1,1,3224,0,1.624818," ","integrate((e*x^3+d)/(c*x^6+a),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, {\left(\sqrt{3} {\left(a^{4} c^{4} d^{2} - a^{5} c^{3} e^{2}\right)} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e - 3 \, a^{3} c^{2} d^{2} e^{3}\right)}\right)} \sqrt{\frac{{\left(c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}\right)} x^{2} + {\left(2 \, a^{5} c^{3} d e \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + a^{2} c^{3} d^{5} - 4 \, a^{3} c^{2} d^{3} e^{2} + 3 \, a^{4} c d e^{4}\right)} \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - {\left({\left(a^{4} c^{3} d^{2} e + a^{5} c^{2} e^{3}\right)} x \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + {\left(a c^{3} d^{6} - 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a^{3} c d^{2} e^{4}\right)} x\right)} \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}}{c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}}} \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} {\left(a^{4} c^{4} d^{2} - a^{5} c^{3} e^{2}\right)} x \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e - 3 \, a^{3} c^{2} d^{2} e^{3}\right)} x\right)} \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - \sqrt{3} {\left(c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}\right)}}{3 \, {\left(c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}\right)}}\right) - \frac{1}{3} \, \sqrt{3} \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, {\left(\sqrt{3} {\left(a^{4} c^{4} d^{2} - a^{5} c^{3} e^{2}\right)} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e - 3 \, a^{3} c^{2} d^{2} e^{3}\right)}\right)} \sqrt{\frac{{\left(c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}\right)} x^{2} - {\left(2 \, a^{5} c^{3} d e \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - a^{2} c^{3} d^{5} + 4 \, a^{3} c^{2} d^{3} e^{2} - 3 \, a^{4} c d e^{4}\right)} \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} + {\left({\left(a^{4} c^{3} d^{2} e + a^{5} c^{2} e^{3}\right)} x \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - {\left(a c^{3} d^{6} - 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a^{3} c d^{2} e^{4}\right)} x\right)} \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}}{c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}}} \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} {\left(a^{4} c^{4} d^{2} - a^{5} c^{3} e^{2}\right)} x \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e - 3 \, a^{3} c^{2} d^{2} e^{3}\right)} x\right)} \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} + \sqrt{3} {\left(c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}\right)}}{3 \, {\left(c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}\right)}}\right) - \frac{1}{12} \, \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \log\left(-{\left(c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}\right)} x^{2} - {\left(2 \, a^{5} c^{3} d e \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + a^{2} c^{3} d^{5} - 4 \, a^{3} c^{2} d^{3} e^{2} + 3 \, a^{4} c d e^{4}\right)} \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} + {\left({\left(a^{4} c^{3} d^{2} e + a^{5} c^{2} e^{3}\right)} x \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + {\left(a c^{3} d^{6} - 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a^{3} c d^{2} e^{4}\right)} x\right)} \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}\right) - \frac{1}{12} \, \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \log\left(-{\left(c^{3} d^{7} - a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} - 3 \, a^{3} d e^{6}\right)} x^{2} + {\left(2 \, a^{5} c^{3} d e \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - a^{2} c^{3} d^{5} + 4 \, a^{3} c^{2} d^{3} e^{2} - 3 \, a^{4} c d e^{4}\right)} \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - {\left({\left(a^{4} c^{3} d^{2} e + a^{5} c^{2} e^{3}\right)} x \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - {\left(a c^{3} d^{6} - 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a^{3} c d^{2} e^{4}\right)} x\right)} \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}\right) + \frac{1}{6} \, \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \log\left(-{\left(c^{2} d^{5} - 2 \, a c d^{3} e^{2} - 3 \, a^{2} d e^{4}\right)} x - {\left(a^{4} c^{2} e \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + a c^{2} d^{4} - 3 \, a^{2} c d^{2} e^{2}\right)} \left(\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}\right) + \frac{1}{6} \, \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \log\left(-{\left(c^{2} d^{5} - 2 \, a c d^{3} e^{2} - 3 \, a^{2} d e^{4}\right)} x + {\left(a^{4} c^{2} e \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - a c^{2} d^{4} + 3 \, a^{2} c d^{2} e^{2}\right)} \left(-\frac{a^{2} c^{2} \sqrt{-\frac{c^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}\right)"," ",0,"1/3*sqrt(3)*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)*arctan(1/3*(2*(sqrt(3)*(a^4*c^4*d^2 - a^5*c^3*e^2)*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 2*sqrt(3)*(a^2*c^3*d^4*e - 3*a^3*c^2*d^2*e^3))*sqrt(((c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6)*x^2 + (2*a^5*c^3*d*e*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + a^2*c^3*d^5 - 4*a^3*c^2*d^3*e^2 + 3*a^4*c*d*e^4)*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(2/3) - ((a^4*c^3*d^2*e + a^5*c^2*e^3)*x*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + (a*c^3*d^6 - 2*a^2*c^2*d^4*e^2 - 3*a^3*c*d^2*e^4)*x)*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3))/(c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6))*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(2/3) - 2*(sqrt(3)*(a^4*c^4*d^2 - a^5*c^3*e^2)*x*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 2*sqrt(3)*(a^2*c^3*d^4*e - 3*a^3*c^2*d^2*e^3)*x)*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(2/3) - sqrt(3)*(c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6))/(c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6)) - 1/3*sqrt(3)*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)*arctan(1/3*(2*(sqrt(3)*(a^4*c^4*d^2 - a^5*c^3*e^2)*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 2*sqrt(3)*(a^2*c^3*d^4*e - 3*a^3*c^2*d^2*e^3))*sqrt(((c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6)*x^2 - (2*a^5*c^3*d*e*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - a^2*c^3*d^5 + 4*a^3*c^2*d^3*e^2 - 3*a^4*c*d*e^4)*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(2/3) + ((a^4*c^3*d^2*e + a^5*c^2*e^3)*x*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - (a*c^3*d^6 - 2*a^2*c^2*d^4*e^2 - 3*a^3*c*d^2*e^4)*x)*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3))/(c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6))*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(2/3) - 2*(sqrt(3)*(a^4*c^4*d^2 - a^5*c^3*e^2)*x*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 2*sqrt(3)*(a^2*c^3*d^4*e - 3*a^3*c^2*d^2*e^3)*x)*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(2/3) + sqrt(3)*(c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6))/(c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6)) - 1/12*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)*log(-(c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6)*x^2 - (2*a^5*c^3*d*e*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + a^2*c^3*d^5 - 4*a^3*c^2*d^3*e^2 + 3*a^4*c*d*e^4)*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(2/3) + ((a^4*c^3*d^2*e + a^5*c^2*e^3)*x*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + (a*c^3*d^6 - 2*a^2*c^2*d^4*e^2 - 3*a^3*c*d^2*e^4)*x)*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)) - 1/12*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)*log(-(c^3*d^7 - a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 - 3*a^3*d*e^6)*x^2 + (2*a^5*c^3*d*e*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - a^2*c^3*d^5 + 4*a^3*c^2*d^3*e^2 - 3*a^4*c*d*e^4)*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(2/3) - ((a^4*c^3*d^2*e + a^5*c^2*e^3)*x*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - (a*c^3*d^6 - 2*a^2*c^2*d^4*e^2 - 3*a^3*c*d^2*e^4)*x)*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)) + 1/6*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)*log(-(c^2*d^5 - 2*a*c*d^3*e^2 - 3*a^2*d*e^4)*x - (a^4*c^2*e*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + a*c^2*d^4 - 3*a^2*c*d^2*e^2)*((a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)) + 1/6*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)*log(-(c^2*d^5 - 2*a*c*d^3*e^2 - 3*a^2*d*e^4)*x + (a^4*c^2*e*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - a*c^2*d^4 + 3*a^2*c*d^2*e^2)*(-(a^2*c^2*sqrt(-(c^2*d^6 - 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3))","B",0
2,1,3178,0,1.943365," ","integrate((e*x^3+d)/(-c*x^6+a),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, {\left(\sqrt{3} {\left(a^{4} c^{4} d^{2} + a^{5} c^{3} e^{2}\right)} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e + 3 \, a^{3} c^{2} d^{2} e^{3}\right)}\right)} \sqrt{\frac{{\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)} x^{2} - {\left(2 \, a^{5} c^{3} d e \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - a^{2} c^{3} d^{5} - 4 \, a^{3} c^{2} d^{3} e^{2} - 3 \, a^{4} c d e^{4}\right)} \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} + {\left({\left(a^{4} c^{3} d^{2} e - a^{5} c^{2} e^{3}\right)} x \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - {\left(a c^{3} d^{6} + 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a^{3} c d^{2} e^{4}\right)} x\right)} \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}}{c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}}} \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} {\left(a^{4} c^{4} d^{2} + a^{5} c^{3} e^{2}\right)} x \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e + 3 \, a^{3} c^{2} d^{2} e^{3}\right)} x\right)} \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - \sqrt{3} {\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)}}{3 \, {\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)}}\right) - \frac{1}{3} \, \sqrt{3} \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, {\left(\sqrt{3} {\left(a^{4} c^{4} d^{2} + a^{5} c^{3} e^{2}\right)} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e + 3 \, a^{3} c^{2} d^{2} e^{3}\right)}\right)} \sqrt{\frac{{\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)} x^{2} + {\left(2 \, a^{5} c^{3} d e \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + a^{2} c^{3} d^{5} + 4 \, a^{3} c^{2} d^{3} e^{2} + 3 \, a^{4} c d e^{4}\right)} \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - {\left({\left(a^{4} c^{3} d^{2} e - a^{5} c^{2} e^{3}\right)} x \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + {\left(a c^{3} d^{6} + 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a^{3} c d^{2} e^{4}\right)} x\right)} \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}}{c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}}} \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} {\left(a^{4} c^{4} d^{2} + a^{5} c^{3} e^{2}\right)} x \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e + 3 \, a^{3} c^{2} d^{2} e^{3}\right)} x\right)} \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} + \sqrt{3} {\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)}}{3 \, {\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)}}\right) - \frac{1}{12} \, \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \log\left({\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)} x^{2} - {\left(2 \, a^{5} c^{3} d e \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - a^{2} c^{3} d^{5} - 4 \, a^{3} c^{2} d^{3} e^{2} - 3 \, a^{4} c d e^{4}\right)} \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} + {\left({\left(a^{4} c^{3} d^{2} e - a^{5} c^{2} e^{3}\right)} x \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - {\left(a c^{3} d^{6} + 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a^{3} c d^{2} e^{4}\right)} x\right)} \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}\right) - \frac{1}{12} \, \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \log\left({\left(c^{3} d^{7} + a c^{2} d^{5} e^{2} - 5 \, a^{2} c d^{3} e^{4} + 3 \, a^{3} d e^{6}\right)} x^{2} + {\left(2 \, a^{5} c^{3} d e \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + a^{2} c^{3} d^{5} + 4 \, a^{3} c^{2} d^{3} e^{2} + 3 \, a^{4} c d e^{4}\right)} \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{2}{3}} - {\left({\left(a^{4} c^{3} d^{2} e - a^{5} c^{2} e^{3}\right)} x \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + {\left(a c^{3} d^{6} + 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a^{3} c d^{2} e^{4}\right)} x\right)} \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}\right) + \frac{1}{6} \, \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \log\left(-{\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} - 3 \, a^{2} d e^{4}\right)} x + {\left(a^{4} c^{2} e \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - a c^{2} d^{4} - 3 \, a^{2} c d^{2} e^{2}\right)} \left(-\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + 3 \, c d^{2} e + a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}\right) + \frac{1}{6} \, \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}} \log\left(-{\left(c^{2} d^{5} + 2 \, a c d^{3} e^{2} - 3 \, a^{2} d e^{4}\right)} x - {\left(a^{4} c^{2} e \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} + a c^{2} d^{4} + 3 \, a^{2} c d^{2} e^{2}\right)} \left(\frac{a^{2} c^{2} \sqrt{\frac{c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 9 \, a^{2} d^{2} e^{4}}{a^{5} c^{3}}} - 3 \, c d^{2} e - a e^{3}}{a^{2} c^{2}}\right)^{\frac{1}{3}}\right)"," ",0,"1/3*sqrt(3)*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)*arctan(1/3*(2*(sqrt(3)*(a^4*c^4*d^2 + a^5*c^3*e^2)*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 2*sqrt(3)*(a^2*c^3*d^4*e + 3*a^3*c^2*d^2*e^3))*sqrt(((c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)*x^2 - (2*a^5*c^3*d*e*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - a^2*c^3*d^5 - 4*a^3*c^2*d^3*e^2 - 3*a^4*c*d*e^4)*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(2/3) + ((a^4*c^3*d^2*e - a^5*c^2*e^3)*x*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - (a*c^3*d^6 + 2*a^2*c^2*d^4*e^2 - 3*a^3*c*d^2*e^4)*x)*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3))/(c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6))*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(2/3) - 2*(sqrt(3)*(a^4*c^4*d^2 + a^5*c^3*e^2)*x*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 2*sqrt(3)*(a^2*c^3*d^4*e + 3*a^3*c^2*d^2*e^3)*x)*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(2/3) - sqrt(3)*(c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6))/(c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)) - 1/3*sqrt(3)*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)*arctan(1/3*(2*(sqrt(3)*(a^4*c^4*d^2 + a^5*c^3*e^2)*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 2*sqrt(3)*(a^2*c^3*d^4*e + 3*a^3*c^2*d^2*e^3))*sqrt(((c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)*x^2 + (2*a^5*c^3*d*e*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + a^2*c^3*d^5 + 4*a^3*c^2*d^3*e^2 + 3*a^4*c*d*e^4)*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(2/3) - ((a^4*c^3*d^2*e - a^5*c^2*e^3)*x*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + (a*c^3*d^6 + 2*a^2*c^2*d^4*e^2 - 3*a^3*c*d^2*e^4)*x)*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3))/(c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6))*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(2/3) - 2*(sqrt(3)*(a^4*c^4*d^2 + a^5*c^3*e^2)*x*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 2*sqrt(3)*(a^2*c^3*d^4*e + 3*a^3*c^2*d^2*e^3)*x)*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(2/3) + sqrt(3)*(c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6))/(c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)) - 1/12*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)*log((c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)*x^2 - (2*a^5*c^3*d*e*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - a^2*c^3*d^5 - 4*a^3*c^2*d^3*e^2 - 3*a^4*c*d*e^4)*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(2/3) + ((a^4*c^3*d^2*e - a^5*c^2*e^3)*x*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - (a*c^3*d^6 + 2*a^2*c^2*d^4*e^2 - 3*a^3*c*d^2*e^4)*x)*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)) - 1/12*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)*log((c^3*d^7 + a*c^2*d^5*e^2 - 5*a^2*c*d^3*e^4 + 3*a^3*d*e^6)*x^2 + (2*a^5*c^3*d*e*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + a^2*c^3*d^5 + 4*a^3*c^2*d^3*e^2 + 3*a^4*c*d*e^4)*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(2/3) - ((a^4*c^3*d^2*e - a^5*c^2*e^3)*x*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + (a*c^3*d^6 + 2*a^2*c^2*d^4*e^2 - 3*a^3*c*d^2*e^4)*x)*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)) + 1/6*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)*log(-(c^2*d^5 + 2*a*c*d^3*e^2 - 3*a^2*d*e^4)*x + (a^4*c^2*e*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - a*c^2*d^4 - 3*a^2*c*d^2*e^2)*(-(a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + 3*c*d^2*e + a*e^3)/(a^2*c^2))^(1/3)) + 1/6*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3)*log(-(c^2*d^5 + 2*a*c*d^3*e^2 - 3*a^2*d*e^4)*x - (a^4*c^2*e*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) + a*c^2*d^4 + 3*a^2*c*d^2*e^2)*((a^2*c^2*sqrt((c^2*d^6 + 6*a*c*d^4*e^2 + 9*a^2*d^2*e^4)/(a^5*c^3)) - 3*c*d^2*e - a*e^3)/(a^2*c^2))^(1/3))","B",0
3,1,3406,0,2.405539," ","integrate((e*x^4+d)/(c*x^8+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \left(\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left({\left(3 \, a^{3} c^{5} d^{6} e - 19 \, a^{4} c^{4} d^{4} e^{3} + 9 \, a^{5} c^{3} d^{2} e^{5} - a^{6} c^{2} e^{7} + {\left(a^{6} c^{6} d^{3} - 3 \, a^{7} c^{5} d e^{2}\right)} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}}\right)} \sqrt{\frac{{\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} x^{2} - {\left(2 \, a^{6} c^{4} d e \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - a^{2} c^{4} d^{6} + 7 \, a^{3} c^{3} d^{4} e^{2} - 7 \, a^{4} c^{2} d^{2} e^{4} + a^{5} c e^{6}\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}} - {\left({\left(a^{6} c^{6} d^{3} - 3 \, a^{7} c^{5} d e^{2}\right)} x \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + {\left(3 \, a^{3} c^{5} d^{6} e - 19 \, a^{4} c^{4} d^{4} e^{3} + 9 \, a^{5} c^{3} d^{2} e^{5} - a^{6} c^{2} e^{7}\right)} x\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}}\right)} \left(\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}}{c^{5} d^{10} - 3 \, a c^{4} d^{8} e^{2} - 14 \, a^{2} c^{3} d^{6} e^{4} - 14 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d^{2} e^{8} + a^{5} e^{10}}\right) + \frac{1}{2} \, \left(-\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(3 \, a^{3} c^{5} d^{6} e - 19 \, a^{4} c^{4} d^{4} e^{3} + 9 \, a^{5} c^{3} d^{2} e^{5} - a^{6} c^{2} e^{7} - {\left(a^{6} c^{6} d^{3} - 3 \, a^{7} c^{5} d e^{2}\right)} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}}\right)} \sqrt{\frac{{\left(c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} x^{2} + {\left(2 \, a^{6} c^{4} d e \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + a^{2} c^{4} d^{6} - 7 \, a^{3} c^{3} d^{4} e^{2} + 7 \, a^{4} c^{2} d^{2} e^{4} - a^{5} c e^{6}\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}}}{c^{4} d^{8} - 4 \, a c^{3} d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}} \left(-\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{3}{4}} + {\left({\left(a^{6} c^{6} d^{3} - 3 \, a^{7} c^{5} d e^{2}\right)} x \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - {\left(3 \, a^{3} c^{5} d^{6} e - 19 \, a^{4} c^{4} d^{4} e^{3} + 9 \, a^{5} c^{3} d^{2} e^{5} - a^{6} c^{2} e^{7}\right)} x\right)} \left(-\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{3}{4}}}{c^{5} d^{10} - 3 \, a c^{4} d^{8} e^{2} - 14 \, a^{2} c^{3} d^{6} e^{4} - 14 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d^{2} e^{8} + a^{5} e^{10}}\right) + \frac{1}{8} \, \left(-\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \log\left({\left(c^{3} d^{6} - 5 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} x + {\left(a^{5} c^{3} e \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + a c^{3} d^{5} - 6 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \left(-\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}\right) - \frac{1}{8} \, \left(-\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \log\left({\left(c^{3} d^{6} - 5 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} x - {\left(a^{5} c^{3} e \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + a c^{3} d^{5} - 6 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \left(-\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}\right) - \frac{1}{8} \, \left(\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \log\left({\left(c^{3} d^{6} - 5 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} x + {\left(a^{5} c^{3} e \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - a c^{3} d^{5} + 6 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} \left(\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}\right) + \frac{1}{8} \, \left(\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \log\left({\left(c^{3} d^{6} - 5 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} + a^{3} e^{6}\right)} x - {\left(a^{5} c^{3} e \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - a c^{3} d^{5} + 6 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} \left(\frac{a^{3} c^{2} \sqrt{-\frac{c^{4} d^{8} - 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}\right)"," ",0,"-1/2*((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)*arctan(-((3*a^3*c^5*d^6*e - 19*a^4*c^4*d^4*e^3 + 9*a^5*c^3*d^2*e^5 - a^6*c^2*e^7 + (a^6*c^6*d^3 - 3*a^7*c^5*d*e^2)*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)))*sqrt(((c^4*d^8 - 4*a*c^3*d^6*e^2 - 10*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*x^2 - (2*a^6*c^4*d*e*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - a^2*c^4*d^6 + 7*a^3*c^3*d^4*e^2 - 7*a^4*c^2*d^2*e^4 + a^5*c*e^6)*sqrt((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2)))/(c^4*d^8 - 4*a*c^3*d^6*e^2 - 10*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*sqrt((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2)) - ((a^6*c^6*d^3 - 3*a^7*c^5*d*e^2)*x*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + (3*a^3*c^5*d^6*e - 19*a^4*c^4*d^4*e^3 + 9*a^5*c^3*d^2*e^5 - a^6*c^2*e^7)*x)*sqrt((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2)))*((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)/(c^5*d^10 - 3*a*c^4*d^8*e^2 - 14*a^2*c^3*d^6*e^4 - 14*a^3*c^2*d^4*e^6 - 3*a^4*c*d^2*e^8 + a^5*e^10)) + 1/2*(-(a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)*arctan(((3*a^3*c^5*d^6*e - 19*a^4*c^4*d^4*e^3 + 9*a^5*c^3*d^2*e^5 - a^6*c^2*e^7 - (a^6*c^6*d^3 - 3*a^7*c^5*d*e^2)*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)))*sqrt(((c^4*d^8 - 4*a*c^3*d^6*e^2 - 10*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8)*x^2 + (2*a^6*c^4*d*e*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + a^2*c^4*d^6 - 7*a^3*c^3*d^4*e^2 + 7*a^4*c^2*d^2*e^4 - a^5*c*e^6)*sqrt(-(a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2)))/(c^4*d^8 - 4*a*c^3*d^6*e^2 - 10*a^2*c^2*d^4*e^4 - 4*a^3*c*d^2*e^6 + a^4*e^8))*(-(a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(3/4) + ((a^6*c^6*d^3 - 3*a^7*c^5*d*e^2)*x*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - (3*a^3*c^5*d^6*e - 19*a^4*c^4*d^4*e^3 + 9*a^5*c^3*d^2*e^5 - a^6*c^2*e^7)*x)*(-(a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(3/4))/(c^5*d^10 - 3*a*c^4*d^8*e^2 - 14*a^2*c^3*d^6*e^4 - 14*a^3*c^2*d^4*e^6 - 3*a^4*c*d^2*e^8 + a^5*e^10)) + 1/8*(-(a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)*log((c^3*d^6 - 5*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 + a^3*e^6)*x + (a^5*c^3*e*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + a*c^3*d^5 - 6*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*(-(a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)) - 1/8*(-(a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)*log((c^3*d^6 - 5*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 + a^3*e^6)*x - (a^5*c^3*e*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + a*c^3*d^5 - 6*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*(-(a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)) - 1/8*((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)*log((c^3*d^6 - 5*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 + a^3*e^6)*x + (a^5*c^3*e*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - a*c^3*d^5 + 6*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)) + 1/8*((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)*log((c^3*d^6 - 5*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 + a^3*e^6)*x - (a^5*c^3*e*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - a*c^3*d^5 + 6*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*((a^3*c^2*sqrt(-(c^4*d^8 - 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4))","B",0
4,1,3385,0,2.843374," ","integrate((e*x^4+d)/(-c*x^8+a),x, algorithm=""fricas"")","\frac{1}{2} \, \left(\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left({\left(3 \, a^{3} c^{5} d^{6} e + 19 \, a^{4} c^{4} d^{4} e^{3} + 9 \, a^{5} c^{3} d^{2} e^{5} + a^{6} c^{2} e^{7} - {\left(a^{6} c^{6} d^{3} + 3 \, a^{7} c^{5} d e^{2}\right)} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}}\right)} \sqrt{\frac{{\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} x^{2} - {\left(2 \, a^{6} c^{4} d e \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - a^{2} c^{4} d^{6} - 7 \, a^{3} c^{3} d^{4} e^{2} - 7 \, a^{4} c^{2} d^{2} e^{4} - a^{5} c e^{6}\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}}}{c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}} \sqrt{\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}} + {\left({\left(a^{6} c^{6} d^{3} + 3 \, a^{7} c^{5} d e^{2}\right)} x \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - {\left(3 \, a^{3} c^{5} d^{6} e + 19 \, a^{4} c^{4} d^{4} e^{3} + 9 \, a^{5} c^{3} d^{2} e^{5} + a^{6} c^{2} e^{7}\right)} x\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}}\right)} \left(\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}}{c^{5} d^{10} + 3 \, a c^{4} d^{8} e^{2} - 14 \, a^{2} c^{3} d^{6} e^{4} + 14 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}}\right) - \frac{1}{2} \, \left(-\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left(3 \, a^{3} c^{5} d^{6} e + 19 \, a^{4} c^{4} d^{4} e^{3} + 9 \, a^{5} c^{3} d^{2} e^{5} + a^{6} c^{2} e^{7} + {\left(a^{6} c^{6} d^{3} + 3 \, a^{7} c^{5} d e^{2}\right)} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}}\right)} \sqrt{\frac{{\left(c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}\right)} x^{2} + {\left(2 \, a^{6} c^{4} d e \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + a^{2} c^{4} d^{6} + 7 \, a^{3} c^{3} d^{4} e^{2} + 7 \, a^{4} c^{2} d^{2} e^{4} + a^{5} c e^{6}\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}}}{c^{4} d^{8} + 4 \, a c^{3} d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}} \left(-\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{3}{4}} - {\left({\left(a^{6} c^{6} d^{3} + 3 \, a^{7} c^{5} d e^{2}\right)} x \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + {\left(3 \, a^{3} c^{5} d^{6} e + 19 \, a^{4} c^{4} d^{4} e^{3} + 9 \, a^{5} c^{3} d^{2} e^{5} + a^{6} c^{2} e^{7}\right)} x\right)} \left(-\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{3}{4}}}{c^{5} d^{10} + 3 \, a c^{4} d^{8} e^{2} - 14 \, a^{2} c^{3} d^{6} e^{4} + 14 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}}\right) + \frac{1}{8} \, \left(\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \log\left(-{\left(c^{3} d^{6} + 5 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} x + {\left(a^{5} c^{3} e \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - a c^{3} d^{5} - 6 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} \left(\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}\right) - \frac{1}{8} \, \left(\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \log\left(-{\left(c^{3} d^{6} + 5 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} x - {\left(a^{5} c^{3} e \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - a c^{3} d^{5} - 6 \, a^{2} c^{2} d^{3} e^{2} - a^{3} c d e^{4}\right)} \left(\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 4 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}\right) - \frac{1}{8} \, \left(-\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \log\left(-{\left(c^{3} d^{6} + 5 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} x + {\left(a^{5} c^{3} e \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + a c^{3} d^{5} + 6 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \left(-\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}\right) + \frac{1}{8} \, \left(-\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}} \log\left(-{\left(c^{3} d^{6} + 5 \, a c^{2} d^{4} e^{2} - 5 \, a^{2} c d^{2} e^{4} - a^{3} e^{6}\right)} x - {\left(a^{5} c^{3} e \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + a c^{3} d^{5} + 6 \, a^{2} c^{2} d^{3} e^{2} + a^{3} c d e^{4}\right)} \left(-\frac{a^{3} c^{2} \sqrt{\frac{c^{4} d^{8} + 12 \, a c^{3} d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} + 12 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 4 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}\right)^{\frac{1}{4}}\right)"," ",0,"1/2*((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)*arctan(((3*a^3*c^5*d^6*e + 19*a^4*c^4*d^4*e^3 + 9*a^5*c^3*d^2*e^5 + a^6*c^2*e^7 - (a^6*c^6*d^3 + 3*a^7*c^5*d*e^2)*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)))*sqrt(((c^4*d^8 + 4*a*c^3*d^6*e^2 - 10*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*x^2 - (2*a^6*c^4*d*e*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - a^2*c^4*d^6 - 7*a^3*c^3*d^4*e^2 - 7*a^4*c^2*d^2*e^4 - a^5*c*e^6)*sqrt((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2)))/(c^4*d^8 + 4*a*c^3*d^6*e^2 - 10*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8))*sqrt((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2)) + ((a^6*c^6*d^3 + 3*a^7*c^5*d*e^2)*x*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - (3*a^3*c^5*d^6*e + 19*a^4*c^4*d^4*e^3 + 9*a^5*c^3*d^2*e^5 + a^6*c^2*e^7)*x)*sqrt((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2)))*((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)/(c^5*d^10 + 3*a*c^4*d^8*e^2 - 14*a^2*c^3*d^6*e^4 + 14*a^3*c^2*d^4*e^6 - 3*a^4*c*d^2*e^8 - a^5*e^10)) - 1/2*(-(a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)*arctan(-((3*a^3*c^5*d^6*e + 19*a^4*c^4*d^4*e^3 + 9*a^5*c^3*d^2*e^5 + a^6*c^2*e^7 + (a^6*c^6*d^3 + 3*a^7*c^5*d*e^2)*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)))*sqrt(((c^4*d^8 + 4*a*c^3*d^6*e^2 - 10*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)*x^2 + (2*a^6*c^4*d*e*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + a^2*c^4*d^6 + 7*a^3*c^3*d^4*e^2 + 7*a^4*c^2*d^2*e^4 + a^5*c*e^6)*sqrt(-(a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2)))/(c^4*d^8 + 4*a*c^3*d^6*e^2 - 10*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8))*(-(a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(3/4) - ((a^6*c^6*d^3 + 3*a^7*c^5*d*e^2)*x*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + (3*a^3*c^5*d^6*e + 19*a^4*c^4*d^4*e^3 + 9*a^5*c^3*d^2*e^5 + a^6*c^2*e^7)*x)*(-(a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(3/4))/(c^5*d^10 + 3*a*c^4*d^8*e^2 - 14*a^2*c^3*d^6*e^4 + 14*a^3*c^2*d^4*e^6 - 3*a^4*c*d^2*e^8 - a^5*e^10)) + 1/8*((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)*log(-(c^3*d^6 + 5*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 - a^3*e^6)*x + (a^5*c^3*e*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - a*c^3*d^5 - 6*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)) - 1/8*((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)*log(-(c^3*d^6 + 5*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 - a^3*e^6)*x - (a^5*c^3*e*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - a*c^3*d^5 - 6*a^2*c^2*d^3*e^2 - a^3*c*d*e^4)*((a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 4*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))^(1/4)) - 1/8*(-(a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)*log(-(c^3*d^6 + 5*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 - a^3*e^6)*x + (a^5*c^3*e*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + a*c^3*d^5 + 6*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*(-(a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)) + 1/8*(-(a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4)*log(-(c^3*d^6 + 5*a*c^2*d^4*e^2 - 5*a^2*c*d^2*e^4 - a^3*e^6)*x - (a^5*c^3*e*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + a*c^3*d^5 + 6*a^2*c^2*d^3*e^2 + a^3*c*d*e^4)*(-(a^3*c^2*sqrt((c^4*d^8 + 12*a*c^3*d^6*e^2 + 38*a^2*c^2*d^4*e^4 + 12*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 4*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))^(1/4))","B",0
5,1,3059,0,1.857918," ","integrate((e*x^4+d)/(e^2*x^8+b*x^4+d^2),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}} \arctan\left(-\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left(8 \, d^{5} e^{3} + 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e + b^{3} d^{2}\right)} x \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - {\left(4 \, d^{2} e^{2} + 4 \, b d e + b^{2}\right)} x\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}} + {\left(4 \, d^{2} e^{2} + 4 \, b d e + b^{2} - {\left(8 \, d^{5} e^{3} + 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e + b^{3} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}}\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}} \sqrt{\frac{2 \, e^{2} x^{2} + \sqrt{\frac{1}{2}} {\left(2 \, b d e + b^{2} - {\left(8 \, d^{5} e^{3} + 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e + b^{3} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}}\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}}{e^{2}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}}}{4 \, e}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}} \arctan\left(-\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left(8 \, d^{5} e^{3} + 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e + b^{3} d^{2}\right)} x \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + {\left(4 \, d^{2} e^{2} + 4 \, b d e + b^{2}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}} - {\left(4 \, d^{2} e^{2} + 4 \, b d e + b^{2} + {\left(8 \, d^{5} e^{3} + 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e + b^{3} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}} \sqrt{\frac{2 \, e^{2} x^{2} + \sqrt{\frac{1}{2}} {\left(2 \, b d e + b^{2} + {\left(8 \, d^{5} e^{3} + 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e + b^{3} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}}\right)} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}}{e^{2}}}}{4 \, e}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}} \log\left(e x + \frac{1}{2} \, {\left(2 \, d e - {\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}} \log\left(e x - \frac{1}{2} \, {\left(2 \, d e - {\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}} \log\left(e x + \frac{1}{2} \, {\left(2 \, d e + {\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}} \log\left(e x - \frac{1}{2} \, {\left(2 \, d e + {\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} + b\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e - b}{8 \, d^{7} e^{3} + 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e + b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} + 4 \, b d^{3} e + b^{2} d^{2}}}}\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))*arctan(-1/4*(2*sqrt(1/2)*((8*d^5*e^3 + 12*b*d^4*e^2 + 6*b^2*d^3*e + b^3*d^2)*x*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - (4*d^2*e^2 + 4*b*d*e + b^2)*x)*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)) + (4*d^2*e^2 + 4*b*d*e + b^2 - (8*d^5*e^3 + 12*b*d^4*e^2 + 6*b^2*d^3*e + b^3*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)))*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2))*sqrt((2*e^2*x^2 + sqrt(1/2)*(2*b*d*e + b^2 - (8*d^5*e^3 + 12*b*d^4*e^2 + 6*b^2*d^3*e + b^3*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)))*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))/e^2))*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))/e) + sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))*arctan(-1/4*(2*sqrt(1/2)*((8*d^5*e^3 + 12*b*d^4*e^2 + 6*b^2*d^3*e + b^3*d^2)*x*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + (4*d^2*e^2 + 4*b*d*e + b^2)*x)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)) - (4*d^2*e^2 + 4*b*d*e + b^2 + (8*d^5*e^3 + 12*b*d^4*e^2 + 6*b^2*d^3*e + b^3*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)))*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2))*sqrt((2*e^2*x^2 + sqrt(1/2)*(2*b*d*e + b^2 + (8*d^5*e^3 + 12*b*d^4*e^2 + 6*b^2*d^3*e + b^3*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)))*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))/e^2))/e) + 1/4*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))*log(e*x + 1/2*(2*d*e - (4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))*log(e*x - 1/2*(2*d*e - (4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))) + 1/4*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))*log(e*x + 1/2*(2*d*e + (4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)))*log(e*x - 1/2*(2*d*e + (4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) + b)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e - b)/(8*d^7*e^3 + 12*b*d^6*e^2 + 6*b^2*d^5*e + b^3*d^4)) - b)/(4*d^4*e^2 + 4*b*d^3*e + b^2*d^2))))","B",0
6,1,3059,0,1.797888," ","integrate((e*x^4+d)/(e^2*x^8+f*x^4+d^2),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}} \arctan\left(-\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left(8 \, d^{5} e^{3} + 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - {\left(4 \, d^{2} e^{2} + 4 \, d e f + f^{2}\right)} x\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}} + {\left(4 \, d^{2} e^{2} + 4 \, d e f + f^{2} - {\left(8 \, d^{5} e^{3} + 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} + d^{2} f^{3}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}}\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}} \sqrt{\frac{2 \, e^{2} x^{2} + \sqrt{\frac{1}{2}} {\left(2 \, d e f + f^{2} - {\left(8 \, d^{5} e^{3} + 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} + d^{2} f^{3}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}}\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}}{e^{2}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}}}{4 \, e}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}} \arctan\left(-\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left(8 \, d^{5} e^{3} + 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} + d^{2} f^{3}\right)} x \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + {\left(4 \, d^{2} e^{2} + 4 \, d e f + f^{2}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}} - {\left(4 \, d^{2} e^{2} + 4 \, d e f + f^{2} + {\left(8 \, d^{5} e^{3} + 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} + d^{2} f^{3}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}} \sqrt{\frac{2 \, e^{2} x^{2} + \sqrt{\frac{1}{2}} {\left(2 \, d e f + f^{2} + {\left(8 \, d^{5} e^{3} + 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} + d^{2} f^{3}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}}\right)} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}}{e^{2}}}}{4 \, e}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}} \log\left(e x + \frac{1}{2} \, {\left(2 \, d e - {\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}} \log\left(e x - \frac{1}{2} \, {\left(2 \, d e - {\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}} \log\left(e x + \frac{1}{2} \, {\left(2 \, d e + {\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}} \log\left(e x - \frac{1}{2} \, {\left(2 \, d e + {\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} + f\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e - f}{8 \, d^{7} e^{3} + 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} + d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} + 4 \, d^{3} e f + d^{2} f^{2}}}}\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))*arctan(-1/4*(2*sqrt(1/2)*((8*d^5*e^3 + 12*d^4*e^2*f + 6*d^3*e*f^2 + d^2*f^3)*x*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - (4*d^2*e^2 + 4*d*e*f + f^2)*x)*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)) + (4*d^2*e^2 + 4*d*e*f + f^2 - (8*d^5*e^3 + 12*d^4*e^2*f + 6*d^3*e*f^2 + d^2*f^3)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)))*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2))*sqrt((2*e^2*x^2 + sqrt(1/2)*(2*d*e*f + f^2 - (8*d^5*e^3 + 12*d^4*e^2*f + 6*d^3*e*f^2 + d^2*f^3)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)))*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))/e^2))*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))/e) + sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))*arctan(-1/4*(2*sqrt(1/2)*((8*d^5*e^3 + 12*d^4*e^2*f + 6*d^3*e*f^2 + d^2*f^3)*x*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + (4*d^2*e^2 + 4*d*e*f + f^2)*x)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)) - (4*d^2*e^2 + 4*d*e*f + f^2 + (8*d^5*e^3 + 12*d^4*e^2*f + 6*d^3*e*f^2 + d^2*f^3)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)))*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2))*sqrt((2*e^2*x^2 + sqrt(1/2)*(2*d*e*f + f^2 + (8*d^5*e^3 + 12*d^4*e^2*f + 6*d^3*e*f^2 + d^2*f^3)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)))*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))/e^2))/e) + 1/4*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))*log(e*x + 1/2*(2*d*e - (4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))*log(e*x - 1/2*(2*d*e - (4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))) + 1/4*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))*log(e*x + 1/2*(2*d*e + (4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)))*log(e*x - 1/2*(2*d*e + (4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) + f)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 + 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e - f)/(8*d^7*e^3 + 12*d^6*e^2*f + 6*d^5*e*f^2 + d^4*f^3)) - f)/(4*d^4*e^2 + 4*d^3*e*f + d^2*f^2))))","B",0
7,1,3048,0,1.706172," ","integrate((e*x^4+d)/(e^2*x^8-b*x^4+d^2),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}} \arctan\left(-\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left(8 \, d^{5} e^{3} - 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e - b^{3} d^{2}\right)} x \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - {\left(4 \, d^{2} e^{2} - 4 \, b d e + b^{2}\right)} x\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}} + {\left(4 \, d^{2} e^{2} - 4 \, b d e + b^{2} - {\left(8 \, d^{5} e^{3} - 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e - b^{3} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}}\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}} \sqrt{\frac{2 \, e^{2} x^{2} - \sqrt{\frac{1}{2}} {\left(2 \, b d e - b^{2} + {\left(8 \, d^{5} e^{3} - 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e - b^{3} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}}\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}}{e^{2}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}}}{4 \, e}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}} \arctan\left(-\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left(8 \, d^{5} e^{3} - 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e - b^{3} d^{2}\right)} x \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + {\left(4 \, d^{2} e^{2} - 4 \, b d e + b^{2}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}} - {\left(4 \, d^{2} e^{2} - 4 \, b d e + b^{2} + {\left(8 \, d^{5} e^{3} - 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e - b^{3} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}} \sqrt{\frac{2 \, e^{2} x^{2} - \sqrt{\frac{1}{2}} {\left(2 \, b d e - b^{2} - {\left(8 \, d^{5} e^{3} - 12 \, b d^{4} e^{2} + 6 \, b^{2} d^{3} e - b^{3} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}}\right)} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}}{e^{2}}}}{4 \, e}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}} \log\left(e x + \frac{1}{2} \, {\left(2 \, d e + {\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}} \log\left(e x - \frac{1}{2} \, {\left(2 \, d e + {\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} + b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}} \log\left(e x + \frac{1}{2} \, {\left(2 \, d e - {\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}} \log\left(e x - \frac{1}{2} \, {\left(2 \, d e - {\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}\right)} \sqrt{-\frac{2 \, d e + b}{8 \, d^{7} e^{3} - 12 \, b d^{6} e^{2} + 6 \, b^{2} d^{5} e - b^{3} d^{4}}} - b}{4 \, d^{4} e^{2} - 4 \, b d^{3} e + b^{2} d^{2}}}}\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))*arctan(-1/4*(2*sqrt(1/2)*((8*d^5*e^3 - 12*b*d^4*e^2 + 6*b^2*d^3*e - b^3*d^2)*x*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - (4*d^2*e^2 - 4*b*d*e + b^2)*x)*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)) + (4*d^2*e^2 - 4*b*d*e + b^2 - (8*d^5*e^3 - 12*b*d^4*e^2 + 6*b^2*d^3*e - b^3*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)))*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2))*sqrt((2*e^2*x^2 - sqrt(1/2)*(2*b*d*e - b^2 + (8*d^5*e^3 - 12*b*d^4*e^2 + 6*b^2*d^3*e - b^3*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)))*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))/e^2))*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))/e) + sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))*arctan(-1/4*(2*sqrt(1/2)*((8*d^5*e^3 - 12*b*d^4*e^2 + 6*b^2*d^3*e - b^3*d^2)*x*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + (4*d^2*e^2 - 4*b*d*e + b^2)*x)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)) - (4*d^2*e^2 - 4*b*d*e + b^2 + (8*d^5*e^3 - 12*b*d^4*e^2 + 6*b^2*d^3*e - b^3*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)))*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2))*sqrt((2*e^2*x^2 - sqrt(1/2)*(2*b*d*e - b^2 - (8*d^5*e^3 - 12*b*d^4*e^2 + 6*b^2*d^3*e - b^3*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)))*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))/e^2))/e) + 1/4*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))*log(e*x + 1/2*(2*d*e + (4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))*log(e*x - 1/2*(2*d*e + (4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) + b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))) + 1/4*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))*log(e*x + 1/2*(2*d*e - (4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)))*log(e*x - 1/2*(2*d*e - (4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*b*d^3*e + b^2*d^2)*sqrt(-(2*d*e + b)/(8*d^7*e^3 - 12*b*d^6*e^2 + 6*b^2*d^5*e - b^3*d^4)) - b)/(4*d^4*e^2 - 4*b*d^3*e + b^2*d^2))))","B",0
8,1,3051,0,1.615202," ","integrate((e*x^4+d)/(e^2*x^8-f*x^4+d^2),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}} \arctan\left(\frac{{\left(2 \, \sqrt{\frac{1}{2}} {\left({\left(8 \, d^{5} e^{3} - 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} - d^{2} f^{3}\right)} x \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + {\left(4 \, d^{2} e^{2} - 4 \, d e f + f^{2}\right)} x\right)} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}} - {\left(4 \, d^{2} e^{2} - 4 \, d e f + f^{2} + {\left(8 \, d^{5} e^{3} - 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} - d^{2} f^{3}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}}\right)} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}} \sqrt{\frac{2 \, e^{2} x^{2} - \sqrt{\frac{1}{2}} {\left(2 \, d e f - f^{2} - {\left(8 \, d^{5} e^{3} - 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} - d^{2} f^{3}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}}\right)} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}}{e^{2}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}}}{4 \, e}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}} \arctan\left(\frac{2 \, \sqrt{\frac{1}{2}} {\left({\left(8 \, d^{5} e^{3} - 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} - d^{2} f^{3}\right)} x \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - {\left(4 \, d^{2} e^{2} - 4 \, d e f + f^{2}\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}} + {\left(4 \, d^{2} e^{2} - 4 \, d e f + f^{2} - {\left(8 \, d^{5} e^{3} - 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} - d^{2} f^{3}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}} \sqrt{\frac{2 \, e^{2} x^{2} - \sqrt{\frac{1}{2}} {\left(2 \, d e f - f^{2} + {\left(8 \, d^{5} e^{3} - 12 \, d^{4} e^{2} f + 6 \, d^{3} e f^{2} - d^{2} f^{3}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}}\right)} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}}{e^{2}}}}{4 \, e}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}} \log\left(e x + \frac{1}{2} \, {\left(2 \, d e + {\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}} \log\left(e x - \frac{1}{2} \, {\left(2 \, d e + {\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} + f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}} \log\left(e x + \frac{1}{2} \, {\left(2 \, d e - {\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}} \log\left(e x - \frac{1}{2} \, {\left(2 \, d e - {\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}\right)} \sqrt{-\frac{2 \, d e + f}{8 \, d^{7} e^{3} - 12 \, d^{6} e^{2} f + 6 \, d^{5} e f^{2} - d^{4} f^{3}}} - f}{4 \, d^{4} e^{2} - 4 \, d^{3} e f + d^{2} f^{2}}}}\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))*arctan(1/4*(2*sqrt(1/2)*((8*d^5*e^3 - 12*d^4*e^2*f + 6*d^3*e*f^2 - d^2*f^3)*x*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + (4*d^2*e^2 - 4*d*e*f + f^2)*x)*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)) - (4*d^2*e^2 - 4*d*e*f + f^2 + (8*d^5*e^3 - 12*d^4*e^2*f + 6*d^3*e*f^2 - d^2*f^3)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)))*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2))*sqrt((2*e^2*x^2 - sqrt(1/2)*(2*d*e*f - f^2 - (8*d^5*e^3 - 12*d^4*e^2*f + 6*d^3*e*f^2 - d^2*f^3)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)))*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))/e^2))*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))/e) + sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))*arctan(1/4*(2*sqrt(1/2)*((8*d^5*e^3 - 12*d^4*e^2*f + 6*d^3*e*f^2 - d^2*f^3)*x*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - (4*d^2*e^2 - 4*d*e*f + f^2)*x)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)) + (4*d^2*e^2 - 4*d*e*f + f^2 - (8*d^5*e^3 - 12*d^4*e^2*f + 6*d^3*e*f^2 - d^2*f^3)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)))*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2))*sqrt((2*e^2*x^2 - sqrt(1/2)*(2*d*e*f - f^2 + (8*d^5*e^3 - 12*d^4*e^2*f + 6*d^3*e*f^2 - d^2*f^3)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)))*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))/e^2))/e) + 1/4*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))*log(e*x + 1/2*(2*d*e + (4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))*log(e*x - 1/2*(2*d*e + (4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)*sqrt(sqrt(1/2)*sqrt(((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) + f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))) + 1/4*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))*log(e*x + 1/2*(2*d*e - (4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)))*log(e*x - 1/2*(2*d*e - (4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)*sqrt(sqrt(1/2)*sqrt(-((4*d^4*e^2 - 4*d^3*e*f + d^2*f^2)*sqrt(-(2*d*e + f)/(8*d^7*e^3 - 12*d^6*e^2*f + 6*d^5*e*f^2 - d^4*f^3)) - f)/(4*d^4*e^2 - 4*d^3*e*f + d^2*f^2))))","B",0
9,1,1443,0,1.408254," ","integrate((x^4+1)/(x^8+b*x^4+1),x, algorithm=""fricas"")","\sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} + {\left(b^{3} + 6 \, b^{2} + 12 \, b + 8\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + 4 \, b + 4\right)} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} + {\left(b^{3} + 6 \, b^{2} + 12 \, b + 8\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + 2 \, b\right)} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{3} + 6 \, b^{2} + 12 \, b + 8\right)} x \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + {\left(b^{2} + 4 \, b + 4\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}\right) - \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}}} \arctan\left(-\frac{1}{2} \, {\left(\sqrt{\frac{1}{2}} {\left(b^{2} - {\left(b^{3} + 6 \, b^{2} + 12 \, b + 8\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + 4 \, b + 4\right)} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - {\left(b^{3} + 6 \, b^{2} + 12 \, b + 8\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + 2 \, b\right)} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}}} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}} + \sqrt{\frac{1}{2}} {\left({\left(b^{3} + 6 \, b^{2} + 12 \, b + 8\right)} x \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - {\left(b^{2} + 4 \, b + 4\right)} x\right)} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}}}\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}}} \log\left(\frac{1}{2} \, {\left({\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b - 2\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}}} + x\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}}} \log\left(-\frac{1}{2} \, {\left({\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b - 2\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b}{b^{2} + 4 \, b + 4}}} + x\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}} \log\left(\frac{1}{2} \, {\left({\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b + 2\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}} + x\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}} \log\left(-\frac{1}{2} \, {\left({\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} + b + 2\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} + 4 \, b + 4\right)} \sqrt{\frac{b - 2}{b^{3} + 6 \, b^{2} + 12 \, b + 8}} - b}{b^{2} + 4 \, b + 4}}} + x\right)"," ",0,"sqrt(sqrt(1/2)*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4)))*arctan(1/2*sqrt(1/2)*(b^2 + (b^3 + 6*b^2 + 12*b + 8)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + 4*b + 4)*sqrt(x^2 + 1/2*sqrt(1/2)*(b^2 + (b^3 + 6*b^2 + 12*b + 8)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + 2*b)*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4)))*sqrt(sqrt(1/2)*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4)))*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4)) - 1/2*sqrt(1/2)*((b^3 + 6*b^2 + 12*b + 8)*x*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + (b^2 + 4*b + 4)*x)*sqrt(sqrt(1/2)*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4)))*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4))) - sqrt(sqrt(1/2)*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4)))*arctan(-1/2*(sqrt(1/2)*(b^2 - (b^3 + 6*b^2 + 12*b + 8)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + 4*b + 4)*sqrt(x^2 + 1/2*sqrt(1/2)*(b^2 - (b^3 + 6*b^2 + 12*b + 8)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + 2*b)*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4)))*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4)) + sqrt(1/2)*((b^3 + 6*b^2 + 12*b + 8)*x*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - (b^2 + 4*b + 4)*x)*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4)))*sqrt(sqrt(1/2)*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4)))) - 1/4*sqrt(sqrt(1/2)*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4)))*log(1/2*((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b - 2)*sqrt(sqrt(1/2)*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4))) + x) + 1/4*sqrt(sqrt(1/2)*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4)))*log(-1/2*((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b - 2)*sqrt(sqrt(1/2)*sqrt(-((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b)/(b^2 + 4*b + 4))) + x) + 1/4*sqrt(sqrt(1/2)*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4)))*log(1/2*((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b + 2)*sqrt(sqrt(1/2)*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4))) + x) - 1/4*sqrt(sqrt(1/2)*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4)))*log(-1/2*((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) + b + 2)*sqrt(sqrt(1/2)*sqrt(((b^2 + 4*b + 4)*sqrt((b - 2)/(b^3 + 6*b^2 + 12*b + 8)) - b)/(b^2 + 4*b + 4))) + x)","B",0
10,1,951,0,1.242512," ","integrate((x^4+1)/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{80} \, \sqrt{10} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} + \sqrt{10} {\left(\sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} - 5 \, \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)}} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 2\right)} + \frac{1}{40} \, \sqrt{10} {\left(2 \, \sqrt{5} x - 5 \, x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} - \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{2 \, \sqrt{5} + 6} \sqrt{\sqrt{5} + 3}\right) + \frac{1}{80} \, \sqrt{10} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} - \sqrt{10} {\left(\sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} - 5 \, \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)}} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 2\right)} + \frac{1}{40} \, \sqrt{10} {\left(2 \, \sqrt{5} x - 5 \, x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} + \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{2 \, \sqrt{5} + 6} \sqrt{\sqrt{5} + 3}\right) - \frac{1}{80} \, \sqrt{10} {\left(\sqrt{5} + 3\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} + \sqrt{10} {\left(\sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 5 \, {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6}} {\left(\sqrt{5} + 2\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - \frac{1}{40} \, {\left(\sqrt{10} {\left(2 \, \sqrt{5} x + 5 \, x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} + 5 \, {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)} \sqrt{-\sqrt{5} + 3}\right) - \frac{1}{80} \, \sqrt{10} {\left(\sqrt{5} + 3\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{80} \, \sqrt{10} \sqrt{20 \, x^{2} - \sqrt{10} {\left(\sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 5 \, {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6}} {\left(\sqrt{5} + 2\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - \frac{1}{40} \, {\left(\sqrt{10} {\left(2 \, \sqrt{5} x + 5 \, x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - 5 \, {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)} \sqrt{-\sqrt{5} + 3}\right) - \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} + \sqrt{10} {\left(\sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} - 5 \, \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)}\right) + \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} - \sqrt{10} {\left(\sqrt{5} \sqrt{2} x - 5 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} - 5 \, \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)}\right) + \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} + \sqrt{10} {\left(\sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 5 \, {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6}\right) - \frac{1}{80} \, \sqrt{10} \sqrt{2} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(20 \, x^{2} - \sqrt{10} {\left(\sqrt{5} \sqrt{2} x + 5 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} + 5 \, {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)"," ",0,"1/80*sqrt(10)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3)*arctan(1/80*sqrt(10)*sqrt(20*x^2 + sqrt(10)*(sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(2*sqrt(5) + 6)^(1/4) - 5*sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3))*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3)*(sqrt(5) - 2) + 1/40*sqrt(10)*(2*sqrt(5)*x - 5*x)*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) - 1/8*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(2*sqrt(5) + 6)*sqrt(sqrt(5) + 3)) + 1/80*sqrt(10)*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3)*arctan(1/80*sqrt(10)*sqrt(20*x^2 - sqrt(10)*(sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(2*sqrt(5) + 6)^(1/4) - 5*sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3))*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3)*(sqrt(5) - 2) + 1/40*sqrt(10)*(2*sqrt(5)*x - 5*x)*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) + 1/8*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(2*sqrt(5) + 6)*sqrt(sqrt(5) + 3)) - 1/80*sqrt(10)*(sqrt(5) + 3)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4)*arctan(1/80*sqrt(10)*sqrt(20*x^2 + sqrt(10)*(sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-2*sqrt(5) + 6)^(1/4) + 5*(sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6))*(sqrt(5) + 2)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(5/4) - 1/40*(sqrt(10)*(2*sqrt(5)*x + 5*x)*(-2*sqrt(5) + 6)^(5/4) + 5*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-2*sqrt(5) + 6))*sqrt(-sqrt(5) + 3)) - 1/80*sqrt(10)*(sqrt(5) + 3)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4)*arctan(1/80*sqrt(10)*sqrt(20*x^2 - sqrt(10)*(sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-2*sqrt(5) + 6)^(1/4) + 5*(sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6))*(sqrt(5) + 2)*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(5/4) - 1/40*(sqrt(10)*(2*sqrt(5)*x + 5*x)*(-2*sqrt(5) + 6)^(5/4) - 5*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-2*sqrt(5) + 6))*sqrt(-sqrt(5) + 3)) - 1/80*sqrt(10)*sqrt(2)*(2*sqrt(5) + 6)^(1/4)*log(20*x^2 + sqrt(10)*(sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(2*sqrt(5) + 6)^(1/4) - 5*sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3)) + 1/80*sqrt(10)*sqrt(2)*(2*sqrt(5) + 6)^(1/4)*log(20*x^2 - sqrt(10)*(sqrt(5)*sqrt(2)*x - 5*sqrt(2)*x)*(2*sqrt(5) + 6)^(1/4) - 5*sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3)) + 1/80*sqrt(10)*sqrt(2)*(-2*sqrt(5) + 6)^(1/4)*log(20*x^2 + sqrt(10)*(sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-2*sqrt(5) + 6)^(1/4) + 5*(sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6)) - 1/80*sqrt(10)*sqrt(2)*(-2*sqrt(5) + 6)^(1/4)*log(20*x^2 - sqrt(10)*(sqrt(5)*sqrt(2)*x + 5*sqrt(2)*x)*(-2*sqrt(5) + 6)^(1/4) + 5*(sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6))","B",0
11,1,95,0,1.010022," ","integrate((x^4+1)/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) - \frac{1}{2} \, \sqrt{2} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) + \frac{1}{8} \, \sqrt{2} \log\left(x^{2} + \sqrt{2} x + 1\right) - \frac{1}{8} \, \sqrt{2} \log\left(x^{2} - \sqrt{2} x + 1\right)"," ",0,"-1/2*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) - 1/2*sqrt(2)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) + 1/8*sqrt(2)*log(x^2 + sqrt(2)*x + 1) - 1/8*sqrt(2)*log(x^2 - sqrt(2)*x + 1)","A",0
12,1,211,0,1.461277," ","integrate((x^4+1)/(x^8+x^4+1),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} - \sqrt{3}\right) - \frac{1}{12} \, \sqrt{6} \sqrt{3} \sqrt{2} \arctan\left(-\frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{2} x + \frac{1}{3} \, \sqrt{6} \sqrt{3} \sqrt{-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2} + \sqrt{3}\right) + \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) - \frac{1}{48} \, \sqrt{6} \sqrt{2} \log\left(-\sqrt{6} \sqrt{2} x + 2 \, x^{2} + 2\right) + \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{12} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, \log\left(x^{2} + x + 1\right) - \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"-1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - sqrt(3)) - 1/12*sqrt(6)*sqrt(3)*sqrt(2)*arctan(-1/3*sqrt(6)*sqrt(3)*sqrt(2)*x + 1/3*sqrt(6)*sqrt(3)*sqrt(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + sqrt(3)) + 1/48*sqrt(6)*sqrt(2)*log(sqrt(6)*sqrt(2)*x + 2*x^2 + 2) - 1/48*sqrt(6)*sqrt(2)*log(-sqrt(6)*sqrt(2)*x + 2*x^2 + 2) + 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/12*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*log(x^2 + x + 1) - 1/8*log(x^2 - x + 1)","A",0
13,1,991,0,1.342424," ","integrate((x^4+1)/(x^8+1),x, algorithm=""fricas"")","-\frac{1}{8} \, {\left(\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, {\left(\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, {\left(\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, {\left(\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2} \sqrt{-\sqrt{2} + 2} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{2} \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, \sqrt{2} \sqrt{\sqrt{2} + 2} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{32} \, \sqrt{2} \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, \sqrt{2} \sqrt{\sqrt{2} + 2} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, \sqrt{2} \sqrt{\sqrt{2} + 2} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, \sqrt{2} \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, {\left(\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, {\left(\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, {\left(\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, {\left(\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"-1/8*(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(2)*sqrt(-sqrt(2) + 2)*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) - 1/8*sqrt(2)*sqrt(-sqrt(2) + 2)*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) + 1/8*sqrt(2)*sqrt(sqrt(2) + 2)*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) + 1/8*sqrt(2)*sqrt(sqrt(2) + 2)*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) + 1/32*sqrt(2)*sqrt(-sqrt(2) + 2)*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/32*sqrt(2)*sqrt(sqrt(2) + 2)*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/32*sqrt(2)*sqrt(sqrt(2) + 2)*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/32*sqrt(2)*sqrt(-sqrt(2) + 2)*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/32*(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/32*(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) + 1/32*(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) - 1/32*(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","B",0
14,1,377,0,1.321076," ","integrate((x^4+1)/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{8} \, \sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)} \log\left(2 \, x^{2} + 2 \, x \sqrt{\sqrt{3} + 2} + 2\right) + \frac{1}{8} \, \sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)} \log\left(2 \, x^{2} - 2 \, x \sqrt{\sqrt{3} + 2} + 2\right) + \frac{1}{16} \, {\left(\sqrt{3} + 2\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(2 \, x^{2} + x \sqrt{-4 \, \sqrt{3} + 8} + 2\right) - \frac{1}{16} \, {\left(\sqrt{3} + 2\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(2 \, x^{2} - x \sqrt{-4 \, \sqrt{3} + 8} + 2\right) - \frac{1}{2} \, \sqrt{\sqrt{3} + 2} \arctan\left(\sqrt{2} \sqrt{2 \, x^{2} + 2 \, x \sqrt{\sqrt{3} + 2} + 2} \sqrt{\sqrt{3} + 2} - 2 \, x \sqrt{\sqrt{3} + 2} - \sqrt{3} - 2\right) - \frac{1}{2} \, \sqrt{\sqrt{3} + 2} \arctan\left(\sqrt{2} \sqrt{2 \, x^{2} - 2 \, x \sqrt{\sqrt{3} + 2} + 2} \sqrt{\sqrt{3} + 2} - 2 \, x \sqrt{\sqrt{3} + 2} + \sqrt{3} + 2\right) - \frac{1}{4} \, \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{2 \, x^{2} + x \sqrt{-4 \, \sqrt{3} + 8} + 2} \sqrt{-4 \, \sqrt{3} + 8} - x \sqrt{-4 \, \sqrt{3} + 8} + \sqrt{3} - 2\right) - \frac{1}{4} \, \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(\frac{1}{2} \, \sqrt{2} \sqrt{2 \, x^{2} - x \sqrt{-4 \, \sqrt{3} + 8} + 2} \sqrt{-4 \, \sqrt{3} + 8} - x \sqrt{-4 \, \sqrt{3} + 8} - \sqrt{3} + 2\right)"," ",0,"-1/8*sqrt(sqrt(3) + 2)*(sqrt(3) - 2)*log(2*x^2 + 2*x*sqrt(sqrt(3) + 2) + 2) + 1/8*sqrt(sqrt(3) + 2)*(sqrt(3) - 2)*log(2*x^2 - 2*x*sqrt(sqrt(3) + 2) + 2) + 1/16*(sqrt(3) + 2)*sqrt(-4*sqrt(3) + 8)*log(2*x^2 + x*sqrt(-4*sqrt(3) + 8) + 2) - 1/16*(sqrt(3) + 2)*sqrt(-4*sqrt(3) + 8)*log(2*x^2 - x*sqrt(-4*sqrt(3) + 8) + 2) - 1/2*sqrt(sqrt(3) + 2)*arctan(sqrt(2)*sqrt(2*x^2 + 2*x*sqrt(sqrt(3) + 2) + 2)*sqrt(sqrt(3) + 2) - 2*x*sqrt(sqrt(3) + 2) - sqrt(3) - 2) - 1/2*sqrt(sqrt(3) + 2)*arctan(sqrt(2)*sqrt(2*x^2 - 2*x*sqrt(sqrt(3) + 2) + 2)*sqrt(sqrt(3) + 2) - 2*x*sqrt(sqrt(3) + 2) + sqrt(3) + 2) - 1/4*sqrt(-4*sqrt(3) + 8)*arctan(1/2*sqrt(2)*sqrt(2*x^2 + x*sqrt(-4*sqrt(3) + 8) + 2)*sqrt(-4*sqrt(3) + 8) - x*sqrt(-4*sqrt(3) + 8) + sqrt(3) - 2) - 1/4*sqrt(-4*sqrt(3) + 8)*arctan(1/2*sqrt(2)*sqrt(2*x^2 - x*sqrt(-4*sqrt(3) + 8) + 2)*sqrt(-4*sqrt(3) + 8) - x*sqrt(-4*sqrt(3) + 8) - sqrt(3) + 2)","A",0
15,1,43,0,1.489785," ","integrate((x^4+1)/(x^8-2*x^4+1),x, algorithm=""fricas"")","\frac{2 \, {\left(x^{4} - 1\right)} \arctan\left(x\right) + {\left(x^{4} - 1\right)} \log\left(x + 1\right) - {\left(x^{4} - 1\right)} \log\left(x - 1\right) - 4 \, x}{8 \, {\left(x^{4} - 1\right)}}"," ",0,"1/8*(2*(x^4 - 1)*arctan(x) + (x^4 - 1)*log(x + 1) - (x^4 - 1)*log(x - 1) - 4*x)/(x^4 - 1)","B",0
16,1,247,0,1.570223," ","integrate((x^4+1)/(x^8-3*x^4+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{2} \sqrt{\sqrt{5} + 1} \arctan\left(-\frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{5} + 1} + \frac{1}{2} \, \sqrt{2 \, x^{2} + \sqrt{5} - 1} \sqrt{\sqrt{5} + 1}\right) + \frac{1}{2} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \arctan\left(-\frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{5} - 1} + \frac{1}{2} \, \sqrt{2 \, x^{2} + \sqrt{5} + 1} \sqrt{\sqrt{5} - 1}\right) + \frac{1}{8} \, \sqrt{2} \sqrt{\sqrt{5} + 1} \log\left({\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 1} + 4 \, x\right) - \frac{1}{8} \, \sqrt{2} \sqrt{\sqrt{5} + 1} \log\left(-{\left(\sqrt{5} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{5} + 1} + 4 \, x\right) - \frac{1}{8} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left({\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{\sqrt{5} - 1} + 4 \, x\right) + \frac{1}{8} \, \sqrt{2} \sqrt{\sqrt{5} - 1} \log\left(-{\left(\sqrt{5} \sqrt{2} + \sqrt{2}\right)} \sqrt{\sqrt{5} - 1} + 4 \, x\right)"," ",0,"-1/2*sqrt(2)*sqrt(sqrt(5) + 1)*arctan(-1/2*sqrt(2)*x*sqrt(sqrt(5) + 1) + 1/2*sqrt(2*x^2 + sqrt(5) - 1)*sqrt(sqrt(5) + 1)) + 1/2*sqrt(2)*sqrt(sqrt(5) - 1)*arctan(-1/2*sqrt(2)*x*sqrt(sqrt(5) - 1) + 1/2*sqrt(2*x^2 + sqrt(5) + 1)*sqrt(sqrt(5) - 1)) + 1/8*sqrt(2)*sqrt(sqrt(5) + 1)*log((sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 1) + 4*x) - 1/8*sqrt(2)*sqrt(sqrt(5) + 1)*log(-(sqrt(5)*sqrt(2) - sqrt(2))*sqrt(sqrt(5) + 1) + 4*x) - 1/8*sqrt(2)*sqrt(sqrt(5) - 1)*log((sqrt(5)*sqrt(2) + sqrt(2))*sqrt(sqrt(5) - 1) + 4*x) + 1/8*sqrt(2)*sqrt(sqrt(5) - 1)*log(-(sqrt(5)*sqrt(2) + sqrt(2))*sqrt(sqrt(5) - 1) + 4*x)","B",0
17,1,331,0,1.260114," ","integrate((x^4+1)/(x^8-4*x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, \sqrt{x^{2} + {\left(\sqrt{3} + 2\right)} \sqrt{-\sqrt{3} + 2}} {\left(\sqrt{3} \sqrt{2} + \sqrt{2}\right)} {\left(-\sqrt{3} + 2\right)}^{\frac{3}{4}} - \frac{1}{2} \, {\left(\sqrt{3} \sqrt{2} x + \sqrt{2} x\right)} {\left(-\sqrt{3} + 2\right)}^{\frac{3}{4}}\right) - \frac{1}{2} \, \sqrt{2} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{2} \, {\left(\sqrt{x^{2} - \sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)}} {\left(\sqrt{3} \sqrt{2} - \sqrt{2}\right)} \sqrt{\sqrt{3} + 2} - {\left(\sqrt{3} \sqrt{2} x - \sqrt{2} x\right)} \sqrt{\sqrt{3} + 2}\right)} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \, \sqrt{2} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} \log\left({\left(\sqrt{3} \sqrt{2} - \sqrt{2}\right)} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} + 2 \, x\right) - \frac{1}{8} \, \sqrt{2} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} \log\left(-{\left(\sqrt{3} \sqrt{2} - \sqrt{2}\right)} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} + 2 \, x\right) - \frac{1}{8} \, \sqrt{2} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} \log\left({\left(\sqrt{3} \sqrt{2} + \sqrt{2}\right)} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} + 2 \, x\right) + \frac{1}{8} \, \sqrt{2} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} \log\left(-{\left(\sqrt{3} \sqrt{2} + \sqrt{2}\right)} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} + 2 \, x\right)"," ",0,"1/2*sqrt(2)*(-sqrt(3) + 2)^(1/4)*arctan(1/2*sqrt(x^2 + (sqrt(3) + 2)*sqrt(-sqrt(3) + 2))*(sqrt(3)*sqrt(2) + sqrt(2))*(-sqrt(3) + 2)^(3/4) - 1/2*(sqrt(3)*sqrt(2)*x + sqrt(2)*x)*(-sqrt(3) + 2)^(3/4)) - 1/2*sqrt(2)*(sqrt(3) + 2)^(1/4)*arctan(1/2*(sqrt(x^2 - sqrt(sqrt(3) + 2)*(sqrt(3) - 2))*(sqrt(3)*sqrt(2) - sqrt(2))*sqrt(sqrt(3) + 2) - (sqrt(3)*sqrt(2)*x - sqrt(2)*x)*sqrt(sqrt(3) + 2))*(sqrt(3) + 2)^(1/4)) + 1/8*sqrt(2)*(sqrt(3) + 2)^(1/4)*log((sqrt(3)*sqrt(2) - sqrt(2))*(sqrt(3) + 2)^(1/4) + 2*x) - 1/8*sqrt(2)*(sqrt(3) + 2)^(1/4)*log(-(sqrt(3)*sqrt(2) - sqrt(2))*(sqrt(3) + 2)^(1/4) + 2*x) - 1/8*sqrt(2)*(-sqrt(3) + 2)^(1/4)*log((sqrt(3)*sqrt(2) + sqrt(2))*(-sqrt(3) + 2)^(1/4) + 2*x) + 1/8*sqrt(2)*(-sqrt(3) + 2)^(1/4)*log(-(sqrt(3)*sqrt(2) + sqrt(2))*(-sqrt(3) + 2)^(1/4) + 2*x)","B",0
18,1,574,0,1.650771," ","integrate((x^4+1)/(x^8-5*x^4+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{6} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} \arctan\left(\frac{1}{48} \, {\left(\sqrt{7} \sqrt{6} \sqrt{3} \sqrt{2} + 3 \, \sqrt{6} \sqrt{2}\right)} \sqrt{4 \, x^{2} + {\left(\sqrt{7} \sqrt{3} \sqrt{2} + 5 \, \sqrt{2}\right)} \sqrt{-\sqrt{7} \sqrt{3} + 5}} \sqrt{-\sqrt{7} \sqrt{3} + 5} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} - \frac{1}{24} \, {\left(\sqrt{7} \sqrt{6} \sqrt{3} \sqrt{2} x + 3 \, \sqrt{6} \sqrt{2} x\right)} \sqrt{-\sqrt{7} \sqrt{3} + 5} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}}\right) - \frac{1}{6} \, \sqrt{6} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} \arctan\left(\frac{1}{48} \, {\left({\left(\sqrt{7} \sqrt{6} \sqrt{3} \sqrt{2} - 3 \, \sqrt{6} \sqrt{2}\right)} \sqrt{4 \, x^{2} - {\left(\sqrt{7} \sqrt{3} \sqrt{2} - 5 \, \sqrt{2}\right)} \sqrt{\sqrt{7} \sqrt{3} + 5}} \sqrt{\sqrt{7} \sqrt{3} + 5} - 2 \, {\left(\sqrt{7} \sqrt{6} \sqrt{3} \sqrt{2} x - 3 \, \sqrt{6} \sqrt{2} x\right)} \sqrt{\sqrt{7} \sqrt{3} + 5}\right)} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}}\right) + \frac{1}{24} \, \sqrt{6} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} \log\left({\left(\sqrt{7} \sqrt{6} \sqrt{3} - 3 \, \sqrt{6}\right)} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} + 12 \, x\right) - \frac{1}{24} \, \sqrt{6} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} \log\left(-{\left(\sqrt{7} \sqrt{6} \sqrt{3} - 3 \, \sqrt{6}\right)} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} + 12 \, x\right) - \frac{1}{24} \, \sqrt{6} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} \log\left({\left(\sqrt{7} \sqrt{6} \sqrt{3} + 3 \, \sqrt{6}\right)} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} + 12 \, x\right) + \frac{1}{24} \, \sqrt{6} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} \log\left(-{\left(\sqrt{7} \sqrt{6} \sqrt{3} + 3 \, \sqrt{6}\right)} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} + 12 \, x\right)"," ",0,"1/6*sqrt(6)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5))*arctan(1/48*(sqrt(7)*sqrt(6)*sqrt(3)*sqrt(2) + 3*sqrt(6)*sqrt(2))*sqrt(4*x^2 + (sqrt(7)*sqrt(3)*sqrt(2) + 5*sqrt(2))*sqrt(-sqrt(7)*sqrt(3) + 5))*sqrt(-sqrt(7)*sqrt(3) + 5)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5)) - 1/24*(sqrt(7)*sqrt(6)*sqrt(3)*sqrt(2)*x + 3*sqrt(6)*sqrt(2)*x)*sqrt(-sqrt(7)*sqrt(3) + 5)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5))) - 1/6*sqrt(6)*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5))*arctan(1/48*((sqrt(7)*sqrt(6)*sqrt(3)*sqrt(2) - 3*sqrt(6)*sqrt(2))*sqrt(4*x^2 - (sqrt(7)*sqrt(3)*sqrt(2) - 5*sqrt(2))*sqrt(sqrt(7)*sqrt(3) + 5))*sqrt(sqrt(7)*sqrt(3) + 5) - 2*(sqrt(7)*sqrt(6)*sqrt(3)*sqrt(2)*x - 3*sqrt(6)*sqrt(2)*x)*sqrt(sqrt(7)*sqrt(3) + 5))*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5))) + 1/24*sqrt(6)*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5))*log((sqrt(7)*sqrt(6)*sqrt(3) - 3*sqrt(6))*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5)) + 12*x) - 1/24*sqrt(6)*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5))*log(-(sqrt(7)*sqrt(6)*sqrt(3) - 3*sqrt(6))*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5)) + 12*x) - 1/24*sqrt(6)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5))*log((sqrt(7)*sqrt(6)*sqrt(3) + 3*sqrt(6))*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5)) + 12*x) + 1/24*sqrt(6)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5))*log(-(sqrt(7)*sqrt(6)*sqrt(3) + 3*sqrt(6))*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5)) + 12*x)","B",0
19,1,181,0,1.233464," ","integrate((x^4+1)/(x^8-6*x^4+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\sqrt{2} + 1} \arctan\left(-x \sqrt{\sqrt{2} + 1} + \sqrt{x^{2} + \sqrt{2} - 1} \sqrt{\sqrt{2} + 1}\right) + \frac{1}{2} \, \sqrt{\sqrt{2} - 1} \arctan\left(-x \sqrt{\sqrt{2} - 1} + \sqrt{x^{2} + \sqrt{2} + 1} \sqrt{\sqrt{2} - 1}\right) - \frac{1}{8} \, \sqrt{\sqrt{2} - 1} \log\left({\left(\sqrt{2} + 1\right)} \sqrt{\sqrt{2} - 1} + x\right) + \frac{1}{8} \, \sqrt{\sqrt{2} - 1} \log\left(-{\left(\sqrt{2} + 1\right)} \sqrt{\sqrt{2} - 1} + x\right) + \frac{1}{8} \, \sqrt{\sqrt{2} + 1} \log\left(\sqrt{\sqrt{2} + 1} {\left(\sqrt{2} - 1\right)} + x\right) - \frac{1}{8} \, \sqrt{\sqrt{2} + 1} \log\left(-\sqrt{\sqrt{2} + 1} {\left(\sqrt{2} - 1\right)} + x\right)"," ",0,"-1/2*sqrt(sqrt(2) + 1)*arctan(-x*sqrt(sqrt(2) + 1) + sqrt(x^2 + sqrt(2) - 1)*sqrt(sqrt(2) + 1)) + 1/2*sqrt(sqrt(2) - 1)*arctan(-x*sqrt(sqrt(2) - 1) + sqrt(x^2 + sqrt(2) + 1)*sqrt(sqrt(2) - 1)) - 1/8*sqrt(sqrt(2) - 1)*log((sqrt(2) + 1)*sqrt(sqrt(2) - 1) + x) + 1/8*sqrt(sqrt(2) - 1)*log(-(sqrt(2) + 1)*sqrt(sqrt(2) - 1) + x) + 1/8*sqrt(sqrt(2) + 1)*log(sqrt(sqrt(2) + 1)*(sqrt(2) - 1) + x) - 1/8*sqrt(sqrt(2) + 1)*log(-sqrt(sqrt(2) + 1)*(sqrt(2) - 1) + x)","B",0
20,1,1443,0,1.354393," ","integrate((-x^4+1)/(x^8+b*x^4+1),x, algorithm=""fricas"")","-\sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} + {\left(b^{3} - 6 \, b^{2} + 12 \, b - 8\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - 4 \, b + 4\right)} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} + {\left(b^{3} - 6 \, b^{2} + 12 \, b - 8\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - 2 \, b\right)} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}} - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{3} - 6 \, b^{2} + 12 \, b - 8\right)} x \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + {\left(b^{2} - 4 \, b + 4\right)} x\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}\right) + \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}}} \arctan\left(-\frac{1}{2} \, {\left(\sqrt{\frac{1}{2}} {\left(b^{2} - {\left(b^{3} - 6 \, b^{2} + 12 \, b - 8\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - 4 \, b + 4\right)} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - {\left(b^{3} - 6 \, b^{2} + 12 \, b - 8\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - 2 \, b\right)} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}}} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}} + \sqrt{\frac{1}{2}} {\left({\left(b^{3} - 6 \, b^{2} + 12 \, b - 8\right)} x \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - {\left(b^{2} - 4 \, b + 4\right)} x\right)} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}}\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}}}\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}}} \log\left(\frac{1}{2} \, {\left({\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b + 2\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}}} + x\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}}} \log\left(-\frac{1}{2} \, {\left({\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b + 2\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{-\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b}{b^{2} - 4 \, b + 4}}} + x\right) - \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}} \log\left(\frac{1}{2} \, {\left({\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b - 2\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}} + x\right) + \frac{1}{4} \, \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}} \log\left(-\frac{1}{2} \, {\left({\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} + b - 2\right)} \sqrt{\sqrt{\frac{1}{2}} \sqrt{\frac{{\left(b^{2} - 4 \, b + 4\right)} \sqrt{\frac{b + 2}{b^{3} - 6 \, b^{2} + 12 \, b - 8}} - b}{b^{2} - 4 \, b + 4}}} + x\right)"," ",0,"-sqrt(sqrt(1/2)*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4)))*arctan(1/2*sqrt(1/2)*(b^2 + (b^3 - 6*b^2 + 12*b - 8)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - 4*b + 4)*sqrt(x^2 + 1/2*sqrt(1/2)*(b^2 + (b^3 - 6*b^2 + 12*b - 8)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - 2*b)*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4)))*sqrt(sqrt(1/2)*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4)))*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4)) - 1/2*sqrt(1/2)*((b^3 - 6*b^2 + 12*b - 8)*x*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + (b^2 - 4*b + 4)*x)*sqrt(sqrt(1/2)*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4)))*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4))) + sqrt(sqrt(1/2)*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4)))*arctan(-1/2*(sqrt(1/2)*(b^2 - (b^3 - 6*b^2 + 12*b - 8)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - 4*b + 4)*sqrt(x^2 + 1/2*sqrt(1/2)*(b^2 - (b^3 - 6*b^2 + 12*b - 8)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - 2*b)*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4)))*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4)) + sqrt(1/2)*((b^3 - 6*b^2 + 12*b - 8)*x*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - (b^2 - 4*b + 4)*x)*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4)))*sqrt(sqrt(1/2)*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4)))) + 1/4*sqrt(sqrt(1/2)*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4)))*log(1/2*((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b + 2)*sqrt(sqrt(1/2)*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4))) + x) - 1/4*sqrt(sqrt(1/2)*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4)))*log(-1/2*((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b + 2)*sqrt(sqrt(1/2)*sqrt(-((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b)/(b^2 - 4*b + 4))) + x) - 1/4*sqrt(sqrt(1/2)*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4)))*log(1/2*((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b - 2)*sqrt(sqrt(1/2)*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4))) + x) + 1/4*sqrt(sqrt(1/2)*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4)))*log(-1/2*((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) + b - 2)*sqrt(sqrt(1/2)*sqrt(((b^2 - 4*b + 4)*sqrt((b + 2)/(b^3 - 6*b^2 + 12*b - 8)) - b)/(b^2 - 4*b + 4))) + x)","B",0
21,1,894,0,1.582742," ","integrate((-x^4+1)/(x^8+3*x^4+1),x, algorithm=""fricas"")","\frac{1}{16} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} \arctan\left(\frac{1}{16} \, \sqrt{4 \, x^{2} - \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)} + 2 \, {\left(\sqrt{5} x - x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}}} {\left(\sqrt{5} \sqrt{2} - 2 \, \sqrt{2}\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} - \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} x - 2 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} + \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{2 \, \sqrt{5} + 6} \sqrt{\sqrt{5} + 3}\right) + \frac{1}{16} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \sqrt{\sqrt{5} + 3} \arctan\left(\frac{1}{16} \, \sqrt{4 \, x^{2} - \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)} - 2 \, {\left(\sqrt{5} x - x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}}} {\left(\sqrt{5} \sqrt{2} - 2 \, \sqrt{2}\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} - \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} x - 2 \, \sqrt{2} x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} \sqrt{\sqrt{5} + 3} - \frac{1}{8} \, {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} \sqrt{2 \, \sqrt{5} + 6} \sqrt{\sqrt{5} + 3}\right) + \frac{1}{16} \, {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{16} \, \sqrt{4 \, x^{2} + {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6} + 2 \, {\left(\sqrt{5} x + x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}}} {\left(\sqrt{5} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - \frac{1}{8} \, {\left({\left(\sqrt{5} \sqrt{2} x + 2 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} + {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)} \sqrt{-\sqrt{5} + 3}\right) + \frac{1}{16} \, {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{3}{4}} \arctan\left(\frac{1}{16} \, \sqrt{4 \, x^{2} + {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6} - 2 \, {\left(\sqrt{5} x + x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}}} {\left(\sqrt{5} \sqrt{2} + 2 \, \sqrt{2}\right)} \sqrt{-\sqrt{5} + 3} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - \frac{1}{8} \, {\left({\left(\sqrt{5} \sqrt{2} x + 2 \, \sqrt{2} x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{5}{4}} - {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-2 \, \sqrt{5} + 6}\right)} \sqrt{-\sqrt{5} + 3}\right) + \frac{1}{8} \, {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(4 \, x^{2} - \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)} + 2 \, {\left(\sqrt{5} x - x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \, {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(4 \, x^{2} - \sqrt{2 \, \sqrt{5} + 6} {\left(\sqrt{5} - 3\right)} - 2 \, {\left(\sqrt{5} x - x\right)} {\left(2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}}\right) - \frac{1}{8} \, {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(4 \, x^{2} + {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6} + 2 \, {\left(\sqrt{5} x + x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}}\right) + \frac{1}{8} \, {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}} \log\left(4 \, x^{2} + {\left(\sqrt{5} + 3\right)} \sqrt{-2 \, \sqrt{5} + 6} - 2 \, {\left(\sqrt{5} x + x\right)} {\left(-2 \, \sqrt{5} + 6\right)}^{\frac{1}{4}}\right)"," ",0,"1/16*(sqrt(5)*sqrt(2) - 3*sqrt(2))*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3)*arctan(1/16*sqrt(4*x^2 - sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3) + 2*(sqrt(5)*x - x)*(2*sqrt(5) + 6)^(1/4))*(sqrt(5)*sqrt(2) - 2*sqrt(2))*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) - 1/8*(sqrt(5)*sqrt(2)*x - 2*sqrt(2)*x)*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) + 1/8*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(2*sqrt(5) + 6)*sqrt(sqrt(5) + 3)) + 1/16*(sqrt(5)*sqrt(2) - 3*sqrt(2))*(2*sqrt(5) + 6)^(3/4)*sqrt(sqrt(5) + 3)*arctan(1/16*sqrt(4*x^2 - sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3) - 2*(sqrt(5)*x - x)*(2*sqrt(5) + 6)^(1/4))*(sqrt(5)*sqrt(2) - 2*sqrt(2))*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) - 1/8*(sqrt(5)*sqrt(2)*x - 2*sqrt(2)*x)*(2*sqrt(5) + 6)^(5/4)*sqrt(sqrt(5) + 3) - 1/8*(sqrt(5)*sqrt(2) - 3*sqrt(2))*sqrt(2*sqrt(5) + 6)*sqrt(sqrt(5) + 3)) + 1/16*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4)*arctan(1/16*sqrt(4*x^2 + (sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6) + 2*(sqrt(5)*x + x)*(-2*sqrt(5) + 6)^(1/4))*(sqrt(5)*sqrt(2) + 2*sqrt(2))*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(5/4) - 1/8*((sqrt(5)*sqrt(2)*x + 2*sqrt(2)*x)*(-2*sqrt(5) + 6)^(5/4) + (sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-2*sqrt(5) + 6))*sqrt(-sqrt(5) + 3)) + 1/16*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(3/4)*arctan(1/16*sqrt(4*x^2 + (sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6) - 2*(sqrt(5)*x + x)*(-2*sqrt(5) + 6)^(1/4))*(sqrt(5)*sqrt(2) + 2*sqrt(2))*sqrt(-sqrt(5) + 3)*(-2*sqrt(5) + 6)^(5/4) - 1/8*((sqrt(5)*sqrt(2)*x + 2*sqrt(2)*x)*(-2*sqrt(5) + 6)^(5/4) - (sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-2*sqrt(5) + 6))*sqrt(-sqrt(5) + 3)) + 1/8*(2*sqrt(5) + 6)^(1/4)*log(4*x^2 - sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3) + 2*(sqrt(5)*x - x)*(2*sqrt(5) + 6)^(1/4)) - 1/8*(2*sqrt(5) + 6)^(1/4)*log(4*x^2 - sqrt(2*sqrt(5) + 6)*(sqrt(5) - 3) - 2*(sqrt(5)*x - x)*(2*sqrt(5) + 6)^(1/4)) - 1/8*(-2*sqrt(5) + 6)^(1/4)*log(4*x^2 + (sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6) + 2*(sqrt(5)*x + x)*(-2*sqrt(5) + 6)^(1/4)) + 1/8*(-2*sqrt(5) + 6)^(1/4)*log(4*x^2 + (sqrt(5) + 3)*sqrt(-2*sqrt(5) + 6) - 2*(sqrt(5)*x + x)*(-2*sqrt(5) + 6)^(1/4))","B",0
22,1,126,0,1.229580," ","integrate((-x^4+1)/(x^8+2*x^4+1),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} + \sqrt{2} x + 1} - 1\right) + 4 \, \sqrt{2} {\left(x^{4} + 1\right)} \arctan\left(-\sqrt{2} x + \sqrt{2} \sqrt{x^{2} - \sqrt{2} x + 1} + 1\right) - \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} + \sqrt{2} x + 1\right) + \sqrt{2} {\left(x^{4} + 1\right)} \log\left(x^{2} - \sqrt{2} x + 1\right) - 8 \, x}{16 \, {\left(x^{4} + 1\right)}}"," ",0,"-1/16*(4*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 + sqrt(2)*x + 1) - 1) + 4*sqrt(2)*(x^4 + 1)*arctan(-sqrt(2)*x + sqrt(2)*sqrt(x^2 - sqrt(2)*x + 1) + 1) - sqrt(2)*(x^4 + 1)*log(x^2 + sqrt(2)*x + 1) + sqrt(2)*(x^4 + 1)*log(x^2 - sqrt(2)*x + 1) - 8*x)/(x^4 + 1)","A",0
23,1,137,0,1.161257," ","integrate((-x^4+1)/(x^8+x^4+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{4} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{8} \, \sqrt{3} \log\left(x^{2} + \sqrt{3} x + 1\right) - \frac{1}{8} \, \sqrt{3} \log\left(x^{2} - \sqrt{3} x + 1\right) + \frac{1}{2} \, \arctan\left(-2 \, x + \sqrt{3} + 2 \, \sqrt{x^{2} - \sqrt{3} x + 1}\right) + \frac{1}{2} \, \arctan\left(-2 \, x - \sqrt{3} + 2 \, \sqrt{x^{2} + \sqrt{3} x + 1}\right) - \frac{1}{8} \, \log\left(x^{2} + x + 1\right) + \frac{1}{8} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/4*sqrt(3)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/8*sqrt(3)*log(x^2 + sqrt(3)*x + 1) - 1/8*sqrt(3)*log(x^2 - sqrt(3)*x + 1) + 1/2*arctan(-2*x + sqrt(3) + 2*sqrt(x^2 - sqrt(3)*x + 1)) + 1/2*arctan(-2*x - sqrt(3) + 2*sqrt(x^2 + sqrt(3)*x + 1)) - 1/8*log(x^2 + x + 1) + 1/8*log(x^2 - x + 1)","A",0
24,1,991,0,1.556318," ","integrate((-x^4+1)/(x^8+1),x, algorithm=""fricas"")","-\frac{1}{8} \, {\left(\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) - \frac{1}{8} \, {\left(\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2}}\right) + \frac{1}{8} \, {\left(\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} + x \sqrt{\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{8} \, {\left(\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}\right)} \arctan\left(-\frac{2 \, x - 2 \, \sqrt{x^{2} - x \sqrt{\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2}}{\sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2} \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2} \sqrt{\sqrt{2} + 2} \arctan\left(-\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2} \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} + \sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) - \frac{1}{8} \, \sqrt{2} \sqrt{-\sqrt{2} + 2} \arctan\left(\frac{2 \, \sqrt{2} x - 2 \, \sqrt{2} \sqrt{x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1} - \sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}{\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}}\right) + \frac{1}{32} \, \sqrt{2} \sqrt{\sqrt{2} + 2} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, \sqrt{2} \sqrt{-\sqrt{2} + 2} \log\left(x^{2} + \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, \sqrt{2} \sqrt{-\sqrt{2} + 2} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} + \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, \sqrt{2} \sqrt{\sqrt{2} + 2} \log\left(x^{2} - \frac{1}{2} \, \sqrt{2} x \sqrt{\sqrt{2} + 2} - \frac{1}{2} \, \sqrt{2} x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, {\left(\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, {\left(\sqrt{\sqrt{2} + 2} + \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - x \sqrt{\sqrt{2} + 2} + 1\right) - \frac{1}{32} \, {\left(\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} + x \sqrt{-\sqrt{2} + 2} + 1\right) + \frac{1}{32} \, {\left(\sqrt{\sqrt{2} + 2} - \sqrt{-\sqrt{2} + 2}\right)} \log\left(x^{2} - x \sqrt{-\sqrt{2} + 2} + 1\right)"," ",0,"-1/8*(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) - 1/8*(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(-sqrt(2) + 2) + 1) - sqrt(-sqrt(2) + 2))/sqrt(sqrt(2) + 2)) + 1/8*(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))*arctan(-(2*x - 2*sqrt(x^2 + x*sqrt(sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) + 1/8*(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))*arctan(-(2*x - 2*sqrt(x^2 - x*sqrt(sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2))/sqrt(-sqrt(2) + 2)) - 1/8*sqrt(2)*sqrt(sqrt(2) + 2)*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) - 1/8*sqrt(2)*sqrt(sqrt(2) + 2)*arctan(-(2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))) - 1/8*sqrt(2)*sqrt(-sqrt(2) + 2)*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) - 1/8*sqrt(2)*sqrt(-sqrt(2) + 2)*arctan((2*sqrt(2)*x - 2*sqrt(2)*sqrt(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))/(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))) + 1/32*sqrt(2)*sqrt(sqrt(2) + 2)*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/32*sqrt(2)*sqrt(-sqrt(2) + 2)*log(x^2 + 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/32*sqrt(2)*sqrt(-sqrt(2) + 2)*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) + 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) - 1/32*sqrt(2)*sqrt(sqrt(2) + 2)*log(x^2 - 1/2*sqrt(2)*x*sqrt(sqrt(2) + 2) - 1/2*sqrt(2)*x*sqrt(-sqrt(2) + 2) + 1) + 1/32*(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))*log(x^2 + x*sqrt(sqrt(2) + 2) + 1) - 1/32*(sqrt(sqrt(2) + 2) + sqrt(-sqrt(2) + 2))*log(x^2 - x*sqrt(sqrt(2) + 2) + 1) - 1/32*(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))*log(x^2 + x*sqrt(-sqrt(2) + 2) + 1) + 1/32*(sqrt(sqrt(2) + 2) - sqrt(-sqrt(2) + 2))*log(x^2 - x*sqrt(-sqrt(2) + 2) + 1)","B",0
25,1,715,0,1.627130," ","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
26,1,17,0,1.420104," ","integrate((-x^4+1)/(x^8-2*x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(x\right) + \frac{1}{4} \, \log\left(x + 1\right) - \frac{1}{4} \, \log\left(x - 1\right)"," ",0,"1/2*arctan(x) + 1/4*log(x + 1) - 1/4*log(x - 1)","A",0
27,1,255,0,1.441964," ","integrate((-x^4+1)/(x^8-3*x^4+1),x, algorithm=""fricas"")","-\frac{1}{10} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \arctan\left(\frac{1}{20} \, \sqrt{10} \sqrt{5} \sqrt{2} \sqrt{2 \, x^{2} + \sqrt{5} - 1} \sqrt{\sqrt{5} + 1} - \frac{1}{10} \, \sqrt{10} \sqrt{5} x \sqrt{\sqrt{5} + 1}\right) - \frac{1}{10} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \arctan\left(\frac{1}{20} \, \sqrt{10} \sqrt{5} \sqrt{2} \sqrt{2 \, x^{2} + \sqrt{5} + 1} \sqrt{\sqrt{5} - 1} - \frac{1}{10} \, \sqrt{10} \sqrt{5} x \sqrt{\sqrt{5} - 1}\right) + \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \log\left(\sqrt{10} {\left(\sqrt{5} + 5\right)} \sqrt{\sqrt{5} - 1} + 20 \, x\right) - \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} - 1} \log\left(-\sqrt{10} {\left(\sqrt{5} + 5\right)} \sqrt{\sqrt{5} - 1} + 20 \, x\right) - \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \log\left(\sqrt{10} \sqrt{\sqrt{5} + 1} {\left(\sqrt{5} - 5\right)} + 20 \, x\right) + \frac{1}{40} \, \sqrt{10} \sqrt{\sqrt{5} + 1} \log\left(-\sqrt{10} \sqrt{\sqrt{5} + 1} {\left(\sqrt{5} - 5\right)} + 20 \, x\right)"," ",0,"-1/10*sqrt(10)*sqrt(sqrt(5) + 1)*arctan(1/20*sqrt(10)*sqrt(5)*sqrt(2)*sqrt(2*x^2 + sqrt(5) - 1)*sqrt(sqrt(5) + 1) - 1/10*sqrt(10)*sqrt(5)*x*sqrt(sqrt(5) + 1)) - 1/10*sqrt(10)*sqrt(sqrt(5) - 1)*arctan(1/20*sqrt(10)*sqrt(5)*sqrt(2)*sqrt(2*x^2 + sqrt(5) + 1)*sqrt(sqrt(5) - 1) - 1/10*sqrt(10)*sqrt(5)*x*sqrt(sqrt(5) - 1)) + 1/40*sqrt(10)*sqrt(sqrt(5) - 1)*log(sqrt(10)*(sqrt(5) + 5)*sqrt(sqrt(5) - 1) + 20*x) - 1/40*sqrt(10)*sqrt(sqrt(5) - 1)*log(-sqrt(10)*(sqrt(5) + 5)*sqrt(sqrt(5) - 1) + 20*x) - 1/40*sqrt(10)*sqrt(sqrt(5) + 1)*log(sqrt(10)*sqrt(sqrt(5) + 1)*(sqrt(5) - 5) + 20*x) + 1/40*sqrt(10)*sqrt(sqrt(5) + 1)*log(-sqrt(10)*sqrt(sqrt(5) + 1)*(sqrt(5) - 5) + 20*x)","B",0
28,1,302,0,1.579212," ","integrate((-x^4+1)/(x^8-4*x^4+1),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{6} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{6} \, \sqrt{6} \sqrt{x^{2} + {\left(\sqrt{3} + 2\right)} \sqrt{-\sqrt{3} + 2}} {\left(\sqrt{3} + 3\right)} {\left(-\sqrt{3} + 2\right)}^{\frac{3}{4}} - \frac{1}{6} \, \sqrt{6} {\left(\sqrt{3} x + 3 \, x\right)} {\left(-\sqrt{3} + 2\right)}^{\frac{3}{4}}\right) + \frac{1}{6} \, \sqrt{6} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} \arctan\left(\frac{1}{6} \, {\left(\sqrt{6} \sqrt{x^{2} - \sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)}} \sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 3\right)} - \sqrt{6} {\left(\sqrt{3} x - 3 \, x\right)} \sqrt{\sqrt{3} + 2}\right)} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}}\right) - \frac{1}{24} \, \sqrt{6} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} \log\left(\sqrt{6} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} {\left(\sqrt{3} - 3\right)} + 6 \, x\right) + \frac{1}{24} \, \sqrt{6} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} \log\left(-\sqrt{6} {\left(\sqrt{3} + 2\right)}^{\frac{1}{4}} {\left(\sqrt{3} - 3\right)} + 6 \, x\right) + \frac{1}{24} \, \sqrt{6} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} \log\left(\sqrt{6} {\left(\sqrt{3} + 3\right)} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} + 6 \, x\right) - \frac{1}{24} \, \sqrt{6} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} \log\left(-\sqrt{6} {\left(\sqrt{3} + 3\right)} {\left(-\sqrt{3} + 2\right)}^{\frac{1}{4}} + 6 \, x\right)"," ",0,"-1/6*sqrt(6)*(-sqrt(3) + 2)^(1/4)*arctan(1/6*sqrt(6)*sqrt(x^2 + (sqrt(3) + 2)*sqrt(-sqrt(3) + 2))*(sqrt(3) + 3)*(-sqrt(3) + 2)^(3/4) - 1/6*sqrt(6)*(sqrt(3)*x + 3*x)*(-sqrt(3) + 2)^(3/4)) + 1/6*sqrt(6)*(sqrt(3) + 2)^(1/4)*arctan(1/6*(sqrt(6)*sqrt(x^2 - sqrt(sqrt(3) + 2)*(sqrt(3) - 2))*sqrt(sqrt(3) + 2)*(sqrt(3) - 3) - sqrt(6)*(sqrt(3)*x - 3*x)*sqrt(sqrt(3) + 2))*(sqrt(3) + 2)^(1/4)) - 1/24*sqrt(6)*(sqrt(3) + 2)^(1/4)*log(sqrt(6)*(sqrt(3) + 2)^(1/4)*(sqrt(3) - 3) + 6*x) + 1/24*sqrt(6)*(sqrt(3) + 2)^(1/4)*log(-sqrt(6)*(sqrt(3) + 2)^(1/4)*(sqrt(3) - 3) + 6*x) + 1/24*sqrt(6)*(-sqrt(3) + 2)^(1/4)*log(sqrt(6)*(sqrt(3) + 3)*(-sqrt(3) + 2)^(1/4) + 6*x) - 1/24*sqrt(6)*(-sqrt(3) + 2)^(1/4)*log(-sqrt(6)*(sqrt(3) + 3)*(-sqrt(3) + 2)^(1/4) + 6*x)","B",0
29,1,546,0,1.808805," ","integrate((-x^4+1)/(x^8-5*x^4+1),x, algorithm=""fricas"")","-\frac{1}{14} \, \sqrt{14} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} \arctan\left(\frac{1}{112} \, \sqrt{14} \sqrt{4 \, x^{2} + {\left(\sqrt{7} \sqrt{3} \sqrt{2} + 5 \, \sqrt{2}\right)} \sqrt{-\sqrt{7} \sqrt{3} + 5}} {\left(\sqrt{7} \sqrt{3} \sqrt{2} + 7 \, \sqrt{2}\right)} \sqrt{-\sqrt{7} \sqrt{3} + 5} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} - \frac{1}{56} \, \sqrt{14} {\left(\sqrt{7} \sqrt{3} \sqrt{2} x + 7 \, \sqrt{2} x\right)} \sqrt{-\sqrt{7} \sqrt{3} + 5} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}}\right) + \frac{1}{14} \, \sqrt{14} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} \arctan\left(\frac{1}{112} \, {\left(\sqrt{14} \sqrt{4 \, x^{2} - {\left(\sqrt{7} \sqrt{3} \sqrt{2} - 5 \, \sqrt{2}\right)} \sqrt{\sqrt{7} \sqrt{3} + 5}} {\left(\sqrt{7} \sqrt{3} \sqrt{2} - 7 \, \sqrt{2}\right)} \sqrt{\sqrt{7} \sqrt{3} + 5} - 2 \, \sqrt{14} {\left(\sqrt{7} \sqrt{3} \sqrt{2} x - 7 \, \sqrt{2} x\right)} \sqrt{\sqrt{7} \sqrt{3} + 5}\right)} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}}\right) - \frac{1}{56} \, \sqrt{14} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} \log\left(\sqrt{14} {\left(\sqrt{7} \sqrt{3} - 7\right)} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} + 28 \, x\right) + \frac{1}{56} \, \sqrt{14} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} \log\left(-\sqrt{14} {\left(\sqrt{7} \sqrt{3} - 7\right)} \sqrt{\sqrt{2} \sqrt{\sqrt{7} \sqrt{3} + 5}} + 28 \, x\right) + \frac{1}{56} \, \sqrt{14} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} \log\left(\sqrt{14} {\left(\sqrt{7} \sqrt{3} + 7\right)} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} + 28 \, x\right) - \frac{1}{56} \, \sqrt{14} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} \log\left(-\sqrt{14} {\left(\sqrt{7} \sqrt{3} + 7\right)} \sqrt{\sqrt{2} \sqrt{-\sqrt{7} \sqrt{3} + 5}} + 28 \, x\right)"," ",0,"-1/14*sqrt(14)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5))*arctan(1/112*sqrt(14)*sqrt(4*x^2 + (sqrt(7)*sqrt(3)*sqrt(2) + 5*sqrt(2))*sqrt(-sqrt(7)*sqrt(3) + 5))*(sqrt(7)*sqrt(3)*sqrt(2) + 7*sqrt(2))*sqrt(-sqrt(7)*sqrt(3) + 5)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5)) - 1/56*sqrt(14)*(sqrt(7)*sqrt(3)*sqrt(2)*x + 7*sqrt(2)*x)*sqrt(-sqrt(7)*sqrt(3) + 5)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5))) + 1/14*sqrt(14)*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5))*arctan(1/112*(sqrt(14)*sqrt(4*x^2 - (sqrt(7)*sqrt(3)*sqrt(2) - 5*sqrt(2))*sqrt(sqrt(7)*sqrt(3) + 5))*(sqrt(7)*sqrt(3)*sqrt(2) - 7*sqrt(2))*sqrt(sqrt(7)*sqrt(3) + 5) - 2*sqrt(14)*(sqrt(7)*sqrt(3)*sqrt(2)*x - 7*sqrt(2)*x)*sqrt(sqrt(7)*sqrt(3) + 5))*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5))) - 1/56*sqrt(14)*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5))*log(sqrt(14)*(sqrt(7)*sqrt(3) - 7)*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5)) + 28*x) + 1/56*sqrt(14)*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5))*log(-sqrt(14)*(sqrt(7)*sqrt(3) - 7)*sqrt(sqrt(2)*sqrt(sqrt(7)*sqrt(3) + 5)) + 28*x) + 1/56*sqrt(14)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5))*log(sqrt(14)*(sqrt(7)*sqrt(3) + 7)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5)) + 28*x) - 1/56*sqrt(14)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5))*log(-sqrt(14)*(sqrt(7)*sqrt(3) + 7)*sqrt(sqrt(2)*sqrt(-sqrt(7)*sqrt(3) + 5)) + 28*x)","B",0
30,1,199,0,1.402734," ","integrate((-x^4+1)/(x^8-6*x^4+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{2} + 1} \arctan\left(-x \sqrt{\sqrt{2} + 1} + \sqrt{x^{2} + \sqrt{2} - 1} \sqrt{\sqrt{2} + 1}\right) - \frac{1}{4} \, \sqrt{2} \sqrt{\sqrt{2} - 1} \arctan\left(-x \sqrt{\sqrt{2} - 1} + \sqrt{x^{2} + \sqrt{2} + 1} \sqrt{\sqrt{2} - 1}\right) + \frac{1}{16} \, \sqrt{2} \sqrt{\sqrt{2} - 1} \log\left({\left(\sqrt{2} + 1\right)} \sqrt{\sqrt{2} - 1} + x\right) - \frac{1}{16} \, \sqrt{2} \sqrt{\sqrt{2} - 1} \log\left(-{\left(\sqrt{2} + 1\right)} \sqrt{\sqrt{2} - 1} + x\right) + \frac{1}{16} \, \sqrt{2} \sqrt{\sqrt{2} + 1} \log\left(\sqrt{\sqrt{2} + 1} {\left(\sqrt{2} - 1\right)} + x\right) - \frac{1}{16} \, \sqrt{2} \sqrt{\sqrt{2} + 1} \log\left(-\sqrt{\sqrt{2} + 1} {\left(\sqrt{2} - 1\right)} + x\right)"," ",0,"-1/4*sqrt(2)*sqrt(sqrt(2) + 1)*arctan(-x*sqrt(sqrt(2) + 1) + sqrt(x^2 + sqrt(2) - 1)*sqrt(sqrt(2) + 1)) - 1/4*sqrt(2)*sqrt(sqrt(2) - 1)*arctan(-x*sqrt(sqrt(2) - 1) + sqrt(x^2 + sqrt(2) + 1)*sqrt(sqrt(2) - 1)) + 1/16*sqrt(2)*sqrt(sqrt(2) - 1)*log((sqrt(2) + 1)*sqrt(sqrt(2) - 1) + x) - 1/16*sqrt(2)*sqrt(sqrt(2) - 1)*log(-(sqrt(2) + 1)*sqrt(sqrt(2) - 1) + x) + 1/16*sqrt(2)*sqrt(sqrt(2) + 1)*log(sqrt(sqrt(2) + 1)*(sqrt(2) - 1) + x) - 1/16*sqrt(2)*sqrt(sqrt(2) + 1)*log(-sqrt(sqrt(2) + 1)*(sqrt(2) - 1) + x)","B",0
31,1,104,0,0.774334," ","integrate((-1+2*x^4+3^(1/2))/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, {\left(\sqrt{3} \sqrt{2} + \sqrt{2}\right)} x^{3} - \sqrt{2} x\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, {\left(\sqrt{3} \sqrt{2} + \sqrt{2}\right)} x\right) + \frac{1}{4} \, \sqrt{2} \log\left(-\frac{{\left(\sqrt{3} \sqrt{2} - \sqrt{2}\right)} x + 2 \, x^{2} + 2}{{\left(\sqrt{3} \sqrt{2} - \sqrt{2}\right)} x - 2 \, x^{2} - 2}\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*(sqrt(3)*sqrt(2) + sqrt(2))*x^3 - sqrt(2)*x) + 1/2*sqrt(2)*arctan(1/2*(sqrt(3)*sqrt(2) + sqrt(2))*x) + 1/4*sqrt(2)*log(-((sqrt(3)*sqrt(2) - sqrt(2))*x + 2*x^2 + 2)/((sqrt(3)*sqrt(2) - sqrt(2))*x - 2*x^2 - 2))","A",0
32,1,111,0,1.228642," ","integrate((1+x^4*(1+3^(1/2)))/(x^8-x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\sqrt{3} + 2} \arctan\left(x^{3} \sqrt{\sqrt{3} + 2} - x \sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 1\right)}\right) + \frac{1}{2} \, \sqrt{\sqrt{3} + 2} \arctan\left(x \sqrt{\sqrt{3} + 2}\right) + \frac{1}{4} \, \sqrt{\sqrt{3} + 2} \log\left(-\frac{x \sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)} - x^{2} - 1}{x \sqrt{\sqrt{3} + 2} {\left(\sqrt{3} - 2\right)} + x^{2} + 1}\right)"," ",0,"1/2*sqrt(sqrt(3) + 2)*arctan(x^3*sqrt(sqrt(3) + 2) - x*sqrt(sqrt(3) + 2)*(sqrt(3) - 1)) + 1/2*sqrt(sqrt(3) + 2)*arctan(x*sqrt(sqrt(3) + 2)) + 1/4*sqrt(sqrt(3) + 2)*log(-(x*sqrt(sqrt(3) + 2)*(sqrt(3) - 2) - x^2 - 1)/(x*sqrt(sqrt(3) + 2)*(sqrt(3) - 2) + x^2 + 1))","A",0
33,1,141,0,1.552452," ","integrate((3+x^4*(-3+3^(1/2))-2*3^(1/2))/(x^8-x^4+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{-3 \, \sqrt{3} + 6} \arctan\left(\frac{1}{3} \, x^{3} {\left(2 \, \sqrt{3} + 3\right)} \sqrt{-3 \, \sqrt{3} + 6} - \frac{1}{3} \, x {\left(\sqrt{3} + 3\right)} \sqrt{-3 \, \sqrt{3} + 6}\right) - \frac{1}{2} \, \sqrt{-3 \, \sqrt{3} + 6} \arctan\left(\frac{1}{3} \, x {\left(2 \, \sqrt{3} + 3\right)} \sqrt{-3 \, \sqrt{3} + 6}\right) + \frac{1}{4} \, \sqrt{-3 \, \sqrt{3} + 6} \log\left(\frac{3 \, x^{2} - \sqrt{3} x \sqrt{-3 \, \sqrt{3} + 6} + 3}{3 \, x^{2} + \sqrt{3} x \sqrt{-3 \, \sqrt{3} + 6} + 3}\right)"," ",0,"-1/2*sqrt(-3*sqrt(3) + 6)*arctan(1/3*x^3*(2*sqrt(3) + 3)*sqrt(-3*sqrt(3) + 6) - 1/3*x*(sqrt(3) + 3)*sqrt(-3*sqrt(3) + 6)) - 1/2*sqrt(-3*sqrt(3) + 6)*arctan(1/3*x*(2*sqrt(3) + 3)*sqrt(-3*sqrt(3) + 6)) + 1/4*sqrt(-3*sqrt(3) + 6)*log((3*x^2 - sqrt(3)*x*sqrt(-3*sqrt(3) + 6) + 3)/(3*x^2 + sqrt(3)*x*sqrt(-3*sqrt(3) + 6) + 3))","A",0
34,1,108,0,0.748898," ","integrate((d+e/x)/(c+a/x^2),x, algorithm=""fricas"")","\left[\frac{d \sqrt{-\frac{a}{c}} \log\left(\frac{c x^{2} - 2 \, c x \sqrt{-\frac{a}{c}} - a}{c x^{2} + a}\right) + 2 \, d x + e \log\left(c x^{2} + a\right)}{2 \, c}, -\frac{2 \, d \sqrt{\frac{a}{c}} \arctan\left(\frac{c x \sqrt{\frac{a}{c}}}{a}\right) - 2 \, d x - e \log\left(c x^{2} + a\right)}{2 \, c}\right]"," ",0,"[1/2*(d*sqrt(-a/c)*log((c*x^2 - 2*c*x*sqrt(-a/c) - a)/(c*x^2 + a)) + 2*d*x + e*log(c*x^2 + a))/c, -1/2*(2*d*sqrt(a/c)*arctan(c*x*sqrt(a/c)/a) - 2*d*x - e*log(c*x^2 + a))/c]","A",0
35,1,291,0,1.199612," ","integrate((d+e/x)/(c+a/x^2+b/x),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d x + {\left(b c e - {\left(b^{2} - 2 \, a c\right)} d\right)} \sqrt{b^{2} - 4 \, a c} \log\left(\frac{2 \, c^{2} x^{2} + 2 \, b c x + b^{2} - 2 \, a c + \sqrt{b^{2} - 4 \, a c} {\left(2 \, c x + b\right)}}{c x^{2} + b x + a}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(b^{2} c - 4 \, a c^{2}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}, \frac{2 \, {\left(b^{2} c - 4 \, a c^{2}\right)} d x + 2 \, {\left(b c e - {\left(b^{2} - 2 \, a c\right)} d\right)} \sqrt{-b^{2} + 4 \, a c} \arctan\left(-\frac{\sqrt{-b^{2} + 4 \, a c} {\left(2 \, c x + b\right)}}{b^{2} - 4 \, a c}\right) - {\left({\left(b^{3} - 4 \, a b c\right)} d - {\left(b^{2} c - 4 \, a c^{2}\right)} e\right)} \log\left(c x^{2} + b x + a\right)}{2 \, {\left(b^{2} c^{2} - 4 \, a c^{3}\right)}}\right]"," ",0,"[1/2*(2*(b^2*c - 4*a*c^2)*d*x + (b*c*e - (b^2 - 2*a*c)*d)*sqrt(b^2 - 4*a*c)*log((2*c^2*x^2 + 2*b*c*x + b^2 - 2*a*c + sqrt(b^2 - 4*a*c)*(2*c*x + b))/(c*x^2 + b*x + a)) - ((b^3 - 4*a*b*c)*d - (b^2*c - 4*a*c^2)*e)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3), 1/2*(2*(b^2*c - 4*a*c^2)*d*x + 2*(b*c*e - (b^2 - 2*a*c)*d)*sqrt(-b^2 + 4*a*c)*arctan(-sqrt(-b^2 + 4*a*c)*(2*c*x + b)/(b^2 - 4*a*c)) - ((b^3 - 4*a*b*c)*d - (b^2*c - 4*a*c^2)*e)*log(c*x^2 + b*x + a))/(b^2*c^2 - 4*a*c^3)]","A",0
36,1,754,0,1.355772," ","integrate((d+e/x^2)/(c+a/x^4),x, algorithm=""fricas"")","\frac{c \sqrt{\frac{c^{2} \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} + 2 \, d e}{c^{2}}} \log\left(-{\left(a^{2} d^{4} - c^{2} e^{4}\right)} x + {\left(a c^{4} e \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} + a^{2} c d^{3} - a c^{2} d e^{2}\right)} \sqrt{\frac{c^{2} \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} + 2 \, d e}{c^{2}}}\right) - c \sqrt{\frac{c^{2} \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} + 2 \, d e}{c^{2}}} \log\left(-{\left(a^{2} d^{4} - c^{2} e^{4}\right)} x - {\left(a c^{4} e \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} + a^{2} c d^{3} - a c^{2} d e^{2}\right)} \sqrt{\frac{c^{2} \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} + 2 \, d e}{c^{2}}}\right) - c \sqrt{-\frac{c^{2} \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} - 2 \, d e}{c^{2}}} \log\left(-{\left(a^{2} d^{4} - c^{2} e^{4}\right)} x + {\left(a c^{4} e \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} - a^{2} c d^{3} + a c^{2} d e^{2}\right)} \sqrt{-\frac{c^{2} \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} - 2 \, d e}{c^{2}}}\right) + c \sqrt{-\frac{c^{2} \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} - 2 \, d e}{c^{2}}} \log\left(-{\left(a^{2} d^{4} - c^{2} e^{4}\right)} x - {\left(a c^{4} e \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} - a^{2} c d^{3} + a c^{2} d e^{2}\right)} \sqrt{-\frac{c^{2} \sqrt{-\frac{a^{2} d^{4} - 2 \, a c d^{2} e^{2} + c^{2} e^{4}}{a c^{5}}} - 2 \, d e}{c^{2}}}\right) + 4 \, d x}{4 \, c}"," ",0,"1/4*(c*sqrt((c^2*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) + 2*d*e)/c^2)*log(-(a^2*d^4 - c^2*e^4)*x + (a*c^4*e*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) + a^2*c*d^3 - a*c^2*d*e^2)*sqrt((c^2*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) + 2*d*e)/c^2)) - c*sqrt((c^2*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) + 2*d*e)/c^2)*log(-(a^2*d^4 - c^2*e^4)*x - (a*c^4*e*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) + a^2*c*d^3 - a*c^2*d*e^2)*sqrt((c^2*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) + 2*d*e)/c^2)) - c*sqrt(-(c^2*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) - 2*d*e)/c^2)*log(-(a^2*d^4 - c^2*e^4)*x + (a*c^4*e*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) - a^2*c*d^3 + a*c^2*d*e^2)*sqrt(-(c^2*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) - 2*d*e)/c^2)) + c*sqrt(-(c^2*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) - 2*d*e)/c^2)*log(-(a^2*d^4 - c^2*e^4)*x - (a*c^4*e*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) - a^2*c*d^3 + a*c^2*d*e^2)*sqrt(-(c^2*sqrt(-(a^2*d^4 - 2*a*c*d^2*e^2 + c^2*e^4)/(a*c^5)) - 2*d*e)/c^2)) + 4*d*x)/c","B",0
37,1,2540,0,1.671937," ","integrate((d+e/x^2)/(c+a/x^4+b/x^2),x, algorithm=""fricas"")","\frac{\sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(2 \, {\left(3 \, b^{2} c d^{2} e^{2} - 3 \, b c^{2} d e^{3} + c^{3} e^{4} + {\left(a b^{2} - a^{2} c\right)} d^{4} - {\left(b^{3} + a b c\right)} d^{3} e\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b c^{2} e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(2 \, {\left(3 \, b^{2} c d^{2} e^{2} - 3 \, b c^{2} d e^{3} + c^{3} e^{4} + {\left(a b^{2} - a^{2} c\right)} d^{4} - {\left(b^{3} + a b c\right)} d^{3} e\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} - {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b c^{2} e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(2 \, {\left(3 \, b^{2} c d^{2} e^{2} - 3 \, b c^{2} d e^{3} + c^{3} e^{4} + {\left(a b^{2} - a^{2} c\right)} d^{4} - {\left(b^{3} + a b c\right)} d^{3} e\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b c^{2} e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{2} e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}} \log\left(2 \, {\left(3 \, b^{2} c d^{2} e^{2} - 3 \, b c^{2} d e^{3} + c^{3} e^{4} + {\left(a b^{2} - a^{2} c\right)} d^{4} - {\left(b^{3} + a b c\right)} d^{3} e\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{4} - 5 \, a b^{2} c + 4 \, a^{2} c^{2}\right)} d^{3} - 2 \, {\left(b^{3} c - 4 \, a b c^{2}\right)} d^{2} e + {\left(b^{2} c^{2} - 4 \, a c^{3}\right)} d e^{2} + {\left({\left(b^{3} c^{3} - 4 \, a b c^{4}\right)} d - 2 \, {\left(b^{2} c^{4} - 4 \, a c^{5}\right)} e\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}\right)} \sqrt{-\frac{b c^{2} e^{2} + {\left(b^{3} - 3 \, a b c\right)} d^{2} - 2 \, {\left(b^{2} c - 2 \, a c^{2}\right)} d e - {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} \sqrt{-\frac{4 \, b c^{3} d e^{3} - c^{4} e^{4} - {\left(b^{4} - 2 \, a b^{2} c + a^{2} c^{2}\right)} d^{4} + 4 \, {\left(b^{3} c - a b c^{2}\right)} d^{3} e - 2 \, {\left(3 \, b^{2} c^{2} - a c^{3}\right)} d^{2} e^{2}}{b^{2} c^{6} - 4 \, a c^{7}}}}{b^{2} c^{3} - 4 \, a c^{4}}}\right) + 2 \, d x}{2 \, c}"," ",0,"1/2*(sqrt(1/2)*c*sqrt(-(b*c^2*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(b^2*c - 2*a*c^2)*d*e + (b^2*c^3 - 4*a*c^4)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(2*(3*b^2*c*d^2*e^2 - 3*b*c^2*d*e^3 + c^3*e^4 + (a*b^2 - a^2*c)*d^4 - (b^3 + a*b*c)*d^3*e)*x + sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(b^3*c - 4*a*b*c^2)*d^2*e + (b^2*c^2 - 4*a*c^3)*d*e^2 - ((b^3*c^3 - 4*a*b*c^4)*d - 2*(b^2*c^4 - 4*a*c^5)*e)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b*c^2*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(b^2*c - 2*a*c^2)*d*e + (b^2*c^3 - 4*a*c^4)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(b*c^2*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(b^2*c - 2*a*c^2)*d*e + (b^2*c^3 - 4*a*c^4)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(2*(3*b^2*c*d^2*e^2 - 3*b*c^2*d*e^3 + c^3*e^4 + (a*b^2 - a^2*c)*d^4 - (b^3 + a*b*c)*d^3*e)*x - sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(b^3*c - 4*a*b*c^2)*d^2*e + (b^2*c^2 - 4*a*c^3)*d*e^2 - ((b^3*c^3 - 4*a*b*c^4)*d - 2*(b^2*c^4 - 4*a*c^5)*e)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b*c^2*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(b^2*c - 2*a*c^2)*d*e + (b^2*c^3 - 4*a*c^4)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) + sqrt(1/2)*c*sqrt(-(b*c^2*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(b^2*c - 2*a*c^2)*d*e - (b^2*c^3 - 4*a*c^4)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(2*(3*b^2*c*d^2*e^2 - 3*b*c^2*d*e^3 + c^3*e^4 + (a*b^2 - a^2*c)*d^4 - (b^3 + a*b*c)*d^3*e)*x + sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(b^3*c - 4*a*b*c^2)*d^2*e + (b^2*c^2 - 4*a*c^3)*d*e^2 + ((b^3*c^3 - 4*a*b*c^4)*d - 2*(b^2*c^4 - 4*a*c^5)*e)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b*c^2*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(b^2*c - 2*a*c^2)*d*e - (b^2*c^3 - 4*a*c^4)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) - sqrt(1/2)*c*sqrt(-(b*c^2*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(b^2*c - 2*a*c^2)*d*e - (b^2*c^3 - 4*a*c^4)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))*log(2*(3*b^2*c*d^2*e^2 - 3*b*c^2*d*e^3 + c^3*e^4 + (a*b^2 - a^2*c)*d^4 - (b^3 + a*b*c)*d^3*e)*x - sqrt(1/2)*((b^4 - 5*a*b^2*c + 4*a^2*c^2)*d^3 - 2*(b^3*c - 4*a*b*c^2)*d^2*e + (b^2*c^2 - 4*a*c^3)*d*e^2 + ((b^3*c^3 - 4*a*b*c^4)*d - 2*(b^2*c^4 - 4*a*c^5)*e)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))*sqrt(-(b*c^2*e^2 + (b^3 - 3*a*b*c)*d^2 - 2*(b^2*c - 2*a*c^2)*d*e - (b^2*c^3 - 4*a*c^4)*sqrt(-(4*b*c^3*d*e^3 - c^4*e^4 - (b^4 - 2*a*b^2*c + a^2*c^2)*d^4 + 4*(b^3*c - a*b*c^2)*d^3*e - 2*(3*b^2*c^2 - a*c^3)*d^2*e^2)/(b^2*c^6 - 4*a*c^7)))/(b^2*c^3 - 4*a*c^4))) + 2*d*x)/c","B",0
38,1,3169,0,2.134430," ","integrate((d+e/x^3)/(c+a/x^6),x, algorithm=""fricas"")","-\frac{4 \, \sqrt{3} c \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, {\left(\sqrt{3} {\left(a^{2} c^{6} d^{2} - a c^{7} e^{2}\right)} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e - 3 \, a c^{4} d^{2} e^{3}\right)}\right)} \sqrt{\frac{{\left(a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}\right)} x^{2} + {\left(2 \, a^{2} c^{6} d e \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + a^{3} c^{2} d^{5} - 4 \, a^{2} c^{3} d^{3} e^{2} + 3 \, a c^{4} d e^{4}\right)} \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{2}{3}} + {\left({\left(a^{2} c^{5} d^{2} e + a c^{6} e^{3}\right)} x \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + {\left(a^{3} c d^{6} - 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a c^{3} d^{2} e^{4}\right)} x\right)} \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{1}{3}}}{a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}}} \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} {\left(a^{2} c^{6} d^{2} - a c^{7} e^{2}\right)} x \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e - 3 \, a c^{4} d^{2} e^{3}\right)} x\right)} \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{2}{3}} + \sqrt{3} {\left(a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}\right)}}{3 \, {\left(a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}\right)}}\right) - 4 \, \sqrt{3} c \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{1}{3}} \arctan\left(\frac{2 \, {\left(\sqrt{3} {\left(a^{2} c^{6} d^{2} - a c^{7} e^{2}\right)} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e - 3 \, a c^{4} d^{2} e^{3}\right)}\right)} \sqrt{\frac{{\left(a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}\right)} x^{2} - {\left(2 \, a^{2} c^{6} d e \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - a^{3} c^{2} d^{5} + 4 \, a^{2} c^{3} d^{3} e^{2} - 3 \, a c^{4} d e^{4}\right)} \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{2}{3}} - {\left({\left(a^{2} c^{5} d^{2} e + a c^{6} e^{3}\right)} x \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - {\left(a^{3} c d^{6} - 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a c^{3} d^{2} e^{4}\right)} x\right)} \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{1}{3}}}{a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}}} \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{2}{3}} - 2 \, {\left(\sqrt{3} {\left(a^{2} c^{6} d^{2} - a c^{7} e^{2}\right)} x \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 2 \, \sqrt{3} {\left(a^{2} c^{3} d^{4} e - 3 \, a c^{4} d^{2} e^{3}\right)} x\right)} \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{2}{3}} - \sqrt{3} {\left(a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}\right)}}{3 \, {\left(a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}\right)}}\right) + c \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{1}{3}} \log\left(-{\left(a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}\right)} x^{2} - {\left(2 \, a^{2} c^{6} d e \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + a^{3} c^{2} d^{5} - 4 \, a^{2} c^{3} d^{3} e^{2} + 3 \, a c^{4} d e^{4}\right)} \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{2}{3}} - {\left({\left(a^{2} c^{5} d^{2} e + a c^{6} e^{3}\right)} x \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + {\left(a^{3} c d^{6} - 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a c^{3} d^{2} e^{4}\right)} x\right)} \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{1}{3}}\right) + c \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{1}{3}} \log\left(-{\left(a^{3} d^{7} - a^{2} c d^{5} e^{2} - 5 \, a c^{2} d^{3} e^{4} - 3 \, c^{3} d e^{6}\right)} x^{2} + {\left(2 \, a^{2} c^{6} d e \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - a^{3} c^{2} d^{5} + 4 \, a^{2} c^{3} d^{3} e^{2} - 3 \, a c^{4} d e^{4}\right)} \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{2}{3}} + {\left({\left(a^{2} c^{5} d^{2} e + a c^{6} e^{3}\right)} x \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - {\left(a^{3} c d^{6} - 2 \, a^{2} c^{2} d^{4} e^{2} - 3 \, a c^{3} d^{2} e^{4}\right)} x\right)} \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{1}{3}}\right) - 2 \, c \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{1}{3}} \log\left(-{\left(a^{2} d^{5} - 2 \, a c d^{3} e^{2} - 3 \, c^{2} d e^{4}\right)} x + {\left(a c^{5} e \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + a^{2} c d^{4} - 3 \, a c^{2} d^{2} e^{2}\right)} \left(\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} + 3 \, a d^{2} e - c e^{3}}{a c^{3}}\right)^{\frac{1}{3}}\right) - 2 \, c \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{1}{3}} \log\left(-{\left(a^{2} d^{5} - 2 \, a c d^{3} e^{2} - 3 \, c^{2} d e^{4}\right)} x - {\left(a c^{5} e \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - a^{2} c d^{4} + 3 \, a c^{2} d^{2} e^{2}\right)} \left(-\frac{a c^{3} \sqrt{-\frac{a^{2} d^{6} - 6 \, a c d^{4} e^{2} + 9 \, c^{2} d^{2} e^{4}}{a c^{7}}} - 3 \, a d^{2} e + c e^{3}}{a c^{3}}\right)^{\frac{1}{3}}\right) - 12 \, d x}{12 \, c}"," ",0,"-1/12*(4*sqrt(3)*c*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(1/3)*arctan(1/3*(2*(sqrt(3)*(a^2*c^6*d^2 - a*c^7*e^2)*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 2*sqrt(3)*(a^2*c^3*d^4*e - 3*a*c^4*d^2*e^3))*sqrt(((a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6)*x^2 + (2*a^2*c^6*d*e*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + a^3*c^2*d^5 - 4*a^2*c^3*d^3*e^2 + 3*a*c^4*d*e^4)*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(2/3) + ((a^2*c^5*d^2*e + a*c^6*e^3)*x*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + (a^3*c*d^6 - 2*a^2*c^2*d^4*e^2 - 3*a*c^3*d^2*e^4)*x)*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(1/3))/(a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6))*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(2/3) - 2*(sqrt(3)*(a^2*c^6*d^2 - a*c^7*e^2)*x*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 2*sqrt(3)*(a^2*c^3*d^4*e - 3*a*c^4*d^2*e^3)*x)*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(2/3) + sqrt(3)*(a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6))/(a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6)) - 4*sqrt(3)*c*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(1/3)*arctan(1/3*(2*(sqrt(3)*(a^2*c^6*d^2 - a*c^7*e^2)*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 2*sqrt(3)*(a^2*c^3*d^4*e - 3*a*c^4*d^2*e^3))*sqrt(((a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6)*x^2 - (2*a^2*c^6*d*e*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - a^3*c^2*d^5 + 4*a^2*c^3*d^3*e^2 - 3*a*c^4*d*e^4)*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(2/3) - ((a^2*c^5*d^2*e + a*c^6*e^3)*x*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - (a^3*c*d^6 - 2*a^2*c^2*d^4*e^2 - 3*a*c^3*d^2*e^4)*x)*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(1/3))/(a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6))*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(2/3) - 2*(sqrt(3)*(a^2*c^6*d^2 - a*c^7*e^2)*x*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 2*sqrt(3)*(a^2*c^3*d^4*e - 3*a*c^4*d^2*e^3)*x)*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(2/3) - sqrt(3)*(a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6))/(a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6)) + c*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(1/3)*log(-(a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6)*x^2 - (2*a^2*c^6*d*e*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + a^3*c^2*d^5 - 4*a^2*c^3*d^3*e^2 + 3*a*c^4*d*e^4)*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(2/3) - ((a^2*c^5*d^2*e + a*c^6*e^3)*x*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + (a^3*c*d^6 - 2*a^2*c^2*d^4*e^2 - 3*a*c^3*d^2*e^4)*x)*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(1/3)) + c*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(1/3)*log(-(a^3*d^7 - a^2*c*d^5*e^2 - 5*a*c^2*d^3*e^4 - 3*c^3*d*e^6)*x^2 + (2*a^2*c^6*d*e*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - a^3*c^2*d^5 + 4*a^2*c^3*d^3*e^2 - 3*a*c^4*d*e^4)*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(2/3) + ((a^2*c^5*d^2*e + a*c^6*e^3)*x*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - (a^3*c*d^6 - 2*a^2*c^2*d^4*e^2 - 3*a*c^3*d^2*e^4)*x)*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(1/3)) - 2*c*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(1/3)*log(-(a^2*d^5 - 2*a*c*d^3*e^2 - 3*c^2*d*e^4)*x + (a*c^5*e*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + a^2*c*d^4 - 3*a*c^2*d^2*e^2)*((a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) + 3*a*d^2*e - c*e^3)/(a*c^3))^(1/3)) - 2*c*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(1/3)*log(-(a^2*d^5 - 2*a*c*d^3*e^2 - 3*c^2*d*e^4)*x - (a*c^5*e*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - a^2*c*d^4 + 3*a*c^2*d^2*e^2)*(-(a*c^3*sqrt(-(a^2*d^6 - 6*a*c*d^4*e^2 + 9*c^2*d^2*e^4)/(a*c^7)) - 3*a*d^2*e + c*e^3)/(a*c^3))^(1/3)) - 12*d*x)/c","B",0
39,-1,0,0,0.000000," ","integrate((d+e/x^3)/(c+a/x^6+b/x^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
40,1,3378,0,2.071896," ","integrate((d+e/x^4)/(c+a/x^8),x, algorithm=""fricas"")","-\frac{4 \, c \left(-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}} \arctan\left(-\frac{{\left({\left(3 \, a^{4} c^{4} d^{6} e - 19 \, a^{3} c^{5} d^{4} e^{3} + 9 \, a^{2} c^{6} d^{2} e^{5} - a c^{7} e^{7} + {\left(a^{4} c^{8} d^{3} - 3 \, a^{3} c^{9} d e^{2}\right)} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}}\right)} \sqrt{\frac{{\left(a^{4} d^{8} - 4 \, a^{3} c d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}\right)} x^{2} - {\left(2 \, a^{3} c^{7} d e \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - a^{4} c^{2} d^{6} + 7 \, a^{3} c^{3} d^{4} e^{2} - 7 \, a^{2} c^{4} d^{2} e^{4} + a c^{5} e^{6}\right)} \sqrt{-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}}}{a^{4} d^{8} - 4 \, a^{3} c d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}} \sqrt{-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}} - {\left({\left(a^{4} c^{8} d^{3} - 3 \, a^{3} c^{9} d e^{2}\right)} x \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + {\left(3 \, a^{4} c^{4} d^{6} e - 19 \, a^{3} c^{5} d^{4} e^{3} + 9 \, a^{2} c^{6} d^{2} e^{5} - a c^{7} e^{7}\right)} x\right)} \sqrt{-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}}\right)} \left(-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}}}{a^{5} d^{10} - 3 \, a^{4} c d^{8} e^{2} - 14 \, a^{3} c^{2} d^{6} e^{4} - 14 \, a^{2} c^{3} d^{4} e^{6} - 3 \, a c^{4} d^{2} e^{8} + c^{5} e^{10}}\right) - 4 \, c \left(\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + 4 \, a d^{3} e - 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}} \arctan\left(\frac{{\left(3 \, a^{4} c^{4} d^{6} e - 19 \, a^{3} c^{5} d^{4} e^{3} + 9 \, a^{2} c^{6} d^{2} e^{5} - a c^{7} e^{7} - {\left(a^{4} c^{8} d^{3} - 3 \, a^{3} c^{9} d e^{2}\right)} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}}\right)} \sqrt{\frac{{\left(a^{4} d^{8} - 4 \, a^{3} c d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}\right)} x^{2} + {\left(2 \, a^{3} c^{7} d e \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + a^{4} c^{2} d^{6} - 7 \, a^{3} c^{3} d^{4} e^{2} + 7 \, a^{2} c^{4} d^{2} e^{4} - a c^{5} e^{6}\right)} \sqrt{\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + 4 \, a d^{3} e - 4 \, c d e^{3}}{a c^{4}}}}{a^{4} d^{8} - 4 \, a^{3} c d^{6} e^{2} - 10 \, a^{2} c^{2} d^{4} e^{4} - 4 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}} \left(\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + 4 \, a d^{3} e - 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{3}{4}} + {\left({\left(a^{4} c^{8} d^{3} - 3 \, a^{3} c^{9} d e^{2}\right)} x \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - {\left(3 \, a^{4} c^{4} d^{6} e - 19 \, a^{3} c^{5} d^{4} e^{3} + 9 \, a^{2} c^{6} d^{2} e^{5} - a c^{7} e^{7}\right)} x\right)} \left(\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + 4 \, a d^{3} e - 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{3}{4}}}{a^{5} d^{10} - 3 \, a^{4} c d^{8} e^{2} - 14 \, a^{3} c^{2} d^{6} e^{4} - 14 \, a^{2} c^{3} d^{4} e^{6} - 3 \, a c^{4} d^{2} e^{8} + c^{5} e^{10}}\right) + c \left(\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + 4 \, a d^{3} e - 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}} \log\left({\left(a^{3} d^{6} - 5 \, a^{2} c d^{4} e^{2} - 5 \, a c^{2} d^{2} e^{4} + c^{3} e^{6}\right)} x + {\left(a^{2} c^{6} e \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + a^{3} c d^{5} - 6 \, a^{2} c^{2} d^{3} e^{2} + a c^{3} d e^{4}\right)} \left(\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + 4 \, a d^{3} e - 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}}\right) - c \left(\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + 4 \, a d^{3} e - 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}} \log\left({\left(a^{3} d^{6} - 5 \, a^{2} c d^{4} e^{2} - 5 \, a c^{2} d^{2} e^{4} + c^{3} e^{6}\right)} x - {\left(a^{2} c^{6} e \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + a^{3} c d^{5} - 6 \, a^{2} c^{2} d^{3} e^{2} + a c^{3} d e^{4}\right)} \left(\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} + 4 \, a d^{3} e - 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}}\right) - c \left(-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}} \log\left({\left(a^{3} d^{6} - 5 \, a^{2} c d^{4} e^{2} - 5 \, a c^{2} d^{2} e^{4} + c^{3} e^{6}\right)} x + {\left(a^{2} c^{6} e \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - a^{3} c d^{5} + 6 \, a^{2} c^{2} d^{3} e^{2} - a c^{3} d e^{4}\right)} \left(-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}}\right) + c \left(-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}} \log\left({\left(a^{3} d^{6} - 5 \, a^{2} c d^{4} e^{2} - 5 \, a c^{2} d^{2} e^{4} + c^{3} e^{6}\right)} x - {\left(a^{2} c^{6} e \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - a^{3} c d^{5} + 6 \, a^{2} c^{2} d^{3} e^{2} - a c^{3} d e^{4}\right)} \left(-\frac{a c^{4} \sqrt{-\frac{a^{4} d^{8} - 12 \, a^{3} c d^{6} e^{2} + 38 \, a^{2} c^{2} d^{4} e^{4} - 12 \, a c^{3} d^{2} e^{6} + c^{4} e^{8}}{a^{3} c^{9}}} - 4 \, a d^{3} e + 4 \, c d e^{3}}{a c^{4}}\right)^{\frac{1}{4}}\right) - 8 \, d x}{8 \, c}"," ",0,"-1/8*(4*c*(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4))^(1/4)*arctan(-((3*a^4*c^4*d^6*e - 19*a^3*c^5*d^4*e^3 + 9*a^2*c^6*d^2*e^5 - a*c^7*e^7 + (a^4*c^8*d^3 - 3*a^3*c^9*d*e^2)*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)))*sqrt(((a^4*d^8 - 4*a^3*c*d^6*e^2 - 10*a^2*c^2*d^4*e^4 - 4*a*c^3*d^2*e^6 + c^4*e^8)*x^2 - (2*a^3*c^7*d*e*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - a^4*c^2*d^6 + 7*a^3*c^3*d^4*e^2 - 7*a^2*c^4*d^2*e^4 + a*c^5*e^6)*sqrt(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4)))/(a^4*d^8 - 4*a^3*c*d^6*e^2 - 10*a^2*c^2*d^4*e^4 - 4*a*c^3*d^2*e^6 + c^4*e^8))*sqrt(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4)) - ((a^4*c^8*d^3 - 3*a^3*c^9*d*e^2)*x*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + (3*a^4*c^4*d^6*e - 19*a^3*c^5*d^4*e^3 + 9*a^2*c^6*d^2*e^5 - a*c^7*e^7)*x)*sqrt(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4)))*(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4))^(1/4)/(a^5*d^10 - 3*a^4*c*d^8*e^2 - 14*a^3*c^2*d^6*e^4 - 14*a^2*c^3*d^4*e^6 - 3*a*c^4*d^2*e^8 + c^5*e^10)) - 4*c*((a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + 4*a*d^3*e - 4*c*d*e^3)/(a*c^4))^(1/4)*arctan(((3*a^4*c^4*d^6*e - 19*a^3*c^5*d^4*e^3 + 9*a^2*c^6*d^2*e^5 - a*c^7*e^7 - (a^4*c^8*d^3 - 3*a^3*c^9*d*e^2)*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)))*sqrt(((a^4*d^8 - 4*a^3*c*d^6*e^2 - 10*a^2*c^2*d^4*e^4 - 4*a*c^3*d^2*e^6 + c^4*e^8)*x^2 + (2*a^3*c^7*d*e*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + a^4*c^2*d^6 - 7*a^3*c^3*d^4*e^2 + 7*a^2*c^4*d^2*e^4 - a*c^5*e^6)*sqrt((a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + 4*a*d^3*e - 4*c*d*e^3)/(a*c^4)))/(a^4*d^8 - 4*a^3*c*d^6*e^2 - 10*a^2*c^2*d^4*e^4 - 4*a*c^3*d^2*e^6 + c^4*e^8))*((a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + 4*a*d^3*e - 4*c*d*e^3)/(a*c^4))^(3/4) + ((a^4*c^8*d^3 - 3*a^3*c^9*d*e^2)*x*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - (3*a^4*c^4*d^6*e - 19*a^3*c^5*d^4*e^3 + 9*a^2*c^6*d^2*e^5 - a*c^7*e^7)*x)*((a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + 4*a*d^3*e - 4*c*d*e^3)/(a*c^4))^(3/4))/(a^5*d^10 - 3*a^4*c*d^8*e^2 - 14*a^3*c^2*d^6*e^4 - 14*a^2*c^3*d^4*e^6 - 3*a*c^4*d^2*e^8 + c^5*e^10)) + c*((a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + 4*a*d^3*e - 4*c*d*e^3)/(a*c^4))^(1/4)*log((a^3*d^6 - 5*a^2*c*d^4*e^2 - 5*a*c^2*d^2*e^4 + c^3*e^6)*x + (a^2*c^6*e*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + a^3*c*d^5 - 6*a^2*c^2*d^3*e^2 + a*c^3*d*e^4)*((a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + 4*a*d^3*e - 4*c*d*e^3)/(a*c^4))^(1/4)) - c*((a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + 4*a*d^3*e - 4*c*d*e^3)/(a*c^4))^(1/4)*log((a^3*d^6 - 5*a^2*c*d^4*e^2 - 5*a*c^2*d^2*e^4 + c^3*e^6)*x - (a^2*c^6*e*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + a^3*c*d^5 - 6*a^2*c^2*d^3*e^2 + a*c^3*d*e^4)*((a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) + 4*a*d^3*e - 4*c*d*e^3)/(a*c^4))^(1/4)) - c*(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4))^(1/4)*log((a^3*d^6 - 5*a^2*c*d^4*e^2 - 5*a*c^2*d^2*e^4 + c^3*e^6)*x + (a^2*c^6*e*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - a^3*c*d^5 + 6*a^2*c^2*d^3*e^2 - a*c^3*d*e^4)*(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4))^(1/4)) + c*(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4))^(1/4)*log((a^3*d^6 - 5*a^2*c*d^4*e^2 - 5*a*c^2*d^2*e^4 + c^3*e^6)*x - (a^2*c^6*e*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - a^3*c*d^5 + 6*a^2*c^2*d^3*e^2 - a*c^3*d*e^4)*(-(a*c^4*sqrt(-(a^4*d^8 - 12*a^3*c*d^6*e^2 + 38*a^2*c^2*d^4*e^4 - 12*a*c^3*d^2*e^6 + c^4*e^8)/(a^3*c^9)) - 4*a*d^3*e + 4*c*d*e^3)/(a*c^4))^(1/4)) - 8*d*x)/c","B",0
41,-1,0,0,0.000000," ","integrate((d+e/x^4)/(c+a/x^8+b/x^4),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,0,0,0,0.891363," ","integrate((d+e*x^n)^3/(a+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{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}, 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), x)","F",0
43,0,0,0,0.799182," ","integrate((d+e*x^n)^2/(a+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}{c x^{2 \, n} + a}, x\right)"," ",0,"integral((e^2*x^(2*n) + 2*d*e*x^n + d^2)/(c*x^(2*n) + a), x)","F",0
44,0,0,0,0.652088," ","integrate((d+e*x^n)/(a+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{n} + d}{c x^{2 \, n} + a}, x\right)"," ",0,"integral((e*x^n + d)/(c*x^(2*n) + a), x)","F",0
45,0,0,0,0.866532," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a e x^{n} + a d + {\left(c e x^{n} + c d\right)} x^{2 \, n}}, x\right)"," ",0,"integral(1/(a*e*x^n + a*d + (c*e*x^n + c*d)*x^(2*n)), x)","F",0
46,0,0,0,1.203907," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a e^{2} x^{2 \, n} + 2 \, a d e x^{n} + a d^{2} + {\left(c e^{2} x^{2 \, n} + 2 \, c d e x^{n} + c d^{2}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(1/(a*e^2*x^(2*n) + 2*a*d*e*x^n + a*d^2 + (c*e^2*x^(2*n) + 2*c*d*e*x^n + c*d^2)*x^(2*n)), x)","F",0
47,0,0,0,0.878223," ","integrate((d+e*x^n)/(a-c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{e x^{n} + d}{c x^{2 \, n} - a}, x\right)"," ",0,"integral(-(e*x^n + d)/(c*x^(2*n) - a), x)","F",0
48,0,0,0,0.934676," ","integrate((d+e*x^n)^3/(a+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}}{c^{2} x^{4 \, n} + 2 \, a c x^{2 \, n} + a^{2}}, 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^2*x^(4*n) + 2*a*c*x^(2*n) + a^2), x)","F",0
49,0,0,0,0.858607," ","integrate((d+e*x^n)^2/(a+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}{c^{2} x^{4 \, n} + 2 \, a c x^{2 \, n} + a^{2}}, x\right)"," ",0,"integral((e^2*x^(2*n) + 2*d*e*x^n + d^2)/(c^2*x^(4*n) + 2*a*c*x^(2*n) + a^2), x)","F",0
50,0,0,0,0.861781," ","integrate((d+e*x^n)/(a+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{n} + d}{c^{2} x^{4 \, n} + 2 \, a c x^{2 \, n} + a^{2}}, x\right)"," ",0,"integral((e*x^n + d)/(c^2*x^(4*n) + 2*a*c*x^(2*n) + a^2), x)","F",0
51,0,0,0,0.954046," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} e x^{n} + a^{2} d + {\left(c^{2} e x^{n} + c^{2} d\right)} x^{4 \, n} + 2 \, {\left(a c e x^{n} + a c d\right)} x^{2 \, n}}, x\right)"," ",0,"integral(1/(a^2*e*x^n + a^2*d + (c^2*e*x^n + c^2*d)*x^(4*n) + 2*(a*c*e*x^n + a*c*d)*x^(2*n)), x)","F",0
52,0,0,0,1.411770," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{2} e^{2} x^{2 \, n} + 2 \, a^{2} d e x^{n} + a^{2} d^{2} + {\left(c^{2} e^{2} x^{2 \, n} + 2 \, c^{2} d e x^{n} + c^{2} d^{2}\right)} x^{4 \, n} + 2 \, {\left(a c e^{2} x^{2 \, n} + 2 \, a c d e x^{n} + a c d^{2}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(1/(a^2*e^2*x^(2*n) + 2*a^2*d*e*x^n + a^2*d^2 + (c^2*e^2*x^(2*n) + 2*c^2*d*e*x^n + c^2*d^2)*x^(4*n) + 2*(a*c*e^2*x^(2*n) + 2*a*c*d*e*x^n + a*c*d^2)*x^(2*n)), x)","F",0
53,0,0,0,0.880653," ","integrate((d+e*x^n)^3/(a+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}}{c^{3} x^{6 \, n} + 3 \, a c^{2} x^{4 \, n} + 3 \, a^{2} c x^{2 \, n} + a^{3}}, 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^3*x^(6*n) + 3*a*c^2*x^(4*n) + 3*a^2*c*x^(2*n) + a^3), x)","F",0
54,0,0,0,0.921306," ","integrate((d+e*x^n)^2/(a+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}{c^{3} x^{6 \, n} + 3 \, a c^{2} x^{4 \, n} + 3 \, a^{2} c x^{2 \, n} + a^{3}}, x\right)"," ",0,"integral((e^2*x^(2*n) + 2*d*e*x^n + d^2)/(c^3*x^(6*n) + 3*a*c^2*x^(4*n) + 3*a^2*c*x^(2*n) + a^3), x)","F",0
55,0,0,0,0.850344," ","integrate((d+e*x^n)/(a+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{n} + d}{c^{3} x^{6 \, n} + 3 \, a c^{2} x^{4 \, n} + 3 \, a^{2} c x^{2 \, n} + a^{3}}, x\right)"," ",0,"integral((e*x^n + d)/(c^3*x^(6*n) + 3*a*c^2*x^(4*n) + 3*a^2*c*x^(2*n) + a^3), x)","F",0
56,0,0,0,1.265747," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{3} e x^{n} + a^{3} d + {\left(c^{3} e x^{n} + c^{3} d\right)} x^{6 \, n} + 3 \, {\left(a c^{2} e x^{n} + a c^{2} d\right)} x^{4 \, n} + 3 \, {\left(a^{2} c e x^{n} + a^{2} c d\right)} x^{2 \, n}}, x\right)"," ",0,"integral(1/(a^3*e*x^n + a^3*d + (c^3*e*x^n + c^3*d)*x^(6*n) + 3*(a*c^2*e*x^n + a*c^2*d)*x^(4*n) + 3*(a^2*c*e*x^n + a^2*c*d)*x^(2*n)), x)","F",0
57,0,0,0,2.796142," ","integrate(1/(d+e*x^n)^2/(a+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{a^{3} e^{2} x^{2 \, n} + 2 \, a^{3} d e x^{n} + a^{3} d^{2} + {\left(c^{3} e^{2} x^{2 \, n} + 2 \, c^{3} d e x^{n} + c^{3} d^{2}\right)} x^{6 \, n} + 3 \, {\left(a c^{2} e^{2} x^{2 \, n} + 2 \, a c^{2} d e x^{n} + a c^{2} d^{2}\right)} x^{4 \, n} + 3 \, {\left(a^{2} c e^{2} x^{2 \, n} + 2 \, a^{2} c d e x^{n} + a^{2} c d^{2}\right)} x^{2 \, n}}, x\right)"," ",0,"integral(1/(a^3*e^2*x^(2*n) + 2*a^3*d*e*x^n + a^3*d^2 + (c^3*e^2*x^(2*n) + 2*c^3*d*e*x^n + c^3*d^2)*x^(6*n) + 3*(a*c^2*e^2*x^(2*n) + 2*a*c^2*d*e*x^n + a*c^2*d^2)*x^(4*n) + 3*(a^2*c*e^2*x^(2*n) + 2*a^2*c*d*e*x^n + a^2*c*d^2)*x^(2*n)), x)","F",0
58,0,0,0,1.169331," ","integrate(1/(d+e*x^n)/(a+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{2 \, n} + a}}{a e x^{n} + a d + {\left(c e x^{n} + c d\right)} x^{2 \, n}}, x\right)"," ",0,"integral(sqrt(c*x^(2*n) + a)/(a*e*x^n + a*d + (c*e*x^n + c*d)*x^(2*n)), x)","F",0
59,0,0,0,0.801556," ","integrate((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}, x\right)"," ",0,"integral((c*x^(2*n) + a)^p*(e*x^n + d)^q, x)","F",0
60,0,0,0,0.779950," ","integrate((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}, 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, x)","F",0
61,0,0,0,0.903343," ","integrate((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}, x\right)"," ",0,"integral((e^2*x^(2*n) + 2*d*e*x^n + d^2)*(c*x^(2*n) + a)^p, x)","F",0
62,0,0,0,0.827363," ","integrate((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}, x\right)"," ",0,"integral((e*x^n + d)*(c*x^(2*n) + a)^p, x)","F",0
63,0,0,0,0.928711," ","integrate((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}}{e x^{n} + d}, x\right)"," ",0,"integral((c*x^(2*n) + a)^p/(e*x^n + d), x)","F",0
64,0,0,0,1.129768," ","integrate((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}}{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}, x\right)"," ",0,"integral((c*x^(2*n) + a)^p/(e^2*x^(2*n) + 2*d*e*x^n + d^2), x)","F",0
65,0,0,0,0.966511," ","integrate((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}}{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/(e^3*x^(3*n) + 3*d*e^2*x^(2*n) + 3*d^2*e*x^n + d^3), x)","F",0
66,1,137,0,0.937912," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","\frac{{\left(2 \, c e n^{2} + 3 \, c e n + c e\right)} x x^{3 \, n} + {\left(3 \, {\left(c d + b e\right)} n^{2} + c d + b e + 4 \, {\left(c d + b e\right)} n\right)} x x^{2 \, n} + {\left(6 \, {\left(b d + a e\right)} n^{2} + b d + a e + 5 \, {\left(b d + a e\right)} n\right)} x x^{n} + {\left(6 \, a d n^{3} + 11 \, a d n^{2} + 6 \, a d n + a d\right)} x}{6 \, n^{3} + 11 \, n^{2} + 6 \, n + 1}"," ",0,"((2*c*e*n^2 + 3*c*e*n + c*e)*x*x^(3*n) + (3*(c*d + b*e)*n^2 + c*d + b*e + 4*(c*d + b*e)*n)*x*x^(2*n) + (6*(b*d + a*e)*n^2 + b*d + a*e + 5*(b*d + a*e)*n)*x*x^n + (6*a*d*n^3 + 11*a*d*n^2 + 6*a*d*n + a*d)*x)/(6*n^3 + 11*n^2 + 6*n + 1)","B",0
67,1,495,0,0.765651," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","\frac{{\left(24 \, c^{2} e n^{4} + 50 \, c^{2} e n^{3} + 35 \, c^{2} e n^{2} + 10 \, c^{2} e n + c^{2} e\right)} x x^{5 \, n} + {\left(30 \, {\left(c^{2} d + 2 \, b c e\right)} n^{4} + 61 \, {\left(c^{2} d + 2 \, b c e\right)} n^{3} + c^{2} d + 2 \, b c e + 41 \, {\left(c^{2} d + 2 \, b c e\right)} n^{2} + 11 \, {\left(c^{2} d + 2 \, b c e\right)} n\right)} x x^{4 \, n} + {\left(40 \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} n^{4} + 78 \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} n^{3} + 2 \, b c d + 49 \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} n^{2} + {\left(b^{2} + 2 \, a c\right)} e + 12 \, {\left(2 \, b c d + {\left(b^{2} + 2 \, a c\right)} e\right)} n\right)} x x^{3 \, n} + {\left(60 \, {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} n^{4} + 107 \, {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} n^{3} + 2 \, a b e + 59 \, {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} n^{2} + {\left(b^{2} + 2 \, a c\right)} d + 13 \, {\left(2 \, a b e + {\left(b^{2} + 2 \, a c\right)} d\right)} n\right)} x x^{2 \, n} + {\left(120 \, {\left(2 \, a b d + a^{2} e\right)} n^{4} + 154 \, {\left(2 \, a b d + a^{2} e\right)} n^{3} + 2 \, a b d + a^{2} e + 71 \, {\left(2 \, a b d + a^{2} e\right)} n^{2} + 14 \, {\left(2 \, a b d + a^{2} e\right)} n\right)} x x^{n} + {\left(120 \, a^{2} d n^{5} + 274 \, a^{2} d n^{4} + 225 \, a^{2} d n^{3} + 85 \, a^{2} d n^{2} + 15 \, a^{2} d n + a^{2} d\right)} x}{120 \, n^{5} + 274 \, n^{4} + 225 \, n^{3} + 85 \, n^{2} + 15 \, n + 1}"," ",0,"((24*c^2*e*n^4 + 50*c^2*e*n^3 + 35*c^2*e*n^2 + 10*c^2*e*n + c^2*e)*x*x^(5*n) + (30*(c^2*d + 2*b*c*e)*n^4 + 61*(c^2*d + 2*b*c*e)*n^3 + c^2*d + 2*b*c*e + 41*(c^2*d + 2*b*c*e)*n^2 + 11*(c^2*d + 2*b*c*e)*n)*x*x^(4*n) + (40*(2*b*c*d + (b^2 + 2*a*c)*e)*n^4 + 78*(2*b*c*d + (b^2 + 2*a*c)*e)*n^3 + 2*b*c*d + 49*(2*b*c*d + (b^2 + 2*a*c)*e)*n^2 + (b^2 + 2*a*c)*e + 12*(2*b*c*d + (b^2 + 2*a*c)*e)*n)*x*x^(3*n) + (60*(2*a*b*e + (b^2 + 2*a*c)*d)*n^4 + 107*(2*a*b*e + (b^2 + 2*a*c)*d)*n^3 + 2*a*b*e + 59*(2*a*b*e + (b^2 + 2*a*c)*d)*n^2 + (b^2 + 2*a*c)*d + 13*(2*a*b*e + (b^2 + 2*a*c)*d)*n)*x*x^(2*n) + (120*(2*a*b*d + a^2*e)*n^4 + 154*(2*a*b*d + a^2*e)*n^3 + 2*a*b*d + a^2*e + 71*(2*a*b*d + a^2*e)*n^2 + 14*(2*a*b*d + a^2*e)*n)*x*x^n + (120*a^2*d*n^5 + 274*a^2*d*n^4 + 225*a^2*d*n^3 + 85*a^2*d*n^2 + 15*a^2*d*n + a^2*d)*x)/(120*n^5 + 274*n^4 + 225*n^3 + 85*n^2 + 15*n + 1)","B",0
68,1,1209,0,0.876436," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","\frac{{\left(720 \, c^{3} e n^{6} + 1764 \, c^{3} e n^{5} + 1624 \, c^{3} e n^{4} + 735 \, c^{3} e n^{3} + 175 \, c^{3} e n^{2} + 21 \, c^{3} e n + c^{3} e\right)} x x^{7 \, n} + {\left(840 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} n^{6} + 2038 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} n^{5} + 1849 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} n^{4} + c^{3} d + 3 \, b c^{2} e + 820 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} n^{3} + 190 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} n^{2} + 22 \, {\left(c^{3} d + 3 \, b c^{2} e\right)} n\right)} x x^{6 \, n} + 3 \, {\left(1008 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} n^{6} + 2412 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} n^{5} + 2144 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} n^{4} + b c^{2} d + 925 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} n^{3} + 207 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} n^{2} + {\left(b^{2} c + a c^{2}\right)} e + 23 \, {\left(b c^{2} d + {\left(b^{2} c + a c^{2}\right)} e\right)} n\right)} x x^{5 \, n} + {\left(1260 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} n^{6} + 2952 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} n^{5} + 2545 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} n^{4} + 1056 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} n^{3} + 226 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} n^{2} + 3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e + 24 \, {\left(3 \, {\left(b^{2} c + a c^{2}\right)} d + {\left(b^{3} + 6 \, a b c\right)} e\right)} n\right)} x x^{4 \, n} + {\left(1680 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} n^{6} + 3796 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} n^{5} + 3112 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} n^{4} + 1219 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} n^{3} + 247 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} n^{2} + {\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e + 25 \, {\left({\left(b^{3} + 6 \, a b c\right)} d + 3 \, {\left(a b^{2} + a^{2} c\right)} e\right)} n\right)} x x^{3 \, n} + 3 \, {\left(2520 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} n^{6} + 5274 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} n^{5} + 3929 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} n^{4} + a^{2} b e + 1420 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} n^{3} + 270 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} n^{2} + {\left(a b^{2} + a^{2} c\right)} d + 26 \, {\left(a^{2} b e + {\left(a b^{2} + a^{2} c\right)} d\right)} n\right)} x x^{2 \, n} + {\left(5040 \, {\left(3 \, a^{2} b d + a^{3} e\right)} n^{6} + 8028 \, {\left(3 \, a^{2} b d + a^{3} e\right)} n^{5} + 5104 \, {\left(3 \, a^{2} b d + a^{3} e\right)} n^{4} + 3 \, a^{2} b d + a^{3} e + 1665 \, {\left(3 \, a^{2} b d + a^{3} e\right)} n^{3} + 295 \, {\left(3 \, a^{2} b d + a^{3} e\right)} n^{2} + 27 \, {\left(3 \, a^{2} b d + a^{3} e\right)} n\right)} x x^{n} + {\left(5040 \, a^{3} d n^{7} + 13068 \, a^{3} d n^{6} + 13132 \, a^{3} d n^{5} + 6769 \, a^{3} d n^{4} + 1960 \, a^{3} d n^{3} + 322 \, a^{3} d n^{2} + 28 \, a^{3} d n + a^{3} d\right)} x}{5040 \, n^{7} + 13068 \, n^{6} + 13132 \, n^{5} + 6769 \, n^{4} + 1960 \, n^{3} + 322 \, n^{2} + 28 \, n + 1}"," ",0,"((720*c^3*e*n^6 + 1764*c^3*e*n^5 + 1624*c^3*e*n^4 + 735*c^3*e*n^3 + 175*c^3*e*n^2 + 21*c^3*e*n + c^3*e)*x*x^(7*n) + (840*(c^3*d + 3*b*c^2*e)*n^6 + 2038*(c^3*d + 3*b*c^2*e)*n^5 + 1849*(c^3*d + 3*b*c^2*e)*n^4 + c^3*d + 3*b*c^2*e + 820*(c^3*d + 3*b*c^2*e)*n^3 + 190*(c^3*d + 3*b*c^2*e)*n^2 + 22*(c^3*d + 3*b*c^2*e)*n)*x*x^(6*n) + 3*(1008*(b*c^2*d + (b^2*c + a*c^2)*e)*n^6 + 2412*(b*c^2*d + (b^2*c + a*c^2)*e)*n^5 + 2144*(b*c^2*d + (b^2*c + a*c^2)*e)*n^4 + b*c^2*d + 925*(b*c^2*d + (b^2*c + a*c^2)*e)*n^3 + 207*(b*c^2*d + (b^2*c + a*c^2)*e)*n^2 + (b^2*c + a*c^2)*e + 23*(b*c^2*d + (b^2*c + a*c^2)*e)*n)*x*x^(5*n) + (1260*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*n^6 + 2952*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*n^5 + 2545*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*n^4 + 1056*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*n^3 + 226*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*n^2 + 3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e + 24*(3*(b^2*c + a*c^2)*d + (b^3 + 6*a*b*c)*e)*n)*x*x^(4*n) + (1680*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*n^6 + 3796*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*n^5 + 3112*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*n^4 + 1219*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*n^3 + 247*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*n^2 + (b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e + 25*((b^3 + 6*a*b*c)*d + 3*(a*b^2 + a^2*c)*e)*n)*x*x^(3*n) + 3*(2520*(a^2*b*e + (a*b^2 + a^2*c)*d)*n^6 + 5274*(a^2*b*e + (a*b^2 + a^2*c)*d)*n^5 + 3929*(a^2*b*e + (a*b^2 + a^2*c)*d)*n^4 + a^2*b*e + 1420*(a^2*b*e + (a*b^2 + a^2*c)*d)*n^3 + 270*(a^2*b*e + (a*b^2 + a^2*c)*d)*n^2 + (a*b^2 + a^2*c)*d + 26*(a^2*b*e + (a*b^2 + a^2*c)*d)*n)*x*x^(2*n) + (5040*(3*a^2*b*d + a^3*e)*n^6 + 8028*(3*a^2*b*d + a^3*e)*n^5 + 5104*(3*a^2*b*d + a^3*e)*n^4 + 3*a^2*b*d + a^3*e + 1665*(3*a^2*b*d + a^3*e)*n^3 + 295*(3*a^2*b*d + a^3*e)*n^2 + 27*(3*a^2*b*d + a^3*e)*n)*x*x^n + (5040*a^3*d*n^7 + 13068*a^3*d*n^6 + 13132*a^3*d*n^5 + 6769*a^3*d*n^4 + 1960*a^3*d*n^3 + 322*a^3*d*n^2 + 28*a^3*d*n + a^3*d)*x)/(5040*n^7 + 13068*n^6 + 13132*n^5 + 6769*n^4 + 1960*n^3 + 322*n^2 + 28*n + 1)","B",0
69,0,0,0,0.666095," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}}{c x^{2 \, n} + b x^{n} + a}, 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) + b*x^n + a), x)","F",0
70,0,0,0,0.634398," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral((e^2*x^(2*n) + 2*d*e*x^n + d^2)/(c*x^(2*n) + b*x^n + a), x)","F",0
71,0,0,0,1.158296," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{n} + d}{c x^{2 \, n} + b x^{n} + a}, x\right)"," ",0,"integral((e*x^n + d)/(c*x^(2*n) + b*x^n + a), x)","F",0
72,0,0,0,0.988008," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b e x^{2 \, n} + a d + {\left(c e x^{n} + c d\right)} x^{2 \, n} + {\left(b d + a e\right)} x^{n}}, x\right)"," ",0,"integral(1/(b*e*x^(2*n) + a*d + (c*e*x^n + c*d)*x^(2*n) + (b*d + a*e)*x^n), x)","F",0
73,0,0,0,1.319629," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b e^{2} x^{3 \, n} + a d^{2} + {\left(c e^{2} x^{2 \, n} + 2 \, c d e x^{n} + c d^{2}\right)} x^{2 \, n} + {\left(2 \, b d e + a e^{2}\right)} x^{2 \, n} + {\left(b d^{2} + 2 \, a d e\right)} x^{n}}, x\right)"," ",0,"integral(1/(b*e^2*x^(3*n) + a*d^2 + (c*e^2*x^(2*n) + 2*c*d*e*x^n + c*d^2)*x^(2*n) + (2*b*d*e + a*e^2)*x^(2*n) + (b*d^2 + 2*a*d*e)*x^n), x)","F",0
74,0,0,0,3.491403," ","integrate(1/(d+e*x^n)^3/(a+b*x^n+c*x^(2*n)),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b e^{3} x^{4 \, n} + a d^{3} + {\left(3 \, b d e^{2} + a e^{3}\right)} x^{3 \, n} + {\left(c e^{3} x^{3 \, n} + 3 \, c d e^{2} x^{2 \, n} + 3 \, c d^{2} e x^{n} + c d^{3}\right)} x^{2 \, n} + 3 \, {\left(b d^{2} e + a d e^{2}\right)} x^{2 \, n} + {\left(b d^{3} + 3 \, a d^{2} e\right)} x^{n}}, x\right)"," ",0,"integral(1/(b*e^3*x^(4*n) + a*d^3 + (3*b*d*e^2 + a*e^3)*x^(3*n) + (c*e^3*x^(3*n) + 3*c*d*e^2*x^(2*n) + 3*c*d^2*e*x^n + c*d^3)*x^(2*n) + 3*(b*d^2*e + a*d*e^2)*x^(2*n) + (b*d^3 + 3*a*d^2*e)*x^n), x)","F",0
75,0,0,0,1.201137," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}}{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^3*x^(3*n) + 3*d*e^2*x^(2*n) + 3*d^2*e*x^n + d^3)/(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
76,0,0,0,0.987913," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}{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^2*x^(2*n) + 2*d*e*x^n + d^2)/(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
77,0,0,0,1.092545," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{n} + d}{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)/(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
78,0,0,0,1.829528," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} e x^{3 \, n} + a^{2} d + {\left(c^{2} e x^{n} + c^{2} d\right)} x^{4 \, n} + 2 \, {\left(b c e x^{2 \, n} + a c d + {\left(b c d + a c e\right)} x^{n}\right)} x^{2 \, n} + {\left(b^{2} d + 2 \, a b e\right)} x^{2 \, n} + {\left(2 \, a b d + a^{2} e\right)} x^{n}}, x\right)"," ",0,"integral(1/(b^2*e*x^(3*n) + a^2*d + (c^2*e*x^n + c^2*d)*x^(4*n) + 2*(b*c*e*x^(2*n) + a*c*d + (b*c*d + a*c*e)*x^n)*x^(2*n) + (b^2*d + 2*a*b*e)*x^(2*n) + (2*a*b*d + a^2*e)*x^n), x)","F",0
79,0,0,0,6.268080," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{2} e^{2} x^{4 \, n} + a^{2} d^{2} + {\left(c^{2} e^{2} x^{2 \, n} + 2 \, c^{2} d e x^{n} + c^{2} d^{2}\right)} x^{4 \, n} + 2 \, {\left(b^{2} d e + a b e^{2}\right)} x^{3 \, n} + 2 \, {\left(b c e^{2} x^{3 \, n} + a c d^{2} + {\left(2 \, b c d e + a c e^{2}\right)} x^{2 \, n} + {\left(b c d^{2} + 2 \, a c d e\right)} x^{n}\right)} x^{2 \, n} + {\left(b^{2} d^{2} + 4 \, a b d e + a^{2} e^{2}\right)} x^{2 \, n} + 2 \, {\left(a b d^{2} + a^{2} d e\right)} x^{n}}, x\right)"," ",0,"integral(1/(b^2*e^2*x^(4*n) + a^2*d^2 + (c^2*e^2*x^(2*n) + 2*c^2*d*e*x^n + c^2*d^2)*x^(4*n) + 2*(b^2*d*e + a*b*e^2)*x^(3*n) + 2*(b*c*e^2*x^(3*n) + a*c*d^2 + (2*b*c*d*e + a*c*e^2)*x^(2*n) + (b*c*d^2 + 2*a*c*d*e)*x^n)*x^(2*n) + (b^2*d^2 + 4*a*b*d*e + a^2*e^2)*x^(2*n) + 2*(a*b*d^2 + a^2*d*e)*x^n), x)","F",0
80,0,0,0,1.117805," ","integrate((d+e*x^n)^3/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{3 \, n} + 3 \, d e^{2} x^{2 \, n} + 3 \, d^{2} e x^{n} + d^{3}}{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^3*x^(3*n) + 3*d*e^2*x^(2*n) + 3*d^2*e*x^n + d^3)/(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
81,0,0,0,0.906543," ","integrate((d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{2 \, n} + 2 \, d e x^{n} + d^{2}}{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^2*x^(2*n) + 2*d*e*x^n + d^2)/(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
82,0,0,0,0.990833," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{n} + d}{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)/(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
83,0,0,0,17.898570," ","integrate(1/(d+e*x^n)/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} e x^{4 \, n} + a^{3} d + {\left(c^{3} e x^{n} + c^{3} d\right)} x^{6 \, n} + 3 \, {\left(b c^{2} e x^{2 \, n} + a c^{2} d + {\left(b c^{2} d + a c^{2} e\right)} x^{n}\right)} x^{4 \, n} + {\left(b^{3} d + 3 \, a b^{2} e\right)} x^{3 \, n} + 3 \, {\left(b^{2} c e x^{3 \, n} + a^{2} c d + {\left(b^{2} c d + 2 \, a b c e\right)} x^{2 \, n} + {\left(2 \, a b c d + a^{2} c e\right)} x^{n}\right)} x^{2 \, n} + 3 \, {\left(a b^{2} d + a^{2} b e\right)} x^{2 \, n} + {\left(3 \, a^{2} b d + a^{3} e\right)} x^{n}}, x\right)"," ",0,"integral(1/(b^3*e*x^(4*n) + a^3*d + (c^3*e*x^n + c^3*d)*x^(6*n) + 3*(b*c^2*e*x^(2*n) + a*c^2*d + (b*c^2*d + a*c^2*e)*x^n)*x^(4*n) + (b^3*d + 3*a*b^2*e)*x^(3*n) + 3*(b^2*c*e*x^(3*n) + a^2*c*d + (b^2*c*d + 2*a*b*c*e)*x^(2*n) + (2*a*b*c*d + a^2*c*e)*x^n)*x^(2*n) + 3*(a*b^2*d + a^2*b*e)*x^(2*n) + (3*a^2*b*d + a^3*e)*x^n), x)","F",0
84,0,0,0,62.831851," ","integrate(1/(d+e*x^n)^2/(a+b*x^n+c*x^(2*n))^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{b^{3} e^{2} x^{5 \, n} + a^{3} d^{2} + {\left(c^{3} e^{2} x^{2 \, n} + 2 \, c^{3} d e x^{n} + c^{3} d^{2}\right)} x^{6 \, n} + 3 \, {\left(b c^{2} e^{2} x^{3 \, n} + a c^{2} d^{2} + {\left(2 \, b c^{2} d e + a c^{2} e^{2}\right)} x^{2 \, n} + {\left(b c^{2} d^{2} + 2 \, a c^{2} d e\right)} x^{n}\right)} x^{4 \, n} + {\left(2 \, b^{3} d e + 3 \, a b^{2} e^{2}\right)} x^{4 \, n} + {\left(b^{3} d^{2} + 6 \, a b^{2} d e + 3 \, a^{2} b e^{2}\right)} x^{3 \, n} + 3 \, {\left(b^{2} c e^{2} x^{4 \, n} + a^{2} c d^{2} + 2 \, {\left(b^{2} c d e + a b c e^{2}\right)} x^{3 \, n} + {\left(b^{2} c d^{2} + 4 \, a b c d e + a^{2} c e^{2}\right)} x^{2 \, n} + 2 \, {\left(a b c d^{2} + a^{2} c d e\right)} x^{n}\right)} x^{2 \, n} + {\left(3 \, a b^{2} d^{2} + 6 \, a^{2} b d e + a^{3} e^{2}\right)} x^{2 \, n} + {\left(3 \, a^{2} b d^{2} + 2 \, a^{3} d e\right)} x^{n}}, x\right)"," ",0,"integral(1/(b^3*e^2*x^(5*n) + a^3*d^2 + (c^3*e^2*x^(2*n) + 2*c^3*d*e*x^n + c^3*d^2)*x^(6*n) + 3*(b*c^2*e^2*x^(3*n) + a*c^2*d^2 + (2*b*c^2*d*e + a*c^2*e^2)*x^(2*n) + (b*c^2*d^2 + 2*a*c^2*d*e)*x^n)*x^(4*n) + (2*b^3*d*e + 3*a*b^2*e^2)*x^(4*n) + (b^3*d^2 + 6*a*b^2*d*e + 3*a^2*b*e^2)*x^(3*n) + 3*(b^2*c*e^2*x^(4*n) + a^2*c*d^2 + 2*(b^2*c*d*e + a*b*c*e^2)*x^(3*n) + (b^2*c*d^2 + 4*a*b*c*d*e + a^2*c*e^2)*x^(2*n) + 2*(a*b*c*d^2 + a^2*c*d*e)*x^n)*x^(2*n) + (3*a*b^2*d^2 + 6*a^2*b*d*e + a^3*e^2)*x^(2*n) + (3*a^2*b*d^2 + 2*a^3*d*e)*x^n), x)","F",0
85,-2,0,0,0.000000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
86,-2,0,0,0.000000," ","integrate((d+e*x^n)*(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (has polynomial part)","F(-2)",0
87,-2,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
88,-2,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(3/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
89,-2,0,0,0.000000," ","integrate((d+e*x^n)/(a+b*x^n+c*x^(2*n))^(5/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   integrate: implementation incomplete (constant residues)","F(-2)",0
90,0,0,0,1.116832," ","integrate((d+e*x^n)^q*(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(e x^{n} + d\right)}^{q}, x\right)"," ",0,"integral((c*x^(2*n) + b*x^n + a)^p*(e*x^n + d)^q, x)","F",0
91,0,0,0,1.165266," ","integrate((d+e*x^n)^3*(a+b*x^n+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} + b x^{n} + a\right)}^{p}, 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) + b*x^n + a)^p, x)","F",0
92,0,0,0,0.911484," ","integrate((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}, 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, x)","F",0
93,0,0,0,1.042296," ","integrate((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}, x\right)"," ",0,"integral((e*x^n + d)*(c*x^(2*n) + b*x^n + a)^p, x)","F",0
94,0,0,0,1.047956," ","integrate((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}}{e x^{n} + d}, x\right)"," ",0,"integral((c*x^(2*n) + b*x^n + a)^p/(e*x^n + d), x)","F",0
95,0,0,0,1.084831," ","integrate((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}}{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/(e^2*x^(2*n) + 2*d*e*x^n + d^2), x)","F",0
96,0,0,0,1.339064," ","integrate((a+b*x^n+c*x^(2*n))^p/(d+e*x^n)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(c x^{2 \, n} + b x^{n} + a\right)}^{p}}{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) + b*x^n + a)^p/(e^3*x^(3*n) + 3*d*e^2*x^(2*n) + 3*d^2*e*x^n + d^3), x)","F",0
