqrt{341} {\left(2950932 \, x^{7} - 11691762 \, x^{6} + 24397746 \, x^{5} - 40053004 \, x^{4} + 20309552 \, x^{3} - 10145376 \, x^{2} - \sqrt{2} {\left(2248634 \, x^{7} - 8421787 \, x^{6} + 17801494 \, x^{5} - 27869789 \, x^{4} + 13808040 \, x^{3} - 6172200 \, x^{2} - 15724800 \, x + 10596096\right)} - 21192192 \, x + 15724800\right)} + 520397 \cdot 563606738^{\frac{1}{4}} \sqrt{341} {\left(226651 \, x^{7} - 3496629 \, x^{6} + 18614024 \, x^{5} - 42860780 \, x^{4} + 55586592 \, x^{3} - 36274464 \, x^{2} - \sqrt{2} {\left(168871 \, x^{7} - 2579646 \, x^{6} + 13533020 \, x^{5} - 30582616 \, x^{4} + 39345120 \, x^{3} - 23947200 \, x^{2} - 28449792 \, x + 19450368\right)} - 38900736 \, x + 28449792\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{2343727 \, \sqrt{2} + 3357400} + 20160232886887690715272 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{33574}{2191}} {\left(\sqrt{33574} {\left(22 \cdot 563606738^{\frac{3}{4}} \sqrt{341} {\left(10257392 \, x^{7} - 14773368 \, x^{6} + 47877288 \, x^{5} - 20710528 \, x^{4} + 26321472 \, x^{3} + 17079552 \, x^{2} - \sqrt{2} {\left(8292238 \, x^{7} - 11867543 \, x^{6} + 37968813 \, x^{5} - 13449840 \, x^{4} + 14570280 \, x^{3} + 20176128 \, x^{2} - 20176128 \, x\right)} - 17079552 \, x\right)} + 520397 \cdot 563606738^{\frac{1}{4}} \sqrt{341} {\left(795513 \, x^{7} - 10292932 \, x^{6} + 39734380 \, x^{5} - 51864768 \, x^{4} + 68281632 \, x^{3} + 34255872 \, x^{2} - 8 \, \sqrt{2} {\left(77213 \, x^{7} - 998548 \, x^{6} + 3846220 \, x^{5} - 4943520 \, x^{4} + 6215760 \, x^{3} + 4318272 \, x^{2} - 4318272 \, x\right)} - 34255872 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{2343727 \, \sqrt{2} + 3357400} + 421088065768678 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 19140366625849 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{563606738^{\frac{1}{4}} \sqrt{33574} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(1123 \, x + 898\right)} - 2021 \, x - 225\right)} \sqrt{2343727 \, \sqrt{2} + 3357400} - 1731948347213 \, x^{2} - 1555218924028 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 5337228580187 \, x - 7069176927400}{x^{2}}} + 229093555532814667219 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{7101900221517254683789 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 8422204 \cdot 563606738^{\frac{1}{4}} \sqrt{33574} \sqrt{341} \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} \sqrt{2343727 \, \sqrt{2} + 3357400} \arctan\left(\frac{47876524 \, \sqrt{33574} {\left(22 \cdot 563606738^{\frac{3}{4}} \sqrt{341} {\left(2950932 \, x^{7} - 11691762 \, x^{6} + 24397746 \, x^{5} - 40053004 \, x^{4} + 20309552 \, x^{3} - 10145376 \, x^{2} - \sqrt{2} {\left(2248634 \, x^{7} - 8421787 \, x^{6} + 17801494 \, x^{5} - 27869789 \, x^{4} + 13808040 \, x^{3} - 6172200 \, x^{2} - 15724800 \, x + 10596096\right)} - 21192192 \, x + 15724800\right)} + 520397 \cdot 563606738^{\frac{1}{4}} \sqrt{341} {\left(226651 \, x^{7} - 3496629 \, x^{6} + 18614024 \, x^{5} - 42860780 \, x^{4} + 55586592 \, x^{3} - 36274464 \, x^{2} - \sqrt{2} {\left(168871 \, x^{7} - 2579646 \, x^{6} + 13533020 \, x^{5} - 30582616 \, x^{4} + 39345120 \, x^{3} - 23947200 \, x^{2} - 28449792 \, x + 19450368\right)} - 38900736 \, x + 28449792\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{2343727 \, \sqrt{2} + 3357400} - 20160232886887690715272 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{33574}{2191}} {\left(\sqrt{33574} {\left(22 \cdot 563606738^{\frac{3}{4}} \sqrt{341} {\left(10257392 \, x^{7} - 14773368 \, x^{6} + 47877288 \, x^{5} - 20710528 \, x^{4} + 26321472 \, x^{3} + 17079552 \, x^{2} - \sqrt{2} {\left(8292238 \, x^{7} - 11867543 \, x^{6} + 37968813 \, x^{5} - 13449840 \, x^{4} + 14570280 \, x^{3} + 20176128 \, x^{2} - 20176128 \, x\right)} - 17079552 \, x\right)} + 520397 \cdot 563606738^{\frac{1}{4}} \sqrt{341} {\left(795513 \, x^{7} - 10292932 \, x^{6} + 39734380 \, x^{5} - 51864768 \, x^{4} + 68281632 \, x^{3} + 34255872 \, x^{2} - 8 \, \sqrt{2} {\left(77213 \, x^{7} - 998548 \, x^{6} + 3846220 \, x^{5} - 4943520 \, x^{4} + 6215760 \, x^{3} + 4318272 \, x^{2} - 4318272 \, x\right)} - 34255872 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{2343727 \, \sqrt{2} + 3357400} - 421088065768678 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 19140366625849 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{563606738^{\frac{1}{4}} \sqrt{33574} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(1123 \, x + 898\right)} - 2021 \, x - 225\right)} \sqrt{2343727 \, \sqrt{2} + 3357400} + 1731948347213 \, x^{2} + 1555218924028 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 5337228580187 \, x + 7069176927400}{x^{2}}} - 229093555532814667219 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{7101900221517254683789 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 563606738^{\frac{1}{4}} \sqrt{33574} \sqrt{341} \sqrt{31} {\left(16787000 \, x^{2} - 2343727 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 10072200 \, x + 6714800\right)} \sqrt{2343727 \, \sqrt{2} + 3357400} \log\left(\frac{335740000 \, {\left(563606738^{\frac{1}{4}} \sqrt{33574} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(1123 \, x + 898\right)} - 2021 \, x - 225\right)} \sqrt{2343727 \, \sqrt{2} + 3357400} + 1731948347213 \, x^{2} + 1555218924028 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 5337228580187 \, x + 7069176927400\right)}}{2191 \, x^{2}}\right) - 563606738^{\frac{1}{4}} \sqrt{33574} \sqrt{341} \sqrt{31} {\left(16787000 \, x^{2} - 2343727 \, \sqrt{2} {\left(5 \, x^{2} + 3 \, x + 2\right)} + 10072200 \, x + 6714800\right)} \sqrt{2343727 \, \sqrt{2} + 3357400} \log\left(-\frac{335740000 \, {\left(563606738^{\frac{1}{4}} \sqrt{33574} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(1123 \, x + 898\right)} - 2021 \, x - 225\right)} \sqrt{2343727 \, \sqrt{2} + 3357400} - 1731948347213 \, x^{2} - 1555218924028 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 5337228580187 \, x - 7069176927400\right)}}{2191 \, x^{2}}\right) + 385694293158944 \, \sqrt{2 \, x^{2} - x + 3} {\left(65 \, x + 4\right)}}{263043507934399808 \, {\left(5 \, x^{2} + 3 \, x + 2\right)}}"," ",0,"1/263043507934399808*(8422204*563606738^(1/4)*sqrt(33574)*sqrt(341)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(2343727*sqrt(2) + 3357400)*arctan(1/7101900221517254683789*(47876524*sqrt(33574)*(22*563606738^(3/4)*sqrt(341)*(2950932*x^7 - 11691762*x^6 + 24397746*x^5 - 40053004*x^4 + 20309552*x^3 - 10145376*x^2 - sqrt(2)*(2248634*x^7 - 8421787*x^6 + 17801494*x^5 - 27869789*x^4 + 13808040*x^3 - 6172200*x^2 - 15724800*x + 10596096) - 21192192*x + 15724800) + 520397*563606738^(1/4)*sqrt(341)*(226651*x^7 - 3496629*x^6 + 18614024*x^5 - 42860780*x^4 + 55586592*x^3 - 36274464*x^2 - sqrt(2)*(168871*x^7 - 2579646*x^6 + 13533020*x^5 - 30582616*x^4 + 39345120*x^3 - 23947200*x^2 - 28449792*x + 19450368) - 38900736*x + 28449792))*sqrt(2*x^2 - x + 3)*sqrt(2343727*sqrt(2) + 3357400) + 20160232886887690715272*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(33574/2191)*(sqrt(33574)*(22*563606738^(3/4)*sqrt(341)*(10257392*x^7 - 14773368*x^6 + 47877288*x^5 - 20710528*x^4 + 26321472*x^3 + 17079552*x^2 - sqrt(2)*(8292238*x^7 - 11867543*x^6 + 37968813*x^5 - 13449840*x^4 + 14570280*x^3 + 20176128*x^2 - 20176128*x) - 17079552*x) + 520397*563606738^(1/4)*sqrt(341)*(795513*x^7 - 10292932*x^6 + 39734380*x^5 - 51864768*x^4 + 68281632*x^3 + 34255872*x^2 - 8*sqrt(2)*(77213*x^7 - 998548*x^6 + 3846220*x^5 - 4943520*x^4 + 6215760*x^3 + 4318272*x^2 - 4318272*x) - 34255872*x))*sqrt(2*x^2 - x + 3)*sqrt(2343727*sqrt(2) + 3357400) + 421088065768678*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 19140366625849*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(563606738^(1/4)*sqrt(33574)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(1123*x + 898) - 2021*x - 225)*sqrt(2343727*sqrt(2) + 3357400) - 1731948347213*x^2 - 1555218924028*sqrt(2)*(2*x^2 - x + 3) + 5337228580187*x - 7069176927400)/x^2) + 229093555532814667219*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 8422204*563606738^(1/4)*sqrt(33574)*sqrt(341)*sqrt(2)*(5*x^2 + 3*x + 2)*sqrt(2343727*sqrt(2) + 3357400)*arctan(1/7101900221517254683789*(47876524*sqrt(33574)*(22*563606738^(3/4)*sqrt(341)*(2950932*x^7 - 11691762*x^6 + 24397746*x^5 - 40053004*x^4 + 20309552*x^3 - 10145376*x^2 - sqrt(2)*(2248634*x^7 - 8421787*x^6 + 17801494*x^5 - 27869789*x^4 + 13808040*x^3 - 6172200*x^2 - 15724800*x + 10596096) - 21192192*x + 15724800) + 520397*563606738^(1/4)*sqrt(341)*(226651*x^7 - 3496629*x^6 + 18614024*x^5 - 42860780*x^4 + 55586592*x^3 - 36274464*x^2 - sqrt(2)*(168871*x^7 - 2579646*x^6 + 13533020*x^5 - 30582616*x^4 + 39345120*x^3 - 23947200*x^2 - 28449792*x + 19450368) - 38900736*x + 28449792))*sqrt(2*x^2 - x + 3)*sqrt(2343727*sqrt(2) + 3357400) - 20160232886887690715272*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(33574/2191)*(sqrt(33574)*(22*563606738^(3/4)*sqrt(341)*(10257392*x^7 - 14773368*x^6 + 47877288*x^5 - 20710528*x^4 + 26321472*x^3 + 17079552*x^2 - sqrt(2)*(8292238*x^7 - 11867543*x^6 + 37968813*x^5 - 13449840*x^4 + 14570280*x^3 + 20176128*x^2 - 20176128*x) - 17079552*x) + 520397*563606738^(1/4)*sqrt(341)*(795513*x^7 - 10292932*x^6 + 39734380*x^5 - 51864768*x^4 + 68281632*x^3 + 34255872*x^2 - 8*sqrt(2)*(77213*x^7 - 998548*x^6 + 3846220*x^5 - 4943520*x^4 + 6215760*x^3 + 4318272*x^2 - 4318272*x) - 34255872*x))*sqrt(2*x^2 - x + 3)*sqrt(2343727*sqrt(2) + 3357400) - 421088065768678*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 19140366625849*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((563606738^(1/4)*sqrt(33574)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(1123*x + 898) - 2021*x - 225)*sqrt(2343727*sqrt(2) + 3357400) + 1731948347213*x^2 + 1555218924028*sqrt(2)*(2*x^2 - x + 3) - 5337228580187*x + 7069176927400)/x^2) - 229093555532814667219*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 563606738^(1/4)*sqrt(33574)*sqrt(341)*sqrt(31)*(16787000*x^2 - 2343727*sqrt(2)*(5*x^2 + 3*x + 2) + 10072200*x + 6714800)*sqrt(2343727*sqrt(2) + 3357400)*log(335740000/2191*(563606738^(1/4)*sqrt(33574)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(1123*x + 898) - 2021*x - 225)*sqrt(2343727*sqrt(2) + 3357400) + 1731948347213*x^2 + 1555218924028*sqrt(2)*(2*x^2 - x + 3) - 5337228580187*x + 7069176927400)/x^2) - 563606738^(1/4)*sqrt(33574)*sqrt(341)*sqrt(31)*(16787000*x^2 - 2343727*sqrt(2)*(5*x^2 + 3*x + 2) + 10072200*x + 6714800)*sqrt(2343727*sqrt(2) + 3357400)*log(-335740000/2191*(563606738^(1/4)*sqrt(33574)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(1123*x + 898) - 2021*x - 225)*sqrt(2343727*sqrt(2) + 3357400) - 1731948347213*x^2 - 1555218924028*sqrt(2)*(2*x^2 - x + 3) + 5337228580187*x - 7069176927400)/x^2) + 385694293158944*sqrt(2*x^2 - x + 3)*(65*x + 4))/(5*x^2 + 3*x + 2)","B",0
85,1,2183,0,1.283664," ","integrate(1/(5*x^2+3*x+2)^3/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","-\frac{46113488900 \cdot 4115738902305032^{\frac{1}{4}} \sqrt{22681873} \sqrt{341} \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{6414867847 \, \sqrt{2} + 9072749200} \arctan\left(\frac{64688701796 \, \sqrt{22681873} {\left(11 \cdot 4115738902305032^{\frac{3}{4}} \sqrt{341} {\left(160344708 \, x^{7} - 615873378 \, x^{6} + 1294230774 \, x^{5} - 2070733376 \, x^{4} + 1037098288 \, x^{3} - 489164544 \, x^{2} - \sqrt{2} {\left(112700446 \, x^{7} - 434839553 \, x^{6} + 912850886 \, x^{5} - 1466127691 \, x^{4} + 735661560 \, x^{3} - 350098200 \, x^{2} - 799200000 \, x + 567316224\right)} - 1134632448 \, x + 799200000\right)} + 703138063 \cdot 4115738902305032^{\frac{1}{4}} \sqrt{341} {\left(12162569 \, x^{7} - 186616851 \, x^{6} + 985490056 \, x^{5} - 2246141620 \, x^{4} + 2900382048 \, x^{3} - 1823848416 \, x^{2} - \sqrt{2} {\left(8564099 \, x^{7} - 131508024 \, x^{6} + 695288980 \, x^{5} - 1587105104 \, x^{4} + 2050714080 \, x^{3} - 1296806400 \, x^{2} - 1457077248 \, x + 1033108992\right)} - 2066217984 \, x + 1457077248\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{6414867847 \, \sqrt{2} + 9072749200} + 10891187458641059311133302222822312 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{45363746}{479849}} {\left(\sqrt{22681873} {\left(11 \cdot 4115738902305032^{\frac{3}{4}} \sqrt{341} {\left(576322648 \, x^{7} - 827050092 \, x^{6} + 2660713572 \, x^{5} - 1032439232 \, x^{4} + 1211604768 \, x^{3} + 1213394688 \, x^{2} - \sqrt{2} {\left(403157522 \, x^{7} - 578844217 \, x^{6} + 1864129347 \, x^{5} - 735062160 \, x^{4} + 873708120 \, x^{3} + 823986432 \, x^{2} - 823986432 \, x\right)} - 1213394688 \, x\right)} + 703138063 \cdot 4115738902305032^{\frac{1}{4}} \sqrt{341} {\left(43684647 \, x^{7} - 565067708 \, x^{6} + 2178643220 \, x^{5} - 2819241792 \, x^{4} + 3618371808 \, x^{3} + 2197767168 \, x^{2} - 2 \, \sqrt{2} {\left(15328963 \, x^{7} - 198290348 \, x^{6} + 764653220 \, x^{5} - 990717120 \, x^{4} + 1276256160 \, x^{3} + 755350272 \, x^{2} - 755350272 \, x\right)} - 2197767168 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{6414867847 \, \sqrt{2} + 9072749200} + 168363055004367262339322 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 7652866136562148288151 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{4115738902305032^{\frac{1}{4}} \sqrt{22681873} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(67187 \, x + 26012\right)} - 93199 \, x - 41175\right)} \sqrt{6414867847 \, \sqrt{2} + 9072749200} - 512510746420187753 \, x^{2} - 460213731479352268 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 1579369851213231647 \, x - 2091880597633419400}{x^{2}}} + 123763493848193855808332979804799 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{3836668309294009530058322373948769 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 46113488900 \cdot 4115738902305032^{\frac{1}{4}} \sqrt{22681873} \sqrt{341} \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} \sqrt{6414867847 \, \sqrt{2} + 9072749200} \arctan\left(\frac{64688701796 \, \sqrt{22681873} {\left(11 \cdot 4115738902305032^{\frac{3}{4}} \sqrt{341} {\left(160344708 \, x^{7} - 615873378 \, x^{6} + 1294230774 \, x^{5} - 2070733376 \, x^{4} + 1037098288 \, x^{3} - 489164544 \, x^{2} - \sqrt{2} {\left(112700446 \, x^{7} - 434839553 \, x^{6} + 912850886 \, x^{5} - 1466127691 \, x^{4} + 735661560 \, x^{3} - 350098200 \, x^{2} - 799200000 \, x + 567316224\right)} - 1134632448 \, x + 799200000\right)} + 703138063 \cdot 4115738902305032^{\frac{1}{4}} \sqrt{341} {\left(12162569 \, x^{7} - 186616851 \, x^{6} + 985490056 \, x^{5} - 2246141620 \, x^{4} + 2900382048 \, x^{3} - 1823848416 \, x^{2} - \sqrt{2} {\left(8564099 \, x^{7} - 131508024 \, x^{6} + 695288980 \, x^{5} - 1587105104 \, x^{4} + 2050714080 \, x^{3} - 1296806400 \, x^{2} - 1457077248 \, x + 1033108992\right)} - 2066217984 \, x + 1457077248\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{6414867847 \, \sqrt{2} + 9072749200} - 10891187458641059311133302222822312 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{45363746}{479849}} {\left(\sqrt{22681873} {\left(11 \cdot 4115738902305032^{\frac{3}{4}} \sqrt{341} {\left(576322648 \, x^{7} - 827050092 \, x^{6} + 2660713572 \, x^{5} - 1032439232 \, x^{4} + 1211604768 \, x^{3} + 1213394688 \, x^{2} - \sqrt{2} {\left(403157522 \, x^{7} - 578844217 \, x^{6} + 1864129347 \, x^{5} - 735062160 \, x^{4} + 873708120 \, x^{3} + 823986432 \, x^{2} - 823986432 \, x\right)} - 1213394688 \, x\right)} + 703138063 \cdot 4115738902305032^{\frac{1}{4}} \sqrt{341} {\left(43684647 \, x^{7} - 565067708 \, x^{6} + 2178643220 \, x^{5} - 2819241792 \, x^{4} + 3618371808 \, x^{3} + 2197767168 \, x^{2} - 2 \, \sqrt{2} {\left(15328963 \, x^{7} - 198290348 \, x^{6} + 764653220 \, x^{5} - 990717120 \, x^{4} + 1276256160 \, x^{3} + 755350272 \, x^{2} - 755350272 \, x\right)} - 2197767168 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{6414867847 \, \sqrt{2} + 9072749200} - 168363055004367262339322 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 7652866136562148288151 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{4115738902305032^{\frac{1}{4}} \sqrt{22681873} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(67187 \, x + 26012\right)} - 93199 \, x - 41175\right)} \sqrt{6414867847 \, \sqrt{2} + 9072749200} + 512510746420187753 \, x^{2} + 460213731479352268 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 1579369851213231647 \, x + 2091880597633419400}{x^{2}}} - 123763493848193855808332979804799 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{3836668309294009530058322373948769 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) - 25 \cdot 4115738902305032^{\frac{1}{4}} \sqrt{22681873} \sqrt{341} \sqrt{31} {\left(226818730000 \, x^{4} + 272182476000 \, x^{3} + 263109726800 \, x^{2} - 6414867847 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} + 108872990400 \, x + 36290996800\right)} \sqrt{6414867847 \, \sqrt{2} + 9072749200} \log\left(\frac{1134093650000000 \, {\left(4115738902305032^{\frac{1}{4}} \sqrt{22681873} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(67187 \, x + 26012\right)} - 93199 \, x - 41175\right)} \sqrt{6414867847 \, \sqrt{2} + 9072749200} + 512510746420187753 \, x^{2} + 460213731479352268 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 1579369851213231647 \, x + 2091880597633419400\right)}}{479849 \, x^{2}}\right) + 25 \cdot 4115738902305032^{\frac{1}{4}} \sqrt{22681873} \sqrt{341} \sqrt{31} {\left(226818730000 \, x^{4} + 272182476000 \, x^{3} + 263109726800 \, x^{2} - 6414867847 \, \sqrt{2} {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)} + 108872990400 \, x + 36290996800\right)} \sqrt{6414867847 \, \sqrt{2} + 9072749200} \log\left(-\frac{1134093650000000 \, {\left(4115738902305032^{\frac{1}{4}} \sqrt{22681873} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(67187 \, x + 26012\right)} - 93199 \, x - 41175\right)} \sqrt{6414867847 \, \sqrt{2} + 9072749200} - 512510746420187753 \, x^{2} - 460213731479352268 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 1579369851213231647 \, x - 2091880597633419400\right)}}{479849 \, x^{2}}\right) - 114133005406879362464 \, {\left(431325 \, x^{3} + 392765 \, x^{2} + 341572 \, x + 59044\right)} \sqrt{2 \, x^{2} - x + 3}}{212344000027477426346822144 \, {\left(25 \, x^{4} + 30 \, x^{3} + 29 \, x^{2} + 12 \, x + 4\right)}}"," ",0,"-1/212344000027477426346822144*(46113488900*4115738902305032^(1/4)*sqrt(22681873)*sqrt(341)*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(6414867847*sqrt(2) + 9072749200)*arctan(1/3836668309294009530058322373948769*(64688701796*sqrt(22681873)*(11*4115738902305032^(3/4)*sqrt(341)*(160344708*x^7 - 615873378*x^6 + 1294230774*x^5 - 2070733376*x^4 + 1037098288*x^3 - 489164544*x^2 - sqrt(2)*(112700446*x^7 - 434839553*x^6 + 912850886*x^5 - 1466127691*x^4 + 735661560*x^3 - 350098200*x^2 - 799200000*x + 567316224) - 1134632448*x + 799200000) + 703138063*4115738902305032^(1/4)*sqrt(341)*(12162569*x^7 - 186616851*x^6 + 985490056*x^5 - 2246141620*x^4 + 2900382048*x^3 - 1823848416*x^2 - sqrt(2)*(8564099*x^7 - 131508024*x^6 + 695288980*x^5 - 1587105104*x^4 + 2050714080*x^3 - 1296806400*x^2 - 1457077248*x + 1033108992) - 2066217984*x + 1457077248))*sqrt(2*x^2 - x + 3)*sqrt(6414867847*sqrt(2) + 9072749200) + 10891187458641059311133302222822312*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(45363746/479849)*(sqrt(22681873)*(11*4115738902305032^(3/4)*sqrt(341)*(576322648*x^7 - 827050092*x^6 + 2660713572*x^5 - 1032439232*x^4 + 1211604768*x^3 + 1213394688*x^2 - sqrt(2)*(403157522*x^7 - 578844217*x^6 + 1864129347*x^5 - 735062160*x^4 + 873708120*x^3 + 823986432*x^2 - 823986432*x) - 1213394688*x) + 703138063*4115738902305032^(1/4)*sqrt(341)*(43684647*x^7 - 565067708*x^6 + 2178643220*x^5 - 2819241792*x^4 + 3618371808*x^3 + 2197767168*x^2 - 2*sqrt(2)*(15328963*x^7 - 198290348*x^6 + 764653220*x^5 - 990717120*x^4 + 1276256160*x^3 + 755350272*x^2 - 755350272*x) - 2197767168*x))*sqrt(2*x^2 - x + 3)*sqrt(6414867847*sqrt(2) + 9072749200) + 168363055004367262339322*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 7652866136562148288151*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(4115738902305032^(1/4)*sqrt(22681873)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(67187*x + 26012) - 93199*x - 41175)*sqrt(6414867847*sqrt(2) + 9072749200) - 512510746420187753*x^2 - 460213731479352268*sqrt(2)*(2*x^2 - x + 3) + 1579369851213231647*x - 2091880597633419400)/x^2) + 123763493848193855808332979804799*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 46113488900*4115738902305032^(1/4)*sqrt(22681873)*sqrt(341)*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)*sqrt(6414867847*sqrt(2) + 9072749200)*arctan(1/3836668309294009530058322373948769*(64688701796*sqrt(22681873)*(11*4115738902305032^(3/4)*sqrt(341)*(160344708*x^7 - 615873378*x^6 + 1294230774*x^5 - 2070733376*x^4 + 1037098288*x^3 - 489164544*x^2 - sqrt(2)*(112700446*x^7 - 434839553*x^6 + 912850886*x^5 - 1466127691*x^4 + 735661560*x^3 - 350098200*x^2 - 799200000*x + 567316224) - 1134632448*x + 799200000) + 703138063*4115738902305032^(1/4)*sqrt(341)*(12162569*x^7 - 186616851*x^6 + 985490056*x^5 - 2246141620*x^4 + 2900382048*x^3 - 1823848416*x^2 - sqrt(2)*(8564099*x^7 - 131508024*x^6 + 695288980*x^5 - 1587105104*x^4 + 2050714080*x^3 - 1296806400*x^2 - 1457077248*x + 1033108992) - 2066217984*x + 1457077248))*sqrt(2*x^2 - x + 3)*sqrt(6414867847*sqrt(2) + 9072749200) - 10891187458641059311133302222822312*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(45363746/479849)*(sqrt(22681873)*(11*4115738902305032^(3/4)*sqrt(341)*(576322648*x^7 - 827050092*x^6 + 2660713572*x^5 - 1032439232*x^4 + 1211604768*x^3 + 1213394688*x^2 - sqrt(2)*(403157522*x^7 - 578844217*x^6 + 1864129347*x^5 - 735062160*x^4 + 873708120*x^3 + 823986432*x^2 - 823986432*x) - 1213394688*x) + 703138063*4115738902305032^(1/4)*sqrt(341)*(43684647*x^7 - 565067708*x^6 + 2178643220*x^5 - 2819241792*x^4 + 3618371808*x^3 + 2197767168*x^2 - 2*sqrt(2)*(15328963*x^7 - 198290348*x^6 + 764653220*x^5 - 990717120*x^4 + 1276256160*x^3 + 755350272*x^2 - 755350272*x) - 2197767168*x))*sqrt(2*x^2 - x + 3)*sqrt(6414867847*sqrt(2) + 9072749200) - 168363055004367262339322*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 7652866136562148288151*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((4115738902305032^(1/4)*sqrt(22681873)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(67187*x + 26012) - 93199*x - 41175)*sqrt(6414867847*sqrt(2) + 9072749200) + 512510746420187753*x^2 + 460213731479352268*sqrt(2)*(2*x^2 - x + 3) - 1579369851213231647*x + 2091880597633419400)/x^2) - 123763493848193855808332979804799*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) - 25*4115738902305032^(1/4)*sqrt(22681873)*sqrt(341)*sqrt(31)*(226818730000*x^4 + 272182476000*x^3 + 263109726800*x^2 - 6414867847*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) + 108872990400*x + 36290996800)*sqrt(6414867847*sqrt(2) + 9072749200)*log(1134093650000000/479849*(4115738902305032^(1/4)*sqrt(22681873)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(67187*x + 26012) - 93199*x - 41175)*sqrt(6414867847*sqrt(2) + 9072749200) + 512510746420187753*x^2 + 460213731479352268*sqrt(2)*(2*x^2 - x + 3) - 1579369851213231647*x + 2091880597633419400)/x^2) + 25*4115738902305032^(1/4)*sqrt(22681873)*sqrt(341)*sqrt(31)*(226818730000*x^4 + 272182476000*x^3 + 263109726800*x^2 - 6414867847*sqrt(2)*(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4) + 108872990400*x + 36290996800)*sqrt(6414867847*sqrt(2) + 9072749200)*log(-1134093650000000/479849*(4115738902305032^(1/4)*sqrt(22681873)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(67187*x + 26012) - 93199*x - 41175)*sqrt(6414867847*sqrt(2) + 9072749200) - 512510746420187753*x^2 - 460213731479352268*sqrt(2)*(2*x^2 - x + 3) + 1579369851213231647*x - 2091880597633419400)/x^2) - 114133005406879362464*(431325*x^3 + 392765*x^2 + 341572*x + 59044)*sqrt(2*x^2 - x + 3))/(25*x^4 + 30*x^3 + 29*x^2 + 12*x + 4)","B",0
86,1,112,0,0.411301," ","integrate((5*x^2+3*x+2)^4/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{21420745503 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(235520000 \, x^{7} + 831385600 \, x^{6} + 1281670400 \, x^{5} + 230669760 \, x^{4} - 2613624504 \, x^{3} - 2534760678 \, x^{2} - 8859305979 \, x - 10961697147\right)} \sqrt{2 \, x^{2} - x + 3}}{36175872 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/36175872*(21420745503*sqrt(2)*(2*x^2 - x + 3)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(235520000*x^7 + 831385600*x^6 + 1281670400*x^5 + 230669760*x^4 - 2613624504*x^3 - 2534760678*x^2 - 8859305979*x - 10961697147)*sqrt(2*x^2 - x + 3))/(2*x^2 - x + 3)","A",0
87,1,102,0,0.418607," ","integrate((5*x^2+3*x+2)^3/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{26884263 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(736000 \, x^{5} + 2318400 \, x^{4} + 2624760 \, x^{3} - 5754186 \, x^{2} + 16138403 \, x - 15423965\right)} \sqrt{2 \, x^{2} - x + 3}}{376832 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/376832*(26884263*sqrt(2)*(2*x^2 - x + 3)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(736000*x^5 + 2318400*x^4 + 2624760*x^3 - 5754186*x^2 + 16138403*x - 15423965)*sqrt(2*x^2 - x + 3))/(2*x^2 - x + 3)","A",0
88,1,92,0,0.414631," ","integrate((5*x^2+3*x+2)^2/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{5129 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(4600 \, x^{3} + 16790 \, x^{2} - 9421 \, x + 47027\right)} \sqrt{2 \, x^{2} - x + 3}}{5888 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/5888*(5129*sqrt(2)*(2*x^2 - x + 3)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(4600*x^3 + 16790*x^2 - 9421*x + 47027)*sqrt(2*x^2 - x + 3))/(2*x^2 - x + 3)","A",0
89,1,82,0,0.414734," ","integrate((5*x^2+3*x+2)/(2*x^2-x+3)^(3/2),x, algorithm=""fricas"")","\frac{115 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) - 88 \, \sqrt{2 \, x^{2} - x + 3} {\left(3 \, x + 5\right)}}{184 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"1/184*(115*sqrt(2)*(2*x^2 - x + 3)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) - 88*sqrt(2*x^2 - x + 3)*(3*x + 5))/(2*x^2 - x + 3)","B",0
90,1,2083,0,1.167592," ","integrate(1/(2*x^2-x+3)^(3/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","-\frac{339388 \, \sqrt{341} 50^{\frac{1}{4}} \sqrt{10} \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \sqrt{247 \, \sqrt{2} + 1000} \arctan\left(\frac{14260 \, \sqrt{341} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(22 \cdot 50^{\frac{3}{4}} {\left(57708 \, x^{7} - 181278 \, x^{6} + 400374 \, x^{5} - 525676 \, x^{4} + 235088 \, x^{3} - 46944 \, x^{2} - \sqrt{2} {\left(20846 \, x^{7} - 109153 \, x^{6} + 215386 \, x^{5} - 427391 \, x^{4} + 234360 \, x^{3} - 156600 \, x^{2} - 172800 \, x + 186624\right)} - 373248 \, x + 172800\right)} + 5 \cdot 50^{\frac{1}{4}} {\left(125839 \, x^{7} - 1864281 \, x^{6} + 9323336 \, x^{5} - 19725020 \, x^{4} + 24624288 \, x^{3} - 10862496 \, x^{2} - \sqrt{2} {\left(56119 \, x^{7} - 908994 \, x^{6} + 5175980 \, x^{5} - 12895624 \, x^{4} + 17261280 \, x^{3} - 14184000 \, x^{2} - 10533888 \, x + 9994752\right)} - 19989504 \, x + 10533888\right)}\right)} \sqrt{247 \, \sqrt{2} + 1000} + 933317000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{310}{119}} {\left(\sqrt{341} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(22 \cdot 50^{\frac{3}{4}} {\left(246848 \, x^{7} - 348192 \, x^{6} + 1080672 \, x^{5} - 178432 \, x^{4} - 18432 \, x^{3} + 1029888 \, x^{2} - \sqrt{2} {\left(46522 \, x^{7} - 71117 \, x^{6} + 257247 \, x^{5} - 273360 \, x^{4} + 484920 \, x^{3} - 269568 \, x^{2} + 269568 \, x\right)} - 1029888 \, x\right)} + 5 \cdot 50^{\frac{1}{4}} {\left(516957 \, x^{7} - 6676948 \, x^{6} + 25569820 \, x^{5} - 31522752 \, x^{4} + 34450848 \, x^{3} + 46199808 \, x^{2} - 4 \, \sqrt{2} {\left(38689 \, x^{7} - 502244 \, x^{6} + 1967660 \, x^{5} - 2828160 \, x^{4} + 4711680 \, x^{3} - 1689984 \, x^{2} + 1689984 \, x\right)} - 46199808 \, x\right)}\right)} \sqrt{247 \, \sqrt{2} + 1000} + 65450 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 2975 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{\sqrt{341} 50^{\frac{1}{4}} \sqrt{31} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(37 \, x - 38\right)} + x - 75\right)} \sqrt{247 \, \sqrt{2} + 1000} - 903805 \, x^{2} - 811580 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 2785195 \, x - 3689000}{x^{2}}} + 10605875 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{328782125 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 339388 \, \sqrt{341} 50^{\frac{1}{4}} \sqrt{10} \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} \sqrt{247 \, \sqrt{2} + 1000} \arctan\left(\frac{14260 \, \sqrt{341} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(22 \cdot 50^{\frac{3}{4}} {\left(57708 \, x^{7} - 181278 \, x^{6} + 400374 \, x^{5} - 525676 \, x^{4} + 235088 \, x^{3} - 46944 \, x^{2} - \sqrt{2} {\left(20846 \, x^{7} - 109153 \, x^{6} + 215386 \, x^{5} - 427391 \, x^{4} + 234360 \, x^{3} - 156600 \, x^{2} - 172800 \, x + 186624\right)} - 373248 \, x + 172800\right)} + 5 \cdot 50^{\frac{1}{4}} {\left(125839 \, x^{7} - 1864281 \, x^{6} + 9323336 \, x^{5} - 19725020 \, x^{4} + 24624288 \, x^{3} - 10862496 \, x^{2} - \sqrt{2} {\left(56119 \, x^{7} - 908994 \, x^{6} + 5175980 \, x^{5} - 12895624 \, x^{4} + 17261280 \, x^{3} - 14184000 \, x^{2} - 10533888 \, x + 9994752\right)} - 19989504 \, x + 10533888\right)}\right)} \sqrt{247 \, \sqrt{2} + 1000} - 933317000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{310}{119}} {\left(\sqrt{341} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(22 \cdot 50^{\frac{3}{4}} {\left(246848 \, x^{7} - 348192 \, x^{6} + 1080672 \, x^{5} - 178432 \, x^{4} - 18432 \, x^{3} + 1029888 \, x^{2} - \sqrt{2} {\left(46522 \, x^{7} - 71117 \, x^{6} + 257247 \, x^{5} - 273360 \, x^{4} + 484920 \, x^{3} - 269568 \, x^{2} + 269568 \, x\right)} - 1029888 \, x\right)} + 5 \cdot 50^{\frac{1}{4}} {\left(516957 \, x^{7} - 6676948 \, x^{6} + 25569820 \, x^{5} - 31522752 \, x^{4} + 34450848 \, x^{3} + 46199808 \, x^{2} - 4 \, \sqrt{2} {\left(38689 \, x^{7} - 502244 \, x^{6} + 1967660 \, x^{5} - 2828160 \, x^{4} + 4711680 \, x^{3} - 1689984 \, x^{2} + 1689984 \, x\right)} - 46199808 \, x\right)}\right)} \sqrt{247 \, \sqrt{2} + 1000} - 65450 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 2975 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{\sqrt{341} 50^{\frac{1}{4}} \sqrt{31} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(37 \, x - 38\right)} + x - 75\right)} \sqrt{247 \, \sqrt{2} + 1000} + 903805 \, x^{2} + 811580 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 2785195 \, x + 3689000}{x^{2}}} - 10605875 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{328782125 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) - 23 \, \sqrt{341} 50^{\frac{1}{4}} \sqrt{31} \sqrt{10} {\left(2000 \, x^{2} - 247 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 1000 \, x + 3000\right)} \sqrt{247 \, \sqrt{2} + 1000} \log\left(\frac{3100000 \, {\left(\sqrt{341} 50^{\frac{1}{4}} \sqrt{31} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(37 \, x - 38\right)} + x - 75\right)} \sqrt{247 \, \sqrt{2} + 1000} + 903805 \, x^{2} + 811580 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 2785195 \, x + 3689000\right)}}{119 \, x^{2}}\right) + 23 \, \sqrt{341} 50^{\frac{1}{4}} \sqrt{31} \sqrt{10} {\left(2000 \, x^{2} - 247 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 1000 \, x + 3000\right)} \sqrt{247 \, \sqrt{2} + 1000} \log\left(-\frac{3100000 \, {\left(\sqrt{341} 50^{\frac{1}{4}} \sqrt{31} \sqrt{10} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(37 \, x - 38\right)} + x - 75\right)} \sqrt{247 \, \sqrt{2} + 1000} - 903805 \, x^{2} - 811580 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 2785195 \, x - 3689000\right)}}{119 \, x^{2}}\right) + 201271840 \, \sqrt{2 \, x^{2} - x + 3} {\left(6 \, x - 13\right)}}{50921775520 \, {\left(2 \, x^{2} - x + 3\right)}}"," ",0,"-1/50921775520*(339388*sqrt(341)*50^(1/4)*sqrt(10)*sqrt(2)*(2*x^2 - x + 3)*sqrt(247*sqrt(2) + 1000)*arctan(1/328782125*(14260*sqrt(341)*sqrt(10)*sqrt(2*x^2 - x + 3)*(22*50^(3/4)*(57708*x^7 - 181278*x^6 + 400374*x^5 - 525676*x^4 + 235088*x^3 - 46944*x^2 - sqrt(2)*(20846*x^7 - 109153*x^6 + 215386*x^5 - 427391*x^4 + 234360*x^3 - 156600*x^2 - 172800*x + 186624) - 373248*x + 172800) + 5*50^(1/4)*(125839*x^7 - 1864281*x^6 + 9323336*x^5 - 19725020*x^4 + 24624288*x^3 - 10862496*x^2 - sqrt(2)*(56119*x^7 - 908994*x^6 + 5175980*x^5 - 12895624*x^4 + 17261280*x^3 - 14184000*x^2 - 10533888*x + 9994752) - 19989504*x + 10533888))*sqrt(247*sqrt(2) + 1000) + 933317000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(310/119)*(sqrt(341)*sqrt(10)*sqrt(2*x^2 - x + 3)*(22*50^(3/4)*(246848*x^7 - 348192*x^6 + 1080672*x^5 - 178432*x^4 - 18432*x^3 + 1029888*x^2 - sqrt(2)*(46522*x^7 - 71117*x^6 + 257247*x^5 - 273360*x^4 + 484920*x^3 - 269568*x^2 + 269568*x) - 1029888*x) + 5*50^(1/4)*(516957*x^7 - 6676948*x^6 + 25569820*x^5 - 31522752*x^4 + 34450848*x^3 + 46199808*x^2 - 4*sqrt(2)*(38689*x^7 - 502244*x^6 + 1967660*x^5 - 2828160*x^4 + 4711680*x^3 - 1689984*x^2 + 1689984*x) - 46199808*x))*sqrt(247*sqrt(2) + 1000) + 65450*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 2975*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(sqrt(341)*50^(1/4)*sqrt(31)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(37*x - 38) + x - 75)*sqrt(247*sqrt(2) + 1000) - 903805*x^2 - 811580*sqrt(2)*(2*x^2 - x + 3) + 2785195*x - 3689000)/x^2) + 10605875*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 339388*sqrt(341)*50^(1/4)*sqrt(10)*sqrt(2)*(2*x^2 - x + 3)*sqrt(247*sqrt(2) + 1000)*arctan(1/328782125*(14260*sqrt(341)*sqrt(10)*sqrt(2*x^2 - x + 3)*(22*50^(3/4)*(57708*x^7 - 181278*x^6 + 400374*x^5 - 525676*x^4 + 235088*x^3 - 46944*x^2 - sqrt(2)*(20846*x^7 - 109153*x^6 + 215386*x^5 - 427391*x^4 + 234360*x^3 - 156600*x^2 - 172800*x + 186624) - 373248*x + 172800) + 5*50^(1/4)*(125839*x^7 - 1864281*x^6 + 9323336*x^5 - 19725020*x^4 + 24624288*x^3 - 10862496*x^2 - sqrt(2)*(56119*x^7 - 908994*x^6 + 5175980*x^5 - 12895624*x^4 + 17261280*x^3 - 14184000*x^2 - 10533888*x + 9994752) - 19989504*x + 10533888))*sqrt(247*sqrt(2) + 1000) - 933317000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(310/119)*(sqrt(341)*sqrt(10)*sqrt(2*x^2 - x + 3)*(22*50^(3/4)*(246848*x^7 - 348192*x^6 + 1080672*x^5 - 178432*x^4 - 18432*x^3 + 1029888*x^2 - sqrt(2)*(46522*x^7 - 71117*x^6 + 257247*x^5 - 273360*x^4 + 484920*x^3 - 269568*x^2 + 269568*x) - 1029888*x) + 5*50^(1/4)*(516957*x^7 - 6676948*x^6 + 25569820*x^5 - 31522752*x^4 + 34450848*x^3 + 46199808*x^2 - 4*sqrt(2)*(38689*x^7 - 502244*x^6 + 1967660*x^5 - 2828160*x^4 + 4711680*x^3 - 1689984*x^2 + 1689984*x) - 46199808*x))*sqrt(247*sqrt(2) + 1000) - 65450*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 2975*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((sqrt(341)*50^(1/4)*sqrt(31)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(37*x - 38) + x - 75)*sqrt(247*sqrt(2) + 1000) + 903805*x^2 + 811580*sqrt(2)*(2*x^2 - x + 3) - 2785195*x + 3689000)/x^2) - 10605875*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) - 23*sqrt(341)*50^(1/4)*sqrt(31)*sqrt(10)*(2000*x^2 - 247*sqrt(2)*(2*x^2 - x + 3) - 1000*x + 3000)*sqrt(247*sqrt(2) + 1000)*log(3100000/119*(sqrt(341)*50^(1/4)*sqrt(31)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(37*x - 38) + x - 75)*sqrt(247*sqrt(2) + 1000) + 903805*x^2 + 811580*sqrt(2)*(2*x^2 - x + 3) - 2785195*x + 3689000)/x^2) + 23*sqrt(341)*50^(1/4)*sqrt(31)*sqrt(10)*(2000*x^2 - 247*sqrt(2)*(2*x^2 - x + 3) - 1000*x + 3000)*sqrt(247*sqrt(2) + 1000)*log(-3100000/119*(sqrt(341)*50^(1/4)*sqrt(31)*sqrt(10)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(37*x - 38) + x - 75)*sqrt(247*sqrt(2) + 1000) - 903805*x^2 - 811580*sqrt(2)*(2*x^2 - x + 3) + 2785195*x - 3689000)/x^2) + 201271840*sqrt(2*x^2 - x + 3)*(6*x - 13))/(2*x^2 - x + 3)","B",0
91,1,2173,0,1.258645," ","integrate(1/(2*x^2-x+3)^(3/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{35183643812 \cdot 3446160200^{\frac{1}{4}} \sqrt{20755} \sqrt{341} \sqrt{2} {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)} \sqrt{129694447 \, \sqrt{2} + 207550000} \arctan\left(\frac{59193260 \, \sqrt{20755} {\left(11 \cdot 3446160200^{\frac{3}{4}} \sqrt{341} {\left(20748108 \, x^{7} - 87744678 \, x^{6} + 180517074 \, x^{5} - 311740976 \, x^{4} + 161753488 \, x^{3} - 89046144 \, x^{2} - \sqrt{2} {\left(18515146 \, x^{7} - 65709803 \, x^{6} + 140687186 \, x^{5} - 209710441 \, x^{4} + 101256360 \, x^{3} - 39198600 \, x^{2} - 126316800 \, x + 76909824\right)} - 153819648 \, x + 126316800\right)} + 643405 \cdot 3446160200^{\frac{1}{4}} \sqrt{341} {\left(1637219 \, x^{7} - 25548801 \, x^{6} + 138274456 \, x^{5} - 324967420 \, x^{4} + 425065248 \, x^{3} - 297030816 \, x^{2} - \sqrt{2} {\left(1361849 \, x^{7} - 20608224 \, x^{6} + 106575580 \, x^{5} - 236322704 \, x^{4} + 301502880 \, x^{3} - 169632000 \, x^{2} - 225358848 \, x + 143534592\right)} - 287069184 \, x + 225358848\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{129694447 \, \sqrt{2} + 207550000} + 6920408156831705561333000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{41510}{397951}} {\left(\sqrt{20755} {\left(11 \cdot 3446160200^{\frac{3}{4}} \sqrt{341} {\left(66710248 \, x^{7} - 96938292 \, x^{6} + 319739772 \, x^{5} - 172116032 \, x^{4} + 247423968 \, x^{3} + 38700288 \, x^{2} - \sqrt{2} {\left(71827622 \, x^{7} - 102266467 \, x^{6} + 323714097 \, x^{5} - 93357360 \, x^{4} + 79054920 \, x^{3} + 219532032 \, x^{2} - 219532032 \, x\right)} - 38700288 \, x\right)} + 643405 \cdot 3446160200^{\frac{1}{4}} \sqrt{341} {\left(5462397 \, x^{7} - 70721108 \, x^{6} + 273784220 \, x^{5} - 364358592 \, x^{4} + 506287008 \, x^{3} + 144903168 \, x^{2} - 2 \, \sqrt{2} {\left(2586013 \, x^{7} - 33428948 \, x^{6} + 128512220 \, x^{5} - 162918720 \, x^{4} + 196126560 \, x^{3} + 173705472 \, x^{2} - 173705472 \, x\right)} - 144903168 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{129694447 \, \sqrt{2} + 207550000} + 116912097033204550 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 5314186228782025 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{3446160200^{\frac{1}{4}} \sqrt{20755} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(6137 \, x + 12812\right)} - 18949 \, x + 6675\right)} \sqrt{129694447 \, \sqrt{2} + 207550000} - 388930324332445 \, x^{2} - 349243556543420 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 1198540387228555 \, x - 1587470711561000}{x^{2}}} + 78641001782178472287875 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{2437871055247532640924125 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 35183643812 \cdot 3446160200^{\frac{1}{4}} \sqrt{20755} \sqrt{341} \sqrt{2} {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)} \sqrt{129694447 \, \sqrt{2} + 207550000} \arctan\left(\frac{59193260 \, \sqrt{20755} {\left(11 \cdot 3446160200^{\frac{3}{4}} \sqrt{341} {\left(20748108 \, x^{7} - 87744678 \, x^{6} + 180517074 \, x^{5} - 311740976 \, x^{4} + 161753488 \, x^{3} - 89046144 \, x^{2} - \sqrt{2} {\left(18515146 \, x^{7} - 65709803 \, x^{6} + 140687186 \, x^{5} - 209710441 \, x^{4} + 101256360 \, x^{3} - 39198600 \, x^{2} - 126316800 \, x + 76909824\right)} - 153819648 \, x + 126316800\right)} + 643405 \cdot 3446160200^{\frac{1}{4}} \sqrt{341} {\left(1637219 \, x^{7} - 25548801 \, x^{6} + 138274456 \, x^{5} - 324967420 \, x^{4} + 425065248 \, x^{3} - 297030816 \, x^{2} - \sqrt{2} {\left(1361849 \, x^{7} - 20608224 \, x^{6} + 106575580 \, x^{5} - 236322704 \, x^{4} + 301502880 \, x^{3} - 169632000 \, x^{2} - 225358848 \, x + 143534592\right)} - 287069184 \, x + 225358848\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{129694447 \, \sqrt{2} + 207550000} - 6920408156831705561333000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{41510}{397951}} {\left(\sqrt{20755} {\left(11 \cdot 3446160200^{\frac{3}{4}} \sqrt{341} {\left(66710248 \, x^{7} - 96938292 \, x^{6} + 319739772 \, x^{5} - 172116032 \, x^{4} + 247423968 \, x^{3} + 38700288 \, x^{2} - \sqrt{2} {\left(71827622 \, x^{7} - 102266467 \, x^{6} + 323714097 \, x^{5} - 93357360 \, x^{4} + 79054920 \, x^{3} + 219532032 \, x^{2} - 219532032 \, x\right)} - 38700288 \, x\right)} + 643405 \cdot 3446160200^{\frac{1}{4}} \sqrt{341} {\left(5462397 \, x^{7} - 70721108 \, x^{6} + 273784220 \, x^{5} - 364358592 \, x^{4} + 506287008 \, x^{3} + 144903168 \, x^{2} - 2 \, \sqrt{2} {\left(2586013 \, x^{7} - 33428948 \, x^{6} + 128512220 \, x^{5} - 162918720 \, x^{4} + 196126560 \, x^{3} + 173705472 \, x^{2} - 173705472 \, x\right)} - 144903168 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{129694447 \, \sqrt{2} + 207550000} - 116912097033204550 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 5314186228782025 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{3446160200^{\frac{1}{4}} \sqrt{20755} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(6137 \, x + 12812\right)} - 18949 \, x + 6675\right)} \sqrt{129694447 \, \sqrt{2} + 207550000} + 388930324332445 \, x^{2} + 349243556543420 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 1198540387228555 \, x + 1587470711561000}{x^{2}}} - 78641001782178472287875 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{2437871055247532640924125 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 23 \cdot 3446160200^{\frac{1}{4}} \sqrt{20755} \sqrt{341} \sqrt{31} {\left(2075500000 \, x^{4} + 207550000 \, x^{3} + 3320800000 \, x^{2} - 129694447 \, \sqrt{2} {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)} + 1452850000 \, x + 1245300000\right)} \sqrt{129694447 \, \sqrt{2} + 207550000} \log\left(\frac{1037750000000 \, {\left(3446160200^{\frac{1}{4}} \sqrt{20755} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(6137 \, x + 12812\right)} - 18949 \, x + 6675\right)} \sqrt{129694447 \, \sqrt{2} + 207550000} + 388930324332445 \, x^{2} + 349243556543420 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 1198540387228555 \, x + 1587470711561000\right)}}{397951 \, x^{2}}\right) - 23 \cdot 3446160200^{\frac{1}{4}} \sqrt{20755} \sqrt{341} \sqrt{31} {\left(2075500000 \, x^{4} + 207550000 \, x^{3} + 3320800000 \, x^{2} - 129694447 \, \sqrt{2} {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)} + 1452850000 \, x + 1245300000\right)} \sqrt{129694447 \, \sqrt{2} + 207550000} \log\left(-\frac{1037750000000 \, {\left(3446160200^{\frac{1}{4}} \sqrt{20755} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(6137 \, x + 12812\right)} - 18949 \, x + 6675\right)} \sqrt{129694447 \, \sqrt{2} + 207550000} - 388930324332445 \, x^{2} - 349243556543420 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 1198540387228555 \, x - 1587470711561000\right)}}{397951 \, x^{2}}\right) + 86612402022768160 \, {\left(11530 \, x^{3} - 24657 \, x^{2} + 18557 \, x - 10606\right)} \sqrt{2 \, x^{2} - x + 3}}{29889247038841109870720 \, {\left(10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6\right)}}"," ",0,"1/29889247038841109870720*(35183643812*3446160200^(1/4)*sqrt(20755)*sqrt(341)*sqrt(2)*(10*x^4 + x^3 + 16*x^2 + 7*x + 6)*sqrt(129694447*sqrt(2) + 207550000)*arctan(1/2437871055247532640924125*(59193260*sqrt(20755)*(11*3446160200^(3/4)*sqrt(341)*(20748108*x^7 - 87744678*x^6 + 180517074*x^5 - 311740976*x^4 + 161753488*x^3 - 89046144*x^2 - sqrt(2)*(18515146*x^7 - 65709803*x^6 + 140687186*x^5 - 209710441*x^4 + 101256360*x^3 - 39198600*x^2 - 126316800*x + 76909824) - 153819648*x + 126316800) + 643405*3446160200^(1/4)*sqrt(341)*(1637219*x^7 - 25548801*x^6 + 138274456*x^5 - 324967420*x^4 + 425065248*x^3 - 297030816*x^2 - sqrt(2)*(1361849*x^7 - 20608224*x^6 + 106575580*x^5 - 236322704*x^4 + 301502880*x^3 - 169632000*x^2 - 225358848*x + 143534592) - 287069184*x + 225358848))*sqrt(2*x^2 - x + 3)*sqrt(129694447*sqrt(2) + 207550000) + 6920408156831705561333000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(41510/397951)*(sqrt(20755)*(11*3446160200^(3/4)*sqrt(341)*(66710248*x^7 - 96938292*x^6 + 319739772*x^5 - 172116032*x^4 + 247423968*x^3 + 38700288*x^2 - sqrt(2)*(71827622*x^7 - 102266467*x^6 + 323714097*x^5 - 93357360*x^4 + 79054920*x^3 + 219532032*x^2 - 219532032*x) - 38700288*x) + 643405*3446160200^(1/4)*sqrt(341)*(5462397*x^7 - 70721108*x^6 + 273784220*x^5 - 364358592*x^4 + 506287008*x^3 + 144903168*x^2 - 2*sqrt(2)*(2586013*x^7 - 33428948*x^6 + 128512220*x^5 - 162918720*x^4 + 196126560*x^3 + 173705472*x^2 - 173705472*x) - 144903168*x))*sqrt(2*x^2 - x + 3)*sqrt(129694447*sqrt(2) + 207550000) + 116912097033204550*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 5314186228782025*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(3446160200^(1/4)*sqrt(20755)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(6137*x + 12812) - 18949*x + 6675)*sqrt(129694447*sqrt(2) + 207550000) - 388930324332445*x^2 - 349243556543420*sqrt(2)*(2*x^2 - x + 3) + 1198540387228555*x - 1587470711561000)/x^2) + 78641001782178472287875*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 35183643812*3446160200^(1/4)*sqrt(20755)*sqrt(341)*sqrt(2)*(10*x^4 + x^3 + 16*x^2 + 7*x + 6)*sqrt(129694447*sqrt(2) + 207550000)*arctan(1/2437871055247532640924125*(59193260*sqrt(20755)*(11*3446160200^(3/4)*sqrt(341)*(20748108*x^7 - 87744678*x^6 + 180517074*x^5 - 311740976*x^4 + 161753488*x^3 - 89046144*x^2 - sqrt(2)*(18515146*x^7 - 65709803*x^6 + 140687186*x^5 - 209710441*x^4 + 101256360*x^3 - 39198600*x^2 - 126316800*x + 76909824) - 153819648*x + 126316800) + 643405*3446160200^(1/4)*sqrt(341)*(1637219*x^7 - 25548801*x^6 + 138274456*x^5 - 324967420*x^4 + 425065248*x^3 - 297030816*x^2 - sqrt(2)*(1361849*x^7 - 20608224*x^6 + 106575580*x^5 - 236322704*x^4 + 301502880*x^3 - 169632000*x^2 - 225358848*x + 143534592) - 287069184*x + 225358848))*sqrt(2*x^2 - x + 3)*sqrt(129694447*sqrt(2) + 207550000) - 6920408156831705561333000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(41510/397951)*(sqrt(20755)*(11*3446160200^(3/4)*sqrt(341)*(66710248*x^7 - 96938292*x^6 + 319739772*x^5 - 172116032*x^4 + 247423968*x^3 + 38700288*x^2 - sqrt(2)*(71827622*x^7 - 102266467*x^6 + 323714097*x^5 - 93357360*x^4 + 79054920*x^3 + 219532032*x^2 - 219532032*x) - 38700288*x) + 643405*3446160200^(1/4)*sqrt(341)*(5462397*x^7 - 70721108*x^6 + 273784220*x^5 - 364358592*x^4 + 506287008*x^3 + 144903168*x^2 - 2*sqrt(2)*(2586013*x^7 - 33428948*x^6 + 128512220*x^5 - 162918720*x^4 + 196126560*x^3 + 173705472*x^2 - 173705472*x) - 144903168*x))*sqrt(2*x^2 - x + 3)*sqrt(129694447*sqrt(2) + 207550000) - 116912097033204550*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 5314186228782025*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((3446160200^(1/4)*sqrt(20755)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(6137*x + 12812) - 18949*x + 6675)*sqrt(129694447*sqrt(2) + 207550000) + 388930324332445*x^2 + 349243556543420*sqrt(2)*(2*x^2 - x + 3) - 1198540387228555*x + 1587470711561000)/x^2) - 78641001782178472287875*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 23*3446160200^(1/4)*sqrt(20755)*sqrt(341)*sqrt(31)*(2075500000*x^4 + 207550000*x^3 + 3320800000*x^2 - 129694447*sqrt(2)*(10*x^4 + x^3 + 16*x^2 + 7*x + 6) + 1452850000*x + 1245300000)*sqrt(129694447*sqrt(2) + 207550000)*log(1037750000000/397951*(3446160200^(1/4)*sqrt(20755)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(6137*x + 12812) - 18949*x + 6675)*sqrt(129694447*sqrt(2) + 207550000) + 388930324332445*x^2 + 349243556543420*sqrt(2)*(2*x^2 - x + 3) - 1198540387228555*x + 1587470711561000)/x^2) - 23*3446160200^(1/4)*sqrt(20755)*sqrt(341)*sqrt(31)*(2075500000*x^4 + 207550000*x^3 + 3320800000*x^2 - 129694447*sqrt(2)*(10*x^4 + x^3 + 16*x^2 + 7*x + 6) + 1452850000*x + 1245300000)*sqrt(129694447*sqrt(2) + 207550000)*log(-1037750000000/397951*(3446160200^(1/4)*sqrt(20755)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(6137*x + 12812) - 18949*x + 6675)*sqrt(129694447*sqrt(2) + 207550000) - 388930324332445*x^2 - 349243556543420*sqrt(2)*(2*x^2 - x + 3) + 1198540387228555*x - 1587470711561000)/x^2) + 86612402022768160*(11530*x^3 - 24657*x^2 + 18557*x - 10606)*sqrt(2*x^2 - x + 3))/(10*x^4 + x^3 + 16*x^2 + 7*x + 6)","B",0
92,1,2263,0,1.386383," ","integrate(1/(2*x^2-x+3)^(3/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{920746859815884 \cdot 1928545343086076450^{\frac{1}{4}} \sqrt{1963947730} \sqrt{341} \sqrt{2} {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} \arctan\left(\frac{2800589462980 \, \sqrt{1963947730} {\left(22 \cdot 1928545343086076450^{\frac{3}{4}} \sqrt{341} {\left(7361410004 \, x^{7} - 28555361914 \, x^{6} + 59872788262 \, x^{5} - 96593638888 \, x^{4} + 48573560944 \, x^{3} - 23355012672 \, x^{2} - \sqrt{2} {\left(5311119598 \, x^{7} - 20292577289 \, x^{6} + 42695479118 \, x^{5} - 68006818683 \, x^{4} + 33985514680 \, x^{3} - 15860251800 \, x^{2} - 37489478400 \, x + 26167456512\right)} - 52334913024 \, x + 37489478400\right)} + 30441189815 \cdot 1928545343086076450^{\frac{1}{4}} \sqrt{341} {\left(560592897 \, x^{7} - 8616399363 \, x^{6} + 45618625128 \, x^{5} - 104316505460 \, x^{4} + 134890825824 \, x^{3} - 85859939808 \, x^{2} - \sqrt{2} {\left(402019087 \, x^{7} - 6162703212 \, x^{6} + 32499503540 \, x^{5} - 73942829952 \, x^{4} + 95407993440 \, x^{3} - 59600016000 \, x^{2} - 68177562624 \, x + 47773380096\right)} - 95546760192 \, x + 68177562624\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} + 6393541085981955453231134497759874144159000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{1963947730}{3471424919}} {\left(\sqrt{1963947730} {\left(22 \cdot 1928545343086076450^{\frac{3}{4}} \sqrt{341} {\left(26184810824 \, x^{7} - 37618468196 \, x^{6} + 121297463436 \, x^{5} - 48741866816 \, x^{4} + 58784153184 \, x^{3} + 51583129344 \, x^{2} - \sqrt{2} {\left(19194187986 \, x^{7} - 27528525721 \, x^{6} + 88457613411 \, x^{5} - 33685377680 \, x^{4} + 38926767960 \, x^{3} + 41764674816 \, x^{2} - 41764674816 \, x\right)} - 51583129344 \, x\right)} + 30441189815 \cdot 1928545343086076450^{\frac{1}{4}} \sqrt{341} {\left(1998926311 \, x^{7} - 25858659004 \, x^{6} + 99738083860 \, x^{5} - 129415692096 \, x^{4} + 167446420704 \, x^{3} + 96037622784 \, x^{2} - 22 \, \sqrt{2} {\left(65886479 \, x^{7} - 852213084 \, x^{6} + 3285070260 \, x^{5} - 4244909760 \, x^{4} + 5424792480 \, x^{3} + 3393259776 \, x^{2} - 3393259776 \, x\right)} - 96037622784 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} + 2282926923240949861309948624550 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 103769405601861357332270392025 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{1928545343086076450^{\frac{1}{4}} \sqrt{1963947730} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(2995431 \, x + 1523456\right)} - 4518887 \, x - 1471975\right)} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} - 160519269124568199977215 \, x^{2} - 144139751866959199979540 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 494661421179791799929785 \, x - 655180690304359999907000}{x^{2}}} + 72653875977067675604899255656362206183625 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{2252270155289097943751876925347228391692375 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 920746859815884 \cdot 1928545343086076450^{\frac{1}{4}} \sqrt{1963947730} \sqrt{341} \sqrt{2} {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} \arctan\left(\frac{2800589462980 \, \sqrt{1963947730} {\left(22 \cdot 1928545343086076450^{\frac{3}{4}} \sqrt{341} {\left(7361410004 \, x^{7} - 28555361914 \, x^{6} + 59872788262 \, x^{5} - 96593638888 \, x^{4} + 48573560944 \, x^{3} - 23355012672 \, x^{2} - \sqrt{2} {\left(5311119598 \, x^{7} - 20292577289 \, x^{6} + 42695479118 \, x^{5} - 68006818683 \, x^{4} + 33985514680 \, x^{3} - 15860251800 \, x^{2} - 37489478400 \, x + 26167456512\right)} - 52334913024 \, x + 37489478400\right)} + 30441189815 \cdot 1928545343086076450^{\frac{1}{4}} \sqrt{341} {\left(560592897 \, x^{7} - 8616399363 \, x^{6} + 45618625128 \, x^{5} - 104316505460 \, x^{4} + 134890825824 \, x^{3} - 85859939808 \, x^{2} - \sqrt{2} {\left(402019087 \, x^{7} - 6162703212 \, x^{6} + 32499503540 \, x^{5} - 73942829952 \, x^{4} + 95407993440 \, x^{3} - 59600016000 \, x^{2} - 68177562624 \, x + 47773380096\right)} - 95546760192 \, x + 68177562624\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} - 6393541085981955453231134497759874144159000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{1963947730}{3471424919}} {\left(\sqrt{1963947730} {\left(22 \cdot 1928545343086076450^{\frac{3}{4}} \sqrt{341} {\left(26184810824 \, x^{7} - 37618468196 \, x^{6} + 121297463436 \, x^{5} - 48741866816 \, x^{4} + 58784153184 \, x^{3} + 51583129344 \, x^{2} - \sqrt{2} {\left(19194187986 \, x^{7} - 27528525721 \, x^{6} + 88457613411 \, x^{5} - 33685377680 \, x^{4} + 38926767960 \, x^{3} + 41764674816 \, x^{2} - 41764674816 \, x\right)} - 51583129344 \, x\right)} + 30441189815 \cdot 1928545343086076450^{\frac{1}{4}} \sqrt{341} {\left(1998926311 \, x^{7} - 25858659004 \, x^{6} + 99738083860 \, x^{5} - 129415692096 \, x^{4} + 167446420704 \, x^{3} + 96037622784 \, x^{2} - 22 \, \sqrt{2} {\left(65886479 \, x^{7} - 852213084 \, x^{6} + 3285070260 \, x^{5} - 4244909760 \, x^{4} + 5424792480 \, x^{3} + 3393259776 \, x^{2} - 3393259776 \, x\right)} - 96037622784 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} - 2282926923240949861309948624550 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 103769405601861357332270392025 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{1928545343086076450^{\frac{1}{4}} \sqrt{1963947730} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(2995431 \, x + 1523456\right)} - 4518887 \, x - 1471975\right)} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} + 160519269124568199977215 \, x^{2} + 144139751866959199979540 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 494661421179791799929785 \, x + 655180690304359999907000}{x^{2}}} - 72653875977067675604899255656362206183625 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{2252270155289097943751876925347228391692375 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 69 \cdot 1928545343086076450^{\frac{1}{4}} \sqrt{1963947730} \sqrt{341} \sqrt{31} {\left(981973865000000 \, x^{6} + 687381705500000 \, x^{5} + 2022866161900000 \, x^{4} + 1669355570500000 \, x^{3} + 1630076615900000 \, x^{2} - 13874275807943 \, \sqrt{2} {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)} + 628463273600000 \, x + 235673727600000\right)} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} \log\left(\frac{1767552957000000000 \, {\left(1928545343086076450^{\frac{1}{4}} \sqrt{1963947730} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(2995431 \, x + 1523456\right)} - 4518887 \, x - 1471975\right)} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} + 160519269124568199977215 \, x^{2} + 144139751866959199979540 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 494661421179791799929785 \, x + 655180690304359999907000\right)}}{3471424919 \, x^{2}}\right) - 69 \cdot 1928545343086076450^{\frac{1}{4}} \sqrt{1963947730} \sqrt{341} \sqrt{31} {\left(981973865000000 \, x^{6} + 687381705500000 \, x^{5} + 2022866161900000 \, x^{4} + 1669355570500000 \, x^{3} + 1630076615900000 \, x^{2} - 13874275807943 \, \sqrt{2} {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)} + 628463273600000 \, x + 235673727600000\right)} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} \log\left(-\frac{1767552957000000000 \, {\left(1928545343086076450^{\frac{1}{4}} \sqrt{1963947730} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(2995431 \, x + 1523456\right)} - 4518887 \, x - 1471975\right)} \sqrt{13874275807943 \, \sqrt{2} + 19639477300000} - 160519269124568199977215 \, x^{2} - 144139751866959199979540 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 494661421179791799929785 \, x - 655180690304359999907000\right)}}{3471424919 \, x^{2}}\right) + 35746658463005881594925920 \, {\left(162716650 \, x^{5} + 86411405 \, x^{4} + 277167774 \, x^{3} + 175833195 \, x^{2} + 161806828 \, x + 22374044\right)} \sqrt{2 \, x^{2} - x + 3}}{33652296632397026886019646994897920 \, {\left(50 \, x^{6} + 35 \, x^{5} + 103 \, x^{4} + 85 \, x^{3} + 83 \, x^{2} + 32 \, x + 12\right)}}"," ",0,"1/33652296632397026886019646994897920*(920746859815884*1928545343086076450^(1/4)*sqrt(1963947730)*sqrt(341)*sqrt(2)*(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12)*sqrt(13874275807943*sqrt(2) + 19639477300000)*arctan(1/2252270155289097943751876925347228391692375*(2800589462980*sqrt(1963947730)*(22*1928545343086076450^(3/4)*sqrt(341)*(7361410004*x^7 - 28555361914*x^6 + 59872788262*x^5 - 96593638888*x^4 + 48573560944*x^3 - 23355012672*x^2 - sqrt(2)*(5311119598*x^7 - 20292577289*x^6 + 42695479118*x^5 - 68006818683*x^4 + 33985514680*x^3 - 15860251800*x^2 - 37489478400*x + 26167456512) - 52334913024*x + 37489478400) + 30441189815*1928545343086076450^(1/4)*sqrt(341)*(560592897*x^7 - 8616399363*x^6 + 45618625128*x^5 - 104316505460*x^4 + 134890825824*x^3 - 85859939808*x^2 - sqrt(2)*(402019087*x^7 - 6162703212*x^6 + 32499503540*x^5 - 73942829952*x^4 + 95407993440*x^3 - 59600016000*x^2 - 68177562624*x + 47773380096) - 95546760192*x + 68177562624))*sqrt(2*x^2 - x + 3)*sqrt(13874275807943*sqrt(2) + 19639477300000) + 6393541085981955453231134497759874144159000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(1963947730/3471424919)*(sqrt(1963947730)*(22*1928545343086076450^(3/4)*sqrt(341)*(26184810824*x^7 - 37618468196*x^6 + 121297463436*x^5 - 48741866816*x^4 + 58784153184*x^3 + 51583129344*x^2 - sqrt(2)*(19194187986*x^7 - 27528525721*x^6 + 88457613411*x^5 - 33685377680*x^4 + 38926767960*x^3 + 41764674816*x^2 - 41764674816*x) - 51583129344*x) + 30441189815*1928545343086076450^(1/4)*sqrt(341)*(1998926311*x^7 - 25858659004*x^6 + 99738083860*x^5 - 129415692096*x^4 + 167446420704*x^3 + 96037622784*x^2 - 22*sqrt(2)*(65886479*x^7 - 852213084*x^6 + 3285070260*x^5 - 4244909760*x^4 + 5424792480*x^3 + 3393259776*x^2 - 3393259776*x) - 96037622784*x))*sqrt(2*x^2 - x + 3)*sqrt(13874275807943*sqrt(2) + 19639477300000) + 2282926923240949861309948624550*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 103769405601861357332270392025*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(1928545343086076450^(1/4)*sqrt(1963947730)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(2995431*x + 1523456) - 4518887*x - 1471975)*sqrt(13874275807943*sqrt(2) + 19639477300000) - 160519269124568199977215*x^2 - 144139751866959199979540*sqrt(2)*(2*x^2 - x + 3) + 494661421179791799929785*x - 655180690304359999907000)/x^2) + 72653875977067675604899255656362206183625*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 920746859815884*1928545343086076450^(1/4)*sqrt(1963947730)*sqrt(341)*sqrt(2)*(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12)*sqrt(13874275807943*sqrt(2) + 19639477300000)*arctan(1/2252270155289097943751876925347228391692375*(2800589462980*sqrt(1963947730)*(22*1928545343086076450^(3/4)*sqrt(341)*(7361410004*x^7 - 28555361914*x^6 + 59872788262*x^5 - 96593638888*x^4 + 48573560944*x^3 - 23355012672*x^2 - sqrt(2)*(5311119598*x^7 - 20292577289*x^6 + 42695479118*x^5 - 68006818683*x^4 + 33985514680*x^3 - 15860251800*x^2 - 37489478400*x + 26167456512) - 52334913024*x + 37489478400) + 30441189815*1928545343086076450^(1/4)*sqrt(341)*(560592897*x^7 - 8616399363*x^6 + 45618625128*x^5 - 104316505460*x^4 + 134890825824*x^3 - 85859939808*x^2 - sqrt(2)*(402019087*x^7 - 6162703212*x^6 + 32499503540*x^5 - 73942829952*x^4 + 95407993440*x^3 - 59600016000*x^2 - 68177562624*x + 47773380096) - 95546760192*x + 68177562624))*sqrt(2*x^2 - x + 3)*sqrt(13874275807943*sqrt(2) + 19639477300000) - 6393541085981955453231134497759874144159000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(1963947730/3471424919)*(sqrt(1963947730)*(22*1928545343086076450^(3/4)*sqrt(341)*(26184810824*x^7 - 37618468196*x^6 + 121297463436*x^5 - 48741866816*x^4 + 58784153184*x^3 + 51583129344*x^2 - sqrt(2)*(19194187986*x^7 - 27528525721*x^6 + 88457613411*x^5 - 33685377680*x^4 + 38926767960*x^3 + 41764674816*x^2 - 41764674816*x) - 51583129344*x) + 30441189815*1928545343086076450^(1/4)*sqrt(341)*(1998926311*x^7 - 25858659004*x^6 + 99738083860*x^5 - 129415692096*x^4 + 167446420704*x^3 + 96037622784*x^2 - 22*sqrt(2)*(65886479*x^7 - 852213084*x^6 + 3285070260*x^5 - 4244909760*x^4 + 5424792480*x^3 + 3393259776*x^2 - 3393259776*x) - 96037622784*x))*sqrt(2*x^2 - x + 3)*sqrt(13874275807943*sqrt(2) + 19639477300000) - 2282926923240949861309948624550*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 103769405601861357332270392025*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((1928545343086076450^(1/4)*sqrt(1963947730)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(2995431*x + 1523456) - 4518887*x - 1471975)*sqrt(13874275807943*sqrt(2) + 19639477300000) + 160519269124568199977215*x^2 + 144139751866959199979540*sqrt(2)*(2*x^2 - x + 3) - 494661421179791799929785*x + 655180690304359999907000)/x^2) - 72653875977067675604899255656362206183625*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 69*1928545343086076450^(1/4)*sqrt(1963947730)*sqrt(341)*sqrt(31)*(981973865000000*x^6 + 687381705500000*x^5 + 2022866161900000*x^4 + 1669355570500000*x^3 + 1630076615900000*x^2 - 13874275807943*sqrt(2)*(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12) + 628463273600000*x + 235673727600000)*sqrt(13874275807943*sqrt(2) + 19639477300000)*log(1767552957000000000/3471424919*(1928545343086076450^(1/4)*sqrt(1963947730)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(2995431*x + 1523456) - 4518887*x - 1471975)*sqrt(13874275807943*sqrt(2) + 19639477300000) + 160519269124568199977215*x^2 + 144139751866959199979540*sqrt(2)*(2*x^2 - x + 3) - 494661421179791799929785*x + 655180690304359999907000)/x^2) - 69*1928545343086076450^(1/4)*sqrt(1963947730)*sqrt(341)*sqrt(31)*(981973865000000*x^6 + 687381705500000*x^5 + 2022866161900000*x^4 + 1669355570500000*x^3 + 1630076615900000*x^2 - 13874275807943*sqrt(2)*(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12) + 628463273600000*x + 235673727600000)*sqrt(13874275807943*sqrt(2) + 19639477300000)*log(-1767552957000000000/3471424919*(1928545343086076450^(1/4)*sqrt(1963947730)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(2995431*x + 1523456) - 4518887*x - 1471975)*sqrt(13874275807943*sqrt(2) + 19639477300000) - 160519269124568199977215*x^2 - 144139751866959199979540*sqrt(2)*(2*x^2 - x + 3) + 494661421179791799929785*x - 655180690304359999907000)/x^2) + 35746658463005881594925920*(162716650*x^5 + 86411405*x^4 + 277167774*x^3 + 175833195*x^2 + 161806828*x + 22374044)*sqrt(2*x^2 - x + 3))/(50*x^6 + 35*x^5 + 103*x^4 + 85*x^3 + 83*x^2 + 32*x + 12)","B",0
93,1,132,0,0.422554," ","integrate((5*x^2+3*x+2)^4/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{26907897639 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(507840000 \, x^{7} + 2090608000 \, x^{6} + 3504730800 \, x^{5} - 5076781260 \, x^{4} + 39848900984 \, x^{3} - 36481630395 \, x^{2} + 49883864262 \, x - 18974698519\right)} \sqrt{2 \, x^{2} - x + 3}}{52002816 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/52002816*(26907897639*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(507840000*x^7 + 2090608000*x^6 + 3504730800*x^5 - 5076781260*x^4 + 39848900984*x^3 - 36481630395*x^2 + 49883864262*x - 18974698519)*sqrt(2*x^2 - x + 3))/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
94,1,122,0,0.425669," ","integrate((5*x^2+3*x+2)^3/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{11894565 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) + 8 \, {\left(3174000 \, x^{5} + 16980900 \, x^{4} - 29423976 \, x^{3} + 101546529 \, x^{2} - 62463282 \, x + 89784565\right)} \sqrt{2 \, x^{2} - x + 3}}{812544 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/812544*(11894565*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) + 8*(3174000*x^5 + 16980900*x^4 - 29423976*x^3 + 101546529*x^2 - 62463282*x + 89784565)*sqrt(2*x^2 - x + 3))/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
95,1,112,0,0.407619," ","integrate((5*x^2+3*x+2)^2/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{39675 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \log\left(-4 \, \sqrt{2} \sqrt{2 \, x^{2} - x + 3} {\left(4 \, x - 1\right)} - 32 \, x^{2} + 16 \, x - 25\right) - 88 \, {\left(2336 \, x^{3} + 6183 \, x^{2} + 714 \, x + 8623\right)} \sqrt{2 \, x^{2} - x + 3}}{25392 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/25392*(39675*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*log(-4*sqrt(2)*sqrt(2*x^2 - x + 3)*(4*x - 1) - 32*x^2 + 16*x - 25) - 88*(2336*x^3 + 6183*x^2 + 714*x + 8623)*sqrt(2*x^2 - x + 3))/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","B",0
96,1,51,0,0.404058," ","integrate((5*x^2+3*x+2)/(2*x^2-x+3)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(852 \, x^{3} - 639 \, x^{2} + 1005 \, x - 952\right)} \sqrt{2 \, x^{2} - x + 3}}{1587 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"2/1587*(852*x^3 - 639*x^2 + 1005*x - 952)*sqrt(2*x^2 - x + 3)/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","A",0
97,1,2133,0,1.238767," ","integrate(1/(2*x^2-x+3)^(5/2)/(5*x^2+3*x+2),x, algorithm=""fricas"")","\frac{1123856268 \, \sqrt{341} 200^{\frac{1}{4}} \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} \arctan\left(-\frac{71300 \, \sqrt{341} \sqrt{2 \, x^{2} - x + 3} {\left(11 \cdot 200^{\frac{3}{4}} {\left(347404 \, x^{7} - 907814 \, x^{6} + 2112962 \, x^{5} - 2166688 \, x^{4} + 787344 \, x^{3} + 304128 \, x^{2} - \sqrt{2} {\left(35898 \, x^{7} - 441939 \, x^{6} + 782418 \, x^{5} - 2117233 \, x^{4} + 1272680 \, x^{3} - 1081800 \, x^{2} - 518400 \, x + 1043712\right)} - 2087424 \, x + 518400\right)} + 5 \cdot 200^{\frac{1}{4}} {\left(712757 \, x^{7} - 10233303 \, x^{6} + 48529768 \, x^{5} - 94500260 \, x^{4} + 113086944 \, x^{3} - 22282848 \, x^{2} - \sqrt{2} {\left(158647 \, x^{7} - 2935272 \, x^{6} + 19428740 \, x^{5} - 55765712 \, x^{4} + 78380640 \, x^{3} - 84096000 \, x^{2} - 37407744 \, x + 53208576\right)} - 106417152 \, x + 37407744\right)}\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} + 22395686500000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{310}{5711}} {\left(\sqrt{341} \sqrt{2 \, x^{2} - x + 3} {\left(11 \cdot 200^{\frac{3}{4}} {\left(1665224 \, x^{7} - 2325796 \, x^{6} + 7065036 \, x^{5} - 196416 \, x^{4} - 2176416 \, x^{3} + 8895744 \, x^{2} + \sqrt{2} {\left(167914 \, x^{7} - 195429 \, x^{6} + 331239 \, x^{5} + 1685680 \, x^{4} - 3693960 \, x^{3} + 4195584 \, x^{2} - 4195584 \, x\right)} - 8895744 \, x\right)} + 5 \cdot 200^{\frac{1}{4}} {\left(3246491 \, x^{7} - 41888524 \, x^{6} + 159670660 \, x^{5} - 190080576 \, x^{4} + 180496224 \, x^{3} + 376648704 \, x^{2} - 2 \, \sqrt{2} {\left(40239 \, x^{7} - 558044 \, x^{6} + 2804660 \, x^{5} - 9524160 \, x^{4} + 34843680 \, x^{3} - 74006784 \, x^{2} + 74006784 \, x\right)} - 376648704 \, x\right)}\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} + 314105000 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 14277500 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{\sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(281 \, x - 444\right)} + 163 \, x - 725\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} - 4337504500 \, x^{2} - 3894902000 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 13366595500 \, x - 17704100000}{x^{2}}} + 254496437500 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{7889389562500 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 1123856268 \, \sqrt{341} 200^{\frac{1}{4}} \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} \arctan\left(-\frac{71300 \, \sqrt{341} \sqrt{2 \, x^{2} - x + 3} {\left(11 \cdot 200^{\frac{3}{4}} {\left(347404 \, x^{7} - 907814 \, x^{6} + 2112962 \, x^{5} - 2166688 \, x^{4} + 787344 \, x^{3} + 304128 \, x^{2} - \sqrt{2} {\left(35898 \, x^{7} - 441939 \, x^{6} + 782418 \, x^{5} - 2117233 \, x^{4} + 1272680 \, x^{3} - 1081800 \, x^{2} - 518400 \, x + 1043712\right)} - 2087424 \, x + 518400\right)} + 5 \cdot 200^{\frac{1}{4}} {\left(712757 \, x^{7} - 10233303 \, x^{6} + 48529768 \, x^{5} - 94500260 \, x^{4} + 113086944 \, x^{3} - 22282848 \, x^{2} - \sqrt{2} {\left(158647 \, x^{7} - 2935272 \, x^{6} + 19428740 \, x^{5} - 55765712 \, x^{4} + 78380640 \, x^{3} - 84096000 \, x^{2} - 37407744 \, x + 53208576\right)} - 106417152 \, x + 37407744\right)}\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} - 22395686500000 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - \sqrt{\frac{310}{5711}} {\left(\sqrt{341} \sqrt{2 \, x^{2} - x + 3} {\left(11 \cdot 200^{\frac{3}{4}} {\left(1665224 \, x^{7} - 2325796 \, x^{6} + 7065036 \, x^{5} - 196416 \, x^{4} - 2176416 \, x^{3} + 8895744 \, x^{2} + \sqrt{2} {\left(167914 \, x^{7} - 195429 \, x^{6} + 331239 \, x^{5} + 1685680 \, x^{4} - 3693960 \, x^{3} + 4195584 \, x^{2} - 4195584 \, x\right)} - 8895744 \, x\right)} + 5 \cdot 200^{\frac{1}{4}} {\left(3246491 \, x^{7} - 41888524 \, x^{6} + 159670660 \, x^{5} - 190080576 \, x^{4} + 180496224 \, x^{3} + 376648704 \, x^{2} - 2 \, \sqrt{2} {\left(40239 \, x^{7} - 558044 \, x^{6} + 2804660 \, x^{5} - 9524160 \, x^{4} + 34843680 \, x^{3} - 74006784 \, x^{2} + 74006784 \, x\right)} - 376648704 \, x\right)}\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} - 314105000 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 14277500 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{\sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(281 \, x - 444\right)} + 163 \, x - 725\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} + 4337504500 \, x^{2} + 3894902000 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 13366595500 \, x + 17704100000}{x^{2}}} - 254496437500 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{7889389562500 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 1587 \, \sqrt{341} 200^{\frac{1}{4}} \sqrt{31} {\left(200000 \, x^{4} - 200000 \, x^{3} + 650000 \, x^{2} + 15457 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} - 300000 \, x + 450000\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} \log\left(\frac{77500000 \, {\left(\sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(281 \, x - 444\right)} + 163 \, x - 725\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} + 4337504500 \, x^{2} + 3894902000 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 13366595500 \, x + 17704100000\right)}}{5711 \, x^{2}}\right) - 1587 \, \sqrt{341} 200^{\frac{1}{4}} \sqrt{31} {\left(200000 \, x^{4} - 200000 \, x^{3} + 650000 \, x^{2} + 15457 \, \sqrt{2} {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)} - 300000 \, x + 450000\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} \log\left(-\frac{77500000 \, {\left(\sqrt{341} 200^{\frac{1}{4}} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(281 \, x - 444\right)} + 163 \, x - 725\right)} \sqrt{-772850000 \, \sqrt{2} + 2500000000} - 4337504500 \, x^{2} - 3894902000 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 13366595500 \, x - 17704100000\right)}}{5711 \, x^{2}}\right) - 965935696000 \, {\left(3948 \, x^{3} - 23592 \, x^{2} + 19767 \, x - 39005\right)} \sqrt{2 \, x^{2} - x + 3}}{370971467791584000 \, {\left(4 \, x^{4} - 4 \, x^{3} + 13 \, x^{2} - 6 \, x + 9\right)}}"," ",0,"1/370971467791584000*(1123856268*sqrt(341)*200^(1/4)*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*sqrt(-772850000*sqrt(2) + 2500000000)*arctan(-1/7889389562500*(71300*sqrt(341)*sqrt(2*x^2 - x + 3)*(11*200^(3/4)*(347404*x^7 - 907814*x^6 + 2112962*x^5 - 2166688*x^4 + 787344*x^3 + 304128*x^2 - sqrt(2)*(35898*x^7 - 441939*x^6 + 782418*x^5 - 2117233*x^4 + 1272680*x^3 - 1081800*x^2 - 518400*x + 1043712) - 2087424*x + 518400) + 5*200^(1/4)*(712757*x^7 - 10233303*x^6 + 48529768*x^5 - 94500260*x^4 + 113086944*x^3 - 22282848*x^2 - sqrt(2)*(158647*x^7 - 2935272*x^6 + 19428740*x^5 - 55765712*x^4 + 78380640*x^3 - 84096000*x^2 - 37407744*x + 53208576) - 106417152*x + 37407744))*sqrt(-772850000*sqrt(2) + 2500000000) + 22395686500000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(310/5711)*(sqrt(341)*sqrt(2*x^2 - x + 3)*(11*200^(3/4)*(1665224*x^7 - 2325796*x^6 + 7065036*x^5 - 196416*x^4 - 2176416*x^3 + 8895744*x^2 + sqrt(2)*(167914*x^7 - 195429*x^6 + 331239*x^5 + 1685680*x^4 - 3693960*x^3 + 4195584*x^2 - 4195584*x) - 8895744*x) + 5*200^(1/4)*(3246491*x^7 - 41888524*x^6 + 159670660*x^5 - 190080576*x^4 + 180496224*x^3 + 376648704*x^2 - 2*sqrt(2)*(40239*x^7 - 558044*x^6 + 2804660*x^5 - 9524160*x^4 + 34843680*x^3 - 74006784*x^2 + 74006784*x) - 376648704*x))*sqrt(-772850000*sqrt(2) + 2500000000) + 314105000*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 14277500*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(sqrt(341)*200^(1/4)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(281*x - 444) + 163*x - 725)*sqrt(-772850000*sqrt(2) + 2500000000) - 4337504500*x^2 - 3894902000*sqrt(2)*(2*x^2 - x + 3) + 13366595500*x - 17704100000)/x^2) + 254496437500*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 1123856268*sqrt(341)*200^(1/4)*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)*sqrt(-772850000*sqrt(2) + 2500000000)*arctan(-1/7889389562500*(71300*sqrt(341)*sqrt(2*x^2 - x + 3)*(11*200^(3/4)*(347404*x^7 - 907814*x^6 + 2112962*x^5 - 2166688*x^4 + 787344*x^3 + 304128*x^2 - sqrt(2)*(35898*x^7 - 441939*x^6 + 782418*x^5 - 2117233*x^4 + 1272680*x^3 - 1081800*x^2 - 518400*x + 1043712) - 2087424*x + 518400) + 5*200^(1/4)*(712757*x^7 - 10233303*x^6 + 48529768*x^5 - 94500260*x^4 + 113086944*x^3 - 22282848*x^2 - sqrt(2)*(158647*x^7 - 2935272*x^6 + 19428740*x^5 - 55765712*x^4 + 78380640*x^3 - 84096000*x^2 - 37407744*x + 53208576) - 106417152*x + 37407744))*sqrt(-772850000*sqrt(2) + 2500000000) - 22395686500000*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - sqrt(310/5711)*(sqrt(341)*sqrt(2*x^2 - x + 3)*(11*200^(3/4)*(1665224*x^7 - 2325796*x^6 + 7065036*x^5 - 196416*x^4 - 2176416*x^3 + 8895744*x^2 + sqrt(2)*(167914*x^7 - 195429*x^6 + 331239*x^5 + 1685680*x^4 - 3693960*x^3 + 4195584*x^2 - 4195584*x) - 8895744*x) + 5*200^(1/4)*(3246491*x^7 - 41888524*x^6 + 159670660*x^5 - 190080576*x^4 + 180496224*x^3 + 376648704*x^2 - 2*sqrt(2)*(40239*x^7 - 558044*x^6 + 2804660*x^5 - 9524160*x^4 + 34843680*x^3 - 74006784*x^2 + 74006784*x) - 376648704*x))*sqrt(-772850000*sqrt(2) + 2500000000) - 314105000*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 14277500*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((sqrt(341)*200^(1/4)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(281*x - 444) + 163*x - 725)*sqrt(-772850000*sqrt(2) + 2500000000) + 4337504500*x^2 + 3894902000*sqrt(2)*(2*x^2 - x + 3) - 13366595500*x + 17704100000)/x^2) - 254496437500*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 1587*sqrt(341)*200^(1/4)*sqrt(31)*(200000*x^4 - 200000*x^3 + 650000*x^2 + 15457*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9) - 300000*x + 450000)*sqrt(-772850000*sqrt(2) + 2500000000)*log(77500000/5711*(sqrt(341)*200^(1/4)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(281*x - 444) + 163*x - 725)*sqrt(-772850000*sqrt(2) + 2500000000) + 4337504500*x^2 + 3894902000*sqrt(2)*(2*x^2 - x + 3) - 13366595500*x + 17704100000)/x^2) - 1587*sqrt(341)*200^(1/4)*sqrt(31)*(200000*x^4 - 200000*x^3 + 650000*x^2 + 15457*sqrt(2)*(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9) - 300000*x + 450000)*sqrt(-772850000*sqrt(2) + 2500000000)*log(-77500000/5711*(sqrt(341)*200^(1/4)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(281*x - 444) + 163*x - 725)*sqrt(-772850000*sqrt(2) + 2500000000) - 4337504500*x^2 - 3894902000*sqrt(2)*(2*x^2 - x + 3) + 13366595500*x - 17704100000)/x^2) - 965935696000*(3948*x^3 - 23592*x^2 + 19767*x - 39005)*sqrt(2*x^2 - x + 3))/(4*x^4 - 4*x^3 + 13*x^2 - 6*x + 9)","B",0
98,1,2253,0,1.193990," ","integrate(1/(2*x^2-x+3)^(5/2)/(5*x^2+3*x+2)^2,x, algorithm=""fricas"")","\frac{301208632500 \cdot 6962^{\frac{1}{4}} \sqrt{341} \sqrt{118} \sqrt{2} {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)} \sqrt{30463 \, \sqrt{2} + 47200} \arctan\left(\frac{168268 \, \sqrt{118} {\left(22 \cdot 6962^{\frac{3}{4}} \sqrt{341} {\left(321084 \, x^{7} - 1338894 \, x^{6} + 2762802 \, x^{5} - 4721048 \, x^{4} + 2438224 \, x^{3} - 1317312 \, x^{2} - \sqrt{2} {\left(277258 \, x^{7} - 994619 \, x^{6} + 2123978 \, x^{5} - 3198193 \, x^{4} + 1552680 \, x^{3} - 621000 \, x^{2} - 1900800 \, x + 1181952\right)} - 2363904 \, x + 1900800\right)} + 1829 \cdot 6962^{\frac{1}{4}} \sqrt{341} {\left(25187 \, x^{7} - 392073 \, x^{6} + 2114488 \, x^{5} - 4948060 \, x^{4} + 6460704 \, x^{3} - 4452768 \, x^{2} - \sqrt{2} {\left(20477 \, x^{7} - 310452 \, x^{6} + 1610140 \, x^{5} - 3584192 \, x^{4} + 4580640 \, x^{3} - 2620800 \, x^{2} - 3400704 \, x + 2198016\right)} - 4396032 \, x + 3400704\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{30463 \, \sqrt{2} + 47200} + 31558548641224 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{118}{79}} {\left(\sqrt{118} {\left(22 \cdot 6962^{\frac{3}{4}} \sqrt{341} {\left(1050904 \, x^{7} - 1523916 \, x^{6} + 5005956 \, x^{5} - 2572736 \, x^{4} + 3615264 \, x^{3} + 877824 \, x^{2} - \sqrt{2} {\left(1065206 \, x^{7} - 1518091 \, x^{6} + 4815081 \, x^{5} - 1448880 \, x^{4} + 1303560 \, x^{3} + 3131136 \, x^{2} - 3131136 \, x\right)} - 877824 \, x\right)} + 1829 \cdot 6962^{\frac{1}{4}} \sqrt{341} {\left(84981 \, x^{7} - 1100084 \, x^{6} + 4256060 \, x^{5} - 5639616 \, x^{4} + 7745184 \, x^{3} + 2571264 \, x^{2} - 242 \, \sqrt{2} {\left(319 \, x^{7} - 4124 \, x^{6} + 15860 \, x^{5} - 20160 \, x^{4} + 24480 \, x^{3} + 20736 \, x^{2} - 20736 \, x\right)} - 2571264 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{30463 \, \sqrt{2} + 47200} + 187549318 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 8524969 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{6962^{\frac{1}{4}} \sqrt{341} \sqrt{118} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(101 \, x + 176\right)} - 277 \, x + 75\right)} \sqrt{30463 \, \sqrt{2} + 47200} - 219481829 \, x^{2} - 197085724 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 676362371 \, x - 895844200}{x^{2}}} + 358619870923 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{11117215998613 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 301208632500 \cdot 6962^{\frac{1}{4}} \sqrt{341} \sqrt{118} \sqrt{2} {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)} \sqrt{30463 \, \sqrt{2} + 47200} \arctan\left(\frac{168268 \, \sqrt{118} {\left(22 \cdot 6962^{\frac{3}{4}} \sqrt{341} {\left(321084 \, x^{7} - 1338894 \, x^{6} + 2762802 \, x^{5} - 4721048 \, x^{4} + 2438224 \, x^{3} - 1317312 \, x^{2} - \sqrt{2} {\left(277258 \, x^{7} - 994619 \, x^{6} + 2123978 \, x^{5} - 3198193 \, x^{4} + 1552680 \, x^{3} - 621000 \, x^{2} - 1900800 \, x + 1181952\right)} - 2363904 \, x + 1900800\right)} + 1829 \cdot 6962^{\frac{1}{4}} \sqrt{341} {\left(25187 \, x^{7} - 392073 \, x^{6} + 2114488 \, x^{5} - 4948060 \, x^{4} + 6460704 \, x^{3} - 4452768 \, x^{2} - \sqrt{2} {\left(20477 \, x^{7} - 310452 \, x^{6} + 1610140 \, x^{5} - 3584192 \, x^{4} + 4580640 \, x^{3} - 2620800 \, x^{2} - 3400704 \, x + 2198016\right)} - 4396032 \, x + 3400704\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{30463 \, \sqrt{2} + 47200} - 31558548641224 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{118}{79}} {\left(\sqrt{118} {\left(22 \cdot 6962^{\frac{3}{4}} \sqrt{341} {\left(1050904 \, x^{7} - 1523916 \, x^{6} + 5005956 \, x^{5} - 2572736 \, x^{4} + 3615264 \, x^{3} + 877824 \, x^{2} - \sqrt{2} {\left(1065206 \, x^{7} - 1518091 \, x^{6} + 4815081 \, x^{5} - 1448880 \, x^{4} + 1303560 \, x^{3} + 3131136 \, x^{2} - 3131136 \, x\right)} - 877824 \, x\right)} + 1829 \cdot 6962^{\frac{1}{4}} \sqrt{341} {\left(84981 \, x^{7} - 1100084 \, x^{6} + 4256060 \, x^{5} - 5639616 \, x^{4} + 7745184 \, x^{3} + 2571264 \, x^{2} - 242 \, \sqrt{2} {\left(319 \, x^{7} - 4124 \, x^{6} + 15860 \, x^{5} - 20160 \, x^{4} + 24480 \, x^{3} + 20736 \, x^{2} - 20736 \, x\right)} - 2571264 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{30463 \, \sqrt{2} + 47200} - 187549318 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 8524969 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{6962^{\frac{1}{4}} \sqrt{341} \sqrt{118} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(101 \, x + 176\right)} - 277 \, x + 75\right)} \sqrt{30463 \, \sqrt{2} + 47200} + 219481829 \, x^{2} + 197085724 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 676362371 \, x + 895844200}{x^{2}}} - 358619870923 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{11117215998613 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 991875 \cdot 6962^{\frac{1}{4}} \sqrt{341} \sqrt{118} \sqrt{31} {\left(944000 \, x^{6} - 377600 \, x^{5} + 2879200 \, x^{4} + 47200 \, x^{3} + 2501600 \, x^{2} - 30463 \, \sqrt{2} {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)} + 708000 \, x + 849600\right)} \sqrt{30463 \, \sqrt{2} + 47200} \log\left(\frac{7375000000000 \, {\left(6962^{\frac{1}{4}} \sqrt{341} \sqrt{118} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(101 \, x + 176\right)} - 277 \, x + 75\right)} \sqrt{30463 \, \sqrt{2} + 47200} + 219481829 \, x^{2} + 197085724 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 676362371 \, x + 895844200\right)}}{79 \, x^{2}}\right) - 991875 \cdot 6962^{\frac{1}{4}} \sqrt{341} \sqrt{118} \sqrt{31} {\left(944000 \, x^{6} - 377600 \, x^{5} + 2879200 \, x^{4} + 47200 \, x^{3} + 2501600 \, x^{2} - 30463 \, \sqrt{2} {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)} + 708000 \, x + 849600\right)} \sqrt{30463 \, \sqrt{2} + 47200} \log\left(-\frac{7375000000000 \, {\left(6962^{\frac{1}{4}} \sqrt{341} \sqrt{118} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(101 \, x + 176\right)} - 277 \, x + 75\right)} \sqrt{30463 \, \sqrt{2} + 47200} - 219481829 \, x^{2} - 197085724 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 676362371 \, x - 895844200\right)}}{79 \, x^{2}}\right) - 48877259552 \, {\left(13525420 \, x^{5} + 32686812 \, x^{4} + 2879479 \, x^{3} + 84671384 \, x^{2} - 5712309 \, x + 31010342\right)} \sqrt{2 \, x^{2} - x + 3}}{25604335602537914112 \, {\left(20 \, x^{6} - 8 \, x^{5} + 61 \, x^{4} + x^{3} + 53 \, x^{2} + 15 \, x + 18\right)}}"," ",0,"1/25604335602537914112*(301208632500*6962^(1/4)*sqrt(341)*sqrt(118)*sqrt(2)*(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18)*sqrt(30463*sqrt(2) + 47200)*arctan(1/11117215998613*(168268*sqrt(118)*(22*6962^(3/4)*sqrt(341)*(321084*x^7 - 1338894*x^6 + 2762802*x^5 - 4721048*x^4 + 2438224*x^3 - 1317312*x^2 - sqrt(2)*(277258*x^7 - 994619*x^6 + 2123978*x^5 - 3198193*x^4 + 1552680*x^3 - 621000*x^2 - 1900800*x + 1181952) - 2363904*x + 1900800) + 1829*6962^(1/4)*sqrt(341)*(25187*x^7 - 392073*x^6 + 2114488*x^5 - 4948060*x^4 + 6460704*x^3 - 4452768*x^2 - sqrt(2)*(20477*x^7 - 310452*x^6 + 1610140*x^5 - 3584192*x^4 + 4580640*x^3 - 2620800*x^2 - 3400704*x + 2198016) - 4396032*x + 3400704))*sqrt(2*x^2 - x + 3)*sqrt(30463*sqrt(2) + 47200) + 31558548641224*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(118/79)*(sqrt(118)*(22*6962^(3/4)*sqrt(341)*(1050904*x^7 - 1523916*x^6 + 5005956*x^5 - 2572736*x^4 + 3615264*x^3 + 877824*x^2 - sqrt(2)*(1065206*x^7 - 1518091*x^6 + 4815081*x^5 - 1448880*x^4 + 1303560*x^3 + 3131136*x^2 - 3131136*x) - 877824*x) + 1829*6962^(1/4)*sqrt(341)*(84981*x^7 - 1100084*x^6 + 4256060*x^5 - 5639616*x^4 + 7745184*x^3 + 2571264*x^2 - 242*sqrt(2)*(319*x^7 - 4124*x^6 + 15860*x^5 - 20160*x^4 + 24480*x^3 + 20736*x^2 - 20736*x) - 2571264*x))*sqrt(2*x^2 - x + 3)*sqrt(30463*sqrt(2) + 47200) + 187549318*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 8524969*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(6962^(1/4)*sqrt(341)*sqrt(118)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(101*x + 176) - 277*x + 75)*sqrt(30463*sqrt(2) + 47200) - 219481829*x^2 - 197085724*sqrt(2)*(2*x^2 - x + 3) + 676362371*x - 895844200)/x^2) + 358619870923*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 301208632500*6962^(1/4)*sqrt(341)*sqrt(118)*sqrt(2)*(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18)*sqrt(30463*sqrt(2) + 47200)*arctan(1/11117215998613*(168268*sqrt(118)*(22*6962^(3/4)*sqrt(341)*(321084*x^7 - 1338894*x^6 + 2762802*x^5 - 4721048*x^4 + 2438224*x^3 - 1317312*x^2 - sqrt(2)*(277258*x^7 - 994619*x^6 + 2123978*x^5 - 3198193*x^4 + 1552680*x^3 - 621000*x^2 - 1900800*x + 1181952) - 2363904*x + 1900800) + 1829*6962^(1/4)*sqrt(341)*(25187*x^7 - 392073*x^6 + 2114488*x^5 - 4948060*x^4 + 6460704*x^3 - 4452768*x^2 - sqrt(2)*(20477*x^7 - 310452*x^6 + 1610140*x^5 - 3584192*x^4 + 4580640*x^3 - 2620800*x^2 - 3400704*x + 2198016) - 4396032*x + 3400704))*sqrt(2*x^2 - x + 3)*sqrt(30463*sqrt(2) + 47200) - 31558548641224*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(118/79)*(sqrt(118)*(22*6962^(3/4)*sqrt(341)*(1050904*x^7 - 1523916*x^6 + 5005956*x^5 - 2572736*x^4 + 3615264*x^3 + 877824*x^2 - sqrt(2)*(1065206*x^7 - 1518091*x^6 + 4815081*x^5 - 1448880*x^4 + 1303560*x^3 + 3131136*x^2 - 3131136*x) - 877824*x) + 1829*6962^(1/4)*sqrt(341)*(84981*x^7 - 1100084*x^6 + 4256060*x^5 - 5639616*x^4 + 7745184*x^3 + 2571264*x^2 - 242*sqrt(2)*(319*x^7 - 4124*x^6 + 15860*x^5 - 20160*x^4 + 24480*x^3 + 20736*x^2 - 20736*x) - 2571264*x))*sqrt(2*x^2 - x + 3)*sqrt(30463*sqrt(2) + 47200) - 187549318*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 8524969*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((6962^(1/4)*sqrt(341)*sqrt(118)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(101*x + 176) - 277*x + 75)*sqrt(30463*sqrt(2) + 47200) + 219481829*x^2 + 197085724*sqrt(2)*(2*x^2 - x + 3) - 676362371*x + 895844200)/x^2) - 358619870923*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 991875*6962^(1/4)*sqrt(341)*sqrt(118)*sqrt(31)*(944000*x^6 - 377600*x^5 + 2879200*x^4 + 47200*x^3 + 2501600*x^2 - 30463*sqrt(2)*(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18) + 708000*x + 849600)*sqrt(30463*sqrt(2) + 47200)*log(7375000000000/79*(6962^(1/4)*sqrt(341)*sqrt(118)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(101*x + 176) - 277*x + 75)*sqrt(30463*sqrt(2) + 47200) + 219481829*x^2 + 197085724*sqrt(2)*(2*x^2 - x + 3) - 676362371*x + 895844200)/x^2) - 991875*6962^(1/4)*sqrt(341)*sqrt(118)*sqrt(31)*(944000*x^6 - 377600*x^5 + 2879200*x^4 + 47200*x^3 + 2501600*x^2 - 30463*sqrt(2)*(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18) + 708000*x + 849600)*sqrt(30463*sqrt(2) + 47200)*log(-7375000000000/79*(6962^(1/4)*sqrt(341)*sqrt(118)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(101*x + 176) - 277*x + 75)*sqrt(30463*sqrt(2) + 47200) - 219481829*x^2 - 197085724*sqrt(2)*(2*x^2 - x + 3) + 676362371*x - 895844200)/x^2) - 48877259552*(13525420*x^5 + 32686812*x^4 + 2879479*x^3 + 84671384*x^2 - 5712309*x + 31010342)*sqrt(2*x^2 - x + 3))/(20*x^6 - 8*x^5 + 61*x^4 + x^3 + 53*x^2 + 15*x + 18)","B",0
99,1,2343,0,1.327404," ","integrate(1/(2*x^2-x+3)^(5/2)/(5*x^2+3*x+2)^3,x, algorithm=""fricas"")","\frac{2164988593398757980 \cdot 129508224872072^{\frac{1}{4}} \sqrt{4023497} \sqrt{341} \sqrt{2} {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} \arctan\left(\frac{11475013444 \, \sqrt{4023497} {\left(11 \cdot 129508224872072^{\frac{3}{4}} \sqrt{341} {\left(2673027292 \, x^{7} - 11768684222 \, x^{6} + 24008796626 \, x^{5} - 42687622824 \, x^{4} + 22428040912 \, x^{3} - 12956821056 \, x^{2} - \sqrt{2} {\left(2612082154 \, x^{7} - 9010050347 \, x^{6} + 19426337114 \, x^{5} - 28170626609 \, x^{4} + 13394761640 \, x^{3} - 4698131400 \, x^{2} - 17594323200 \, x + 10110341376\right)} - 20220682752 \, x + 17594323200\right)} + 124728407 \cdot 129508224872072^{\frac{1}{4}} \sqrt{341} {\left(214583731 \, x^{7} - 3372306249 \, x^{6} + 18434388344 \, x^{5} - 43845503580 \, x^{4} + 57631717152 \, x^{3} - 41786349984 \, x^{2} - \sqrt{2} {\left(190078101 \, x^{7} - 2862100476 \, x^{6} + 14688003420 \, x^{5} - 32231022496 \, x^{4} + 40927641120 \, x^{3} - 21959568000 \, x^{2} - 31156503552 \, x + 19060075008\right)} - 38120150016 \, x + 31156503552\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} + 1284612678018299582239382547725536472 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{8046994}{10139750351}} {\left(\sqrt{4023497} {\left(11 \cdot 129508224872072^{\frac{3}{4}} \sqrt{341} {\left(8140972152 \, x^{7} - 11907581308 \, x^{6} + 39777303828 \, x^{5} - 24395365568 \, x^{4} + 37103094432 \, x^{3} - 1836165888 \, x^{2} - \sqrt{2} {\left(10387383478 \, x^{7} - 14753211883 \, x^{6} + 46462095753 \, x^{5} - 11926110640 \, x^{4} + 8224291080 \, x^{3} + 34793549568 \, x^{2} - 34793549568 \, x\right)} + 1836165888 \, x\right)} + 124728407 \cdot 129508224872072^{\frac{1}{4}} \sqrt{341} {\left(692762453 \, x^{7} - 8972954292 \, x^{6} + 34803726780 \, x^{5} - 46915651008 \, x^{4} + 67421983392 \, x^{3} + 10625375232 \, x^{2} - 2 \, \sqrt{2} {\left(367903387 \, x^{7} - 4754813452 \, x^{6} + 18261523780 \, x^{5} - 22991417280 \, x^{4} + 27054001440 \, x^{3} + 26759248128 \, x^{2} - 26759248128 \, x\right)} - 10625375232 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} + 111948686098489209076292438 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} + 5088576640840418594376929 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{-\frac{129508224872072^{\frac{1}{4}} \sqrt{4023497} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(643213 \, x + 2195288\right)} - 2838501 \, x + 1552075\right)} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} - 1921101946251381781783 \, x^{2} - 1725071135409404048948 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 5920130487427727531617 \, x - 7841232433679109313400}{x^{2}}} + 14597871341117040707265710769608369 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{452534011574628261925237033857859439 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 2164988593398757980 \cdot 129508224872072^{\frac{1}{4}} \sqrt{4023497} \sqrt{341} \sqrt{2} {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} \arctan\left(\frac{11475013444 \, \sqrt{4023497} {\left(11 \cdot 129508224872072^{\frac{3}{4}} \sqrt{341} {\left(2673027292 \, x^{7} - 11768684222 \, x^{6} + 24008796626 \, x^{5} - 42687622824 \, x^{4} + 22428040912 \, x^{3} - 12956821056 \, x^{2} - \sqrt{2} {\left(2612082154 \, x^{7} - 9010050347 \, x^{6} + 19426337114 \, x^{5} - 28170626609 \, x^{4} + 13394761640 \, x^{3} - 4698131400 \, x^{2} - 17594323200 \, x + 10110341376\right)} - 20220682752 \, x + 17594323200\right)} + 124728407 \cdot 129508224872072^{\frac{1}{4}} \sqrt{341} {\left(214583731 \, x^{7} - 3372306249 \, x^{6} + 18434388344 \, x^{5} - 43845503580 \, x^{4} + 57631717152 \, x^{3} - 41786349984 \, x^{2} - \sqrt{2} {\left(190078101 \, x^{7} - 2862100476 \, x^{6} + 14688003420 \, x^{5} - 32231022496 \, x^{4} + 40927641120 \, x^{3} - 21959568000 \, x^{2} - 31156503552 \, x + 19060075008\right)} - 38120150016 \, x + 31156503552\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} - 1284612678018299582239382547725536472 \, \sqrt{31} \sqrt{2} {\left(28180 \, x^{8} - 254666 \, x^{7} + 704270 \, x^{6} - 1385256 \, x^{5} + 1549144 \, x^{4} - 642048 \, x^{3} - 98496 \, x^{2} - \sqrt{2} {\left(8746 \, x^{8} - 102335 \, x^{7} + 396104 \, x^{6} - 783113 \, x^{5} + 1320710 \, x^{4} - 752088 \, x^{3} + 396144 \, x^{2} + 546048 \, x - 539136\right)} + 1154304 \, x - 456192\right)} - 2 \, \sqrt{\frac{8046994}{10139750351}} {\left(\sqrt{4023497} {\left(11 \cdot 129508224872072^{\frac{3}{4}} \sqrt{341} {\left(8140972152 \, x^{7} - 11907581308 \, x^{6} + 39777303828 \, x^{5} - 24395365568 \, x^{4} + 37103094432 \, x^{3} - 1836165888 \, x^{2} - \sqrt{2} {\left(10387383478 \, x^{7} - 14753211883 \, x^{6} + 46462095753 \, x^{5} - 11926110640 \, x^{4} + 8224291080 \, x^{3} + 34793549568 \, x^{2} - 34793549568 \, x\right)} + 1836165888 \, x\right)} + 124728407 \cdot 129508224872072^{\frac{1}{4}} \sqrt{341} {\left(692762453 \, x^{7} - 8972954292 \, x^{6} + 34803726780 \, x^{5} - 46915651008 \, x^{4} + 67421983392 \, x^{3} + 10625375232 \, x^{2} - 2 \, \sqrt{2} {\left(367903387 \, x^{7} - 4754813452 \, x^{6} + 18261523780 \, x^{5} - 22991417280 \, x^{4} + 27054001440 \, x^{3} + 26759248128 \, x^{2} - 26759248128 \, x\right)} - 10625375232 \, x\right)}\right)} \sqrt{2 \, x^{2} - x + 3} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} - 111948686098489209076292438 \, \sqrt{31} \sqrt{2} {\left(123408 \, x^{8} - 914152 \, x^{7} + 1578888 \, x^{6} - 3293072 \, x^{5} + 396480 \, x^{4} + 798336 \, x^{3} - 3822336 \, x^{2} - \sqrt{2} {\left(15550 \, x^{8} - 118051 \, x^{7} + 244047 \, x^{6} - 707374 \, x^{5} + 1053960 \, x^{4} - 1667952 \, x^{3} + 1209600 \, x^{2} - 1036800 \, x\right)} + 3276288 \, x\right)} - 5088576640840418594376929 \, \sqrt{31} {\left(254591 \, x^{8} - 4815126 \, x^{7} + 32303580 \, x^{6} - 90866808 \, x^{5} + 108781920 \, x^{4} - 74219328 \, x^{3} - 168956928 \, x^{2} - 15488 \, \sqrt{2} {\left(4 \, x^{8} - 76 \, x^{7} + 517 \, x^{6} - 1536 \, x^{5} + 2385 \, x^{4} - 3618 \, x^{3} + 2268 \, x^{2} - 1944 \, x\right)} + 144820224 \, x\right)}\right)} \sqrt{\frac{129508224872072^{\frac{1}{4}} \sqrt{4023497} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(643213 \, x + 2195288\right)} - 2838501 \, x + 1552075\right)} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} + 1921101946251381781783 \, x^{2} + 1725071135409404048948 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 5920130487427727531617 \, x + 7841232433679109313400}{x^{2}}} - 14597871341117040707265710769608369 \, \sqrt{31} {\left(2828123 \, x^{8} - 9696916 \, x^{7} + 53385560 \, x^{6} - 142835344 \, x^{5} + 254146592 \, x^{4} - 249300096 \, x^{3} + 37981440 \, x^{2} - 7744 \, \sqrt{2} {\left(1348 \, x^{8} - 2692 \, x^{7} + 9789 \, x^{6} - 10070 \, x^{5} + 15569 \, x^{4} - 5568 \, x^{3} + 1080 \, x^{2} + 4320 \, x - 5184\right)} + 223064064 \, x - 94887936\right)}}{452534011574628261925237033857859439 \, {\left(2585191 \, x^{8} - 4661200 \, x^{7} + 14191920 \, x^{6} + 490880 \, x^{5} - 13562944 \, x^{4} + 44249088 \, x^{3} - 34615296 \, x^{2} - 24772608 \, x + 18579456\right)}}\right) + 55545 \cdot 129508224872072^{\frac{1}{4}} \sqrt{4023497} \sqrt{341} \sqrt{31} {\left(402349700000000 \, x^{8} + 80469940000000 \, x^{7} + 1291542537000000 \, x^{6} + 692041484000000 \, x^{5} + 1569163830000000 \, x^{4} + 949545292000000 \, x^{3} + 969662777000000 \, x^{2} - 2243059557247 \, \sqrt{2} {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)} + 337973748000000 \, x + 144845892000000\right)} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} \log\left(\frac{2464391912500000000000 \, {\left(129508224872072^{\frac{1}{4}} \sqrt{4023497} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(643213 \, x + 2195288\right)} - 2838501 \, x + 1552075\right)} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} + 1921101946251381781783 \, x^{2} + 1725071135409404048948 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} - 5920130487427727531617 \, x + 7841232433679109313400\right)}}{10139750351 \, x^{2}}\right) - 55545 \cdot 129508224872072^{\frac{1}{4}} \sqrt{4023497} \sqrt{341} \sqrt{31} {\left(402349700000000 \, x^{8} + 80469940000000 \, x^{7} + 1291542537000000 \, x^{6} + 692041484000000 \, x^{5} + 1569163830000000 \, x^{4} + 949545292000000 \, x^{3} + 969662777000000 \, x^{2} - 2243059557247 \, \sqrt{2} {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)} + 337973748000000 \, x + 144845892000000\right)} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} \log\left(-\frac{2464391912500000000000 \, {\left(129508224872072^{\frac{1}{4}} \sqrt{4023497} \sqrt{341} \sqrt{31} \sqrt{2 \, x^{2} - x + 3} {\left(\sqrt{2} {\left(643213 \, x + 2195288\right)} - 2838501 \, x + 1552075\right)} \sqrt{2243059557247 \, \sqrt{2} + 4023497000000} - 1921101946251381781783 \, x^{2} - 1725071135409404048948 \, \sqrt{2} {\left(2 \, x^{2} - x + 3\right)} + 5920130487427727531617 \, x - 7841232433679109313400\right)}}{10139750351 \, x^{2}}\right) + 427817641581532204139104 \, {\left(225699113100 \, x^{7} - 12234606480 \, x^{6} + 592923725931 \, x^{5} + 174241614961 \, x^{4} + 519223213785 \, x^{3} + 178650961091 \, x^{2} + 218659985088 \, x + 9739335532\right)} \sqrt{2 \, x^{2} - x + 3}}{611377875290135815296770157063555072 \, {\left(100 \, x^{8} + 20 \, x^{7} + 321 \, x^{6} + 172 \, x^{5} + 390 \, x^{4} + 236 \, x^{3} + 241 \, x^{2} + 84 \, x + 36\right)}}"," ",0,"1/611377875290135815296770157063555072*(2164988593398757980*129508224872072^(1/4)*sqrt(4023497)*sqrt(341)*sqrt(2)*(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36)*sqrt(2243059557247*sqrt(2) + 4023497000000)*arctan(1/452534011574628261925237033857859439*(11475013444*sqrt(4023497)*(11*129508224872072^(3/4)*sqrt(341)*(2673027292*x^7 - 11768684222*x^6 + 24008796626*x^5 - 42687622824*x^4 + 22428040912*x^3 - 12956821056*x^2 - sqrt(2)*(2612082154*x^7 - 9010050347*x^6 + 19426337114*x^5 - 28170626609*x^4 + 13394761640*x^3 - 4698131400*x^2 - 17594323200*x + 10110341376) - 20220682752*x + 17594323200) + 124728407*129508224872072^(1/4)*sqrt(341)*(214583731*x^7 - 3372306249*x^6 + 18434388344*x^5 - 43845503580*x^4 + 57631717152*x^3 - 41786349984*x^2 - sqrt(2)*(190078101*x^7 - 2862100476*x^6 + 14688003420*x^5 - 32231022496*x^4 + 40927641120*x^3 - 21959568000*x^2 - 31156503552*x + 19060075008) - 38120150016*x + 31156503552))*sqrt(2*x^2 - x + 3)*sqrt(2243059557247*sqrt(2) + 4023497000000) + 1284612678018299582239382547725536472*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(8046994/10139750351)*(sqrt(4023497)*(11*129508224872072^(3/4)*sqrt(341)*(8140972152*x^7 - 11907581308*x^6 + 39777303828*x^5 - 24395365568*x^4 + 37103094432*x^3 - 1836165888*x^2 - sqrt(2)*(10387383478*x^7 - 14753211883*x^6 + 46462095753*x^5 - 11926110640*x^4 + 8224291080*x^3 + 34793549568*x^2 - 34793549568*x) + 1836165888*x) + 124728407*129508224872072^(1/4)*sqrt(341)*(692762453*x^7 - 8972954292*x^6 + 34803726780*x^5 - 46915651008*x^4 + 67421983392*x^3 + 10625375232*x^2 - 2*sqrt(2)*(367903387*x^7 - 4754813452*x^6 + 18261523780*x^5 - 22991417280*x^4 + 27054001440*x^3 + 26759248128*x^2 - 26759248128*x) - 10625375232*x))*sqrt(2*x^2 - x + 3)*sqrt(2243059557247*sqrt(2) + 4023497000000) + 111948686098489209076292438*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) + 5088576640840418594376929*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt(-(129508224872072^(1/4)*sqrt(4023497)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(643213*x + 2195288) - 2838501*x + 1552075)*sqrt(2243059557247*sqrt(2) + 4023497000000) - 1921101946251381781783*x^2 - 1725071135409404048948*sqrt(2)*(2*x^2 - x + 3) + 5920130487427727531617*x - 7841232433679109313400)/x^2) + 14597871341117040707265710769608369*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 2164988593398757980*129508224872072^(1/4)*sqrt(4023497)*sqrt(341)*sqrt(2)*(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36)*sqrt(2243059557247*sqrt(2) + 4023497000000)*arctan(1/452534011574628261925237033857859439*(11475013444*sqrt(4023497)*(11*129508224872072^(3/4)*sqrt(341)*(2673027292*x^7 - 11768684222*x^6 + 24008796626*x^5 - 42687622824*x^4 + 22428040912*x^3 - 12956821056*x^2 - sqrt(2)*(2612082154*x^7 - 9010050347*x^6 + 19426337114*x^5 - 28170626609*x^4 + 13394761640*x^3 - 4698131400*x^2 - 17594323200*x + 10110341376) - 20220682752*x + 17594323200) + 124728407*129508224872072^(1/4)*sqrt(341)*(214583731*x^7 - 3372306249*x^6 + 18434388344*x^5 - 43845503580*x^4 + 57631717152*x^3 - 41786349984*x^2 - sqrt(2)*(190078101*x^7 - 2862100476*x^6 + 14688003420*x^5 - 32231022496*x^4 + 40927641120*x^3 - 21959568000*x^2 - 31156503552*x + 19060075008) - 38120150016*x + 31156503552))*sqrt(2*x^2 - x + 3)*sqrt(2243059557247*sqrt(2) + 4023497000000) - 1284612678018299582239382547725536472*sqrt(31)*sqrt(2)*(28180*x^8 - 254666*x^7 + 704270*x^6 - 1385256*x^5 + 1549144*x^4 - 642048*x^3 - 98496*x^2 - sqrt(2)*(8746*x^8 - 102335*x^7 + 396104*x^6 - 783113*x^5 + 1320710*x^4 - 752088*x^3 + 396144*x^2 + 546048*x - 539136) + 1154304*x - 456192) - 2*sqrt(8046994/10139750351)*(sqrt(4023497)*(11*129508224872072^(3/4)*sqrt(341)*(8140972152*x^7 - 11907581308*x^6 + 39777303828*x^5 - 24395365568*x^4 + 37103094432*x^3 - 1836165888*x^2 - sqrt(2)*(10387383478*x^7 - 14753211883*x^6 + 46462095753*x^5 - 11926110640*x^4 + 8224291080*x^3 + 34793549568*x^2 - 34793549568*x) + 1836165888*x) + 124728407*129508224872072^(1/4)*sqrt(341)*(692762453*x^7 - 8972954292*x^6 + 34803726780*x^5 - 46915651008*x^4 + 67421983392*x^3 + 10625375232*x^2 - 2*sqrt(2)*(367903387*x^7 - 4754813452*x^6 + 18261523780*x^5 - 22991417280*x^4 + 27054001440*x^3 + 26759248128*x^2 - 26759248128*x) - 10625375232*x))*sqrt(2*x^2 - x + 3)*sqrt(2243059557247*sqrt(2) + 4023497000000) - 111948686098489209076292438*sqrt(31)*sqrt(2)*(123408*x^8 - 914152*x^7 + 1578888*x^6 - 3293072*x^5 + 396480*x^4 + 798336*x^3 - 3822336*x^2 - sqrt(2)*(15550*x^8 - 118051*x^7 + 244047*x^6 - 707374*x^5 + 1053960*x^4 - 1667952*x^3 + 1209600*x^2 - 1036800*x) + 3276288*x) - 5088576640840418594376929*sqrt(31)*(254591*x^8 - 4815126*x^7 + 32303580*x^6 - 90866808*x^5 + 108781920*x^4 - 74219328*x^3 - 168956928*x^2 - 15488*sqrt(2)*(4*x^8 - 76*x^7 + 517*x^6 - 1536*x^5 + 2385*x^4 - 3618*x^3 + 2268*x^2 - 1944*x) + 144820224*x))*sqrt((129508224872072^(1/4)*sqrt(4023497)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(643213*x + 2195288) - 2838501*x + 1552075)*sqrt(2243059557247*sqrt(2) + 4023497000000) + 1921101946251381781783*x^2 + 1725071135409404048948*sqrt(2)*(2*x^2 - x + 3) - 5920130487427727531617*x + 7841232433679109313400)/x^2) - 14597871341117040707265710769608369*sqrt(31)*(2828123*x^8 - 9696916*x^7 + 53385560*x^6 - 142835344*x^5 + 254146592*x^4 - 249300096*x^3 + 37981440*x^2 - 7744*sqrt(2)*(1348*x^8 - 2692*x^7 + 9789*x^6 - 10070*x^5 + 15569*x^4 - 5568*x^3 + 1080*x^2 + 4320*x - 5184) + 223064064*x - 94887936))/(2585191*x^8 - 4661200*x^7 + 14191920*x^6 + 490880*x^5 - 13562944*x^4 + 44249088*x^3 - 34615296*x^2 - 24772608*x + 18579456)) + 55545*129508224872072^(1/4)*sqrt(4023497)*sqrt(341)*sqrt(31)*(402349700000000*x^8 + 80469940000000*x^7 + 1291542537000000*x^6 + 692041484000000*x^5 + 1569163830000000*x^4 + 949545292000000*x^3 + 969662777000000*x^2 - 2243059557247*sqrt(2)*(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36) + 337973748000000*x + 144845892000000)*sqrt(2243059557247*sqrt(2) + 4023497000000)*log(2464391912500000000000/10139750351*(129508224872072^(1/4)*sqrt(4023497)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(643213*x + 2195288) - 2838501*x + 1552075)*sqrt(2243059557247*sqrt(2) + 4023497000000) + 1921101946251381781783*x^2 + 1725071135409404048948*sqrt(2)*(2*x^2 - x + 3) - 5920130487427727531617*x + 7841232433679109313400)/x^2) - 55545*129508224872072^(1/4)*sqrt(4023497)*sqrt(341)*sqrt(31)*(402349700000000*x^8 + 80469940000000*x^7 + 1291542537000000*x^6 + 692041484000000*x^5 + 1569163830000000*x^4 + 949545292000000*x^3 + 969662777000000*x^2 - 2243059557247*sqrt(2)*(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36) + 337973748000000*x + 144845892000000)*sqrt(2243059557247*sqrt(2) + 4023497000000)*log(-2464391912500000000000/10139750351*(129508224872072^(1/4)*sqrt(4023497)*sqrt(341)*sqrt(31)*sqrt(2*x^2 - x + 3)*(sqrt(2)*(643213*x + 2195288) - 2838501*x + 1552075)*sqrt(2243059557247*sqrt(2) + 4023497000000) - 1921101946251381781783*x^2 - 1725071135409404048948*sqrt(2)*(2*x^2 - x + 3) + 5920130487427727531617*x - 7841232433679109313400)/x^2) + 427817641581532204139104*(225699113100*x^7 - 12234606480*x^6 + 592923725931*x^5 + 174241614961*x^4 + 519223213785*x^3 + 178650961091*x^2 + 218659985088*x + 9739335532)*sqrt(2*x^2 - x + 3))/(100*x^8 + 20*x^7 + 321*x^6 + 172*x^5 + 390*x^4 + 236*x^3 + 241*x^2 + 84*x + 36)","B",0
100,1,1269,0,0.738541," ","integrate((c*x^2+b*x+a)^(1/2)*(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(128 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} - 128 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e + 8 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{2} + {\left(21 \, b^{6} - 140 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} f^{2} + 8 \, {\left(2 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} e\right)} f\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(1280 \, c^{6} f^{2} x^{5} + 1920 \, b c^{5} d^{2} + 128 \, {\left(24 \, c^{6} e f + b c^{5} f^{2}\right)} x^{4} + 16 \, {\left(120 \, c^{6} e^{2} - {\left(9 \, b^{2} c^{4} - 20 \, a c^{5}\right)} f^{2} + 24 \, {\left(10 \, c^{6} d + b c^{5} e\right)} f\right)} x^{3} - 640 \, {\left(3 \, b^{2} c^{4} - 8 \, a c^{5}\right)} d e + 40 \, {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} e^{2} + {\left(315 \, b^{5} c - 1680 \, a b^{3} c^{2} + 1808 \, a^{2} b c^{3}\right)} f^{2} + 8 \, {\left(640 \, c^{6} d e + 40 \, b c^{5} e^{2} + {\left(21 \, b^{3} c^{3} - 68 \, a b c^{4}\right)} f^{2} + 8 \, {\left(10 \, b c^{5} d - {\left(7 \, b^{2} c^{4} - 16 \, a c^{5}\right)} e\right)} f\right)} x^{2} + 8 \, {\left(10 \, {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} d - {\left(105 \, b^{4} c^{2} - 460 \, a b^{2} c^{3} + 256 \, a^{2} c^{4}\right)} e\right)} f + 2 \, {\left(1920 \, c^{6} d^{2} + 640 \, b c^{5} d e - 40 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} e^{2} - {\left(105 \, b^{4} c^{2} - 448 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} f^{2} - 8 \, {\left(10 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} d - {\left(35 \, b^{3} c^{3} - 116 \, a b c^{4}\right)} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{6}}, \frac{15 \, {\left(128 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} - 128 \, {\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d e + 8 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} e^{2} + {\left(21 \, b^{6} - 140 \, a b^{4} c + 240 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} f^{2} + 8 \, {\left(2 \, {\left(5 \, b^{4} c^{2} - 24 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - {\left(7 \, b^{5} c - 40 \, a b^{3} c^{2} + 48 \, a^{2} b c^{3}\right)} e\right)} f\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(1280 \, c^{6} f^{2} x^{5} + 1920 \, b c^{5} d^{2} + 128 \, {\left(24 \, c^{6} e f + b c^{5} f^{2}\right)} x^{4} + 16 \, {\left(120 \, c^{6} e^{2} - {\left(9 \, b^{2} c^{4} - 20 \, a c^{5}\right)} f^{2} + 24 \, {\left(10 \, c^{6} d + b c^{5} e\right)} f\right)} x^{3} - 640 \, {\left(3 \, b^{2} c^{4} - 8 \, a c^{5}\right)} d e + 40 \, {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} e^{2} + {\left(315 \, b^{5} c - 1680 \, a b^{3} c^{2} + 1808 \, a^{2} b c^{3}\right)} f^{2} + 8 \, {\left(640 \, c^{6} d e + 40 \, b c^{5} e^{2} + {\left(21 \, b^{3} c^{3} - 68 \, a b c^{4}\right)} f^{2} + 8 \, {\left(10 \, b c^{5} d - {\left(7 \, b^{2} c^{4} - 16 \, a c^{5}\right)} e\right)} f\right)} x^{2} + 8 \, {\left(10 \, {\left(15 \, b^{3} c^{3} - 52 \, a b c^{4}\right)} d - {\left(105 \, b^{4} c^{2} - 460 \, a b^{2} c^{3} + 256 \, a^{2} c^{4}\right)} e\right)} f + 2 \, {\left(1920 \, c^{6} d^{2} + 640 \, b c^{5} d e - 40 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} e^{2} - {\left(105 \, b^{4} c^{2} - 448 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} f^{2} - 8 \, {\left(10 \, {\left(5 \, b^{2} c^{4} - 12 \, a c^{5}\right)} d - {\left(35 \, b^{3} c^{3} - 116 \, a b c^{4}\right)} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{6}}\right]"," ",0,"[-1/30720*(15*(128*(b^2*c^4 - 4*a*c^5)*d^2 - 128*(b^3*c^3 - 4*a*b*c^4)*d*e + 8*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*e^2 + (21*b^6 - 140*a*b^4*c + 240*a^2*b^2*c^2 - 64*a^3*c^3)*f^2 + 8*(2*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*d - (7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*e)*f)*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*(1280*c^6*f^2*x^5 + 1920*b*c^5*d^2 + 128*(24*c^6*e*f + b*c^5*f^2)*x^4 + 16*(120*c^6*e^2 - (9*b^2*c^4 - 20*a*c^5)*f^2 + 24*(10*c^6*d + b*c^5*e)*f)*x^3 - 640*(3*b^2*c^4 - 8*a*c^5)*d*e + 40*(15*b^3*c^3 - 52*a*b*c^4)*e^2 + (315*b^5*c - 1680*a*b^3*c^2 + 1808*a^2*b*c^3)*f^2 + 8*(640*c^6*d*e + 40*b*c^5*e^2 + (21*b^3*c^3 - 68*a*b*c^4)*f^2 + 8*(10*b*c^5*d - (7*b^2*c^4 - 16*a*c^5)*e)*f)*x^2 + 8*(10*(15*b^3*c^3 - 52*a*b*c^4)*d - (105*b^4*c^2 - 460*a*b^2*c^3 + 256*a^2*c^4)*e)*f + 2*(1920*c^6*d^2 + 640*b*c^5*d*e - 40*(5*b^2*c^4 - 12*a*c^5)*e^2 - (105*b^4*c^2 - 448*a*b^2*c^3 + 240*a^2*c^4)*f^2 - 8*(10*(5*b^2*c^4 - 12*a*c^5)*d - (35*b^3*c^3 - 116*a*b*c^4)*e)*f)*x)*sqrt(c*x^2 + b*x + a))/c^6, 1/15360*(15*(128*(b^2*c^4 - 4*a*c^5)*d^2 - 128*(b^3*c^3 - 4*a*b*c^4)*d*e + 8*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*e^2 + (21*b^6 - 140*a*b^4*c + 240*a^2*b^2*c^2 - 64*a^3*c^3)*f^2 + 8*(2*(5*b^4*c^2 - 24*a*b^2*c^3 + 16*a^2*c^4)*d - (7*b^5*c - 40*a*b^3*c^2 + 48*a^2*b*c^3)*e)*f)*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*(1280*c^6*f^2*x^5 + 1920*b*c^5*d^2 + 128*(24*c^6*e*f + b*c^5*f^2)*x^4 + 16*(120*c^6*e^2 - (9*b^2*c^4 - 20*a*c^5)*f^2 + 24*(10*c^6*d + b*c^5*e)*f)*x^3 - 640*(3*b^2*c^4 - 8*a*c^5)*d*e + 40*(15*b^3*c^3 - 52*a*b*c^4)*e^2 + (315*b^5*c - 1680*a*b^3*c^2 + 1808*a^2*b*c^3)*f^2 + 8*(640*c^6*d*e + 40*b*c^5*e^2 + (21*b^3*c^3 - 68*a*b*c^4)*f^2 + 8*(10*b*c^5*d - (7*b^2*c^4 - 16*a*c^5)*e)*f)*x^2 + 8*(10*(15*b^3*c^3 - 52*a*b*c^4)*d - (105*b^4*c^2 - 460*a*b^2*c^3 + 256*a^2*c^4)*e)*f + 2*(1920*c^6*d^2 + 640*b*c^5*d*e - 40*(5*b^2*c^4 - 12*a*c^5)*e^2 - (105*b^4*c^2 - 448*a*b^2*c^3 + 240*a^2*c^4)*f^2 - 8*(10*(5*b^2*c^4 - 12*a*c^5)*d - (35*b^3*c^3 - 116*a*b*c^4)*e)*f)*x)*sqrt(c*x^2 + b*x + a))/c^6]","A",0
101,1,465,0,0.471846," ","integrate((c*x^2+b*x+a)^(1/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - 8 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} f\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(48 \, c^{4} f x^{3} + 48 \, b c^{3} d + 8 \, {\left(8 \, c^{4} e + b c^{3} f\right)} x^{2} - 8 \, {\left(3 \, b^{2} c^{2} - 8 \, a c^{3}\right)} e + {\left(15 \, b^{3} c - 52 \, a b c^{2}\right)} f + 2 \, {\left(48 \, c^{4} d + 8 \, b c^{3} e - {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{4}}, \frac{3 \, {\left(16 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - 8 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} e + {\left(5 \, b^{4} - 24 \, a b^{2} c + 16 \, a^{2} c^{2}\right)} f\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(48 \, c^{4} f x^{3} + 48 \, b c^{3} d + 8 \, {\left(8 \, c^{4} e + b c^{3} f\right)} x^{2} - 8 \, {\left(3 \, b^{2} c^{2} - 8 \, a c^{3}\right)} e + {\left(15 \, b^{3} c - 52 \, a b c^{2}\right)} f + 2 \, {\left(48 \, c^{4} d + 8 \, b c^{3} e - {\left(5 \, b^{2} c^{2} - 12 \, a c^{3}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{4}}\right]"," ",0,"[1/768*(3*(16*(b^2*c^2 - 4*a*c^3)*d - 8*(b^3*c - 4*a*b*c^2)*e + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*f)*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*(48*c^4*f*x^3 + 48*b*c^3*d + 8*(8*c^4*e + b*c^3*f)*x^2 - 8*(3*b^2*c^2 - 8*a*c^3)*e + (15*b^3*c - 52*a*b*c^2)*f + 2*(48*c^4*d + 8*b*c^3*e - (5*b^2*c^2 - 12*a*c^3)*f)*x)*sqrt(c*x^2 + b*x + a))/c^4, 1/384*(3*(16*(b^2*c^2 - 4*a*c^3)*d - 8*(b^3*c - 4*a*b*c^2)*e + (5*b^4 - 24*a*b^2*c + 16*a^2*c^2)*f)*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*(48*c^4*f*x^3 + 48*b*c^3*d + 8*(8*c^4*e + b*c^3*f)*x^2 - 8*(3*b^2*c^2 - 8*a*c^3)*e + (15*b^3*c - 52*a*b*c^2)*f + 2*(48*c^4*d + 8*b*c^3*e - (5*b^2*c^2 - 12*a*c^3)*f)*x)*sqrt(c*x^2 + b*x + a))/c^4]","A",0
102,-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
103,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
104,1,2179,0,1.938806," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{105 \, {\left(768 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{2} - 768 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d e + 32 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{2} + 3 \, {\left(33 \, b^{8} - 336 \, a b^{6} c + 1120 \, a^{2} b^{4} c^{2} - 1280 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} f^{2} + 32 \, {\left(2 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d - 3 \, {\left(3 \, b^{7} c - 28 \, a b^{5} c^{2} + 80 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)} f\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(215040 \, c^{8} f^{2} x^{7} + 15360 \, {\left(32 \, c^{8} e f + 17 \, b c^{7} f^{2}\right)} x^{6} + 1280 \, {\left(224 \, c^{8} e^{2} + 3 \, {\left(b^{2} c^{6} + 84 \, a c^{7}\right)} f^{2} + 32 \, {\left(14 \, c^{8} d + 15 \, b c^{7} e\right)} f\right)} x^{5} + 128 \, {\left(5376 \, c^{8} d e + 2912 \, b c^{7} e^{2} - 3 \, {\left(11 \, b^{3} c^{5} - 52 \, a b c^{6}\right)} f^{2} + 32 \, {\left(182 \, b c^{7} d + 3 \, {\left(b^{2} c^{6} + 64 \, a c^{7}\right)} e\right)} f\right)} x^{4} + 16 \, {\left(26880 \, c^{8} d^{2} + 59136 \, b c^{7} d e + 224 \, {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} e^{2} + 3 \, {\left(99 \, b^{4} c^{4} - 568 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} f^{2} + 32 \, {\left(14 \, {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} d - 3 \, {\left(9 \, b^{3} c^{5} - 44 \, a b c^{6}\right)} e\right)} f\right)} x^{3} - 26880 \, {\left(3 \, b^{3} c^{5} - 20 \, a b c^{6}\right)} d^{2} + 5376 \, {\left(15 \, b^{4} c^{4} - 100 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} d e - 224 \, {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} e^{2} - 3 \, {\left(3465 \, b^{7} c - 30660 \, a b^{5} c^{2} + 81648 \, a^{2} b^{3} c^{3} - 58816 \, a^{3} b c^{4}\right)} f^{2} + 8 \, {\left(80640 \, b c^{7} d^{2} + 5376 \, {\left(b^{2} c^{6} + 32 \, a c^{7}\right)} d e - 224 \, {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} e^{2} - 3 \, {\left(231 \, b^{5} c^{3} - 1560 \, a b^{3} c^{4} + 2416 \, a^{2} b c^{5}\right)} f^{2} - 32 \, {\left(14 \, {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} d - 3 \, {\left(21 \, b^{4} c^{4} - 124 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} e\right)} f\right)} x^{2} - 32 \, {\left(14 \, {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} d - 3 \, {\left(315 \, b^{6} c^{2} - 2520 \, a b^{4} c^{3} + 5488 \, a^{2} b^{2} c^{4} - 2048 \, a^{3} c^{5}\right)} e\right)} f + 2 \, {\left(26880 \, {\left(b^{2} c^{6} + 20 \, a c^{7}\right)} d^{2} - 5376 \, {\left(5 \, b^{3} c^{5} - 28 \, a b c^{6}\right)} d e + 224 \, {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} e^{2} + 3 \, {\left(1155 \, b^{6} c^{2} - 8988 \, a b^{4} c^{3} + 18896 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} f^{2} + 32 \, {\left(14 \, {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} d - 3 \, {\left(105 \, b^{5} c^{3} - 728 \, a b^{3} c^{4} + 1168 \, a^{2} b c^{5}\right)} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6881280 \, c^{7}}, -\frac{105 \, {\left(768 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d^{2} - 768 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d e + 32 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} e^{2} + 3 \, {\left(33 \, b^{8} - 336 \, a b^{6} c + 1120 \, a^{2} b^{4} c^{2} - 1280 \, a^{3} b^{2} c^{3} + 256 \, a^{4} c^{4}\right)} f^{2} + 32 \, {\left(2 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} d - 3 \, {\left(3 \, b^{7} c - 28 \, a b^{5} c^{2} + 80 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} e\right)} f\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(215040 \, c^{8} f^{2} x^{7} + 15360 \, {\left(32 \, c^{8} e f + 17 \, b c^{7} f^{2}\right)} x^{6} + 1280 \, {\left(224 \, c^{8} e^{2} + 3 \, {\left(b^{2} c^{6} + 84 \, a c^{7}\right)} f^{2} + 32 \, {\left(14 \, c^{8} d + 15 \, b c^{7} e\right)} f\right)} x^{5} + 128 \, {\left(5376 \, c^{8} d e + 2912 \, b c^{7} e^{2} - 3 \, {\left(11 \, b^{3} c^{5} - 52 \, a b c^{6}\right)} f^{2} + 32 \, {\left(182 \, b c^{7} d + 3 \, {\left(b^{2} c^{6} + 64 \, a c^{7}\right)} e\right)} f\right)} x^{4} + 16 \, {\left(26880 \, c^{8} d^{2} + 59136 \, b c^{7} d e + 224 \, {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} e^{2} + 3 \, {\left(99 \, b^{4} c^{4} - 568 \, a b^{2} c^{5} + 560 \, a^{2} c^{6}\right)} f^{2} + 32 \, {\left(14 \, {\left(3 \, b^{2} c^{6} + 140 \, a c^{7}\right)} d - 3 \, {\left(9 \, b^{3} c^{5} - 44 \, a b c^{6}\right)} e\right)} f\right)} x^{3} - 26880 \, {\left(3 \, b^{3} c^{5} - 20 \, a b c^{6}\right)} d^{2} + 5376 \, {\left(15 \, b^{4} c^{4} - 100 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} d e - 224 \, {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} e^{2} - 3 \, {\left(3465 \, b^{7} c - 30660 \, a b^{5} c^{2} + 81648 \, a^{2} b^{3} c^{3} - 58816 \, a^{3} b c^{4}\right)} f^{2} + 8 \, {\left(80640 \, b c^{7} d^{2} + 5376 \, {\left(b^{2} c^{6} + 32 \, a c^{7}\right)} d e - 224 \, {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} e^{2} - 3 \, {\left(231 \, b^{5} c^{3} - 1560 \, a b^{3} c^{4} + 2416 \, a^{2} b c^{5}\right)} f^{2} - 32 \, {\left(14 \, {\left(7 \, b^{3} c^{5} - 36 \, a b c^{6}\right)} d - 3 \, {\left(21 \, b^{4} c^{4} - 124 \, a b^{2} c^{5} + 128 \, a^{2} c^{6}\right)} e\right)} f\right)} x^{2} - 32 \, {\left(14 \, {\left(105 \, b^{5} c^{3} - 760 \, a b^{3} c^{4} + 1296 \, a^{2} b c^{5}\right)} d - 3 \, {\left(315 \, b^{6} c^{2} - 2520 \, a b^{4} c^{3} + 5488 \, a^{2} b^{2} c^{4} - 2048 \, a^{3} c^{5}\right)} e\right)} f + 2 \, {\left(26880 \, {\left(b^{2} c^{6} + 20 \, a c^{7}\right)} d^{2} - 5376 \, {\left(5 \, b^{3} c^{5} - 28 \, a b c^{6}\right)} d e + 224 \, {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} e^{2} + 3 \, {\left(1155 \, b^{6} c^{2} - 8988 \, a b^{4} c^{3} + 18896 \, a^{2} b^{2} c^{4} - 6720 \, a^{3} c^{5}\right)} f^{2} + 32 \, {\left(14 \, {\left(35 \, b^{4} c^{4} - 216 \, a b^{2} c^{5} + 240 \, a^{2} c^{6}\right)} d - 3 \, {\left(105 \, b^{5} c^{3} - 728 \, a b^{3} c^{4} + 1168 \, a^{2} b c^{5}\right)} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3440640 \, c^{7}}\right]"," ",0,"[1/6881280*(105*(768*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^2 - 768*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d*e + 32*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*e^2 + 3*(33*b^8 - 336*a*b^6*c + 1120*a^2*b^4*c^2 - 1280*a^3*b^2*c^3 + 256*a^4*c^4)*f^2 + 32*(2*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*d - 3*(3*b^7*c - 28*a*b^5*c^2 + 80*a^2*b^3*c^3 - 64*a^3*b*c^4)*e)*f)*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*(215040*c^8*f^2*x^7 + 15360*(32*c^8*e*f + 17*b*c^7*f^2)*x^6 + 1280*(224*c^8*e^2 + 3*(b^2*c^6 + 84*a*c^7)*f^2 + 32*(14*c^8*d + 15*b*c^7*e)*f)*x^5 + 128*(5376*c^8*d*e + 2912*b*c^7*e^2 - 3*(11*b^3*c^5 - 52*a*b*c^6)*f^2 + 32*(182*b*c^7*d + 3*(b^2*c^6 + 64*a*c^7)*e)*f)*x^4 + 16*(26880*c^8*d^2 + 59136*b*c^7*d*e + 224*(3*b^2*c^6 + 140*a*c^7)*e^2 + 3*(99*b^4*c^4 - 568*a*b^2*c^5 + 560*a^2*c^6)*f^2 + 32*(14*(3*b^2*c^6 + 140*a*c^7)*d - 3*(9*b^3*c^5 - 44*a*b*c^6)*e)*f)*x^3 - 26880*(3*b^3*c^5 - 20*a*b*c^6)*d^2 + 5376*(15*b^4*c^4 - 100*a*b^2*c^5 + 128*a^2*c^6)*d*e - 224*(105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*e^2 - 3*(3465*b^7*c - 30660*a*b^5*c^2 + 81648*a^2*b^3*c^3 - 58816*a^3*b*c^4)*f^2 + 8*(80640*b*c^7*d^2 + 5376*(b^2*c^6 + 32*a*c^7)*d*e - 224*(7*b^3*c^5 - 36*a*b*c^6)*e^2 - 3*(231*b^5*c^3 - 1560*a*b^3*c^4 + 2416*a^2*b*c^5)*f^2 - 32*(14*(7*b^3*c^5 - 36*a*b*c^6)*d - 3*(21*b^4*c^4 - 124*a*b^2*c^5 + 128*a^2*c^6)*e)*f)*x^2 - 32*(14*(105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*d - 3*(315*b^6*c^2 - 2520*a*b^4*c^3 + 5488*a^2*b^2*c^4 - 2048*a^3*c^5)*e)*f + 2*(26880*(b^2*c^6 + 20*a*c^7)*d^2 - 5376*(5*b^3*c^5 - 28*a*b*c^6)*d*e + 224*(35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*e^2 + 3*(1155*b^6*c^2 - 8988*a*b^4*c^3 + 18896*a^2*b^2*c^4 - 6720*a^3*c^5)*f^2 + 32*(14*(35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*d - 3*(105*b^5*c^3 - 728*a*b^3*c^4 + 1168*a^2*b*c^5)*e)*f)*x)*sqrt(c*x^2 + b*x + a))/c^7, -1/3440640*(105*(768*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d^2 - 768*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d*e + 32*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*e^2 + 3*(33*b^8 - 336*a*b^6*c + 1120*a^2*b^4*c^2 - 1280*a^3*b^2*c^3 + 256*a^4*c^4)*f^2 + 32*(2*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*d - 3*(3*b^7*c - 28*a*b^5*c^2 + 80*a^2*b^3*c^3 - 64*a^3*b*c^4)*e)*f)*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*(215040*c^8*f^2*x^7 + 15360*(32*c^8*e*f + 17*b*c^7*f^2)*x^6 + 1280*(224*c^8*e^2 + 3*(b^2*c^6 + 84*a*c^7)*f^2 + 32*(14*c^8*d + 15*b*c^7*e)*f)*x^5 + 128*(5376*c^8*d*e + 2912*b*c^7*e^2 - 3*(11*b^3*c^5 - 52*a*b*c^6)*f^2 + 32*(182*b*c^7*d + 3*(b^2*c^6 + 64*a*c^7)*e)*f)*x^4 + 16*(26880*c^8*d^2 + 59136*b*c^7*d*e + 224*(3*b^2*c^6 + 140*a*c^7)*e^2 + 3*(99*b^4*c^4 - 568*a*b^2*c^5 + 560*a^2*c^6)*f^2 + 32*(14*(3*b^2*c^6 + 140*a*c^7)*d - 3*(9*b^3*c^5 - 44*a*b*c^6)*e)*f)*x^3 - 26880*(3*b^3*c^5 - 20*a*b*c^6)*d^2 + 5376*(15*b^4*c^4 - 100*a*b^2*c^5 + 128*a^2*c^6)*d*e - 224*(105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*e^2 - 3*(3465*b^7*c - 30660*a*b^5*c^2 + 81648*a^2*b^3*c^3 - 58816*a^3*b*c^4)*f^2 + 8*(80640*b*c^7*d^2 + 5376*(b^2*c^6 + 32*a*c^7)*d*e - 224*(7*b^3*c^5 - 36*a*b*c^6)*e^2 - 3*(231*b^5*c^3 - 1560*a*b^3*c^4 + 2416*a^2*b*c^5)*f^2 - 32*(14*(7*b^3*c^5 - 36*a*b*c^6)*d - 3*(21*b^4*c^4 - 124*a*b^2*c^5 + 128*a^2*c^6)*e)*f)*x^2 - 32*(14*(105*b^5*c^3 - 760*a*b^3*c^4 + 1296*a^2*b*c^5)*d - 3*(315*b^6*c^2 - 2520*a*b^4*c^3 + 5488*a^2*b^2*c^4 - 2048*a^3*c^5)*e)*f + 2*(26880*(b^2*c^6 + 20*a*c^7)*d^2 - 5376*(5*b^3*c^5 - 28*a*b*c^6)*d*e + 224*(35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*e^2 + 3*(1155*b^6*c^2 - 8988*a*b^4*c^3 + 18896*a^2*b^2*c^4 - 6720*a^3*c^5)*f^2 + 32*(14*(35*b^4*c^4 - 216*a*b^2*c^5 + 240*a^2*c^6)*d - 3*(105*b^5*c^3 - 728*a*b^3*c^4 + 1168*a^2*b*c^5)*e)*f)*x)*sqrt(c*x^2 + b*x + a))/c^7]","B",0
105,1,839,0,0.841872," ","integrate((c*x^2+b*x+a)^(3/2)*(f*x^2+e*x+d),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - 12 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} f\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(1280 \, c^{6} f x^{5} + 128 \, {\left(12 \, c^{6} e + 13 \, b c^{5} f\right)} x^{4} + 16 \, {\left(120 \, c^{6} d + 132 \, b c^{5} e + {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} f\right)} x^{3} + 8 \, {\left(360 \, b c^{5} d + 12 \, {\left(b^{2} c^{4} + 32 \, a c^{5}\right)} e - {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} f\right)} x^{2} - 120 \, {\left(3 \, b^{3} c^{3} - 20 \, a b c^{4}\right)} d + 12 \, {\left(15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} e - {\left(105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right)} f + 2 \, {\left(120 \, {\left(b^{2} c^{4} + 20 \, a c^{5}\right)} d - 12 \, {\left(5 \, b^{3} c^{3} - 28 \, a b c^{4}\right)} e + {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{5}}, -\frac{15 \, {\left(24 \, {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} d - 12 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} e + {\left(7 \, b^{6} - 60 \, a b^{4} c + 144 \, a^{2} b^{2} c^{2} - 64 \, a^{3} c^{3}\right)} f\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(1280 \, c^{6} f x^{5} + 128 \, {\left(12 \, c^{6} e + 13 \, b c^{5} f\right)} x^{4} + 16 \, {\left(120 \, c^{6} d + 132 \, b c^{5} e + {\left(3 \, b^{2} c^{4} + 140 \, a c^{5}\right)} f\right)} x^{3} + 8 \, {\left(360 \, b c^{5} d + 12 \, {\left(b^{2} c^{4} + 32 \, a c^{5}\right)} e - {\left(7 \, b^{3} c^{3} - 36 \, a b c^{4}\right)} f\right)} x^{2} - 120 \, {\left(3 \, b^{3} c^{3} - 20 \, a b c^{4}\right)} d + 12 \, {\left(15 \, b^{4} c^{2} - 100 \, a b^{2} c^{3} + 128 \, a^{2} c^{4}\right)} e - {\left(105 \, b^{5} c - 760 \, a b^{3} c^{2} + 1296 \, a^{2} b c^{3}\right)} f + 2 \, {\left(120 \, {\left(b^{2} c^{4} + 20 \, a c^{5}\right)} d - 12 \, {\left(5 \, b^{3} c^{3} - 28 \, a b c^{4}\right)} e + {\left(35 \, b^{4} c^{2} - 216 \, a b^{2} c^{3} + 240 \, a^{2} c^{4}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{5}}\right]"," ",0,"[-1/30720*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d - 12*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*f)*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*(1280*c^6*f*x^5 + 128*(12*c^6*e + 13*b*c^5*f)*x^4 + 16*(120*c^6*d + 132*b*c^5*e + (3*b^2*c^4 + 140*a*c^5)*f)*x^3 + 8*(360*b*c^5*d + 12*(b^2*c^4 + 32*a*c^5)*e - (7*b^3*c^3 - 36*a*b*c^4)*f)*x^2 - 120*(3*b^3*c^3 - 20*a*b*c^4)*d + 12*(15*b^4*c^2 - 100*a*b^2*c^3 + 128*a^2*c^4)*e - (105*b^5*c - 760*a*b^3*c^2 + 1296*a^2*b*c^3)*f + 2*(120*(b^2*c^4 + 20*a*c^5)*d - 12*(5*b^3*c^3 - 28*a*b*c^4)*e + (35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*f)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/15360*(15*(24*(b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*d - 12*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*e + (7*b^6 - 60*a*b^4*c + 144*a^2*b^2*c^2 - 64*a^3*c^3)*f)*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*(1280*c^6*f*x^5 + 128*(12*c^6*e + 13*b*c^5*f)*x^4 + 16*(120*c^6*d + 132*b*c^5*e + (3*b^2*c^4 + 140*a*c^5)*f)*x^3 + 8*(360*b*c^5*d + 12*(b^2*c^4 + 32*a*c^5)*e - (7*b^3*c^3 - 36*a*b*c^4)*f)*x^2 - 120*(3*b^3*c^3 - 20*a*b*c^4)*d + 12*(15*b^4*c^2 - 100*a*b^2*c^3 + 128*a^2*c^4)*e - (105*b^5*c - 760*a*b^3*c^2 + 1296*a^2*b*c^3)*f + 2*(120*(b^2*c^4 + 20*a*c^5)*d - 12*(5*b^3*c^3 - 28*a*b*c^4)*e + (35*b^4*c^2 - 216*a*b^2*c^3 + 240*a^2*c^4)*f)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
106,-1,0,0,0.000000," ","integrate((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
107,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
108,-1,0,0,0.000000," ","integrate((c*x^2+b*x+a)^(3/2)/(f*x^2+e*x+d)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
109,1,1583,0,1.407034," ","integrate((f*x^2+e*x+d)^3/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{15 \, {\left(1024 \, c^{6} d^{3} - 1536 \, b c^{5} d^{2} e + 384 \, {\left(3 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d e^{2} - 64 \, {\left(5 \, b^{3} c^{3} - 12 \, a b c^{4}\right)} e^{3} + {\left(231 \, b^{6} - 1260 \, a b^{4} c + 1680 \, a^{2} b^{2} c^{2} - 320 \, a^{3} c^{3}\right)} f^{3} + 12 \, {\left(2 \, {\left(35 \, b^{4} c^{2} - 120 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d - {\left(63 \, b^{5} c - 280 \, a b^{3} c^{2} + 240 \, a^{2} b c^{3}\right)} e\right)} f^{2} + 24 \, {\left(16 \, {\left(3 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} - 16 \, {\left(5 \, b^{3} c^{3} - 12 \, a b c^{4}\right)} d e + {\left(35 \, b^{4} c^{2} - 120 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} e^{2}\right)} f\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(1280 \, c^{6} f^{3} x^{5} + 23040 \, c^{6} d^{2} e - 17280 \, b c^{5} d e^{2} + 128 \, {\left(36 \, c^{6} e f^{2} - 11 \, b c^{5} f^{3}\right)} x^{4} + 320 \, {\left(15 \, b^{2} c^{4} - 16 \, a c^{5}\right)} e^{3} - 21 \, {\left(165 \, b^{5} c - 680 \, a b^{3} c^{2} + 528 \, a^{2} b c^{3}\right)} f^{3} + 16 \, {\left(360 \, c^{6} e^{2} f + {\left(99 \, b^{2} c^{4} - 100 \, a c^{5}\right)} f^{3} + 36 \, {\left(10 \, c^{6} d - 9 \, b c^{5} e\right)} f^{2}\right)} x^{3} - 12 \, {\left(50 \, {\left(21 \, b^{3} c^{3} - 44 \, a b c^{4}\right)} d - {\left(945 \, b^{4} c^{2} - 2940 \, a b^{2} c^{3} + 1024 \, a^{2} c^{4}\right)} e\right)} f^{2} + 8 \, {\left(320 \, c^{6} e^{3} - 3 \, {\left(77 \, b^{3} c^{3} - 156 \, a b c^{4}\right)} f^{3} - 12 \, {\left(70 \, b c^{5} d - {\left(63 \, b^{2} c^{4} - 64 \, a c^{5}\right)} e\right)} f^{2} + 120 \, {\left(16 \, c^{6} d e - 7 \, b c^{5} e^{2}\right)} f\right)} x^{2} - 120 \, {\left(144 \, b c^{5} d^{2} - 16 \, {\left(15 \, b^{2} c^{4} - 16 \, a c^{5}\right)} d e + 5 \, {\left(21 \, b^{3} c^{3} - 44 \, a b c^{4}\right)} e^{2}\right)} f + 2 \, {\left(5760 \, c^{6} d e^{2} - 1600 \, b c^{5} e^{3} + 3 \, {\left(385 \, b^{4} c^{2} - 1176 \, a b^{2} c^{3} + 400 \, a^{2} c^{4}\right)} f^{3} + 12 \, {\left(10 \, {\left(35 \, b^{2} c^{4} - 36 \, a c^{5}\right)} d - 7 \, {\left(45 \, b^{3} c^{3} - 92 \, a b c^{4}\right)} e\right)} f^{2} + 120 \, {\left(48 \, c^{6} d^{2} - 80 \, b c^{5} d e + {\left(35 \, b^{2} c^{4} - 36 \, a c^{5}\right)} e^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{30720 \, c^{7}}, -\frac{15 \, {\left(1024 \, c^{6} d^{3} - 1536 \, b c^{5} d^{2} e + 384 \, {\left(3 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d e^{2} - 64 \, {\left(5 \, b^{3} c^{3} - 12 \, a b c^{4}\right)} e^{3} + {\left(231 \, b^{6} - 1260 \, a b^{4} c + 1680 \, a^{2} b^{2} c^{2} - 320 \, a^{3} c^{3}\right)} f^{3} + 12 \, {\left(2 \, {\left(35 \, b^{4} c^{2} - 120 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} d - {\left(63 \, b^{5} c - 280 \, a b^{3} c^{2} + 240 \, a^{2} b c^{3}\right)} e\right)} f^{2} + 24 \, {\left(16 \, {\left(3 \, b^{2} c^{4} - 4 \, a c^{5}\right)} d^{2} - 16 \, {\left(5 \, b^{3} c^{3} - 12 \, a b c^{4}\right)} d e + {\left(35 \, b^{4} c^{2} - 120 \, a b^{2} c^{3} + 48 \, a^{2} c^{4}\right)} e^{2}\right)} f\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(1280 \, c^{6} f^{3} x^{5} + 23040 \, c^{6} d^{2} e - 17280 \, b c^{5} d e^{2} + 128 \, {\left(36 \, c^{6} e f^{2} - 11 \, b c^{5} f^{3}\right)} x^{4} + 320 \, {\left(15 \, b^{2} c^{4} - 16 \, a c^{5}\right)} e^{3} - 21 \, {\left(165 \, b^{5} c - 680 \, a b^{3} c^{2} + 528 \, a^{2} b c^{3}\right)} f^{3} + 16 \, {\left(360 \, c^{6} e^{2} f + {\left(99 \, b^{2} c^{4} - 100 \, a c^{5}\right)} f^{3} + 36 \, {\left(10 \, c^{6} d - 9 \, b c^{5} e\right)} f^{2}\right)} x^{3} - 12 \, {\left(50 \, {\left(21 \, b^{3} c^{3} - 44 \, a b c^{4}\right)} d - {\left(945 \, b^{4} c^{2} - 2940 \, a b^{2} c^{3} + 1024 \, a^{2} c^{4}\right)} e\right)} f^{2} + 8 \, {\left(320 \, c^{6} e^{3} - 3 \, {\left(77 \, b^{3} c^{3} - 156 \, a b c^{4}\right)} f^{3} - 12 \, {\left(70 \, b c^{5} d - {\left(63 \, b^{2} c^{4} - 64 \, a c^{5}\right)} e\right)} f^{2} + 120 \, {\left(16 \, c^{6} d e - 7 \, b c^{5} e^{2}\right)} f\right)} x^{2} - 120 \, {\left(144 \, b c^{5} d^{2} - 16 \, {\left(15 \, b^{2} c^{4} - 16 \, a c^{5}\right)} d e + 5 \, {\left(21 \, b^{3} c^{3} - 44 \, a b c^{4}\right)} e^{2}\right)} f + 2 \, {\left(5760 \, c^{6} d e^{2} - 1600 \, b c^{5} e^{3} + 3 \, {\left(385 \, b^{4} c^{2} - 1176 \, a b^{2} c^{3} + 400 \, a^{2} c^{4}\right)} f^{3} + 12 \, {\left(10 \, {\left(35 \, b^{2} c^{4} - 36 \, a c^{5}\right)} d - 7 \, {\left(45 \, b^{3} c^{3} - 92 \, a b c^{4}\right)} e\right)} f^{2} + 120 \, {\left(48 \, c^{6} d^{2} - 80 \, b c^{5} d e + {\left(35 \, b^{2} c^{4} - 36 \, a c^{5}\right)} e^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{15360 \, c^{7}}\right]"," ",0,"[-1/30720*(15*(1024*c^6*d^3 - 1536*b*c^5*d^2*e + 384*(3*b^2*c^4 - 4*a*c^5)*d*e^2 - 64*(5*b^3*c^3 - 12*a*b*c^4)*e^3 + (231*b^6 - 1260*a*b^4*c + 1680*a^2*b^2*c^2 - 320*a^3*c^3)*f^3 + 12*(2*(35*b^4*c^2 - 120*a*b^2*c^3 + 48*a^2*c^4)*d - (63*b^5*c - 280*a*b^3*c^2 + 240*a^2*b*c^3)*e)*f^2 + 24*(16*(3*b^2*c^4 - 4*a*c^5)*d^2 - 16*(5*b^3*c^3 - 12*a*b*c^4)*d*e + (35*b^4*c^2 - 120*a*b^2*c^3 + 48*a^2*c^4)*e^2)*f)*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*(1280*c^6*f^3*x^5 + 23040*c^6*d^2*e - 17280*b*c^5*d*e^2 + 128*(36*c^6*e*f^2 - 11*b*c^5*f^3)*x^4 + 320*(15*b^2*c^4 - 16*a*c^5)*e^3 - 21*(165*b^5*c - 680*a*b^3*c^2 + 528*a^2*b*c^3)*f^3 + 16*(360*c^6*e^2*f + (99*b^2*c^4 - 100*a*c^5)*f^3 + 36*(10*c^6*d - 9*b*c^5*e)*f^2)*x^3 - 12*(50*(21*b^3*c^3 - 44*a*b*c^4)*d - (945*b^4*c^2 - 2940*a*b^2*c^3 + 1024*a^2*c^4)*e)*f^2 + 8*(320*c^6*e^3 - 3*(77*b^3*c^3 - 156*a*b*c^4)*f^3 - 12*(70*b*c^5*d - (63*b^2*c^4 - 64*a*c^5)*e)*f^2 + 120*(16*c^6*d*e - 7*b*c^5*e^2)*f)*x^2 - 120*(144*b*c^5*d^2 - 16*(15*b^2*c^4 - 16*a*c^5)*d*e + 5*(21*b^3*c^3 - 44*a*b*c^4)*e^2)*f + 2*(5760*c^6*d*e^2 - 1600*b*c^5*e^3 + 3*(385*b^4*c^2 - 1176*a*b^2*c^3 + 400*a^2*c^4)*f^3 + 12*(10*(35*b^2*c^4 - 36*a*c^5)*d - 7*(45*b^3*c^3 - 92*a*b*c^4)*e)*f^2 + 120*(48*c^6*d^2 - 80*b*c^5*d*e + (35*b^2*c^4 - 36*a*c^5)*e^2)*f)*x)*sqrt(c*x^2 + b*x + a))/c^7, -1/15360*(15*(1024*c^6*d^3 - 1536*b*c^5*d^2*e + 384*(3*b^2*c^4 - 4*a*c^5)*d*e^2 - 64*(5*b^3*c^3 - 12*a*b*c^4)*e^3 + (231*b^6 - 1260*a*b^4*c + 1680*a^2*b^2*c^2 - 320*a^3*c^3)*f^3 + 12*(2*(35*b^4*c^2 - 120*a*b^2*c^3 + 48*a^2*c^4)*d - (63*b^5*c - 280*a*b^3*c^2 + 240*a^2*b*c^3)*e)*f^2 + 24*(16*(3*b^2*c^4 - 4*a*c^5)*d^2 - 16*(5*b^3*c^3 - 12*a*b*c^4)*d*e + (35*b^4*c^2 - 120*a*b^2*c^3 + 48*a^2*c^4)*e^2)*f)*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*(1280*c^6*f^3*x^5 + 23040*c^6*d^2*e - 17280*b*c^5*d*e^2 + 128*(36*c^6*e*f^2 - 11*b*c^5*f^3)*x^4 + 320*(15*b^2*c^4 - 16*a*c^5)*e^3 - 21*(165*b^5*c - 680*a*b^3*c^2 + 528*a^2*b*c^3)*f^3 + 16*(360*c^6*e^2*f + (99*b^2*c^4 - 100*a*c^5)*f^3 + 36*(10*c^6*d - 9*b*c^5*e)*f^2)*x^3 - 12*(50*(21*b^3*c^3 - 44*a*b*c^4)*d - (945*b^4*c^2 - 2940*a*b^2*c^3 + 1024*a^2*c^4)*e)*f^2 + 8*(320*c^6*e^3 - 3*(77*b^3*c^3 - 156*a*b*c^4)*f^3 - 12*(70*b*c^5*d - (63*b^2*c^4 - 64*a*c^5)*e)*f^2 + 120*(16*c^6*d*e - 7*b*c^5*e^2)*f)*x^2 - 120*(144*b*c^5*d^2 - 16*(15*b^2*c^4 - 16*a*c^5)*d*e + 5*(21*b^3*c^3 - 44*a*b*c^4)*e^2)*f + 2*(5760*c^6*d*e^2 - 1600*b*c^5*e^3 + 3*(385*b^4*c^2 - 1176*a*b^2*c^3 + 400*a^2*c^4)*f^3 + 12*(10*(35*b^2*c^4 - 36*a*c^5)*d - 7*(45*b^3*c^3 - 92*a*b*c^4)*e)*f^2 + 120*(48*c^6*d^2 - 80*b*c^5*d*e + (35*b^2*c^4 - 36*a*c^5)*e^2)*f)*x)*sqrt(c*x^2 + b*x + a))/c^7]","A",0
110,1,637,0,0.799857," ","integrate((f*x^2+e*x+d)^2/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(128 \, c^{4} d^{2} - 128 \, b c^{3} d e + 16 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} e^{2} + {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} f^{2} + 16 \, {\left(2 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} e\right)} f\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(48 \, c^{4} f^{2} x^{3} + 384 \, c^{4} d e - 144 \, b c^{3} e^{2} - 5 \, {\left(21 \, b^{3} c - 44 \, a b c^{2}\right)} f^{2} + 8 \, {\left(16 \, c^{4} e f - 7 \, b c^{3} f^{2}\right)} x^{2} - 16 \, {\left(18 \, b c^{3} d - {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} e\right)} f + 2 \, {\left(48 \, c^{4} e^{2} + {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} f^{2} + 16 \, {\left(6 \, c^{4} d - 5 \, b c^{3} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{768 \, c^{5}}, -\frac{3 \, {\left(128 \, c^{4} d^{2} - 128 \, b c^{3} d e + 16 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} e^{2} + {\left(35 \, b^{4} - 120 \, a b^{2} c + 48 \, a^{2} c^{2}\right)} f^{2} + 16 \, {\left(2 \, {\left(3 \, b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(5 \, b^{3} c - 12 \, a b c^{2}\right)} e\right)} f\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(48 \, c^{4} f^{2} x^{3} + 384 \, c^{4} d e - 144 \, b c^{3} e^{2} - 5 \, {\left(21 \, b^{3} c - 44 \, a b c^{2}\right)} f^{2} + 8 \, {\left(16 \, c^{4} e f - 7 \, b c^{3} f^{2}\right)} x^{2} - 16 \, {\left(18 \, b c^{3} d - {\left(15 \, b^{2} c^{2} - 16 \, a c^{3}\right)} e\right)} f + 2 \, {\left(48 \, c^{4} e^{2} + {\left(35 \, b^{2} c^{2} - 36 \, a c^{3}\right)} f^{2} + 16 \, {\left(6 \, c^{4} d - 5 \, b c^{3} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{384 \, c^{5}}\right]"," ",0,"[1/768*(3*(128*c^4*d^2 - 128*b*c^3*d*e + 16*(3*b^2*c^2 - 4*a*c^3)*e^2 + (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*f^2 + 16*(2*(3*b^2*c^2 - 4*a*c^3)*d - (5*b^3*c - 12*a*b*c^2)*e)*f)*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*(48*c^4*f^2*x^3 + 384*c^4*d*e - 144*b*c^3*e^2 - 5*(21*b^3*c - 44*a*b*c^2)*f^2 + 8*(16*c^4*e*f - 7*b*c^3*f^2)*x^2 - 16*(18*b*c^3*d - (15*b^2*c^2 - 16*a*c^3)*e)*f + 2*(48*c^4*e^2 + (35*b^2*c^2 - 36*a*c^3)*f^2 + 16*(6*c^4*d - 5*b*c^3*e)*f)*x)*sqrt(c*x^2 + b*x + a))/c^5, -1/384*(3*(128*c^4*d^2 - 128*b*c^3*d*e + 16*(3*b^2*c^2 - 4*a*c^3)*e^2 + (35*b^4 - 120*a*b^2*c + 48*a^2*c^2)*f^2 + 16*(2*(3*b^2*c^2 - 4*a*c^3)*d - (5*b^3*c - 12*a*b*c^2)*e)*f)*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*(48*c^4*f^2*x^3 + 384*c^4*d*e - 144*b*c^3*e^2 - 5*(21*b^3*c - 44*a*b*c^2)*f^2 + 8*(16*c^4*e*f - 7*b*c^3*f^2)*x^2 - 16*(18*b*c^3*d - (15*b^2*c^2 - 16*a*c^3)*e)*f + 2*(48*c^4*e^2 + (35*b^2*c^2 - 36*a*c^3)*f^2 + 16*(6*c^4*d - 5*b*c^3*e)*f)*x)*sqrt(c*x^2 + b*x + a))/c^5]","A",0
111,1,227,0,0.633791," ","integrate((f*x^2+e*x+d)/(c*x^2+b*x+a)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, c^{2} d - 4 \, b c e + {\left(3 \, b^{2} - 4 \, a c\right)} f\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} f x + 4 \, c^{2} e - 3 \, b c f\right)} \sqrt{c x^{2} + b x + a}}{16 \, c^{3}}, -\frac{{\left(8 \, c^{2} d - 4 \, b c e + {\left(3 \, b^{2} - 4 \, a c\right)} f\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} f x + 4 \, c^{2} e - 3 \, b c f\right)} \sqrt{c x^{2} + b x + a}}{8 \, c^{3}}\right]"," ",0,"[-1/16*((8*c^2*d - 4*b*c*e + (3*b^2 - 4*a*c)*f)*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*f*x + 4*c^2*e - 3*b*c*f)*sqrt(c*x^2 + b*x + a))/c^3, -1/8*((8*c^2*d - 4*b*c*e + (3*b^2 - 4*a*c)*f)*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*f*x + 4*c^2*e - 3*b*c*f)*sqrt(c*x^2 + b*x + a))/c^3]","A",0
112,1,11287,0,7.139316," ","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
113,-1,0,0,0.000000," ","integrate(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
114,1,3143,0,1.951665," ","integrate((f*x^2+e*x+d)^3/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(128 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d e^{2} - 64 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} e^{3} + 5 \, {\left(21 \, a b^{6} - 140 \, a^{2} b^{4} c + 240 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} f^{3} + 8 \, {\left(6 \, {\left(5 \, a b^{4} c^{2} - 24 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d - 5 \, {\left(7 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2} + 48 \, a^{3} b c^{3}\right)} e\right)} f^{2} + {\left(128 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d e^{2} - 64 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e^{3} + 5 \, {\left(21 \, b^{6} c - 140 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} f^{3} + 8 \, {\left(6 \, {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - 5 \, {\left(7 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} e\right)} f^{2} + 16 \, {\left(8 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{2} - 24 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d e + 3 \, {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e^{2}\right)} f\right)} x^{2} + 16 \, {\left(8 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{2} - 24 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e + 3 \, {\left(5 \, a b^{4} c^{2} - 24 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} e^{2}\right)} f + {\left(128 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d e^{2} - 64 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} e^{3} + 5 \, {\left(21 \, b^{7} - 140 \, a b^{5} c + 240 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} f^{3} + 8 \, {\left(6 \, {\left(5 \, b^{5} c^{2} - 24 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d - 5 \, {\left(7 \, b^{6} c - 40 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3}\right)} e\right)} f^{2} + 16 \, {\left(8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{2} - 24 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d e + 3 \, {\left(5 \, b^{5} c^{2} - 24 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{2}\right)} f\right)} x\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(128 \, b c^{6} d^{3} - 768 \, a c^{6} d^{2} e + 384 \, a b c^{5} d e^{2} - 16 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} f^{3} x^{5} - 8 \, {\left(8 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} e f^{2} - 3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} f^{3}\right)} x^{4} - 64 \, {\left(3 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} e^{3} + {\left(315 \, a b^{5} c - 1680 \, a^{2} b^{3} c^{2} + 1808 \, a^{3} b c^{3}\right)} f^{3} - 2 \, {\left(48 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} e^{2} f + {\left(21 \, b^{4} c^{3} - 104 \, a b^{2} c^{4} + 80 \, a^{2} c^{5}\right)} f^{3} + 8 \, {\left(6 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d - 7 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e\right)} f^{2}\right)} x^{3} + 8 \, {\left(6 \, {\left(15 \, a b^{3} c^{3} - 52 \, a^{2} b c^{4}\right)} d - {\left(105 \, a b^{4} c^{2} - 460 \, a^{2} b^{2} c^{3} + 256 \, a^{3} c^{4}\right)} e\right)} f^{2} - {\left(64 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} e^{3} - 7 \, {\left(15 \, b^{5} c^{2} - 88 \, a b^{3} c^{3} + 112 \, a^{2} b c^{4}\right)} f^{3} - 8 \, {\left(30 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d - {\left(35 \, b^{4} c^{3} - 172 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} e\right)} f^{2} + 48 \, {\left(8 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d e - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e^{2}\right)} f\right)} x^{2} + 48 \, {\left(8 \, a b c^{5} d^{2} - 8 \, {\left(3 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d e + {\left(15 \, a b^{3} c^{3} - 52 \, a^{2} b c^{4}\right)} e^{2}\right)} f + {\left(256 \, c^{7} d^{3} - 384 \, b c^{6} d^{2} e + 384 \, {\left(b^{2} c^{5} - 2 \, a c^{6}\right)} d e^{2} - 64 \, {\left(3 \, b^{3} c^{4} - 10 \, a b c^{5}\right)} e^{3} + {\left(315 \, b^{6} c - 1890 \, a b^{4} c^{2} + 2704 \, a^{2} b^{2} c^{3} - 480 \, a^{3} c^{4}\right)} f^{3} + 8 \, {\left(6 \, {\left(15 \, b^{4} c^{3} - 62 \, a b^{2} c^{4} + 24 \, a^{2} c^{5}\right)} d - {\left(105 \, b^{5} c^{2} - 530 \, a b^{3} c^{3} + 488 \, a^{2} b c^{4}\right)} e\right)} f^{2} + 48 \, {\left(8 \, {\left(b^{2} c^{5} - 2 \, a c^{6}\right)} d^{2} - 8 \, {\left(3 \, b^{3} c^{4} - 10 \, a b c^{5}\right)} d e + {\left(15 \, b^{4} c^{3} - 62 \, a b^{2} c^{4} + 24 \, a^{2} c^{5}\right)} e^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{256 \, {\left(a b^{2} c^{6} - 4 \, a^{2} c^{7} + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} x^{2} + {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} x\right)}}, -\frac{3 \, {\left(128 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d e^{2} - 64 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} e^{3} + 5 \, {\left(21 \, a b^{6} - 140 \, a^{2} b^{4} c + 240 \, a^{3} b^{2} c^{2} - 64 \, a^{4} c^{3}\right)} f^{3} + 8 \, {\left(6 \, {\left(5 \, a b^{4} c^{2} - 24 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} d - 5 \, {\left(7 \, a b^{5} c - 40 \, a^{2} b^{3} c^{2} + 48 \, a^{3} b c^{3}\right)} e\right)} f^{2} + {\left(128 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d e^{2} - 64 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e^{3} + 5 \, {\left(21 \, b^{6} c - 140 \, a b^{4} c^{2} + 240 \, a^{2} b^{2} c^{3} - 64 \, a^{3} c^{4}\right)} f^{3} + 8 \, {\left(6 \, {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} d - 5 \, {\left(7 \, b^{5} c^{2} - 40 \, a b^{3} c^{3} + 48 \, a^{2} b c^{4}\right)} e\right)} f^{2} + 16 \, {\left(8 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d^{2} - 24 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d e + 3 \, {\left(5 \, b^{4} c^{3} - 24 \, a b^{2} c^{4} + 16 \, a^{2} c^{5}\right)} e^{2}\right)} f\right)} x^{2} + 16 \, {\left(8 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{2} - 24 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d e + 3 \, {\left(5 \, a b^{4} c^{2} - 24 \, a^{2} b^{2} c^{3} + 16 \, a^{3} c^{4}\right)} e^{2}\right)} f + {\left(128 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d e^{2} - 64 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} e^{3} + 5 \, {\left(21 \, b^{7} - 140 \, a b^{5} c + 240 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} f^{3} + 8 \, {\left(6 \, {\left(5 \, b^{5} c^{2} - 24 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} d - 5 \, {\left(7 \, b^{6} c - 40 \, a b^{4} c^{2} + 48 \, a^{2} b^{2} c^{3}\right)} e\right)} f^{2} + 16 \, {\left(8 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{2} - 24 \, {\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d e + 3 \, {\left(5 \, b^{5} c^{2} - 24 \, a b^{3} c^{3} + 16 \, a^{2} b c^{4}\right)} e^{2}\right)} f\right)} x\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(128 \, b c^{6} d^{3} - 768 \, a c^{6} d^{2} e + 384 \, a b c^{5} d e^{2} - 16 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} f^{3} x^{5} - 8 \, {\left(8 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} e f^{2} - 3 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} f^{3}\right)} x^{4} - 64 \, {\left(3 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} e^{3} + {\left(315 \, a b^{5} c - 1680 \, a^{2} b^{3} c^{2} + 1808 \, a^{3} b c^{3}\right)} f^{3} - 2 \, {\left(48 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} e^{2} f + {\left(21 \, b^{4} c^{3} - 104 \, a b^{2} c^{4} + 80 \, a^{2} c^{5}\right)} f^{3} + 8 \, {\left(6 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d - 7 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e\right)} f^{2}\right)} x^{3} + 8 \, {\left(6 \, {\left(15 \, a b^{3} c^{3} - 52 \, a^{2} b c^{4}\right)} d - {\left(105 \, a b^{4} c^{2} - 460 \, a^{2} b^{2} c^{3} + 256 \, a^{3} c^{4}\right)} e\right)} f^{2} - {\left(64 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} e^{3} - 7 \, {\left(15 \, b^{5} c^{2} - 88 \, a b^{3} c^{3} + 112 \, a^{2} b c^{4}\right)} f^{3} - 8 \, {\left(30 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d - {\left(35 \, b^{4} c^{3} - 172 \, a b^{2} c^{4} + 128 \, a^{2} c^{5}\right)} e\right)} f^{2} + 48 \, {\left(8 \, {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} d e - 5 \, {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} e^{2}\right)} f\right)} x^{2} + 48 \, {\left(8 \, a b c^{5} d^{2} - 8 \, {\left(3 \, a b^{2} c^{4} - 8 \, a^{2} c^{5}\right)} d e + {\left(15 \, a b^{3} c^{3} - 52 \, a^{2} b c^{4}\right)} e^{2}\right)} f + {\left(256 \, c^{7} d^{3} - 384 \, b c^{6} d^{2} e + 384 \, {\left(b^{2} c^{5} - 2 \, a c^{6}\right)} d e^{2} - 64 \, {\left(3 \, b^{3} c^{4} - 10 \, a b c^{5}\right)} e^{3} + {\left(315 \, b^{6} c - 1890 \, a b^{4} c^{2} + 2704 \, a^{2} b^{2} c^{3} - 480 \, a^{3} c^{4}\right)} f^{3} + 8 \, {\left(6 \, {\left(15 \, b^{4} c^{3} - 62 \, a b^{2} c^{4} + 24 \, a^{2} c^{5}\right)} d - {\left(105 \, b^{5} c^{2} - 530 \, a b^{3} c^{3} + 488 \, a^{2} b c^{4}\right)} e\right)} f^{2} + 48 \, {\left(8 \, {\left(b^{2} c^{5} - 2 \, a c^{6}\right)} d^{2} - 8 \, {\left(3 \, b^{3} c^{4} - 10 \, a b c^{5}\right)} d e + {\left(15 \, b^{4} c^{3} - 62 \, a b^{2} c^{4} + 24 \, a^{2} c^{5}\right)} e^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{128 \, {\left(a b^{2} c^{6} - 4 \, a^{2} c^{7} + {\left(b^{2} c^{7} - 4 \, a c^{8}\right)} x^{2} + {\left(b^{3} c^{6} - 4 \, a b c^{7}\right)} x\right)}}\right]"," ",0,"[1/256*(3*(128*(a*b^2*c^4 - 4*a^2*c^5)*d*e^2 - 64*(a*b^3*c^3 - 4*a^2*b*c^4)*e^3 + 5*(21*a*b^6 - 140*a^2*b^4*c + 240*a^3*b^2*c^2 - 64*a^4*c^3)*f^3 + 8*(6*(5*a*b^4*c^2 - 24*a^2*b^2*c^3 + 16*a^3*c^4)*d - 5*(7*a*b^5*c - 40*a^2*b^3*c^2 + 48*a^3*b*c^3)*e)*f^2 + (128*(b^2*c^5 - 4*a*c^6)*d*e^2 - 64*(b^3*c^4 - 4*a*b*c^5)*e^3 + 5*(21*b^6*c - 140*a*b^4*c^2 + 240*a^2*b^2*c^3 - 64*a^3*c^4)*f^3 + 8*(6*(5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*d - 5*(7*b^5*c^2 - 40*a*b^3*c^3 + 48*a^2*b*c^4)*e)*f^2 + 16*(8*(b^2*c^5 - 4*a*c^6)*d^2 - 24*(b^3*c^4 - 4*a*b*c^5)*d*e + 3*(5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*e^2)*f)*x^2 + 16*(8*(a*b^2*c^4 - 4*a^2*c^5)*d^2 - 24*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e + 3*(5*a*b^4*c^2 - 24*a^2*b^2*c^3 + 16*a^3*c^4)*e^2)*f + (128*(b^3*c^4 - 4*a*b*c^5)*d*e^2 - 64*(b^4*c^3 - 4*a*b^2*c^4)*e^3 + 5*(21*b^7 - 140*a*b^5*c + 240*a^2*b^3*c^2 - 64*a^3*b*c^3)*f^3 + 8*(6*(5*b^5*c^2 - 24*a*b^3*c^3 + 16*a^2*b*c^4)*d - 5*(7*b^6*c - 40*a*b^4*c^2 + 48*a^2*b^2*c^3)*e)*f^2 + 16*(8*(b^3*c^4 - 4*a*b*c^5)*d^2 - 24*(b^4*c^3 - 4*a*b^2*c^4)*d*e + 3*(5*b^5*c^2 - 24*a*b^3*c^3 + 16*a^2*b*c^4)*e^2)*f)*x)*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*(128*b*c^6*d^3 - 768*a*c^6*d^2*e + 384*a*b*c^5*d*e^2 - 16*(b^2*c^5 - 4*a*c^6)*f^3*x^5 - 8*(8*(b^2*c^5 - 4*a*c^6)*e*f^2 - 3*(b^3*c^4 - 4*a*b*c^5)*f^3)*x^4 - 64*(3*a*b^2*c^4 - 8*a^2*c^5)*e^3 + (315*a*b^5*c - 1680*a^2*b^3*c^2 + 1808*a^3*b*c^3)*f^3 - 2*(48*(b^2*c^5 - 4*a*c^6)*e^2*f + (21*b^4*c^3 - 104*a*b^2*c^4 + 80*a^2*c^5)*f^3 + 8*(6*(b^2*c^5 - 4*a*c^6)*d - 7*(b^3*c^4 - 4*a*b*c^5)*e)*f^2)*x^3 + 8*(6*(15*a*b^3*c^3 - 52*a^2*b*c^4)*d - (105*a*b^4*c^2 - 460*a^2*b^2*c^3 + 256*a^3*c^4)*e)*f^2 - (64*(b^2*c^5 - 4*a*c^6)*e^3 - 7*(15*b^5*c^2 - 88*a*b^3*c^3 + 112*a^2*b*c^4)*f^3 - 8*(30*(b^3*c^4 - 4*a*b*c^5)*d - (35*b^4*c^3 - 172*a*b^2*c^4 + 128*a^2*c^5)*e)*f^2 + 48*(8*(b^2*c^5 - 4*a*c^6)*d*e - 5*(b^3*c^4 - 4*a*b*c^5)*e^2)*f)*x^2 + 48*(8*a*b*c^5*d^2 - 8*(3*a*b^2*c^4 - 8*a^2*c^5)*d*e + (15*a*b^3*c^3 - 52*a^2*b*c^4)*e^2)*f + (256*c^7*d^3 - 384*b*c^6*d^2*e + 384*(b^2*c^5 - 2*a*c^6)*d*e^2 - 64*(3*b^3*c^4 - 10*a*b*c^5)*e^3 + (315*b^6*c - 1890*a*b^4*c^2 + 2704*a^2*b^2*c^3 - 480*a^3*c^4)*f^3 + 8*(6*(15*b^4*c^3 - 62*a*b^2*c^4 + 24*a^2*c^5)*d - (105*b^5*c^2 - 530*a*b^3*c^3 + 488*a^2*b*c^4)*e)*f^2 + 48*(8*(b^2*c^5 - 2*a*c^6)*d^2 - 8*(3*b^3*c^4 - 10*a*b*c^5)*d*e + (15*b^4*c^3 - 62*a*b^2*c^4 + 24*a^2*c^5)*e^2)*f)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^6 - 4*a^2*c^7 + (b^2*c^7 - 4*a*c^8)*x^2 + (b^3*c^6 - 4*a*b*c^7)*x), -1/128*(3*(128*(a*b^2*c^4 - 4*a^2*c^5)*d*e^2 - 64*(a*b^3*c^3 - 4*a^2*b*c^4)*e^3 + 5*(21*a*b^6 - 140*a^2*b^4*c + 240*a^3*b^2*c^2 - 64*a^4*c^3)*f^3 + 8*(6*(5*a*b^4*c^2 - 24*a^2*b^2*c^3 + 16*a^3*c^4)*d - 5*(7*a*b^5*c - 40*a^2*b^3*c^2 + 48*a^3*b*c^3)*e)*f^2 + (128*(b^2*c^5 - 4*a*c^6)*d*e^2 - 64*(b^3*c^4 - 4*a*b*c^5)*e^3 + 5*(21*b^6*c - 140*a*b^4*c^2 + 240*a^2*b^2*c^3 - 64*a^3*c^4)*f^3 + 8*(6*(5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*d - 5*(7*b^5*c^2 - 40*a*b^3*c^3 + 48*a^2*b*c^4)*e)*f^2 + 16*(8*(b^2*c^5 - 4*a*c^6)*d^2 - 24*(b^3*c^4 - 4*a*b*c^5)*d*e + 3*(5*b^4*c^3 - 24*a*b^2*c^4 + 16*a^2*c^5)*e^2)*f)*x^2 + 16*(8*(a*b^2*c^4 - 4*a^2*c^5)*d^2 - 24*(a*b^3*c^3 - 4*a^2*b*c^4)*d*e + 3*(5*a*b^4*c^2 - 24*a^2*b^2*c^3 + 16*a^3*c^4)*e^2)*f + (128*(b^3*c^4 - 4*a*b*c^5)*d*e^2 - 64*(b^4*c^3 - 4*a*b^2*c^4)*e^3 + 5*(21*b^7 - 140*a*b^5*c + 240*a^2*b^3*c^2 - 64*a^3*b*c^3)*f^3 + 8*(6*(5*b^5*c^2 - 24*a*b^3*c^3 + 16*a^2*b*c^4)*d - 5*(7*b^6*c - 40*a*b^4*c^2 + 48*a^2*b^2*c^3)*e)*f^2 + 16*(8*(b^3*c^4 - 4*a*b*c^5)*d^2 - 24*(b^4*c^3 - 4*a*b^2*c^4)*d*e + 3*(5*b^5*c^2 - 24*a*b^3*c^3 + 16*a^2*b*c^4)*e^2)*f)*x)*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*(128*b*c^6*d^3 - 768*a*c^6*d^2*e + 384*a*b*c^5*d*e^2 - 16*(b^2*c^5 - 4*a*c^6)*f^3*x^5 - 8*(8*(b^2*c^5 - 4*a*c^6)*e*f^2 - 3*(b^3*c^4 - 4*a*b*c^5)*f^3)*x^4 - 64*(3*a*b^2*c^4 - 8*a^2*c^5)*e^3 + (315*a*b^5*c - 1680*a^2*b^3*c^2 + 1808*a^3*b*c^3)*f^3 - 2*(48*(b^2*c^5 - 4*a*c^6)*e^2*f + (21*b^4*c^3 - 104*a*b^2*c^4 + 80*a^2*c^5)*f^3 + 8*(6*(b^2*c^5 - 4*a*c^6)*d - 7*(b^3*c^4 - 4*a*b*c^5)*e)*f^2)*x^3 + 8*(6*(15*a*b^3*c^3 - 52*a^2*b*c^4)*d - (105*a*b^4*c^2 - 460*a^2*b^2*c^3 + 256*a^3*c^4)*e)*f^2 - (64*(b^2*c^5 - 4*a*c^6)*e^3 - 7*(15*b^5*c^2 - 88*a*b^3*c^3 + 112*a^2*b*c^4)*f^3 - 8*(30*(b^3*c^4 - 4*a*b*c^5)*d - (35*b^4*c^3 - 172*a*b^2*c^4 + 128*a^2*c^5)*e)*f^2 + 48*(8*(b^2*c^5 - 4*a*c^6)*d*e - 5*(b^3*c^4 - 4*a*b*c^5)*e^2)*f)*x^2 + 48*(8*a*b*c^5*d^2 - 8*(3*a*b^2*c^4 - 8*a^2*c^5)*d*e + (15*a*b^3*c^3 - 52*a^2*b*c^4)*e^2)*f + (256*c^7*d^3 - 384*b*c^6*d^2*e + 384*(b^2*c^5 - 2*a*c^6)*d*e^2 - 64*(3*b^3*c^4 - 10*a*b*c^5)*e^3 + (315*b^6*c - 1890*a*b^4*c^2 + 2704*a^2*b^2*c^3 - 480*a^3*c^4)*f^3 + 8*(6*(15*b^4*c^3 - 62*a*b^2*c^4 + 24*a^2*c^5)*d - (105*b^5*c^2 - 530*a*b^3*c^3 + 488*a^2*b*c^4)*e)*f^2 + 48*(8*(b^2*c^5 - 2*a*c^6)*d^2 - 8*(3*b^3*c^4 - 10*a*b*c^5)*d*e + (15*b^4*c^3 - 62*a*b^2*c^4 + 24*a^2*c^5)*e^2)*f)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^6 - 4*a^2*c^7 + (b^2*c^7 - 4*a*c^8)*x^2 + (b^3*c^6 - 4*a*b*c^7)*x)]","B",0
115,1,1305,0,1.237592," ","integrate((f*x^2+e*x+d)^2/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(8 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2} + 3 \, {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} f^{2} + {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} + 3 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} f^{2} + 8 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} f\right)} x^{2} + 8 \, {\left(2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e\right)} f + {\left(8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{2} + 3 \, {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} f^{2} + 8 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e\right)} f\right)} x\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(8 \, b c^{4} d^{2} - 32 \, a c^{4} d e + 8 \, a b c^{3} e^{2} - 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f^{2} x^{3} + {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} f^{2} - {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e f - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f^{2}\right)} x^{2} + 8 \, {\left(2 \, a b c^{3} d - {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e\right)} f + {\left(16 \, c^{5} d^{2} - 16 \, b c^{4} d e + 8 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} e^{2} + {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} f^{2} + 8 \, {\left(2 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d - {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{16 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}, -\frac{{\left(8 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{2} + 3 \, {\left(5 \, a b^{4} - 24 \, a^{2} b^{2} c + 16 \, a^{3} c^{2}\right)} f^{2} + {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e^{2} + 3 \, {\left(5 \, b^{4} c - 24 \, a b^{2} c^{2} + 16 \, a^{2} c^{3}\right)} f^{2} + 8 \, {\left(2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d - 3 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e\right)} f\right)} x^{2} + 8 \, {\left(2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e\right)} f + {\left(8 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{2} + 3 \, {\left(5 \, b^{5} - 24 \, a b^{3} c + 16 \, a^{2} b c^{2}\right)} f^{2} + 8 \, {\left(2 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d - 3 \, {\left(b^{4} c - 4 \, a b^{2} c^{2}\right)} e\right)} f\right)} x\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(8 \, b c^{4} d^{2} - 32 \, a c^{4} d e + 8 \, a b c^{3} e^{2} - 2 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} f^{2} x^{3} + {\left(15 \, a b^{3} c - 52 \, a^{2} b c^{2}\right)} f^{2} - {\left(8 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} e f - 5 \, {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} f^{2}\right)} x^{2} + 8 \, {\left(2 \, a b c^{3} d - {\left(3 \, a b^{2} c^{2} - 8 \, a^{2} c^{3}\right)} e\right)} f + {\left(16 \, c^{5} d^{2} - 16 \, b c^{4} d e + 8 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} e^{2} + {\left(15 \, b^{4} c - 62 \, a b^{2} c^{2} + 24 \, a^{2} c^{3}\right)} f^{2} + 8 \, {\left(2 \, {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d - {\left(3 \, b^{3} c^{2} - 10 \, a b c^{3}\right)} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{8 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5} + {\left(b^{2} c^{5} - 4 \, a c^{6}\right)} x^{2} + {\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} x\right)}}\right]"," ",0,"[-1/16*((8*(a*b^2*c^2 - 4*a^2*c^3)*e^2 + 3*(5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*f^2 + (8*(b^2*c^3 - 4*a*c^4)*e^2 + 3*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*f^2 + 8*(2*(b^2*c^3 - 4*a*c^4)*d - 3*(b^3*c^2 - 4*a*b*c^3)*e)*f)*x^2 + 8*(2*(a*b^2*c^2 - 4*a^2*c^3)*d - 3*(a*b^3*c - 4*a^2*b*c^2)*e)*f + (8*(b^3*c^2 - 4*a*b*c^3)*e^2 + 3*(5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*f^2 + 8*(2*(b^3*c^2 - 4*a*b*c^3)*d - 3*(b^4*c - 4*a*b^2*c^2)*e)*f)*x)*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*(8*b*c^4*d^2 - 32*a*c^4*d*e + 8*a*b*c^3*e^2 - 2*(b^2*c^3 - 4*a*c^4)*f^2*x^3 + (15*a*b^3*c - 52*a^2*b*c^2)*f^2 - (8*(b^2*c^3 - 4*a*c^4)*e*f - 5*(b^3*c^2 - 4*a*b*c^3)*f^2)*x^2 + 8*(2*a*b*c^3*d - (3*a*b^2*c^2 - 8*a^2*c^3)*e)*f + (16*c^5*d^2 - 16*b*c^4*d*e + 8*(b^2*c^3 - 2*a*c^4)*e^2 + (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*f^2 + 8*(2*(b^2*c^3 - 2*a*c^4)*d - (3*b^3*c^2 - 10*a*b*c^3)*e)*f)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x), -1/8*((8*(a*b^2*c^2 - 4*a^2*c^3)*e^2 + 3*(5*a*b^4 - 24*a^2*b^2*c + 16*a^3*c^2)*f^2 + (8*(b^2*c^3 - 4*a*c^4)*e^2 + 3*(5*b^4*c - 24*a*b^2*c^2 + 16*a^2*c^3)*f^2 + 8*(2*(b^2*c^3 - 4*a*c^4)*d - 3*(b^3*c^2 - 4*a*b*c^3)*e)*f)*x^2 + 8*(2*(a*b^2*c^2 - 4*a^2*c^3)*d - 3*(a*b^3*c - 4*a^2*b*c^2)*e)*f + (8*(b^3*c^2 - 4*a*b*c^3)*e^2 + 3*(5*b^5 - 24*a*b^3*c + 16*a^2*b*c^2)*f^2 + 8*(2*(b^3*c^2 - 4*a*b*c^3)*d - 3*(b^4*c - 4*a*b^2*c^2)*e)*f)*x)*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*(8*b*c^4*d^2 - 32*a*c^4*d*e + 8*a*b*c^3*e^2 - 2*(b^2*c^3 - 4*a*c^4)*f^2*x^3 + (15*a*b^3*c - 52*a^2*b*c^2)*f^2 - (8*(b^2*c^3 - 4*a*c^4)*e*f - 5*(b^3*c^2 - 4*a*b*c^3)*f^2)*x^2 + 8*(2*a*b*c^3*d - (3*a*b^2*c^2 - 8*a^2*c^3)*e)*f + (16*c^5*d^2 - 16*b*c^4*d*e + 8*(b^2*c^3 - 2*a*c^4)*e^2 + (15*b^4*c - 62*a*b^2*c^2 + 24*a^2*c^3)*f^2 + 8*(2*(b^2*c^3 - 2*a*c^4)*d - (3*b^3*c^2 - 10*a*b*c^3)*e)*f)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^4 - 4*a^2*c^5 + (b^2*c^5 - 4*a*c^6)*x^2 + (b^3*c^4 - 4*a*b*c^5)*x)]","B",0
116,1,429,0,0.784266," ","integrate((f*x^2+e*x+d)/(c*x^2+b*x+a)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} f x^{2} + {\left(b^{3} - 4 \, a b c\right)} f x + {\left(a b^{2} - 4 \, a^{2} c\right)} f\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(b c^{2} d - 2 \, a c^{2} e + a b c f + {\left(2 \, c^{3} d - b c^{2} e + {\left(b^{2} c - 2 \, a c^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{2 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x\right)}}, -\frac{{\left({\left(b^{2} c - 4 \, a c^{2}\right)} f x^{2} + {\left(b^{3} - 4 \, a b c\right)} f x + {\left(a b^{2} - 4 \, a^{2} c\right)} f\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(b c^{2} d - 2 \, a c^{2} e + a b c f + {\left(2 \, c^{3} d - b c^{2} e + {\left(b^{2} c - 2 \, a c^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{a b^{2} c^{2} - 4 \, a^{2} c^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} x^{2} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} x}\right]"," ",0,"[1/2*(((b^2*c - 4*a*c^2)*f*x^2 + (b^3 - 4*a*b*c)*f*x + (a*b^2 - 4*a^2*c)*f)*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*(b*c^2*d - 2*a*c^2*e + a*b*c*f + (2*c^3*d - b*c^2*e + (b^2*c - 2*a*c^2)*f)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x), -(((b^2*c - 4*a*c^2)*f*x^2 + (b^3 - 4*a*b*c)*f*x + (a*b^2 - 4*a^2*c)*f)*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*(b*c^2*d - 2*a*c^2*e + a*b*c*f + (2*c^3*d - b*c^2*e + (b^2*c - 2*a*c^2)*f)*x)*sqrt(c*x^2 + b*x + a))/(a*b^2*c^2 - 4*a^2*c^3 + (b^2*c^3 - 4*a*c^4)*x^2 + (b^3*c^2 - 4*a*b*c^3)*x)]","B",0
117,-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
118,1,3995,0,5.384755," ","integrate((f*x^2+e*x+d)^3/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} e^{2} f + 5 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} f^{3} + 12 \, {\left(2 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d - 5 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} e\right)} f^{2}\right)} x^{4} + 24 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} e^{2} f + 5 \, {\left(7 \, a^{2} b^{6} - 60 \, a^{3} b^{4} c + 144 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} f^{3} + 2 \, {\left(24 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} e^{2} f + 5 \, {\left(7 \, b^{7} c - 60 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} f^{3} + 12 \, {\left(2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d - 5 \, {\left(b^{6} c^{2} - 8 \, a b^{4} c^{3} + 16 \, a^{2} b^{2} c^{4}\right)} e\right)} f^{2}\right)} x^{3} + 12 \, {\left(2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d - 5 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} e\right)} f^{2} + {\left(24 \, {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} e^{2} f + 5 \, {\left(7 \, b^{8} - 46 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 224 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} f^{3} + 12 \, {\left(2 \, {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} d - 5 \, {\left(b^{7} c - 6 \, a b^{5} c^{2} + 32 \, a^{3} b c^{4}\right)} e\right)} f^{2}\right)} x^{2} + 2 \, {\left(24 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} e^{2} f + 5 \, {\left(7 \, a b^{7} - 60 \, a^{2} b^{5} c + 144 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} f^{3} + 12 \, {\left(2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d - 5 \, {\left(a b^{6} c - 8 \, a^{2} b^{4} c^{2} + 16 \, a^{3} b^{2} c^{3}\right)} e\right)} f^{2}\right)} x\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(192 \, a^{2} b c^{5} d e^{2} - 128 \, a^{3} c^{5} e^{3} + 6 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} f^{3} x^{5} + 3 \, {\left(12 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} e f^{2} - 7 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} f^{3}\right)} x^{4} - 8 \, {\left(b^{3} c^{5} - 12 \, a b c^{6}\right)} d^{3} - 48 \, {\left(a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} d^{2} e - {\left(105 \, a^{2} b^{5} c - 760 \, a^{3} b^{3} c^{2} + 1296 \, a^{4} b c^{3}\right)} f^{3} + 4 \, {\left(32 \, c^{8} d^{3} - 48 \, b c^{7} d^{2} e + 12 \, {\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d e^{2} + 2 \, {\left(b^{3} c^{5} - 12 \, a b c^{6}\right)} e^{3} - {\left(35 \, b^{6} c^{2} - 279 \, a b^{4} c^{3} + 588 \, a^{2} b^{2} c^{4} - 160 \, a^{3} c^{5}\right)} f^{3} - 12 \, {\left(2 \, {\left(b^{4} c^{4} - 7 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} d - {\left(5 \, b^{5} c^{3} - 37 \, a b^{3} c^{4} + 64 \, a^{2} b c^{5}\right)} e\right)} f^{2} + 12 \, {\left({\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d^{2} + {\left(b^{3} c^{5} - 12 \, a b c^{6}\right)} d e - 2 \, {\left(b^{4} c^{4} - 7 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} e^{2}\right)} f\right)} x^{3} - 12 \, {\left(2 \, {\left(3 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d - {\left(15 \, a^{2} b^{4} c^{2} - 100 \, a^{3} b^{2} c^{3} + 128 \, a^{4} c^{4}\right)} e\right)} f^{2} + 3 \, {\left(64 \, b c^{7} d^{3} - 96 \, b^{2} c^{6} d^{2} e + 24 \, {\left(b^{3} c^{5} + 4 \, a b c^{6}\right)} d e^{2} - 16 \, {\left(a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} e^{3} - {\left(35 \, b^{7} c - 230 \, a b^{5} c^{2} + 232 \, a^{2} b^{3} c^{3} + 448 \, a^{3} b c^{4}\right)} f^{3} - 12 \, {\left(2 \, {\left(b^{5} c^{3} - 6 \, a b^{3} c^{4}\right)} d - {\left(5 \, b^{6} c^{2} - 30 \, a b^{4} c^{3} + 16 \, a^{2} b^{2} c^{4} + 64 \, a^{3} c^{5}\right)} e\right)} f^{2} + 24 \, {\left({\left(b^{3} c^{5} + 4 \, a b c^{6}\right)} d^{2} - 4 \, {\left(a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} d e - {\left(b^{5} c^{3} - 6 \, a b^{3} c^{4}\right)} e^{2}\right)} f\right)} x^{2} + 24 \, {\left(8 \, a^{2} b c^{5} d^{2} - 32 \, a^{3} c^{5} d e - {\left(3 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} e^{2}\right)} f + 6 \, {\left(48 \, a b^{2} c^{5} d e^{2} - 32 \, a^{2} b c^{5} e^{3} + 8 \, {\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d^{3} - 12 \, {\left(b^{3} c^{5} + 4 \, a b c^{6}\right)} d^{2} e - {\left(35 \, a b^{6} c - 265 \, a^{2} b^{4} c^{2} + 504 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} f^{3} - 12 \, {\left(2 \, {\left(a b^{4} c^{3} - 7 \, a^{2} b^{2} c^{4} + 4 \, a^{3} c^{5}\right)} d - {\left(5 \, a b^{5} c^{2} - 35 \, a^{2} b^{3} c^{3} + 52 \, a^{3} b c^{4}\right)} e\right)} f^{2} + 24 \, {\left(2 \, a b^{2} c^{5} d^{2} - 8 \, a^{2} b c^{5} d e - {\left(a b^{4} c^{3} - 7 \, a^{2} b^{2} c^{4} + 4 \, a^{3} c^{5}\right)} e^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{48 \, {\left(a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 16 \, a^{4} c^{7} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} x^{4} + 2 \, {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} x^{3} + {\left(b^{6} c^{5} - 6 \, a b^{4} c^{6} + 32 \, a^{3} c^{8}\right)} x^{2} + 2 \, {\left(a b^{5} c^{5} - 8 \, a^{2} b^{3} c^{6} + 16 \, a^{3} b c^{7}\right)} x\right)}}, -\frac{3 \, {\left({\left(24 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} e^{2} f + 5 \, {\left(7 \, b^{6} c^{2} - 60 \, a b^{4} c^{3} + 144 \, a^{2} b^{2} c^{4} - 64 \, a^{3} c^{5}\right)} f^{3} + 12 \, {\left(2 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} d - 5 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} e\right)} f^{2}\right)} x^{4} + 24 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} e^{2} f + 5 \, {\left(7 \, a^{2} b^{6} - 60 \, a^{3} b^{4} c + 144 \, a^{4} b^{2} c^{2} - 64 \, a^{5} c^{3}\right)} f^{3} + 2 \, {\left(24 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} e^{2} f + 5 \, {\left(7 \, b^{7} c - 60 \, a b^{5} c^{2} + 144 \, a^{2} b^{3} c^{3} - 64 \, a^{3} b c^{4}\right)} f^{3} + 12 \, {\left(2 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} d - 5 \, {\left(b^{6} c^{2} - 8 \, a b^{4} c^{3} + 16 \, a^{2} b^{2} c^{4}\right)} e\right)} f^{2}\right)} x^{3} + 12 \, {\left(2 \, {\left(a^{2} b^{4} c^{2} - 8 \, a^{3} b^{2} c^{3} + 16 \, a^{4} c^{4}\right)} d - 5 \, {\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} e\right)} f^{2} + {\left(24 \, {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} e^{2} f + 5 \, {\left(7 \, b^{8} - 46 \, a b^{6} c + 24 \, a^{2} b^{4} c^{2} + 224 \, a^{3} b^{2} c^{3} - 128 \, a^{4} c^{4}\right)} f^{3} + 12 \, {\left(2 \, {\left(b^{6} c^{2} - 6 \, a b^{4} c^{3} + 32 \, a^{3} c^{5}\right)} d - 5 \, {\left(b^{7} c - 6 \, a b^{5} c^{2} + 32 \, a^{3} b c^{4}\right)} e\right)} f^{2}\right)} x^{2} + 2 \, {\left(24 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} e^{2} f + 5 \, {\left(7 \, a b^{7} - 60 \, a^{2} b^{5} c + 144 \, a^{3} b^{3} c^{2} - 64 \, a^{4} b c^{3}\right)} f^{3} + 12 \, {\left(2 \, {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} d - 5 \, {\left(a b^{6} c - 8 \, a^{2} b^{4} c^{2} + 16 \, a^{3} b^{2} c^{3}\right)} e\right)} f^{2}\right)} x\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(192 \, a^{2} b c^{5} d e^{2} - 128 \, a^{3} c^{5} e^{3} + 6 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} f^{3} x^{5} + 3 \, {\left(12 \, {\left(b^{4} c^{4} - 8 \, a b^{2} c^{5} + 16 \, a^{2} c^{6}\right)} e f^{2} - 7 \, {\left(b^{5} c^{3} - 8 \, a b^{3} c^{4} + 16 \, a^{2} b c^{5}\right)} f^{3}\right)} x^{4} - 8 \, {\left(b^{3} c^{5} - 12 \, a b c^{6}\right)} d^{3} - 48 \, {\left(a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} d^{2} e - {\left(105 \, a^{2} b^{5} c - 760 \, a^{3} b^{3} c^{2} + 1296 \, a^{4} b c^{3}\right)} f^{3} + 4 \, {\left(32 \, c^{8} d^{3} - 48 \, b c^{7} d^{2} e + 12 \, {\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d e^{2} + 2 \, {\left(b^{3} c^{5} - 12 \, a b c^{6}\right)} e^{3} - {\left(35 \, b^{6} c^{2} - 279 \, a b^{4} c^{3} + 588 \, a^{2} b^{2} c^{4} - 160 \, a^{3} c^{5}\right)} f^{3} - 12 \, {\left(2 \, {\left(b^{4} c^{4} - 7 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} d - {\left(5 \, b^{5} c^{3} - 37 \, a b^{3} c^{4} + 64 \, a^{2} b c^{5}\right)} e\right)} f^{2} + 12 \, {\left({\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d^{2} + {\left(b^{3} c^{5} - 12 \, a b c^{6}\right)} d e - 2 \, {\left(b^{4} c^{4} - 7 \, a b^{2} c^{5} + 8 \, a^{2} c^{6}\right)} e^{2}\right)} f\right)} x^{3} - 12 \, {\left(2 \, {\left(3 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} d - {\left(15 \, a^{2} b^{4} c^{2} - 100 \, a^{3} b^{2} c^{3} + 128 \, a^{4} c^{4}\right)} e\right)} f^{2} + 3 \, {\left(64 \, b c^{7} d^{3} - 96 \, b^{2} c^{6} d^{2} e + 24 \, {\left(b^{3} c^{5} + 4 \, a b c^{6}\right)} d e^{2} - 16 \, {\left(a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} e^{3} - {\left(35 \, b^{7} c - 230 \, a b^{5} c^{2} + 232 \, a^{2} b^{3} c^{3} + 448 \, a^{3} b c^{4}\right)} f^{3} - 12 \, {\left(2 \, {\left(b^{5} c^{3} - 6 \, a b^{3} c^{4}\right)} d - {\left(5 \, b^{6} c^{2} - 30 \, a b^{4} c^{3} + 16 \, a^{2} b^{2} c^{4} + 64 \, a^{3} c^{5}\right)} e\right)} f^{2} + 24 \, {\left({\left(b^{3} c^{5} + 4 \, a b c^{6}\right)} d^{2} - 4 \, {\left(a b^{2} c^{5} + 4 \, a^{2} c^{6}\right)} d e - {\left(b^{5} c^{3} - 6 \, a b^{3} c^{4}\right)} e^{2}\right)} f\right)} x^{2} + 24 \, {\left(8 \, a^{2} b c^{5} d^{2} - 32 \, a^{3} c^{5} d e - {\left(3 \, a^{2} b^{3} c^{3} - 20 \, a^{3} b c^{4}\right)} e^{2}\right)} f + 6 \, {\left(48 \, a b^{2} c^{5} d e^{2} - 32 \, a^{2} b c^{5} e^{3} + 8 \, {\left(b^{2} c^{6} + 4 \, a c^{7}\right)} d^{3} - 12 \, {\left(b^{3} c^{5} + 4 \, a b c^{6}\right)} d^{2} e - {\left(35 \, a b^{6} c - 265 \, a^{2} b^{4} c^{2} + 504 \, a^{3} b^{2} c^{3} - 80 \, a^{4} c^{4}\right)} f^{3} - 12 \, {\left(2 \, {\left(a b^{4} c^{3} - 7 \, a^{2} b^{2} c^{4} + 4 \, a^{3} c^{5}\right)} d - {\left(5 \, a b^{5} c^{2} - 35 \, a^{2} b^{3} c^{3} + 52 \, a^{3} b c^{4}\right)} e\right)} f^{2} + 24 \, {\left(2 \, a b^{2} c^{5} d^{2} - 8 \, a^{2} b c^{5} d e - {\left(a b^{4} c^{3} - 7 \, a^{2} b^{2} c^{4} + 4 \, a^{3} c^{5}\right)} e^{2}\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{24 \, {\left(a^{2} b^{4} c^{5} - 8 \, a^{3} b^{2} c^{6} + 16 \, a^{4} c^{7} + {\left(b^{4} c^{7} - 8 \, a b^{2} c^{8} + 16 \, a^{2} c^{9}\right)} x^{4} + 2 \, {\left(b^{5} c^{6} - 8 \, a b^{3} c^{7} + 16 \, a^{2} b c^{8}\right)} x^{3} + {\left(b^{6} c^{5} - 6 \, a b^{4} c^{6} + 32 \, a^{3} c^{8}\right)} x^{2} + 2 \, {\left(a b^{5} c^{5} - 8 \, a^{2} b^{3} c^{6} + 16 \, a^{3} b c^{7}\right)} x\right)}}\right]"," ",0,"[-1/48*(3*((24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*e^2*f + 5*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*f^3 + 12*(2*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d - 5*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*e)*f^2)*x^4 + 24*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*e^2*f + 5*(7*a^2*b^6 - 60*a^3*b^4*c + 144*a^4*b^2*c^2 - 64*a^5*c^3)*f^3 + 2*(24*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*e^2*f + 5*(7*b^7*c - 60*a*b^5*c^2 + 144*a^2*b^3*c^3 - 64*a^3*b*c^4)*f^3 + 12*(2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d - 5*(b^6*c^2 - 8*a*b^4*c^3 + 16*a^2*b^2*c^4)*e)*f^2)*x^3 + 12*(2*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d - 5*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*e)*f^2 + (24*(b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*e^2*f + 5*(7*b^8 - 46*a*b^6*c + 24*a^2*b^4*c^2 + 224*a^3*b^2*c^3 - 128*a^4*c^4)*f^3 + 12*(2*(b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*d - 5*(b^7*c - 6*a*b^5*c^2 + 32*a^3*b*c^4)*e)*f^2)*x^2 + 2*(24*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*e^2*f + 5*(7*a*b^7 - 60*a^2*b^5*c + 144*a^3*b^3*c^2 - 64*a^4*b*c^3)*f^3 + 12*(2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d - 5*(a*b^6*c - 8*a^2*b^4*c^2 + 16*a^3*b^2*c^3)*e)*f^2)*x)*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*(192*a^2*b*c^5*d*e^2 - 128*a^3*c^5*e^3 + 6*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*f^3*x^5 + 3*(12*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*e*f^2 - 7*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*f^3)*x^4 - 8*(b^3*c^5 - 12*a*b*c^6)*d^3 - 48*(a*b^2*c^5 + 4*a^2*c^6)*d^2*e - (105*a^2*b^5*c - 760*a^3*b^3*c^2 + 1296*a^4*b*c^3)*f^3 + 4*(32*c^8*d^3 - 48*b*c^7*d^2*e + 12*(b^2*c^6 + 4*a*c^7)*d*e^2 + 2*(b^3*c^5 - 12*a*b*c^6)*e^3 - (35*b^6*c^2 - 279*a*b^4*c^3 + 588*a^2*b^2*c^4 - 160*a^3*c^5)*f^3 - 12*(2*(b^4*c^4 - 7*a*b^2*c^5 + 8*a^2*c^6)*d - (5*b^5*c^3 - 37*a*b^3*c^4 + 64*a^2*b*c^5)*e)*f^2 + 12*((b^2*c^6 + 4*a*c^7)*d^2 + (b^3*c^5 - 12*a*b*c^6)*d*e - 2*(b^4*c^4 - 7*a*b^2*c^5 + 8*a^2*c^6)*e^2)*f)*x^3 - 12*(2*(3*a^2*b^3*c^3 - 20*a^3*b*c^4)*d - (15*a^2*b^4*c^2 - 100*a^3*b^2*c^3 + 128*a^4*c^4)*e)*f^2 + 3*(64*b*c^7*d^3 - 96*b^2*c^6*d^2*e + 24*(b^3*c^5 + 4*a*b*c^6)*d*e^2 - 16*(a*b^2*c^5 + 4*a^2*c^6)*e^3 - (35*b^7*c - 230*a*b^5*c^2 + 232*a^2*b^3*c^3 + 448*a^3*b*c^4)*f^3 - 12*(2*(b^5*c^3 - 6*a*b^3*c^4)*d - (5*b^6*c^2 - 30*a*b^4*c^3 + 16*a^2*b^2*c^4 + 64*a^3*c^5)*e)*f^2 + 24*((b^3*c^5 + 4*a*b*c^6)*d^2 - 4*(a*b^2*c^5 + 4*a^2*c^6)*d*e - (b^5*c^3 - 6*a*b^3*c^4)*e^2)*f)*x^2 + 24*(8*a^2*b*c^5*d^2 - 32*a^3*c^5*d*e - (3*a^2*b^3*c^3 - 20*a^3*b*c^4)*e^2)*f + 6*(48*a*b^2*c^5*d*e^2 - 32*a^2*b*c^5*e^3 + 8*(b^2*c^6 + 4*a*c^7)*d^3 - 12*(b^3*c^5 + 4*a*b*c^6)*d^2*e - (35*a*b^6*c - 265*a^2*b^4*c^2 + 504*a^3*b^2*c^3 - 80*a^4*c^4)*f^3 - 12*(2*(a*b^4*c^3 - 7*a^2*b^2*c^4 + 4*a^3*c^5)*d - (5*a*b^5*c^2 - 35*a^2*b^3*c^3 + 52*a^3*b*c^4)*e)*f^2 + 24*(2*a*b^2*c^5*d^2 - 8*a^2*b*c^5*d*e - (a*b^4*c^3 - 7*a^2*b^2*c^4 + 4*a^3*c^5)*e^2)*f)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 16*a^4*c^7 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*x^4 + 2*(b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*x^3 + (b^6*c^5 - 6*a*b^4*c^6 + 32*a^3*c^8)*x^2 + 2*(a*b^5*c^5 - 8*a^2*b^3*c^6 + 16*a^3*b*c^7)*x), -1/24*(3*((24*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*e^2*f + 5*(7*b^6*c^2 - 60*a*b^4*c^3 + 144*a^2*b^2*c^4 - 64*a^3*c^5)*f^3 + 12*(2*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*d - 5*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*e)*f^2)*x^4 + 24*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*e^2*f + 5*(7*a^2*b^6 - 60*a^3*b^4*c + 144*a^4*b^2*c^2 - 64*a^5*c^3)*f^3 + 2*(24*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*e^2*f + 5*(7*b^7*c - 60*a*b^5*c^2 + 144*a^2*b^3*c^3 - 64*a^3*b*c^4)*f^3 + 12*(2*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*d - 5*(b^6*c^2 - 8*a*b^4*c^3 + 16*a^2*b^2*c^4)*e)*f^2)*x^3 + 12*(2*(a^2*b^4*c^2 - 8*a^3*b^2*c^3 + 16*a^4*c^4)*d - 5*(a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*e)*f^2 + (24*(b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*e^2*f + 5*(7*b^8 - 46*a*b^6*c + 24*a^2*b^4*c^2 + 224*a^3*b^2*c^3 - 128*a^4*c^4)*f^3 + 12*(2*(b^6*c^2 - 6*a*b^4*c^3 + 32*a^3*c^5)*d - 5*(b^7*c - 6*a*b^5*c^2 + 32*a^3*b*c^4)*e)*f^2)*x^2 + 2*(24*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*e^2*f + 5*(7*a*b^7 - 60*a^2*b^5*c + 144*a^3*b^3*c^2 - 64*a^4*b*c^3)*f^3 + 12*(2*(a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*d - 5*(a*b^6*c - 8*a^2*b^4*c^2 + 16*a^3*b^2*c^3)*e)*f^2)*x)*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*(192*a^2*b*c^5*d*e^2 - 128*a^3*c^5*e^3 + 6*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*f^3*x^5 + 3*(12*(b^4*c^4 - 8*a*b^2*c^5 + 16*a^2*c^6)*e*f^2 - 7*(b^5*c^3 - 8*a*b^3*c^4 + 16*a^2*b*c^5)*f^3)*x^4 - 8*(b^3*c^5 - 12*a*b*c^6)*d^3 - 48*(a*b^2*c^5 + 4*a^2*c^6)*d^2*e - (105*a^2*b^5*c - 760*a^3*b^3*c^2 + 1296*a^4*b*c^3)*f^3 + 4*(32*c^8*d^3 - 48*b*c^7*d^2*e + 12*(b^2*c^6 + 4*a*c^7)*d*e^2 + 2*(b^3*c^5 - 12*a*b*c^6)*e^3 - (35*b^6*c^2 - 279*a*b^4*c^3 + 588*a^2*b^2*c^4 - 160*a^3*c^5)*f^3 - 12*(2*(b^4*c^4 - 7*a*b^2*c^5 + 8*a^2*c^6)*d - (5*b^5*c^3 - 37*a*b^3*c^4 + 64*a^2*b*c^5)*e)*f^2 + 12*((b^2*c^6 + 4*a*c^7)*d^2 + (b^3*c^5 - 12*a*b*c^6)*d*e - 2*(b^4*c^4 - 7*a*b^2*c^5 + 8*a^2*c^6)*e^2)*f)*x^3 - 12*(2*(3*a^2*b^3*c^3 - 20*a^3*b*c^4)*d - (15*a^2*b^4*c^2 - 100*a^3*b^2*c^3 + 128*a^4*c^4)*e)*f^2 + 3*(64*b*c^7*d^3 - 96*b^2*c^6*d^2*e + 24*(b^3*c^5 + 4*a*b*c^6)*d*e^2 - 16*(a*b^2*c^5 + 4*a^2*c^6)*e^3 - (35*b^7*c - 230*a*b^5*c^2 + 232*a^2*b^3*c^3 + 448*a^3*b*c^4)*f^3 - 12*(2*(b^5*c^3 - 6*a*b^3*c^4)*d - (5*b^6*c^2 - 30*a*b^4*c^3 + 16*a^2*b^2*c^4 + 64*a^3*c^5)*e)*f^2 + 24*((b^3*c^5 + 4*a*b*c^6)*d^2 - 4*(a*b^2*c^5 + 4*a^2*c^6)*d*e - (b^5*c^3 - 6*a*b^3*c^4)*e^2)*f)*x^2 + 24*(8*a^2*b*c^5*d^2 - 32*a^3*c^5*d*e - (3*a^2*b^3*c^3 - 20*a^3*b*c^4)*e^2)*f + 6*(48*a*b^2*c^5*d*e^2 - 32*a^2*b*c^5*e^3 + 8*(b^2*c^6 + 4*a*c^7)*d^3 - 12*(b^3*c^5 + 4*a*b*c^6)*d^2*e - (35*a*b^6*c - 265*a^2*b^4*c^2 + 504*a^3*b^2*c^3 - 80*a^4*c^4)*f^3 - 12*(2*(a*b^4*c^3 - 7*a^2*b^2*c^4 + 4*a^3*c^5)*d - (5*a*b^5*c^2 - 35*a^2*b^3*c^3 + 52*a^3*b*c^4)*e)*f^2 + 24*(2*a*b^2*c^5*d^2 - 8*a^2*b*c^5*d*e - (a*b^4*c^3 - 7*a^2*b^2*c^4 + 4*a^3*c^5)*e^2)*f)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^5 - 8*a^3*b^2*c^6 + 16*a^4*c^7 + (b^4*c^7 - 8*a*b^2*c^8 + 16*a^2*c^9)*x^4 + 2*(b^5*c^6 - 8*a*b^3*c^7 + 16*a^2*b*c^8)*x^3 + (b^6*c^5 - 6*a*b^4*c^6 + 32*a^3*c^8)*x^2 + 2*(a*b^5*c^5 - 8*a^2*b^3*c^6 + 16*a^3*b*c^7)*x)]","B",0
119,1,1581,0,3.503423," ","integrate((f*x^2+e*x+d)^2/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} f^{2} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} f^{2} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} f^{2} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} f^{2} x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} f^{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(8 \, a^{2} b c^{3} e^{2} + 2 \, {\left(8 \, c^{6} d^{2} - 8 \, b c^{5} d e + {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} e^{2} - 2 \, {\left(b^{4} c^{2} - 7 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} f^{2} + {\left(2 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d + {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} e\right)} f\right)} x^{3} - {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} d^{2} - 4 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e - {\left(3 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} f^{2} + 3 \, {\left(8 \, b c^{5} d^{2} - 8 \, b^{2} c^{4} d e + {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} e^{2} - {\left(b^{5} c - 6 \, a b^{3} c^{2}\right)} f^{2} + 2 \, {\left({\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d - 2 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e\right)} f\right)} x^{2} + 16 \, {\left(a^{2} b c^{3} d - 2 \, a^{3} c^{3} e\right)} f + 6 \, {\left(2 \, a b^{2} c^{3} e^{2} + {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{2} - {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d e - {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} f^{2} + 4 \, {\left(a b^{2} c^{3} d - 2 \, a^{2} b c^{3} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{6 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}, -\frac{3 \, {\left({\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} f^{2} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} f^{2} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} f^{2} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} f^{2} x + {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2}\right)} f^{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(8 \, a^{2} b c^{3} e^{2} + 2 \, {\left(8 \, c^{6} d^{2} - 8 \, b c^{5} d e + {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} e^{2} - 2 \, {\left(b^{4} c^{2} - 7 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} f^{2} + {\left(2 \, {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d + {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} e\right)} f\right)} x^{3} - {\left(b^{3} c^{3} - 12 \, a b c^{4}\right)} d^{2} - 4 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d e - {\left(3 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} f^{2} + 3 \, {\left(8 \, b c^{5} d^{2} - 8 \, b^{2} c^{4} d e + {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} e^{2} - {\left(b^{5} c - 6 \, a b^{3} c^{2}\right)} f^{2} + 2 \, {\left({\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d - 2 \, {\left(a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} e\right)} f\right)} x^{2} + 16 \, {\left(a^{2} b c^{3} d - 2 \, a^{3} c^{3} e\right)} f + 6 \, {\left(2 \, a b^{2} c^{3} e^{2} + {\left(b^{2} c^{4} + 4 \, a c^{5}\right)} d^{2} - {\left(b^{3} c^{3} + 4 \, a b c^{4}\right)} d e - {\left(a b^{4} c - 7 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} f^{2} + 4 \, {\left(a b^{2} c^{3} d - 2 \, a^{2} b c^{3} e\right)} f\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} c^{3} - 8 \, a^{3} b^{2} c^{4} + 16 \, a^{4} c^{5} + {\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} x^{4} + 2 \, {\left(b^{5} c^{4} - 8 \, a b^{3} c^{5} + 16 \, a^{2} b c^{6}\right)} x^{3} + {\left(b^{6} c^{3} - 6 \, a b^{4} c^{4} + 32 \, a^{3} c^{6}\right)} x^{2} + 2 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} x\right)}}\right]"," ",0,"[1/6*(3*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*f^2*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*f^2*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*f^2*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*f^2*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*f^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*(8*a^2*b*c^3*e^2 + 2*(8*c^6*d^2 - 8*b*c^5*d*e + (b^2*c^4 + 4*a*c^5)*e^2 - 2*(b^4*c^2 - 7*a*b^2*c^3 + 8*a^2*c^4)*f^2 + (2*(b^2*c^4 + 4*a*c^5)*d + (b^3*c^3 - 12*a*b*c^4)*e)*f)*x^3 - (b^3*c^3 - 12*a*b*c^4)*d^2 - 4*(a*b^2*c^3 + 4*a^2*c^4)*d*e - (3*a^2*b^3*c - 20*a^3*b*c^2)*f^2 + 3*(8*b*c^5*d^2 - 8*b^2*c^4*d*e + (b^3*c^3 + 4*a*b*c^4)*e^2 - (b^5*c - 6*a*b^3*c^2)*f^2 + 2*((b^3*c^3 + 4*a*b*c^4)*d - 2*(a*b^2*c^3 + 4*a^2*c^4)*e)*f)*x^2 + 16*(a^2*b*c^3*d - 2*a^3*c^3*e)*f + 6*(2*a*b^2*c^3*e^2 + (b^2*c^4 + 4*a*c^5)*d^2 - (b^3*c^3 + 4*a*b*c^4)*d*e - (a*b^4*c - 7*a^2*b^2*c^2 + 4*a^3*c^3)*f^2 + 4*(a*b^2*c^3*d - 2*a^2*b*c^3*e)*f)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x), -1/3*(3*((b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*f^2*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*f^2*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*f^2*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*f^2*x + (a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2)*f^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*(8*a^2*b*c^3*e^2 + 2*(8*c^6*d^2 - 8*b*c^5*d*e + (b^2*c^4 + 4*a*c^5)*e^2 - 2*(b^4*c^2 - 7*a*b^2*c^3 + 8*a^2*c^4)*f^2 + (2*(b^2*c^4 + 4*a*c^5)*d + (b^3*c^3 - 12*a*b*c^4)*e)*f)*x^3 - (b^3*c^3 - 12*a*b*c^4)*d^2 - 4*(a*b^2*c^3 + 4*a^2*c^4)*d*e - (3*a^2*b^3*c - 20*a^3*b*c^2)*f^2 + 3*(8*b*c^5*d^2 - 8*b^2*c^4*d*e + (b^3*c^3 + 4*a*b*c^4)*e^2 - (b^5*c - 6*a*b^3*c^2)*f^2 + 2*((b^3*c^3 + 4*a*b*c^4)*d - 2*(a*b^2*c^3 + 4*a^2*c^4)*e)*f)*x^2 + 16*(a^2*b*c^3*d - 2*a^3*c^3*e)*f + 6*(2*a*b^2*c^3*e^2 + (b^2*c^4 + 4*a*c^5)*d^2 - (b^3*c^3 + 4*a*b*c^4)*d*e - (a*b^4*c - 7*a^2*b^2*c^2 + 4*a^3*c^3)*f^2 + 4*(a*b^2*c^3*d - 2*a^2*b*c^3*e)*f)*x)*sqrt(c*x^2 + b*x + a))/(a^2*b^4*c^3 - 8*a^3*b^2*c^4 + 16*a^4*c^5 + (b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*x^4 + 2*(b^5*c^4 - 8*a*b^3*c^5 + 16*a^2*b*c^6)*x^3 + (b^6*c^3 - 6*a*b^4*c^4 + 32*a^3*c^6)*x^2 + 2*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*x)]","A",0
120,1,286,0,2.597457," ","integrate((f*x^2+e*x+d)/(c*x^2+b*x+a)^(5/2),x, algorithm=""fricas"")","\frac{2 \, {\left(8 \, a^{2} b f + 2 \, {\left(8 \, c^{3} d - 4 \, b c^{2} e + {\left(b^{2} c + 4 \, a c^{2}\right)} f\right)} x^{3} + 3 \, {\left(8 \, b c^{2} d - 4 \, b^{2} c e + {\left(b^{3} + 4 \, a b c\right)} f\right)} x^{2} - {\left(b^{3} - 12 \, a b c\right)} d - 2 \, {\left(a b^{2} + 4 \, a^{2} c\right)} e + 3 \, {\left(4 \, a b^{2} f + 2 \, {\left(b^{2} c + 4 \, a c^{2}\right)} d - {\left(b^{3} + 4 \, a b c\right)} e\right)} x\right)} \sqrt{c x^{2} + b x + a}}{3 \, {\left(a^{2} b^{4} - 8 \, a^{3} b^{2} c + 16 \, a^{4} c^{2} + {\left(b^{4} c^{2} - 8 \, a b^{2} c^{3} + 16 \, a^{2} c^{4}\right)} x^{4} + 2 \, {\left(b^{5} c - 8 \, a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} x^{3} + {\left(b^{6} - 6 \, a b^{4} c + 32 \, a^{3} c^{3}\right)} x^{2} + 2 \, {\left(a b^{5} - 8 \, a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} x\right)}}"," ",0,"2/3*(8*a^2*b*f + 2*(8*c^3*d - 4*b*c^2*e + (b^2*c + 4*a*c^2)*f)*x^3 + 3*(8*b*c^2*d - 4*b^2*c*e + (b^3 + 4*a*b*c)*f)*x^2 - (b^3 - 12*a*b*c)*d - 2*(a*b^2 + 4*a^2*c)*e + 3*(4*a*b^2*f + 2*(b^2*c + 4*a*c^2)*d - (b^3 + 4*a*b*c)*e)*x)*sqrt(c*x^2 + b*x + a)/(a^2*b^4 - 8*a^3*b^2*c + 16*a^4*c^2 + (b^4*c^2 - 8*a*b^2*c^3 + 16*a^2*c^4)*x^4 + 2*(b^5*c - 8*a*b^3*c^2 + 16*a^2*b*c^3)*x^3 + (b^6 - 6*a*b^4*c + 32*a^3*c^3)*x^2 + 2*(a*b^5 - 8*a^2*b^3*c + 16*a^3*b*c^2)*x)","B",0
121,1,154,0,0.445014," ","integrate(1/(5*x^2+12*x+8)/(5*x^2+2*x-7)^(1/2),x, algorithm=""fricas"")","\frac{1}{20} \, \arctan\left(\frac{27 \, x^{2} + 20 \, \sqrt{5 \, x^{2} + 2 \, x - 7} {\left(x + 2\right)} + 36 \, x}{31 \, x^{2} + 16 \, x - 56}\right) + \frac{1}{20} \, \arctan\left(-\frac{27 \, x^{2} - 20 \, \sqrt{5 \, x^{2} + 2 \, x - 7} {\left(x + 2\right)} + 36 \, x}{31 \, x^{2} + 16 \, x - 56}\right) + \frac{1}{20} \, \log\left(\frac{15 \, x^{2} + 5 \, \sqrt{5 \, x^{2} + 2 \, x - 7} {\left(x + 1\right)} + 26 \, x + 9}{x^{2}}\right) - \frac{1}{20} \, \log\left(\frac{15 \, x^{2} - 5 \, \sqrt{5 \, x^{2} + 2 \, x - 7} {\left(x + 1\right)} + 26 \, x + 9}{x^{2}}\right)"," ",0,"1/20*arctan((27*x^2 + 20*sqrt(5*x^2 + 2*x - 7)*(x + 2) + 36*x)/(31*x^2 + 16*x - 56)) + 1/20*arctan(-(27*x^2 - 20*sqrt(5*x^2 + 2*x - 7)*(x + 2) + 36*x)/(31*x^2 + 16*x - 56)) + 1/20*log((15*x^2 + 5*sqrt(5*x^2 + 2*x - 7)*(x + 1) + 26*x + 9)/x^2) - 1/20*log((15*x^2 - 5*sqrt(5*x^2 + 2*x - 7)*(x + 1) + 26*x + 9)/x^2)","B",0
122,0,0,0,0.539560," ","integrate(1/(c*x^2+b*x+a)^(1/2)/(f*x^2+e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2} + b x + a} \sqrt{f x^{2} + e x + d}}{c f x^{4} + {\left(c e + b f\right)} x^{3} + {\left(c d + b e + a f\right)} x^{2} + a d + {\left(b d + a e\right)} x}, x\right)"," ",0,"integral(sqrt(c*x^2 + b*x + a)*sqrt(f*x^2 + e*x + d)/(c*f*x^4 + (c*e + b*f)*x^3 + (c*d + b*e + a*f)*x^2 + a*d + (b*d + a*e)*x), x)","F",0
123,0,0,0,0.421770," ","integrate(1/(5*x^2+3*x+2)^(1/2)/(2*x^2-x+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x^{2} + 3 \, x + 2} \sqrt{2 \, x^{2} - x + 3}}{10 \, x^{4} + x^{3} + 16 \, x^{2} + 7 \, x + 6}, x\right)"," ",0,"integral(sqrt(5*x^2 + 3*x + 2)*sqrt(2*x^2 - x + 3)/(10*x^4 + x^3 + 16*x^2 + 7*x + 6), x)","F",0
