1,1,182,0,1.072667," ","integrate((e*x^3+d)^5*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{1}{22} x^{22} e^{5} c + \frac{5}{19} x^{19} e^{4} d c + \frac{1}{19} x^{19} e^{5} b + \frac{5}{8} x^{16} e^{3} d^{2} c + \frac{5}{16} x^{16} e^{4} d b + \frac{1}{16} x^{16} e^{5} a + \frac{10}{13} x^{13} e^{2} d^{3} c + \frac{10}{13} x^{13} e^{3} d^{2} b + \frac{5}{13} x^{13} e^{4} d a + \frac{1}{2} x^{10} e d^{4} c + x^{10} e^{2} d^{3} b + x^{10} e^{3} d^{2} a + \frac{1}{7} x^{7} d^{5} c + \frac{5}{7} x^{7} e d^{4} b + \frac{10}{7} x^{7} e^{2} d^{3} a + \frac{1}{4} x^{4} d^{5} b + \frac{5}{4} x^{4} e d^{4} a + x d^{5} a"," ",0,"1/22*x^22*e^5*c + 5/19*x^19*e^4*d*c + 1/19*x^19*e^5*b + 5/8*x^16*e^3*d^2*c + 5/16*x^16*e^4*d*b + 1/16*x^16*e^5*a + 10/13*x^13*e^2*d^3*c + 10/13*x^13*e^3*d^2*b + 5/13*x^13*e^4*d*a + 1/2*x^10*e*d^4*c + x^10*e^2*d^3*b + x^10*e^3*d^2*a + 1/7*x^7*d^5*c + 5/7*x^7*e*d^4*b + 10/7*x^7*e^2*d^3*a + 1/4*x^4*d^5*b + 5/4*x^4*e*d^4*a + x*d^5*a","A",0
2,1,147,0,0.639133," ","integrate((e*x^3+d)^4*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{1}{19} x^{19} e^{4} c + \frac{1}{4} x^{16} e^{3} d c + \frac{1}{16} x^{16} e^{4} b + \frac{6}{13} x^{13} e^{2} d^{2} c + \frac{4}{13} x^{13} e^{3} d b + \frac{1}{13} x^{13} e^{4} a + \frac{2}{5} x^{10} e d^{3} c + \frac{3}{5} x^{10} e^{2} d^{2} b + \frac{2}{5} x^{10} e^{3} d a + \frac{1}{7} x^{7} d^{4} c + \frac{4}{7} x^{7} e d^{3} b + \frac{6}{7} x^{7} e^{2} d^{2} a + \frac{1}{4} x^{4} d^{4} b + x^{4} e d^{3} a + x d^{4} a"," ",0,"1/19*x^19*e^4*c + 1/4*x^16*e^3*d*c + 1/16*x^16*e^4*b + 6/13*x^13*e^2*d^2*c + 4/13*x^13*e^3*d*b + 1/13*x^13*e^4*a + 2/5*x^10*e*d^3*c + 3/5*x^10*e^2*d^2*b + 2/5*x^10*e^3*d*a + 1/7*x^7*d^4*c + 4/7*x^7*e*d^3*b + 6/7*x^7*e^2*d^2*a + 1/4*x^4*d^4*b + x^4*e*d^3*a + x*d^4*a","A",0
3,1,112,0,0.864987," ","integrate((e*x^3+d)^3*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{1}{16} x^{16} e^{3} c + \frac{3}{13} x^{13} e^{2} d c + \frac{1}{13} x^{13} e^{3} b + \frac{3}{10} x^{10} e d^{2} c + \frac{3}{10} x^{10} e^{2} d b + \frac{1}{10} x^{10} e^{3} a + \frac{1}{7} x^{7} d^{3} c + \frac{3}{7} x^{7} e d^{2} b + \frac{3}{7} x^{7} e^{2} d a + \frac{1}{4} x^{4} d^{3} b + \frac{3}{4} x^{4} e d^{2} a + x d^{3} a"," ",0,"1/16*x^16*e^3*c + 3/13*x^13*e^2*d*c + 1/13*x^13*e^3*b + 3/10*x^10*e*d^2*c + 3/10*x^10*e^2*d*b + 1/10*x^10*e^3*a + 1/7*x^7*d^3*c + 3/7*x^7*e*d^2*b + 3/7*x^7*e^2*d*a + 1/4*x^4*d^3*b + 3/4*x^4*e*d^2*a + x*d^3*a","A",0
4,1,76,0,0.914038," ","integrate((e*x^3+d)^2*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{2} c + \frac{1}{5} x^{10} e d c + \frac{1}{10} x^{10} e^{2} b + \frac{1}{7} x^{7} d^{2} c + \frac{2}{7} x^{7} e d b + \frac{1}{7} x^{7} e^{2} a + \frac{1}{4} x^{4} d^{2} b + \frac{1}{2} x^{4} e d a + x d^{2} a"," ",0,"1/13*x^13*e^2*c + 1/5*x^10*e*d*c + 1/10*x^10*e^2*b + 1/7*x^7*d^2*c + 2/7*x^7*e*d*b + 1/7*x^7*e^2*a + 1/4*x^4*d^2*b + 1/2*x^4*e*d*a + x*d^2*a","A",0
5,1,40,0,1.027563," ","integrate((e*x^3+d)*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{1}{10} x^{10} e c + \frac{1}{7} x^{7} d c + \frac{1}{7} x^{7} e b + \frac{1}{4} x^{4} d b + \frac{1}{4} x^{4} e a + x d a"," ",0,"1/10*x^10*e*c + 1/7*x^7*d*c + 1/7*x^7*e*b + 1/4*x^4*d*b + 1/4*x^4*e*a + x*d*a","A",0
6,1,465,0,0.976630," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d),x, algorithm=""fricas"")","\left[\frac{3 \, c d^{2} e^{2} x^{4} + 6 \, \sqrt{\frac{1}{3}} {\left(c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} \sqrt{-\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}} \log\left(\frac{2 \, d e x^{3} - 3 \, \left(d^{2} e\right)^{\frac{1}{3}} d x - d^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, d e x^{2} + \left(d^{2} e\right)^{\frac{2}{3}} x - \left(d^{2} e\right)^{\frac{1}{3}} d\right)} \sqrt{-\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}}}{e x^{3} + d}\right) - 2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x^{2} - \left(d^{2} e\right)^{\frac{2}{3}} x + \left(d^{2} e\right)^{\frac{1}{3}} d\right) + 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x + \left(d^{2} e\right)^{\frac{2}{3}}\right) - 12 \, {\left(c d^{3} e - b d^{2} e^{2}\right)} x}{12 \, d^{2} e^{3}}, \frac{3 \, c d^{2} e^{2} x^{4} + 12 \, \sqrt{\frac{1}{3}} {\left(c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} \sqrt{\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(d^{2} e\right)^{\frac{2}{3}} x - \left(d^{2} e\right)^{\frac{1}{3}} d\right)} \sqrt{\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}}}{d^{2}}\right) - 2 \, {\left(c d^{2} - b d e + a e^{2}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x^{2} - \left(d^{2} e\right)^{\frac{2}{3}} x + \left(d^{2} e\right)^{\frac{1}{3}} d\right) + 4 \, {\left(c d^{2} - b d e + a e^{2}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x + \left(d^{2} e\right)^{\frac{2}{3}}\right) - 12 \, {\left(c d^{3} e - b d^{2} e^{2}\right)} x}{12 \, d^{2} e^{3}}\right]"," ",0,"[1/12*(3*c*d^2*e^2*x^4 + 6*sqrt(1/3)*(c*d^3*e - b*d^2*e^2 + a*d*e^3)*sqrt(-(d^2*e)^(1/3)/e)*log((2*d*e*x^3 - 3*(d^2*e)^(1/3)*d*x - d^2 + 3*sqrt(1/3)*(2*d*e*x^2 + (d^2*e)^(2/3)*x - (d^2*e)^(1/3)*d)*sqrt(-(d^2*e)^(1/3)/e))/(e*x^3 + d)) - 2*(c*d^2 - b*d*e + a*e^2)*(d^2*e)^(2/3)*log(d*e*x^2 - (d^2*e)^(2/3)*x + (d^2*e)^(1/3)*d) + 4*(c*d^2 - b*d*e + a*e^2)*(d^2*e)^(2/3)*log(d*e*x + (d^2*e)^(2/3)) - 12*(c*d^3*e - b*d^2*e^2)*x)/(d^2*e^3), 1/12*(3*c*d^2*e^2*x^4 + 12*sqrt(1/3)*(c*d^3*e - b*d^2*e^2 + a*d*e^3)*sqrt((d^2*e)^(1/3)/e)*arctan(sqrt(1/3)*(2*(d^2*e)^(2/3)*x - (d^2*e)^(1/3)*d)*sqrt((d^2*e)^(1/3)/e)/d^2) - 2*(c*d^2 - b*d*e + a*e^2)*(d^2*e)^(2/3)*log(d*e*x^2 - (d^2*e)^(2/3)*x + (d^2*e)^(1/3)*d) + 4*(c*d^2 - b*d*e + a*e^2)*(d^2*e)^(2/3)*log(d*e*x + (d^2*e)^(2/3)) - 12*(c*d^3*e - b*d^2*e^2)*x)/(d^2*e^3)]","A",0
7,1,697,0,1.084185," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^2,x, algorithm=""fricas"")","\left[\frac{18 \, c d^{3} e^{2} x^{4} - 3 \, \sqrt{\frac{1}{3}} {\left(4 \, c d^{4} e - b d^{3} e^{2} - 2 \, a d^{2} e^{3} + {\left(4 \, c d^{3} e^{2} - b d^{2} e^{3} - 2 \, a d e^{4}\right)} x^{3}\right)} \sqrt{-\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}} \log\left(\frac{2 \, d e x^{3} - 3 \, \left(d^{2} e\right)^{\frac{1}{3}} d x - d^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, d e x^{2} + \left(d^{2} e\right)^{\frac{2}{3}} x - \left(d^{2} e\right)^{\frac{1}{3}} d\right)} \sqrt{-\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}}}{e x^{3} + d}\right) + {\left(4 \, c d^{3} - b d^{2} e - 2 \, a d e^{2} + {\left(4 \, c d^{2} e - b d e^{2} - 2 \, a e^{3}\right)} x^{3}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x^{2} - \left(d^{2} e\right)^{\frac{2}{3}} x + \left(d^{2} e\right)^{\frac{1}{3}} d\right) - 2 \, {\left(4 \, c d^{3} - b d^{2} e - 2 \, a d e^{2} + {\left(4 \, c d^{2} e - b d e^{2} - 2 \, a e^{3}\right)} x^{3}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x + \left(d^{2} e\right)^{\frac{2}{3}}\right) + 6 \, {\left(4 \, c d^{4} e - b d^{3} e^{2} + a d^{2} e^{3}\right)} x}{18 \, {\left(d^{3} e^{4} x^{3} + d^{4} e^{3}\right)}}, \frac{18 \, c d^{3} e^{2} x^{4} - 6 \, \sqrt{\frac{1}{3}} {\left(4 \, c d^{4} e - b d^{3} e^{2} - 2 \, a d^{2} e^{3} + {\left(4 \, c d^{3} e^{2} - b d^{2} e^{3} - 2 \, a d e^{4}\right)} x^{3}\right)} \sqrt{\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(d^{2} e\right)^{\frac{2}{3}} x - \left(d^{2} e\right)^{\frac{1}{3}} d\right)} \sqrt{\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}}}{d^{2}}\right) + {\left(4 \, c d^{3} - b d^{2} e - 2 \, a d e^{2} + {\left(4 \, c d^{2} e - b d e^{2} - 2 \, a e^{3}\right)} x^{3}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x^{2} - \left(d^{2} e\right)^{\frac{2}{3}} x + \left(d^{2} e\right)^{\frac{1}{3}} d\right) - 2 \, {\left(4 \, c d^{3} - b d^{2} e - 2 \, a d e^{2} + {\left(4 \, c d^{2} e - b d e^{2} - 2 \, a e^{3}\right)} x^{3}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x + \left(d^{2} e\right)^{\frac{2}{3}}\right) + 6 \, {\left(4 \, c d^{4} e - b d^{3} e^{2} + a d^{2} e^{3}\right)} x}{18 \, {\left(d^{3} e^{4} x^{3} + d^{4} e^{3}\right)}}\right]"," ",0,"[1/18*(18*c*d^3*e^2*x^4 - 3*sqrt(1/3)*(4*c*d^4*e - b*d^3*e^2 - 2*a*d^2*e^3 + (4*c*d^3*e^2 - b*d^2*e^3 - 2*a*d*e^4)*x^3)*sqrt(-(d^2*e)^(1/3)/e)*log((2*d*e*x^3 - 3*(d^2*e)^(1/3)*d*x - d^2 + 3*sqrt(1/3)*(2*d*e*x^2 + (d^2*e)^(2/3)*x - (d^2*e)^(1/3)*d)*sqrt(-(d^2*e)^(1/3)/e))/(e*x^3 + d)) + (4*c*d^3 - b*d^2*e - 2*a*d*e^2 + (4*c*d^2*e - b*d*e^2 - 2*a*e^3)*x^3)*(d^2*e)^(2/3)*log(d*e*x^2 - (d^2*e)^(2/3)*x + (d^2*e)^(1/3)*d) - 2*(4*c*d^3 - b*d^2*e - 2*a*d*e^2 + (4*c*d^2*e - b*d*e^2 - 2*a*e^3)*x^3)*(d^2*e)^(2/3)*log(d*e*x + (d^2*e)^(2/3)) + 6*(4*c*d^4*e - b*d^3*e^2 + a*d^2*e^3)*x)/(d^3*e^4*x^3 + d^4*e^3), 1/18*(18*c*d^3*e^2*x^4 - 6*sqrt(1/3)*(4*c*d^4*e - b*d^3*e^2 - 2*a*d^2*e^3 + (4*c*d^3*e^2 - b*d^2*e^3 - 2*a*d*e^4)*x^3)*sqrt((d^2*e)^(1/3)/e)*arctan(sqrt(1/3)*(2*(d^2*e)^(2/3)*x - (d^2*e)^(1/3)*d)*sqrt((d^2*e)^(1/3)/e)/d^2) + (4*c*d^3 - b*d^2*e - 2*a*d*e^2 + (4*c*d^2*e - b*d*e^2 - 2*a*e^3)*x^3)*(d^2*e)^(2/3)*log(d*e*x^2 - (d^2*e)^(2/3)*x + (d^2*e)^(1/3)*d) - 2*(4*c*d^3 - b*d^2*e - 2*a*d*e^2 + (4*c*d^2*e - b*d*e^2 - 2*a*e^3)*x^3)*(d^2*e)^(2/3)*log(d*e*x + (d^2*e)^(2/3)) + 6*(4*c*d^4*e - b*d^3*e^2 + a*d^2*e^3)*x)/(d^3*e^4*x^3 + d^4*e^3)]","A",0
8,1,941,0,0.862596," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^3,x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(7 \, c d^{4} e^{2} - b d^{3} e^{3} - 5 \, a d^{2} e^{4}\right)} x^{4} - 3 \, \sqrt{\frac{1}{3}} {\left(2 \, c d^{5} e + b d^{4} e^{2} + 5 \, a d^{3} e^{3} + {\left(2 \, c d^{3} e^{3} + b d^{2} e^{4} + 5 \, a d e^{5}\right)} x^{6} + 2 \, {\left(2 \, c d^{4} e^{2} + b d^{3} e^{3} + 5 \, a d^{2} e^{4}\right)} x^{3}\right)} \sqrt{-\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}} \log\left(\frac{2 \, d e x^{3} - 3 \, \left(d^{2} e\right)^{\frac{1}{3}} d x - d^{2} + 3 \, \sqrt{\frac{1}{3}} {\left(2 \, d e x^{2} + \left(d^{2} e\right)^{\frac{2}{3}} x - \left(d^{2} e\right)^{\frac{1}{3}} d\right)} \sqrt{-\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}}}{e x^{3} + d}\right) + {\left({\left(2 \, c d^{2} e^{2} + b d e^{3} + 5 \, a e^{4}\right)} x^{6} + 2 \, c d^{4} + b d^{3} e + 5 \, a d^{2} e^{2} + 2 \, {\left(2 \, c d^{3} e + b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{3}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x^{2} - \left(d^{2} e\right)^{\frac{2}{3}} x + \left(d^{2} e\right)^{\frac{1}{3}} d\right) - 2 \, {\left({\left(2 \, c d^{2} e^{2} + b d e^{3} + 5 \, a e^{4}\right)} x^{6} + 2 \, c d^{4} + b d^{3} e + 5 \, a d^{2} e^{2} + 2 \, {\left(2 \, c d^{3} e + b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{3}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x + \left(d^{2} e\right)^{\frac{2}{3}}\right) + 6 \, {\left(2 \, c d^{5} e + b d^{4} e^{2} - 4 \, a d^{3} e^{3}\right)} x}{54 \, {\left(d^{4} e^{5} x^{6} + 2 \, d^{5} e^{4} x^{3} + d^{6} e^{3}\right)}}, -\frac{3 \, {\left(7 \, c d^{4} e^{2} - b d^{3} e^{3} - 5 \, a d^{2} e^{4}\right)} x^{4} - 6 \, \sqrt{\frac{1}{3}} {\left(2 \, c d^{5} e + b d^{4} e^{2} + 5 \, a d^{3} e^{3} + {\left(2 \, c d^{3} e^{3} + b d^{2} e^{4} + 5 \, a d e^{5}\right)} x^{6} + 2 \, {\left(2 \, c d^{4} e^{2} + b d^{3} e^{3} + 5 \, a d^{2} e^{4}\right)} x^{3}\right)} \sqrt{\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}} \arctan\left(\frac{\sqrt{\frac{1}{3}} {\left(2 \, \left(d^{2} e\right)^{\frac{2}{3}} x - \left(d^{2} e\right)^{\frac{1}{3}} d\right)} \sqrt{\frac{\left(d^{2} e\right)^{\frac{1}{3}}}{e}}}{d^{2}}\right) + {\left({\left(2 \, c d^{2} e^{2} + b d e^{3} + 5 \, a e^{4}\right)} x^{6} + 2 \, c d^{4} + b d^{3} e + 5 \, a d^{2} e^{2} + 2 \, {\left(2 \, c d^{3} e + b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{3}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x^{2} - \left(d^{2} e\right)^{\frac{2}{3}} x + \left(d^{2} e\right)^{\frac{1}{3}} d\right) - 2 \, {\left({\left(2 \, c d^{2} e^{2} + b d e^{3} + 5 \, a e^{4}\right)} x^{6} + 2 \, c d^{4} + b d^{3} e + 5 \, a d^{2} e^{2} + 2 \, {\left(2 \, c d^{3} e + b d^{2} e^{2} + 5 \, a d e^{3}\right)} x^{3}\right)} \left(d^{2} e\right)^{\frac{2}{3}} \log\left(d e x + \left(d^{2} e\right)^{\frac{2}{3}}\right) + 6 \, {\left(2 \, c d^{5} e + b d^{4} e^{2} - 4 \, a d^{3} e^{3}\right)} x}{54 \, {\left(d^{4} e^{5} x^{6} + 2 \, d^{5} e^{4} x^{3} + d^{6} e^{3}\right)}}\right]"," ",0,"[-1/54*(3*(7*c*d^4*e^2 - b*d^3*e^3 - 5*a*d^2*e^4)*x^4 - 3*sqrt(1/3)*(2*c*d^5*e + b*d^4*e^2 + 5*a*d^3*e^3 + (2*c*d^3*e^3 + b*d^2*e^4 + 5*a*d*e^5)*x^6 + 2*(2*c*d^4*e^2 + b*d^3*e^3 + 5*a*d^2*e^4)*x^3)*sqrt(-(d^2*e)^(1/3)/e)*log((2*d*e*x^3 - 3*(d^2*e)^(1/3)*d*x - d^2 + 3*sqrt(1/3)*(2*d*e*x^2 + (d^2*e)^(2/3)*x - (d^2*e)^(1/3)*d)*sqrt(-(d^2*e)^(1/3)/e))/(e*x^3 + d)) + ((2*c*d^2*e^2 + b*d*e^3 + 5*a*e^4)*x^6 + 2*c*d^4 + b*d^3*e + 5*a*d^2*e^2 + 2*(2*c*d^3*e + b*d^2*e^2 + 5*a*d*e^3)*x^3)*(d^2*e)^(2/3)*log(d*e*x^2 - (d^2*e)^(2/3)*x + (d^2*e)^(1/3)*d) - 2*((2*c*d^2*e^2 + b*d*e^3 + 5*a*e^4)*x^6 + 2*c*d^4 + b*d^3*e + 5*a*d^2*e^2 + 2*(2*c*d^3*e + b*d^2*e^2 + 5*a*d*e^3)*x^3)*(d^2*e)^(2/3)*log(d*e*x + (d^2*e)^(2/3)) + 6*(2*c*d^5*e + b*d^4*e^2 - 4*a*d^3*e^3)*x)/(d^4*e^5*x^6 + 2*d^5*e^4*x^3 + d^6*e^3), -1/54*(3*(7*c*d^4*e^2 - b*d^3*e^3 - 5*a*d^2*e^4)*x^4 - 6*sqrt(1/3)*(2*c*d^5*e + b*d^4*e^2 + 5*a*d^3*e^3 + (2*c*d^3*e^3 + b*d^2*e^4 + 5*a*d*e^5)*x^6 + 2*(2*c*d^4*e^2 + b*d^3*e^3 + 5*a*d^2*e^4)*x^3)*sqrt((d^2*e)^(1/3)/e)*arctan(sqrt(1/3)*(2*(d^2*e)^(2/3)*x - (d^2*e)^(1/3)*d)*sqrt((d^2*e)^(1/3)/e)/d^2) + ((2*c*d^2*e^2 + b*d*e^3 + 5*a*e^4)*x^6 + 2*c*d^4 + b*d^3*e + 5*a*d^2*e^2 + 2*(2*c*d^3*e + b*d^2*e^2 + 5*a*d*e^3)*x^3)*(d^2*e)^(2/3)*log(d*e*x^2 - (d^2*e)^(2/3)*x + (d^2*e)^(1/3)*d) - 2*((2*c*d^2*e^2 + b*d*e^3 + 5*a*e^4)*x^6 + 2*c*d^4 + b*d^3*e + 5*a*d^2*e^2 + 2*(2*c*d^3*e + b*d^2*e^2 + 5*a*d*e^3)*x^3)*(d^2*e)^(2/3)*log(d*e*x + (d^2*e)^(2/3)) + 6*(2*c*d^5*e + b*d^4*e^2 - 4*a*d^3*e^3)*x)/(d^4*e^5*x^6 + 2*d^5*e^4*x^3 + d^6*e^3)]","B",0
9,1,430,0,1.769970," ","integrate(x^8*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e x^{6} + 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(b^{3} c - 4 \, a b c^{2}\right)} e\right)} x^{3} + \sqrt{b^{2} - 4 \, a c} {\left({\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e\right)} \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c - {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right) - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}, \frac{{\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e x^{6} + 2 \, {\left({\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d - {\left(b^{3} c - 4 \, a b c^{2}\right)} e\right)} x^{3} - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left({\left(b^{2} c - 2 \, a c^{2}\right)} d - {\left(b^{3} - 3 \, a b c\right)} e\right)} \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{3} c - 4 \, a b c^{2}\right)} d - {\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} e\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, {\left(b^{2} c^{3} - 4 \, a c^{4}\right)}}\right]"," ",0,"[1/6*((b^2*c^2 - 4*a*c^3)*e*x^6 + 2*((b^2*c^2 - 4*a*c^3)*d - (b^3*c - 4*a*b*c^2)*e)*x^3 + sqrt(b^2 - 4*a*c)*((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e)*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c - (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)) - ((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*log(c*x^6 + b*x^3 + a))/(b^2*c^3 - 4*a*c^4), 1/6*((b^2*c^2 - 4*a*c^3)*e*x^6 + 2*((b^2*c^2 - 4*a*c^3)*d - (b^3*c - 4*a*b*c^2)*e)*x^3 - 2*sqrt(-b^2 + 4*a*c)*((b^2*c - 2*a*c^2)*d - (b^3 - 3*a*b*c)*e)*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) - ((b^3*c - 4*a*b*c^2)*d - (b^4 - 5*a*b^2*c + 4*a^2*c^2)*e)*log(c*x^6 + b*x^3 + a))/(b^2*c^3 - 4*a*c^4)]","A",0
10,1,305,0,1.161486," ","integrate(x^5*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e x^{3} + {\left(b c d - {\left(b^{2} - 2 \, a c\right)} e\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c + {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right) + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e x^{3} + 2 \, {\left(b c d - {\left(b^{2} - 2 \, a c\right)} e\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d - {\left(b^{3} - 4 \, a b c\right)} e\right)} \log\left(c x^{6} + b x^{3} + a\right)}{6 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/6*(2*(b^2*c - 4*a*c^2)*e*x^3 + (b*c*d - (b^2 - 2*a*c)*e)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c + (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)) + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*log(c*x^6 + b*x^3 + a))/(b^2*c^2 - 4*a*c^3), 1/6*(2*(b^2*c - 4*a*c^2)*e*x^3 + 2*(b*c*d - (b^2 - 2*a*c)*e)*sqrt(-b^2 + 4*a*c)*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + ((b^2*c - 4*a*c^2)*d - (b^3 - 4*a*b*c)*e)*log(c*x^6 + b*x^3 + a))/(b^2*c^2 - 4*a*c^3)]","A",0
11,1,216,0,1.284764," ","integrate(x^2*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{6} + b x^{3} + a\right) - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c d - b e\right)} \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c + {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right)}{6 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{6} + b x^{3} + a\right) - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{6 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/6*((b^2 - 4*a*c)*e*log(c*x^6 + b*x^3 + a) - sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c + (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)))/(b^2*c - 4*a*c^2), 1/6*((b^2 - 4*a*c)*e*log(c*x^6 + b*x^3 + a) - 2*sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/(b^2*c - 4*a*c^2)]","A",0
12,1,240,0,1.355691," ","integrate((e*x^3+d)/x/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(c x^{6} + b x^{3} + a\right) - 6 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(x\right) + \sqrt{b^{2} - 4 \, a c} {\left(b d - 2 \, a e\right)} \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c - {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right)}{6 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, -\frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(c x^{6} + b x^{3} + a\right) - 6 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(x\right) - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(b d - 2 \, a e\right)} \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{6 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[-1/6*((b^2 - 4*a*c)*d*log(c*x^6 + b*x^3 + a) - 6*(b^2 - 4*a*c)*d*log(x) + sqrt(b^2 - 4*a*c)*(b*d - 2*a*e)*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c - (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)))/(a*b^2 - 4*a^2*c), -1/6*((b^2 - 4*a*c)*d*log(c*x^6 + b*x^3 + a) - 6*(b^2 - 4*a*c)*d*log(x) - 2*sqrt(-b^2 + 4*a*c)*(b*d - 2*a*e)*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/(a*b^2 - 4*a^2*c)]","A",0
13,1,385,0,2.596917," ","integrate((e*x^3+d)/x^4/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\left[\frac{{\left(a b e - {\left(b^{2} - 2 \, a c\right)} d\right)} \sqrt{b^{2} - 4 \, a c} x^{3} \log\left(\frac{2 \, c^{2} x^{6} + 2 \, b c x^{3} + b^{2} - 2 \, a c + {\left(2 \, c x^{3} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{6} + b x^{3} + a}\right) + {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} x^{3} \log\left(c x^{6} + b x^{3} + a\right) - 6 \, {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} x^{3} \log\left(x\right) - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d}{6 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{3}}, \frac{2 \, {\left(a b e - {\left(b^{2} - 2 \, a c\right)} d\right)} \sqrt{-b^{2} + 4 \, a c} x^{3} \arctan\left(-\frac{{\left(2 \, c x^{3} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right) + {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} x^{3} \log\left(c x^{6} + b x^{3} + a\right) - 6 \, {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(a b^{2} - 4 \, a^{2} c\right)} e\right)} x^{3} \log\left(x\right) - 2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d}{6 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} x^{3}}\right]"," ",0,"[1/6*((a*b*e - (b^2 - 2*a*c)*d)*sqrt(b^2 - 4*a*c)*x^3*log((2*c^2*x^6 + 2*b*c*x^3 + b^2 - 2*a*c + (2*c*x^3 + b)*sqrt(b^2 - 4*a*c))/(c*x^6 + b*x^3 + a)) + ((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*x^3*log(c*x^6 + b*x^3 + a) - 6*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*x^3*log(x) - 2*(a*b^2 - 4*a^2*c)*d)/((a^2*b^2 - 4*a^3*c)*x^3), 1/6*(2*(a*b*e - (b^2 - 2*a*c)*d)*sqrt(-b^2 + 4*a*c)*x^3*arctan(-(2*c*x^3 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)) + ((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*x^3*log(c*x^6 + b*x^3 + a) - 6*((b^3 - 4*a*b*c)*d - (a*b^2 - 4*a^2*c)*e)*x^3*log(x) - 2*(a*b^2 - 4*a^2*c)*d)/((a^2*b^2 - 4*a^3*c)*x^3)]","A",0
14,-1,0,0,0.000000," ","integrate(x^4*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
15,-1,0,0,0.000000," ","integrate(x^3*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
16,1,13607,0,119.715687," ","integrate(x*(e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(\sqrt{3} {\left(2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d - {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} e\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}} - \sqrt{3} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e - 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} + 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{4}\right)}\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} \sqrt{\frac{2 \, {\left(b c^{4} d^{7} - 2 \, {\left(b^{2} c^{3} + 3 \, a c^{4}\right)} d^{6} e + {\left(b^{3} c^{2} + 17 \, a b c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{3} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e^{5} + {\left(2 \, a^{2} b^{3} - a^{3} b c\right)} d e^{6} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{7}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left({\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} + 48 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{2} - {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} e^{2}\right)} x \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}} - {\left({\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{5} - 10 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e + 4 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{2} e^{3} + {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 6 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} e^{5}\right)} x\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} - {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} - 24 \, a^{2} c^{4}\right)} d^{5} e + 10 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{4} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{3} + {\left(a b^{5} - 3 \, a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e^{4} - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d e^{5} - {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{3} - {\left(a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{4} c^{5}\right)} d^{2} e + 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{2} - 2 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}}}{b c^{4} d^{7} - 2 \, {\left(b^{2} c^{3} + 3 \, a c^{4}\right)} d^{6} e + {\left(b^{3} c^{2} + 17 \, a b c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{3} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e^{5} + {\left(2 \, a^{2} b^{3} - a^{3} b c\right)} d e^{6} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{7}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\sqrt{3} {\left(2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d - {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} e\right)} x \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}} - \sqrt{3} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e - 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} + 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{4}\right)} x\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} - \sqrt{3} {\left(b c^{3} d^{5} + 10 \, a b c^{2} d^{3} e^{2} - {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{4} e - 4 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{2} e^{3} + {\left(a b^{3} + a^{2} b c\right)} d e^{4} - {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} e^{5}\right)}}{3 \, {\left(b c^{3} d^{5} + 10 \, a b c^{2} d^{3} e^{2} - {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{4} e - 4 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{2} e^{3} + {\left(a b^{3} + a^{2} b c\right)} d e^{4} - {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} e^{5}\right)}}\right) - \frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} \arctan\left(-\frac{\left(\frac{1}{2}\right)^{\frac{5}{6}} {\left(\sqrt{3} {\left(2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d - {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} e\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}} + \sqrt{3} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e - 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} + 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{4}\right)}\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} \sqrt{\frac{2 \, {\left(b c^{4} d^{7} - 2 \, {\left(b^{2} c^{3} + 3 \, a c^{4}\right)} d^{6} e + {\left(b^{3} c^{2} + 17 \, a b c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{3} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e^{5} + {\left(2 \, a^{2} b^{3} - a^{3} b c\right)} d e^{6} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{7}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left({\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} + 48 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{2} - {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} e^{2}\right)} x \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}} + {\left({\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{5} - 10 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e + 4 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{2} e^{3} + {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 6 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} e^{5}\right)} x\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} - {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} - 24 \, a^{2} c^{4}\right)} d^{5} e + 10 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{4} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{3} + {\left(a b^{5} - 3 \, a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e^{4} - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d e^{5} + {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{3} - {\left(a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{4} c^{5}\right)} d^{2} e + 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{2} - 2 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}}}{b c^{4} d^{7} - 2 \, {\left(b^{2} c^{3} + 3 \, a c^{4}\right)} d^{6} e + {\left(b^{3} c^{2} + 17 \, a b c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{3} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e^{5} + {\left(2 \, a^{2} b^{3} - a^{3} b c\right)} d e^{6} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{7}}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(\sqrt{3} {\left(2 \, {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} d - {\left(a b^{5} c^{2} - 8 \, a^{2} b^{3} c^{3} + 16 \, a^{3} b c^{4}\right)} e\right)} x \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}} + \sqrt{3} {\left({\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d^{3} e - 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{2} + 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{3} - {\left(a b^{4} - 6 \, a^{2} b^{2} c + 8 \, a^{3} c^{2}\right)} e^{4}\right)} x\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} + \sqrt{3} {\left(b c^{3} d^{5} + 10 \, a b c^{2} d^{3} e^{2} - {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{4} e - 4 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{2} e^{3} + {\left(a b^{3} + a^{2} b c\right)} d e^{4} - {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} e^{5}\right)}}{3 \, {\left(b c^{3} d^{5} + 10 \, a b c^{2} d^{3} e^{2} - {\left(b^{2} c^{2} + 6 \, a c^{3}\right)} d^{4} e - 4 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{2} e^{3} + {\left(a b^{3} + a^{2} b c\right)} d e^{4} - {\left(a^{2} b^{2} - 2 \, a^{3} c\right)} e^{5}\right)}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(b c^{4} d^{7} - 2 \, {\left(b^{2} c^{3} + 3 \, a c^{4}\right)} d^{6} e + {\left(b^{3} c^{2} + 17 \, a b c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{3} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e^{5} + {\left(2 \, a^{2} b^{3} - a^{3} b c\right)} d e^{6} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{7}\right)} x^{2} + \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left({\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} + 48 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{2} - {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} e^{2}\right)} x \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}} - {\left({\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{5} - 10 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e + 4 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{2} e^{3} + {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 6 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} e^{5}\right)} x\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} - {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} - 24 \, a^{2} c^{4}\right)} d^{5} e + 10 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{4} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{3} + {\left(a b^{5} - 3 \, a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e^{4} - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d e^{5} - {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{3} - {\left(a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{4} c^{5}\right)} d^{2} e + 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{2} - 2 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(b c^{4} d^{7} - 2 \, {\left(b^{2} c^{3} + 3 \, a c^{4}\right)} d^{6} e + {\left(b^{3} c^{2} + 17 \, a b c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{3} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e^{5} + {\left(2 \, a^{2} b^{3} - a^{3} b c\right)} d e^{6} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{7}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left({\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} + 48 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{2} - {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} e^{2}\right)} x \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}} + {\left({\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{5} - 10 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e + 4 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{2} e^{3} + {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 6 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} e^{5}\right)} x\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d^{6} - {\left(b^{4} c^{2} + 2 \, a b^{2} c^{3} - 24 \, a^{2} c^{4}\right)} d^{5} e + 10 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{4} e^{2} - 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{3} e^{3} + {\left(a b^{5} - 3 \, a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e^{4} - {\left(a^{2} b^{4} - 6 \, a^{3} b^{2} c + 8 \, a^{4} c^{2}\right)} d e^{5} + {\left({\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{3} - {\left(a b^{6} c^{2} - 6 \, a^{2} b^{4} c^{3} + 32 \, a^{4} c^{5}\right)} d^{2} e + 3 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d e^{2} - 2 \, {\left(a^{3} b^{4} c^{2} - 8 \, a^{4} b^{2} c^{3} + 16 \, a^{5} c^{4}\right)} e^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{5} - 10 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e + 4 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{2} e^{3} + {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 6 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} e^{5} - {\left({\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} + 48 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{2} - {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} e^{2}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{2}{3}} + 2 \, {\left(b c^{4} d^{7} - 2 \, {\left(b^{2} c^{3} + 3 \, a c^{4}\right)} d^{6} e + {\left(b^{3} c^{2} + 17 \, a b c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{3} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e^{5} + {\left(2 \, a^{2} b^{3} - a^{3} b c\right)} d e^{6} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{7}\right)} x\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{1}{3}} \log\left(\left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{4} c^{3} - 4 \, a b^{2} c^{4}\right)} d^{5} - 10 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e + 4 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{3} e^{2} - {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{2} e^{3} + {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d e^{4} - {\left(a^{2} b^{5} - 6 \, a^{3} b^{3} c + 8 \, a^{4} b c^{2}\right)} e^{5} + {\left({\left(a b^{6} c^{3} - 12 \, a^{2} b^{4} c^{4} + 48 \, a^{3} b^{2} c^{5} - 64 \, a^{4} c^{6}\right)} d^{2} - {\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} e^{2}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}\right)} \left(-\frac{c^{2} d^{3} - 3 \, a c d e^{2} + a b e^{3} - {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} \sqrt{\frac{b^{2} c^{4} d^{6} - 12 \, a b c^{4} d^{5} e + 6 \, {\left(a b^{2} c^{3} + 6 \, a^{2} c^{4}\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} c^{2} + 16 \, a^{2} b c^{3}\right)} d^{3} e^{3} + 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a^{2} b^{3} c - 2 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 4 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6}}{a^{2} b^{6} c^{4} - 12 \, a^{3} b^{4} c^{5} + 48 \, a^{4} b^{2} c^{6} - 64 \, a^{5} c^{7}}}}{a b^{2} c^{2} - 4 \, a^{2} c^{3}}\right)^{\frac{2}{3}} + 2 \, {\left(b c^{4} d^{7} - 2 \, {\left(b^{2} c^{3} + 3 \, a c^{4}\right)} d^{6} e + {\left(b^{3} c^{2} + 17 \, a b c^{3}\right)} d^{5} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{3} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{4} - {\left(a b^{4} + 6 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{2} e^{5} + {\left(2 \, a^{2} b^{3} - a^{3} b c\right)} d e^{6} - {\left(a^{3} b^{2} - 2 \, a^{4} c\right)} e^{7}\right)} x\right)"," ",0,"2/3*sqrt(3)*(1/2)^(1/3)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)*arctan(-1/3*((1/2)^(5/6)*(sqrt(3)*(2*(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d - (a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*e)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)) - sqrt(3)*((b^3*c^2 - 4*a*b*c^3)*d^3*e - 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 + 3*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 - (a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e^4))*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)*sqrt((2*(b*c^4*d^7 - 2*(b^2*c^3 + 3*a*c^4)*d^6*e + (b^3*c^2 + 17*a*b*c^3)*d^5*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^3 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^4 - (a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^2*e^5 + (2*a^2*b^3 - a^3*b*c)*d*e^6 - (a^3*b^2 - 2*a^4*c)*e^7)*x^2 + (1/2)^(2/3)*(((a*b^6*c^3 - 12*a^2*b^4*c^4 + 48*a^3*b^2*c^5 - 64*a^4*c^6)*d^2 - (a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*e^2)*x*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)) - ((b^4*c^3 - 4*a*b^2*c^4)*d^5 - 10*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e + 4*(a*b^4*c^2 + 2*a^2*b^2*c^3 - 24*a^3*c^4)*d^3*e^2 - (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^2*e^3 + (7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d*e^4 - (a^2*b^5 - 6*a^3*b^3*c + 8*a^4*b*c^2)*e^5)*x)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(2/3) + (1/2)^(1/3)*((b^3*c^3 - 4*a*b*c^4)*d^6 - (b^4*c^2 + 2*a*b^2*c^3 - 24*a^2*c^4)*d^5*e + 10*(a*b^3*c^2 - 4*a^2*b*c^3)*d^4*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^3 + (a*b^5 - 3*a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^4 - (a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*e^5 - ((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^3 - (a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^4*c^5)*d^2*e + 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^2 - 2*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3))/(b*c^4*d^7 - 2*(b^2*c^3 + 3*a*c^4)*d^6*e + (b^3*c^2 + 17*a*b*c^3)*d^5*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^3 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^4 - (a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^2*e^5 + (2*a^2*b^3 - a^3*b*c)*d*e^6 - (a^3*b^2 - 2*a^4*c)*e^7)) - (1/2)^(1/3)*(sqrt(3)*(2*(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d - (a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*e)*x*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)) - sqrt(3)*((b^3*c^2 - 4*a*b*c^3)*d^3*e - 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 + 3*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 - (a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e^4)*x)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3) - sqrt(3)*(b*c^3*d^5 + 10*a*b*c^2*d^3*e^2 - (b^2*c^2 + 6*a*c^3)*d^4*e - 4*(a*b^2*c + a^2*c^2)*d^2*e^3 + (a*b^3 + a^2*b*c)*d*e^4 - (a^2*b^2 - 2*a^3*c)*e^5))/(b*c^3*d^5 + 10*a*b*c^2*d^3*e^2 - (b^2*c^2 + 6*a*c^3)*d^4*e - 4*(a*b^2*c + a^2*c^2)*d^2*e^3 + (a*b^3 + a^2*b*c)*d*e^4 - (a^2*b^2 - 2*a^3*c)*e^5)) - 2/3*sqrt(3)*(1/2)^(1/3)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)*arctan(-1/3*((1/2)^(5/6)*(sqrt(3)*(2*(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d - (a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*e)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)) + sqrt(3)*((b^3*c^2 - 4*a*b*c^3)*d^3*e - 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 + 3*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 - (a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e^4))*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)*sqrt((2*(b*c^4*d^7 - 2*(b^2*c^3 + 3*a*c^4)*d^6*e + (b^3*c^2 + 17*a*b*c^3)*d^5*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^3 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^4 - (a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^2*e^5 + (2*a^2*b^3 - a^3*b*c)*d*e^6 - (a^3*b^2 - 2*a^4*c)*e^7)*x^2 - (1/2)^(2/3)*(((a*b^6*c^3 - 12*a^2*b^4*c^4 + 48*a^3*b^2*c^5 - 64*a^4*c^6)*d^2 - (a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*e^2)*x*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)) + ((b^4*c^3 - 4*a*b^2*c^4)*d^5 - 10*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e + 4*(a*b^4*c^2 + 2*a^2*b^2*c^3 - 24*a^3*c^4)*d^3*e^2 - (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^2*e^3 + (7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d*e^4 - (a^2*b^5 - 6*a^3*b^3*c + 8*a^4*b*c^2)*e^5)*x)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(2/3) + (1/2)^(1/3)*((b^3*c^3 - 4*a*b*c^4)*d^6 - (b^4*c^2 + 2*a*b^2*c^3 - 24*a^2*c^4)*d^5*e + 10*(a*b^3*c^2 - 4*a^2*b*c^3)*d^4*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^3 + (a*b^5 - 3*a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^4 - (a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*e^5 + ((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^3 - (a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^4*c^5)*d^2*e + 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^2 - 2*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3))/(b*c^4*d^7 - 2*(b^2*c^3 + 3*a*c^4)*d^6*e + (b^3*c^2 + 17*a*b*c^3)*d^5*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^3 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^4 - (a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^2*e^5 + (2*a^2*b^3 - a^3*b*c)*d*e^6 - (a^3*b^2 - 2*a^4*c)*e^7)) - (1/2)^(1/3)*(sqrt(3)*(2*(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*d - (a*b^5*c^2 - 8*a^2*b^3*c^3 + 16*a^3*b*c^4)*e)*x*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)) + sqrt(3)*((b^3*c^2 - 4*a*b*c^3)*d^3*e - 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^2 + 3*(a*b^3*c - 4*a^2*b*c^2)*d*e^3 - (a*b^4 - 6*a^2*b^2*c + 8*a^3*c^2)*e^4)*x)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3) + sqrt(3)*(b*c^3*d^5 + 10*a*b*c^2*d^3*e^2 - (b^2*c^2 + 6*a*c^3)*d^4*e - 4*(a*b^2*c + a^2*c^2)*d^2*e^3 + (a*b^3 + a^2*b*c)*d*e^4 - (a^2*b^2 - 2*a^3*c)*e^5))/(b*c^3*d^5 + 10*a*b*c^2*d^3*e^2 - (b^2*c^2 + 6*a*c^3)*d^4*e - 4*(a*b^2*c + a^2*c^2)*d^2*e^3 + (a*b^3 + a^2*b*c)*d*e^4 - (a^2*b^2 - 2*a^3*c)*e^5)) - 1/6*(1/2)^(1/3)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)*log(2*(b*c^4*d^7 - 2*(b^2*c^3 + 3*a*c^4)*d^6*e + (b^3*c^2 + 17*a*b*c^3)*d^5*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^3 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^4 - (a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^2*e^5 + (2*a^2*b^3 - a^3*b*c)*d*e^6 - (a^3*b^2 - 2*a^4*c)*e^7)*x^2 + (1/2)^(2/3)*(((a*b^6*c^3 - 12*a^2*b^4*c^4 + 48*a^3*b^2*c^5 - 64*a^4*c^6)*d^2 - (a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*e^2)*x*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)) - ((b^4*c^3 - 4*a*b^2*c^4)*d^5 - 10*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e + 4*(a*b^4*c^2 + 2*a^2*b^2*c^3 - 24*a^3*c^4)*d^3*e^2 - (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^2*e^3 + (7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d*e^4 - (a^2*b^5 - 6*a^3*b^3*c + 8*a^4*b*c^2)*e^5)*x)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(2/3) + (1/2)^(1/3)*((b^3*c^3 - 4*a*b*c^4)*d^6 - (b^4*c^2 + 2*a*b^2*c^3 - 24*a^2*c^4)*d^5*e + 10*(a*b^3*c^2 - 4*a^2*b*c^3)*d^4*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^3 + (a*b^5 - 3*a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^4 - (a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*e^5 - ((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^3 - (a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^4*c^5)*d^2*e + 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^2 - 2*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)) - 1/6*(1/2)^(1/3)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)*log(2*(b*c^4*d^7 - 2*(b^2*c^3 + 3*a*c^4)*d^6*e + (b^3*c^2 + 17*a*b*c^3)*d^5*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^3 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^4 - (a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^2*e^5 + (2*a^2*b^3 - a^3*b*c)*d*e^6 - (a^3*b^2 - 2*a^4*c)*e^7)*x^2 - (1/2)^(2/3)*(((a*b^6*c^3 - 12*a^2*b^4*c^4 + 48*a^3*b^2*c^5 - 64*a^4*c^6)*d^2 - (a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*e^2)*x*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)) + ((b^4*c^3 - 4*a*b^2*c^4)*d^5 - 10*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e + 4*(a*b^4*c^2 + 2*a^2*b^2*c^3 - 24*a^3*c^4)*d^3*e^2 - (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^2*e^3 + (7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d*e^4 - (a^2*b^5 - 6*a^3*b^3*c + 8*a^4*b*c^2)*e^5)*x)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(2/3) + (1/2)^(1/3)*((b^3*c^3 - 4*a*b*c^4)*d^6 - (b^4*c^2 + 2*a*b^2*c^3 - 24*a^2*c^4)*d^5*e + 10*(a*b^3*c^2 - 4*a^2*b*c^3)*d^4*e^2 - 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^3*e^3 + (a*b^5 - 3*a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^4 - (a^2*b^4 - 6*a^3*b^2*c + 8*a^4*c^2)*d*e^5 + ((a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^3 - (a*b^6*c^2 - 6*a^2*b^4*c^3 + 32*a^4*c^5)*d^2*e + 3*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d*e^2 - 2*(a^3*b^4*c^2 - 8*a^4*b^2*c^3 + 16*a^5*c^4)*e^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)) + 1/3*(1/2)^(1/3)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)*log((1/2)^(2/3)*((b^4*c^3 - 4*a*b^2*c^4)*d^5 - 10*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e + 4*(a*b^4*c^2 + 2*a^2*b^2*c^3 - 24*a^3*c^4)*d^3*e^2 - (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^2*e^3 + (7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d*e^4 - (a^2*b^5 - 6*a^3*b^3*c + 8*a^4*b*c^2)*e^5 - ((a*b^6*c^3 - 12*a^2*b^4*c^4 + 48*a^3*b^2*c^5 - 64*a^4*c^6)*d^2 - (a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*e^2)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 + (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(2/3) + 2*(b*c^4*d^7 - 2*(b^2*c^3 + 3*a*c^4)*d^6*e + (b^3*c^2 + 17*a*b*c^3)*d^5*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^3 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^4 - (a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^2*e^5 + (2*a^2*b^3 - a^3*b*c)*d*e^6 - (a^3*b^2 - 2*a^4*c)*e^7)*x) + 1/3*(1/2)^(1/3)*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(1/3)*log((1/2)^(2/3)*((b^4*c^3 - 4*a*b^2*c^4)*d^5 - 10*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e + 4*(a*b^4*c^2 + 2*a^2*b^2*c^3 - 24*a^3*c^4)*d^3*e^2 - (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^2*e^3 + (7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d*e^4 - (a^2*b^5 - 6*a^3*b^3*c + 8*a^4*b*c^2)*e^5 + ((a*b^6*c^3 - 12*a^2*b^4*c^4 + 48*a^3*b^2*c^5 - 64*a^4*c^6)*d^2 - (a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*e^2)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))*(-(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3 - (a*b^2*c^2 - 4*a^2*c^3)*sqrt((b^2*c^4*d^6 - 12*a*b*c^4*d^5*e + 6*(a*b^2*c^3 + 6*a^2*c^4)*d^4*e^2 - 2*(a*b^3*c^2 + 16*a^2*b*c^3)*d^3*e^3 + 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^2*e^4 - 6*(a^2*b^3*c - 2*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 4*a^3*b^2*c + 4*a^4*c^2)*e^6)/(a^2*b^6*c^4 - 12*a^3*b^4*c^5 + 48*a^4*b^2*c^6 - 64*a^5*c^7)))/(a*b^2*c^2 - 4*a^2*c^3))^(2/3) + 2*(b*c^4*d^7 - 2*(b^2*c^3 + 3*a*c^4)*d^6*e + (b^3*c^2 + 17*a*b*c^3)*d^5*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^3 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^4 - (a*b^4 + 6*a^2*b^2*c + 2*a^3*c^2)*d^2*e^5 + (2*a^2*b^3 - a^3*b*c)*d*e^6 - (a^3*b^2 - 2*a^4*c)*e^7)*x)","B",0
17,1,14094,0,39.393790," ","integrate((e*x^3+d)/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","-\frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left({\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} d^{2} - {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} e^{2}\right)} x \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}} - \sqrt{3} {\left({\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{5} - {\left(7 \, a b^{4} c^{2} - 36 \, a^{2} b^{2} c^{3} + 32 \, a^{3} c^{4}\right)} d^{4} e + {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} c + 2 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} d^{2} e^{3} + 10 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d e^{4} - {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} e^{5}\right)} x\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left({\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} d^{2} - {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} e^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}} - \sqrt{3} {\left({\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{5} - {\left(7 \, a b^{4} c^{2} - 36 \, a^{2} b^{2} c^{3} + 32 \, a^{3} c^{4}\right)} d^{4} e + {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} c + 2 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} d^{2} e^{3} + 10 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d e^{4} - {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} e^{5}\right)}\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{2}{3}} \sqrt{\frac{2 \, {\left(a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{6} c - 8 \, a b^{4} c^{2} + 20 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} d^{5} - 5 \, {\left(a b^{5} c - 6 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} d^{4} e + 2 \, {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d^{3} e^{2} - {\left(a^{2} b^{5} + 12 \, a^{3} b^{3} c - 64 \, a^{4} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a^{3} b^{4} + 2 \, a^{4} b^{2} c - 24 \, a^{5} c^{2}\right)} d e^{4} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{5} - {\left({\left(a^{2} b^{7} c - 12 \, a^{3} b^{5} c^{2} + 48 \, a^{4} b^{3} c^{3} - 64 \, a^{5} b c^{4}\right)} d^{2} - 2 \, {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} d e\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left({\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{3} - {\left(a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{5} c^{4}\right)} d^{2} e + 3 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d e^{2} - 2 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} e^{3}\right)} x \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}} - {\left({\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{6} - {\left(b^{5} c - 3 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} e + 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} e^{2} - 10 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e^{3} + {\left(a^{2} b^{4} + 2 \, a^{3} b^{2} c - 24 \, a^{4} c^{2}\right)} d^{2} e^{4} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{5}\right)} x\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}}}{a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}}} - 2 \, \sqrt{3} {\left(a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}\right)}}{6 \, {\left(a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}\right)}}\right) + \frac{2}{3} \, \sqrt{3} \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}} \arctan\left(-\frac{2 \, \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left(\sqrt{3} {\left({\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} d^{2} - {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} e^{2}\right)} x \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}} + \sqrt{3} {\left({\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{5} - {\left(7 \, a b^{4} c^{2} - 36 \, a^{2} b^{2} c^{3} + 32 \, a^{3} c^{4}\right)} d^{4} e + {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} c + 2 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} d^{2} e^{3} + 10 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d e^{4} - {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} e^{5}\right)} x\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{6}} {\left(\sqrt{3} {\left({\left(a^{2} b^{6} c^{2} - 12 \, a^{3} b^{4} c^{3} + 48 \, a^{4} b^{2} c^{4} - 64 \, a^{5} c^{5}\right)} d^{2} - {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} e^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}} + \sqrt{3} {\left({\left(b^{5} c^{2} - 6 \, a b^{3} c^{3} + 8 \, a^{2} b c^{4}\right)} d^{5} - {\left(7 \, a b^{4} c^{2} - 36 \, a^{2} b^{2} c^{3} + 32 \, a^{3} c^{4}\right)} d^{4} e + {\left(a b^{5} c + 12 \, a^{2} b^{3} c^{2} - 64 \, a^{3} b c^{3}\right)} d^{3} e^{2} - 4 \, {\left(a^{2} b^{4} c + 2 \, a^{3} b^{2} c^{2} - 24 \, a^{4} c^{3}\right)} d^{2} e^{3} + 10 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d e^{4} - {\left(a^{3} b^{4} - 4 \, a^{4} b^{2} c\right)} e^{5}\right)}\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{2}{3}} \sqrt{\frac{2 \, {\left(a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{6} c - 8 \, a b^{4} c^{2} + 20 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} d^{5} - 5 \, {\left(a b^{5} c - 6 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} d^{4} e + 2 \, {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d^{3} e^{2} - {\left(a^{2} b^{5} + 12 \, a^{3} b^{3} c - 64 \, a^{4} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a^{3} b^{4} + 2 \, a^{4} b^{2} c - 24 \, a^{5} c^{2}\right)} d e^{4} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{5} + {\left({\left(a^{2} b^{7} c - 12 \, a^{3} b^{5} c^{2} + 48 \, a^{4} b^{3} c^{3} - 64 \, a^{5} b c^{4}\right)} d^{2} - 2 \, {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} d e\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left({\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{3} - {\left(a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{5} c^{4}\right)} d^{2} e + 3 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d e^{2} - 2 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} e^{3}\right)} x \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}} + {\left({\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{6} - {\left(b^{5} c - 3 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} e + 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} e^{2} - 10 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e^{3} + {\left(a^{2} b^{4} + 2 \, a^{3} b^{2} c - 24 \, a^{4} c^{2}\right)} d^{2} e^{4} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{5}\right)} x\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}}}{a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}}} + 2 \, \sqrt{3} {\left(a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}\right)}}{6 \, {\left(a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}\right)}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{6} c - 8 \, a b^{4} c^{2} + 20 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} d^{5} - 5 \, {\left(a b^{5} c - 6 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} d^{4} e + 2 \, {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d^{3} e^{2} - {\left(a^{2} b^{5} + 12 \, a^{3} b^{3} c - 64 \, a^{4} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a^{3} b^{4} + 2 \, a^{4} b^{2} c - 24 \, a^{5} c^{2}\right)} d e^{4} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{5} - {\left({\left(a^{2} b^{7} c - 12 \, a^{3} b^{5} c^{2} + 48 \, a^{4} b^{3} c^{3} - 64 \, a^{5} b c^{4}\right)} d^{2} - 2 \, {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} d e\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{2}{3}} + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left({\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{3} - {\left(a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{5} c^{4}\right)} d^{2} e + 3 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d e^{2} - 2 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} e^{3}\right)} x \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}} - {\left({\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{6} - {\left(b^{5} c - 3 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} e + 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} e^{2} - 10 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e^{3} + {\left(a^{2} b^{4} + 2 \, a^{3} b^{2} c - 24 \, a^{4} c^{2}\right)} d^{2} e^{4} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{5}\right)} x\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}}\right) - \frac{1}{6} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(a^{4} b e^{7} - {\left(b^{2} c^{3} - 2 \, a c^{4}\right)} d^{7} + {\left(2 \, b^{3} c^{2} - a b c^{3}\right)} d^{6} e - {\left(b^{4} c + 6 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{5} e^{2} + 5 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{4} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{3} e^{4} + {\left(a^{2} b^{3} + 17 \, a^{3} b c\right)} d^{2} e^{5} - 2 \, {\left(a^{3} b^{2} + 3 \, a^{4} c\right)} d e^{6}\right)} x^{2} - \left(\frac{1}{2}\right)^{\frac{2}{3}} {\left({\left(b^{6} c - 8 \, a b^{4} c^{2} + 20 \, a^{2} b^{2} c^{3} - 16 \, a^{3} c^{4}\right)} d^{5} - 5 \, {\left(a b^{5} c - 6 \, a^{2} b^{3} c^{2} + 8 \, a^{3} b c^{3}\right)} d^{4} e + 2 \, {\left(7 \, a^{2} b^{4} c - 36 \, a^{3} b^{2} c^{2} + 32 \, a^{4} c^{3}\right)} d^{3} e^{2} - {\left(a^{2} b^{5} + 12 \, a^{3} b^{3} c - 64 \, a^{4} b c^{2}\right)} d^{2} e^{3} + 2 \, {\left(a^{3} b^{4} + 2 \, a^{4} b^{2} c - 24 \, a^{5} c^{2}\right)} d e^{4} - 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e^{5} + {\left({\left(a^{2} b^{7} c - 12 \, a^{3} b^{5} c^{2} + 48 \, a^{4} b^{3} c^{3} - 64 \, a^{5} b c^{4}\right)} d^{2} - 2 \, {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} d e\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{2}{3}} - \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left({\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{3} - {\left(a^{2} b^{6} c - 6 \, a^{3} b^{4} c^{2} + 32 \, a^{5} c^{4}\right)} d^{2} e + 3 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d e^{2} - 2 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} e^{3}\right)} x \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}} + {\left({\left(b^{4} c^{2} - 6 \, a b^{2} c^{3} + 8 \, a^{2} c^{4}\right)} d^{6} - {\left(b^{5} c - 3 \, a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{5} e + 4 \, {\left(a b^{4} c - 3 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d^{4} e^{2} - 10 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{3} e^{3} + {\left(a^{2} b^{4} + 2 \, a^{3} b^{2} c - 24 \, a^{4} c^{2}\right)} d^{2} e^{4} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{5}\right)} x\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(10 \, a^{2} b c d^{2} e^{3} + a^{3} b e^{5} - {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{5} + {\left(b^{3} c + a b c^{2}\right)} d^{4} e - 4 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{3} e^{2} - {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{4}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{4} - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} - {\left({\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d - 2 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}}\right) + \frac{1}{3} \, \left(\frac{1}{2}\right)^{\frac{1}{3}} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}} \log\left(2 \, {\left(10 \, a^{2} b c d^{2} e^{3} + a^{3} b e^{5} - {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d^{5} + {\left(b^{3} c + a b c^{2}\right)} d^{4} e - 4 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{3} e^{2} - {\left(a^{2} b^{2} + 6 \, a^{3} c\right)} d e^{4}\right)} x + \left(\frac{1}{2}\right)^{\frac{1}{3}} {\left({\left(b^{4} c - 6 \, a b^{2} c^{2} + 8 \, a^{2} c^{3}\right)} d^{4} - 3 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left({\left(a^{2} b^{5} c - 8 \, a^{3} b^{3} c^{2} + 16 \, a^{4} b c^{3}\right)} d - 2 \, {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} e\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}\right)} \left(\frac{b c d^{3} - 3 \, a c d^{2} e + a^{2} e^{3} - {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} \sqrt{-\frac{12 \, a^{4} b c d e^{5} - a^{4} b^{2} e^{6} - {\left(b^{4} c^{2} - 4 \, a b^{2} c^{3} + 4 \, a^{2} c^{4}\right)} d^{6} + 6 \, {\left(a b^{3} c^{2} - 2 \, a^{2} b c^{3}\right)} d^{5} e - 3 \, {\left(7 \, a^{2} b^{2} c^{2} - 8 \, a^{3} c^{3}\right)} d^{4} e^{2} + 2 \, {\left(a^{2} b^{3} c + 16 \, a^{3} b c^{2}\right)} d^{3} e^{3} - 6 \, {\left(a^{3} b^{2} c + 6 \, a^{4} c^{2}\right)} d^{2} e^{4}}{a^{4} b^{6} c^{2} - 12 \, a^{5} b^{4} c^{3} + 48 \, a^{6} b^{2} c^{4} - 64 \, a^{7} c^{5}}}}{a^{2} b^{2} c - 4 \, a^{3} c^{2}}\right)^{\frac{1}{3}}\right)"," ",0,"-2/3*sqrt(3)*(1/2)^(1/3)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*((a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*d^2 - (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*e^2)*x*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)) - sqrt(3)*((b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^5 - (7*a*b^4*c^2 - 36*a^2*b^2*c^3 + 32*a^3*c^4)*d^4*e + (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^3*e^2 - 4*(a^2*b^4*c + 2*a^3*b^2*c^2 - 24*a^4*c^3)*d^2*e^3 + 10*(a^3*b^3*c - 4*a^4*b*c^2)*d*e^4 - (a^3*b^4 - 4*a^4*b^2*c)*e^5)*x)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(2/3) - (1/2)^(1/6)*(sqrt(3)*((a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*d^2 - (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*e^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)) - sqrt(3)*((b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^5 - (7*a*b^4*c^2 - 36*a^2*b^2*c^3 + 32*a^3*c^4)*d^4*e + (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^3*e^2 - 4*(a^2*b^4*c + 2*a^3*b^2*c^2 - 24*a^4*c^3)*d^2*e^3 + 10*(a^3*b^3*c - 4*a^4*b*c^2)*d*e^4 - (a^3*b^4 - 4*a^4*b^2*c)*e^5))*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(2/3)*sqrt((2*(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6)*x^2 - (1/2)^(2/3)*((b^6*c - 8*a*b^4*c^2 + 20*a^2*b^2*c^3 - 16*a^3*c^4)*d^5 - 5*(a*b^5*c - 6*a^2*b^3*c^2 + 8*a^3*b*c^3)*d^4*e + 2*(7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d^3*e^2 - (a^2*b^5 + 12*a^3*b^3*c - 64*a^4*b*c^2)*d^2*e^3 + 2*(a^3*b^4 + 2*a^4*b^2*c - 24*a^5*c^2)*d*e^4 - 2*(a^4*b^3 - 4*a^5*b*c)*e^5 - ((a^2*b^7*c - 12*a^3*b^5*c^2 + 48*a^4*b^3*c^3 - 64*a^5*b*c^4)*d^2 - 2*(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*d*e)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(2/3) + (1/2)^(1/3)*(((a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^3 - (a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^5*c^4)*d^2*e + 3*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d*e^2 - 2*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*e^3)*x*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)) - ((b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^6 - (b^5*c - 3*a*b^3*c^2 - 4*a^2*b*c^3)*d^5*e + 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^4*e^2 - 10*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e^3 + (a^2*b^4 + 2*a^3*b^2*c - 24*a^4*c^2)*d^2*e^4 - (a^3*b^3 - 4*a^4*b*c)*d*e^5)*x)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3))/(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6)) - 2*sqrt(3)*(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6))/(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6)) + 2/3*sqrt(3)*(1/2)^(1/3)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)*arctan(-1/6*(2*(1/2)^(2/3)*(sqrt(3)*((a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*d^2 - (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*e^2)*x*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)) + sqrt(3)*((b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^5 - (7*a*b^4*c^2 - 36*a^2*b^2*c^3 + 32*a^3*c^4)*d^4*e + (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^3*e^2 - 4*(a^2*b^4*c + 2*a^3*b^2*c^2 - 24*a^4*c^3)*d^2*e^3 + 10*(a^3*b^3*c - 4*a^4*b*c^2)*d*e^4 - (a^3*b^4 - 4*a^4*b^2*c)*e^5)*x)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(2/3) - (1/2)^(1/6)*(sqrt(3)*((a^2*b^6*c^2 - 12*a^3*b^4*c^3 + 48*a^4*b^2*c^4 - 64*a^5*c^5)*d^2 - (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*e^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)) + sqrt(3)*((b^5*c^2 - 6*a*b^3*c^3 + 8*a^2*b*c^4)*d^5 - (7*a*b^4*c^2 - 36*a^2*b^2*c^3 + 32*a^3*c^4)*d^4*e + (a*b^5*c + 12*a^2*b^3*c^2 - 64*a^3*b*c^3)*d^3*e^2 - 4*(a^2*b^4*c + 2*a^3*b^2*c^2 - 24*a^4*c^3)*d^2*e^3 + 10*(a^3*b^3*c - 4*a^4*b*c^2)*d*e^4 - (a^3*b^4 - 4*a^4*b^2*c)*e^5))*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(2/3)*sqrt((2*(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6)*x^2 - (1/2)^(2/3)*((b^6*c - 8*a*b^4*c^2 + 20*a^2*b^2*c^3 - 16*a^3*c^4)*d^5 - 5*(a*b^5*c - 6*a^2*b^3*c^2 + 8*a^3*b*c^3)*d^4*e + 2*(7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d^3*e^2 - (a^2*b^5 + 12*a^3*b^3*c - 64*a^4*b*c^2)*d^2*e^3 + 2*(a^3*b^4 + 2*a^4*b^2*c - 24*a^5*c^2)*d*e^4 - 2*(a^4*b^3 - 4*a^5*b*c)*e^5 + ((a^2*b^7*c - 12*a^3*b^5*c^2 + 48*a^4*b^3*c^3 - 64*a^5*b*c^4)*d^2 - 2*(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*d*e)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(2/3) - (1/2)^(1/3)*(((a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^3 - (a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^5*c^4)*d^2*e + 3*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d*e^2 - 2*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*e^3)*x*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)) + ((b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^6 - (b^5*c - 3*a*b^3*c^2 - 4*a^2*b*c^3)*d^5*e + 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^4*e^2 - 10*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e^3 + (a^2*b^4 + 2*a^3*b^2*c - 24*a^4*c^2)*d^2*e^4 - (a^3*b^3 - 4*a^4*b*c)*d*e^5)*x)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3))/(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6)) + 2*sqrt(3)*(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6))/(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6)) - 1/6*(1/2)^(1/3)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)*log(2*(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6)*x^2 - (1/2)^(2/3)*((b^6*c - 8*a*b^4*c^2 + 20*a^2*b^2*c^3 - 16*a^3*c^4)*d^5 - 5*(a*b^5*c - 6*a^2*b^3*c^2 + 8*a^3*b*c^3)*d^4*e + 2*(7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d^3*e^2 - (a^2*b^5 + 12*a^3*b^3*c - 64*a^4*b*c^2)*d^2*e^3 + 2*(a^3*b^4 + 2*a^4*b^2*c - 24*a^5*c^2)*d*e^4 - 2*(a^4*b^3 - 4*a^5*b*c)*e^5 - ((a^2*b^7*c - 12*a^3*b^5*c^2 + 48*a^4*b^3*c^3 - 64*a^5*b*c^4)*d^2 - 2*(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*d*e)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(2/3) + (1/2)^(1/3)*(((a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^3 - (a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^5*c^4)*d^2*e + 3*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d*e^2 - 2*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*e^3)*x*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)) - ((b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^6 - (b^5*c - 3*a*b^3*c^2 - 4*a^2*b*c^3)*d^5*e + 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^4*e^2 - 10*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e^3 + (a^2*b^4 + 2*a^3*b^2*c - 24*a^4*c^2)*d^2*e^4 - (a^3*b^3 - 4*a^4*b*c)*d*e^5)*x)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)) - 1/6*(1/2)^(1/3)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)*log(2*(a^4*b*e^7 - (b^2*c^3 - 2*a*c^4)*d^7 + (2*b^3*c^2 - a*b*c^3)*d^6*e - (b^4*c + 6*a*b^2*c^2 + 2*a^2*c^3)*d^5*e^2 + 5*(a*b^3*c + 3*a^2*b*c^2)*d^4*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^3*e^4 + (a^2*b^3 + 17*a^3*b*c)*d^2*e^5 - 2*(a^3*b^2 + 3*a^4*c)*d*e^6)*x^2 - (1/2)^(2/3)*((b^6*c - 8*a*b^4*c^2 + 20*a^2*b^2*c^3 - 16*a^3*c^4)*d^5 - 5*(a*b^5*c - 6*a^2*b^3*c^2 + 8*a^3*b*c^3)*d^4*e + 2*(7*a^2*b^4*c - 36*a^3*b^2*c^2 + 32*a^4*c^3)*d^3*e^2 - (a^2*b^5 + 12*a^3*b^3*c - 64*a^4*b*c^2)*d^2*e^3 + 2*(a^3*b^4 + 2*a^4*b^2*c - 24*a^5*c^2)*d*e^4 - 2*(a^4*b^3 - 4*a^5*b*c)*e^5 + ((a^2*b^7*c - 12*a^3*b^5*c^2 + 48*a^4*b^3*c^3 - 64*a^5*b*c^4)*d^2 - 2*(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*d*e)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(2/3) - (1/2)^(1/3)*(((a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^3 - (a^2*b^6*c - 6*a^3*b^4*c^2 + 32*a^5*c^4)*d^2*e + 3*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d*e^2 - 2*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*e^3)*x*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)) + ((b^4*c^2 - 6*a*b^2*c^3 + 8*a^2*c^4)*d^6 - (b^5*c - 3*a*b^3*c^2 - 4*a^2*b*c^3)*d^5*e + 4*(a*b^4*c - 3*a^2*b^2*c^2 - 4*a^3*c^3)*d^4*e^2 - 10*(a^2*b^3*c - 4*a^3*b*c^2)*d^3*e^3 + (a^2*b^4 + 2*a^3*b^2*c - 24*a^4*c^2)*d^2*e^4 - (a^3*b^3 - 4*a^4*b*c)*d*e^5)*x)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)) + 1/3*(1/2)^(1/3)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)*log(2*(10*a^2*b*c*d^2*e^3 + a^3*b*e^5 - (b^2*c^2 - 2*a*c^3)*d^5 + (b^3*c + a*b*c^2)*d^4*e - 4*(a*b^2*c + a^2*c^2)*d^3*e^2 - (a^2*b^2 + 6*a^3*c)*d*e^4)*x + (1/2)^(1/3)*((b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^4 - 3*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + 6*(a^2*b^2*c - 4*a^3*c^2)*d^2*e^2 - (a^2*b^3 - 4*a^3*b*c)*d*e^3 - ((a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d - 2*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*e)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 + (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)) + 1/3*(1/2)^(1/3)*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3)*log(2*(10*a^2*b*c*d^2*e^3 + a^3*b*e^5 - (b^2*c^2 - 2*a*c^3)*d^5 + (b^3*c + a*b*c^2)*d^4*e - 4*(a*b^2*c + a^2*c^2)*d^3*e^2 - (a^2*b^2 + 6*a^3*c)*d*e^4)*x + (1/2)^(1/3)*((b^4*c - 6*a*b^2*c^2 + 8*a^2*c^3)*d^4 - 3*(a*b^3*c - 4*a^2*b*c^2)*d^3*e + 6*(a^2*b^2*c - 4*a^3*c^2)*d^2*e^2 - (a^2*b^3 - 4*a^3*b*c)*d*e^3 + ((a^2*b^5*c - 8*a^3*b^3*c^2 + 16*a^4*b*c^3)*d - 2*(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*e)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))*((b*c*d^3 - 3*a*c*d^2*e + a^2*e^3 - (a^2*b^2*c - 4*a^3*c^2)*sqrt(-(12*a^4*b*c*d*e^5 - a^4*b^2*e^6 - (b^4*c^2 - 4*a*b^2*c^3 + 4*a^2*c^4)*d^6 + 6*(a*b^3*c^2 - 2*a^2*b*c^3)*d^5*e - 3*(7*a^2*b^2*c^2 - 8*a^3*c^3)*d^4*e^2 + 2*(a^2*b^3*c + 16*a^3*b*c^2)*d^3*e^3 - 6*(a^3*b^2*c + 6*a^4*c^2)*d^2*e^4)/(a^4*b^6*c^2 - 12*a^5*b^4*c^3 + 48*a^6*b^2*c^4 - 64*a^7*c^5)))/(a^2*b^2*c - 4*a^3*c^2))^(1/3))","B",0
18,-1,0,0,0.000000," ","integrate((e*x^3+d)/x^2/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
19,-1,0,0,0.000000," ","integrate((e*x^3+d)/x^3/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
20,1,37,0,1.459726," ","integrate(x^8*(-x^3+1)/(x^6-x^3+1),x, algorithm=""fricas"")","-\frac{1}{6} \, x^{6} + \frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) + \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right)"," ",0,"-1/6*x^6 + 1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) + 1/6*log(x^6 - x^3 + 1)","A",0
21,1,24,0,1.638944," ","integrate(x^5*(-x^3+1)/(x^6-x^3+1),x, algorithm=""fricas"")","-\frac{1}{3} \, x^{3} + \frac{2}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right)"," ",0,"-1/3*x^3 + 2/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1))","A",0
22,1,32,0,1.353014," ","integrate(x^2*(-x^3+1)/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) - \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right)"," ",0,"1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/6*log(x^6 - x^3 + 1)","A",0
23,1,34,0,1.457139," ","integrate((-x^3+1)/x/(x^6-x^3+1),x, algorithm=""fricas"")","-\frac{1}{9} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) - \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right) + \log\left(x\right)"," ",0,"-1/9*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/6*log(x^6 - x^3 + 1) + log(x)","A",0
24,1,28,0,1.063055," ","integrate((-x^3+1)/x^4/(x^6-x^3+1),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{3} x^{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) + 3}{9 \, x^{3}}"," ",0,"-1/9*(2*sqrt(3)*x^3*arctan(1/3*sqrt(3)*(2*x^3 - 1)) + 3)/x^3","A",0
25,1,1036,0,1.327919," ","integrate(x^6*(-x^3+1)/(x^6-x^3+1),x, algorithm=""fricas"")","-\frac{1}{4} \, x^{4} + \frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \log\left(2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) + \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(\frac{18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \sqrt{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} - 6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x - 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}{216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x + 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)}}\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x - 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)}}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right)"," ",0,"-1/4*x^4 + 1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2))*log(2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) + 2/27*18^(2/3)*12^(1/6)*arctan(1/216*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*sqrt(2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - 6*18^(1/3)*12^(5/6)*sqrt(3)*x - 216*sin(2/3*arctan(sqrt(3) + 2)))/cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(-1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 - 18*(18^(1/3)*12^(5/6)*x + 24*cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) + 2)) - 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) + 2))))/(cos(2/3*arctan(sqrt(3) + 2))^2 - 3*sin(2/3*arctan(sqrt(3) + 2))^2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) - 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*(18^(1/3)*12^(5/6)*x - 24*cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) + 2))))/(cos(2/3*arctan(sqrt(3) + 2))^2 - 3*sin(2/3*arctan(sqrt(3) + 2))^2)) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)","B",0
26,1,1588,0,1.470767," ","integrate(x^4*(-x^3+1)/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) - \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \frac{1}{2} \, x^{2} - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4}\right)}}\right) + \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} x - 216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}}}{432 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right)"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) - 2/27*18^(2/3)*12^(1/6)*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 864*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2)*sin(2/3*arctan(sqrt(3) - 2))^2 + 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 72*cos(2/3*arctan(sqrt(3) - 2))^3)*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))))/(3*cos(2/3*arctan(sqrt(3) - 2))^4 - 10*cos(2/3*arctan(sqrt(3) - 2))^2*sin(2/3*arctan(sqrt(3) - 2))^2 + 3*sin(2/3*arctan(sqrt(3) - 2))^4))*sin(2/3*arctan(sqrt(3) - 2)) - 1/2*x^2 - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 864*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2)*sin(2/3*arctan(sqrt(3) - 2))^2 - 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 72*cos(2/3*arctan(sqrt(3) - 2))^3)*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 - 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))))/(3*cos(2/3*arctan(sqrt(3) - 2))^4 - 10*cos(2/3*arctan(sqrt(3) - 2))^2*sin(2/3*arctan(sqrt(3) - 2))^2 + 3*sin(2/3*arctan(sqrt(3) - 2))^4)) + 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(-1/432*(6*18^(2/3)*12^(2/3)*x - 216*cos(2/3*arctan(sqrt(3) - 2))^2 + 216*sin(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2))/(cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)))) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)","B",0
27,1,1030,0,1.386210," ","integrate(x^3*(-x^3+1)/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) - \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x + 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x - 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)}}\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \sqrt{-2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} - 6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}{216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(-2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) - x"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2))*log(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 2/27*18^(2/3)*12^(1/6)*arctan(1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*(18^(1/3)*12^(5/6)*x + 24*cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) - 2))))/(cos(2/3*arctan(sqrt(3) - 2))^2 - 3*sin(2/3*arctan(sqrt(3) - 2))^2))*sin(2/3*arctan(sqrt(3) - 2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(-1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) - 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 - 18*(18^(1/3)*12^(5/6)*x - 24*cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) - 2)) - 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) - 2))))/(cos(2/3*arctan(sqrt(3) - 2))^2 - 3*sin(2/3*arctan(sqrt(3) - 2))^2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/216*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*sqrt(-2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 6*18^(1/3)*12^(5/6)*sqrt(3)*x + 216*sin(2/3*arctan(sqrt(3) - 2)))/cos(2/3*arctan(sqrt(3) - 2))) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) - 2)))*log(-2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - x","B",0
28,1,1583,0,1.521029," ","integrate(x*(-x^3+1)/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right) + \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(-\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} x - 216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}}}{432 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4}\right)}}\right) + \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4}\right)}}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 36 \, x^{2}\right)"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2) + 2/27*18^(2/3)*12^(1/6)*arctan(-1/432*(6*18^(2/3)*12^(2/3)*x - 216*cos(2/3*arctan(sqrt(3) + 2))^2 + 216*sin(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2))/(cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))))*sin(2/3*arctan(sqrt(3) + 2)) + 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 864*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2)*sin(2/3*arctan(sqrt(3) + 2))^2 - 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 72*cos(2/3*arctan(sqrt(3) + 2))^3)*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 - 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))))/(3*cos(2/3*arctan(sqrt(3) + 2))^4 - 10*cos(2/3*arctan(sqrt(3) + 2))^2*sin(2/3*arctan(sqrt(3) + 2))^2 + 3*sin(2/3*arctan(sqrt(3) + 2))^4)) + 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 864*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2)*sin(2/3*arctan(sqrt(3) + 2))^2 + 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 72*cos(2/3*arctan(sqrt(3) + 2))^3)*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2))))/(3*cos(2/3*arctan(sqrt(3) + 2))^4 - 10*cos(2/3*arctan(sqrt(3) + 2))^2*sin(2/3*arctan(sqrt(3) + 2))^2 + 3*sin(2/3*arctan(sqrt(3) + 2))^4)) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) + 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2))*sin(2/3*arctan(sqrt(3) + 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) + 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) + 2))^2 + 36*x^2)","B",0
29,1,1031,0,1.269950," ","integrate((-x^3+1)/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{54} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) \log\left(-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) - \frac{2}{27} \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \arctan\left(-\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x + 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x - 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - \sqrt{-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2}\right)}}\right) - \frac{1}{27} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \arctan\left(\frac{18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \sqrt{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}} - 6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x - 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}{216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)}\right) + \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right) - \frac{1}{108} \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)\right)} \log\left(-18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} + 2\right)\right)^{2} + 18 \, x^{2}\right)"," ",0,"1/54*18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2))*log(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - 2/27*18^(2/3)*12^(1/6)*arctan(-1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 - 18*(18^(1/3)*12^(5/6)*x + 24*cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) + 2)) - 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) + 2))))/(cos(2/3*arctan(sqrt(3) + 2))^2 - 3*sin(2/3*arctan(sqrt(3) + 2))^2))*sin(2/3*arctan(sqrt(3) + 2)) + 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) + 2)) - 108*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2))^2 - 108*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*(18^(1/3)*12^(5/6)*x - 24*cos(2/3*arctan(sqrt(3) + 2)))*sin(2/3*arctan(sqrt(3) + 2)) - sqrt(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) + 2))))/(cos(2/3*arctan(sqrt(3) + 2))^2 - 3*sin(2/3*arctan(sqrt(3) + 2))^2)) - 1/27*(18^(2/3)*12^(1/6)*sqrt(3)*cos(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*sin(2/3*arctan(sqrt(3) + 2)))*arctan(1/216*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*sqrt(2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - 6*18^(1/3)*12^(5/6)*sqrt(3)*x - 216*sin(2/3*arctan(sqrt(3) + 2)))/cos(2/3*arctan(sqrt(3) + 2))) + 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) - 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2) - 1/108*(18^(2/3)*12^(1/6)*sqrt(3)*sin(2/3*arctan(sqrt(3) + 2)) + 18^(2/3)*12^(1/6)*cos(2/3*arctan(sqrt(3) + 2)))*log(-18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) + 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) + 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) + 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) + 2))^2 + 18*x^2)","B",0
30,1,1598,0,1.512169," ","integrate((-x^3+1)/x^2/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) + 8 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4}\right)}}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 864 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3} - 6 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} x - 36 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 12 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 72 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{3}\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}} {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(3 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 10 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4}\right)}}\right) - 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{2}{3}} 12^{\frac{2}{3}} x - 216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sqrt{18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}}}{432 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}\right) - {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) + {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} + 18^{\frac{2}{3}} 12^{\frac{2}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{4} - 12 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 2 \, {\left(18^{\frac{2}{3}} 12^{\frac{2}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 6 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} x\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 36 \, x^{2}\right) - 108}{108 \, x}"," ",0,"1/108*(2*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) + 8*18^(2/3)*12^(1/6)*x*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 864*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2)*sin(2/3*arctan(sqrt(3) - 2))^2 - 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 72*cos(2/3*arctan(sqrt(3) - 2))^3)*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 - 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))))/(3*cos(2/3*arctan(sqrt(3) - 2))^4 - 10*cos(2/3*arctan(sqrt(3) - 2))^2*sin(2/3*arctan(sqrt(3) - 2))^2 + 3*sin(2/3*arctan(sqrt(3) - 2))^4))*sin(2/3*arctan(sqrt(3) - 2)) - 4*(18^(2/3)*12^(1/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*x*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/108*(6*18^(2/3)*12^(2/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 864*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))^3 - 6*(18^(2/3)*12^(2/3)*sqrt(3)*x - 36*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2)*sin(2/3*arctan(sqrt(3) - 2))^2 + 12*(18^(2/3)*12^(2/3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 72*cos(2/3*arctan(sqrt(3) - 2))^3)*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2)*(18^(2/3)*12^(2/3)*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 2*18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2))))/(3*cos(2/3*arctan(sqrt(3) - 2))^4 - 10*cos(2/3*arctan(sqrt(3) - 2))^2*sin(2/3*arctan(sqrt(3) - 2))^2 + 3*sin(2/3*arctan(sqrt(3) - 2))^4)) - 4*(18^(2/3)*12^(1/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*x*sin(2/3*arctan(sqrt(3) - 2)))*arctan(-1/432*(6*18^(2/3)*12^(2/3)*x - 216*cos(2/3*arctan(sqrt(3) - 2))^2 + 216*sin(2/3*arctan(sqrt(3) - 2))^2 - 18^(2/3)*12^(2/3)*sqrt(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2))/(cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)))) - (18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 + 12*18^(1/3)*12^(1/3)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2))*sin(2/3*arctan(sqrt(3) - 2)) + 6*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 3*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) + (18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^4 + 18^(2/3)*12^(2/3)*sin(2/3*arctan(sqrt(3) - 2))^4 - 12*18^(1/3)*12^(1/3)*x*cos(2/3*arctan(sqrt(3) - 2))^2 + 2*(18^(2/3)*12^(2/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 6*18^(1/3)*12^(1/3)*x)*sin(2/3*arctan(sqrt(3) - 2))^2 + 36*x^2) - 108)/x","B",0
31,1,1062,0,1.346541," ","integrate((-x^3+1)/x^3/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) \log\left(-2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) - 8 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \arctan\left(\frac{18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \sqrt{-2 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} - 6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x + 216 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}{216 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)}\right) \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x + 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)}}\right) + 4 \, {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \arctan\left(-\frac{6 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 108 \, \sqrt{3} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 108 \, \sqrt{3} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 18 \, {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} x - 24 \, \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - \sqrt{18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}} {\left(18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{3} \sqrt{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{1}{3}} 12^{\frac{5}{6}} \sqrt{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)}}{108 \, {\left(\cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} - 3 \, \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2}\right)}}\right) + {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) - {\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x^{2} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 18^{\frac{2}{3}} 12^{\frac{1}{6}} x^{2} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)\right)} \log\left(18^{\frac{2}{3}} 12^{\frac{1}{6}} \sqrt{3} x \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) - 3 \cdot 18^{\frac{2}{3}} 12^{\frac{1}{6}} x \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right) + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \cos\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 3 \cdot 18^{\frac{1}{3}} 12^{\frac{1}{3}} \sin\left(\frac{2}{3} \, \arctan\left(\sqrt{3} - 2\right)\right)^{2} + 18 \, x^{2}\right) - 54}{108 \, x^{2}}"," ",0,"1/108*(2*18^(2/3)*12^(1/6)*x^2*cos(2/3*arctan(sqrt(3) - 2))*log(-2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 8*18^(2/3)*12^(1/6)*x^2*arctan(1/216*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*sqrt(-2*18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 6*18^(1/3)*12^(5/6)*sqrt(3)*x + 216*sin(2/3*arctan(sqrt(3) - 2)))/cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) + 4*(18^(2/3)*12^(1/6)*sqrt(3)*x^2*cos(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*x^2*sin(2/3*arctan(sqrt(3) - 2)))*arctan(1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) + 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*(18^(1/3)*12^(5/6)*x + 24*cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) - 2))))/(cos(2/3*arctan(sqrt(3) - 2))^2 - 3*sin(2/3*arctan(sqrt(3) - 2))^2)) + 4*(18^(2/3)*12^(1/6)*sqrt(3)*x^2*cos(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*x^2*sin(2/3*arctan(sqrt(3) - 2)))*arctan(-1/108*(6*18^(1/3)*12^(5/6)*sqrt(3)*x*cos(2/3*arctan(sqrt(3) - 2)) - 108*sqrt(3)*cos(2/3*arctan(sqrt(3) - 2))^2 - 108*sqrt(3)*sin(2/3*arctan(sqrt(3) - 2))^2 - 18*(18^(1/3)*12^(5/6)*x - 24*cos(2/3*arctan(sqrt(3) - 2)))*sin(2/3*arctan(sqrt(3) - 2)) - sqrt(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2)*(18^(1/3)*12^(5/6)*sqrt(3)*sqrt(2)*cos(2/3*arctan(sqrt(3) - 2)) - 3*18^(1/3)*12^(5/6)*sqrt(2)*sin(2/3*arctan(sqrt(3) - 2))))/(cos(2/3*arctan(sqrt(3) - 2))^2 - 3*sin(2/3*arctan(sqrt(3) - 2))^2)) + (18^(2/3)*12^(1/6)*sqrt(3)*x^2*sin(2/3*arctan(sqrt(3) - 2)) - 18^(2/3)*12^(1/6)*x^2*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) + 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - (18^(2/3)*12^(1/6)*sqrt(3)*x^2*sin(2/3*arctan(sqrt(3) - 2)) + 18^(2/3)*12^(1/6)*x^2*cos(2/3*arctan(sqrt(3) - 2)))*log(18^(2/3)*12^(1/6)*sqrt(3)*x*sin(2/3*arctan(sqrt(3) - 2)) - 3*18^(2/3)*12^(1/6)*x*cos(2/3*arctan(sqrt(3) - 2)) + 3*18^(1/3)*12^(1/3)*cos(2/3*arctan(sqrt(3) - 2))^2 + 3*18^(1/3)*12^(1/3)*sin(2/3*arctan(sqrt(3) - 2))^2 + 18*x^2) - 54)/x^2","B",0
32,1,32,0,1.093376," ","integrate(x^2*(x^3-2)/(x^6-x^3+1),x, algorithm=""fricas"")","-\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) + \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right)"," ",0,"-1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) + 1/6*log(x^6 - x^3 + 1)","A",0
33,1,34,0,1.099650," ","integrate((x^3+1)/x/(x^6-x^3+1),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) - \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right) + \log\left(x\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/6*log(x^6 - x^3 + 1) + log(x)","A",0
34,1,34,0,1.576357," ","integrate((x^3+1)/(x^7-x^4+x),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{3} - 1\right)}\right) - \frac{1}{6} \, \log\left(x^{6} - x^{3} + 1\right) + \log\left(x\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^3 - 1)) - 1/6*log(x^6 - x^3 + 1) + log(x)","A",0
35,0,0,0,1.192707," ","integrate((e*x^3+d)^(5/2)*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e^{2} x^{12} + {\left(2 \, c d e + b e^{2}\right)} x^{9} + {\left(c d^{2} + 2 \, b d e + a e^{2}\right)} x^{6} + {\left(b d^{2} + 2 \, a d e\right)} x^{3} + a d^{2}\right)} \sqrt{e x^{3} + d}, x\right)"," ",0,"integral((c*e^2*x^12 + (2*c*d*e + b*e^2)*x^9 + (c*d^2 + 2*b*d*e + a*e^2)*x^6 + (b*d^2 + 2*a*d*e)*x^3 + a*d^2)*sqrt(e*x^3 + d), x)","F",0
36,0,0,0,1.283331," ","integrate((e*x^3+d)^(3/2)*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(c e x^{9} + {\left(c d + b e\right)} x^{6} + {\left(b d + a e\right)} x^{3} + a d\right)} \sqrt{e x^{3} + d}, x\right)"," ",0,"integral((c*e*x^9 + (c*d + b*e)*x^6 + (b*d + a*e)*x^3 + a*d)*sqrt(e*x^3 + d), x)","F",0
37,0,0,0,0.728763," ","integrate((e*x^3+d)^(1/2)*(c*x^6+b*x^3+a),x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{6} + b x^{3} + a\right)} \sqrt{e x^{3} + d}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)*sqrt(e*x^3 + d), x)","F",0
38,0,0,0,1.085100," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{c x^{6} + b x^{3} + a}{\sqrt{e x^{3} + d}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)/sqrt(e*x^3 + d), x)","F",0
39,0,0,0,1.208855," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)} \sqrt{e x^{3} + d}}{e^{2} x^{6} + 2 \, d e x^{3} + d^{2}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)*sqrt(e*x^3 + d)/(e^2*x^6 + 2*d*e*x^3 + d^2), x)","F",0
40,0,0,0,1.111794," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)} \sqrt{e x^{3} + d}}{e^{3} x^{9} + 3 \, d e^{2} x^{6} + 3 \, d^{2} e x^{3} + d^{3}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)*sqrt(e*x^3 + d)/(e^3*x^9 + 3*d*e^2*x^6 + 3*d^2*e*x^3 + d^3), x)","F",0
41,0,0,0,0.837984," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(7/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)} \sqrt{e x^{3} + d}}{e^{4} x^{12} + 4 \, d e^{3} x^{9} + 6 \, d^{2} e^{2} x^{6} + 4 \, d^{3} e x^{3} + d^{4}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)*sqrt(e*x^3 + d)/(e^4*x^12 + 4*d*e^3*x^9 + 6*d^2*e^2*x^6 + 4*d^3*e*x^3 + d^4), x)","F",0
42,0,0,0,1.181813," ","integrate((c*x^6+b*x^3+a)/(e*x^3+d)^(9/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{6} + b x^{3} + a\right)} \sqrt{e x^{3} + d}}{e^{5} x^{15} + 5 \, d e^{4} x^{12} + 10 \, d^{2} e^{3} x^{9} + 10 \, d^{3} e^{2} x^{6} + 5 \, d^{4} e x^{3} + d^{5}}, x\right)"," ",0,"integral((c*x^6 + b*x^3 + a)*sqrt(e*x^3 + d)/(e^5*x^15 + 5*d*e^4*x^12 + 10*d^2*e^3*x^9 + 10*d^3*e^2*x^6 + 5*d^4*e*x^3 + d^5), x)","F",0
43,-1,0,0,0.000000," ","integrate(x^4*(e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
44,1,216,0,1.104584," ","integrate(x^3*(e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{8} + b x^{4} + a\right) - \sqrt{b^{2} - 4 \, a c} {\left(2 \, c d - b e\right)} \log\left(\frac{2 \, c^{2} x^{8} + 2 \, b c x^{4} + b^{2} - 2 \, a c + {\left(2 \, c x^{4} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{8} + b x^{4} + a}\right)}{8 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}, \frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(c x^{8} + b x^{4} + a\right) - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{{\left(2 \, c x^{4} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{8 \, {\left(b^{2} c - 4 \, a c^{2}\right)}}\right]"," ",0,"[1/8*((b^2 - 4*a*c)*e*log(c*x^8 + b*x^4 + a) - sqrt(b^2 - 4*a*c)*(2*c*d - b*e)*log((2*c^2*x^8 + 2*b*c*x^4 + b^2 - 2*a*c + (2*c*x^4 + b)*sqrt(b^2 - 4*a*c))/(c*x^8 + b*x^4 + a)))/(b^2*c - 4*a*c^2), 1/8*((b^2 - 4*a*c)*e*log(c*x^8 + b*x^4 + a) - 2*sqrt(-b^2 + 4*a*c)*(2*c*d - b*e)*arctan(-(2*c*x^4 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/(b^2*c - 4*a*c^2)]","A",0
45,1,13521,0,47.545264," ","integrate(x^2*(e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \arctan\left(\frac{{\left({\left(2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d - {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} e\right)} x \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}} + {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e - 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{3} + 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{4} - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e - 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{3} + 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{4} - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5} + {\left(2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d - {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} e\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}\right)} \sqrt{\frac{2 \, {\left(c^{5} d^{8} - 2 \, b c^{4} d^{7} e + 14 \, a b c^{3} d^{5} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{5} - {\left(a b^{4} + 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e^{6} + 2 \, {\left(a^{2} b^{3} + a^{3} b c\right)} d e^{7} - {\left(a^{3} b^{2} - a^{4} c\right)} e^{8}\right)} x^{2} - \sqrt{\frac{1}{2}} {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} - 4 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{5} e - 5 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e^{2} + 4 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{3} e^{3} - {\left(a b^{5} c + 17 \, a^{2} b^{3} c^{2} - 84 \, a^{3} b c^{3}\right)} d^{2} e^{4} + 4 \, {\left(2 \, a^{2} b^{4} c - 9 \, a^{3} b^{2} c^{2} + 4 \, a^{4} c^{3}\right)} d e^{5} - {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 4 \, a^{4} b c^{2}\right)} e^{6} + {\left({\left(a b^{6} c^{4} - 12 \, a^{2} b^{4} c^{5} + 48 \, a^{3} b^{2} c^{6} - 64 \, a^{4} c^{7}\right)} d^{2} - {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6}\right)} e^{2}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}\right)} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}}{c^{5} d^{8} - 2 \, b c^{4} d^{7} e + 14 \, a b c^{3} d^{5} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{5} - {\left(a b^{4} + 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e^{6} + 2 \, {\left(a^{2} b^{3} + a^{3} b c\right)} d e^{7} - {\left(a^{3} b^{2} - a^{4} c\right)} e^{8}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}}}{2 \, {\left(c^{4} d^{6} - b c^{3} d^{5} e - 5 \, a c^{3} d^{4} e^{2} + 10 \, a b c^{2} d^{3} e^{3} - 5 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{2} e^{4} + {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{5} - {\left(a^{2} b^{2} - a^{3} c\right)} e^{6}\right)}}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e - 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{3} + 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{4} - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5} - {\left(2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d - {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} e\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \sqrt{\frac{2 \, {\left(c^{5} d^{8} - 2 \, b c^{4} d^{7} e + 14 \, a b c^{3} d^{5} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{5} - {\left(a b^{4} + 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e^{6} + 2 \, {\left(a^{2} b^{3} + a^{3} b c\right)} d e^{7} - {\left(a^{3} b^{2} - a^{4} c\right)} e^{8}\right)} x^{2} - \sqrt{\frac{1}{2}} {\left({\left(b^{3} c^{4} - 4 \, a b c^{5}\right)} d^{6} - 4 \, {\left(a b^{2} c^{4} - 4 \, a^{2} c^{5}\right)} d^{5} e - 5 \, {\left(a b^{3} c^{3} - 4 \, a^{2} b c^{4}\right)} d^{4} e^{2} + 4 \, {\left(a b^{4} c^{2} + 2 \, a^{2} b^{2} c^{3} - 24 \, a^{3} c^{4}\right)} d^{3} e^{3} - {\left(a b^{5} c + 17 \, a^{2} b^{3} c^{2} - 84 \, a^{3} b c^{3}\right)} d^{2} e^{4} + 4 \, {\left(2 \, a^{2} b^{4} c - 9 \, a^{3} b^{2} c^{2} + 4 \, a^{4} c^{3}\right)} d e^{5} - {\left(a^{2} b^{5} - 5 \, a^{3} b^{3} c + 4 \, a^{4} b c^{2}\right)} e^{6} - {\left({\left(a b^{6} c^{4} - 12 \, a^{2} b^{4} c^{5} + 48 \, a^{3} b^{2} c^{6} - 64 \, a^{4} c^{7}\right)} d^{2} - {\left(a^{2} b^{6} c^{3} - 12 \, a^{3} b^{4} c^{4} + 48 \, a^{4} b^{2} c^{5} - 64 \, a^{5} c^{6}\right)} e^{2}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}\right)} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}}{c^{5} d^{8} - 2 \, b c^{4} d^{7} e + 14 \, a b c^{3} d^{5} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{5} - {\left(a b^{4} + 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e^{6} + 2 \, {\left(a^{2} b^{3} + a^{3} b c\right)} d e^{7} - {\left(a^{3} b^{2} - a^{4} c\right)} e^{8}}} + {\left({\left(2 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d - {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} e\right)} x \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}} - {\left({\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{4} e - 6 \, {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d^{2} e^{3} + 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{4} - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} e^{5}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}}}{2 \, {\left(c^{4} d^{6} - b c^{3} d^{5} e - 5 \, a c^{3} d^{4} e^{2} + 10 \, a b c^{2} d^{3} e^{3} - 5 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{2} e^{4} + {\left(a b^{3} + 3 \, a^{2} b c\right)} d e^{5} - {\left(a^{2} b^{2} - a^{3} c\right)} e^{6}\right)}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{7} - 9 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{5} e^{2} + 5 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{3} - {\left(a b^{6} c^{2} - 27 \, a^{2} b^{4} c^{3} + 168 \, a^{3} b^{2} c^{4} - 304 \, a^{4} c^{5}\right)} d^{3} e^{4} - 18 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{5} + {\left(7 \, a^{2} b^{6} c - 59 \, a^{3} b^{4} c^{2} + 136 \, a^{4} b^{2} c^{3} - 48 \, a^{5} c^{4}\right)} d e^{6} - {\left(a^{2} b^{7} - 9 \, a^{3} b^{5} c + 24 \, a^{4} b^{3} c^{2} - 16 \, a^{5} b c^{3}\right)} e^{7} - {\left({\left(a b^{7} c^{5} - 12 \, a^{2} b^{5} c^{6} + 48 \, a^{3} b^{3} c^{7} - 64 \, a^{4} b c^{8}\right)} d^{3} - 6 \, {\left(a^{2} b^{6} c^{5} - 12 \, a^{3} b^{4} c^{6} + 48 \, a^{4} b^{2} c^{7} - 64 \, a^{5} c^{8}\right)} d^{2} e + 3 \, {\left(a^{2} b^{7} c^{4} - 12 \, a^{3} b^{5} c^{5} + 48 \, a^{4} b^{3} c^{6} - 64 \, a^{5} b c^{7}\right)} d e^{2} - {\left(a^{2} b^{8} c^{3} - 14 \, a^{3} b^{6} c^{4} + 72 \, a^{4} b^{4} c^{5} - 160 \, a^{5} b^{2} c^{6} + 128 \, a^{6} c^{7}\right)} e^{3}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}} + {\left(c^{6} d^{10} - 3 \, b c^{5} d^{9} e + 3 \, {\left(b^{2} c^{4} - a c^{5}\right)} d^{8} e^{2} - {\left(b^{3} c^{3} - 16 \, a b c^{4}\right)} d^{7} e^{3} - 14 \, {\left(2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{6} e^{4} + 21 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d^{5} e^{5} - 7 \, {\left(a b^{4} c + 6 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{4} e^{6} + {\left(a b^{5} + 17 \, a^{2} b^{3} c + 24 \, a^{3} b c^{2}\right)} d^{3} e^{7} - 3 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{8} + {\left(3 \, a^{3} b^{3} + a^{4} b c\right)} d e^{9} - {\left(a^{4} b^{2} - a^{5} c\right)} e^{10}\right)} x\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{7} - 9 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{5} e^{2} + 5 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{3} - {\left(a b^{6} c^{2} - 27 \, a^{2} b^{4} c^{3} + 168 \, a^{3} b^{2} c^{4} - 304 \, a^{4} c^{5}\right)} d^{3} e^{4} - 18 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{5} + {\left(7 \, a^{2} b^{6} c - 59 \, a^{3} b^{4} c^{2} + 136 \, a^{4} b^{2} c^{3} - 48 \, a^{5} c^{4}\right)} d e^{6} - {\left(a^{2} b^{7} - 9 \, a^{3} b^{5} c + 24 \, a^{4} b^{3} c^{2} - 16 \, a^{5} b c^{3}\right)} e^{7} - {\left({\left(a b^{7} c^{5} - 12 \, a^{2} b^{5} c^{6} + 48 \, a^{3} b^{3} c^{7} - 64 \, a^{4} b c^{8}\right)} d^{3} - 6 \, {\left(a^{2} b^{6} c^{5} - 12 \, a^{3} b^{4} c^{6} + 48 \, a^{4} b^{2} c^{7} - 64 \, a^{5} c^{8}\right)} d^{2} e + 3 \, {\left(a^{2} b^{7} c^{4} - 12 \, a^{3} b^{5} c^{5} + 48 \, a^{4} b^{3} c^{6} - 64 \, a^{5} b c^{7}\right)} d e^{2} - {\left(a^{2} b^{8} c^{3} - 14 \, a^{3} b^{6} c^{4} + 72 \, a^{4} b^{4} c^{5} - 160 \, a^{5} b^{2} c^{6} + 128 \, a^{6} c^{7}\right)} e^{3}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}} + {\left(c^{6} d^{10} - 3 \, b c^{5} d^{9} e + 3 \, {\left(b^{2} c^{4} - a c^{5}\right)} d^{8} e^{2} - {\left(b^{3} c^{3} - 16 \, a b c^{4}\right)} d^{7} e^{3} - 14 \, {\left(2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{6} e^{4} + 21 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d^{5} e^{5} - 7 \, {\left(a b^{4} c + 6 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{4} e^{6} + {\left(a b^{5} + 17 \, a^{2} b^{3} c + 24 \, a^{3} b c^{2}\right)} d^{3} e^{7} - 3 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{8} + {\left(3 \, a^{3} b^{3} + a^{4} b c\right)} d e^{9} - {\left(a^{4} b^{2} - a^{5} c\right)} e^{10}\right)} x\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \log\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{7} - 9 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{5} e^{2} + 5 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{3} - {\left(a b^{6} c^{2} - 27 \, a^{2} b^{4} c^{3} + 168 \, a^{3} b^{2} c^{4} - 304 \, a^{4} c^{5}\right)} d^{3} e^{4} - 18 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{5} + {\left(7 \, a^{2} b^{6} c - 59 \, a^{3} b^{4} c^{2} + 136 \, a^{4} b^{2} c^{3} - 48 \, a^{5} c^{4}\right)} d e^{6} - {\left(a^{2} b^{7} - 9 \, a^{3} b^{5} c + 24 \, a^{4} b^{3} c^{2} - 16 \, a^{5} b c^{3}\right)} e^{7} + {\left({\left(a b^{7} c^{5} - 12 \, a^{2} b^{5} c^{6} + 48 \, a^{3} b^{3} c^{7} - 64 \, a^{4} b c^{8}\right)} d^{3} - 6 \, {\left(a^{2} b^{6} c^{5} - 12 \, a^{3} b^{4} c^{6} + 48 \, a^{4} b^{2} c^{7} - 64 \, a^{5} c^{8}\right)} d^{2} e + 3 \, {\left(a^{2} b^{7} c^{4} - 12 \, a^{3} b^{5} c^{5} + 48 \, a^{4} b^{3} c^{6} - 64 \, a^{5} b c^{7}\right)} d e^{2} - {\left(a^{2} b^{8} c^{3} - 14 \, a^{3} b^{6} c^{4} + 72 \, a^{4} b^{4} c^{5} - 160 \, a^{5} b^{2} c^{6} + 128 \, a^{6} c^{7}\right)} e^{3}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}} + {\left(c^{6} d^{10} - 3 \, b c^{5} d^{9} e + 3 \, {\left(b^{2} c^{4} - a c^{5}\right)} d^{8} e^{2} - {\left(b^{3} c^{3} - 16 \, a b c^{4}\right)} d^{7} e^{3} - 14 \, {\left(2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{6} e^{4} + 21 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d^{5} e^{5} - 7 \, {\left(a b^{4} c + 6 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{4} e^{6} + {\left(a b^{5} + 17 \, a^{2} b^{3} c + 24 \, a^{3} b c^{2}\right)} d^{3} e^{7} - 3 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{8} + {\left(3 \, a^{3} b^{3} + a^{4} b c\right)} d e^{9} - {\left(a^{4} b^{2} - a^{5} c\right)} e^{10}\right)} x\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \log\left(-\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{4} c^{5} - 8 \, a b^{2} c^{6} + 16 \, a^{2} c^{7}\right)} d^{7} - 9 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{5} e^{2} + 5 \, {\left(a b^{5} c^{3} - 8 \, a^{2} b^{3} c^{4} + 16 \, a^{3} b c^{5}\right)} d^{4} e^{3} - {\left(a b^{6} c^{2} - 27 \, a^{2} b^{4} c^{3} + 168 \, a^{3} b^{2} c^{4} - 304 \, a^{4} c^{5}\right)} d^{3} e^{4} - 18 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{2} e^{5} + {\left(7 \, a^{2} b^{6} c - 59 \, a^{3} b^{4} c^{2} + 136 \, a^{4} b^{2} c^{3} - 48 \, a^{5} c^{4}\right)} d e^{6} - {\left(a^{2} b^{7} - 9 \, a^{3} b^{5} c + 24 \, a^{4} b^{3} c^{2} - 16 \, a^{5} b c^{3}\right)} e^{7} + {\left({\left(a b^{7} c^{5} - 12 \, a^{2} b^{5} c^{6} + 48 \, a^{3} b^{3} c^{7} - 64 \, a^{4} b c^{8}\right)} d^{3} - 6 \, {\left(a^{2} b^{6} c^{5} - 12 \, a^{3} b^{4} c^{6} + 48 \, a^{4} b^{2} c^{7} - 64 \, a^{5} c^{8}\right)} d^{2} e + 3 \, {\left(a^{2} b^{7} c^{4} - 12 \, a^{3} b^{5} c^{5} + 48 \, a^{4} b^{3} c^{6} - 64 \, a^{5} b c^{7}\right)} d e^{2} - {\left(a^{2} b^{8} c^{3} - 14 \, a^{3} b^{6} c^{4} + 72 \, a^{4} b^{4} c^{5} - 160 \, a^{5} b^{2} c^{6} + 128 \, a^{6} c^{7}\right)} e^{3}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}}} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{6} c^{6} - 12 \, a^{3} b^{4} c^{7} + 48 \, a^{4} b^{2} c^{8} - 64 \, a^{5} c^{9}}}}{a b^{4} c^{3} - 8 \, a^{2} b^{2} c^{4} + 16 \, a^{3} c^{5}}} + {\left(c^{6} d^{10} - 3 \, b c^{5} d^{9} e + 3 \, {\left(b^{2} c^{4} - a c^{5}\right)} d^{8} e^{2} - {\left(b^{3} c^{3} - 16 \, a b c^{4}\right)} d^{7} e^{3} - 14 \, {\left(2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{6} e^{4} + 21 \, {\left(a b^{3} c^{2} + 2 \, a^{2} b c^{3}\right)} d^{5} e^{5} - 7 \, {\left(a b^{4} c + 6 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{4} e^{6} + {\left(a b^{5} + 17 \, a^{2} b^{3} c + 24 \, a^{3} b c^{2}\right)} d^{3} e^{7} - 3 \, {\left(a^{2} b^{4} + 4 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{2} e^{8} + {\left(3 \, a^{3} b^{3} + a^{4} b c\right)} d e^{9} - {\left(a^{4} b^{2} - a^{5} c\right)} e^{10}\right)} x\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*arctan(1/2*((2*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d - (a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*e)*x*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)) + ((b^2*c^3 - 4*a*c^4)*d^4*e - 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^3 + 4*(a*b^3*c - 4*a^2*b*c^2)*d*e^4 - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^5)*x - sqrt(1/2)*((b^2*c^3 - 4*a*c^4)*d^4*e - 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^3 + 4*(a*b^3*c - 4*a^2*b*c^2)*d*e^4 - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^5 + (2*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d - (a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*e)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))*sqrt((2*(c^5*d^8 - 2*b*c^4*d^7*e + 14*a*b*c^3*d^5*e^3 + (b^2*c^3 - 4*a*c^4)*d^6*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^4 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^5 - (a*b^4 + 9*a^2*b^2*c + 4*a^3*c^2)*d^2*e^6 + 2*(a^2*b^3 + a^3*b*c)*d*e^7 - (a^3*b^2 - a^4*c)*e^8)*x^2 - sqrt(1/2)*((b^3*c^4 - 4*a*b*c^5)*d^6 - 4*(a*b^2*c^4 - 4*a^2*c^5)*d^5*e - 5*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e^2 + 4*(a*b^4*c^2 + 2*a^2*b^2*c^3 - 24*a^3*c^4)*d^3*e^3 - (a*b^5*c + 17*a^2*b^3*c^2 - 84*a^3*b*c^3)*d^2*e^4 + 4*(2*a^2*b^4*c - 9*a^3*b^2*c^2 + 4*a^4*c^3)*d*e^5 - (a^2*b^5 - 5*a^3*b^3*c + 4*a^4*b*c^2)*e^6 + ((a*b^6*c^4 - 12*a^2*b^4*c^5 + 48*a^3*b^2*c^6 - 64*a^4*c^7)*d^2 - (a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6)*e^2)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))/(c^5*d^8 - 2*b*c^4*d^7*e + 14*a*b*c^3*d^5*e^3 + (b^2*c^3 - 4*a*c^4)*d^6*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^4 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^5 - (a*b^4 + 9*a^2*b^2*c + 4*a^3*c^2)*d^2*e^6 + 2*(a^2*b^3 + a^3*b*c)*d*e^7 - (a^3*b^2 - a^4*c)*e^8)))*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))/(c^4*d^6 - b*c^3*d^5*e - 5*a*c^3*d^4*e^2 + 10*a*b*c^2*d^3*e^3 - 5*(a*b^2*c + a^2*c^2)*d^2*e^4 + (a*b^3 + 3*a^2*b*c)*d*e^5 - (a^2*b^2 - a^3*c)*e^6)) + sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*arctan(1/2*(sqrt(1/2)*((b^2*c^3 - 4*a*c^4)*d^4*e - 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^3 + 4*(a*b^3*c - 4*a^2*b*c^2)*d*e^4 - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^5 - (2*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d - (a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*e)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*sqrt((2*(c^5*d^8 - 2*b*c^4*d^7*e + 14*a*b*c^3*d^5*e^3 + (b^2*c^3 - 4*a*c^4)*d^6*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^4 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^5 - (a*b^4 + 9*a^2*b^2*c + 4*a^3*c^2)*d^2*e^6 + 2*(a^2*b^3 + a^3*b*c)*d*e^7 - (a^3*b^2 - a^4*c)*e^8)*x^2 - sqrt(1/2)*((b^3*c^4 - 4*a*b*c^5)*d^6 - 4*(a*b^2*c^4 - 4*a^2*c^5)*d^5*e - 5*(a*b^3*c^3 - 4*a^2*b*c^4)*d^4*e^2 + 4*(a*b^4*c^2 + 2*a^2*b^2*c^3 - 24*a^3*c^4)*d^3*e^3 - (a*b^5*c + 17*a^2*b^3*c^2 - 84*a^3*b*c^3)*d^2*e^4 + 4*(2*a^2*b^4*c - 9*a^3*b^2*c^2 + 4*a^4*c^3)*d*e^5 - (a^2*b^5 - 5*a^3*b^3*c + 4*a^4*b*c^2)*e^6 - ((a*b^6*c^4 - 12*a^2*b^4*c^5 + 48*a^3*b^2*c^6 - 64*a^4*c^7)*d^2 - (a^2*b^6*c^3 - 12*a^3*b^4*c^4 + 48*a^4*b^2*c^5 - 64*a^5*c^6)*e^2)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))/(c^5*d^8 - 2*b*c^4*d^7*e + 14*a*b*c^3*d^5*e^3 + (b^2*c^3 - 4*a*c^4)*d^6*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^4 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^5 - (a*b^4 + 9*a^2*b^2*c + 4*a^3*c^2)*d^2*e^6 + 2*(a^2*b^3 + a^3*b*c)*d*e^7 - (a^3*b^2 - a^4*c)*e^8)) + ((2*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d - (a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*e)*x*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)) - ((b^2*c^3 - 4*a*c^4)*d^4*e - 6*(a*b^2*c^2 - 4*a^2*c^3)*d^2*e^3 + 4*(a*b^3*c - 4*a^2*b*c^2)*d*e^4 - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*e^5)*x)*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5))))/(c^4*d^6 - b*c^3*d^5*e - 5*a*c^3*d^4*e^2 + 10*a*b*c^2*d^3*e^3 - 5*(a*b^2*c + a^2*c^2)*d^2*e^4 + (a*b^3 + 3*a^2*b*c)*d*e^5 - (a^2*b^2 - a^3*c)*e^6)) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*log(1/2*sqrt(1/2)*((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^7 - 9*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^5*e^2 + 5*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^3 - (a*b^6*c^2 - 27*a^2*b^4*c^3 + 168*a^3*b^2*c^4 - 304*a^4*c^5)*d^3*e^4 - 18*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^5 + (7*a^2*b^6*c - 59*a^3*b^4*c^2 + 136*a^4*b^2*c^3 - 48*a^5*c^4)*d*e^6 - (a^2*b^7 - 9*a^3*b^5*c + 24*a^4*b^3*c^2 - 16*a^5*b*c^3)*e^7 - ((a*b^7*c^5 - 12*a^2*b^5*c^6 + 48*a^3*b^3*c^7 - 64*a^4*b*c^8)*d^3 - 6*(a^2*b^6*c^5 - 12*a^3*b^4*c^6 + 48*a^4*b^2*c^7 - 64*a^5*c^8)*d^2*e + 3*(a^2*b^7*c^4 - 12*a^3*b^5*c^5 + 48*a^4*b^3*c^6 - 64*a^5*b*c^7)*d*e^2 - (a^2*b^8*c^3 - 14*a^3*b^6*c^4 + 72*a^4*b^4*c^5 - 160*a^5*b^2*c^6 + 128*a^6*c^7)*e^3)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)) + (c^6*d^10 - 3*b*c^5*d^9*e + 3*(b^2*c^4 - a*c^5)*d^8*e^2 - (b^3*c^3 - 16*a*b*c^4)*d^7*e^3 - 14*(2*a*b^2*c^3 + a^2*c^4)*d^6*e^4 + 21*(a*b^3*c^2 + 2*a^2*b*c^3)*d^5*e^5 - 7*(a*b^4*c + 6*a^2*b^2*c^2 + 2*a^3*c^3)*d^4*e^6 + (a*b^5 + 17*a^2*b^3*c + 24*a^3*b*c^2)*d^3*e^7 - 3*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^2*e^8 + (3*a^3*b^3 + a^4*b*c)*d*e^9 - (a^4*b^2 - a^5*c)*e^10)*x) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*log(-1/2*sqrt(1/2)*((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^7 - 9*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^5*e^2 + 5*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^3 - (a*b^6*c^2 - 27*a^2*b^4*c^3 + 168*a^3*b^2*c^4 - 304*a^4*c^5)*d^3*e^4 - 18*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^5 + (7*a^2*b^6*c - 59*a^3*b^4*c^2 + 136*a^4*b^2*c^3 - 48*a^5*c^4)*d*e^6 - (a^2*b^7 - 9*a^3*b^5*c + 24*a^4*b^3*c^2 - 16*a^5*b*c^3)*e^7 - ((a*b^7*c^5 - 12*a^2*b^5*c^6 + 48*a^3*b^3*c^7 - 64*a^4*b*c^8)*d^3 - 6*(a^2*b^6*c^5 - 12*a^3*b^4*c^6 + 48*a^4*b^2*c^7 - 64*a^5*c^8)*d^2*e + 3*(a^2*b^7*c^4 - 12*a^3*b^5*c^5 + 48*a^4*b^3*c^6 - 64*a^5*b*c^7)*d*e^2 - (a^2*b^8*c^3 - 14*a^3*b^6*c^4 + 72*a^4*b^4*c^5 - 160*a^5*b^2*c^6 + 128*a^6*c^7)*e^3)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)) + (c^6*d^10 - 3*b*c^5*d^9*e + 3*(b^2*c^4 - a*c^5)*d^8*e^2 - (b^3*c^3 - 16*a*b*c^4)*d^7*e^3 - 14*(2*a*b^2*c^3 + a^2*c^4)*d^6*e^4 + 21*(a*b^3*c^2 + 2*a^2*b*c^3)*d^5*e^5 - 7*(a*b^4*c + 6*a^2*b^2*c^2 + 2*a^3*c^3)*d^4*e^6 + (a*b^5 + 17*a^2*b^3*c + 24*a^3*b*c^2)*d^3*e^7 - 3*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^2*e^8 + (3*a^3*b^3 + a^4*b*c)*d*e^9 - (a^4*b^2 - a^5*c)*e^10)*x) - 1/4*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*log(1/2*sqrt(1/2)*((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^7 - 9*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^5*e^2 + 5*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^3 - (a*b^6*c^2 - 27*a^2*b^4*c^3 + 168*a^3*b^2*c^4 - 304*a^4*c^5)*d^3*e^4 - 18*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^5 + (7*a^2*b^6*c - 59*a^3*b^4*c^2 + 136*a^4*b^2*c^3 - 48*a^5*c^4)*d*e^6 - (a^2*b^7 - 9*a^3*b^5*c + 24*a^4*b^3*c^2 - 16*a^5*b*c^3)*e^7 + ((a*b^7*c^5 - 12*a^2*b^5*c^6 + 48*a^3*b^3*c^7 - 64*a^4*b*c^8)*d^3 - 6*(a^2*b^6*c^5 - 12*a^3*b^4*c^6 + 48*a^4*b^2*c^7 - 64*a^5*c^8)*d^2*e + 3*(a^2*b^7*c^4 - 12*a^3*b^5*c^5 + 48*a^4*b^3*c^6 - 64*a^5*b*c^7)*d*e^2 - (a^2*b^8*c^3 - 14*a^3*b^6*c^4 + 72*a^4*b^4*c^5 - 160*a^5*b^2*c^6 + 128*a^6*c^7)*e^3)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)) + (c^6*d^10 - 3*b*c^5*d^9*e + 3*(b^2*c^4 - a*c^5)*d^8*e^2 - (b^3*c^3 - 16*a*b*c^4)*d^7*e^3 - 14*(2*a*b^2*c^3 + a^2*c^4)*d^6*e^4 + 21*(a*b^3*c^2 + 2*a^2*b*c^3)*d^5*e^5 - 7*(a*b^4*c + 6*a^2*b^2*c^2 + 2*a^3*c^3)*d^4*e^6 + (a*b^5 + 17*a^2*b^3*c + 24*a^3*b*c^2)*d^3*e^7 - 3*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^2*e^8 + (3*a^3*b^3 + a^4*b*c)*d*e^9 - (a^4*b^2 - a^5*c)*e^10)*x) + 1/4*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*log(-1/2*sqrt(1/2)*((b^4*c^5 - 8*a*b^2*c^6 + 16*a^2*c^7)*d^7 - 9*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^5*e^2 + 5*(a*b^5*c^3 - 8*a^2*b^3*c^4 + 16*a^3*b*c^5)*d^4*e^3 - (a*b^6*c^2 - 27*a^2*b^4*c^3 + 168*a^3*b^2*c^4 - 304*a^4*c^5)*d^3*e^4 - 18*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^2*e^5 + (7*a^2*b^6*c - 59*a^3*b^4*c^2 + 136*a^4*b^2*c^3 - 48*a^5*c^4)*d*e^6 - (a^2*b^7 - 9*a^3*b^5*c + 24*a^4*b^3*c^2 - 16*a^5*b*c^3)*e^7 + ((a*b^7*c^5 - 12*a^2*b^5*c^6 + 48*a^3*b^3*c^7 - 64*a^4*b*c^8)*d^3 - 6*(a^2*b^6*c^5 - 12*a^3*b^4*c^6 + 48*a^4*b^2*c^7 - 64*a^5*c^8)*d^2*e + 3*(a^2*b^7*c^4 - 12*a^3*b^5*c^5 + 48*a^4*b^3*c^6 - 64*a^5*b*c^7)*d*e^2 - (a^2*b^8*c^3 - 14*a^3*b^6*c^4 + 72*a^4*b^4*c^5 - 160*a^5*b^2*c^6 + 128*a^6*c^7)*e^3)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))*sqrt(sqrt(1/2)*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^6*c^6 - 12*a^3*b^4*c^7 + 48*a^4*b^2*c^8 - 64*a^5*c^9)))/(a*b^4*c^3 - 8*a^2*b^2*c^4 + 16*a^3*c^5)) + (c^6*d^10 - 3*b*c^5*d^9*e + 3*(b^2*c^4 - a*c^5)*d^8*e^2 - (b^3*c^3 - 16*a*b*c^4)*d^7*e^3 - 14*(2*a*b^2*c^3 + a^2*c^4)*d^6*e^4 + 21*(a*b^3*c^2 + 2*a^2*b*c^3)*d^5*e^5 - 7*(a*b^4*c + 6*a^2*b^2*c^2 + 2*a^3*c^3)*d^4*e^6 + (a*b^5 + 17*a^2*b^3*c + 24*a^3*b*c^2)*d^3*e^7 - 3*(a^2*b^4 + 4*a^3*b^2*c + a^4*c^2)*d^2*e^8 + (3*a^3*b^3 + a^4*b*c)*d*e^9 - (a^4*b^2 - a^5*c)*e^10)*x)","B",0
46,1,1535,0,1.322257," ","integrate(x*(e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-{\left(c^{2} d^{4} - b c d^{3} e + a b d e^{3} - a^{2} e^{4}\right)} x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} - {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-{\left(c^{2} d^{4} - b c d^{3} e + a b d e^{3} - a^{2} e^{4}\right)} x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} - {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) + \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-{\left(c^{2} d^{4} - b c d^{3} e + a b d e^{3} - a^{2} e^{4}\right)} x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} + {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) - \frac{1}{4} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-{\left(c^{2} d^{4} - b c d^{3} e + a b d e^{3} - a^{2} e^{4}\right)} x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} + {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right)"," ",0,"1/4*sqrt(1/2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-(c^2*d^4 - b*c*d^3*e + a*b*d*e^3 - a^2*e^4)*x^2 + 1/2*sqrt(1/2)*((b^2*c - 4*a*c^2)*d^3 - (a*b^2 - 4*a^2*c)*d*e^2 - ((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) - 1/4*sqrt(1/2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-(c^2*d^4 - b*c*d^3*e + a*b*d*e^3 - a^2*e^4)*x^2 - 1/2*sqrt(1/2)*((b^2*c - 4*a*c^2)*d^3 - (a*b^2 - 4*a^2*c)*d*e^2 - ((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) + 1/4*sqrt(1/2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-(c^2*d^4 - b*c*d^3*e + a*b*d*e^3 - a^2*e^4)*x^2 + 1/2*sqrt(1/2)*((b^2*c - 4*a*c^2)*d^3 - (a*b^2 - 4*a^2*c)*d*e^2 + ((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) - 1/4*sqrt(1/2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-(c^2*d^4 - b*c*d^3*e + a*b*d*e^3 - a^2*e^4)*x^2 - 1/2*sqrt(1/2)*((b^2*c - 4*a*c^2)*d^3 - (a*b^2 - 4*a^2*c)*d*e^2 + ((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2)))","B",0
47,1,13304,0,10.109046," ","integrate((e*x^4+d)/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}} \arctan\left(\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left({\left(a^{3} b^{8} c^{2} - 14 \, a^{4} b^{6} c^{3} + 72 \, a^{5} b^{4} c^{4} - 160 \, a^{6} b^{2} c^{5} + 128 \, a^{7} c^{6}\right)} d^{3} - 3 \, {\left(a^{4} b^{7} c^{2} - 12 \, a^{5} b^{5} c^{3} + 48 \, a^{6} b^{3} c^{4} - 64 \, a^{7} b c^{5}\right)} d^{2} e + 6 \, {\left(a^{5} b^{6} c^{2} - 12 \, a^{6} b^{4} c^{3} + 48 \, a^{7} b^{2} c^{4} - 64 \, a^{8} c^{5}\right)} d e^{2} - {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} e^{3}\right)} x \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}} + {\left({\left(b^{7} c^{2} - 9 \, a b^{5} c^{3} + 24 \, a^{2} b^{3} c^{4} - 16 \, a^{3} b c^{5}\right)} d^{7} - {\left(7 \, a b^{6} c^{2} - 59 \, a^{2} b^{4} c^{3} + 136 \, a^{3} b^{2} c^{4} - 48 \, a^{4} c^{5}\right)} d^{6} e + 18 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e^{2} + {\left(a^{2} b^{6} c - 27 \, a^{3} b^{4} c^{2} + 168 \, a^{4} b^{2} c^{3} - 304 \, a^{5} c^{4}\right)} d^{4} e^{3} - 5 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} e^{4} + 9 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{5} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{7}\right)} x\right)} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}} - {\left({\left(b^{7} c^{2} - 9 \, a b^{5} c^{3} + 24 \, a^{2} b^{3} c^{4} - 16 \, a^{3} b c^{5}\right)} d^{7} - {\left(7 \, a b^{6} c^{2} - 59 \, a^{2} b^{4} c^{3} + 136 \, a^{3} b^{2} c^{4} - 48 \, a^{4} c^{5}\right)} d^{6} e + 18 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e^{2} + {\left(a^{2} b^{6} c - 27 \, a^{3} b^{4} c^{2} + 168 \, a^{4} b^{2} c^{3} - 304 \, a^{5} c^{4}\right)} d^{4} e^{3} - 5 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} e^{4} + 9 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{5} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{7} + {\left({\left(a^{3} b^{8} c^{2} - 14 \, a^{4} b^{6} c^{3} + 72 \, a^{5} b^{4} c^{4} - 160 \, a^{6} b^{2} c^{5} + 128 \, a^{7} c^{6}\right)} d^{3} - 3 \, {\left(a^{4} b^{7} c^{2} - 12 \, a^{5} b^{5} c^{3} + 48 \, a^{6} b^{3} c^{4} - 64 \, a^{7} b c^{5}\right)} d^{2} e + 6 \, {\left(a^{5} b^{6} c^{2} - 12 \, a^{6} b^{4} c^{3} + 48 \, a^{7} b^{2} c^{4} - 64 \, a^{8} c^{5}\right)} d e^{2} - {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}} \sqrt{\frac{2 \, {\left(14 \, a^{3} b c d^{3} e^{5} - 2 \, a^{4} b d e^{7} + a^{5} e^{8} - {\left(b^{2} c^{3} - a c^{4}\right)} d^{8} + 2 \, {\left(b^{3} c^{2} + a b c^{3}\right)} d^{7} e - {\left(b^{4} c + 9 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{6} e^{2} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{5} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{4} e^{4} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{6}\right)} x^{2} - \sqrt{\frac{1}{2}} {\left({\left(b^{6} c - 7 \, a b^{4} c^{2} + 14 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{6} - 2 \, {\left(3 \, a b^{5} c - 17 \, a^{2} b^{3} c^{2} + 20 \, a^{3} b c^{3}\right)} d^{5} e + 2 \, {\left(8 \, a^{2} b^{4} c - 39 \, a^{3} b^{2} c^{2} + 28 \, a^{4} c^{3}\right)} d^{4} e^{2} - 20 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{3} e^{3} - {\left(a^{3} b^{4} - 18 \, a^{4} b^{2} c + 56 \, a^{5} c^{2}\right)} d^{2} e^{4} + 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{5} - 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{6} + {\left({\left(a^{3} b^{7} c - 12 \, a^{4} b^{5} c^{2} + 48 \, a^{5} b^{3} c^{3} - 64 \, a^{6} b c^{4}\right)} d^{2} - 2 \, {\left(a^{4} b^{6} c - 12 \, a^{5} b^{4} c^{2} + 48 \, a^{6} b^{2} c^{3} - 64 \, a^{7} c^{4}\right)} d e\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}{14 \, a^{3} b c d^{3} e^{5} - 2 \, a^{4} b d e^{7} + a^{5} e^{8} - {\left(b^{2} c^{3} - a c^{4}\right)} d^{8} + 2 \, {\left(b^{3} c^{2} + a b c^{3}\right)} d^{7} e - {\left(b^{4} c + 9 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{6} e^{2} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{5} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{4} e^{4} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{6}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}}{4 \, {\left(3 \, a^{5} b d e^{9} - a^{6} e^{10} + {\left(b^{2} c^{4} - a c^{5}\right)} d^{10} - {\left(3 \, b^{3} c^{3} + a b c^{4}\right)} d^{9} e + 3 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{2} - {\left(b^{5} c + 17 \, a b^{3} c^{2} + 24 \, a^{2} b c^{3}\right)} d^{7} e^{3} + 7 \, {\left(a b^{4} c + 6 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{6} e^{4} - 21 \, {\left(a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e^{5} + 14 \, {\left(2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{6} + {\left(a^{3} b^{3} - 16 \, a^{4} b c\right)} d^{3} e^{7} - 3 \, {\left(a^{4} b^{2} - a^{5} c\right)} d^{2} e^{8}\right)}}\right) - \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left({\left(a^{3} b^{8} c^{2} - 14 \, a^{4} b^{6} c^{3} + 72 \, a^{5} b^{4} c^{4} - 160 \, a^{6} b^{2} c^{5} + 128 \, a^{7} c^{6}\right)} d^{3} - 3 \, {\left(a^{4} b^{7} c^{2} - 12 \, a^{5} b^{5} c^{3} + 48 \, a^{6} b^{3} c^{4} - 64 \, a^{7} b c^{5}\right)} d^{2} e + 6 \, {\left(a^{5} b^{6} c^{2} - 12 \, a^{6} b^{4} c^{3} + 48 \, a^{7} b^{2} c^{4} - 64 \, a^{8} c^{5}\right)} d e^{2} - {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} e^{3}\right)} x \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}} - {\left({\left(b^{7} c^{2} - 9 \, a b^{5} c^{3} + 24 \, a^{2} b^{3} c^{4} - 16 \, a^{3} b c^{5}\right)} d^{7} - {\left(7 \, a b^{6} c^{2} - 59 \, a^{2} b^{4} c^{3} + 136 \, a^{3} b^{2} c^{4} - 48 \, a^{4} c^{5}\right)} d^{6} e + 18 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e^{2} + {\left(a^{2} b^{6} c - 27 \, a^{3} b^{4} c^{2} + 168 \, a^{4} b^{2} c^{3} - 304 \, a^{5} c^{4}\right)} d^{4} e^{3} - 5 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} e^{4} + 9 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{5} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{7}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}} + {\left({\left(b^{7} c^{2} - 9 \, a b^{5} c^{3} + 24 \, a^{2} b^{3} c^{4} - 16 \, a^{3} b c^{5}\right)} d^{7} - {\left(7 \, a b^{6} c^{2} - 59 \, a^{2} b^{4} c^{3} + 136 \, a^{3} b^{2} c^{4} - 48 \, a^{4} c^{5}\right)} d^{6} e + 18 \, {\left(a^{2} b^{5} c^{2} - 8 \, a^{3} b^{3} c^{3} + 16 \, a^{4} b c^{4}\right)} d^{5} e^{2} + {\left(a^{2} b^{6} c - 27 \, a^{3} b^{4} c^{2} + 168 \, a^{4} b^{2} c^{3} - 304 \, a^{5} c^{4}\right)} d^{4} e^{3} - 5 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} e^{4} + 9 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} d^{2} e^{5} - {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{7} - {\left({\left(a^{3} b^{8} c^{2} - 14 \, a^{4} b^{6} c^{3} + 72 \, a^{5} b^{4} c^{4} - 160 \, a^{6} b^{2} c^{5} + 128 \, a^{7} c^{6}\right)} d^{3} - 3 \, {\left(a^{4} b^{7} c^{2} - 12 \, a^{5} b^{5} c^{3} + 48 \, a^{6} b^{3} c^{4} - 64 \, a^{7} b c^{5}\right)} d^{2} e + 6 \, {\left(a^{5} b^{6} c^{2} - 12 \, a^{6} b^{4} c^{3} + 48 \, a^{7} b^{2} c^{4} - 64 \, a^{8} c^{5}\right)} d e^{2} - {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} e^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}} \sqrt{\frac{2 \, {\left(14 \, a^{3} b c d^{3} e^{5} - 2 \, a^{4} b d e^{7} + a^{5} e^{8} - {\left(b^{2} c^{3} - a c^{4}\right)} d^{8} + 2 \, {\left(b^{3} c^{2} + a b c^{3}\right)} d^{7} e - {\left(b^{4} c + 9 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{6} e^{2} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{5} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{4} e^{4} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{6}\right)} x^{2} - \sqrt{\frac{1}{2}} {\left({\left(b^{6} c - 7 \, a b^{4} c^{2} + 14 \, a^{2} b^{2} c^{3} - 8 \, a^{3} c^{4}\right)} d^{6} - 2 \, {\left(3 \, a b^{5} c - 17 \, a^{2} b^{3} c^{2} + 20 \, a^{3} b c^{3}\right)} d^{5} e + 2 \, {\left(8 \, a^{2} b^{4} c - 39 \, a^{3} b^{2} c^{2} + 28 \, a^{4} c^{3}\right)} d^{4} e^{2} - 20 \, {\left(a^{3} b^{3} c - 4 \, a^{4} b c^{2}\right)} d^{3} e^{3} - {\left(a^{3} b^{4} - 18 \, a^{4} b^{2} c + 56 \, a^{5} c^{2}\right)} d^{2} e^{4} + 2 \, {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{5} - 2 \, {\left(a^{5} b^{2} - 4 \, a^{6} c\right)} e^{6} - {\left({\left(a^{3} b^{7} c - 12 \, a^{4} b^{5} c^{2} + 48 \, a^{5} b^{3} c^{3} - 64 \, a^{6} b c^{4}\right)} d^{2} - 2 \, {\left(a^{4} b^{6} c - 12 \, a^{5} b^{4} c^{2} + 48 \, a^{6} b^{2} c^{3} - 64 \, a^{7} c^{4}\right)} d e\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}{14 \, a^{3} b c d^{3} e^{5} - 2 \, a^{4} b d e^{7} + a^{5} e^{8} - {\left(b^{2} c^{3} - a c^{4}\right)} d^{8} + 2 \, {\left(b^{3} c^{2} + a b c^{3}\right)} d^{7} e - {\left(b^{4} c + 9 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{6} e^{2} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{5} e^{3} - 5 \, {\left(3 \, a^{2} b^{2} c + 2 \, a^{3} c^{2}\right)} d^{4} e^{4} + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{6}}}}{4 \, {\left(3 \, a^{5} b d e^{9} - a^{6} e^{10} + {\left(b^{2} c^{4} - a c^{5}\right)} d^{10} - {\left(3 \, b^{3} c^{3} + a b c^{4}\right)} d^{9} e + 3 \, {\left(b^{4} c^{2} + 4 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} e^{2} - {\left(b^{5} c + 17 \, a b^{3} c^{2} + 24 \, a^{2} b c^{3}\right)} d^{7} e^{3} + 7 \, {\left(a b^{4} c + 6 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d^{6} e^{4} - 21 \, {\left(a^{2} b^{3} c + 2 \, a^{3} b c^{2}\right)} d^{5} e^{5} + 14 \, {\left(2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} d^{4} e^{6} + {\left(a^{3} b^{3} - 16 \, a^{4} b c\right)} d^{3} e^{7} - 3 \, {\left(a^{4} b^{2} - a^{5} c\right)} d^{2} e^{8}\right)}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}} \log\left({\left(10 \, a^{2} b c d^{3} e^{3} - 5 \, a^{3} c d^{2} e^{4} - a^{3} b d e^{5} + a^{4} e^{6} - {\left(b^{2} c^{2} - a c^{3}\right)} d^{6} + {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e - 5 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{4} e^{2}\right)} x + \frac{1}{2} \, {\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{5} - 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{4} e + 6 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} e^{2} - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d e^{4} - {\left({\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d - 2 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} e\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}} \log\left({\left(10 \, a^{2} b c d^{3} e^{3} - 5 \, a^{3} c d^{2} e^{4} - a^{3} b d e^{5} + a^{4} e^{6} - {\left(b^{2} c^{2} - a c^{3}\right)} d^{6} + {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e - 5 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{4} e^{2}\right)} x - \frac{1}{2} \, {\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{5} - 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{4} e + 6 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} e^{2} - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d e^{4} - {\left({\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d - 2 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} e\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e + {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}} \log\left({\left(10 \, a^{2} b c d^{3} e^{3} - 5 \, a^{3} c d^{2} e^{4} - a^{3} b d e^{5} + a^{4} e^{6} - {\left(b^{2} c^{2} - a c^{3}\right)} d^{6} + {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e - 5 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{4} e^{2}\right)} x + \frac{1}{2} \, {\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{5} - 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{4} e + 6 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} e^{2} - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d e^{4} + {\left({\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d - 2 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} e\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}} \log\left({\left(10 \, a^{2} b c d^{3} e^{3} - 5 \, a^{3} c d^{2} e^{4} - a^{3} b d e^{5} + a^{4} e^{6} - {\left(b^{2} c^{2} - a c^{3}\right)} d^{6} + {\left(b^{3} c + 3 \, a b c^{2}\right)} d^{5} e - 5 \, {\left(a b^{2} c + a^{2} c^{2}\right)} d^{4} e^{2}\right)} x - \frac{1}{2} \, {\left({\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{5} - 4 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{4} e + 6 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} e^{2} - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d e^{4} + {\left({\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d - 2 \, {\left(a^{4} b^{4} c - 8 \, a^{5} b^{2} c^{2} + 16 \, a^{6} c^{3}\right)} e\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{6 \, a^{2} b c d^{2} e^{2} - 8 \, a^{3} c d e^{3} + a^{3} b e^{4} + {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{4} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d^{3} e - {\left(a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}\right)} \sqrt{-\frac{48 \, a^{3} b c^{2} d^{5} e^{3} - 8 \, a^{4} b c d^{3} e^{5} + 12 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 2 \, a b^{2} c^{3} + a^{2} c^{4}\right)} d^{8} + 8 \, {\left(a b^{3} c^{2} - a^{2} b c^{3}\right)} d^{7} e - 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 19 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{4} c - 8 \, a^{4} b^{2} c^{2} + 16 \, a^{5} c^{3}}}}\right)"," ",0,"sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))*arctan(1/4*(2*sqrt(1/2)*(((a^3*b^8*c^2 - 14*a^4*b^6*c^3 + 72*a^5*b^4*c^4 - 160*a^6*b^2*c^5 + 128*a^7*c^6)*d^3 - 3*(a^4*b^7*c^2 - 12*a^5*b^5*c^3 + 48*a^6*b^3*c^4 - 64*a^7*b*c^5)*d^2*e + 6*(a^5*b^6*c^2 - 12*a^6*b^4*c^3 + 48*a^7*b^2*c^4 - 64*a^8*c^5)*d*e^2 - (a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*e^3)*x*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)) + ((b^7*c^2 - 9*a*b^5*c^3 + 24*a^2*b^3*c^4 - 16*a^3*b*c^5)*d^7 - (7*a*b^6*c^2 - 59*a^2*b^4*c^3 + 136*a^3*b^2*c^4 - 48*a^4*c^5)*d^6*e + 18*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e^2 + (a^2*b^6*c - 27*a^3*b^4*c^2 + 168*a^4*b^2*c^3 - 304*a^5*c^4)*d^4*e^3 - 5*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3*e^4 + 9*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^5 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^7)*x)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)) - ((b^7*c^2 - 9*a*b^5*c^3 + 24*a^2*b^3*c^4 - 16*a^3*b*c^5)*d^7 - (7*a*b^6*c^2 - 59*a^2*b^4*c^3 + 136*a^3*b^2*c^4 - 48*a^4*c^5)*d^6*e + 18*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e^2 + (a^2*b^6*c - 27*a^3*b^4*c^2 + 168*a^4*b^2*c^3 - 304*a^5*c^4)*d^4*e^3 - 5*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3*e^4 + 9*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^5 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^7 + ((a^3*b^8*c^2 - 14*a^4*b^6*c^3 + 72*a^5*b^4*c^4 - 160*a^6*b^2*c^5 + 128*a^7*c^6)*d^3 - 3*(a^4*b^7*c^2 - 12*a^5*b^5*c^3 + 48*a^6*b^3*c^4 - 64*a^7*b*c^5)*d^2*e + 6*(a^5*b^6*c^2 - 12*a^6*b^4*c^3 + 48*a^7*b^2*c^4 - 64*a^8*c^5)*d*e^2 - (a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*e^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3))*sqrt((2*(14*a^3*b*c*d^3*e^5 - 2*a^4*b*d*e^7 + a^5*e^8 - (b^2*c^3 - a*c^4)*d^8 + 2*(b^3*c^2 + a*b*c^3)*d^7*e - (b^4*c + 9*a*b^2*c^2 + 4*a^2*c^3)*d^6*e^2 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^5*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^4*e^4 + (a^3*b^2 - 4*a^4*c)*d^2*e^6)*x^2 - sqrt(1/2)*((b^6*c - 7*a*b^4*c^2 + 14*a^2*b^2*c^3 - 8*a^3*c^4)*d^6 - 2*(3*a*b^5*c - 17*a^2*b^3*c^2 + 20*a^3*b*c^3)*d^5*e + 2*(8*a^2*b^4*c - 39*a^3*b^2*c^2 + 28*a^4*c^3)*d^4*e^2 - 20*(a^3*b^3*c - 4*a^4*b*c^2)*d^3*e^3 - (a^3*b^4 - 18*a^4*b^2*c + 56*a^5*c^2)*d^2*e^4 + 2*(a^4*b^3 - 4*a^5*b*c)*d*e^5 - 2*(a^5*b^2 - 4*a^6*c)*e^6 + ((a^3*b^7*c - 12*a^4*b^5*c^2 + 48*a^5*b^3*c^3 - 64*a^6*b*c^4)*d^2 - 2*(a^4*b^6*c - 12*a^5*b^4*c^2 + 48*a^6*b^2*c^3 - 64*a^7*c^4)*d*e)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(14*a^3*b*c*d^3*e^5 - 2*a^4*b*d*e^7 + a^5*e^8 - (b^2*c^3 - a*c^4)*d^8 + 2*(b^3*c^2 + a*b*c^3)*d^7*e - (b^4*c + 9*a*b^2*c^2 + 4*a^2*c^3)*d^6*e^2 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^5*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^4*e^4 + (a^3*b^2 - 4*a^4*c)*d^2*e^6)))*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(3*a^5*b*d*e^9 - a^6*e^10 + (b^2*c^4 - a*c^5)*d^10 - (3*b^3*c^3 + a*b*c^4)*d^9*e + 3*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^2 - (b^5*c + 17*a*b^3*c^2 + 24*a^2*b*c^3)*d^7*e^3 + 7*(a*b^4*c + 6*a^2*b^2*c^2 + 2*a^3*c^3)*d^6*e^4 - 21*(a^2*b^3*c + 2*a^3*b*c^2)*d^5*e^5 + 14*(2*a^3*b^2*c + a^4*c^2)*d^4*e^6 + (a^3*b^3 - 16*a^4*b*c)*d^3*e^7 - 3*(a^4*b^2 - a^5*c)*d^2*e^8)) - sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))*arctan(1/4*(2*sqrt(1/2)*(((a^3*b^8*c^2 - 14*a^4*b^6*c^3 + 72*a^5*b^4*c^4 - 160*a^6*b^2*c^5 + 128*a^7*c^6)*d^3 - 3*(a^4*b^7*c^2 - 12*a^5*b^5*c^3 + 48*a^6*b^3*c^4 - 64*a^7*b*c^5)*d^2*e + 6*(a^5*b^6*c^2 - 12*a^6*b^4*c^3 + 48*a^7*b^2*c^4 - 64*a^8*c^5)*d*e^2 - (a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*e^3)*x*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)) - ((b^7*c^2 - 9*a*b^5*c^3 + 24*a^2*b^3*c^4 - 16*a^3*b*c^5)*d^7 - (7*a*b^6*c^2 - 59*a^2*b^4*c^3 + 136*a^3*b^2*c^4 - 48*a^4*c^5)*d^6*e + 18*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e^2 + (a^2*b^6*c - 27*a^3*b^4*c^2 + 168*a^4*b^2*c^3 - 304*a^5*c^4)*d^4*e^3 - 5*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3*e^4 + 9*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^5 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^7)*x)*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)) + ((b^7*c^2 - 9*a*b^5*c^3 + 24*a^2*b^3*c^4 - 16*a^3*b*c^5)*d^7 - (7*a*b^6*c^2 - 59*a^2*b^4*c^3 + 136*a^3*b^2*c^4 - 48*a^4*c^5)*d^6*e + 18*(a^2*b^5*c^2 - 8*a^3*b^3*c^3 + 16*a^4*b*c^4)*d^5*e^2 + (a^2*b^6*c - 27*a^3*b^4*c^2 + 168*a^4*b^2*c^3 - 304*a^5*c^4)*d^4*e^3 - 5*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3*e^4 + 9*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*d^2*e^5 - (a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^7 - ((a^3*b^8*c^2 - 14*a^4*b^6*c^3 + 72*a^5*b^4*c^4 - 160*a^6*b^2*c^5 + 128*a^7*c^6)*d^3 - 3*(a^4*b^7*c^2 - 12*a^5*b^5*c^3 + 48*a^6*b^3*c^4 - 64*a^7*b*c^5)*d^2*e + 6*(a^5*b^6*c^2 - 12*a^6*b^4*c^3 + 48*a^7*b^2*c^4 - 64*a^8*c^5)*d*e^2 - (a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*e^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3))*sqrt((2*(14*a^3*b*c*d^3*e^5 - 2*a^4*b*d*e^7 + a^5*e^8 - (b^2*c^3 - a*c^4)*d^8 + 2*(b^3*c^2 + a*b*c^3)*d^7*e - (b^4*c + 9*a*b^2*c^2 + 4*a^2*c^3)*d^6*e^2 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^5*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^4*e^4 + (a^3*b^2 - 4*a^4*c)*d^2*e^6)*x^2 - sqrt(1/2)*((b^6*c - 7*a*b^4*c^2 + 14*a^2*b^2*c^3 - 8*a^3*c^4)*d^6 - 2*(3*a*b^5*c - 17*a^2*b^3*c^2 + 20*a^3*b*c^3)*d^5*e + 2*(8*a^2*b^4*c - 39*a^3*b^2*c^2 + 28*a^4*c^3)*d^4*e^2 - 20*(a^3*b^3*c - 4*a^4*b*c^2)*d^3*e^3 - (a^3*b^4 - 18*a^4*b^2*c + 56*a^5*c^2)*d^2*e^4 + 2*(a^4*b^3 - 4*a^5*b*c)*d*e^5 - 2*(a^5*b^2 - 4*a^6*c)*e^6 - ((a^3*b^7*c - 12*a^4*b^5*c^2 + 48*a^5*b^3*c^3 - 64*a^6*b*c^4)*d^2 - 2*(a^4*b^6*c - 12*a^5*b^4*c^2 + 48*a^6*b^2*c^3 - 64*a^7*c^4)*d*e)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))/(14*a^3*b*c*d^3*e^5 - 2*a^4*b*d*e^7 + a^5*e^8 - (b^2*c^3 - a*c^4)*d^8 + 2*(b^3*c^2 + a*b*c^3)*d^7*e - (b^4*c + 9*a*b^2*c^2 + 4*a^2*c^3)*d^6*e^2 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^5*e^3 - 5*(3*a^2*b^2*c + 2*a^3*c^2)*d^4*e^4 + (a^3*b^2 - 4*a^4*c)*d^2*e^6)))/(3*a^5*b*d*e^9 - a^6*e^10 + (b^2*c^4 - a*c^5)*d^10 - (3*b^3*c^3 + a*b*c^4)*d^9*e + 3*(b^4*c^2 + 4*a*b^2*c^3 + a^2*c^4)*d^8*e^2 - (b^5*c + 17*a*b^3*c^2 + 24*a^2*b*c^3)*d^7*e^3 + 7*(a*b^4*c + 6*a^2*b^2*c^2 + 2*a^3*c^3)*d^6*e^4 - 21*(a^2*b^3*c + 2*a^3*b*c^2)*d^5*e^5 + 14*(2*a^3*b^2*c + a^4*c^2)*d^4*e^6 + (a^3*b^3 - 16*a^4*b*c)*d^3*e^7 - 3*(a^4*b^2 - a^5*c)*d^2*e^8)) + 1/4*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))*log((10*a^2*b*c*d^3*e^3 - 5*a^3*c*d^2*e^4 - a^3*b*d*e^5 + a^4*e^6 - (b^2*c^2 - a*c^3)*d^6 + (b^3*c + 3*a*b*c^2)*d^5*e - 5*(a*b^2*c + a^2*c^2)*d^4*e^2)*x + 1/2*((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^5 - 4*(a*b^3*c - 4*a^2*b*c^2)*d^4*e + 6*(a^2*b^2*c - 4*a^3*c^2)*d^3*e^2 - (a^3*b^2 - 4*a^4*c)*d*e^4 - ((a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d - 2*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*e)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))*log((10*a^2*b*c*d^3*e^3 - 5*a^3*c*d^2*e^4 - a^3*b*d*e^5 + a^4*e^6 - (b^2*c^2 - a*c^3)*d^6 + (b^3*c + 3*a*b*c^2)*d^5*e - 5*(a*b^2*c + a^2*c^2)*d^4*e^2)*x - 1/2*((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^5 - 4*(a*b^3*c - 4*a^2*b*c^2)*d^4*e + 6*(a^2*b^2*c - 4*a^3*c^2)*d^3*e^2 - (a^3*b^2 - 4*a^4*c)*d*e^4 - ((a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d - 2*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*e)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e + (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))) + 1/4*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))*log((10*a^2*b*c*d^3*e^3 - 5*a^3*c*d^2*e^4 - a^3*b*d*e^5 + a^4*e^6 - (b^2*c^2 - a*c^3)*d^6 + (b^3*c + 3*a*b*c^2)*d^5*e - 5*(a*b^2*c + a^2*c^2)*d^4*e^2)*x + 1/2*((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^5 - 4*(a*b^3*c - 4*a^2*b*c^2)*d^4*e + 6*(a^2*b^2*c - 4*a^3*c^2)*d^3*e^2 - (a^3*b^2 - 4*a^4*c)*d*e^4 + ((a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d - 2*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*e)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)))*log((10*a^2*b*c*d^3*e^3 - 5*a^3*c*d^2*e^4 - a^3*b*d*e^5 + a^4*e^6 - (b^2*c^2 - a*c^3)*d^6 + (b^3*c + 3*a*b*c^2)*d^5*e - 5*(a*b^2*c + a^2*c^2)*d^4*e^2)*x - 1/2*((b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^5 - 4*(a*b^3*c - 4*a^2*b*c^2)*d^4*e + 6*(a^2*b^2*c - 4*a^3*c^2)*d^3*e^2 - (a^3*b^2 - 4*a^4*c)*d*e^4 + ((a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d - 2*(a^4*b^4*c - 8*a^5*b^2*c^2 + 16*a^6*c^3)*e)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(sqrt(1/2)*sqrt(-(6*a^2*b*c*d^2*e^2 - 8*a^3*c*d*e^3 + a^3*b*e^4 + (b^3*c - 3*a*b*c^2)*d^4 - 4*(a*b^2*c - 2*a^2*c^2)*d^3*e - (a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3)*sqrt(-(48*a^3*b*c^2*d^5*e^3 - 8*a^4*b*c*d^3*e^5 + 12*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 2*a*b^2*c^3 + a^2*c^4)*d^8 + 8*(a*b^3*c^2 - a^2*b*c^3)*d^7*e - 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 19*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^4*c - 8*a^4*b^2*c^2 + 16*a^5*c^3))))","B",0
48,1,240,0,2.511301," ","integrate((e*x^4+d)/x/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(c x^{8} + b x^{4} + a\right) - 8 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(x\right) + \sqrt{b^{2} - 4 \, a c} {\left(b d - 2 \, a e\right)} \log\left(\frac{2 \, c^{2} x^{8} + 2 \, b c x^{4} + b^{2} - 2 \, a c - {\left(2 \, c x^{4} + b\right)} \sqrt{b^{2} - 4 \, a c}}{c x^{8} + b x^{4} + a}\right)}{8 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}, -\frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(c x^{8} + b x^{4} + a\right) - 8 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(x\right) - 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(b d - 2 \, a e\right)} \arctan\left(-\frac{{\left(2 \, c x^{4} + b\right)} \sqrt{-b^{2} + 4 \, a c}}{b^{2} - 4 \, a c}\right)}{8 \, {\left(a b^{2} - 4 \, a^{2} c\right)}}\right]"," ",0,"[-1/8*((b^2 - 4*a*c)*d*log(c*x^8 + b*x^4 + a) - 8*(b^2 - 4*a*c)*d*log(x) + sqrt(b^2 - 4*a*c)*(b*d - 2*a*e)*log((2*c^2*x^8 + 2*b*c*x^4 + b^2 - 2*a*c - (2*c*x^4 + b)*sqrt(b^2 - 4*a*c))/(c*x^8 + b*x^4 + a)))/(a*b^2 - 4*a^2*c), -1/8*((b^2 - 4*a*c)*d*log(c*x^8 + b*x^4 + a) - 8*(b^2 - 4*a*c)*d*log(x) - 2*sqrt(-b^2 + 4*a*c)*(b*d - 2*a*e)*arctan(-(2*c*x^4 + b)*sqrt(-b^2 + 4*a*c)/(b^2 - 4*a*c)))/(a*b^2 - 4*a^2*c)]","A",0
49,-1,0,0,0.000000," ","integrate((e*x^4+d)/x^2/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
50,1,2772,0,2.211467," ","integrate((e*x^4+d)/x^3/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} a x^{2} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left({\left(3 \, a b^{2} c d^{2} e^{2} - 3 \, a^{2} b c d e^{3} + a^{3} c e^{4} + {\left(b^{2} c^{2} - a c^{3}\right)} d^{4} - {\left(b^{3} c + a b c^{2}\right)} d^{3} e\right)} x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{3} - {\left(3 \, a b^{4} - 13 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{3} - {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} d - {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - \sqrt{\frac{1}{2}} a x^{2} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left({\left(3 \, a b^{2} c d^{2} e^{2} - 3 \, a^{2} b c d e^{3} + a^{3} c e^{4} + {\left(b^{2} c^{2} - a c^{3}\right)} d^{4} - {\left(b^{3} c + a b c^{2}\right)} d^{3} e\right)} x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{3} - {\left(3 \, a b^{4} - 13 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{3} - {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} d - {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e + {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) + \sqrt{\frac{1}{2}} a x^{2} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left({\left(3 \, a b^{2} c d^{2} e^{2} - 3 \, a^{2} b c d e^{3} + a^{3} c e^{4} + {\left(b^{2} c^{2} - a c^{3}\right)} d^{4} - {\left(b^{3} c + a b c^{2}\right)} d^{3} e\right)} x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{3} - {\left(3 \, a b^{4} - 13 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{3} + {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} d - {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - \sqrt{\frac{1}{2}} a x^{2} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}} \log\left({\left(3 \, a b^{2} c d^{2} e^{2} - 3 \, a^{2} b c d e^{3} + a^{3} c e^{4} + {\left(b^{2} c^{2} - a c^{3}\right)} d^{4} - {\left(b^{3} c + a b c^{2}\right)} d^{3} e\right)} x^{2} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{5} - 5 \, a b^{3} c + 4 \, a^{2} b c^{2}\right)} d^{3} - {\left(3 \, a b^{4} - 13 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{2} - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} e^{3} + {\left({\left(a^{3} b^{4} - 6 \, a^{4} b^{2} c + 8 \, a^{5} c^{2}\right)} d - {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} e\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}\right)} \sqrt{-\frac{a^{2} b e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(a b^{2} - 2 \, a^{2} c\right)} d e - {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} \sqrt{-\frac{4 \, a^{3} b d e^{3} - a^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - a^{2} b c\right)} d^{3} e - 2 \, {\left(3 \, a^{2} b^{2} - a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{2} - 4 \, a^{7} c}}}{a^{3} b^{2} - 4 \, a^{4} c}}\right) - 2 \, d}{4 \, a x^{2}}"," ",0,"1/4*(sqrt(1/2)*a*x^2*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + (a^3*b^2 - 4*a^4*c)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((3*a*b^2*c*d^2*e^2 - 3*a^2*b*c*d*e^3 + a^3*c*e^4 + (b^2*c^2 - a*c^3)*d^4 - (b^3*c + a*b*c^2)*d^3*e)*x^2 + 1/2*sqrt(1/2)*((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^3 - (3*a*b^4 - 13*a^2*b^2*c + 4*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 4*a^3*b*c)*d*e^2 - (a^3*b^2 - 4*a^4*c)*e^3 - ((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*d - (a^4*b^3 - 4*a^5*b*c)*e)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + (a^3*b^2 - 4*a^4*c)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - sqrt(1/2)*a*x^2*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + (a^3*b^2 - 4*a^4*c)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((3*a*b^2*c*d^2*e^2 - 3*a^2*b*c*d*e^3 + a^3*c*e^4 + (b^2*c^2 - a*c^3)*d^4 - (b^3*c + a*b*c^2)*d^3*e)*x^2 - 1/2*sqrt(1/2)*((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^3 - (3*a*b^4 - 13*a^2*b^2*c + 4*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 4*a^3*b*c)*d*e^2 - (a^3*b^2 - 4*a^4*c)*e^3 - ((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*d - (a^4*b^3 - 4*a^5*b*c)*e)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e + (a^3*b^2 - 4*a^4*c)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) + sqrt(1/2)*a*x^2*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - (a^3*b^2 - 4*a^4*c)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((3*a*b^2*c*d^2*e^2 - 3*a^2*b*c*d*e^3 + a^3*c*e^4 + (b^2*c^2 - a*c^3)*d^4 - (b^3*c + a*b*c^2)*d^3*e)*x^2 + 1/2*sqrt(1/2)*((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^3 - (3*a*b^4 - 13*a^2*b^2*c + 4*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 4*a^3*b*c)*d*e^2 - (a^3*b^2 - 4*a^4*c)*e^3 + ((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*d - (a^4*b^3 - 4*a^5*b*c)*e)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - (a^3*b^2 - 4*a^4*c)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - sqrt(1/2)*a*x^2*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - (a^3*b^2 - 4*a^4*c)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))*log((3*a*b^2*c*d^2*e^2 - 3*a^2*b*c*d*e^3 + a^3*c*e^4 + (b^2*c^2 - a*c^3)*d^4 - (b^3*c + a*b*c^2)*d^3*e)*x^2 - 1/2*sqrt(1/2)*((b^5 - 5*a*b^3*c + 4*a^2*b*c^2)*d^3 - (3*a*b^4 - 13*a^2*b^2*c + 4*a^3*c^2)*d^2*e + 3*(a^2*b^3 - 4*a^3*b*c)*d*e^2 - (a^3*b^2 - 4*a^4*c)*e^3 + ((a^3*b^4 - 6*a^4*b^2*c + 8*a^5*c^2)*d - (a^4*b^3 - 4*a^5*b*c)*e)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))*sqrt(-(a^2*b*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(a*b^2 - 2*a^2*c)*d*e - (a^3*b^2 - 4*a^4*c)*sqrt(-(4*a^3*b*d*e^3 - a^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(a*b^3 - a^2*b*c)*d^3*e - 2*(3*a^2*b^2 - a^3*c)*d^2*e^2)/(a^6*b^2 - 4*a^7*c)))/(a^3*b^2 - 4*a^4*c))) - 2*d)/(a*x^2)","B",0
51,-1,0,0,0.000000," ","integrate((e*x^4+d)/x^4/(c*x^8+b*x^4+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,1,218,0,1.269790," ","integrate(x^4*(-x^4+1)/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \sqrt{2} \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} + x^{2} - \sqrt{x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x - 2\right)}}{3 \, x^{2} - 2}\right) - \frac{1}{6} \, \sqrt{3} \sqrt{2} \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} - x^{2} - \sqrt{x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x + 2\right)}}{3 \, x^{2} - 2}\right) + \frac{1}{24} \, \sqrt{3} \sqrt{2} \log\left(x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right) - \frac{1}{24} \, \sqrt{3} \sqrt{2} \log\left(x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right) - x"," ",0,"-1/6*sqrt(3)*sqrt(2)*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) + x^2 - sqrt(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x - 2))/(3*x^2 - 2)) - 1/6*sqrt(3)*sqrt(2)*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) - x^2 - sqrt(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x + 2))/(3*x^2 - 2)) + 1/24*sqrt(3)*sqrt(2)*log(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1) - 1/24*sqrt(3)*sqrt(2)*log(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1) - x","A",0
53,1,32,0,0.731472," ","integrate(x^3*(-x^4+1)/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} - 1\right)}\right) - \frac{1}{8} \, \log\left(x^{8} - x^{4} + 1\right)"," ",0,"1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 - 1)) - 1/8*log(x^8 - x^4 + 1)","A",0
54,1,715,0,1.107653," ","integrate(x^2*(-x^4+1)/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) - \frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) + \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) - \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) - \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} - \sqrt{3} + 2\right) - \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + \sqrt{3} - 2\right) - \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} - 2\right) - \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} + 2\right)"," ",0,"1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) - 1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) + 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) - 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) - 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) - sqrt(3) + 2) - 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + sqrt(3) - 2) - 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) - sqrt(3) - 2) - 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + sqrt(3) + 2)","B",0
55,1,41,0,0.867978," ","integrate(x*(-x^4+1)/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(\frac{x^{8} + 5 \, x^{4} + 2 \, \sqrt{3} {\left(x^{6} + x^{2}\right)} + 1}{x^{8} - x^{4} + 1}\right)"," ",0,"1/12*sqrt(3)*log((x^8 + 5*x^4 + 2*sqrt(3)*(x^6 + x^2) + 1)/(x^8 - x^4 + 1))","A",0
56,1,715,0,0.688968," ","integrate((-x^4+1)/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) - \frac{1}{48} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} \log\left(12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12\right) + \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) - \frac{1}{96} \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12\right) + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} - \sqrt{3} + 2\right) + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{3} + 2} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{12 \, x^{2} - 2 \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + 12} {\left(\sqrt{3} \sqrt{2} - 2 \, \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} + \frac{1}{3} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x - 3 \, \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2} + \sqrt{3} - 2\right) + \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} + \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} - 2\right) + \frac{1}{24} \, \sqrt{6} \sqrt{2} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{12} \, \sqrt{6} \sqrt{12 \, x^{2} - \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + 12} {\left(\sqrt{3} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{3} + 8} - \frac{1}{6} \, \sqrt{6} {\left(2 \, \sqrt{3} \sqrt{2} x + 3 \, \sqrt{2} x\right)} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} + 2\right)"," ",0,"1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) - 1/48*sqrt(6)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2)*log(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12) + 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) - 1/96*sqrt(6)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8)*log(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12) + 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 + 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) - sqrt(3) + 2) + 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(3) + 2)*arctan(1/6*sqrt(6)*sqrt(12*x^2 - 2*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + 12)*(sqrt(3)*sqrt(2) - 2*sqrt(2))*sqrt(sqrt(3) + 2) + 1/3*sqrt(6)*(2*sqrt(3)*sqrt(2)*x - 3*sqrt(2)*x)*sqrt(sqrt(3) + 2) + sqrt(3) - 2) + 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 + sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) - sqrt(3) - 2) + 1/24*sqrt(6)*sqrt(2)*sqrt(-4*sqrt(3) + 8)*arctan(1/12*sqrt(6)*sqrt(12*x^2 - sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + 12)*(sqrt(3)*sqrt(2) + 2*sqrt(2))*sqrt(-4*sqrt(3) + 8) - 1/6*sqrt(6)*(2*sqrt(3)*sqrt(2)*x + 3*sqrt(2)*x)*sqrt(-4*sqrt(3) + 8) + sqrt(3) + 2)","B",0
57,1,34,0,0.889519," ","integrate((-x^4+1)/x/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x^{4} - 1\right)}\right) - \frac{1}{8} \, \log\left(x^{8} - x^{4} + 1\right) + \log\left(x\right)"," ",0,"-1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x^4 - 1)) - 1/8*log(x^8 - x^4 + 1) + log(x)","A",0
58,1,224,0,0.990097," ","integrate((-x^4+1)/x^2/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{4 \, \sqrt{3} \sqrt{2} x \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} + x^{2} - \sqrt{x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x - 2\right)}}{3 \, x^{2} - 2}\right) + 4 \, \sqrt{3} \sqrt{2} x \arctan\left(-\frac{\sqrt{3} \sqrt{2} {\left(x^{3} - x\right)} - x^{2} - \sqrt{x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1} {\left(\sqrt{3} \sqrt{2} x + 2\right)}}{3 \, x^{2} - 2}\right) + \sqrt{3} \sqrt{2} x \log\left(x^{4} + \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right) - \sqrt{3} \sqrt{2} x \log\left(x^{4} - \sqrt{3} \sqrt{2} {\left(x^{3} + x\right)} + 3 \, x^{2} + 1\right) - 24}{24 \, x}"," ",0,"1/24*(4*sqrt(3)*sqrt(2)*x*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) + x^2 - sqrt(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x - 2))/(3*x^2 - 2)) + 4*sqrt(3)*sqrt(2)*x*arctan(-(sqrt(3)*sqrt(2)*(x^3 - x) - x^2 - sqrt(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1)*(sqrt(3)*sqrt(2)*x + 2))/(3*x^2 - 2)) + sqrt(3)*sqrt(2)*x*log(x^4 + sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1) - sqrt(3)*sqrt(2)*x*log(x^4 - sqrt(3)*sqrt(2)*(x^3 + x) + 3*x^2 + 1) - 24)/x","A",0
59,1,188,0,1.032011," ","integrate((-x^4+1)/x^3/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{4 \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2 \, x^{4} + \sqrt{6} \sqrt{2} x^{2} + 2} - \sqrt{3}\right) + 4 \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x^{2} + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2 \, x^{4} - \sqrt{6} \sqrt{2} x^{2} + 2} + \sqrt{3}\right) + \sqrt{6} \sqrt{2} x^{2} \log\left(2 \, x^{4} + \sqrt{6} \sqrt{2} x^{2} + 2\right) - \sqrt{6} \sqrt{2} x^{2} \log\left(2 \, x^{4} - \sqrt{6} \sqrt{2} x^{2} + 2\right) - 24}{48 \, x^{2}}"," ",0,"1/48*(4*sqrt(6)*sqrt(3)*sqrt(2)*x^2*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x^2 + 1/3*sqrt(6)*sqrt(3)*sqrt(2*x^4 + sqrt(6)*sqrt(2)*x^2 + 2) - sqrt(3)) + 4*sqrt(6)*sqrt(3)*sqrt(2)*x^2*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x^2 + 1/3*sqrt(6)*sqrt(3)*sqrt(2*x^4 - sqrt(6)*sqrt(2)*x^2 + 2) + sqrt(3)) + sqrt(6)*sqrt(2)*x^2*log(2*x^4 + sqrt(6)*sqrt(2)*x^2 + 2) - sqrt(6)*sqrt(2)*x^2*log(2*x^4 - sqrt(6)*sqrt(2)*x^2 + 2) - 24)/x^2","B",0
60,1,608,0,1.187656," ","integrate((-x^4+1)/x^4/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{8 \, \sqrt{6} \sqrt{2} x^{3} \sqrt{\sqrt{3} + 2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + \frac{1}{6} \, \sqrt{6} \sqrt{2} \sqrt{2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12} \sqrt{\sqrt{3} + 2} - \sqrt{3} - 2\right) + 8 \, \sqrt{6} \sqrt{2} x^{3} \sqrt{\sqrt{3} + 2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + \frac{1}{6} \, \sqrt{6} \sqrt{2} \sqrt{-2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12} \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2\right) - 4 \, \sqrt{6} \sqrt{2} x^{3} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12} \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} - 2\right) - 4 \, \sqrt{6} \sqrt{2} x^{3} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-\frac{1}{6} \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + \frac{1}{12} \, \sqrt{6} \sqrt{2} \sqrt{-\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12} \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} + 2\right) - 2 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{3} - 2 \, \sqrt{2} x^{3}\right)} \sqrt{\sqrt{3} + 2} \log\left(2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12\right) + 2 \, \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{3} - 2 \, \sqrt{2} x^{3}\right)} \sqrt{\sqrt{3} + 2} \log\left(-2 \, \sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{\sqrt{3} + 2} + 12 \, x^{2} + 12\right) - \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{3} + 2 \, \sqrt{2} x^{3}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12\right) + \sqrt{6} {\left(\sqrt{3} \sqrt{2} x^{3} + 2 \, \sqrt{2} x^{3}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(-\sqrt{6} \sqrt{3} \sqrt{2} x \sqrt{-4 \, \sqrt{3} + 8} + 12 \, x^{2} + 12\right) - 32}{96 \, x^{3}}"," ",0,"1/96*(8*sqrt(6)*sqrt(2)*x^3*sqrt(sqrt(3) + 2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 1/6*sqrt(6)*sqrt(2)*sqrt(2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12)*sqrt(sqrt(3) + 2) - sqrt(3) - 2) + 8*sqrt(6)*sqrt(2)*x^3*sqrt(sqrt(3) + 2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 1/6*sqrt(6)*sqrt(2)*sqrt(-2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12)*sqrt(sqrt(3) + 2) + sqrt(3) + 2) - 4*sqrt(6)*sqrt(2)*x^3*sqrt(-4*sqrt(3) + 8)*arctan(-1/6*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 1/12*sqrt(6)*sqrt(2)*sqrt(sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12)*sqrt(-4*sqrt(3) + 8) + sqrt(3) - 2) - 4*sqrt(6)*sqrt(2)*x^3*sqrt(-4*sqrt(3) + 8)*arctan(-1/6*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 1/12*sqrt(6)*sqrt(2)*sqrt(-sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12)*sqrt(-4*sqrt(3) + 8) - sqrt(3) + 2) - 2*sqrt(6)*(sqrt(3)*sqrt(2)*x^3 - 2*sqrt(2)*x^3)*sqrt(sqrt(3) + 2)*log(2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12) + 2*sqrt(6)*(sqrt(3)*sqrt(2)*x^3 - 2*sqrt(2)*x^3)*sqrt(sqrt(3) + 2)*log(-2*sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(sqrt(3) + 2) + 12*x^2 + 12) - sqrt(6)*(sqrt(3)*sqrt(2)*x^3 + 2*sqrt(2)*x^3)*sqrt(-4*sqrt(3) + 8)*log(sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12) + sqrt(6)*(sqrt(3)*sqrt(2)*x^3 + 2*sqrt(2)*x^3)*sqrt(-4*sqrt(3) + 8)*log(-sqrt(6)*sqrt(3)*sqrt(2)*x*sqrt(-4*sqrt(3) + 8) + 12*x^2 + 12) - 32)/x^3","B",0
61,1,1027,0,94.895071," ","integrate(x^3/(a+c/x^2+b/x)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{5} \log\left(e x + d\right) - 2 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2} e^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} x^{3} + 3 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3} e^{2} - {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{4} + {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} e^{5}\right)} x^{2} + 3 \, {\left({\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d e^{4} - {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} e^{5}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) - 6 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{4} e - {\left(a b^{5} - 6 \, a^{2} b^{3} c + 8 \, a^{3} b c^{2}\right)} d e^{4} + {\left(a b^{4} c - 5 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} e^{5}\right)} x - 3 \, {\left({\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{4} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} e^{5}\right)} \log\left(a x^{2} + b x + c\right)}{6 \, {\left({\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d^{2} e^{4} - {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{5} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} e^{6}\right)}}, -\frac{6 \, {\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{5} \log\left(e x + d\right) - 2 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2} e^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)} x^{3} + 3 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{3} e^{2} - {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{4} + {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} e^{5}\right)} x^{2} - 6 \, {\left({\left(b^{5} - 5 \, a b^{3} c + 5 \, a^{2} b c^{2}\right)} d e^{4} - {\left(b^{4} c - 4 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} e^{5}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) - 6 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{4} e - {\left(a b^{5} - 6 \, a^{2} b^{3} c + 8 \, a^{3} b c^{2}\right)} d e^{4} + {\left(a b^{4} c - 5 \, a^{2} b^{2} c^{2} + 4 \, a^{3} c^{3}\right)} e^{5}\right)} x - 3 \, {\left({\left(b^{6} - 7 \, a b^{4} c + 13 \, a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{4} - {\left(b^{5} c - 6 \, a b^{3} c^{2} + 8 \, a^{2} b c^{3}\right)} e^{5}\right)} \log\left(a x^{2} + b x + c\right)}{6 \, {\left({\left(a^{5} b^{2} - 4 \, a^{6} c\right)} d^{2} e^{4} - {\left(a^{4} b^{3} - 4 \, a^{5} b c\right)} d e^{5} + {\left(a^{4} b^{2} c - 4 \, a^{5} c^{2}\right)} e^{6}\right)}}\right]"," ",0,"[-1/6*(6*(a^4*b^2 - 4*a^5*c)*d^5*log(e*x + d) - 2*((a^4*b^2 - 4*a^5*c)*d^2*e^3 - (a^3*b^3 - 4*a^4*b*c)*d*e^4 + (a^3*b^2*c - 4*a^4*c^2)*e^5)*x^3 + 3*((a^4*b^2 - 4*a^5*c)*d^3*e^2 - (a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*d*e^4 + (a^2*b^3*c - 4*a^3*b*c^2)*e^5)*x^2 + 3*((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d*e^4 - (b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*e^5)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) - 6*((a^4*b^2 - 4*a^5*c)*d^4*e - (a*b^5 - 6*a^2*b^3*c + 8*a^3*b*c^2)*d*e^4 + (a*b^4*c - 5*a^2*b^2*c^2 + 4*a^3*c^3)*e^5)*x - 3*((b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*d*e^4 - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*e^5)*log(a*x^2 + b*x + c))/((a^5*b^2 - 4*a^6*c)*d^2*e^4 - (a^4*b^3 - 4*a^5*b*c)*d*e^5 + (a^4*b^2*c - 4*a^5*c^2)*e^6), -1/6*(6*(a^4*b^2 - 4*a^5*c)*d^5*log(e*x + d) - 2*((a^4*b^2 - 4*a^5*c)*d^2*e^3 - (a^3*b^3 - 4*a^4*b*c)*d*e^4 + (a^3*b^2*c - 4*a^4*c^2)*e^5)*x^3 + 3*((a^4*b^2 - 4*a^5*c)*d^3*e^2 - (a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*d*e^4 + (a^2*b^3*c - 4*a^3*b*c^2)*e^5)*x^2 - 6*((b^5 - 5*a*b^3*c + 5*a^2*b*c^2)*d*e^4 - (b^4*c - 4*a*b^2*c^2 + 2*a^2*c^3)*e^5)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) - 6*((a^4*b^2 - 4*a^5*c)*d^4*e - (a*b^5 - 6*a^2*b^3*c + 8*a^3*b*c^2)*d*e^4 + (a*b^4*c - 5*a^2*b^2*c^2 + 4*a^3*c^3)*e^5)*x - 3*((b^6 - 7*a*b^4*c + 13*a^2*b^2*c^2 - 4*a^3*c^3)*d*e^4 - (b^5*c - 6*a*b^3*c^2 + 8*a^2*b*c^3)*e^5)*log(a*x^2 + b*x + c))/((a^5*b^2 - 4*a^6*c)*d^2*e^4 - (a^4*b^3 - 4*a^5*b*c)*d*e^5 + (a^4*b^2*c - 4*a^5*c^2)*e^6)]","A",0
62,1,798,0,52.349084," ","integrate(x^2/(a+c/x^2+b/x)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{4} \log\left(e x + d\right) + {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} + {\left({\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d e^{3} - {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{4}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) - 2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{3} e - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{4}\right)} x - {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d e^{3} - {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{4}\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2} e^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)}}, \frac{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{4} \log\left(e x + d\right) + {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)} x^{2} - 2 \, {\left({\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d e^{3} - {\left(b^{3} c - 3 \, a b c^{2}\right)} e^{4}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{3} e - {\left(a b^{4} - 5 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d e^{3} + {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} e^{4}\right)} x - {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d e^{3} - {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} e^{4}\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{2} e^{3} - {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d e^{4} + {\left(a^{3} b^{2} c - 4 \, a^{4} c^{2}\right)} e^{5}\right)}}\right]"," ",0,"[1/2*(2*(a^3*b^2 - 4*a^4*c)*d^4*log(e*x + d) + ((a^3*b^2 - 4*a^4*c)*d^2*e^2 - (a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 + ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d*e^3 - (b^3*c - 3*a*b*c^2)*e^4)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) - 2*((a^3*b^2 - 4*a^4*c)*d^3*e - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d*e^3 + (a*b^3*c - 4*a^2*b*c^2)*e^4)*x - ((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d*e^3 - (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^4)*log(a*x^2 + b*x + c))/((a^4*b^2 - 4*a^5*c)*d^2*e^3 - (a^3*b^3 - 4*a^4*b*c)*d*e^4 + (a^3*b^2*c - 4*a^4*c^2)*e^5), 1/2*(2*(a^3*b^2 - 4*a^4*c)*d^4*log(e*x + d) + ((a^3*b^2 - 4*a^4*c)*d^2*e^2 - (a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)*x^2 - 2*((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d*e^3 - (b^3*c - 3*a*b*c^2)*e^4)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) - 2*((a^3*b^2 - 4*a^4*c)*d^3*e - (a*b^4 - 5*a^2*b^2*c + 4*a^3*c^2)*d*e^3 + (a*b^3*c - 4*a^2*b*c^2)*e^4)*x - ((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d*e^3 - (b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*e^4)*log(a*x^2 + b*x + c))/((a^4*b^2 - 4*a^5*c)*d^2*e^3 - (a^3*b^3 - 4*a^4*b*c)*d*e^4 + (a^3*b^2*c - 4*a^4*c^2)*e^5)]","A",0
63,1,596,0,16.037459," ","integrate(x/(a+c/x^2+b/x)/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{3} \log\left(e x + d\right) - {\left({\left(b^{3} - 3 \, a b c\right)} d e^{2} - {\left(b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) - 2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{2} e - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)} x - {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)}}, -\frac{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{3} \log\left(e x + d\right) - 2 \, {\left({\left(b^{3} - 3 \, a b c\right)} d e^{2} - {\left(b^{2} c - 2 \, a c^{2}\right)} e^{3}\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{2} e - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)} x - {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d e^{2} - {\left(b^{3} c - 4 \, a b c^{2}\right)} e^{3}\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{2} e^{2} - {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d e^{3} + {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e^{4}\right)}}\right]"," ",0,"[-1/2*(2*(a^2*b^2 - 4*a^3*c)*d^3*log(e*x + d) - ((b^3 - 3*a*b*c)*d*e^2 - (b^2*c - 2*a*c^2)*e^3)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) - 2*((a^2*b^2 - 4*a^3*c)*d^2*e - (a*b^3 - 4*a^2*b*c)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3)*x - ((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*log(a*x^2 + b*x + c))/((a^3*b^2 - 4*a^4*c)*d^2*e^2 - (a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4), -1/2*(2*(a^2*b^2 - 4*a^3*c)*d^3*log(e*x + d) - 2*((b^3 - 3*a*b*c)*d*e^2 - (b^2*c - 2*a*c^2)*e^3)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) - 2*((a^2*b^2 - 4*a^3*c)*d^2*e - (a*b^3 - 4*a^2*b*c)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3)*x - ((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d*e^2 - (b^3*c - 4*a*b*c^2)*e^3)*log(a*x^2 + b*x + c))/((a^3*b^2 - 4*a^4*c)*d^2*e^2 - (a^2*b^3 - 4*a^3*b*c)*d*e^3 + (a^2*b^2*c - 4*a^3*c^2)*e^4)]","A",0
64,1,405,0,5.759655," ","integrate(1/(a+c/x^2+b/x)/(e*x+d),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} \log\left(e x + d\right) + {\left(b c e^{2} - {\left(b^{2} - 2 \, a c\right)} d e\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} d e - {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{2} e - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)}}, \frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} \log\left(e x + d\right) + 2 \, {\left(b c e^{2} - {\left(b^{2} - 2 \, a c\right)} d e\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} d e - {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}\right)} \log\left(a x^{2} + b x + c\right)}{2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{2} e - {\left(a b^{3} - 4 \, a^{2} b c\right)} d e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} e^{3}\right)}}\right]"," ",0,"[1/2*(2*(a*b^2 - 4*a^2*c)*d^2*log(e*x + d) + (b*c*e^2 - (b^2 - 2*a*c)*d*e)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) - ((b^3 - 4*a*b*c)*d*e - (b^2*c - 4*a*c^2)*e^2)*log(a*x^2 + b*x + c))/((a^2*b^2 - 4*a^3*c)*d^2*e - (a*b^3 - 4*a^2*b*c)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3), 1/2*(2*(a*b^2 - 4*a^2*c)*d^2*log(e*x + d) + 2*(b*c*e^2 - (b^2 - 2*a*c)*d*e)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) - ((b^3 - 4*a*b*c)*d*e - (b^2*c - 4*a*c^2)*e^2)*log(a*x^2 + b*x + c))/((a^2*b^2 - 4*a^3*c)*d^2*e - (a*b^3 - 4*a^2*b*c)*d*e^2 + (a*b^2*c - 4*a^2*c^2)*e^3)]","A",0
65,1,305,0,2.167658," ","integrate(1/(a+c/x^2+b/x)/x/(e*x+d),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(a x^{2} + b x + c\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(e x + d\right) - \sqrt{b^{2} - 4 \, a c} {\left(b d - 2 \, c e\right)} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right)}{2 \, {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}\right)}}, \frac{{\left(b^{2} - 4 \, a c\right)} d \log\left(a x^{2} + b x + c\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} d \log\left(e x + d\right) + 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(b d - 2 \, c e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}\right)}}\right]"," ",0,"[1/2*((b^2 - 4*a*c)*d*log(a*x^2 + b*x + c) - 2*(b^2 - 4*a*c)*d*log(e*x + d) - sqrt(b^2 - 4*a*c)*(b*d - 2*c*e)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)))/((a*b^2 - 4*a^2*c)*d^2 - (b^3 - 4*a*b*c)*d*e + (b^2*c - 4*a*c^2)*e^2), 1/2*((b^2 - 4*a*c)*d*log(a*x^2 + b*x + c) - 2*(b^2 - 4*a*c)*d*log(e*x + d) + 2*sqrt(-b^2 + 4*a*c)*(b*d - 2*c*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)))/((a*b^2 - 4*a^2*c)*d^2 - (b^3 - 4*a*b*c)*d*e + (b^2*c - 4*a*c^2)*e^2)]","A",0
66,1,305,0,2.053521," ","integrate(1/(a+c/x^2+b/x)/x^2/(e*x+d),x, algorithm=""fricas"")","\left[-\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(a x^{2} + b x + c\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} e \log\left(e x + d\right) + \sqrt{b^{2} - 4 \, a c} {\left(2 \, a d - b e\right)} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right)}{2 \, {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}\right)}}, -\frac{{\left(b^{2} - 4 \, a c\right)} e \log\left(a x^{2} + b x + c\right) - 2 \, {\left(b^{2} - 4 \, a c\right)} e \log\left(e x + d\right) + 2 \, \sqrt{-b^{2} + 4 \, a c} {\left(2 \, a d - b e\right)} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right)}{2 \, {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} - {\left(b^{3} - 4 \, a b c\right)} d e + {\left(b^{2} c - 4 \, a c^{2}\right)} e^{2}\right)}}\right]"," ",0,"[-1/2*((b^2 - 4*a*c)*e*log(a*x^2 + b*x + c) - 2*(b^2 - 4*a*c)*e*log(e*x + d) + sqrt(b^2 - 4*a*c)*(2*a*d - b*e)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)))/((a*b^2 - 4*a^2*c)*d^2 - (b^3 - 4*a*b*c)*d*e + (b^2*c - 4*a*c^2)*e^2), -1/2*((b^2 - 4*a*c)*e*log(a*x^2 + b*x + c) - 2*(b^2 - 4*a*c)*e*log(e*x + d) + 2*sqrt(-b^2 + 4*a*c)*(2*a*d - b*e)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)))/((a*b^2 - 4*a^2*c)*d^2 - (b^3 - 4*a*b*c)*d*e + (b^2*c - 4*a*c^2)*e^2)]","A",0
67,-1,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)/x^3/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
68,-1,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)/x^4/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
69,-1,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)/x^5/(e*x+d),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate(x^3/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,1,2139,0,158.654804," ","integrate(x^2/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{6} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{5} e + 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} e^{2} - 2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{4} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e^{3} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{5} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{6}\right)} x^{2} + {\left({\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - 2 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{2} e^{4} + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{5} + {\left({\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{2} e^{4} - 2 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d e^{5} + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e^{6}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) - 2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{5} e - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{4} e^{2} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{3} e^{3} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e^{4} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{5}\right)} x + {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{5} + {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d^{2} e^{4} - 2 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e^{5} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{6}\right)} x\right)} \log\left(a x^{2} + b x + c\right) + 2 \, {\left(2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{6} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{5} e + 4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} e^{2} + {\left(2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{5} e - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{4} e^{2} + 4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{5} e^{3} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} e^{4} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{3} e^{5} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e^{6} + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{7} + {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{4} e^{4} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} e^{5} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{8}\right)} x\right)}}, -\frac{2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{6} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{5} e + 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} e^{2} - 2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{4} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e^{3} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{5} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{6}\right)} x^{2} + 2 \, {\left({\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{3} e^{3} - 2 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d^{2} e^{4} + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} d e^{5} + {\left({\left(b^{4} - 4 \, a b^{2} c + 2 \, a^{2} c^{2}\right)} d^{2} e^{4} - 2 \, {\left(b^{3} c - 3 \, a b c^{2}\right)} d e^{5} + {\left(b^{2} c^{2} - 2 \, a c^{3}\right)} e^{6}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) - 2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{5} e - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{4} e^{2} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{3} e^{3} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e^{4} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{5}\right)} x + {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d^{3} e^{3} - 2 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d^{2} e^{4} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} d e^{5} + {\left({\left(b^{5} - 6 \, a b^{3} c + 8 \, a^{2} b c^{2}\right)} d^{2} e^{4} - 2 \, {\left(b^{4} c - 5 \, a b^{2} c^{2} + 4 \, a^{2} c^{3}\right)} d e^{5} + {\left(b^{3} c^{2} - 4 \, a b c^{3}\right)} e^{6}\right)} x\right)} \log\left(a x^{2} + b x + c\right) + 2 \, {\left(2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{6} - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{5} e + 4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{4} e^{2} + {\left(2 \, {\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{5} e - 3 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{4} e^{2} + 4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} d^{3} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{5} e^{3} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{4} e^{4} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{3} e^{5} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d^{2} e^{6} + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} d e^{7} + {\left({\left(a^{4} b^{2} - 4 \, a^{5} c\right)} d^{4} e^{4} - 2 \, {\left(a^{3} b^{3} - 4 \, a^{4} b c\right)} d^{3} e^{5} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c - 8 \, a^{4} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}\right)} e^{8}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(a^3*b^2 - 4*a^4*c)*d^6 - 2*(a^2*b^3 - 4*a^3*b*c)*d^5*e + 2*(a^2*b^2*c - 4*a^3*c^2)*d^4*e^2 - 2*((a^3*b^2 - 4*a^4*c)*d^4*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d^3*e^3 + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^5 + (a*b^2*c^2 - 4*a^2*c^3)*e^6)*x^2 + ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3*e^3 - 2*(b^3*c - 3*a*b*c^2)*d^2*e^4 + (b^2*c^2 - 2*a*c^3)*d*e^5 + ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^2*e^4 - 2*(b^3*c - 3*a*b*c^2)*d*e^5 + (b^2*c^2 - 2*a*c^3)*e^6)*x)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) - 2*((a^3*b^2 - 4*a^4*c)*d^5*e - 2*(a^2*b^3 - 4*a^3*b*c)*d^4*e^2 + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^3*e^3 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^2*e^4 + (a*b^2*c^2 - 4*a^2*c^3)*d*e^5)*x + ((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d^3*e^3 - 2*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e^4 + (b^3*c^2 - 4*a*b*c^3)*d*e^5 + ((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d^2*e^4 - 2*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d*e^5 + (b^3*c^2 - 4*a*b*c^3)*e^6)*x)*log(a*x^2 + b*x + c) + 2*(2*(a^3*b^2 - 4*a^4*c)*d^6 - 3*(a^2*b^3 - 4*a^3*b*c)*d^5*e + 4*(a^2*b^2*c - 4*a^3*c^2)*d^4*e^2 + (2*(a^3*b^2 - 4*a^4*c)*d^5*e - 3*(a^2*b^3 - 4*a^3*b*c)*d^4*e^2 + 4*(a^2*b^2*c - 4*a^3*c^2)*d^3*e^3)*x)*log(e*x + d))/((a^4*b^2 - 4*a^5*c)*d^5*e^3 - 2*(a^3*b^3 - 4*a^4*b*c)*d^4*e^4 + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^3*e^5 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^6 + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^7 + ((a^4*b^2 - 4*a^5*c)*d^4*e^4 - 2*(a^3*b^3 - 4*a^4*b*c)*d^3*e^5 + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^7 + (a^2*b^2*c^2 - 4*a^3*c^3)*e^8)*x), -1/2*(2*(a^3*b^2 - 4*a^4*c)*d^6 - 2*(a^2*b^3 - 4*a^3*b*c)*d^5*e + 2*(a^2*b^2*c - 4*a^3*c^2)*d^4*e^2 - 2*((a^3*b^2 - 4*a^4*c)*d^4*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d^3*e^3 + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^5 + (a*b^2*c^2 - 4*a^2*c^3)*e^6)*x^2 + 2*((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^3*e^3 - 2*(b^3*c - 3*a*b*c^2)*d^2*e^4 + (b^2*c^2 - 2*a*c^3)*d*e^5 + ((b^4 - 4*a*b^2*c + 2*a^2*c^2)*d^2*e^4 - 2*(b^3*c - 3*a*b*c^2)*d*e^5 + (b^2*c^2 - 2*a*c^3)*e^6)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) - 2*((a^3*b^2 - 4*a^4*c)*d^5*e - 2*(a^2*b^3 - 4*a^3*b*c)*d^4*e^2 + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^3*e^3 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^2*e^4 + (a*b^2*c^2 - 4*a^2*c^3)*d*e^5)*x + ((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d^3*e^3 - 2*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d^2*e^4 + (b^3*c^2 - 4*a*b*c^3)*d*e^5 + ((b^5 - 6*a*b^3*c + 8*a^2*b*c^2)*d^2*e^4 - 2*(b^4*c - 5*a*b^2*c^2 + 4*a^2*c^3)*d*e^5 + (b^3*c^2 - 4*a*b*c^3)*e^6)*x)*log(a*x^2 + b*x + c) + 2*(2*(a^3*b^2 - 4*a^4*c)*d^6 - 3*(a^2*b^3 - 4*a^3*b*c)*d^5*e + 4*(a^2*b^2*c - 4*a^3*c^2)*d^4*e^2 + (2*(a^3*b^2 - 4*a^4*c)*d^5*e - 3*(a^2*b^3 - 4*a^3*b*c)*d^4*e^2 + 4*(a^2*b^2*c - 4*a^3*c^2)*d^3*e^3)*x)*log(e*x + d))/((a^4*b^2 - 4*a^5*c)*d^5*e^3 - 2*(a^3*b^3 - 4*a^4*b*c)*d^4*e^4 + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^3*e^5 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d^2*e^6 + (a^2*b^2*c^2 - 4*a^3*c^3)*d*e^7 + ((a^4*b^2 - 4*a^5*c)*d^4*e^4 - 2*(a^3*b^3 - 4*a^4*b*c)*d^3*e^5 + (a^2*b^4 - 2*a^3*b^2*c - 8*a^4*c^2)*d^2*e^6 - 2*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^7 + (a^2*b^2*c^2 - 4*a^3*c^3)*e^8)*x)]","B",0
72,1,1465,0,56.305945," ","integrate(x/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e + 2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e^{2} + {\left(b c^{2} d e^{4} + {\left(b^{3} - 3 \, a b c\right)} d^{3} e^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{2} e^{3} + {\left(b c^{2} e^{5} + {\left(b^{3} - 3 \, a b c\right)} d^{2} e^{3} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) + {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{4} + {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{5}\right)} x\right)} \log\left(a x^{2} + b x + c\right) + 2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e + 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e^{2} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} e - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{3} e^{2} + 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{5} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{4} e^{3} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{3} e^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e^{5} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{6} + {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{4} e^{3} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e^{4} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{6} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{7}\right)} x\right)}}, \frac{2 \, {\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e + 2 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e^{2} + 2 \, {\left(b c^{2} d e^{4} + {\left(b^{3} - 3 \, a b c\right)} d^{3} e^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d^{2} e^{3} + {\left(b c^{2} e^{5} + {\left(b^{3} - 3 \, a b c\right)} d^{2} e^{3} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e^{4}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{4} + {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{5}\right)} x\right)} \log\left(a x^{2} + b x + c\right) + 2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e + 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{3} e^{2} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} e - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{3} e^{2} + 3 \, {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} d^{2} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{5} e^{2} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{4} e^{3} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{3} e^{4} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d^{2} e^{5} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} d e^{6} + {\left({\left(a^{3} b^{2} - 4 \, a^{4} c\right)} d^{4} e^{3} - 2 \, {\left(a^{2} b^{3} - 4 \, a^{3} b c\right)} d^{3} e^{4} + {\left(a b^{4} - 2 \, a^{2} b^{2} c - 8 \, a^{3} c^{2}\right)} d^{2} e^{5} - 2 \, {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d e^{6} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} e^{7}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(a^2*b^2 - 4*a^3*c)*d^5 - 2*(a*b^3 - 4*a^2*b*c)*d^4*e + 2*(a*b^2*c - 4*a^2*c^2)*d^3*e^2 + (b*c^2*d*e^4 + (b^3 - 3*a*b*c)*d^3*e^2 - 2*(b^2*c - 2*a*c^2)*d^2*e^3 + (b*c^2*e^5 + (b^3 - 3*a*b*c)*d^2*e^3 - 2*(b^2*c - 2*a*c^2)*d*e^4)*x)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) + ((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3*e^2 - 2*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^2*c^2 - 4*a*c^3)*d*e^4 + ((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^2*e^3 - 2*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^2*c^2 - 4*a*c^3)*e^5)*x)*log(a*x^2 + b*x + c) + 2*((a^2*b^2 - 4*a^3*c)*d^5 - 2*(a*b^3 - 4*a^2*b*c)*d^4*e + 3*(a*b^2*c - 4*a^2*c^2)*d^3*e^2 + ((a^2*b^2 - 4*a^3*c)*d^4*e - 2*(a*b^3 - 4*a^2*b*c)*d^3*e^2 + 3*(a*b^2*c - 4*a^2*c^2)*d^2*e^3)*x)*log(e*x + d))/((a^3*b^2 - 4*a^4*c)*d^5*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d^4*e^3 + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^3*e^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^2*e^5 + (a*b^2*c^2 - 4*a^2*c^3)*d*e^6 + ((a^3*b^2 - 4*a^4*c)*d^4*e^3 - 2*(a^2*b^3 - 4*a^3*b*c)*d^3*e^4 + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^5 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^6 + (a*b^2*c^2 - 4*a^2*c^3)*e^7)*x), 1/2*(2*(a^2*b^2 - 4*a^3*c)*d^5 - 2*(a*b^3 - 4*a^2*b*c)*d^4*e + 2*(a*b^2*c - 4*a^2*c^2)*d^3*e^2 + 2*(b*c^2*d*e^4 + (b^3 - 3*a*b*c)*d^3*e^2 - 2*(b^2*c - 2*a*c^2)*d^2*e^3 + (b*c^2*e^5 + (b^3 - 3*a*b*c)*d^2*e^3 - 2*(b^2*c - 2*a*c^2)*d*e^4)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) + ((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3*e^2 - 2*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^2*c^2 - 4*a*c^3)*d*e^4 + ((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^2*e^3 - 2*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^2*c^2 - 4*a*c^3)*e^5)*x)*log(a*x^2 + b*x + c) + 2*((a^2*b^2 - 4*a^3*c)*d^5 - 2*(a*b^3 - 4*a^2*b*c)*d^4*e + 3*(a*b^2*c - 4*a^2*c^2)*d^3*e^2 + ((a^2*b^2 - 4*a^3*c)*d^4*e - 2*(a*b^3 - 4*a^2*b*c)*d^3*e^2 + 3*(a*b^2*c - 4*a^2*c^2)*d^2*e^3)*x)*log(e*x + d))/((a^3*b^2 - 4*a^4*c)*d^5*e^2 - 2*(a^2*b^3 - 4*a^3*b*c)*d^4*e^3 + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^3*e^4 - 2*(a*b^3*c - 4*a^2*b*c^2)*d^2*e^5 + (a*b^2*c^2 - 4*a^2*c^3)*d*e^6 + ((a^3*b^2 - 4*a^4*c)*d^4*e^3 - 2*(a^2*b^3 - 4*a^3*b*c)*d^3*e^4 + (a*b^4 - 2*a^2*b^2*c - 8*a^3*c^2)*d^2*e^5 - 2*(a*b^3*c - 4*a^2*b*c^2)*d*e^6 + (a*b^2*c^2 - 4*a^2*c^3)*e^7)*x)]","B",0
73,1,1120,0,19.721328," ","integrate(1/(a+c/x^2+b/x)/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{4} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d^{3} e + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} + {\left(2 \, b c d^{2} e^{2} - 2 \, c^{2} d e^{3} - {\left(b^{2} - 2 \, a c\right)} d^{3} e + {\left(2 \, b c d e^{3} - 2 \, c^{2} e^{4} - {\left(b^{2} - 2 \, a c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c - \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) + {\left({\left(b^{3} - 4 \, a b c\right)} d^{3} e - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} d^{2} e^{2} - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{3}\right)} x\right)} \log\left(a x^{2} + b x + c\right) - 2 \, {\left({\left(b^{3} - 4 \, a b c\right)} d^{3} e - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} d^{2} e^{2} - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} e - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{5} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{3} e^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{6}\right)} x\right)}}, -\frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{4} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d^{3} e + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} - 2 \, {\left(2 \, b c d^{2} e^{2} - 2 \, c^{2} d e^{3} - {\left(b^{2} - 2 \, a c\right)} d^{3} e + {\left(2 \, b c d e^{3} - 2 \, c^{2} e^{4} - {\left(b^{2} - 2 \, a c\right)} d^{2} e^{2}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(b^{3} - 4 \, a b c\right)} d^{3} e - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} d^{2} e^{2} - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{3}\right)} x\right)} \log\left(a x^{2} + b x + c\right) - 2 \, {\left({\left(b^{3} - 4 \, a b c\right)} d^{3} e - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d^{2} e^{2} + {\left({\left(b^{3} - 4 \, a b c\right)} d^{2} e^{2} - 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} e - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{5} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} e^{2} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{3} e^{3} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{4} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{5} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{6}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(a*b^2 - 4*a^2*c)*d^4 - 2*(b^3 - 4*a*b*c)*d^3*e + 2*(b^2*c - 4*a*c^2)*d^2*e^2 + (2*b*c*d^2*e^2 - 2*c^2*d*e^3 - (b^2 - 2*a*c)*d^3*e + (2*b*c*d*e^3 - 2*c^2*e^4 - (b^2 - 2*a*c)*d^2*e^2)*x)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c - sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) + ((b^3 - 4*a*b*c)*d^3*e - 2*(b^2*c - 4*a*c^2)*d^2*e^2 + ((b^3 - 4*a*b*c)*d^2*e^2 - 2*(b^2*c - 4*a*c^2)*d*e^3)*x)*log(a*x^2 + b*x + c) - 2*((b^3 - 4*a*b*c)*d^3*e - 2*(b^2*c - 4*a*c^2)*d^2*e^2 + ((b^3 - 4*a*b*c)*d^2*e^2 - 2*(b^2*c - 4*a*c^2)*d*e^3)*x)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*d^5*e - 2*(a*b^3 - 4*a^2*b*c)*d^4*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^3 - 2*(b^3*c - 4*a*b*c^2)*d^2*e^4 + (b^2*c^2 - 4*a*c^3)*d*e^5 + ((a^2*b^2 - 4*a^3*c)*d^4*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d^3*e^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^4 - 2*(b^3*c - 4*a*b*c^2)*d*e^5 + (b^2*c^2 - 4*a*c^3)*e^6)*x), -1/2*(2*(a*b^2 - 4*a^2*c)*d^4 - 2*(b^3 - 4*a*b*c)*d^3*e + 2*(b^2*c - 4*a*c^2)*d^2*e^2 - 2*(2*b*c*d^2*e^2 - 2*c^2*d*e^3 - (b^2 - 2*a*c)*d^3*e + (2*b*c*d*e^3 - 2*c^2*e^4 - (b^2 - 2*a*c)*d^2*e^2)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) + ((b^3 - 4*a*b*c)*d^3*e - 2*(b^2*c - 4*a*c^2)*d^2*e^2 + ((b^3 - 4*a*b*c)*d^2*e^2 - 2*(b^2*c - 4*a*c^2)*d*e^3)*x)*log(a*x^2 + b*x + c) - 2*((b^3 - 4*a*b*c)*d^3*e - 2*(b^2*c - 4*a*c^2)*d^2*e^2 + ((b^3 - 4*a*b*c)*d^2*e^2 - 2*(b^2*c - 4*a*c^2)*d*e^3)*x)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*d^5*e - 2*(a*b^3 - 4*a^2*b*c)*d^4*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^3 - 2*(b^3*c - 4*a*b*c^2)*d^2*e^4 + (b^2*c^2 - 4*a*c^3)*d*e^5 + ((a^2*b^2 - 4*a^3*c)*d^4*e^2 - 2*(a*b^3 - 4*a^2*b*c)*d^3*e^3 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^4 - 2*(b^3*c - 4*a*b*c^2)*d*e^5 + (b^2*c^2 - 4*a*c^3)*e^6)*x)]","B",0
74,1,1059,0,16.696681," ","integrate(1/(a+c/x^2+b/x)/x/(e*x+d)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{3} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d^{2} e + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} + {\left(a b d^{3} - 4 \, a c d^{2} e + b c d e^{2} + {\left(a b d^{2} e - 4 \, a c d e^{2} + b c e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) + {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{3} - {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} + {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3}\right)} x\right)} \log\left(a x^{2} + b x + c\right) - 2 \, {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{3} - {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} + {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{4} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} e - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{3} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{5}\right)} x\right)}}, \frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{3} - 2 \, {\left(b^{3} - 4 \, a b c\right)} d^{2} e + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} + 2 \, {\left(a b d^{3} - 4 \, a c d^{2} e + b c d e^{2} + {\left(a b d^{2} e - 4 \, a c d e^{2} + b c e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{3} - {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} + {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3}\right)} x\right)} \log\left(a x^{2} + b x + c\right) - 2 \, {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{3} - {\left(b^{2} c - 4 \, a c^{2}\right)} d e^{2} + {\left({\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{4} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} e - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{3} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{5}\right)} x\right)}}\right]"," ",0,"[1/2*(2*(a*b^2 - 4*a^2*c)*d^3 - 2*(b^3 - 4*a*b*c)*d^2*e + 2*(b^2*c - 4*a*c^2)*d*e^2 + (a*b*d^3 - 4*a*c*d^2*e + b*c*d*e^2 + (a*b*d^2*e - 4*a*c*d*e^2 + b*c*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) + ((a*b^2 - 4*a^2*c)*d^3 - (b^2*c - 4*a*c^2)*d*e^2 + ((a*b^2 - 4*a^2*c)*d^2*e - (b^2*c - 4*a*c^2)*e^3)*x)*log(a*x^2 + b*x + c) - 2*((a*b^2 - 4*a^2*c)*d^3 - (b^2*c - 4*a*c^2)*d*e^2 + ((a*b^2 - 4*a^2*c)*d^2*e - (b^2*c - 4*a*c^2)*e^3)*x)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*d^5 - 2*(a*b^3 - 4*a^2*b*c)*d^4*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^2 - 2*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^2*c^2 - 4*a*c^3)*d*e^4 + ((a^2*b^2 - 4*a^3*c)*d^4*e - 2*(a*b^3 - 4*a^2*b*c)*d^3*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 2*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^2*c^2 - 4*a*c^3)*e^5)*x), 1/2*(2*(a*b^2 - 4*a^2*c)*d^3 - 2*(b^3 - 4*a*b*c)*d^2*e + 2*(b^2*c - 4*a*c^2)*d*e^2 + 2*(a*b*d^3 - 4*a*c*d^2*e + b*c*d*e^2 + (a*b*d^2*e - 4*a*c*d*e^2 + b*c*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) + ((a*b^2 - 4*a^2*c)*d^3 - (b^2*c - 4*a*c^2)*d*e^2 + ((a*b^2 - 4*a^2*c)*d^2*e - (b^2*c - 4*a*c^2)*e^3)*x)*log(a*x^2 + b*x + c) - 2*((a*b^2 - 4*a^2*c)*d^3 - (b^2*c - 4*a*c^2)*d*e^2 + ((a*b^2 - 4*a^2*c)*d^2*e - (b^2*c - 4*a*c^2)*e^3)*x)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*d^5 - 2*(a*b^3 - 4*a^2*b*c)*d^4*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^2 - 2*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^2*c^2 - 4*a*c^3)*d*e^4 + ((a^2*b^2 - 4*a^3*c)*d^4*e - 2*(a*b^3 - 4*a^2*b*c)*d^3*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 2*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^2*c^2 - 4*a*c^3)*e^5)*x)]","B",0
75,1,1079,0,9.279891," ","integrate(1/(a+c/x^2+b/x)/x^2/(e*x+d)^2,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - 2 \, {\left(b^{3} - 4 \, a b c\right)} d e^{2} + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3} + {\left(2 \, a^{2} d^{3} - 2 \, a b d^{2} e + {\left(b^{2} - 2 \, a c\right)} d e^{2} + {\left(2 \, a^{2} d^{2} e - 2 \, a b d e^{2} + {\left(b^{2} - 2 \, a c\right)} e^{3}\right)} x\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, a^{2} x^{2} + 2 \, a b x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, a x + b\right)}}{a x^{2} + b x + c}\right) + {\left(2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - {\left(b^{3} - 4 \, a b c\right)} d e^{2} + {\left(2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} - {\left(b^{3} - 4 \, a b c\right)} e^{3}\right)} x\right)} \log\left(a x^{2} + b x + c\right) - 2 \, {\left(2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - {\left(b^{3} - 4 \, a b c\right)} d e^{2} + {\left(2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} - {\left(b^{3} - 4 \, a b c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{4} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} e - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{3} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{5}\right)} x\right)}}, -\frac{2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - 2 \, {\left(b^{3} - 4 \, a b c\right)} d e^{2} + 2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} e^{3} + 2 \, {\left(2 \, a^{2} d^{3} - 2 \, a b d^{2} e + {\left(b^{2} - 2 \, a c\right)} d e^{2} + {\left(2 \, a^{2} d^{2} e - 2 \, a b d e^{2} + {\left(b^{2} - 2 \, a c\right)} e^{3}\right)} x\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, a x + b\right)}}{b^{2} - 4 \, a c}\right) + {\left(2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - {\left(b^{3} - 4 \, a b c\right)} d e^{2} + {\left(2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} - {\left(b^{3} - 4 \, a b c\right)} e^{3}\right)} x\right)} \log\left(a x^{2} + b x + c\right) - 2 \, {\left(2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d^{2} e - {\left(b^{3} - 4 \, a b c\right)} d e^{2} + {\left(2 \, {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} - {\left(b^{3} - 4 \, a b c\right)} e^{3}\right)} x\right)} \log\left(e x + d\right)}{2 \, {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{5} - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{4} e + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{3} e^{2} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e^{3} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{4} + {\left({\left(a^{2} b^{2} - 4 \, a^{3} c\right)} d^{4} e - 2 \, {\left(a b^{3} - 4 \, a^{2} b c\right)} d^{3} e^{2} + {\left(b^{4} - 2 \, a b^{2} c - 8 \, a^{2} c^{2}\right)} d^{2} e^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d e^{4} + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} e^{5}\right)} x\right)}}\right]"," ",0,"[-1/2*(2*(a*b^2 - 4*a^2*c)*d^2*e - 2*(b^3 - 4*a*b*c)*d*e^2 + 2*(b^2*c - 4*a*c^2)*e^3 + (2*a^2*d^3 - 2*a*b*d^2*e + (b^2 - 2*a*c)*d*e^2 + (2*a^2*d^2*e - 2*a*b*d*e^2 + (b^2 - 2*a*c)*e^3)*x)*sqrt(b^2 - 4*a*c)*log((2*a^2*x^2 + 2*a*b*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*a*x + b))/(a*x^2 + b*x + c)) + (2*(a*b^2 - 4*a^2*c)*d^2*e - (b^3 - 4*a*b*c)*d*e^2 + (2*(a*b^2 - 4*a^2*c)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*x)*log(a*x^2 + b*x + c) - 2*(2*(a*b^2 - 4*a^2*c)*d^2*e - (b^3 - 4*a*b*c)*d*e^2 + (2*(a*b^2 - 4*a^2*c)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*x)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*d^5 - 2*(a*b^3 - 4*a^2*b*c)*d^4*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^2 - 2*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^2*c^2 - 4*a*c^3)*d*e^4 + ((a^2*b^2 - 4*a^3*c)*d^4*e - 2*(a*b^3 - 4*a^2*b*c)*d^3*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 2*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^2*c^2 - 4*a*c^3)*e^5)*x), -1/2*(2*(a*b^2 - 4*a^2*c)*d^2*e - 2*(b^3 - 4*a*b*c)*d*e^2 + 2*(b^2*c - 4*a*c^2)*e^3 + 2*(2*a^2*d^3 - 2*a*b*d^2*e + (b^2 - 2*a*c)*d*e^2 + (2*a^2*d^2*e - 2*a*b*d*e^2 + (b^2 - 2*a*c)*e^3)*x)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*a*x + b)/(b^2 - 4*a*c)) + (2*(a*b^2 - 4*a^2*c)*d^2*e - (b^3 - 4*a*b*c)*d*e^2 + (2*(a*b^2 - 4*a^2*c)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*x)*log(a*x^2 + b*x + c) - 2*(2*(a*b^2 - 4*a^2*c)*d^2*e - (b^3 - 4*a*b*c)*d*e^2 + (2*(a*b^2 - 4*a^2*c)*d*e^2 - (b^3 - 4*a*b*c)*e^3)*x)*log(e*x + d))/((a^2*b^2 - 4*a^3*c)*d^5 - 2*(a*b^3 - 4*a^2*b*c)*d^4*e + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^3*e^2 - 2*(b^3*c - 4*a*b*c^2)*d^2*e^3 + (b^2*c^2 - 4*a*c^3)*d*e^4 + ((a^2*b^2 - 4*a^3*c)*d^4*e - 2*(a*b^3 - 4*a^2*b*c)*d^3*e^2 + (b^4 - 2*a*b^2*c - 8*a^2*c^2)*d^2*e^3 - 2*(b^3*c - 4*a*b*c^2)*d*e^4 + (b^2*c^2 - 4*a*c^3)*e^5)*x)]","B",0
76,-1,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)/x^3/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)/x^4/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,-1,0,0,0.000000," ","integrate(1/(a+c/x^2+b/x)/x^5/(e*x+d)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
79,0,0,0,1.305656," ","integrate(x^4*(a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x + d} x^{4} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}, x\right)"," ",0,"integral(sqrt(e*x + d)*x^4*sqrt((a*x^2 + b*x + c)/x^2), x)","F",0
80,0,0,0,1.689661," ","integrate(x^3*(a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x + d} x^{3} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}, x\right)"," ",0,"integral(sqrt(e*x + d)*x^3*sqrt((a*x^2 + b*x + c)/x^2), x)","F",0
81,0,0,0,1.472064," ","integrate(x^2*(a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x + d} x^{2} \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}, x\right)"," ",0,"integral(sqrt(e*x + d)*x^2*sqrt((a*x^2 + b*x + c)/x^2), x)","F",0
82,0,0,0,1.324412," ","integrate(x*(a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{e x + d} x \sqrt{\frac{a x^{2} + b x + c}{x^{2}}}, x\right)"," ",0,"integral(sqrt(e*x + d)*x*sqrt((a*x^2 + b*x + c)/x^2), x)","F",0
83,-1,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
84,-1,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2)/x,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
85,-1,0,0,0.000000," ","integrate((a+c/x^2+b/x)^(1/2)*(e*x+d)^(1/2)/x^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
86,0,0,0,1.329123," ","integrate((f*x)^m*(d+e*x^n)^q*(a+c*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2 \, n} + a\right)}^{p} {\left(e x^{n} + d\right)}^{q} \left(f x\right)^{m}, x\right)"," ",0,"integral((c*x^(2*n) + a)^p*(e*x^n + d)^q*(f*x)^m, x)","F",0
87,0,0,0,1.133623," ","integrate((f*x)^m*(d+e*x^n)^3*(a+c*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}\right)} {\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}, x\right)"," ",0,"integral((e^3*x^(3*n) + 3*d*e^2*x^(2*n) + 3*d^2*e*x^n + d^3)*(c*x^(2*n) + a)^p*(f*x)^m, x)","F",0
88,0,0,0,1.639859," ","integrate((f*x)^m*(d+e*x^n)^2*(a+c*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}\right)} {\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}, x\right)"," ",0,"integral((e^2*x^(2*n) + 2*d*e*x^n + d^2)*(c*x^(2*n) + a)^p*(f*x)^m, x)","F",0
89,0,0,0,1.178082," ","integrate((f*x)^m*(d+e*x^n)*(a+c*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{n} + d\right)} {\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}, x\right)"," ",0,"integral((e*x^n + d)*(c*x^(2*n) + a)^p*(f*x)^m, x)","F",0
90,0,0,0,0.871814," ","integrate((f*x)^m*(a+c*x^(2*n))^p/(d+e*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}}{e x^{n} + d}, x\right)"," ",0,"integral((c*x^(2*n) + a)^p*(f*x)^m/(e*x^n + d), x)","F",0
91,0,0,0,0.780290," ","integrate((f*x)^m*(a+c*x^(2*n))^p/(d+e*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}}{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}, x\right)"," ",0,"integral((c*x^(2*n) + a)^p*(f*x)^m/(e^2*x^(2*n) + 2*d*e*x^n + d^2), x)","F",0
92,0,0,0,0.738018," ","integrate((f*x)^m*(a+c*x^(2*n))^p/(d+e*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2 \, n} + a\right)}^{p} \left(f x\right)^{m}}{e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}}, x\right)"," ",0,"integral((c*x^(2*n) + a)^p*(f*x)^m/(e^3*x^(3*n) + 3*d*e^2*x^(2*n) + 3*d^2*e*x^n + d^3), x)","F",0
93,1,1446,0,0.762097," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^13,x, algorithm=""fricas"")","\frac{1}{14} x^{28} c^{14} + x^{27} c^{13} b + \frac{13}{2} x^{26} c^{12} b^{2} + x^{26} c^{13} a + 26 x^{25} c^{11} b^{3} + 13 x^{25} c^{12} b a + \frac{143}{2} x^{24} c^{10} b^{4} + 78 x^{24} c^{11} b^{2} a + \frac{13}{2} x^{24} c^{12} a^{2} + 143 x^{23} c^{9} b^{5} + 286 x^{23} c^{10} b^{3} a + 78 x^{23} c^{11} b a^{2} + \frac{429}{2} x^{22} c^{8} b^{6} + 715 x^{22} c^{9} b^{4} a + 429 x^{22} c^{10} b^{2} a^{2} + 26 x^{22} c^{11} a^{3} + \frac{1716}{7} x^{21} c^{7} b^{7} + 1287 x^{21} c^{8} b^{5} a + 1430 x^{21} c^{9} b^{3} a^{2} + 286 x^{21} c^{10} b a^{3} + \frac{429}{2} x^{20} c^{6} b^{8} + 1716 x^{20} c^{7} b^{6} a + \frac{6435}{2} x^{20} c^{8} b^{4} a^{2} + 1430 x^{20} c^{9} b^{2} a^{3} + \frac{143}{2} x^{20} c^{10} a^{4} + 143 x^{19} c^{5} b^{9} + 1716 x^{19} c^{6} b^{7} a + 5148 x^{19} c^{7} b^{5} a^{2} + 4290 x^{19} c^{8} b^{3} a^{3} + 715 x^{19} c^{9} b a^{4} + \frac{143}{2} x^{18} c^{4} b^{10} + 1287 x^{18} c^{5} b^{8} a + 6006 x^{18} c^{6} b^{6} a^{2} + 8580 x^{18} c^{7} b^{4} a^{3} + \frac{6435}{2} x^{18} c^{8} b^{2} a^{4} + 143 x^{18} c^{9} a^{5} + 26 x^{17} c^{3} b^{11} + 715 x^{17} c^{4} b^{9} a + 5148 x^{17} c^{5} b^{7} a^{2} + 12012 x^{17} c^{6} b^{5} a^{3} + 8580 x^{17} c^{7} b^{3} a^{4} + 1287 x^{17} c^{8} b a^{5} + \frac{13}{2} x^{16} c^{2} b^{12} + 286 x^{16} c^{3} b^{10} a + \frac{6435}{2} x^{16} c^{4} b^{8} a^{2} + 12012 x^{16} c^{5} b^{6} a^{3} + 15015 x^{16} c^{6} b^{4} a^{4} + 5148 x^{16} c^{7} b^{2} a^{5} + \frac{429}{2} x^{16} c^{8} a^{6} + x^{15} c b^{13} + 78 x^{15} c^{2} b^{11} a + 1430 x^{15} c^{3} b^{9} a^{2} + 8580 x^{15} c^{4} b^{7} a^{3} + 18018 x^{15} c^{5} b^{5} a^{4} + 12012 x^{15} c^{6} b^{3} a^{5} + 1716 x^{15} c^{7} b a^{6} + \frac{1}{14} x^{14} b^{14} + 13 x^{14} c b^{12} a + 429 x^{14} c^{2} b^{10} a^{2} + 4290 x^{14} c^{3} b^{8} a^{3} + 15015 x^{14} c^{4} b^{6} a^{4} + 18018 x^{14} c^{5} b^{4} a^{5} + 6006 x^{14} c^{6} b^{2} a^{6} + \frac{1716}{7} x^{14} c^{7} a^{7} + x^{13} b^{13} a + 78 x^{13} c b^{11} a^{2} + 1430 x^{13} c^{2} b^{9} a^{3} + 8580 x^{13} c^{3} b^{7} a^{4} + 18018 x^{13} c^{4} b^{5} a^{5} + 12012 x^{13} c^{5} b^{3} a^{6} + 1716 x^{13} c^{6} b a^{7} + \frac{13}{2} x^{12} b^{12} a^{2} + 286 x^{12} c b^{10} a^{3} + \frac{6435}{2} x^{12} c^{2} b^{8} a^{4} + 12012 x^{12} c^{3} b^{6} a^{5} + 15015 x^{12} c^{4} b^{4} a^{6} + 5148 x^{12} c^{5} b^{2} a^{7} + \frac{429}{2} x^{12} c^{6} a^{8} + 26 x^{11} b^{11} a^{3} + 715 x^{11} c b^{9} a^{4} + 5148 x^{11} c^{2} b^{7} a^{5} + 12012 x^{11} c^{3} b^{5} a^{6} + 8580 x^{11} c^{4} b^{3} a^{7} + 1287 x^{11} c^{5} b a^{8} + \frac{143}{2} x^{10} b^{10} a^{4} + 1287 x^{10} c b^{8} a^{5} + 6006 x^{10} c^{2} b^{6} a^{6} + 8580 x^{10} c^{3} b^{4} a^{7} + \frac{6435}{2} x^{10} c^{4} b^{2} a^{8} + 143 x^{10} c^{5} a^{9} + 143 x^{9} b^{9} a^{5} + 1716 x^{9} c b^{7} a^{6} + 5148 x^{9} c^{2} b^{5} a^{7} + 4290 x^{9} c^{3} b^{3} a^{8} + 715 x^{9} c^{4} b a^{9} + \frac{429}{2} x^{8} b^{8} a^{6} + 1716 x^{8} c b^{6} a^{7} + \frac{6435}{2} x^{8} c^{2} b^{4} a^{8} + 1430 x^{8} c^{3} b^{2} a^{9} + \frac{143}{2} x^{8} c^{4} a^{10} + \frac{1716}{7} x^{7} b^{7} a^{7} + 1287 x^{7} c b^{5} a^{8} + 1430 x^{7} c^{2} b^{3} a^{9} + 286 x^{7} c^{3} b a^{10} + \frac{429}{2} x^{6} b^{6} a^{8} + 715 x^{6} c b^{4} a^{9} + 429 x^{6} c^{2} b^{2} a^{10} + 26 x^{6} c^{3} a^{11} + 143 x^{5} b^{5} a^{9} + 286 x^{5} c b^{3} a^{10} + 78 x^{5} c^{2} b a^{11} + \frac{143}{2} x^{4} b^{4} a^{10} + 78 x^{4} c b^{2} a^{11} + \frac{13}{2} x^{4} c^{2} a^{12} + 26 x^{3} b^{3} a^{11} + 13 x^{3} c b a^{12} + \frac{13}{2} x^{2} b^{2} a^{12} + x^{2} c a^{13} + x b a^{13}"," ",0,"1/14*x^28*c^14 + x^27*c^13*b + 13/2*x^26*c^12*b^2 + x^26*c^13*a + 26*x^25*c^11*b^3 + 13*x^25*c^12*b*a + 143/2*x^24*c^10*b^4 + 78*x^24*c^11*b^2*a + 13/2*x^24*c^12*a^2 + 143*x^23*c^9*b^5 + 286*x^23*c^10*b^3*a + 78*x^23*c^11*b*a^2 + 429/2*x^22*c^8*b^6 + 715*x^22*c^9*b^4*a + 429*x^22*c^10*b^2*a^2 + 26*x^22*c^11*a^3 + 1716/7*x^21*c^7*b^7 + 1287*x^21*c^8*b^5*a + 1430*x^21*c^9*b^3*a^2 + 286*x^21*c^10*b*a^3 + 429/2*x^20*c^6*b^8 + 1716*x^20*c^7*b^6*a + 6435/2*x^20*c^8*b^4*a^2 + 1430*x^20*c^9*b^2*a^3 + 143/2*x^20*c^10*a^4 + 143*x^19*c^5*b^9 + 1716*x^19*c^6*b^7*a + 5148*x^19*c^7*b^5*a^2 + 4290*x^19*c^8*b^3*a^3 + 715*x^19*c^9*b*a^4 + 143/2*x^18*c^4*b^10 + 1287*x^18*c^5*b^8*a + 6006*x^18*c^6*b^6*a^2 + 8580*x^18*c^7*b^4*a^3 + 6435/2*x^18*c^8*b^2*a^4 + 143*x^18*c^9*a^5 + 26*x^17*c^3*b^11 + 715*x^17*c^4*b^9*a + 5148*x^17*c^5*b^7*a^2 + 12012*x^17*c^6*b^5*a^3 + 8580*x^17*c^7*b^3*a^4 + 1287*x^17*c^8*b*a^5 + 13/2*x^16*c^2*b^12 + 286*x^16*c^3*b^10*a + 6435/2*x^16*c^4*b^8*a^2 + 12012*x^16*c^5*b^6*a^3 + 15015*x^16*c^6*b^4*a^4 + 5148*x^16*c^7*b^2*a^5 + 429/2*x^16*c^8*a^6 + x^15*c*b^13 + 78*x^15*c^2*b^11*a + 1430*x^15*c^3*b^9*a^2 + 8580*x^15*c^4*b^7*a^3 + 18018*x^15*c^5*b^5*a^4 + 12012*x^15*c^6*b^3*a^5 + 1716*x^15*c^7*b*a^6 + 1/14*x^14*b^14 + 13*x^14*c*b^12*a + 429*x^14*c^2*b^10*a^2 + 4290*x^14*c^3*b^8*a^3 + 15015*x^14*c^4*b^6*a^4 + 18018*x^14*c^5*b^4*a^5 + 6006*x^14*c^6*b^2*a^6 + 1716/7*x^14*c^7*a^7 + x^13*b^13*a + 78*x^13*c*b^11*a^2 + 1430*x^13*c^2*b^9*a^3 + 8580*x^13*c^3*b^7*a^4 + 18018*x^13*c^4*b^5*a^5 + 12012*x^13*c^5*b^3*a^6 + 1716*x^13*c^6*b*a^7 + 13/2*x^12*b^12*a^2 + 286*x^12*c*b^10*a^3 + 6435/2*x^12*c^2*b^8*a^4 + 12012*x^12*c^3*b^6*a^5 + 15015*x^12*c^4*b^4*a^6 + 5148*x^12*c^5*b^2*a^7 + 429/2*x^12*c^6*a^8 + 26*x^11*b^11*a^3 + 715*x^11*c*b^9*a^4 + 5148*x^11*c^2*b^7*a^5 + 12012*x^11*c^3*b^5*a^6 + 8580*x^11*c^4*b^3*a^7 + 1287*x^11*c^5*b*a^8 + 143/2*x^10*b^10*a^4 + 1287*x^10*c*b^8*a^5 + 6006*x^10*c^2*b^6*a^6 + 8580*x^10*c^3*b^4*a^7 + 6435/2*x^10*c^4*b^2*a^8 + 143*x^10*c^5*a^9 + 143*x^9*b^9*a^5 + 1716*x^9*c*b^7*a^6 + 5148*x^9*c^2*b^5*a^7 + 4290*x^9*c^3*b^3*a^8 + 715*x^9*c^4*b*a^9 + 429/2*x^8*b^8*a^6 + 1716*x^8*c*b^6*a^7 + 6435/2*x^8*c^2*b^4*a^8 + 1430*x^8*c^3*b^2*a^9 + 143/2*x^8*c^4*a^10 + 1716/7*x^7*b^7*a^7 + 1287*x^7*c*b^5*a^8 + 1430*x^7*c^2*b^3*a^9 + 286*x^7*c^3*b*a^10 + 429/2*x^6*b^6*a^8 + 715*x^6*c*b^4*a^9 + 429*x^6*c^2*b^2*a^10 + 26*x^6*c^3*a^11 + 143*x^5*b^5*a^9 + 286*x^5*c*b^3*a^10 + 78*x^5*c^2*b*a^11 + 143/2*x^4*b^4*a^10 + 78*x^4*c*b^2*a^11 + 13/2*x^4*c^2*a^12 + 26*x^3*b^3*a^11 + 13*x^3*c*b*a^12 + 13/2*x^2*b^2*a^12 + x^2*c*a^13 + x*b*a^13","B",0
94,1,1454,0,0.762712," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2+a)^13,x, algorithm=""fricas"")","\frac{1}{28} x^{56} c^{14} + \frac{1}{2} x^{54} c^{13} b + \frac{13}{4} x^{52} c^{12} b^{2} + \frac{1}{2} x^{52} c^{13} a + 13 x^{50} c^{11} b^{3} + \frac{13}{2} x^{50} c^{12} b a + \frac{143}{4} x^{48} c^{10} b^{4} + 39 x^{48} c^{11} b^{2} a + \frac{13}{4} x^{48} c^{12} a^{2} + \frac{143}{2} x^{46} c^{9} b^{5} + 143 x^{46} c^{10} b^{3} a + 39 x^{46} c^{11} b a^{2} + \frac{429}{4} x^{44} c^{8} b^{6} + \frac{715}{2} x^{44} c^{9} b^{4} a + \frac{429}{2} x^{44} c^{10} b^{2} a^{2} + 13 x^{44} c^{11} a^{3} + \frac{858}{7} x^{42} c^{7} b^{7} + \frac{1287}{2} x^{42} c^{8} b^{5} a + 715 x^{42} c^{9} b^{3} a^{2} + 143 x^{42} c^{10} b a^{3} + \frac{429}{4} x^{40} c^{6} b^{8} + 858 x^{40} c^{7} b^{6} a + \frac{6435}{4} x^{40} c^{8} b^{4} a^{2} + 715 x^{40} c^{9} b^{2} a^{3} + \frac{143}{4} x^{40} c^{10} a^{4} + \frac{143}{2} x^{38} c^{5} b^{9} + 858 x^{38} c^{6} b^{7} a + 2574 x^{38} c^{7} b^{5} a^{2} + 2145 x^{38} c^{8} b^{3} a^{3} + \frac{715}{2} x^{38} c^{9} b a^{4} + \frac{143}{4} x^{36} c^{4} b^{10} + \frac{1287}{2} x^{36} c^{5} b^{8} a + 3003 x^{36} c^{6} b^{6} a^{2} + 4290 x^{36} c^{7} b^{4} a^{3} + \frac{6435}{4} x^{36} c^{8} b^{2} a^{4} + \frac{143}{2} x^{36} c^{9} a^{5} + 13 x^{34} c^{3} b^{11} + \frac{715}{2} x^{34} c^{4} b^{9} a + 2574 x^{34} c^{5} b^{7} a^{2} + 6006 x^{34} c^{6} b^{5} a^{3} + 4290 x^{34} c^{7} b^{3} a^{4} + \frac{1287}{2} x^{34} c^{8} b a^{5} + \frac{13}{4} x^{32} c^{2} b^{12} + 143 x^{32} c^{3} b^{10} a + \frac{6435}{4} x^{32} c^{4} b^{8} a^{2} + 6006 x^{32} c^{5} b^{6} a^{3} + \frac{15015}{2} x^{32} c^{6} b^{4} a^{4} + 2574 x^{32} c^{7} b^{2} a^{5} + \frac{429}{4} x^{32} c^{8} a^{6} + \frac{1}{2} x^{30} c b^{13} + 39 x^{30} c^{2} b^{11} a + 715 x^{30} c^{3} b^{9} a^{2} + 4290 x^{30} c^{4} b^{7} a^{3} + 9009 x^{30} c^{5} b^{5} a^{4} + 6006 x^{30} c^{6} b^{3} a^{5} + 858 x^{30} c^{7} b a^{6} + \frac{1}{28} x^{28} b^{14} + \frac{13}{2} x^{28} c b^{12} a + \frac{429}{2} x^{28} c^{2} b^{10} a^{2} + 2145 x^{28} c^{3} b^{8} a^{3} + \frac{15015}{2} x^{28} c^{4} b^{6} a^{4} + 9009 x^{28} c^{5} b^{4} a^{5} + 3003 x^{28} c^{6} b^{2} a^{6} + \frac{858}{7} x^{28} c^{7} a^{7} + \frac{1}{2} x^{26} b^{13} a + 39 x^{26} c b^{11} a^{2} + 715 x^{26} c^{2} b^{9} a^{3} + 4290 x^{26} c^{3} b^{7} a^{4} + 9009 x^{26} c^{4} b^{5} a^{5} + 6006 x^{26} c^{5} b^{3} a^{6} + 858 x^{26} c^{6} b a^{7} + \frac{13}{4} x^{24} b^{12} a^{2} + 143 x^{24} c b^{10} a^{3} + \frac{6435}{4} x^{24} c^{2} b^{8} a^{4} + 6006 x^{24} c^{3} b^{6} a^{5} + \frac{15015}{2} x^{24} c^{4} b^{4} a^{6} + 2574 x^{24} c^{5} b^{2} a^{7} + \frac{429}{4} x^{24} c^{6} a^{8} + 13 x^{22} b^{11} a^{3} + \frac{715}{2} x^{22} c b^{9} a^{4} + 2574 x^{22} c^{2} b^{7} a^{5} + 6006 x^{22} c^{3} b^{5} a^{6} + 4290 x^{22} c^{4} b^{3} a^{7} + \frac{1287}{2} x^{22} c^{5} b a^{8} + \frac{143}{4} x^{20} b^{10} a^{4} + \frac{1287}{2} x^{20} c b^{8} a^{5} + 3003 x^{20} c^{2} b^{6} a^{6} + 4290 x^{20} c^{3} b^{4} a^{7} + \frac{6435}{4} x^{20} c^{4} b^{2} a^{8} + \frac{143}{2} x^{20} c^{5} a^{9} + \frac{143}{2} x^{18} b^{9} a^{5} + 858 x^{18} c b^{7} a^{6} + 2574 x^{18} c^{2} b^{5} a^{7} + 2145 x^{18} c^{3} b^{3} a^{8} + \frac{715}{2} x^{18} c^{4} b a^{9} + \frac{429}{4} x^{16} b^{8} a^{6} + 858 x^{16} c b^{6} a^{7} + \frac{6435}{4} x^{16} c^{2} b^{4} a^{8} + 715 x^{16} c^{3} b^{2} a^{9} + \frac{143}{4} x^{16} c^{4} a^{10} + \frac{858}{7} x^{14} b^{7} a^{7} + \frac{1287}{2} x^{14} c b^{5} a^{8} + 715 x^{14} c^{2} b^{3} a^{9} + 143 x^{14} c^{3} b a^{10} + \frac{429}{4} x^{12} b^{6} a^{8} + \frac{715}{2} x^{12} c b^{4} a^{9} + \frac{429}{2} x^{12} c^{2} b^{2} a^{10} + 13 x^{12} c^{3} a^{11} + \frac{143}{2} x^{10} b^{5} a^{9} + 143 x^{10} c b^{3} a^{10} + 39 x^{10} c^{2} b a^{11} + \frac{143}{4} x^{8} b^{4} a^{10} + 39 x^{8} c b^{2} a^{11} + \frac{13}{4} x^{8} c^{2} a^{12} + 13 x^{6} b^{3} a^{11} + \frac{13}{2} x^{6} c b a^{12} + \frac{13}{4} x^{4} b^{2} a^{12} + \frac{1}{2} x^{4} c a^{13} + \frac{1}{2} x^{2} b a^{13}"," ",0,"1/28*x^56*c^14 + 1/2*x^54*c^13*b + 13/4*x^52*c^12*b^2 + 1/2*x^52*c^13*a + 13*x^50*c^11*b^3 + 13/2*x^50*c^12*b*a + 143/4*x^48*c^10*b^4 + 39*x^48*c^11*b^2*a + 13/4*x^48*c^12*a^2 + 143/2*x^46*c^9*b^5 + 143*x^46*c^10*b^3*a + 39*x^46*c^11*b*a^2 + 429/4*x^44*c^8*b^6 + 715/2*x^44*c^9*b^4*a + 429/2*x^44*c^10*b^2*a^2 + 13*x^44*c^11*a^3 + 858/7*x^42*c^7*b^7 + 1287/2*x^42*c^8*b^5*a + 715*x^42*c^9*b^3*a^2 + 143*x^42*c^10*b*a^3 + 429/4*x^40*c^6*b^8 + 858*x^40*c^7*b^6*a + 6435/4*x^40*c^8*b^4*a^2 + 715*x^40*c^9*b^2*a^3 + 143/4*x^40*c^10*a^4 + 143/2*x^38*c^5*b^9 + 858*x^38*c^6*b^7*a + 2574*x^38*c^7*b^5*a^2 + 2145*x^38*c^8*b^3*a^3 + 715/2*x^38*c^9*b*a^4 + 143/4*x^36*c^4*b^10 + 1287/2*x^36*c^5*b^8*a + 3003*x^36*c^6*b^6*a^2 + 4290*x^36*c^7*b^4*a^3 + 6435/4*x^36*c^8*b^2*a^4 + 143/2*x^36*c^9*a^5 + 13*x^34*c^3*b^11 + 715/2*x^34*c^4*b^9*a + 2574*x^34*c^5*b^7*a^2 + 6006*x^34*c^6*b^5*a^3 + 4290*x^34*c^7*b^3*a^4 + 1287/2*x^34*c^8*b*a^5 + 13/4*x^32*c^2*b^12 + 143*x^32*c^3*b^10*a + 6435/4*x^32*c^4*b^8*a^2 + 6006*x^32*c^5*b^6*a^3 + 15015/2*x^32*c^6*b^4*a^4 + 2574*x^32*c^7*b^2*a^5 + 429/4*x^32*c^8*a^6 + 1/2*x^30*c*b^13 + 39*x^30*c^2*b^11*a + 715*x^30*c^3*b^9*a^2 + 4290*x^30*c^4*b^7*a^3 + 9009*x^30*c^5*b^5*a^4 + 6006*x^30*c^6*b^3*a^5 + 858*x^30*c^7*b*a^6 + 1/28*x^28*b^14 + 13/2*x^28*c*b^12*a + 429/2*x^28*c^2*b^10*a^2 + 2145*x^28*c^3*b^8*a^3 + 15015/2*x^28*c^4*b^6*a^4 + 9009*x^28*c^5*b^4*a^5 + 3003*x^28*c^6*b^2*a^6 + 858/7*x^28*c^7*a^7 + 1/2*x^26*b^13*a + 39*x^26*c*b^11*a^2 + 715*x^26*c^2*b^9*a^3 + 4290*x^26*c^3*b^7*a^4 + 9009*x^26*c^4*b^5*a^5 + 6006*x^26*c^5*b^3*a^6 + 858*x^26*c^6*b*a^7 + 13/4*x^24*b^12*a^2 + 143*x^24*c*b^10*a^3 + 6435/4*x^24*c^2*b^8*a^4 + 6006*x^24*c^3*b^6*a^5 + 15015/2*x^24*c^4*b^4*a^6 + 2574*x^24*c^5*b^2*a^7 + 429/4*x^24*c^6*a^8 + 13*x^22*b^11*a^3 + 715/2*x^22*c*b^9*a^4 + 2574*x^22*c^2*b^7*a^5 + 6006*x^22*c^3*b^5*a^6 + 4290*x^22*c^4*b^3*a^7 + 1287/2*x^22*c^5*b*a^8 + 143/4*x^20*b^10*a^4 + 1287/2*x^20*c*b^8*a^5 + 3003*x^20*c^2*b^6*a^6 + 4290*x^20*c^3*b^4*a^7 + 6435/4*x^20*c^4*b^2*a^8 + 143/2*x^20*c^5*a^9 + 143/2*x^18*b^9*a^5 + 858*x^18*c*b^7*a^6 + 2574*x^18*c^2*b^5*a^7 + 2145*x^18*c^3*b^3*a^8 + 715/2*x^18*c^4*b*a^9 + 429/4*x^16*b^8*a^6 + 858*x^16*c*b^6*a^7 + 6435/4*x^16*c^2*b^4*a^8 + 715*x^16*c^3*b^2*a^9 + 143/4*x^16*c^4*a^10 + 858/7*x^14*b^7*a^7 + 1287/2*x^14*c*b^5*a^8 + 715*x^14*c^2*b^3*a^9 + 143*x^14*c^3*b*a^10 + 429/4*x^12*b^6*a^8 + 715/2*x^12*c*b^4*a^9 + 429/2*x^12*c^2*b^2*a^10 + 13*x^12*c^3*a^11 + 143/2*x^10*b^5*a^9 + 143*x^10*c*b^3*a^10 + 39*x^10*c^2*b*a^11 + 143/4*x^8*b^4*a^10 + 39*x^8*c*b^2*a^11 + 13/4*x^8*c^2*a^12 + 13*x^6*b^3*a^11 + 13/2*x^6*c*b*a^12 + 13/4*x^4*b^2*a^12 + 1/2*x^4*c*a^13 + 1/2*x^2*b*a^13","B",0
95,1,1454,0,0.773483," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3+a)^13,x, algorithm=""fricas"")","\frac{1}{42} x^{84} c^{14} + \frac{1}{3} x^{81} c^{13} b + \frac{13}{6} x^{78} c^{12} b^{2} + \frac{1}{3} x^{78} c^{13} a + \frac{26}{3} x^{75} c^{11} b^{3} + \frac{13}{3} x^{75} c^{12} b a + \frac{143}{6} x^{72} c^{10} b^{4} + 26 x^{72} c^{11} b^{2} a + \frac{13}{6} x^{72} c^{12} a^{2} + \frac{143}{3} x^{69} c^{9} b^{5} + \frac{286}{3} x^{69} c^{10} b^{3} a + 26 x^{69} c^{11} b a^{2} + \frac{143}{2} x^{66} c^{8} b^{6} + \frac{715}{3} x^{66} c^{9} b^{4} a + 143 x^{66} c^{10} b^{2} a^{2} + \frac{26}{3} x^{66} c^{11} a^{3} + \frac{572}{7} x^{63} c^{7} b^{7} + 429 x^{63} c^{8} b^{5} a + \frac{1430}{3} x^{63} c^{9} b^{3} a^{2} + \frac{286}{3} x^{63} c^{10} b a^{3} + \frac{143}{2} x^{60} c^{6} b^{8} + 572 x^{60} c^{7} b^{6} a + \frac{2145}{2} x^{60} c^{8} b^{4} a^{2} + \frac{1430}{3} x^{60} c^{9} b^{2} a^{3} + \frac{143}{6} x^{60} c^{10} a^{4} + \frac{143}{3} x^{57} c^{5} b^{9} + 572 x^{57} c^{6} b^{7} a + 1716 x^{57} c^{7} b^{5} a^{2} + 1430 x^{57} c^{8} b^{3} a^{3} + \frac{715}{3} x^{57} c^{9} b a^{4} + \frac{143}{6} x^{54} c^{4} b^{10} + 429 x^{54} c^{5} b^{8} a + 2002 x^{54} c^{6} b^{6} a^{2} + 2860 x^{54} c^{7} b^{4} a^{3} + \frac{2145}{2} x^{54} c^{8} b^{2} a^{4} + \frac{143}{3} x^{54} c^{9} a^{5} + \frac{26}{3} x^{51} c^{3} b^{11} + \frac{715}{3} x^{51} c^{4} b^{9} a + 1716 x^{51} c^{5} b^{7} a^{2} + 4004 x^{51} c^{6} b^{5} a^{3} + 2860 x^{51} c^{7} b^{3} a^{4} + 429 x^{51} c^{8} b a^{5} + \frac{13}{6} x^{48} c^{2} b^{12} + \frac{286}{3} x^{48} c^{3} b^{10} a + \frac{2145}{2} x^{48} c^{4} b^{8} a^{2} + 4004 x^{48} c^{5} b^{6} a^{3} + 5005 x^{48} c^{6} b^{4} a^{4} + 1716 x^{48} c^{7} b^{2} a^{5} + \frac{143}{2} x^{48} c^{8} a^{6} + \frac{1}{3} x^{45} c b^{13} + 26 x^{45} c^{2} b^{11} a + \frac{1430}{3} x^{45} c^{3} b^{9} a^{2} + 2860 x^{45} c^{4} b^{7} a^{3} + 6006 x^{45} c^{5} b^{5} a^{4} + 4004 x^{45} c^{6} b^{3} a^{5} + 572 x^{45} c^{7} b a^{6} + \frac{1}{42} x^{42} b^{14} + \frac{13}{3} x^{42} c b^{12} a + 143 x^{42} c^{2} b^{10} a^{2} + 1430 x^{42} c^{3} b^{8} a^{3} + 5005 x^{42} c^{4} b^{6} a^{4} + 6006 x^{42} c^{5} b^{4} a^{5} + 2002 x^{42} c^{6} b^{2} a^{6} + \frac{572}{7} x^{42} c^{7} a^{7} + \frac{1}{3} x^{39} b^{13} a + 26 x^{39} c b^{11} a^{2} + \frac{1430}{3} x^{39} c^{2} b^{9} a^{3} + 2860 x^{39} c^{3} b^{7} a^{4} + 6006 x^{39} c^{4} b^{5} a^{5} + 4004 x^{39} c^{5} b^{3} a^{6} + 572 x^{39} c^{6} b a^{7} + \frac{13}{6} x^{36} b^{12} a^{2} + \frac{286}{3} x^{36} c b^{10} a^{3} + \frac{2145}{2} x^{36} c^{2} b^{8} a^{4} + 4004 x^{36} c^{3} b^{6} a^{5} + 5005 x^{36} c^{4} b^{4} a^{6} + 1716 x^{36} c^{5} b^{2} a^{7} + \frac{143}{2} x^{36} c^{6} a^{8} + \frac{26}{3} x^{33} b^{11} a^{3} + \frac{715}{3} x^{33} c b^{9} a^{4} + 1716 x^{33} c^{2} b^{7} a^{5} + 4004 x^{33} c^{3} b^{5} a^{6} + 2860 x^{33} c^{4} b^{3} a^{7} + 429 x^{33} c^{5} b a^{8} + \frac{143}{6} x^{30} b^{10} a^{4} + 429 x^{30} c b^{8} a^{5} + 2002 x^{30} c^{2} b^{6} a^{6} + 2860 x^{30} c^{3} b^{4} a^{7} + \frac{2145}{2} x^{30} c^{4} b^{2} a^{8} + \frac{143}{3} x^{30} c^{5} a^{9} + \frac{143}{3} x^{27} b^{9} a^{5} + 572 x^{27} c b^{7} a^{6} + 1716 x^{27} c^{2} b^{5} a^{7} + 1430 x^{27} c^{3} b^{3} a^{8} + \frac{715}{3} x^{27} c^{4} b a^{9} + \frac{143}{2} x^{24} b^{8} a^{6} + 572 x^{24} c b^{6} a^{7} + \frac{2145}{2} x^{24} c^{2} b^{4} a^{8} + \frac{1430}{3} x^{24} c^{3} b^{2} a^{9} + \frac{143}{6} x^{24} c^{4} a^{10} + \frac{572}{7} x^{21} b^{7} a^{7} + 429 x^{21} c b^{5} a^{8} + \frac{1430}{3} x^{21} c^{2} b^{3} a^{9} + \frac{286}{3} x^{21} c^{3} b a^{10} + \frac{143}{2} x^{18} b^{6} a^{8} + \frac{715}{3} x^{18} c b^{4} a^{9} + 143 x^{18} c^{2} b^{2} a^{10} + \frac{26}{3} x^{18} c^{3} a^{11} + \frac{143}{3} x^{15} b^{5} a^{9} + \frac{286}{3} x^{15} c b^{3} a^{10} + 26 x^{15} c^{2} b a^{11} + \frac{143}{6} x^{12} b^{4} a^{10} + 26 x^{12} c b^{2} a^{11} + \frac{13}{6} x^{12} c^{2} a^{12} + \frac{26}{3} x^{9} b^{3} a^{11} + \frac{13}{3} x^{9} c b a^{12} + \frac{13}{6} x^{6} b^{2} a^{12} + \frac{1}{3} x^{6} c a^{13} + \frac{1}{3} x^{3} b a^{13}"," ",0,"1/42*x^84*c^14 + 1/3*x^81*c^13*b + 13/6*x^78*c^12*b^2 + 1/3*x^78*c^13*a + 26/3*x^75*c^11*b^3 + 13/3*x^75*c^12*b*a + 143/6*x^72*c^10*b^4 + 26*x^72*c^11*b^2*a + 13/6*x^72*c^12*a^2 + 143/3*x^69*c^9*b^5 + 286/3*x^69*c^10*b^3*a + 26*x^69*c^11*b*a^2 + 143/2*x^66*c^8*b^6 + 715/3*x^66*c^9*b^4*a + 143*x^66*c^10*b^2*a^2 + 26/3*x^66*c^11*a^3 + 572/7*x^63*c^7*b^7 + 429*x^63*c^8*b^5*a + 1430/3*x^63*c^9*b^3*a^2 + 286/3*x^63*c^10*b*a^3 + 143/2*x^60*c^6*b^8 + 572*x^60*c^7*b^6*a + 2145/2*x^60*c^8*b^4*a^2 + 1430/3*x^60*c^9*b^2*a^3 + 143/6*x^60*c^10*a^4 + 143/3*x^57*c^5*b^9 + 572*x^57*c^6*b^7*a + 1716*x^57*c^7*b^5*a^2 + 1430*x^57*c^8*b^3*a^3 + 715/3*x^57*c^9*b*a^4 + 143/6*x^54*c^4*b^10 + 429*x^54*c^5*b^8*a + 2002*x^54*c^6*b^6*a^2 + 2860*x^54*c^7*b^4*a^3 + 2145/2*x^54*c^8*b^2*a^4 + 143/3*x^54*c^9*a^5 + 26/3*x^51*c^3*b^11 + 715/3*x^51*c^4*b^9*a + 1716*x^51*c^5*b^7*a^2 + 4004*x^51*c^6*b^5*a^3 + 2860*x^51*c^7*b^3*a^4 + 429*x^51*c^8*b*a^5 + 13/6*x^48*c^2*b^12 + 286/3*x^48*c^3*b^10*a + 2145/2*x^48*c^4*b^8*a^2 + 4004*x^48*c^5*b^6*a^3 + 5005*x^48*c^6*b^4*a^4 + 1716*x^48*c^7*b^2*a^5 + 143/2*x^48*c^8*a^6 + 1/3*x^45*c*b^13 + 26*x^45*c^2*b^11*a + 1430/3*x^45*c^3*b^9*a^2 + 2860*x^45*c^4*b^7*a^3 + 6006*x^45*c^5*b^5*a^4 + 4004*x^45*c^6*b^3*a^5 + 572*x^45*c^7*b*a^6 + 1/42*x^42*b^14 + 13/3*x^42*c*b^12*a + 143*x^42*c^2*b^10*a^2 + 1430*x^42*c^3*b^8*a^3 + 5005*x^42*c^4*b^6*a^4 + 6006*x^42*c^5*b^4*a^5 + 2002*x^42*c^6*b^2*a^6 + 572/7*x^42*c^7*a^7 + 1/3*x^39*b^13*a + 26*x^39*c*b^11*a^2 + 1430/3*x^39*c^2*b^9*a^3 + 2860*x^39*c^3*b^7*a^4 + 6006*x^39*c^4*b^5*a^5 + 4004*x^39*c^5*b^3*a^6 + 572*x^39*c^6*b*a^7 + 13/6*x^36*b^12*a^2 + 286/3*x^36*c*b^10*a^3 + 2145/2*x^36*c^2*b^8*a^4 + 4004*x^36*c^3*b^6*a^5 + 5005*x^36*c^4*b^4*a^6 + 1716*x^36*c^5*b^2*a^7 + 143/2*x^36*c^6*a^8 + 26/3*x^33*b^11*a^3 + 715/3*x^33*c*b^9*a^4 + 1716*x^33*c^2*b^7*a^5 + 4004*x^33*c^3*b^5*a^6 + 2860*x^33*c^4*b^3*a^7 + 429*x^33*c^5*b*a^8 + 143/6*x^30*b^10*a^4 + 429*x^30*c*b^8*a^5 + 2002*x^30*c^2*b^6*a^6 + 2860*x^30*c^3*b^4*a^7 + 2145/2*x^30*c^4*b^2*a^8 + 143/3*x^30*c^5*a^9 + 143/3*x^27*b^9*a^5 + 572*x^27*c*b^7*a^6 + 1716*x^27*c^2*b^5*a^7 + 1430*x^27*c^3*b^3*a^8 + 715/3*x^27*c^4*b*a^9 + 143/2*x^24*b^8*a^6 + 572*x^24*c*b^6*a^7 + 2145/2*x^24*c^2*b^4*a^8 + 1430/3*x^24*c^3*b^2*a^9 + 143/6*x^24*c^4*a^10 + 572/7*x^21*b^7*a^7 + 429*x^21*c*b^5*a^8 + 1430/3*x^21*c^2*b^3*a^9 + 286/3*x^21*c^3*b*a^10 + 143/2*x^18*b^6*a^8 + 715/3*x^18*c*b^4*a^9 + 143*x^18*c^2*b^2*a^10 + 26/3*x^18*c^3*a^11 + 143/3*x^15*b^5*a^9 + 286/3*x^15*c*b^3*a^10 + 26*x^15*c^2*b*a^11 + 143/6*x^12*b^4*a^10 + 26*x^12*c*b^2*a^11 + 13/6*x^12*c^2*a^12 + 26/3*x^9*b^3*a^11 + 13/3*x^9*c*b*a^12 + 13/6*x^6*b^2*a^12 + 1/3*x^6*c*a^13 + 1/3*x^3*b*a^13","B",0
96,1,1297,0,1.218453," ","integrate(x^(-1+n)*(b+2*c*x^n)*(a+b*x^n+c*x^(2*n))^13,x, algorithm=""fricas"")","\frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 14 \, a^{13} b x^{n} + 7 \, {\left(13 \, b^{2} c^{12} + 2 \, a c^{13}\right)} x^{26 \, n} + 182 \, {\left(2 \, b^{3} c^{11} + a b c^{12}\right)} x^{25 \, n} + 91 \, {\left(11 \, b^{4} c^{10} + 12 \, a b^{2} c^{11} + a^{2} c^{12}\right)} x^{24 \, n} + 182 \, {\left(11 \, b^{5} c^{9} + 22 \, a b^{3} c^{10} + 6 \, a^{2} b c^{11}\right)} x^{23 \, n} + 91 \, {\left(33 \, b^{6} c^{8} + 110 \, a b^{4} c^{9} + 66 \, a^{2} b^{2} c^{10} + 4 \, a^{3} c^{11}\right)} x^{22 \, n} + 286 \, {\left(12 \, b^{7} c^{7} + 63 \, a b^{5} c^{8} + 70 \, a^{2} b^{3} c^{9} + 14 \, a^{3} b c^{10}\right)} x^{21 \, n} + 1001 \, {\left(3 \, b^{8} c^{6} + 24 \, a b^{6} c^{7} + 45 \, a^{2} b^{4} c^{8} + 20 \, a^{3} b^{2} c^{9} + a^{4} c^{10}\right)} x^{20 \, n} + 2002 \, {\left(b^{9} c^{5} + 12 \, a b^{7} c^{6} + 36 \, a^{2} b^{5} c^{7} + 30 \, a^{3} b^{3} c^{8} + 5 \, a^{4} b c^{9}\right)} x^{19 \, n} + 1001 \, {\left(b^{10} c^{4} + 18 \, a b^{8} c^{5} + 84 \, a^{2} b^{6} c^{6} + 120 \, a^{3} b^{4} c^{7} + 45 \, a^{4} b^{2} c^{8} + 2 \, a^{5} c^{9}\right)} x^{18 \, n} + 182 \, {\left(2 \, b^{11} c^{3} + 55 \, a b^{9} c^{4} + 396 \, a^{2} b^{7} c^{5} + 924 \, a^{3} b^{5} c^{6} + 660 \, a^{4} b^{3} c^{7} + 99 \, a^{5} b c^{8}\right)} x^{17 \, n} + 91 \, {\left(b^{12} c^{2} + 44 \, a b^{10} c^{3} + 495 \, a^{2} b^{8} c^{4} + 1848 \, a^{3} b^{6} c^{5} + 2310 \, a^{4} b^{4} c^{6} + 792 \, a^{5} b^{2} c^{7} + 33 \, a^{6} c^{8}\right)} x^{16 \, n} + 14 \, {\left(b^{13} c + 78 \, a b^{11} c^{2} + 1430 \, a^{2} b^{9} c^{3} + 8580 \, a^{3} b^{7} c^{4} + 18018 \, a^{4} b^{5} c^{5} + 12012 \, a^{5} b^{3} c^{6} + 1716 \, a^{6} b c^{7}\right)} x^{15 \, n} + {\left(b^{14} + 182 \, a b^{12} c + 6006 \, a^{2} b^{10} c^{2} + 60060 \, a^{3} b^{8} c^{3} + 210210 \, a^{4} b^{6} c^{4} + 252252 \, a^{5} b^{4} c^{5} + 84084 \, a^{6} b^{2} c^{6} + 3432 \, a^{7} c^{7}\right)} x^{14 \, n} + 14 \, {\left(a b^{13} + 78 \, a^{2} b^{11} c + 1430 \, a^{3} b^{9} c^{2} + 8580 \, a^{4} b^{7} c^{3} + 18018 \, a^{5} b^{5} c^{4} + 12012 \, a^{6} b^{3} c^{5} + 1716 \, a^{7} b c^{6}\right)} x^{13 \, n} + 91 \, {\left(a^{2} b^{12} + 44 \, a^{3} b^{10} c + 495 \, a^{4} b^{8} c^{2} + 1848 \, a^{5} b^{6} c^{3} + 2310 \, a^{6} b^{4} c^{4} + 792 \, a^{7} b^{2} c^{5} + 33 \, a^{8} c^{6}\right)} x^{12 \, n} + 182 \, {\left(2 \, a^{3} b^{11} + 55 \, a^{4} b^{9} c + 396 \, a^{5} b^{7} c^{2} + 924 \, a^{6} b^{5} c^{3} + 660 \, a^{7} b^{3} c^{4} + 99 \, a^{8} b c^{5}\right)} x^{11 \, n} + 1001 \, {\left(a^{4} b^{10} + 18 \, a^{5} b^{8} c + 84 \, a^{6} b^{6} c^{2} + 120 \, a^{7} b^{4} c^{3} + 45 \, a^{8} b^{2} c^{4} + 2 \, a^{9} c^{5}\right)} x^{10 \, n} + 2002 \, {\left(a^{5} b^{9} + 12 \, a^{6} b^{7} c + 36 \, a^{7} b^{5} c^{2} + 30 \, a^{8} b^{3} c^{3} + 5 \, a^{9} b c^{4}\right)} x^{9 \, n} + 1001 \, {\left(3 \, a^{6} b^{8} + 24 \, a^{7} b^{6} c + 45 \, a^{8} b^{4} c^{2} + 20 \, a^{9} b^{2} c^{3} + a^{10} c^{4}\right)} x^{8 \, n} + 286 \, {\left(12 \, a^{7} b^{7} + 63 \, a^{8} b^{5} c + 70 \, a^{9} b^{3} c^{2} + 14 \, a^{10} b c^{3}\right)} x^{7 \, n} + 91 \, {\left(33 \, a^{8} b^{6} + 110 \, a^{9} b^{4} c + 66 \, a^{10} b^{2} c^{2} + 4 \, a^{11} c^{3}\right)} x^{6 \, n} + 182 \, {\left(11 \, a^{9} b^{5} + 22 \, a^{10} b^{3} c + 6 \, a^{11} b c^{2}\right)} x^{5 \, n} + 91 \, {\left(11 \, a^{10} b^{4} + 12 \, a^{11} b^{2} c + a^{12} c^{2}\right)} x^{4 \, n} + 182 \, {\left(2 \, a^{11} b^{3} + a^{12} b c\right)} x^{3 \, n} + 7 \, {\left(13 \, a^{12} b^{2} + 2 \, a^{13} c\right)} x^{2 \, n}}{14 \, n}"," ",0,"1/14*(c^14*x^(28*n) + 14*b*c^13*x^(27*n) + 14*a^13*b*x^n + 7*(13*b^2*c^12 + 2*a*c^13)*x^(26*n) + 182*(2*b^3*c^11 + a*b*c^12)*x^(25*n) + 91*(11*b^4*c^10 + 12*a*b^2*c^11 + a^2*c^12)*x^(24*n) + 182*(11*b^5*c^9 + 22*a*b^3*c^10 + 6*a^2*b*c^11)*x^(23*n) + 91*(33*b^6*c^8 + 110*a*b^4*c^9 + 66*a^2*b^2*c^10 + 4*a^3*c^11)*x^(22*n) + 286*(12*b^7*c^7 + 63*a*b^5*c^8 + 70*a^2*b^3*c^9 + 14*a^3*b*c^10)*x^(21*n) + 1001*(3*b^8*c^6 + 24*a*b^6*c^7 + 45*a^2*b^4*c^8 + 20*a^3*b^2*c^9 + a^4*c^10)*x^(20*n) + 2002*(b^9*c^5 + 12*a*b^7*c^6 + 36*a^2*b^5*c^7 + 30*a^3*b^3*c^8 + 5*a^4*b*c^9)*x^(19*n) + 1001*(b^10*c^4 + 18*a*b^8*c^5 + 84*a^2*b^6*c^6 + 120*a^3*b^4*c^7 + 45*a^4*b^2*c^8 + 2*a^5*c^9)*x^(18*n) + 182*(2*b^11*c^3 + 55*a*b^9*c^4 + 396*a^2*b^7*c^5 + 924*a^3*b^5*c^6 + 660*a^4*b^3*c^7 + 99*a^5*b*c^8)*x^(17*n) + 91*(b^12*c^2 + 44*a*b^10*c^3 + 495*a^2*b^8*c^4 + 1848*a^3*b^6*c^5 + 2310*a^4*b^4*c^6 + 792*a^5*b^2*c^7 + 33*a^6*c^8)*x^(16*n) + 14*(b^13*c + 78*a*b^11*c^2 + 1430*a^2*b^9*c^3 + 8580*a^3*b^7*c^4 + 18018*a^4*b^5*c^5 + 12012*a^5*b^3*c^6 + 1716*a^6*b*c^7)*x^(15*n) + (b^14 + 182*a*b^12*c + 6006*a^2*b^10*c^2 + 60060*a^3*b^8*c^3 + 210210*a^4*b^6*c^4 + 252252*a^5*b^4*c^5 + 84084*a^6*b^2*c^6 + 3432*a^7*c^7)*x^(14*n) + 14*(a*b^13 + 78*a^2*b^11*c + 1430*a^3*b^9*c^2 + 8580*a^4*b^7*c^3 + 18018*a^5*b^5*c^4 + 12012*a^6*b^3*c^5 + 1716*a^7*b*c^6)*x^(13*n) + 91*(a^2*b^12 + 44*a^3*b^10*c + 495*a^4*b^8*c^2 + 1848*a^5*b^6*c^3 + 2310*a^6*b^4*c^4 + 792*a^7*b^2*c^5 + 33*a^8*c^6)*x^(12*n) + 182*(2*a^3*b^11 + 55*a^4*b^9*c + 396*a^5*b^7*c^2 + 924*a^6*b^5*c^3 + 660*a^7*b^3*c^4 + 99*a^8*b*c^5)*x^(11*n) + 1001*(a^4*b^10 + 18*a^5*b^8*c + 84*a^6*b^6*c^2 + 120*a^7*b^4*c^3 + 45*a^8*b^2*c^4 + 2*a^9*c^5)*x^(10*n) + 2002*(a^5*b^9 + 12*a^6*b^7*c + 36*a^7*b^5*c^2 + 30*a^8*b^3*c^3 + 5*a^9*b*c^4)*x^(9*n) + 1001*(3*a^6*b^8 + 24*a^7*b^6*c + 45*a^8*b^4*c^2 + 20*a^9*b^2*c^3 + a^10*c^4)*x^(8*n) + 286*(12*a^7*b^7 + 63*a^8*b^5*c + 70*a^9*b^3*c^2 + 14*a^10*b*c^3)*x^(7*n) + 91*(33*a^8*b^6 + 110*a^9*b^4*c + 66*a^10*b^2*c^2 + 4*a^11*c^3)*x^(6*n) + 182*(11*a^9*b^5 + 22*a^10*b^3*c + 6*a^11*b*c^2)*x^(5*n) + 91*(11*a^10*b^4 + 12*a^11*b^2*c + a^12*c^2)*x^(4*n) + 182*(2*a^11*b^3 + a^12*b*c)*x^(3*n) + 7*(13*a^12*b^2 + 2*a^13*c)*x^(2*n))/n","B",0
97,1,1450,0,0.888983," ","integrate((2*c*x+b)*(c*x^2+b*x-a)^13,x, algorithm=""fricas"")","\frac{1}{14} x^{28} c^{14} + x^{27} c^{13} b + \frac{13}{2} x^{26} c^{12} b^{2} - x^{26} c^{13} a + 26 x^{25} c^{11} b^{3} - 13 x^{25} c^{12} b a + \frac{143}{2} x^{24} c^{10} b^{4} - 78 x^{24} c^{11} b^{2} a + \frac{13}{2} x^{24} c^{12} a^{2} + 143 x^{23} c^{9} b^{5} - 286 x^{23} c^{10} b^{3} a + 78 x^{23} c^{11} b a^{2} + \frac{429}{2} x^{22} c^{8} b^{6} - 715 x^{22} c^{9} b^{4} a + 429 x^{22} c^{10} b^{2} a^{2} - 26 x^{22} c^{11} a^{3} + \frac{1716}{7} x^{21} c^{7} b^{7} - 1287 x^{21} c^{8} b^{5} a + 1430 x^{21} c^{9} b^{3} a^{2} - 286 x^{21} c^{10} b a^{3} + \frac{429}{2} x^{20} c^{6} b^{8} - 1716 x^{20} c^{7} b^{6} a + \frac{6435}{2} x^{20} c^{8} b^{4} a^{2} - 1430 x^{20} c^{9} b^{2} a^{3} + \frac{143}{2} x^{20} c^{10} a^{4} + 143 x^{19} c^{5} b^{9} - 1716 x^{19} c^{6} b^{7} a + 5148 x^{19} c^{7} b^{5} a^{2} - 4290 x^{19} c^{8} b^{3} a^{3} + 715 x^{19} c^{9} b a^{4} + \frac{143}{2} x^{18} c^{4} b^{10} - 1287 x^{18} c^{5} b^{8} a + 6006 x^{18} c^{6} b^{6} a^{2} - 8580 x^{18} c^{7} b^{4} a^{3} + \frac{6435}{2} x^{18} c^{8} b^{2} a^{4} - 143 x^{18} c^{9} a^{5} + 26 x^{17} c^{3} b^{11} - 715 x^{17} c^{4} b^{9} a + 5148 x^{17} c^{5} b^{7} a^{2} - 12012 x^{17} c^{6} b^{5} a^{3} + 8580 x^{17} c^{7} b^{3} a^{4} - 1287 x^{17} c^{8} b a^{5} + \frac{13}{2} x^{16} c^{2} b^{12} - 286 x^{16} c^{3} b^{10} a + \frac{6435}{2} x^{16} c^{4} b^{8} a^{2} - 12012 x^{16} c^{5} b^{6} a^{3} + 15015 x^{16} c^{6} b^{4} a^{4} - 5148 x^{16} c^{7} b^{2} a^{5} + \frac{429}{2} x^{16} c^{8} a^{6} + x^{15} c b^{13} - 78 x^{15} c^{2} b^{11} a + 1430 x^{15} c^{3} b^{9} a^{2} - 8580 x^{15} c^{4} b^{7} a^{3} + 18018 x^{15} c^{5} b^{5} a^{4} - 12012 x^{15} c^{6} b^{3} a^{5} + 1716 x^{15} c^{7} b a^{6} + \frac{1}{14} x^{14} b^{14} - 13 x^{14} c b^{12} a + 429 x^{14} c^{2} b^{10} a^{2} - 4290 x^{14} c^{3} b^{8} a^{3} + 15015 x^{14} c^{4} b^{6} a^{4} - 18018 x^{14} c^{5} b^{4} a^{5} + 6006 x^{14} c^{6} b^{2} a^{6} - \frac{1716}{7} x^{14} c^{7} a^{7} - x^{13} b^{13} a + 78 x^{13} c b^{11} a^{2} - 1430 x^{13} c^{2} b^{9} a^{3} + 8580 x^{13} c^{3} b^{7} a^{4} - 18018 x^{13} c^{4} b^{5} a^{5} + 12012 x^{13} c^{5} b^{3} a^{6} - 1716 x^{13} c^{6} b a^{7} + \frac{13}{2} x^{12} b^{12} a^{2} - 286 x^{12} c b^{10} a^{3} + \frac{6435}{2} x^{12} c^{2} b^{8} a^{4} - 12012 x^{12} c^{3} b^{6} a^{5} + 15015 x^{12} c^{4} b^{4} a^{6} - 5148 x^{12} c^{5} b^{2} a^{7} + \frac{429}{2} x^{12} c^{6} a^{8} - 26 x^{11} b^{11} a^{3} + 715 x^{11} c b^{9} a^{4} - 5148 x^{11} c^{2} b^{7} a^{5} + 12012 x^{11} c^{3} b^{5} a^{6} - 8580 x^{11} c^{4} b^{3} a^{7} + 1287 x^{11} c^{5} b a^{8} + \frac{143}{2} x^{10} b^{10} a^{4} - 1287 x^{10} c b^{8} a^{5} + 6006 x^{10} c^{2} b^{6} a^{6} - 8580 x^{10} c^{3} b^{4} a^{7} + \frac{6435}{2} x^{10} c^{4} b^{2} a^{8} - 143 x^{10} c^{5} a^{9} - 143 x^{9} b^{9} a^{5} + 1716 x^{9} c b^{7} a^{6} - 5148 x^{9} c^{2} b^{5} a^{7} + 4290 x^{9} c^{3} b^{3} a^{8} - 715 x^{9} c^{4} b a^{9} + \frac{429}{2} x^{8} b^{8} a^{6} - 1716 x^{8} c b^{6} a^{7} + \frac{6435}{2} x^{8} c^{2} b^{4} a^{8} - 1430 x^{8} c^{3} b^{2} a^{9} + \frac{143}{2} x^{8} c^{4} a^{10} - \frac{1716}{7} x^{7} b^{7} a^{7} + 1287 x^{7} c b^{5} a^{8} - 1430 x^{7} c^{2} b^{3} a^{9} + 286 x^{7} c^{3} b a^{10} + \frac{429}{2} x^{6} b^{6} a^{8} - 715 x^{6} c b^{4} a^{9} + 429 x^{6} c^{2} b^{2} a^{10} - 26 x^{6} c^{3} a^{11} - 143 x^{5} b^{5} a^{9} + 286 x^{5} c b^{3} a^{10} - 78 x^{5} c^{2} b a^{11} + \frac{143}{2} x^{4} b^{4} a^{10} - 78 x^{4} c b^{2} a^{11} + \frac{13}{2} x^{4} c^{2} a^{12} - 26 x^{3} b^{3} a^{11} + 13 x^{3} c b a^{12} + \frac{13}{2} x^{2} b^{2} a^{12} - x^{2} c a^{13} - x b a^{13}"," ",0,"1/14*x^28*c^14 + x^27*c^13*b + 13/2*x^26*c^12*b^2 - x^26*c^13*a + 26*x^25*c^11*b^3 - 13*x^25*c^12*b*a + 143/2*x^24*c^10*b^4 - 78*x^24*c^11*b^2*a + 13/2*x^24*c^12*a^2 + 143*x^23*c^9*b^5 - 286*x^23*c^10*b^3*a + 78*x^23*c^11*b*a^2 + 429/2*x^22*c^8*b^6 - 715*x^22*c^9*b^4*a + 429*x^22*c^10*b^2*a^2 - 26*x^22*c^11*a^3 + 1716/7*x^21*c^7*b^7 - 1287*x^21*c^8*b^5*a + 1430*x^21*c^9*b^3*a^2 - 286*x^21*c^10*b*a^3 + 429/2*x^20*c^6*b^8 - 1716*x^20*c^7*b^6*a + 6435/2*x^20*c^8*b^4*a^2 - 1430*x^20*c^9*b^2*a^3 + 143/2*x^20*c^10*a^4 + 143*x^19*c^5*b^9 - 1716*x^19*c^6*b^7*a + 5148*x^19*c^7*b^5*a^2 - 4290*x^19*c^8*b^3*a^3 + 715*x^19*c^9*b*a^4 + 143/2*x^18*c^4*b^10 - 1287*x^18*c^5*b^8*a + 6006*x^18*c^6*b^6*a^2 - 8580*x^18*c^7*b^4*a^3 + 6435/2*x^18*c^8*b^2*a^4 - 143*x^18*c^9*a^5 + 26*x^17*c^3*b^11 - 715*x^17*c^4*b^9*a + 5148*x^17*c^5*b^7*a^2 - 12012*x^17*c^6*b^5*a^3 + 8580*x^17*c^7*b^3*a^4 - 1287*x^17*c^8*b*a^5 + 13/2*x^16*c^2*b^12 - 286*x^16*c^3*b^10*a + 6435/2*x^16*c^4*b^8*a^2 - 12012*x^16*c^5*b^6*a^3 + 15015*x^16*c^6*b^4*a^4 - 5148*x^16*c^7*b^2*a^5 + 429/2*x^16*c^8*a^6 + x^15*c*b^13 - 78*x^15*c^2*b^11*a + 1430*x^15*c^3*b^9*a^2 - 8580*x^15*c^4*b^7*a^3 + 18018*x^15*c^5*b^5*a^4 - 12012*x^15*c^6*b^3*a^5 + 1716*x^15*c^7*b*a^6 + 1/14*x^14*b^14 - 13*x^14*c*b^12*a + 429*x^14*c^2*b^10*a^2 - 4290*x^14*c^3*b^8*a^3 + 15015*x^14*c^4*b^6*a^4 - 18018*x^14*c^5*b^4*a^5 + 6006*x^14*c^6*b^2*a^6 - 1716/7*x^14*c^7*a^7 - x^13*b^13*a + 78*x^13*c*b^11*a^2 - 1430*x^13*c^2*b^9*a^3 + 8580*x^13*c^3*b^7*a^4 - 18018*x^13*c^4*b^5*a^5 + 12012*x^13*c^5*b^3*a^6 - 1716*x^13*c^6*b*a^7 + 13/2*x^12*b^12*a^2 - 286*x^12*c*b^10*a^3 + 6435/2*x^12*c^2*b^8*a^4 - 12012*x^12*c^3*b^6*a^5 + 15015*x^12*c^4*b^4*a^6 - 5148*x^12*c^5*b^2*a^7 + 429/2*x^12*c^6*a^8 - 26*x^11*b^11*a^3 + 715*x^11*c*b^9*a^4 - 5148*x^11*c^2*b^7*a^5 + 12012*x^11*c^3*b^5*a^6 - 8580*x^11*c^4*b^3*a^7 + 1287*x^11*c^5*b*a^8 + 143/2*x^10*b^10*a^4 - 1287*x^10*c*b^8*a^5 + 6006*x^10*c^2*b^6*a^6 - 8580*x^10*c^3*b^4*a^7 + 6435/2*x^10*c^4*b^2*a^8 - 143*x^10*c^5*a^9 - 143*x^9*b^9*a^5 + 1716*x^9*c*b^7*a^6 - 5148*x^9*c^2*b^5*a^7 + 4290*x^9*c^3*b^3*a^8 - 715*x^9*c^4*b*a^9 + 429/2*x^8*b^8*a^6 - 1716*x^8*c*b^6*a^7 + 6435/2*x^8*c^2*b^4*a^8 - 1430*x^8*c^3*b^2*a^9 + 143/2*x^8*c^4*a^10 - 1716/7*x^7*b^7*a^7 + 1287*x^7*c*b^5*a^8 - 1430*x^7*c^2*b^3*a^9 + 286*x^7*c^3*b*a^10 + 429/2*x^6*b^6*a^8 - 715*x^6*c*b^4*a^9 + 429*x^6*c^2*b^2*a^10 - 26*x^6*c^3*a^11 - 143*x^5*b^5*a^9 + 286*x^5*c*b^3*a^10 - 78*x^5*c^2*b*a^11 + 143/2*x^4*b^4*a^10 - 78*x^4*c*b^2*a^11 + 13/2*x^4*c^2*a^12 - 26*x^3*b^3*a^11 + 13*x^3*c*b*a^12 + 13/2*x^2*b^2*a^12 - x^2*c*a^13 - x*b*a^13","B",0
98,1,1454,0,0.814366," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2-a)^13,x, algorithm=""fricas"")","\frac{1}{28} x^{56} c^{14} + \frac{1}{2} x^{54} c^{13} b + \frac{13}{4} x^{52} c^{12} b^{2} - \frac{1}{2} x^{52} c^{13} a + 13 x^{50} c^{11} b^{3} - \frac{13}{2} x^{50} c^{12} b a + \frac{143}{4} x^{48} c^{10} b^{4} - 39 x^{48} c^{11} b^{2} a + \frac{13}{4} x^{48} c^{12} a^{2} + \frac{143}{2} x^{46} c^{9} b^{5} - 143 x^{46} c^{10} b^{3} a + 39 x^{46} c^{11} b a^{2} + \frac{429}{4} x^{44} c^{8} b^{6} - \frac{715}{2} x^{44} c^{9} b^{4} a + \frac{429}{2} x^{44} c^{10} b^{2} a^{2} - 13 x^{44} c^{11} a^{3} + \frac{858}{7} x^{42} c^{7} b^{7} - \frac{1287}{2} x^{42} c^{8} b^{5} a + 715 x^{42} c^{9} b^{3} a^{2} - 143 x^{42} c^{10} b a^{3} + \frac{429}{4} x^{40} c^{6} b^{8} - 858 x^{40} c^{7} b^{6} a + \frac{6435}{4} x^{40} c^{8} b^{4} a^{2} - 715 x^{40} c^{9} b^{2} a^{3} + \frac{143}{4} x^{40} c^{10} a^{4} + \frac{143}{2} x^{38} c^{5} b^{9} - 858 x^{38} c^{6} b^{7} a + 2574 x^{38} c^{7} b^{5} a^{2} - 2145 x^{38} c^{8} b^{3} a^{3} + \frac{715}{2} x^{38} c^{9} b a^{4} + \frac{143}{4} x^{36} c^{4} b^{10} - \frac{1287}{2} x^{36} c^{5} b^{8} a + 3003 x^{36} c^{6} b^{6} a^{2} - 4290 x^{36} c^{7} b^{4} a^{3} + \frac{6435}{4} x^{36} c^{8} b^{2} a^{4} - \frac{143}{2} x^{36} c^{9} a^{5} + 13 x^{34} c^{3} b^{11} - \frac{715}{2} x^{34} c^{4} b^{9} a + 2574 x^{34} c^{5} b^{7} a^{2} - 6006 x^{34} c^{6} b^{5} a^{3} + 4290 x^{34} c^{7} b^{3} a^{4} - \frac{1287}{2} x^{34} c^{8} b a^{5} + \frac{13}{4} x^{32} c^{2} b^{12} - 143 x^{32} c^{3} b^{10} a + \frac{6435}{4} x^{32} c^{4} b^{8} a^{2} - 6006 x^{32} c^{5} b^{6} a^{3} + \frac{15015}{2} x^{32} c^{6} b^{4} a^{4} - 2574 x^{32} c^{7} b^{2} a^{5} + \frac{429}{4} x^{32} c^{8} a^{6} + \frac{1}{2} x^{30} c b^{13} - 39 x^{30} c^{2} b^{11} a + 715 x^{30} c^{3} b^{9} a^{2} - 4290 x^{30} c^{4} b^{7} a^{3} + 9009 x^{30} c^{5} b^{5} a^{4} - 6006 x^{30} c^{6} b^{3} a^{5} + 858 x^{30} c^{7} b a^{6} + \frac{1}{28} x^{28} b^{14} - \frac{13}{2} x^{28} c b^{12} a + \frac{429}{2} x^{28} c^{2} b^{10} a^{2} - 2145 x^{28} c^{3} b^{8} a^{3} + \frac{15015}{2} x^{28} c^{4} b^{6} a^{4} - 9009 x^{28} c^{5} b^{4} a^{5} + 3003 x^{28} c^{6} b^{2} a^{6} - \frac{858}{7} x^{28} c^{7} a^{7} - \frac{1}{2} x^{26} b^{13} a + 39 x^{26} c b^{11} a^{2} - 715 x^{26} c^{2} b^{9} a^{3} + 4290 x^{26} c^{3} b^{7} a^{4} - 9009 x^{26} c^{4} b^{5} a^{5} + 6006 x^{26} c^{5} b^{3} a^{6} - 858 x^{26} c^{6} b a^{7} + \frac{13}{4} x^{24} b^{12} a^{2} - 143 x^{24} c b^{10} a^{3} + \frac{6435}{4} x^{24} c^{2} b^{8} a^{4} - 6006 x^{24} c^{3} b^{6} a^{5} + \frac{15015}{2} x^{24} c^{4} b^{4} a^{6} - 2574 x^{24} c^{5} b^{2} a^{7} + \frac{429}{4} x^{24} c^{6} a^{8} - 13 x^{22} b^{11} a^{3} + \frac{715}{2} x^{22} c b^{9} a^{4} - 2574 x^{22} c^{2} b^{7} a^{5} + 6006 x^{22} c^{3} b^{5} a^{6} - 4290 x^{22} c^{4} b^{3} a^{7} + \frac{1287}{2} x^{22} c^{5} b a^{8} + \frac{143}{4} x^{20} b^{10} a^{4} - \frac{1287}{2} x^{20} c b^{8} a^{5} + 3003 x^{20} c^{2} b^{6} a^{6} - 4290 x^{20} c^{3} b^{4} a^{7} + \frac{6435}{4} x^{20} c^{4} b^{2} a^{8} - \frac{143}{2} x^{20} c^{5} a^{9} - \frac{143}{2} x^{18} b^{9} a^{5} + 858 x^{18} c b^{7} a^{6} - 2574 x^{18} c^{2} b^{5} a^{7} + 2145 x^{18} c^{3} b^{3} a^{8} - \frac{715}{2} x^{18} c^{4} b a^{9} + \frac{429}{4} x^{16} b^{8} a^{6} - 858 x^{16} c b^{6} a^{7} + \frac{6435}{4} x^{16} c^{2} b^{4} a^{8} - 715 x^{16} c^{3} b^{2} a^{9} + \frac{143}{4} x^{16} c^{4} a^{10} - \frac{858}{7} x^{14} b^{7} a^{7} + \frac{1287}{2} x^{14} c b^{5} a^{8} - 715 x^{14} c^{2} b^{3} a^{9} + 143 x^{14} c^{3} b a^{10} + \frac{429}{4} x^{12} b^{6} a^{8} - \frac{715}{2} x^{12} c b^{4} a^{9} + \frac{429}{2} x^{12} c^{2} b^{2} a^{10} - 13 x^{12} c^{3} a^{11} - \frac{143}{2} x^{10} b^{5} a^{9} + 143 x^{10} c b^{3} a^{10} - 39 x^{10} c^{2} b a^{11} + \frac{143}{4} x^{8} b^{4} a^{10} - 39 x^{8} c b^{2} a^{11} + \frac{13}{4} x^{8} c^{2} a^{12} - 13 x^{6} b^{3} a^{11} + \frac{13}{2} x^{6} c b a^{12} + \frac{13}{4} x^{4} b^{2} a^{12} - \frac{1}{2} x^{4} c a^{13} - \frac{1}{2} x^{2} b a^{13}"," ",0,"1/28*x^56*c^14 + 1/2*x^54*c^13*b + 13/4*x^52*c^12*b^2 - 1/2*x^52*c^13*a + 13*x^50*c^11*b^3 - 13/2*x^50*c^12*b*a + 143/4*x^48*c^10*b^4 - 39*x^48*c^11*b^2*a + 13/4*x^48*c^12*a^2 + 143/2*x^46*c^9*b^5 - 143*x^46*c^10*b^3*a + 39*x^46*c^11*b*a^2 + 429/4*x^44*c^8*b^6 - 715/2*x^44*c^9*b^4*a + 429/2*x^44*c^10*b^2*a^2 - 13*x^44*c^11*a^3 + 858/7*x^42*c^7*b^7 - 1287/2*x^42*c^8*b^5*a + 715*x^42*c^9*b^3*a^2 - 143*x^42*c^10*b*a^3 + 429/4*x^40*c^6*b^8 - 858*x^40*c^7*b^6*a + 6435/4*x^40*c^8*b^4*a^2 - 715*x^40*c^9*b^2*a^3 + 143/4*x^40*c^10*a^4 + 143/2*x^38*c^5*b^9 - 858*x^38*c^6*b^7*a + 2574*x^38*c^7*b^5*a^2 - 2145*x^38*c^8*b^3*a^3 + 715/2*x^38*c^9*b*a^4 + 143/4*x^36*c^4*b^10 - 1287/2*x^36*c^5*b^8*a + 3003*x^36*c^6*b^6*a^2 - 4290*x^36*c^7*b^4*a^3 + 6435/4*x^36*c^8*b^2*a^4 - 143/2*x^36*c^9*a^5 + 13*x^34*c^3*b^11 - 715/2*x^34*c^4*b^9*a + 2574*x^34*c^5*b^7*a^2 - 6006*x^34*c^6*b^5*a^3 + 4290*x^34*c^7*b^3*a^4 - 1287/2*x^34*c^8*b*a^5 + 13/4*x^32*c^2*b^12 - 143*x^32*c^3*b^10*a + 6435/4*x^32*c^4*b^8*a^2 - 6006*x^32*c^5*b^6*a^3 + 15015/2*x^32*c^6*b^4*a^4 - 2574*x^32*c^7*b^2*a^5 + 429/4*x^32*c^8*a^6 + 1/2*x^30*c*b^13 - 39*x^30*c^2*b^11*a + 715*x^30*c^3*b^9*a^2 - 4290*x^30*c^4*b^7*a^3 + 9009*x^30*c^5*b^5*a^4 - 6006*x^30*c^6*b^3*a^5 + 858*x^30*c^7*b*a^6 + 1/28*x^28*b^14 - 13/2*x^28*c*b^12*a + 429/2*x^28*c^2*b^10*a^2 - 2145*x^28*c^3*b^8*a^3 + 15015/2*x^28*c^4*b^6*a^4 - 9009*x^28*c^5*b^4*a^5 + 3003*x^28*c^6*b^2*a^6 - 858/7*x^28*c^7*a^7 - 1/2*x^26*b^13*a + 39*x^26*c*b^11*a^2 - 715*x^26*c^2*b^9*a^3 + 4290*x^26*c^3*b^7*a^4 - 9009*x^26*c^4*b^5*a^5 + 6006*x^26*c^5*b^3*a^6 - 858*x^26*c^6*b*a^7 + 13/4*x^24*b^12*a^2 - 143*x^24*c*b^10*a^3 + 6435/4*x^24*c^2*b^8*a^4 - 6006*x^24*c^3*b^6*a^5 + 15015/2*x^24*c^4*b^4*a^6 - 2574*x^24*c^5*b^2*a^7 + 429/4*x^24*c^6*a^8 - 13*x^22*b^11*a^3 + 715/2*x^22*c*b^9*a^4 - 2574*x^22*c^2*b^7*a^5 + 6006*x^22*c^3*b^5*a^6 - 4290*x^22*c^4*b^3*a^7 + 1287/2*x^22*c^5*b*a^8 + 143/4*x^20*b^10*a^4 - 1287/2*x^20*c*b^8*a^5 + 3003*x^20*c^2*b^6*a^6 - 4290*x^20*c^3*b^4*a^7 + 6435/4*x^20*c^4*b^2*a^8 - 143/2*x^20*c^5*a^9 - 143/2*x^18*b^9*a^5 + 858*x^18*c*b^7*a^6 - 2574*x^18*c^2*b^5*a^7 + 2145*x^18*c^3*b^3*a^8 - 715/2*x^18*c^4*b*a^9 + 429/4*x^16*b^8*a^6 - 858*x^16*c*b^6*a^7 + 6435/4*x^16*c^2*b^4*a^8 - 715*x^16*c^3*b^2*a^9 + 143/4*x^16*c^4*a^10 - 858/7*x^14*b^7*a^7 + 1287/2*x^14*c*b^5*a^8 - 715*x^14*c^2*b^3*a^9 + 143*x^14*c^3*b*a^10 + 429/4*x^12*b^6*a^8 - 715/2*x^12*c*b^4*a^9 + 429/2*x^12*c^2*b^2*a^10 - 13*x^12*c^3*a^11 - 143/2*x^10*b^5*a^9 + 143*x^10*c*b^3*a^10 - 39*x^10*c^2*b*a^11 + 143/4*x^8*b^4*a^10 - 39*x^8*c*b^2*a^11 + 13/4*x^8*c^2*a^12 - 13*x^6*b^3*a^11 + 13/2*x^6*c*b*a^12 + 13/4*x^4*b^2*a^12 - 1/2*x^4*c*a^13 - 1/2*x^2*b*a^13","B",0
99,1,1454,0,0.804330," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^13,x, algorithm=""fricas"")","\frac{1}{42} x^{84} c^{14} + \frac{1}{3} x^{81} c^{13} b + \frac{13}{6} x^{78} c^{12} b^{2} - \frac{1}{3} x^{78} c^{13} a + \frac{26}{3} x^{75} c^{11} b^{3} - \frac{13}{3} x^{75} c^{12} b a + \frac{143}{6} x^{72} c^{10} b^{4} - 26 x^{72} c^{11} b^{2} a + \frac{13}{6} x^{72} c^{12} a^{2} + \frac{143}{3} x^{69} c^{9} b^{5} - \frac{286}{3} x^{69} c^{10} b^{3} a + 26 x^{69} c^{11} b a^{2} + \frac{143}{2} x^{66} c^{8} b^{6} - \frac{715}{3} x^{66} c^{9} b^{4} a + 143 x^{66} c^{10} b^{2} a^{2} - \frac{26}{3} x^{66} c^{11} a^{3} + \frac{572}{7} x^{63} c^{7} b^{7} - 429 x^{63} c^{8} b^{5} a + \frac{1430}{3} x^{63} c^{9} b^{3} a^{2} - \frac{286}{3} x^{63} c^{10} b a^{3} + \frac{143}{2} x^{60} c^{6} b^{8} - 572 x^{60} c^{7} b^{6} a + \frac{2145}{2} x^{60} c^{8} b^{4} a^{2} - \frac{1430}{3} x^{60} c^{9} b^{2} a^{3} + \frac{143}{6} x^{60} c^{10} a^{4} + \frac{143}{3} x^{57} c^{5} b^{9} - 572 x^{57} c^{6} b^{7} a + 1716 x^{57} c^{7} b^{5} a^{2} - 1430 x^{57} c^{8} b^{3} a^{3} + \frac{715}{3} x^{57} c^{9} b a^{4} + \frac{143}{6} x^{54} c^{4} b^{10} - 429 x^{54} c^{5} b^{8} a + 2002 x^{54} c^{6} b^{6} a^{2} - 2860 x^{54} c^{7} b^{4} a^{3} + \frac{2145}{2} x^{54} c^{8} b^{2} a^{4} - \frac{143}{3} x^{54} c^{9} a^{5} + \frac{26}{3} x^{51} c^{3} b^{11} - \frac{715}{3} x^{51} c^{4} b^{9} a + 1716 x^{51} c^{5} b^{7} a^{2} - 4004 x^{51} c^{6} b^{5} a^{3} + 2860 x^{51} c^{7} b^{3} a^{4} - 429 x^{51} c^{8} b a^{5} + \frac{13}{6} x^{48} c^{2} b^{12} - \frac{286}{3} x^{48} c^{3} b^{10} a + \frac{2145}{2} x^{48} c^{4} b^{8} a^{2} - 4004 x^{48} c^{5} b^{6} a^{3} + 5005 x^{48} c^{6} b^{4} a^{4} - 1716 x^{48} c^{7} b^{2} a^{5} + \frac{143}{2} x^{48} c^{8} a^{6} + \frac{1}{3} x^{45} c b^{13} - 26 x^{45} c^{2} b^{11} a + \frac{1430}{3} x^{45} c^{3} b^{9} a^{2} - 2860 x^{45} c^{4} b^{7} a^{3} + 6006 x^{45} c^{5} b^{5} a^{4} - 4004 x^{45} c^{6} b^{3} a^{5} + 572 x^{45} c^{7} b a^{6} + \frac{1}{42} x^{42} b^{14} - \frac{13}{3} x^{42} c b^{12} a + 143 x^{42} c^{2} b^{10} a^{2} - 1430 x^{42} c^{3} b^{8} a^{3} + 5005 x^{42} c^{4} b^{6} a^{4} - 6006 x^{42} c^{5} b^{4} a^{5} + 2002 x^{42} c^{6} b^{2} a^{6} - \frac{572}{7} x^{42} c^{7} a^{7} - \frac{1}{3} x^{39} b^{13} a + 26 x^{39} c b^{11} a^{2} - \frac{1430}{3} x^{39} c^{2} b^{9} a^{3} + 2860 x^{39} c^{3} b^{7} a^{4} - 6006 x^{39} c^{4} b^{5} a^{5} + 4004 x^{39} c^{5} b^{3} a^{6} - 572 x^{39} c^{6} b a^{7} + \frac{13}{6} x^{36} b^{12} a^{2} - \frac{286}{3} x^{36} c b^{10} a^{3} + \frac{2145}{2} x^{36} c^{2} b^{8} a^{4} - 4004 x^{36} c^{3} b^{6} a^{5} + 5005 x^{36} c^{4} b^{4} a^{6} - 1716 x^{36} c^{5} b^{2} a^{7} + \frac{143}{2} x^{36} c^{6} a^{8} - \frac{26}{3} x^{33} b^{11} a^{3} + \frac{715}{3} x^{33} c b^{9} a^{4} - 1716 x^{33} c^{2} b^{7} a^{5} + 4004 x^{33} c^{3} b^{5} a^{6} - 2860 x^{33} c^{4} b^{3} a^{7} + 429 x^{33} c^{5} b a^{8} + \frac{143}{6} x^{30} b^{10} a^{4} - 429 x^{30} c b^{8} a^{5} + 2002 x^{30} c^{2} b^{6} a^{6} - 2860 x^{30} c^{3} b^{4} a^{7} + \frac{2145}{2} x^{30} c^{4} b^{2} a^{8} - \frac{143}{3} x^{30} c^{5} a^{9} - \frac{143}{3} x^{27} b^{9} a^{5} + 572 x^{27} c b^{7} a^{6} - 1716 x^{27} c^{2} b^{5} a^{7} + 1430 x^{27} c^{3} b^{3} a^{8} - \frac{715}{3} x^{27} c^{4} b a^{9} + \frac{143}{2} x^{24} b^{8} a^{6} - 572 x^{24} c b^{6} a^{7} + \frac{2145}{2} x^{24} c^{2} b^{4} a^{8} - \frac{1430}{3} x^{24} c^{3} b^{2} a^{9} + \frac{143}{6} x^{24} c^{4} a^{10} - \frac{572}{7} x^{21} b^{7} a^{7} + 429 x^{21} c b^{5} a^{8} - \frac{1430}{3} x^{21} c^{2} b^{3} a^{9} + \frac{286}{3} x^{21} c^{3} b a^{10} + \frac{143}{2} x^{18} b^{6} a^{8} - \frac{715}{3} x^{18} c b^{4} a^{9} + 143 x^{18} c^{2} b^{2} a^{10} - \frac{26}{3} x^{18} c^{3} a^{11} - \frac{143}{3} x^{15} b^{5} a^{9} + \frac{286}{3} x^{15} c b^{3} a^{10} - 26 x^{15} c^{2} b a^{11} + \frac{143}{6} x^{12} b^{4} a^{10} - 26 x^{12} c b^{2} a^{11} + \frac{13}{6} x^{12} c^{2} a^{12} - \frac{26}{3} x^{9} b^{3} a^{11} + \frac{13}{3} x^{9} c b a^{12} + \frac{13}{6} x^{6} b^{2} a^{12} - \frac{1}{3} x^{6} c a^{13} - \frac{1}{3} x^{3} b a^{13}"," ",0,"1/42*x^84*c^14 + 1/3*x^81*c^13*b + 13/6*x^78*c^12*b^2 - 1/3*x^78*c^13*a + 26/3*x^75*c^11*b^3 - 13/3*x^75*c^12*b*a + 143/6*x^72*c^10*b^4 - 26*x^72*c^11*b^2*a + 13/6*x^72*c^12*a^2 + 143/3*x^69*c^9*b^5 - 286/3*x^69*c^10*b^3*a + 26*x^69*c^11*b*a^2 + 143/2*x^66*c^8*b^6 - 715/3*x^66*c^9*b^4*a + 143*x^66*c^10*b^2*a^2 - 26/3*x^66*c^11*a^3 + 572/7*x^63*c^7*b^7 - 429*x^63*c^8*b^5*a + 1430/3*x^63*c^9*b^3*a^2 - 286/3*x^63*c^10*b*a^3 + 143/2*x^60*c^6*b^8 - 572*x^60*c^7*b^6*a + 2145/2*x^60*c^8*b^4*a^2 - 1430/3*x^60*c^9*b^2*a^3 + 143/6*x^60*c^10*a^4 + 143/3*x^57*c^5*b^9 - 572*x^57*c^6*b^7*a + 1716*x^57*c^7*b^5*a^2 - 1430*x^57*c^8*b^3*a^3 + 715/3*x^57*c^9*b*a^4 + 143/6*x^54*c^4*b^10 - 429*x^54*c^5*b^8*a + 2002*x^54*c^6*b^6*a^2 - 2860*x^54*c^7*b^4*a^3 + 2145/2*x^54*c^8*b^2*a^4 - 143/3*x^54*c^9*a^5 + 26/3*x^51*c^3*b^11 - 715/3*x^51*c^4*b^9*a + 1716*x^51*c^5*b^7*a^2 - 4004*x^51*c^6*b^5*a^3 + 2860*x^51*c^7*b^3*a^4 - 429*x^51*c^8*b*a^5 + 13/6*x^48*c^2*b^12 - 286/3*x^48*c^3*b^10*a + 2145/2*x^48*c^4*b^8*a^2 - 4004*x^48*c^5*b^6*a^3 + 5005*x^48*c^6*b^4*a^4 - 1716*x^48*c^7*b^2*a^5 + 143/2*x^48*c^8*a^6 + 1/3*x^45*c*b^13 - 26*x^45*c^2*b^11*a + 1430/3*x^45*c^3*b^9*a^2 - 2860*x^45*c^4*b^7*a^3 + 6006*x^45*c^5*b^5*a^4 - 4004*x^45*c^6*b^3*a^5 + 572*x^45*c^7*b*a^6 + 1/42*x^42*b^14 - 13/3*x^42*c*b^12*a + 143*x^42*c^2*b^10*a^2 - 1430*x^42*c^3*b^8*a^3 + 5005*x^42*c^4*b^6*a^4 - 6006*x^42*c^5*b^4*a^5 + 2002*x^42*c^6*b^2*a^6 - 572/7*x^42*c^7*a^7 - 1/3*x^39*b^13*a + 26*x^39*c*b^11*a^2 - 1430/3*x^39*c^2*b^9*a^3 + 2860*x^39*c^3*b^7*a^4 - 6006*x^39*c^4*b^5*a^5 + 4004*x^39*c^5*b^3*a^6 - 572*x^39*c^6*b*a^7 + 13/6*x^36*b^12*a^2 - 286/3*x^36*c*b^10*a^3 + 2145/2*x^36*c^2*b^8*a^4 - 4004*x^36*c^3*b^6*a^5 + 5005*x^36*c^4*b^4*a^6 - 1716*x^36*c^5*b^2*a^7 + 143/2*x^36*c^6*a^8 - 26/3*x^33*b^11*a^3 + 715/3*x^33*c*b^9*a^4 - 1716*x^33*c^2*b^7*a^5 + 4004*x^33*c^3*b^5*a^6 - 2860*x^33*c^4*b^3*a^7 + 429*x^33*c^5*b*a^8 + 143/6*x^30*b^10*a^4 - 429*x^30*c*b^8*a^5 + 2002*x^30*c^2*b^6*a^6 - 2860*x^30*c^3*b^4*a^7 + 2145/2*x^30*c^4*b^2*a^8 - 143/3*x^30*c^5*a^9 - 143/3*x^27*b^9*a^5 + 572*x^27*c*b^7*a^6 - 1716*x^27*c^2*b^5*a^7 + 1430*x^27*c^3*b^3*a^8 - 715/3*x^27*c^4*b*a^9 + 143/2*x^24*b^8*a^6 - 572*x^24*c*b^6*a^7 + 2145/2*x^24*c^2*b^4*a^8 - 1430/3*x^24*c^3*b^2*a^9 + 143/6*x^24*c^4*a^10 - 572/7*x^21*b^7*a^7 + 429*x^21*c*b^5*a^8 - 1430/3*x^21*c^2*b^3*a^9 + 286/3*x^21*c^3*b*a^10 + 143/2*x^18*b^6*a^8 - 715/3*x^18*c*b^4*a^9 + 143*x^18*c^2*b^2*a^10 - 26/3*x^18*c^3*a^11 - 143/3*x^15*b^5*a^9 + 286/3*x^15*c*b^3*a^10 - 26*x^15*c^2*b*a^11 + 143/6*x^12*b^4*a^10 - 26*x^12*c*b^2*a^11 + 13/6*x^12*c^2*a^12 - 26/3*x^9*b^3*a^11 + 13/3*x^9*c*b*a^12 + 13/6*x^6*b^2*a^12 - 1/3*x^6*c*a^13 - 1/3*x^3*b*a^13","B",0
100,1,1299,0,0.860840," ","integrate(x^(-1+n)*(b+2*c*x^n)*(-a+b*x^n+c*x^(2*n))^13,x, algorithm=""fricas"")","\frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} - 14 \, a^{13} b x^{n} + 7 \, {\left(13 \, b^{2} c^{12} - 2 \, a c^{13}\right)} x^{26 \, n} + 182 \, {\left(2 \, b^{3} c^{11} - a b c^{12}\right)} x^{25 \, n} + 91 \, {\left(11 \, b^{4} c^{10} - 12 \, a b^{2} c^{11} + a^{2} c^{12}\right)} x^{24 \, n} + 182 \, {\left(11 \, b^{5} c^{9} - 22 \, a b^{3} c^{10} + 6 \, a^{2} b c^{11}\right)} x^{23 \, n} + 91 \, {\left(33 \, b^{6} c^{8} - 110 \, a b^{4} c^{9} + 66 \, a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}\right)} x^{22 \, n} + 286 \, {\left(12 \, b^{7} c^{7} - 63 \, a b^{5} c^{8} + 70 \, a^{2} b^{3} c^{9} - 14 \, a^{3} b c^{10}\right)} x^{21 \, n} + 1001 \, {\left(3 \, b^{8} c^{6} - 24 \, a b^{6} c^{7} + 45 \, a^{2} b^{4} c^{8} - 20 \, a^{3} b^{2} c^{9} + a^{4} c^{10}\right)} x^{20 \, n} + 2002 \, {\left(b^{9} c^{5} - 12 \, a b^{7} c^{6} + 36 \, a^{2} b^{5} c^{7} - 30 \, a^{3} b^{3} c^{8} + 5 \, a^{4} b c^{9}\right)} x^{19 \, n} + 1001 \, {\left(b^{10} c^{4} - 18 \, a b^{8} c^{5} + 84 \, a^{2} b^{6} c^{6} - 120 \, a^{3} b^{4} c^{7} + 45 \, a^{4} b^{2} c^{8} - 2 \, a^{5} c^{9}\right)} x^{18 \, n} + 182 \, {\left(2 \, b^{11} c^{3} - 55 \, a b^{9} c^{4} + 396 \, a^{2} b^{7} c^{5} - 924 \, a^{3} b^{5} c^{6} + 660 \, a^{4} b^{3} c^{7} - 99 \, a^{5} b c^{8}\right)} x^{17 \, n} + 91 \, {\left(b^{12} c^{2} - 44 \, a b^{10} c^{3} + 495 \, a^{2} b^{8} c^{4} - 1848 \, a^{3} b^{6} c^{5} + 2310 \, a^{4} b^{4} c^{6} - 792 \, a^{5} b^{2} c^{7} + 33 \, a^{6} c^{8}\right)} x^{16 \, n} + 14 \, {\left(b^{13} c - 78 \, a b^{11} c^{2} + 1430 \, a^{2} b^{9} c^{3} - 8580 \, a^{3} b^{7} c^{4} + 18018 \, a^{4} b^{5} c^{5} - 12012 \, a^{5} b^{3} c^{6} + 1716 \, a^{6} b c^{7}\right)} x^{15 \, n} + {\left(b^{14} - 182 \, a b^{12} c + 6006 \, a^{2} b^{10} c^{2} - 60060 \, a^{3} b^{8} c^{3} + 210210 \, a^{4} b^{6} c^{4} - 252252 \, a^{5} b^{4} c^{5} + 84084 \, a^{6} b^{2} c^{6} - 3432 \, a^{7} c^{7}\right)} x^{14 \, n} - 14 \, {\left(a b^{13} - 78 \, a^{2} b^{11} c + 1430 \, a^{3} b^{9} c^{2} - 8580 \, a^{4} b^{7} c^{3} + 18018 \, a^{5} b^{5} c^{4} - 12012 \, a^{6} b^{3} c^{5} + 1716 \, a^{7} b c^{6}\right)} x^{13 \, n} + 91 \, {\left(a^{2} b^{12} - 44 \, a^{3} b^{10} c + 495 \, a^{4} b^{8} c^{2} - 1848 \, a^{5} b^{6} c^{3} + 2310 \, a^{6} b^{4} c^{4} - 792 \, a^{7} b^{2} c^{5} + 33 \, a^{8} c^{6}\right)} x^{12 \, n} - 182 \, {\left(2 \, a^{3} b^{11} - 55 \, a^{4} b^{9} c + 396 \, a^{5} b^{7} c^{2} - 924 \, a^{6} b^{5} c^{3} + 660 \, a^{7} b^{3} c^{4} - 99 \, a^{8} b c^{5}\right)} x^{11 \, n} + 1001 \, {\left(a^{4} b^{10} - 18 \, a^{5} b^{8} c + 84 \, a^{6} b^{6} c^{2} - 120 \, a^{7} b^{4} c^{3} + 45 \, a^{8} b^{2} c^{4} - 2 \, a^{9} c^{5}\right)} x^{10 \, n} - 2002 \, {\left(a^{5} b^{9} - 12 \, a^{6} b^{7} c + 36 \, a^{7} b^{5} c^{2} - 30 \, a^{8} b^{3} c^{3} + 5 \, a^{9} b c^{4}\right)} x^{9 \, n} + 1001 \, {\left(3 \, a^{6} b^{8} - 24 \, a^{7} b^{6} c + 45 \, a^{8} b^{4} c^{2} - 20 \, a^{9} b^{2} c^{3} + a^{10} c^{4}\right)} x^{8 \, n} - 286 \, {\left(12 \, a^{7} b^{7} - 63 \, a^{8} b^{5} c + 70 \, a^{9} b^{3} c^{2} - 14 \, a^{10} b c^{3}\right)} x^{7 \, n} + 91 \, {\left(33 \, a^{8} b^{6} - 110 \, a^{9} b^{4} c + 66 \, a^{10} b^{2} c^{2} - 4 \, a^{11} c^{3}\right)} x^{6 \, n} - 182 \, {\left(11 \, a^{9} b^{5} - 22 \, a^{10} b^{3} c + 6 \, a^{11} b c^{2}\right)} x^{5 \, n} + 91 \, {\left(11 \, a^{10} b^{4} - 12 \, a^{11} b^{2} c + a^{12} c^{2}\right)} x^{4 \, n} - 182 \, {\left(2 \, a^{11} b^{3} - a^{12} b c\right)} x^{3 \, n} + 7 \, {\left(13 \, a^{12} b^{2} - 2 \, a^{13} c\right)} x^{2 \, n}}{14 \, n}"," ",0,"1/14*(c^14*x^(28*n) + 14*b*c^13*x^(27*n) - 14*a^13*b*x^n + 7*(13*b^2*c^12 - 2*a*c^13)*x^(26*n) + 182*(2*b^3*c^11 - a*b*c^12)*x^(25*n) + 91*(11*b^4*c^10 - 12*a*b^2*c^11 + a^2*c^12)*x^(24*n) + 182*(11*b^5*c^9 - 22*a*b^3*c^10 + 6*a^2*b*c^11)*x^(23*n) + 91*(33*b^6*c^8 - 110*a*b^4*c^9 + 66*a^2*b^2*c^10 - 4*a^3*c^11)*x^(22*n) + 286*(12*b^7*c^7 - 63*a*b^5*c^8 + 70*a^2*b^3*c^9 - 14*a^3*b*c^10)*x^(21*n) + 1001*(3*b^8*c^6 - 24*a*b^6*c^7 + 45*a^2*b^4*c^8 - 20*a^3*b^2*c^9 + a^4*c^10)*x^(20*n) + 2002*(b^9*c^5 - 12*a*b^7*c^6 + 36*a^2*b^5*c^7 - 30*a^3*b^3*c^8 + 5*a^4*b*c^9)*x^(19*n) + 1001*(b^10*c^4 - 18*a*b^8*c^5 + 84*a^2*b^6*c^6 - 120*a^3*b^4*c^7 + 45*a^4*b^2*c^8 - 2*a^5*c^9)*x^(18*n) + 182*(2*b^11*c^3 - 55*a*b^9*c^4 + 396*a^2*b^7*c^5 - 924*a^3*b^5*c^6 + 660*a^4*b^3*c^7 - 99*a^5*b*c^8)*x^(17*n) + 91*(b^12*c^2 - 44*a*b^10*c^3 + 495*a^2*b^8*c^4 - 1848*a^3*b^6*c^5 + 2310*a^4*b^4*c^6 - 792*a^5*b^2*c^7 + 33*a^6*c^8)*x^(16*n) + 14*(b^13*c - 78*a*b^11*c^2 + 1430*a^2*b^9*c^3 - 8580*a^3*b^7*c^4 + 18018*a^4*b^5*c^5 - 12012*a^5*b^3*c^6 + 1716*a^6*b*c^7)*x^(15*n) + (b^14 - 182*a*b^12*c + 6006*a^2*b^10*c^2 - 60060*a^3*b^8*c^3 + 210210*a^4*b^6*c^4 - 252252*a^5*b^4*c^5 + 84084*a^6*b^2*c^6 - 3432*a^7*c^7)*x^(14*n) - 14*(a*b^13 - 78*a^2*b^11*c + 1430*a^3*b^9*c^2 - 8580*a^4*b^7*c^3 + 18018*a^5*b^5*c^4 - 12012*a^6*b^3*c^5 + 1716*a^7*b*c^6)*x^(13*n) + 91*(a^2*b^12 - 44*a^3*b^10*c + 495*a^4*b^8*c^2 - 1848*a^5*b^6*c^3 + 2310*a^6*b^4*c^4 - 792*a^7*b^2*c^5 + 33*a^8*c^6)*x^(12*n) - 182*(2*a^3*b^11 - 55*a^4*b^9*c + 396*a^5*b^7*c^2 - 924*a^6*b^5*c^3 + 660*a^7*b^3*c^4 - 99*a^8*b*c^5)*x^(11*n) + 1001*(a^4*b^10 - 18*a^5*b^8*c + 84*a^6*b^6*c^2 - 120*a^7*b^4*c^3 + 45*a^8*b^2*c^4 - 2*a^9*c^5)*x^(10*n) - 2002*(a^5*b^9 - 12*a^6*b^7*c + 36*a^7*b^5*c^2 - 30*a^8*b^3*c^3 + 5*a^9*b*c^4)*x^(9*n) + 1001*(3*a^6*b^8 - 24*a^7*b^6*c + 45*a^8*b^4*c^2 - 20*a^9*b^2*c^3 + a^10*c^4)*x^(8*n) - 286*(12*a^7*b^7 - 63*a^8*b^5*c + 70*a^9*b^3*c^2 - 14*a^10*b*c^3)*x^(7*n) + 91*(33*a^8*b^6 - 110*a^9*b^4*c + 66*a^10*b^2*c^2 - 4*a^11*c^3)*x^(6*n) - 182*(11*a^9*b^5 - 22*a^10*b^3*c + 6*a^11*b*c^2)*x^(5*n) + 91*(11*a^10*b^4 - 12*a^11*b^2*c + a^12*c^2)*x^(4*n) - 182*(2*a^11*b^3 - a^12*b*c)*x^(3*n) + 7*(13*a^12*b^2 - 2*a^13*c)*x^(2*n))/n","B",0
101,1,154,0,0.550721," ","integrate((2*c*x+b)*(c*x^2+b*x)^13,x, algorithm=""fricas"")","\frac{1}{14} x^{28} c^{14} + x^{27} c^{13} b + \frac{13}{2} x^{26} c^{12} b^{2} + 26 x^{25} c^{11} b^{3} + \frac{143}{2} x^{24} c^{10} b^{4} + 143 x^{23} c^{9} b^{5} + \frac{429}{2} x^{22} c^{8} b^{6} + \frac{1716}{7} x^{21} c^{7} b^{7} + \frac{429}{2} x^{20} c^{6} b^{8} + 143 x^{19} c^{5} b^{9} + \frac{143}{2} x^{18} c^{4} b^{10} + 26 x^{17} c^{3} b^{11} + \frac{13}{2} x^{16} c^{2} b^{12} + x^{15} c b^{13} + \frac{1}{14} x^{14} b^{14}"," ",0,"1/14*x^28*c^14 + x^27*c^13*b + 13/2*x^26*c^12*b^2 + 26*x^25*c^11*b^3 + 143/2*x^24*c^10*b^4 + 143*x^23*c^9*b^5 + 429/2*x^22*c^8*b^6 + 1716/7*x^21*c^7*b^7 + 429/2*x^20*c^6*b^8 + 143*x^19*c^5*b^9 + 143/2*x^18*c^4*b^10 + 26*x^17*c^3*b^11 + 13/2*x^16*c^2*b^12 + x^15*c*b^13 + 1/14*x^14*b^14","B",0
102,1,156,0,0.724253," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2)^13,x, algorithm=""fricas"")","\frac{1}{28} x^{56} c^{14} + \frac{1}{2} x^{54} c^{13} b + \frac{13}{4} x^{52} c^{12} b^{2} + 13 x^{50} c^{11} b^{3} + \frac{143}{4} x^{48} c^{10} b^{4} + \frac{143}{2} x^{46} c^{9} b^{5} + \frac{429}{4} x^{44} c^{8} b^{6} + \frac{858}{7} x^{42} c^{7} b^{7} + \frac{429}{4} x^{40} c^{6} b^{8} + \frac{143}{2} x^{38} c^{5} b^{9} + \frac{143}{4} x^{36} c^{4} b^{10} + 13 x^{34} c^{3} b^{11} + \frac{13}{4} x^{32} c^{2} b^{12} + \frac{1}{2} x^{30} c b^{13} + \frac{1}{28} x^{28} b^{14}"," ",0,"1/28*x^56*c^14 + 1/2*x^54*c^13*b + 13/4*x^52*c^12*b^2 + 13*x^50*c^11*b^3 + 143/4*x^48*c^10*b^4 + 143/2*x^46*c^9*b^5 + 429/4*x^44*c^8*b^6 + 858/7*x^42*c^7*b^7 + 429/4*x^40*c^6*b^8 + 143/2*x^38*c^5*b^9 + 143/4*x^36*c^4*b^10 + 13*x^34*c^3*b^11 + 13/4*x^32*c^2*b^12 + 1/2*x^30*c*b^13 + 1/28*x^28*b^14","B",0
103,1,156,0,0.741184," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3)^13,x, algorithm=""fricas"")","\frac{1}{42} x^{84} c^{14} + \frac{1}{3} x^{81} c^{13} b + \frac{13}{6} x^{78} c^{12} b^{2} + \frac{26}{3} x^{75} c^{11} b^{3} + \frac{143}{6} x^{72} c^{10} b^{4} + \frac{143}{3} x^{69} c^{9} b^{5} + \frac{143}{2} x^{66} c^{8} b^{6} + \frac{572}{7} x^{63} c^{7} b^{7} + \frac{143}{2} x^{60} c^{6} b^{8} + \frac{143}{3} x^{57} c^{5} b^{9} + \frac{143}{6} x^{54} c^{4} b^{10} + \frac{26}{3} x^{51} c^{3} b^{11} + \frac{13}{6} x^{48} c^{2} b^{12} + \frac{1}{3} x^{45} c b^{13} + \frac{1}{42} x^{42} b^{14}"," ",0,"1/42*x^84*c^14 + 1/3*x^81*c^13*b + 13/6*x^78*c^12*b^2 + 26/3*x^75*c^11*b^3 + 143/6*x^72*c^10*b^4 + 143/3*x^69*c^9*b^5 + 143/2*x^66*c^8*b^6 + 572/7*x^63*c^7*b^7 + 143/2*x^60*c^6*b^8 + 143/3*x^57*c^5*b^9 + 143/6*x^54*c^4*b^10 + 26/3*x^51*c^3*b^11 + 13/6*x^48*c^2*b^12 + 1/3*x^45*c*b^13 + 1/42*x^42*b^14","B",0
104,1,189,0,0.866071," ","integrate(x^(-1+n)*(b+2*c*x^n)*(b*x^n+c*x^(2*n))^13,x, algorithm=""fricas"")","\frac{c^{14} x^{28 \, n} + 14 \, b c^{13} x^{27 \, n} + 91 \, b^{2} c^{12} x^{26 \, n} + 364 \, b^{3} c^{11} x^{25 \, n} + 1001 \, b^{4} c^{10} x^{24 \, n} + 2002 \, b^{5} c^{9} x^{23 \, n} + 3003 \, b^{6} c^{8} x^{22 \, n} + 3432 \, b^{7} c^{7} x^{21 \, n} + 3003 \, b^{8} c^{6} x^{20 \, n} + 2002 \, b^{9} c^{5} x^{19 \, n} + 1001 \, b^{10} c^{4} x^{18 \, n} + 364 \, b^{11} c^{3} x^{17 \, n} + 91 \, b^{12} c^{2} x^{16 \, n} + 14 \, b^{13} c x^{15 \, n} + b^{14} x^{14 \, n}}{14 \, n}"," ",0,"1/14*(c^14*x^(28*n) + 14*b*c^13*x^(27*n) + 91*b^2*c^12*x^(26*n) + 364*b^3*c^11*x^(25*n) + 1001*b^4*c^10*x^(24*n) + 2002*b^5*c^9*x^(23*n) + 3003*b^6*c^8*x^(22*n) + 3432*b^7*c^7*x^(21*n) + 3003*b^8*c^6*x^(20*n) + 2002*b^9*c^5*x^(19*n) + 1001*b^10*c^4*x^(18*n) + 364*b^11*c^3*x^(17*n) + 91*b^12*c^2*x^(16*n) + 14*b^13*c*x^(15*n) + b^14*x^(14*n))/n","B",0
105,1,11,0,1.063876," ","integrate((2*c*x+b)/(c*x^2+b*x+a),x, algorithm=""fricas"")","\log\left(c x^{2} + b x + a\right)"," ",0,"log(c*x^2 + b*x + a)","A",0
106,1,15,0,1.037032," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(c x^{4} + b x^{2} + a\right)"," ",0,"1/2*log(c*x^4 + b*x^2 + a)","A",0
107,1,15,0,0.807323," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3+a),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(c x^{6} + b x^{3} + a\right)"," ",0,"1/3*log(c*x^6 + b*x^3 + a)","A",0
108,1,19,0,1.130189," ","integrate(x^(-1+n)*(b+2*c*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{\log\left(c x^{2 \, n} + b x^{n} + a\right)}{n}"," ",0,"log(c*x^(2*n) + b*x^n + a)/n","A",0
109,1,350,0,0.655272," ","integrate((2*c*x+b)/(c*x^2+b*x+a)^8,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{7} x^{14} + 7 \, b c^{6} x^{13} + 7 \, {\left(3 \, b^{2} c^{5} + a c^{6}\right)} x^{12} + 7 \, {\left(5 \, b^{3} c^{4} + 6 \, a b c^{5}\right)} x^{11} + 7 \, {\left(5 \, b^{4} c^{3} + 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right)} x^{10} + 7 \, {\left(3 \, b^{5} c^{2} + 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right)} x^{9} + 7 \, {\left(b^{6} c + 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 5 \, a^{3} c^{4}\right)} x^{8} + 7 \, a^{6} b x + {\left(b^{7} + 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} + 140 \, a^{3} b c^{3}\right)} x^{7} + a^{7} + 7 \, {\left(a b^{6} + 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 5 \, a^{4} c^{3}\right)} x^{6} + 7 \, {\left(3 \, a^{2} b^{5} + 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right)} x^{5} + 7 \, {\left(5 \, a^{3} b^{4} + 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right)} x^{4} + 7 \, {\left(5 \, a^{4} b^{3} + 6 \, a^{5} b c\right)} x^{3} + 7 \, {\left(3 \, a^{5} b^{2} + a^{6} c\right)} x^{2}\right)}}"," ",0,"-1/7/(c^7*x^14 + 7*b*c^6*x^13 + 7*(3*b^2*c^5 + a*c^6)*x^12 + 7*(5*b^3*c^4 + 6*a*b*c^5)*x^11 + 7*(5*b^4*c^3 + 15*a*b^2*c^4 + 3*a^2*c^5)*x^10 + 7*(3*b^5*c^2 + 20*a*b^3*c^3 + 15*a^2*b*c^4)*x^9 + 7*(b^6*c + 15*a*b^4*c^2 + 30*a^2*b^2*c^3 + 5*a^3*c^4)*x^8 + 7*a^6*b*x + (b^7 + 42*a*b^5*c + 210*a^2*b^3*c^2 + 140*a^3*b*c^3)*x^7 + a^7 + 7*(a*b^6 + 15*a^2*b^4*c + 30*a^3*b^2*c^2 + 5*a^4*c^3)*x^6 + 7*(3*a^2*b^5 + 20*a^3*b^3*c + 15*a^4*b*c^2)*x^5 + 7*(5*a^3*b^4 + 15*a^4*b^2*c + 3*a^5*c^2)*x^4 + 7*(5*a^4*b^3 + 6*a^5*b*c)*x^3 + 7*(3*a^5*b^2 + a^6*c)*x^2)","B",0
110,1,352,0,1.052421," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2+a)^8,x, algorithm=""fricas"")","-\frac{1}{14 \, {\left(c^{7} x^{28} + 7 \, b c^{6} x^{26} + 7 \, {\left(3 \, b^{2} c^{5} + a c^{6}\right)} x^{24} + 7 \, {\left(5 \, b^{3} c^{4} + 6 \, a b c^{5}\right)} x^{22} + 7 \, {\left(5 \, b^{4} c^{3} + 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right)} x^{20} + 7 \, {\left(3 \, b^{5} c^{2} + 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right)} x^{18} + 7 \, {\left(b^{6} c + 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 5 \, a^{3} c^{4}\right)} x^{16} + {\left(b^{7} + 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} + 140 \, a^{3} b c^{3}\right)} x^{14} + 7 \, {\left(a b^{6} + 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 5 \, a^{4} c^{3}\right)} x^{12} + 7 \, {\left(3 \, a^{2} b^{5} + 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right)} x^{10} + 7 \, a^{6} b x^{2} + 7 \, {\left(5 \, a^{3} b^{4} + 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right)} x^{8} + a^{7} + 7 \, {\left(5 \, a^{4} b^{3} + 6 \, a^{5} b c\right)} x^{6} + 7 \, {\left(3 \, a^{5} b^{2} + a^{6} c\right)} x^{4}\right)}}"," ",0,"-1/14/(c^7*x^28 + 7*b*c^6*x^26 + 7*(3*b^2*c^5 + a*c^6)*x^24 + 7*(5*b^3*c^4 + 6*a*b*c^5)*x^22 + 7*(5*b^4*c^3 + 15*a*b^2*c^4 + 3*a^2*c^5)*x^20 + 7*(3*b^5*c^2 + 20*a*b^3*c^3 + 15*a^2*b*c^4)*x^18 + 7*(b^6*c + 15*a*b^4*c^2 + 30*a^2*b^2*c^3 + 5*a^3*c^4)*x^16 + (b^7 + 42*a*b^5*c + 210*a^2*b^3*c^2 + 140*a^3*b*c^3)*x^14 + 7*(a*b^6 + 15*a^2*b^4*c + 30*a^3*b^2*c^2 + 5*a^4*c^3)*x^12 + 7*(3*a^2*b^5 + 20*a^3*b^3*c + 15*a^4*b*c^2)*x^10 + 7*a^6*b*x^2 + 7*(5*a^3*b^4 + 15*a^4*b^2*c + 3*a^5*c^2)*x^8 + a^7 + 7*(5*a^4*b^3 + 6*a^5*b*c)*x^6 + 7*(3*a^5*b^2 + a^6*c)*x^4)","B",0
111,1,352,0,1.012436," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3+a)^8,x, algorithm=""fricas"")","-\frac{1}{21 \, {\left(c^{7} x^{42} + 7 \, b c^{6} x^{39} + 7 \, {\left(3 \, b^{2} c^{5} + a c^{6}\right)} x^{36} + 7 \, {\left(5 \, b^{3} c^{4} + 6 \, a b c^{5}\right)} x^{33} + 7 \, {\left(5 \, b^{4} c^{3} + 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right)} x^{30} + 7 \, {\left(3 \, b^{5} c^{2} + 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right)} x^{27} + 7 \, {\left(b^{6} c + 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 5 \, a^{3} c^{4}\right)} x^{24} + {\left(b^{7} + 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} + 140 \, a^{3} b c^{3}\right)} x^{21} + 7 \, {\left(a b^{6} + 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 5 \, a^{4} c^{3}\right)} x^{18} + 7 \, {\left(3 \, a^{2} b^{5} + 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right)} x^{15} + 7 \, {\left(5 \, a^{3} b^{4} + 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right)} x^{12} + 7 \, a^{6} b x^{3} + 7 \, {\left(5 \, a^{4} b^{3} + 6 \, a^{5} b c\right)} x^{9} + a^{7} + 7 \, {\left(3 \, a^{5} b^{2} + a^{6} c\right)} x^{6}\right)}}"," ",0,"-1/21/(c^7*x^42 + 7*b*c^6*x^39 + 7*(3*b^2*c^5 + a*c^6)*x^36 + 7*(5*b^3*c^4 + 6*a*b*c^5)*x^33 + 7*(5*b^4*c^3 + 15*a*b^2*c^4 + 3*a^2*c^5)*x^30 + 7*(3*b^5*c^2 + 20*a*b^3*c^3 + 15*a^2*b*c^4)*x^27 + 7*(b^6*c + 15*a*b^4*c^2 + 30*a^2*b^2*c^3 + 5*a^3*c^4)*x^24 + (b^7 + 42*a*b^5*c + 210*a^2*b^3*c^2 + 140*a^3*b*c^3)*x^21 + 7*(a*b^6 + 15*a^2*b^4*c + 30*a^3*b^2*c^2 + 5*a^4*c^3)*x^18 + 7*(3*a^2*b^5 + 20*a^3*b^3*c + 15*a^4*b*c^2)*x^15 + 7*(5*a^3*b^4 + 15*a^4*b^2*c + 3*a^5*c^2)*x^12 + 7*a^6*b*x^3 + 7*(5*a^4*b^3 + 6*a^5*b*c)*x^9 + a^7 + 7*(3*a^5*b^2 + a^6*c)*x^6)","B",0
112,1,394,0,1.064014," ","integrate(x^(-1+n)*(b+2*c*x^n)/(a+b*x^n+c*x^(2*n))^8,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{7} n x^{14 \, n} + 7 \, b c^{6} n x^{13 \, n} + 7 \, a^{6} b n x^{n} + a^{7} n + 7 \, {\left(3 \, b^{2} c^{5} + a c^{6}\right)} n x^{12 \, n} + 7 \, {\left(5 \, b^{3} c^{4} + 6 \, a b c^{5}\right)} n x^{11 \, n} + 7 \, {\left(5 \, b^{4} c^{3} + 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right)} n x^{10 \, n} + 7 \, {\left(3 \, b^{5} c^{2} + 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right)} n x^{9 \, n} + 7 \, {\left(b^{6} c + 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} + 5 \, a^{3} c^{4}\right)} n x^{8 \, n} + {\left(b^{7} + 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} + 140 \, a^{3} b c^{3}\right)} n x^{7 \, n} + 7 \, {\left(a b^{6} + 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} + 5 \, a^{4} c^{3}\right)} n x^{6 \, n} + 7 \, {\left(3 \, a^{2} b^{5} + 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right)} n x^{5 \, n} + 7 \, {\left(5 \, a^{3} b^{4} + 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right)} n x^{4 \, n} + 7 \, {\left(5 \, a^{4} b^{3} + 6 \, a^{5} b c\right)} n x^{3 \, n} + 7 \, {\left(3 \, a^{5} b^{2} + a^{6} c\right)} n x^{2 \, n}\right)}}"," ",0,"-1/7/(c^7*n*x^(14*n) + 7*b*c^6*n*x^(13*n) + 7*a^6*b*n*x^n + a^7*n + 7*(3*b^2*c^5 + a*c^6)*n*x^(12*n) + 7*(5*b^3*c^4 + 6*a*b*c^5)*n*x^(11*n) + 7*(5*b^4*c^3 + 15*a*b^2*c^4 + 3*a^2*c^5)*n*x^(10*n) + 7*(3*b^5*c^2 + 20*a*b^3*c^3 + 15*a^2*b*c^4)*n*x^(9*n) + 7*(b^6*c + 15*a*b^4*c^2 + 30*a^2*b^2*c^3 + 5*a^3*c^4)*n*x^(8*n) + (b^7 + 42*a*b^5*c + 210*a^2*b^3*c^2 + 140*a^3*b*c^3)*n*x^(7*n) + 7*(a*b^6 + 15*a^2*b^4*c + 30*a^3*b^2*c^2 + 5*a^4*c^3)*n*x^(6*n) + 7*(3*a^2*b^5 + 20*a^3*b^3*c + 15*a^4*b*c^2)*n*x^(5*n) + 7*(5*a^3*b^4 + 15*a^4*b^2*c + 3*a^5*c^2)*n*x^(4*n) + 7*(5*a^4*b^3 + 6*a^5*b*c)*n*x^(3*n) + 7*(3*a^5*b^2 + a^6*c)*n*x^(2*n))","B",0
113,1,13,0,0.847948," ","integrate((2*c*x+b)/(c*x^2+b*x-a),x, algorithm=""fricas"")","\log\left(c x^{2} + b x - a\right)"," ",0,"log(c*x^2 + b*x - a)","A",0
114,1,17,0,0.632220," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2-a),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(c x^{4} + b x^{2} - a\right)"," ",0,"1/2*log(c*x^4 + b*x^2 - a)","A",0
115,1,17,0,0.763927," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3-a),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(c x^{6} + b x^{3} - a\right)"," ",0,"1/3*log(c*x^6 + b*x^3 - a)","A",0
116,1,21,0,1.219112," ","integrate(x^(-1+n)*(b+2*c*x^n)/(-a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{\log\left(c x^{2 \, n} + b x^{n} - a\right)}{n}"," ",0,"log(c*x^(2*n) + b*x^n - a)/n","A",0
117,1,354,0,0.981694," ","integrate((2*c*x+b)/(c*x^2+b*x-a)^8,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{7} x^{14} + 7 \, b c^{6} x^{13} + 7 \, {\left(3 \, b^{2} c^{5} - a c^{6}\right)} x^{12} + 7 \, {\left(5 \, b^{3} c^{4} - 6 \, a b c^{5}\right)} x^{11} + 7 \, {\left(5 \, b^{4} c^{3} - 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right)} x^{10} + 7 \, {\left(3 \, b^{5} c^{2} - 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right)} x^{9} + 7 \, {\left(b^{6} c - 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} - 5 \, a^{3} c^{4}\right)} x^{8} + 7 \, a^{6} b x + {\left(b^{7} - 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} - 140 \, a^{3} b c^{3}\right)} x^{7} - a^{7} - 7 \, {\left(a b^{6} - 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} - 5 \, a^{4} c^{3}\right)} x^{6} + 7 \, {\left(3 \, a^{2} b^{5} - 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right)} x^{5} - 7 \, {\left(5 \, a^{3} b^{4} - 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right)} x^{4} + 7 \, {\left(5 \, a^{4} b^{3} - 6 \, a^{5} b c\right)} x^{3} - 7 \, {\left(3 \, a^{5} b^{2} - a^{6} c\right)} x^{2}\right)}}"," ",0,"-1/7/(c^7*x^14 + 7*b*c^6*x^13 + 7*(3*b^2*c^5 - a*c^6)*x^12 + 7*(5*b^3*c^4 - 6*a*b*c^5)*x^11 + 7*(5*b^4*c^3 - 15*a*b^2*c^4 + 3*a^2*c^5)*x^10 + 7*(3*b^5*c^2 - 20*a*b^3*c^3 + 15*a^2*b*c^4)*x^9 + 7*(b^6*c - 15*a*b^4*c^2 + 30*a^2*b^2*c^3 - 5*a^3*c^4)*x^8 + 7*a^6*b*x + (b^7 - 42*a*b^5*c + 210*a^2*b^3*c^2 - 140*a^3*b*c^3)*x^7 - a^7 - 7*(a*b^6 - 15*a^2*b^4*c + 30*a^3*b^2*c^2 - 5*a^4*c^3)*x^6 + 7*(3*a^2*b^5 - 20*a^3*b^3*c + 15*a^4*b*c^2)*x^5 - 7*(5*a^3*b^4 - 15*a^4*b^2*c + 3*a^5*c^2)*x^4 + 7*(5*a^4*b^3 - 6*a^5*b*c)*x^3 - 7*(3*a^5*b^2 - a^6*c)*x^2)","B",0
118,1,356,0,0.999133," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2-a)^8,x, algorithm=""fricas"")","-\frac{1}{14 \, {\left(c^{7} x^{28} + 7 \, b c^{6} x^{26} + 7 \, {\left(3 \, b^{2} c^{5} - a c^{6}\right)} x^{24} + 7 \, {\left(5 \, b^{3} c^{4} - 6 \, a b c^{5}\right)} x^{22} + 7 \, {\left(5 \, b^{4} c^{3} - 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right)} x^{20} + 7 \, {\left(3 \, b^{5} c^{2} - 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right)} x^{18} + 7 \, {\left(b^{6} c - 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} - 5 \, a^{3} c^{4}\right)} x^{16} + {\left(b^{7} - 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} - 140 \, a^{3} b c^{3}\right)} x^{14} - 7 \, {\left(a b^{6} - 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} - 5 \, a^{4} c^{3}\right)} x^{12} + 7 \, {\left(3 \, a^{2} b^{5} - 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right)} x^{10} + 7 \, a^{6} b x^{2} - 7 \, {\left(5 \, a^{3} b^{4} - 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right)} x^{8} - a^{7} + 7 \, {\left(5 \, a^{4} b^{3} - 6 \, a^{5} b c\right)} x^{6} - 7 \, {\left(3 \, a^{5} b^{2} - a^{6} c\right)} x^{4}\right)}}"," ",0,"-1/14/(c^7*x^28 + 7*b*c^6*x^26 + 7*(3*b^2*c^5 - a*c^6)*x^24 + 7*(5*b^3*c^4 - 6*a*b*c^5)*x^22 + 7*(5*b^4*c^3 - 15*a*b^2*c^4 + 3*a^2*c^5)*x^20 + 7*(3*b^5*c^2 - 20*a*b^3*c^3 + 15*a^2*b*c^4)*x^18 + 7*(b^6*c - 15*a*b^4*c^2 + 30*a^2*b^2*c^3 - 5*a^3*c^4)*x^16 + (b^7 - 42*a*b^5*c + 210*a^2*b^3*c^2 - 140*a^3*b*c^3)*x^14 - 7*(a*b^6 - 15*a^2*b^4*c + 30*a^3*b^2*c^2 - 5*a^4*c^3)*x^12 + 7*(3*a^2*b^5 - 20*a^3*b^3*c + 15*a^4*b*c^2)*x^10 + 7*a^6*b*x^2 - 7*(5*a^3*b^4 - 15*a^4*b^2*c + 3*a^5*c^2)*x^8 - a^7 + 7*(5*a^4*b^3 - 6*a^5*b*c)*x^6 - 7*(3*a^5*b^2 - a^6*c)*x^4)","B",0
119,1,356,0,0.757568," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3-a)^8,x, algorithm=""fricas"")","-\frac{1}{21 \, {\left(c^{7} x^{42} + 7 \, b c^{6} x^{39} + 7 \, {\left(3 \, b^{2} c^{5} - a c^{6}\right)} x^{36} + 7 \, {\left(5 \, b^{3} c^{4} - 6 \, a b c^{5}\right)} x^{33} + 7 \, {\left(5 \, b^{4} c^{3} - 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right)} x^{30} + 7 \, {\left(3 \, b^{5} c^{2} - 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right)} x^{27} + 7 \, {\left(b^{6} c - 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} - 5 \, a^{3} c^{4}\right)} x^{24} + {\left(b^{7} - 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} - 140 \, a^{3} b c^{3}\right)} x^{21} - 7 \, {\left(a b^{6} - 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} - 5 \, a^{4} c^{3}\right)} x^{18} + 7 \, {\left(3 \, a^{2} b^{5} - 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right)} x^{15} - 7 \, {\left(5 \, a^{3} b^{4} - 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right)} x^{12} + 7 \, a^{6} b x^{3} + 7 \, {\left(5 \, a^{4} b^{3} - 6 \, a^{5} b c\right)} x^{9} - a^{7} - 7 \, {\left(3 \, a^{5} b^{2} - a^{6} c\right)} x^{6}\right)}}"," ",0,"-1/21/(c^7*x^42 + 7*b*c^6*x^39 + 7*(3*b^2*c^5 - a*c^6)*x^36 + 7*(5*b^3*c^4 - 6*a*b*c^5)*x^33 + 7*(5*b^4*c^3 - 15*a*b^2*c^4 + 3*a^2*c^5)*x^30 + 7*(3*b^5*c^2 - 20*a*b^3*c^3 + 15*a^2*b*c^4)*x^27 + 7*(b^6*c - 15*a*b^4*c^2 + 30*a^2*b^2*c^3 - 5*a^3*c^4)*x^24 + (b^7 - 42*a*b^5*c + 210*a^2*b^3*c^2 - 140*a^3*b*c^3)*x^21 - 7*(a*b^6 - 15*a^2*b^4*c + 30*a^3*b^2*c^2 - 5*a^4*c^3)*x^18 + 7*(3*a^2*b^5 - 20*a^3*b^3*c + 15*a^4*b*c^2)*x^15 - 7*(5*a^3*b^4 - 15*a^4*b^2*c + 3*a^5*c^2)*x^12 + 7*a^6*b*x^3 + 7*(5*a^4*b^3 - 6*a^5*b*c)*x^9 - a^7 - 7*(3*a^5*b^2 - a^6*c)*x^6)","B",0
120,1,397,0,0.973737," ","integrate(x^(-1+n)*(b+2*c*x^n)/(-a+b*x^n+c*x^(2*n))^8,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{7} n x^{14 \, n} + 7 \, b c^{6} n x^{13 \, n} + 7 \, a^{6} b n x^{n} - a^{7} n + 7 \, {\left(3 \, b^{2} c^{5} - a c^{6}\right)} n x^{12 \, n} + 7 \, {\left(5 \, b^{3} c^{4} - 6 \, a b c^{5}\right)} n x^{11 \, n} + 7 \, {\left(5 \, b^{4} c^{3} - 15 \, a b^{2} c^{4} + 3 \, a^{2} c^{5}\right)} n x^{10 \, n} + 7 \, {\left(3 \, b^{5} c^{2} - 20 \, a b^{3} c^{3} + 15 \, a^{2} b c^{4}\right)} n x^{9 \, n} + 7 \, {\left(b^{6} c - 15 \, a b^{4} c^{2} + 30 \, a^{2} b^{2} c^{3} - 5 \, a^{3} c^{4}\right)} n x^{8 \, n} + {\left(b^{7} - 42 \, a b^{5} c + 210 \, a^{2} b^{3} c^{2} - 140 \, a^{3} b c^{3}\right)} n x^{7 \, n} - 7 \, {\left(a b^{6} - 15 \, a^{2} b^{4} c + 30 \, a^{3} b^{2} c^{2} - 5 \, a^{4} c^{3}\right)} n x^{6 \, n} + 7 \, {\left(3 \, a^{2} b^{5} - 20 \, a^{3} b^{3} c + 15 \, a^{4} b c^{2}\right)} n x^{5 \, n} - 7 \, {\left(5 \, a^{3} b^{4} - 15 \, a^{4} b^{2} c + 3 \, a^{5} c^{2}\right)} n x^{4 \, n} + 7 \, {\left(5 \, a^{4} b^{3} - 6 \, a^{5} b c\right)} n x^{3 \, n} - 7 \, {\left(3 \, a^{5} b^{2} - a^{6} c\right)} n x^{2 \, n}\right)}}"," ",0,"-1/7/(c^7*n*x^(14*n) + 7*b*c^6*n*x^(13*n) + 7*a^6*b*n*x^n - a^7*n + 7*(3*b^2*c^5 - a*c^6)*n*x^(12*n) + 7*(5*b^3*c^4 - 6*a*b*c^5)*n*x^(11*n) + 7*(5*b^4*c^3 - 15*a*b^2*c^4 + 3*a^2*c^5)*n*x^(10*n) + 7*(3*b^5*c^2 - 20*a*b^3*c^3 + 15*a^2*b*c^4)*n*x^(9*n) + 7*(b^6*c - 15*a*b^4*c^2 + 30*a^2*b^2*c^3 - 5*a^3*c^4)*n*x^(8*n) + (b^7 - 42*a*b^5*c + 210*a^2*b^3*c^2 - 140*a^3*b*c^3)*n*x^(7*n) - 7*(a*b^6 - 15*a^2*b^4*c + 30*a^3*b^2*c^2 - 5*a^4*c^3)*n*x^(6*n) + 7*(3*a^2*b^5 - 20*a^3*b^3*c + 15*a^4*b*c^2)*n*x^(5*n) - 7*(5*a^3*b^4 - 15*a^4*b^2*c + 3*a^5*c^2)*n*x^(4*n) + 7*(5*a^4*b^3 - 6*a^5*b*c)*n*x^(3*n) - 7*(3*a^5*b^2 - a^6*c)*n*x^(2*n))","B",0
121,1,10,0,0.812089," ","integrate((2*c*x+b)/(c*x^2+b*x),x, algorithm=""fricas"")","\log\left(c x^{2} + b x\right)"," ",0,"log(c*x^2 + b*x)","A",0
122,1,13,0,0.611926," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(c x^{2} + b\right) + \log\left(x\right)"," ",0,"1/2*log(c*x^2 + b) + log(x)","A",0
123,1,13,0,0.871393," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3),x, algorithm=""fricas"")","\frac{1}{3} \, \log\left(c x^{3} + b\right) + \log\left(x\right)"," ",0,"1/3*log(c*x^3 + b) + log(x)","A",0
124,1,17,0,0.863036," ","integrate(x^(-1+n)*(b+2*c*x^n)/(b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{n \log\left(x\right) + \log\left(c x^{n} + b\right)}{n}"," ",0,"(n*log(x) + log(c*x^n + b))/n","A",0
125,1,81,0,0.856793," ","integrate((2*c*x+b)/(c*x^2+b*x)^8,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{7} x^{14} + 7 \, b c^{6} x^{13} + 21 \, b^{2} c^{5} x^{12} + 35 \, b^{3} c^{4} x^{11} + 35 \, b^{4} c^{3} x^{10} + 21 \, b^{5} c^{2} x^{9} + 7 \, b^{6} c x^{8} + b^{7} x^{7}\right)}}"," ",0,"-1/7/(c^7*x^14 + 7*b*c^6*x^13 + 21*b^2*c^5*x^12 + 35*b^3*c^4*x^11 + 35*b^4*c^3*x^10 + 21*b^5*c^2*x^9 + 7*b^6*c*x^8 + b^7*x^7)","B",0
126,1,81,0,0.884941," ","integrate(x*(2*c*x^2+b)/(c*x^4+b*x^2)^8,x, algorithm=""fricas"")","-\frac{1}{14 \, {\left(c^{7} x^{28} + 7 \, b c^{6} x^{26} + 21 \, b^{2} c^{5} x^{24} + 35 \, b^{3} c^{4} x^{22} + 35 \, b^{4} c^{3} x^{20} + 21 \, b^{5} c^{2} x^{18} + 7 \, b^{6} c x^{16} + b^{7} x^{14}\right)}}"," ",0,"-1/14/(c^7*x^28 + 7*b*c^6*x^26 + 21*b^2*c^5*x^24 + 35*b^3*c^4*x^22 + 35*b^4*c^3*x^20 + 21*b^5*c^2*x^18 + 7*b^6*c*x^16 + b^7*x^14)","B",0
127,1,81,0,0.712515," ","integrate(x^2*(2*c*x^3+b)/(c*x^6+b*x^3)^8,x, algorithm=""fricas"")","-\frac{1}{21 \, {\left(c^{7} x^{42} + 7 \, b c^{6} x^{39} + 21 \, b^{2} c^{5} x^{36} + 35 \, b^{3} c^{4} x^{33} + 35 \, b^{4} c^{3} x^{30} + 21 \, b^{5} c^{2} x^{27} + 7 \, b^{6} c x^{24} + b^{7} x^{21}\right)}}"," ",0,"-1/21/(c^7*x^42 + 7*b*c^6*x^39 + 21*b^2*c^5*x^36 + 35*b^3*c^4*x^33 + 35*b^4*c^3*x^30 + 21*b^5*c^2*x^27 + 7*b^6*c*x^24 + b^7*x^21)","B",0
128,1,105,0,0.912581," ","integrate(x^(-1+n)*(b+2*c*x^n)/(b*x^n+c*x^(2*n))^8,x, algorithm=""fricas"")","-\frac{1}{7 \, {\left(c^{7} n x^{14 \, n} + 7 \, b c^{6} n x^{13 \, n} + 21 \, b^{2} c^{5} n x^{12 \, n} + 35 \, b^{3} c^{4} n x^{11 \, n} + 35 \, b^{4} c^{3} n x^{10 \, n} + 21 \, b^{5} c^{2} n x^{9 \, n} + 7 \, b^{6} c n x^{8 \, n} + b^{7} n x^{7 \, n}\right)}}"," ",0,"-1/7/(c^7*n*x^(14*n) + 7*b*c^6*n*x^(13*n) + 21*b^2*c^5*n*x^(12*n) + 35*b^3*c^4*n*x^(11*n) + 35*b^4*c^3*n*x^(10*n) + 21*b^5*c^2*n*x^(9*n) + 7*b^6*c*n*x^(8*n) + b^7*n*x^(7*n))","B",0
129,1,28,0,0.793502," ","integrate((2*c*x+b)*(c*x^2+b*x+a)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{2} + b x + a\right)} {\left(c x^{2} + b x + a\right)}^{p}}{p + 1}"," ",0,"(c*x^2 + b*x + a)*(c*x^2 + b*x + a)^p/(p + 1)","A",0
130,1,33,0,0.783302," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2+a)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{4} + b x^{2} + a\right)} {\left(c x^{4} + b x^{2} + a\right)}^{p}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^4 + b*x^2 + a)*(c*x^4 + b*x^2 + a)^p/(p + 1)","A",0
131,1,33,0,0.807156," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3+a)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{6} + b x^{3} + a\right)} {\left(c x^{6} + b x^{3} + a\right)}^{p}}{3 \, {\left(p + 1\right)}}"," ",0,"1/3*(c*x^6 + b*x^3 + a)*(c*x^6 + b*x^3 + a)^p/(p + 1)","A",0
132,1,38,0,0.964578," ","integrate(x^(-1+n)*(b+2*c*x^n)*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","\frac{{\left(c x^{2 \, n} + b x^{n} + a\right)} {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}}{n p + n}"," ",0,"(c*x^(2*n) + b*x^n + a)*(c*x^(2*n) + b*x^n + a)^p/(n*p + n)","A",0
133,1,32,0,0.824064," ","integrate((2*c*x+b)*(c*x^2+b*x-a)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{2} + b x - a\right)} {\left(c x^{2} + b x - a\right)}^{p}}{p + 1}"," ",0,"(c*x^2 + b*x - a)*(c*x^2 + b*x - a)^p/(p + 1)","A",0
134,1,37,0,0.834294," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2-a)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{4} + b x^{2} - a\right)} {\left(c x^{4} + b x^{2} - a\right)}^{p}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^4 + b*x^2 - a)*(c*x^4 + b*x^2 - a)^p/(p + 1)","A",0
135,1,37,0,0.876819," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3-a)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{6} + b x^{3} - a\right)} {\left(c x^{6} + b x^{3} - a\right)}^{p}}{3 \, {\left(p + 1\right)}}"," ",0,"1/3*(c*x^6 + b*x^3 - a)*(c*x^6 + b*x^3 - a)^p/(p + 1)","A",0
136,1,42,0,0.876021," ","integrate(x^(-1+n)*(b+2*c*x^n)*(-a+b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","\frac{{\left(c x^{2 \, n} + b x^{n} - a\right)} {\left(c x^{2 \, n} + b x^{n} - a\right)}^{p}}{n p + n}"," ",0,"(c*x^(2*n) + b*x^n - a)*(c*x^(2*n) + b*x^n - a)^p/(n*p + n)","A",0
137,1,26,0,1.002195," ","integrate((2*c*x+b)*(c*x^2+b*x)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{2} + b x\right)} {\left(c x^{2} + b x\right)}^{p}}{p + 1}"," ",0,"(c*x^2 + b*x)*(c*x^2 + b*x)^p/(p + 1)","A",0
138,1,31,0,0.847307," ","integrate(x*(2*c*x^2+b)*(c*x^4+b*x^2)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{4} + b x^{2}\right)} {\left(c x^{4} + b x^{2}\right)}^{p}}{2 \, {\left(p + 1\right)}}"," ",0,"1/2*(c*x^4 + b*x^2)*(c*x^4 + b*x^2)^p/(p + 1)","A",0
139,1,31,0,0.766443," ","integrate(x^2*(2*c*x^3+b)*(c*x^6+b*x^3)^p,x, algorithm=""fricas"")","\frac{{\left(c x^{6} + b x^{3}\right)} {\left(c x^{6} + b x^{3}\right)}^{p}}{3 \, {\left(p + 1\right)}}"," ",0,"1/3*(c*x^6 + b*x^3)*(c*x^6 + b*x^3)^p/(p + 1)","A",0
140,1,36,0,0.880756," ","integrate(x^(-1+n)*(b+2*c*x^n)*(b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","\frac{{\left(c x^{2 \, n} + b x^{n}\right)} {\left(c x^{2 \, n} + b x^{n}\right)}^{p}}{n p + n}"," ",0,"(c*x^(2*n) + b*x^n)*(c*x^(2*n) + b*x^n)^p/(n*p + n)","A",0
141,0,0,0,0.794337," ","integrate((f*x)^m*(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)} \left(f x\right)^{m}}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral((e*x^n + d)*(f*x)^m/(c*x^(2*n) + b*x^n + a), x)","F",0
142,0,0,0,0.699053," ","integrate((f*x)^m*(d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)} \left(f x\right)^{m}}{c^{2} x^{4 \, n} + b^{2} x^{2 \, n} + 2 \, a b x^{n} + a^{2} + 2 \, {\left(b c x^{n} + a c\right)} x^{2 \, n}}, x\right)"," ",0,"integral((e*x^n + d)*(f*x)^m/(c^2*x^(4*n) + b^2*x^(2*n) + 2*a*b*x^n + a^2 + 2*(b*c*x^n + a*c)*x^(2*n)), x)","F",0
143,0,0,0,1.038677," ","integrate((f*x)^m*(d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)} \left(f x\right)^{m}}{c^{3} x^{6 \, n} + b^{3} x^{3 \, n} + 3 \, a b^{2} x^{2 \, n} + 3 \, a^{2} b x^{n} + a^{3} + 3 \, {\left(b c^{2} x^{n} + a c^{2}\right)} x^{4 \, n} + 3 \, {\left(b^{2} c x^{2 \, n} + 2 \, a b c x^{n} + a^{2} c\right)} x^{2 \, n}}, x\right)"," ",0,"integral((e*x^n + d)*(f*x)^m/(c^3*x^(6*n) + b^3*x^(3*n) + 3*a*b^2*x^(2*n) + 3*a^2*b*x^n + a^3 + 3*(b*c^2*x^n + a*c^2)*x^(4*n) + 3*(b^2*c*x^(2*n) + 2*a*b*c*x^n + a^2*c)*x^(2*n)), x)","F",0
144,1,33,0,0.763967," ","integrate((c^(1/3)-2*d^(1/3)*x^(1/3))/(c*d^(1/3)*x^(2/3)-c^(2/3)*d^(2/3)*x+c^(1/3)*d*x^(4/3)),x, algorithm=""fricas"")","-\frac{3 \, \log\left(d x^{\frac{2}{3}} - c^{\frac{1}{3}} d^{\frac{2}{3}} x^{\frac{1}{3}} + c^{\frac{2}{3}} d^{\frac{1}{3}}\right)}{c^{\frac{1}{3}} d^{\frac{2}{3}}}"," ",0,"-3*log(d*x^(2/3) - c^(1/3)*d^(2/3)*x^(1/3) + c^(2/3)*d^(1/3))/(c^(1/3)*d^(2/3))","A",0
145,0,0,0,0.612704," ","integrate((f*x)^m*(d+e*x^n)^q/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)}^{q} \left(f x\right)^{m}}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral((e*x^n + d)^q*(f*x)^m/(c*x^(2*n) + b*x^n + a), x)","F",0
146,0,0,0,0.944179," ","integrate(x^2*(d+e*x^n)^q/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)}^{q} x^{2}}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral((e*x^n + d)^q*x^2/(c*x^(2*n) + b*x^n + a), x)","F",0
147,0,0,0,0.539921," ","integrate(x*(d+e*x^n)^q/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)}^{q} x}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral((e*x^n + d)^q*x/(c*x^(2*n) + b*x^n + a), x)","F",0
148,0,0,0,0.655510," ","integrate((d+e*x^n)^q/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)}^{q}}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral((e*x^n + d)^q/(c*x^(2*n) + b*x^n + a), x)","F",0
149,0,0,0,0.676712," ","integrate((d+e*x^n)^q/x/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)}^{q}}{c x x^{2 \, n} + b x x^{n} + a x}, x\right)"," ",0,"integral((e*x^n + d)^q/(c*x*x^(2*n) + b*x*x^n + a*x), x)","F",0
150,0,0,0,0.806340," ","integrate((d+e*x^n)^q/x^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)}^{q}}{c x^{2} x^{2 \, n} + b x^{2} x^{n} + a x^{2}}, x\right)"," ",0,"integral((e*x^n + d)^q/(c*x^2*x^(2*n) + b*x^2*x^n + a*x^2), x)","F",0
151,0,0,0,0.699149," ","integrate((d+e*x^n)^q/x^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(e x^{n} + d\right)}^{q}}{c x^{3} x^{2 \, n} + b x^{3} x^{n} + a x^{3}}, x\right)"," ",0,"integral((e*x^n + d)^q/(c*x^3*x^(2*n) + b*x^3*x^n + a*x^3), x)","F",0
152,0,0,0,0.937426," ","integrate((f*x)^m*(d+e*x^n)^2*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}\right)} {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(f x\right)^{m}, x\right)"," ",0,"integral((e^2*x^(2*n) + 2*d*e*x^n + d^2)*(c*x^(2*n) + b*x^n + a)^p*(f*x)^m, x)","F",0
153,0,0,0,0.694260," ","integrate((f*x)^m*(d+e*x^n)*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{n} + d\right)} {\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(f x\right)^{m}, x\right)"," ",0,"integral((e*x^n + d)*(c*x^(2*n) + b*x^n + a)^p*(f*x)^m, x)","F",0
154,0,0,0,0.933996," ","integrate((f*x)^m*(a+b*x^n+c*x^(2*n))^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(f x\right)^{m}, x\right)"," ",0,"integral((c*x^(2*n) + b*x^n + a)^p*(f*x)^m, x)","F",0
155,0,0,0,0.869569," ","integrate((f*x)^m*(a+b*x^n+c*x^(2*n))^p/(d+e*x^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(f x\right)^{m}}{e x^{n} + d}, x\right)"," ",0,"integral((c*x^(2*n) + b*x^n + a)^p*(f*x)^m/(e*x^n + d), x)","F",0
156,0,0,0,0.917876," ","integrate((f*x)^m*(a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p} \left(f x\right)^{m}}{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}, x\right)"," ",0,"integral((c*x^(2*n) + b*x^n + a)^p*(f*x)^m/(e^2*x^(2*n) + 2*d*e*x^n + d^2), x)","F",0
