1,1,767,0,0.869456," ","integrate((d*x^2+c)/(b*x^4+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x + {\left(a^{3} b^{2} d \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + a b^{2} c^{3} - a^{2} b c d^{2}\right)} \sqrt{-\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}}\right) + \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x - {\left(a^{3} b^{2} d \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + a b^{2} c^{3} - a^{2} b c d^{2}\right)} \sqrt{-\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}}\right) + \frac{1}{4} \, \sqrt{\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x + {\left(a^{3} b^{2} d \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - a b^{2} c^{3} + a^{2} b c d^{2}\right)} \sqrt{\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}}\right) - \frac{1}{4} \, \sqrt{\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x - {\left(a^{3} b^{2} d \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - a b^{2} c^{3} + a^{2} b c d^{2}\right)} \sqrt{\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}}\right)"," ",0,"-1/4*sqrt(-(a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x + (a^3*b^2*d*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + a*b^2*c^3 - a^2*b*c*d^2)*sqrt(-(a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))) + 1/4*sqrt(-(a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x - (a^3*b^2*d*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + a*b^2*c^3 - a^2*b*c*d^2)*sqrt(-(a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))) + 1/4*sqrt((a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x + (a^3*b^2*d*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - a*b^2*c^3 + a^2*b*c*d^2)*sqrt((a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))) - 1/4*sqrt((a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x - (a^3*b^2*d*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - a*b^2*c^3 + a^2*b*c*d^2)*sqrt((a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b)))","B",0
2,1,767,0,0.660578," ","integrate((-d*x^2+c)/(b*x^4+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x + {\left(a^{3} b^{2} d \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + a b^{2} c^{3} - a^{2} b c d^{2}\right)} \sqrt{\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}}\right) + \frac{1}{4} \, \sqrt{\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x - {\left(a^{3} b^{2} d \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + a b^{2} c^{3} - a^{2} b c d^{2}\right)} \sqrt{\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}}\right) + \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x + {\left(a^{3} b^{2} d \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - a b^{2} c^{3} + a^{2} b c d^{2}\right)} \sqrt{-\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}}\right) - \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x - {\left(a^{3} b^{2} d \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - a b^{2} c^{3} + a^{2} b c d^{2}\right)} \sqrt{-\frac{a b \sqrt{-\frac{b^{2} c^{4} - 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}}\right)"," ",0,"-1/4*sqrt((a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x + (a^3*b^2*d*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + a*b^2*c^3 - a^2*b*c*d^2)*sqrt((a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))) + 1/4*sqrt((a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x - (a^3*b^2*d*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + a*b^2*c^3 - a^2*b*c*d^2)*sqrt((a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))) + 1/4*sqrt(-(a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x + (a^3*b^2*d*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - a*b^2*c^3 + a^2*b*c*d^2)*sqrt(-(a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))) - 1/4*sqrt(-(a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x - (a^3*b^2*d*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - a*b^2*c^3 + a^2*b*c*d^2)*sqrt(-(a*b*sqrt(-(b^2*c^4 - 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b)))","B",0
3,1,755,0,0.902333," ","integrate((d*x^2+c)/(-b*x^4+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x + {\left(a^{3} b^{2} d \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - a b^{2} c^{3} - a^{2} b c d^{2}\right)} \sqrt{\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}}\right) - \frac{1}{4} \, \sqrt{\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x - {\left(a^{3} b^{2} d \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - a b^{2} c^{3} - a^{2} b c d^{2}\right)} \sqrt{\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}}\right) - \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x + {\left(a^{3} b^{2} d \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + a b^{2} c^{3} + a^{2} b c d^{2}\right)} \sqrt{-\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}}\right) + \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x - {\left(a^{3} b^{2} d \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + a b^{2} c^{3} + a^{2} b c d^{2}\right)} \sqrt{-\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}}\right)"," ",0,"1/4*sqrt((a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x + (a^3*b^2*d*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - a*b^2*c^3 - a^2*b*c*d^2)*sqrt((a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))) - 1/4*sqrt((a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x - (a^3*b^2*d*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - a*b^2*c^3 - a^2*b*c*d^2)*sqrt((a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))) - 1/4*sqrt(-(a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x + (a^3*b^2*d*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + a*b^2*c^3 + a^2*b*c*d^2)*sqrt(-(a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))) + 1/4*sqrt(-(a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x - (a^3*b^2*d*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + a*b^2*c^3 + a^2*b*c*d^2)*sqrt(-(a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b)))","B",0
4,1,755,0,0.565860," ","integrate((-d*x^2+c)/(-b*x^4+a),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x + {\left(a^{3} b^{2} d \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - a b^{2} c^{3} - a^{2} b c d^{2}\right)} \sqrt{-\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}}\right) - \frac{1}{4} \, \sqrt{-\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x - {\left(a^{3} b^{2} d \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - a b^{2} c^{3} - a^{2} b c d^{2}\right)} \sqrt{-\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + 2 \, c d}{a b}}\right) - \frac{1}{4} \, \sqrt{\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x + {\left(a^{3} b^{2} d \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + a b^{2} c^{3} + a^{2} b c d^{2}\right)} \sqrt{\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}}\right) + \frac{1}{4} \, \sqrt{\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}} \log\left(-{\left(b^{2} c^{4} - a^{2} d^{4}\right)} x - {\left(a^{3} b^{2} d \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} + a b^{2} c^{3} + a^{2} b c d^{2}\right)} \sqrt{\frac{a b \sqrt{\frac{b^{2} c^{4} + 2 \, a b c^{2} d^{2} + a^{2} d^{4}}{a^{3} b^{3}}} - 2 \, c d}{a b}}\right)"," ",0,"1/4*sqrt(-(a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x + (a^3*b^2*d*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - a*b^2*c^3 - a^2*b*c*d^2)*sqrt(-(a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))) - 1/4*sqrt(-(a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x - (a^3*b^2*d*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - a*b^2*c^3 - a^2*b*c*d^2)*sqrt(-(a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + 2*c*d)/(a*b))) - 1/4*sqrt((a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x + (a^3*b^2*d*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + a*b^2*c^3 + a^2*b*c*d^2)*sqrt((a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))) + 1/4*sqrt((a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b))*log(-(b^2*c^4 - a^2*d^4)*x - (a^3*b^2*d*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) + a*b^2*c^3 + a^2*b*c*d^2)*sqrt((a*b*sqrt((b^2*c^4 + 2*a*b*c^2*d^2 + a^2*d^4)/(a^3*b^3)) - 2*c*d)/(a*b)))","B",0
5,1,33,0,0.689564," ","integrate((3*x^2+2)/(9*x^4+4),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{4} \, \sqrt{3} {\left(3 \, x^{3} + 2 \, x\right)}\right) + \frac{1}{6} \, \sqrt{3} \arctan\left(\frac{1}{2} \, \sqrt{3} x\right)"," ",0,"1/6*sqrt(3)*arctan(1/4*sqrt(3)*(3*x^3 + 2*x)) + 1/6*sqrt(3)*arctan(1/2*sqrt(3)*x)","A",0
6,1,42,0,0.552390," ","integrate((-3*x^2+2)/(9*x^4+4),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{3} \log\left(\frac{9 \, x^{4} + 24 \, x^{2} + 4 \, \sqrt{3} {\left(3 \, x^{3} + 2 \, x\right)} + 4}{9 \, x^{4} + 4}\right)"," ",0,"1/12*sqrt(3)*log((9*x^4 + 24*x^2 + 4*sqrt(3)*(3*x^3 + 2*x) + 4)/(9*x^4 + 4))","A",0
7,1,29,0,0.771674," ","integrate((3*x^2+2)/(-9*x^4+4),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{6} \log\left(\frac{3 \, x^{2} + 2 \, \sqrt{6} x + 2}{3 \, x^{2} - 2}\right)"," ",0,"1/12*sqrt(6)*log((3*x^2 + 2*sqrt(6)*x + 2)/(3*x^2 - 2))","B",0
8,1,12,0,0.862243," ","integrate((-3*x^2+2)/(-9*x^4+4),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{6} \arctan\left(\frac{1}{2} \, \sqrt{6} x\right)"," ",0,"1/6*sqrt(6)*arctan(1/2*sqrt(6)*x)","A",0
9,1,148,0,0.944117," ","integrate((b*x^2+a^(1/2)*b^(1/2))/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{\sqrt{b}}{\sqrt{a}}} \log\left(\frac{b x^{4} - 4 \, \sqrt{a} \sqrt{b} x^{2} + 4 \, \sqrt{\frac{1}{2}} {\left(\sqrt{a} \sqrt{b} x^{3} - a x\right)} \sqrt{-\frac{\sqrt{b}}{\sqrt{a}}} + a}{b x^{4} + a}\right), \sqrt{\frac{1}{2}} \sqrt{\frac{\sqrt{b}}{\sqrt{a}}} \arctan\left(\sqrt{\frac{1}{2}} x \sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\right) + \sqrt{\frac{1}{2}} \sqrt{\frac{\sqrt{b}}{\sqrt{a}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(\sqrt{a} \sqrt{b} x^{3} + a x\right)} \sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}{a}\right)\right]"," ",0,"[1/2*sqrt(1/2)*sqrt(-sqrt(b)/sqrt(a))*log((b*x^4 - 4*sqrt(a)*sqrt(b)*x^2 + 4*sqrt(1/2)*(sqrt(a)*sqrt(b)*x^3 - a*x)*sqrt(-sqrt(b)/sqrt(a)) + a)/(b*x^4 + a)), sqrt(1/2)*sqrt(sqrt(b)/sqrt(a))*arctan(sqrt(1/2)*x*sqrt(sqrt(b)/sqrt(a))) + sqrt(1/2)*sqrt(sqrt(b)/sqrt(a))*arctan(sqrt(1/2)*(sqrt(a)*sqrt(b)*x^3 + a*x)*sqrt(sqrt(b)/sqrt(a))/a)]","A",0
10,1,151,0,0.944429," ","integrate((-b*x^2+a^(1/2)*b^(1/2))/(b*x^4+a),x, algorithm=""fricas"")","\left[\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{\sqrt{b}}{\sqrt{a}}} \log\left(\frac{b x^{4} + 4 \, \sqrt{a} \sqrt{b} x^{2} + 4 \, \sqrt{\frac{1}{2}} {\left(\sqrt{a} \sqrt{b} x^{3} + a x\right)} \sqrt{\frac{\sqrt{b}}{\sqrt{a}}} + a}{b x^{4} + a}\right), -\sqrt{\frac{1}{2}} \sqrt{-\frac{\sqrt{b}}{\sqrt{a}}} \arctan\left(\sqrt{\frac{1}{2}} x \sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}\right) + \sqrt{\frac{1}{2}} \sqrt{-\frac{\sqrt{b}}{\sqrt{a}}} \arctan\left(\frac{\sqrt{\frac{1}{2}} {\left(\sqrt{a} \sqrt{b} x^{3} - a x\right)} \sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{a}\right)\right]"," ",0,"[1/2*sqrt(1/2)*sqrt(sqrt(b)/sqrt(a))*log((b*x^4 + 4*sqrt(a)*sqrt(b)*x^2 + 4*sqrt(1/2)*(sqrt(a)*sqrt(b)*x^3 + a*x)*sqrt(sqrt(b)/sqrt(a)) + a)/(b*x^4 + a)), -sqrt(1/2)*sqrt(-sqrt(b)/sqrt(a))*arctan(sqrt(1/2)*x*sqrt(-sqrt(b)/sqrt(a))) + sqrt(1/2)*sqrt(-sqrt(b)/sqrt(a))*arctan(sqrt(1/2)*(sqrt(a)*sqrt(b)*x^3 - a*x)*sqrt(-sqrt(b)/sqrt(a))/a)]","A",0
11,1,137,0,1.497919," ","integrate((e*x^2+d)/(e^2*x^4+d^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} \sqrt{-d e} \log\left(\frac{e^{2} x^{4} - 4 \, d e x^{2} - 2 \, \sqrt{2} {\left(e x^{3} - d x\right)} \sqrt{-d e} + d^{2}}{e^{2} x^{4} + d^{2}}\right)}{4 \, d e}, \frac{\sqrt{2} \sqrt{d e} \arctan\left(\frac{\sqrt{2} \sqrt{d e} x}{2 \, d}\right) + \sqrt{2} \sqrt{d e} \arctan\left(\frac{\sqrt{2} {\left(e x^{3} + d x\right)} \sqrt{d e}}{2 \, d^{2}}\right)}{2 \, d e}\right]"," ",0,"[-1/4*sqrt(2)*sqrt(-d*e)*log((e^2*x^4 - 4*d*e*x^2 - 2*sqrt(2)*(e*x^3 - d*x)*sqrt(-d*e) + d^2)/(e^2*x^4 + d^2))/(d*e), 1/2*(sqrt(2)*sqrt(d*e)*arctan(1/2*sqrt(2)*sqrt(d*e)*x/d) + sqrt(2)*sqrt(d*e)*arctan(1/2*sqrt(2)*(e*x^3 + d*x)*sqrt(d*e)/d^2))/(d*e)]","A",0
12,1,140,0,0.530333," ","integrate((-e*x^2+d)/(e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{d e} \log\left(\frac{e^{2} x^{4} + 4 \, d e x^{2} + 2 \, \sqrt{2} {\left(e x^{3} + d x\right)} \sqrt{d e} + d^{2}}{e^{2} x^{4} + d^{2}}\right)}{4 \, d e}, -\frac{\sqrt{2} \sqrt{-d e} \arctan\left(\frac{\sqrt{2} \sqrt{-d e} x}{2 \, d}\right) - \sqrt{2} \sqrt{-d e} \arctan\left(\frac{\sqrt{2} {\left(e x^{3} - d x\right)} \sqrt{-d e}}{2 \, d^{2}}\right)}{2 \, d e}\right]"," ",0,"[1/4*sqrt(2)*sqrt(d*e)*log((e^2*x^4 + 4*d*e*x^2 + 2*sqrt(2)*(e*x^3 + d*x)*sqrt(d*e) + d^2)/(e^2*x^4 + d^2))/(d*e), -1/2*(sqrt(2)*sqrt(-d*e)*arctan(1/2*sqrt(2)*sqrt(-d*e)*x/d) - sqrt(2)*sqrt(-d*e)*arctan(1/2*sqrt(2)*(e*x^3 - d*x)*sqrt(-d*e)/d^2))/(d*e)]","A",0
13,1,17,0,0.785491," ","integrate((2*x^2+5)/(x^4-1),x, algorithm=""fricas"")","-\frac{3}{2} \, \arctan\left(x\right) - \frac{7}{4} \, \log\left(x + 1\right) + \frac{7}{4} \, \log\left(x - 1\right)"," ",0,"-3/2*arctan(x) - 7/4*log(x + 1) + 7/4*log(x - 1)","A",0
14,0,0,0,0.941268," ","integrate((b*x^2+1)/(-b^2*x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-b^{2} x^{4} + 1}}{b x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-b^2*x^4 + 1)/(b*x^2 - 1), x)","F",0
15,0,0,0,0.808860," ","integrate((-b*x^2+1)/(-b^2*x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-b^{2} x^{4} + 1}}{b x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-b^2*x^4 + 1)/(b*x^2 + 1), x)","F",0
16,0,0,0,0.682503," ","integrate((b*x^2+1)/(b^2*x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b^{2} x^{4} - 1}}{b x^{2} - 1}, x\right)"," ",0,"integral(sqrt(b^2*x^4 - 1)/(b*x^2 - 1), x)","F",0
17,0,0,0,0.659837," ","integrate((-b*x^2+1)/(b^2*x^4-1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{b^{2} x^{4} - 1}}{b x^{2} + 1}, x\right)"," ",0,"integral(-sqrt(b^2*x^4 - 1)/(b*x^2 + 1), x)","F",0
18,0,0,0,0.718154," ","integrate((-b*x^2+1)/(b^2*x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{b x^{2} - 1}{\sqrt{b^{2} x^{4} + 1}}, x\right)"," ",0,"integral(-(b*x^2 - 1)/sqrt(b^2*x^4 + 1), x)","F",0
19,0,0,0,0.410506," ","integrate((b*x^2+1)/(b^2*x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{b x^{2} + 1}{\sqrt{b^{2} x^{4} + 1}}, x\right)"," ",0,"integral((b*x^2 + 1)/sqrt(b^2*x^4 + 1), x)","F",0
20,0,0,0,0.723522," ","integrate((-b*x^2+1)/(-b^2*x^4-1)^(1/2),x, algorithm=""fricas"")","\frac{b x {\rm integral}\left(-\frac{\sqrt{-b^{2} x^{4} - 1} {\left(b x^{2} - 1\right)}}{b^{3} x^{6} + b x^{2}}, x\right) + \sqrt{-b^{2} x^{4} - 1}}{b x}"," ",0,"(b*x*integral(-sqrt(-b^2*x^4 - 1)*(b*x^2 - 1)/(b^3*x^6 + b*x^2), x) + sqrt(-b^2*x^4 - 1))/(b*x)","F",0
21,0,0,0,0.789634," ","integrate((b*x^2+1)/(-b^2*x^4-1)^(1/2),x, algorithm=""fricas"")","\frac{b x {\rm integral}\left(-\frac{\sqrt{-b^{2} x^{4} - 1} {\left(b x^{2} + 1\right)}}{b^{3} x^{6} + b x^{2}}, x\right) - \sqrt{-b^{2} x^{4} - 1}}{b x}"," ",0,"(b*x*integral(-sqrt(-b^2*x^4 - 1)*(b*x^2 + 1)/(b^3*x^6 + b*x^2), x) - sqrt(-b^2*x^4 - 1))/(b*x)","F",0
22,0,0,0,0.843587," ","integrate((c^2*x^2+1)^(1/2)/(-c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{c^{2} x^{2} + 1} \sqrt{-c^{2} x^{2} + 1}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(c^2*x^2 + 1)*sqrt(-c^2*x^2 + 1)/(c^2*x^2 - 1), x)","F",0
23,0,0,0,0.745804," ","integrate((c^2*x^2+1)/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c^{4} x^{4} + 1}}{c^{2} x^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-c^4*x^4 + 1)/(c^2*x^2 - 1), x)","F",0
24,0,0,0,0.589767," ","integrate((-c^2*x^2+1)^(1/2)/(c^2*x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{2} x^{2} + 1}}{\sqrt{c^{2} x^{2} + 1}}, x\right)"," ",0,"integral(sqrt(-c^2*x^2 + 1)/sqrt(c^2*x^2 + 1), x)","F",0
25,0,0,0,1.050331," ","integrate((-c^2*x^2+1)/(-c^4*x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-c^{4} x^{4} + 1}}{c^{2} x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-c^4*x^4 + 1)/(c^2*x^2 + 1), x)","F",0
26,1,162,0,0.669319," ","integrate((e*x^2+d)/(e^2*x^4+b*x^2+d^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-2 \, d e - b} \log\left(\frac{e^{2} x^{4} - {\left(4 \, d e + b\right)} x^{2} + d^{2} - 2 \, {\left(e x^{3} - d x\right)} \sqrt{-2 \, d e - b}}{e^{2} x^{4} + b x^{2} + d^{2}}\right)}{2 \, {\left(2 \, d e + b\right)}}, \frac{\sqrt{2 \, d e + b} \arctan\left(\frac{e x}{\sqrt{2 \, d e + b}}\right) + \sqrt{2 \, d e + b} \arctan\left(\frac{{\left(e^{2} x^{3} + {\left(d e + b\right)} x\right)} \sqrt{2 \, d e + b}}{2 \, d^{2} e + b d}\right)}{2 \, d e + b}\right]"," ",0,"[-1/2*sqrt(-2*d*e - b)*log((e^2*x^4 - (4*d*e + b)*x^2 + d^2 - 2*(e*x^3 - d*x)*sqrt(-2*d*e - b))/(e^2*x^4 + b*x^2 + d^2))/(2*d*e + b), (sqrt(2*d*e + b)*arctan(e*x/sqrt(2*d*e + b)) + sqrt(2*d*e + b)*arctan((e^2*x^3 + (d*e + b)*x)*sqrt(2*d*e + b)/(2*d^2*e + b*d)))/(2*d*e + b)]","A",0
27,1,162,0,0.742871," ","integrate((e*x^2+d)/(e^2*x^4+f*x^2+d^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-2 \, d e - f} \log\left(\frac{e^{2} x^{4} - {\left(4 \, d e + f\right)} x^{2} + d^{2} - 2 \, {\left(e x^{3} - d x\right)} \sqrt{-2 \, d e - f}}{e^{2} x^{4} + f x^{2} + d^{2}}\right)}{2 \, {\left(2 \, d e + f\right)}}, \frac{\sqrt{2 \, d e + f} \arctan\left(\frac{e x}{\sqrt{2 \, d e + f}}\right) + \sqrt{2 \, d e + f} \arctan\left(\frac{{\left(e^{2} x^{3} + {\left(d e + f\right)} x\right)} \sqrt{2 \, d e + f}}{2 \, d^{2} e + d f}\right)}{2 \, d e + f}\right]"," ",0,"[-1/2*sqrt(-2*d*e - f)*log((e^2*x^4 - (4*d*e + f)*x^2 + d^2 - 2*(e*x^3 - d*x)*sqrt(-2*d*e - f))/(e^2*x^4 + f*x^2 + d^2))/(2*d*e + f), (sqrt(2*d*e + f)*arctan(e*x/sqrt(2*d*e + f)) + sqrt(2*d*e + f)*arctan((e^2*x^3 + (d*e + f)*x)*sqrt(2*d*e + f)/(2*d^2*e + d*f)))/(2*d*e + f)]","A",0
28,1,176,0,0.840254," ","integrate((e*x^2+d)/(e^2*x^4-b*x^2+d^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-2 \, d e + b} \log\left(\frac{e^{2} x^{4} - {\left(4 \, d e - b\right)} x^{2} + d^{2} - 2 \, {\left(e x^{3} - d x\right)} \sqrt{-2 \, d e + b}}{e^{2} x^{4} - b x^{2} + d^{2}}\right)}{2 \, {\left(2 \, d e - b\right)}}, \frac{\sqrt{2 \, d e - b} \arctan\left(\frac{e x}{\sqrt{2 \, d e - b}}\right) + \sqrt{2 \, d e - b} \arctan\left(\frac{{\left(e^{2} x^{3} + {\left(d e - b\right)} x\right)} \sqrt{2 \, d e - b}}{2 \, d^{2} e - b d}\right)}{2 \, d e - b}\right]"," ",0,"[-1/2*sqrt(-2*d*e + b)*log((e^2*x^4 - (4*d*e - b)*x^2 + d^2 - 2*(e*x^3 - d*x)*sqrt(-2*d*e + b))/(e^2*x^4 - b*x^2 + d^2))/(2*d*e - b), (sqrt(2*d*e - b)*arctan(e*x/sqrt(2*d*e - b)) + sqrt(2*d*e - b)*arctan((e^2*x^3 + (d*e - b)*x)*sqrt(2*d*e - b)/(2*d^2*e - b*d)))/(2*d*e - b)]","A",0
29,1,179,0,0.757018," ","integrate((e*x^2+d)/(e^2*x^4-f*x^2+d^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-2 \, d e + f} \log\left(\frac{e^{2} x^{4} - {\left(4 \, d e - f\right)} x^{2} + d^{2} - 2 \, {\left(e x^{3} - d x\right)} \sqrt{-2 \, d e + f}}{e^{2} x^{4} - f x^{2} + d^{2}}\right)}{2 \, {\left(2 \, d e - f\right)}}, -\frac{\sqrt{2 \, d e - f} \arctan\left(-\frac{e x}{\sqrt{2 \, d e - f}}\right) + \sqrt{2 \, d e - f} \arctan\left(-\frac{{\left(e^{2} x^{3} + {\left(d e - f\right)} x\right)} \sqrt{2 \, d e - f}}{2 \, d^{2} e - d f}\right)}{2 \, d e - f}\right]"," ",0,"[-1/2*sqrt(-2*d*e + f)*log((e^2*x^4 - (4*d*e - f)*x^2 + d^2 - 2*(e*x^3 - d*x)*sqrt(-2*d*e + f))/(e^2*x^4 - f*x^2 + d^2))/(2*d*e - f), -(sqrt(2*d*e - f)*arctan(-e*x/sqrt(2*d*e - f)) + sqrt(2*d*e - f)*arctan(-(e^2*x^3 + (d*e - f)*x)*sqrt(2*d*e - f)/(2*d^2*e - d*f)))/(2*d*e - f)]","A",0
30,1,172,0,0.695394," ","integrate((-e*x^2+d)/(e^2*x^4+b*x^2+d^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{e^{2} x^{4} + {\left(4 \, d e - b\right)} x^{2} + d^{2} + 2 \, {\left(e x^{3} + d x\right)} \sqrt{2 \, d e - b}}{e^{2} x^{4} + b x^{2} + d^{2}}\right)}{2 \, \sqrt{2 \, d e - b}}, -\frac{\sqrt{-2 \, d e + b} \arctan\left(\frac{\sqrt{-2 \, d e + b} e x}{2 \, d e - b}\right) - \sqrt{-2 \, d e + b} \arctan\left(\frac{{\left(e^{2} x^{3} - {\left(d e - b\right)} x\right)} \sqrt{-2 \, d e + b}}{2 \, d^{2} e - b d}\right)}{2 \, d e - b}\right]"," ",0,"[1/2*log((e^2*x^4 + (4*d*e - b)*x^2 + d^2 + 2*(e*x^3 + d*x)*sqrt(2*d*e - b))/(e^2*x^4 + b*x^2 + d^2))/sqrt(2*d*e - b), -(sqrt(-2*d*e + b)*arctan(sqrt(-2*d*e + b)*e*x/(2*d*e - b)) - sqrt(-2*d*e + b)*arctan((e^2*x^3 - (d*e - b)*x)*sqrt(-2*d*e + b)/(2*d^2*e - b*d)))/(2*d*e - b)]","A",0
31,1,173,0,0.589846," ","integrate((-e*x^2+d)/(e^2*x^4+f*x^2+d^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{e^{2} x^{4} + {\left(4 \, d e - f\right)} x^{2} + d^{2} + 2 \, {\left(e x^{3} + d x\right)} \sqrt{2 \, d e - f}}{e^{2} x^{4} + f x^{2} + d^{2}}\right)}{2 \, \sqrt{2 \, d e - f}}, \frac{\sqrt{-2 \, d e + f} \arctan\left(-\frac{\sqrt{-2 \, d e + f} e x}{2 \, d e - f}\right) - \sqrt{-2 \, d e + f} \arctan\left(-\frac{{\left(e^{2} x^{3} - {\left(d e - f\right)} x\right)} \sqrt{-2 \, d e + f}}{2 \, d^{2} e - d f}\right)}{2 \, d e - f}\right]"," ",0,"[1/2*log((e^2*x^4 + (4*d*e - f)*x^2 + d^2 + 2*(e*x^3 + d*x)*sqrt(2*d*e - f))/(e^2*x^4 + f*x^2 + d^2))/sqrt(2*d*e - f), (sqrt(-2*d*e + f)*arctan(-sqrt(-2*d*e + f)*e*x/(2*d*e - f)) - sqrt(-2*d*e + f)*arctan(-(e^2*x^3 - (d*e - f)*x)*sqrt(-2*d*e + f)/(2*d^2*e - d*f)))/(2*d*e - f)]","A",0
32,1,168,0,0.671410," ","integrate((-e*x^2+d)/(e^2*x^4-b*x^2+d^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{e^{2} x^{4} + {\left(4 \, d e + b\right)} x^{2} + d^{2} + 2 \, {\left(e x^{3} + d x\right)} \sqrt{2 \, d e + b}}{e^{2} x^{4} - b x^{2} + d^{2}}\right)}{2 \, \sqrt{2 \, d e + b}}, -\frac{\sqrt{-2 \, d e - b} \arctan\left(\frac{\sqrt{-2 \, d e - b} e x}{2 \, d e + b}\right) - \sqrt{-2 \, d e - b} \arctan\left(\frac{{\left(e^{2} x^{3} - {\left(d e + b\right)} x\right)} \sqrt{-2 \, d e - b}}{2 \, d^{2} e + b d}\right)}{2 \, d e + b}\right]"," ",0,"[1/2*log((e^2*x^4 + (4*d*e + b)*x^2 + d^2 + 2*(e*x^3 + d*x)*sqrt(2*d*e + b))/(e^2*x^4 - b*x^2 + d^2))/sqrt(2*d*e + b), -(sqrt(-2*d*e - b)*arctan(sqrt(-2*d*e - b)*e*x/(2*d*e + b)) - sqrt(-2*d*e - b)*arctan((e^2*x^3 - (d*e + b)*x)*sqrt(-2*d*e - b)/(2*d^2*e + b*d)))/(2*d*e + b)]","A",0
33,1,168,0,0.822989," ","integrate((-e*x^2+d)/(e^2*x^4-f*x^2+d^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{e^{2} x^{4} + {\left(4 \, d e + f\right)} x^{2} + d^{2} + 2 \, {\left(e x^{3} + d x\right)} \sqrt{2 \, d e + f}}{e^{2} x^{4} - f x^{2} + d^{2}}\right)}{2 \, \sqrt{2 \, d e + f}}, -\frac{\sqrt{-2 \, d e - f} \arctan\left(\frac{\sqrt{-2 \, d e - f} e x}{2 \, d e + f}\right) - \sqrt{-2 \, d e - f} \arctan\left(\frac{{\left(e^{2} x^{3} - {\left(d e + f\right)} x\right)} \sqrt{-2 \, d e - f}}{2 \, d^{2} e + d f}\right)}{2 \, d e + f}\right]"," ",0,"[1/2*log((e^2*x^4 + (4*d*e + f)*x^2 + d^2 + 2*(e*x^3 + d*x)*sqrt(2*d*e + f))/(e^2*x^4 - f*x^2 + d^2))/sqrt(2*d*e + f), -(sqrt(-2*d*e - f)*arctan(sqrt(-2*d*e - f)*e*x/(2*d*e + f)) - sqrt(-2*d*e - f)*arctan((e^2*x^3 - (d*e + f)*x)*sqrt(-2*d*e - f)/(2*d^2*e + d*f)))/(2*d*e + f)]","A",0
34,1,244,0,0.824426," ","integrate((-e*x^2+d)/(c*d^2/e^2+b*x^2+c*x^4),x, algorithm=""fricas"")","\left[\frac{1}{2} \, e \sqrt{\frac{e}{2 \, c^{2} d - b c e}} \log\left(\frac{c e^{2} x^{4} + c d^{2} + {\left(4 \, c d e - b e^{2}\right)} x^{2} + 2 \, {\left({\left(2 \, c^{2} d e - b c e^{2}\right)} x^{3} + {\left(2 \, c^{2} d^{2} - b c d e\right)} x\right)} \sqrt{\frac{e}{2 \, c^{2} d - b c e}}}{c e^{2} x^{4} + b e^{2} x^{2} + c d^{2}}\right), -e \sqrt{-\frac{e}{2 \, c^{2} d - b c e}} \arctan\left(c x \sqrt{-\frac{e}{2 \, c^{2} d - b c e}}\right) + e \sqrt{-\frac{e}{2 \, c^{2} d - b c e}} \arctan\left(\frac{{\left(c e x^{3} - {\left(c d - b e\right)} x\right)} \sqrt{-\frac{e}{2 \, c^{2} d - b c e}}}{d}\right)\right]"," ",0,"[1/2*e*sqrt(e/(2*c^2*d - b*c*e))*log((c*e^2*x^4 + c*d^2 + (4*c*d*e - b*e^2)*x^2 + 2*((2*c^2*d*e - b*c*e^2)*x^3 + (2*c^2*d^2 - b*c*d*e)*x)*sqrt(e/(2*c^2*d - b*c*e)))/(c*e^2*x^4 + b*e^2*x^2 + c*d^2)), -e*sqrt(-e/(2*c^2*d - b*c*e))*arctan(c*x*sqrt(-e/(2*c^2*d - b*c*e))) + e*sqrt(-e/(2*c^2*d - b*c*e))*arctan((c*e*x^3 - (c*d - b*e)*x)*sqrt(-e/(2*c^2*d - b*c*e))/d)]","A",0
35,1,232,0,0.645047," ","integrate((e*x^2+d)/(c*d^2/e^2+b*x^2+c*x^4),x, algorithm=""fricas"")","\left[\frac{1}{2} \, e \sqrt{-\frac{e}{2 \, c^{2} d + b c e}} \log\left(\frac{c e^{2} x^{4} + c d^{2} - {\left(4 \, c d e + b e^{2}\right)} x^{2} + 2 \, {\left({\left(2 \, c^{2} d e + b c e^{2}\right)} x^{3} - {\left(2 \, c^{2} d^{2} + b c d e\right)} x\right)} \sqrt{-\frac{e}{2 \, c^{2} d + b c e}}}{c e^{2} x^{4} + b e^{2} x^{2} + c d^{2}}\right), e \sqrt{\frac{e}{2 \, c^{2} d + b c e}} \arctan\left(c x \sqrt{\frac{e}{2 \, c^{2} d + b c e}}\right) + e \sqrt{\frac{e}{2 \, c^{2} d + b c e}} \arctan\left(\frac{{\left(c e x^{3} + {\left(c d + b e\right)} x\right)} \sqrt{\frac{e}{2 \, c^{2} d + b c e}}}{d}\right)\right]"," ",0,"[1/2*e*sqrt(-e/(2*c^2*d + b*c*e))*log((c*e^2*x^4 + c*d^2 - (4*c*d*e + b*e^2)*x^2 + 2*((2*c^2*d*e + b*c*e^2)*x^3 - (2*c^2*d^2 + b*c*d*e)*x)*sqrt(-e/(2*c^2*d + b*c*e)))/(c*e^2*x^4 + b*e^2*x^2 + c*d^2)), e*sqrt(e/(2*c^2*d + b*c*e))*arctan(c*x*sqrt(e/(2*c^2*d + b*c*e))) + e*sqrt(e/(2*c^2*d + b*c*e))*arctan((c*e*x^3 + (c*d + b*e)*x)*sqrt(e/(2*c^2*d + b*c*e))/d)]","A",0
36,1,232,0,0.754144," ","integrate((e*x^2+d)/(b*x^2+c*(d^2/e^2+x^4)),x, algorithm=""fricas"")","\left[\frac{1}{2} \, e \sqrt{-\frac{e}{2 \, c^{2} d + b c e}} \log\left(\frac{c e^{2} x^{4} + c d^{2} - {\left(4 \, c d e + b e^{2}\right)} x^{2} + 2 \, {\left({\left(2 \, c^{2} d e + b c e^{2}\right)} x^{3} - {\left(2 \, c^{2} d^{2} + b c d e\right)} x\right)} \sqrt{-\frac{e}{2 \, c^{2} d + b c e}}}{c e^{2} x^{4} + b e^{2} x^{2} + c d^{2}}\right), e \sqrt{\frac{e}{2 \, c^{2} d + b c e}} \arctan\left(c x \sqrt{\frac{e}{2 \, c^{2} d + b c e}}\right) + e \sqrt{\frac{e}{2 \, c^{2} d + b c e}} \arctan\left(\frac{{\left(c e x^{3} + {\left(c d + b e\right)} x\right)} \sqrt{\frac{e}{2 \, c^{2} d + b c e}}}{d}\right)\right]"," ",0,"[1/2*e*sqrt(-e/(2*c^2*d + b*c*e))*log((c*e^2*x^4 + c*d^2 - (4*c*d*e + b*e^2)*x^2 + 2*((2*c^2*d*e + b*c*e^2)*x^3 - (2*c^2*d^2 + b*c*d*e)*x)*sqrt(-e/(2*c^2*d + b*c*e)))/(c*e^2*x^4 + b*e^2*x^2 + c*d^2)), e*sqrt(e/(2*c^2*d + b*c*e))*arctan(c*x*sqrt(e/(2*c^2*d + b*c*e))) + e*sqrt(e/(2*c^2*d + b*c*e))*arctan((c*e*x^3 + (c*d + b*e)*x)*sqrt(e/(2*c^2*d + b*c*e))/d)]","A",0
37,1,25,0,0.678319," ","integrate((-b*x^2+a)/(a^2+(2*a*b-1)*x^2+b^2*x^4),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(b x^{2} + a + x\right) - \frac{1}{2} \, \log\left(b x^{2} + a - x\right)"," ",0,"1/2*log(b*x^2 + a + x) - 1/2*log(b*x^2 + a - x)","A",0
38,1,164,0,0.849292," ","integrate((b*x^2+a)/(a^2+(2*a*b-1)*x^2+b^2*x^4),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-4 \, a b + 1} \log\left(\frac{b^{2} x^{4} - {\left(6 \, a b - 1\right)} x^{2} + a^{2} - 2 \, {\left(b x^{3} - a x\right)} \sqrt{-4 \, a b + 1}}{b^{2} x^{4} + {\left(2 \, a b - 1\right)} x^{2} + a^{2}}\right)}{2 \, {\left(4 \, a b - 1\right)}}, \frac{\sqrt{4 \, a b - 1} \arctan\left(\frac{b x}{\sqrt{4 \, a b - 1}}\right) + \sqrt{4 \, a b - 1} \arctan\left(\frac{{\left(b^{2} x^{3} + {\left(3 \, a b - 1\right)} x\right)} \sqrt{4 \, a b - 1}}{4 \, a^{2} b - a}\right)}{4 \, a b - 1}\right]"," ",0,"[-1/2*sqrt(-4*a*b + 1)*log((b^2*x^4 - (6*a*b - 1)*x^2 + a^2 - 2*(b*x^3 - a*x)*sqrt(-4*a*b + 1))/(b^2*x^4 + (2*a*b - 1)*x^2 + a^2))/(4*a*b - 1), (sqrt(4*a*b - 1)*arctan(b*x/sqrt(4*a*b - 1)) + sqrt(4*a*b - 1)*arctan((b^2*x^3 + (3*a*b - 1)*x)*sqrt(4*a*b - 1)/(4*a^2*b - a)))/(4*a*b - 1)]","A",0
39,1,110,0,0.829240," ","integrate((2*x^2+1)/(4*x^4+b*x^2+1),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b - 4} \log\left(\frac{4 \, x^{4} - {\left(b + 8\right)} x^{2} - 2 \, {\left(2 \, x^{3} - x\right)} \sqrt{-b - 4} + 1}{4 \, x^{4} + b x^{2} + 1}\right)}{2 \, {\left(b + 4\right)}}, \frac{\sqrt{b + 4} \arctan\left(\frac{4 \, x^{3} + {\left(b + 2\right)} x}{\sqrt{b + 4}}\right) + \sqrt{b + 4} \arctan\left(\frac{2 \, x}{\sqrt{b + 4}}\right)}{b + 4}\right]"," ",0,"[-1/2*sqrt(-b - 4)*log((4*x^4 - (b + 8)*x^2 - 2*(2*x^3 - x)*sqrt(-b - 4) + 1)/(4*x^4 + b*x^2 + 1))/(b + 4), (sqrt(b + 4)*arctan((4*x^3 + (b + 2)*x)/sqrt(b + 4)) + sqrt(b + 4)*arctan(2*x/sqrt(b + 4)))/(b + 4)]","A",0
40,1,120,0,0.804795," ","integrate((2*x^2+1)/(4*x^4-b*x^2+1),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{4 \, x^{4} + {\left(b - 8\right)} x^{2} - 2 \, {\left(2 \, x^{3} - x\right)} \sqrt{b - 4} + 1}{4 \, x^{4} - b x^{2} + 1}\right)}{2 \, \sqrt{b - 4}}, \frac{\sqrt{-b + 4} \arctan\left(\frac{{\left(4 \, x^{3} - {\left(b - 2\right)} x\right)} \sqrt{-b + 4}}{b - 4}\right) + \sqrt{-b + 4} \arctan\left(\frac{2 \, \sqrt{-b + 4} x}{b - 4}\right)}{b - 4}\right]"," ",0,"[1/2*log((4*x^4 + (b - 8)*x^2 - 2*(2*x^3 - x)*sqrt(b - 4) + 1)/(4*x^4 - b*x^2 + 1))/sqrt(b - 4), (sqrt(-b + 4)*arctan((4*x^3 - (b - 2)*x)*sqrt(-b + 4)/(b - 4)) + sqrt(-b + 4)*arctan(2*sqrt(-b + 4)*x/(b - 4)))/(b - 4)]","A",0
41,1,31,0,0.799956," ","integrate((2*x^2+1)/(4*x^4+6*x^2+1),x, algorithm=""fricas"")","\frac{1}{10} \, \sqrt{10} \arctan\left(\frac{2}{5} \, \sqrt{10} {\left(x^{3} + 2 \, x\right)}\right) + \frac{1}{10} \, \sqrt{10} \arctan\left(\frac{1}{5} \, \sqrt{10} x\right)"," ",0,"1/10*sqrt(10)*arctan(2/5*sqrt(10)*(x^3 + 2*x)) + 1/10*sqrt(10)*arctan(1/5*sqrt(10)*x)","A",0
42,1,19,0,0.708235," ","integrate((2*x^2+1)/(4*x^4+5*x^2+1),x, algorithm=""fricas"")","\frac{1}{3} \, \arctan\left(\frac{4}{3} \, x^{3} + \frac{7}{3} \, x\right) + \frac{1}{3} \, \arctan\left(\frac{2}{3} \, x\right)"," ",0,"1/3*arctan(4/3*x^3 + 7/3*x) + 1/3*arctan(2/3*x)","A",0
43,1,11,0,0.690559," ","integrate((2*x^2+1)/(4*x^4+4*x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} x\right)"," ",0,"1/2*sqrt(2)*arctan(sqrt(2)*x)","A",0
44,1,33,0,0.919245," ","integrate((2*x^2+1)/(4*x^4+3*x^2+1),x, algorithm=""fricas"")","\frac{1}{7} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(4 \, x^{3} + 5 \, x\right)}\right) + \frac{1}{7} \, \sqrt{7} \arctan\left(\frac{2}{7} \, \sqrt{7} x\right)"," ",0,"1/7*sqrt(7)*arctan(1/7*sqrt(7)*(4*x^3 + 5*x)) + 1/7*sqrt(7)*arctan(2/7*sqrt(7)*x)","A",0
45,1,29,0,0.914382," ","integrate((2*x^2+1)/(4*x^4+2*x^2+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{6} \arctan\left(\frac{2}{3} \, \sqrt{6} {\left(x^{3} + x\right)}\right) + \frac{1}{6} \, \sqrt{6} \arctan\left(\frac{1}{3} \, \sqrt{6} x\right)"," ",0,"1/6*sqrt(6)*arctan(2/3*sqrt(6)*(x^3 + x)) + 1/6*sqrt(6)*arctan(1/3*sqrt(6)*x)","A",0
46,1,33,0,1.771436," ","integrate((2*x^2+1)/(4*x^4+x^2+1),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} {\left(4 \, x^{3} + 3 \, x\right)}\right) + \frac{1}{5} \, \sqrt{5} \arctan\left(\frac{2}{5} \, \sqrt{5} x\right)"," ",0,"1/5*sqrt(5)*arctan(1/5*sqrt(5)*(4*x^3 + 3*x)) + 1/5*sqrt(5)*arctan(2/5*sqrt(5)*x)","A",0
47,1,15,0,0.714137," ","integrate((2*x^2+1)/(4*x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, \arctan\left(2 \, x^{3} + x\right) + \frac{1}{2} \, \arctan\left(x\right)"," ",0,"1/2*arctan(2*x^3 + x) + 1/2*arctan(x)","A",0
48,1,31,0,0.633992," ","integrate((2*x^2+1)/(4*x^4-x^2+1),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(4 \, x^{3} + x\right)}\right) + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{2}{3} \, \sqrt{3} x\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(4*x^3 + x)) + 1/3*sqrt(3)*arctan(2/3*sqrt(3)*x)","A",0
49,1,26,0,0.732397," ","integrate((2*x^2+1)/(4*x^4-2*x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(2 \, \sqrt{2} x^{3}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} x\right)"," ",0,"1/2*sqrt(2)*arctan(2*sqrt(2)*x^3) + 1/2*sqrt(2)*arctan(sqrt(2)*x)","A",0
50,1,15,0,0.709602," ","integrate((2*x^2+1)/(4*x^4-3*x^2+1),x, algorithm=""fricas"")","\arctan\left(4 \, x^{3} - x\right) + \arctan\left(2 \, x\right)"," ",0,"arctan(4*x^3 - x) + arctan(2*x)","A",0
51,1,12,0,0.580471," ","integrate((2*x^2+1)/(4*x^4-4*x^2+1),x, algorithm=""fricas"")","-\frac{x}{2 \, x^{2} - 1}"," ",0,"-x/(2*x^2 - 1)","A",0
52,1,25,0,0.789387," ","integrate((2*x^2+1)/(4*x^4-5*x^2+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(2 \, x^{2} + x - 1\right) + \frac{1}{2} \, \log\left(2 \, x^{2} - x - 1\right)"," ",0,"-1/2*log(2*x^2 + x - 1) + 1/2*log(2*x^2 - x - 1)","A",0
53,1,47,0,0.783918," ","integrate((2*x^2+1)/(4*x^4-6*x^2+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{4 \, x^{4} - 2 \, x^{2} - 2 \, \sqrt{2} {\left(2 \, x^{3} - x\right)} + 1}{4 \, x^{4} - 6 \, x^{2} + 1}\right)"," ",0,"1/4*sqrt(2)*log((4*x^4 - 2*x^2 - 2*sqrt(2)*(2*x^3 - x) + 1)/(4*x^4 - 6*x^2 + 1))","A",0
54,1,109,0,0.811270," ","integrate((-2*x^2+1)/(4*x^4+b*x^2+1),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b + 4} \log\left(\frac{4 \, x^{4} - {\left(b - 8\right)} x^{2} + 2 \, {\left(2 \, x^{3} + x\right)} \sqrt{-b + 4} + 1}{4 \, x^{4} + b x^{2} + 1}\right)}{2 \, {\left(b - 4\right)}}, \frac{\sqrt{b - 4} \arctan\left(\frac{4 \, x^{3} + {\left(b - 2\right)} x}{\sqrt{b - 4}}\right) - \sqrt{b - 4} \arctan\left(\frac{2 \, x}{\sqrt{b - 4}}\right)}{b - 4}\right]"," ",0,"[-1/2*sqrt(-b + 4)*log((4*x^4 - (b - 8)*x^2 + 2*(2*x^3 + x)*sqrt(-b + 4) + 1)/(4*x^4 + b*x^2 + 1))/(b - 4), (sqrt(b - 4)*arctan((4*x^3 + (b - 2)*x)/sqrt(b - 4)) - sqrt(b - 4)*arctan(2*x/sqrt(b - 4)))/(b - 4)]","A",0
55,1,28,0,0.627635," ","integrate((-2*x^2+1)/(4*x^4+6*x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(2 \, \sqrt{2} {\left(x^{3} + x\right)}\right) - \frac{1}{2} \, \sqrt{2} \arctan\left(\sqrt{2} x\right)"," ",0,"1/2*sqrt(2)*arctan(2*sqrt(2)*(x^3 + x)) - 1/2*sqrt(2)*arctan(sqrt(2)*x)","A",0
56,1,17,0,0.912853," ","integrate((-2*x^2+1)/(4*x^4+5*x^2+1),x, algorithm=""fricas"")","\arctan\left(4 \, x^{3} + 3 \, x\right) - \arctan\left(2 \, x\right)"," ",0,"arctan(4*x^3 + 3*x) - arctan(2*x)","A",0
57,1,11,0,0.713287," ","integrate((-2*x^2+1)/(4*x^4+4*x^2+1),x, algorithm=""fricas"")","\frac{x}{2 \, x^{2} + 1}"," ",0,"x/(2*x^2 + 1)","A",0
58,1,25,0,0.867759," ","integrate((-2*x^2+1)/(4*x^4+3*x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(2 \, x^{2} + x + 1\right) - \frac{1}{2} \, \log\left(2 \, x^{2} - x + 1\right)"," ",0,"1/2*log(2*x^2 + x + 1) - 1/2*log(2*x^2 - x + 1)","A",0
59,1,45,0,0.728177," ","integrate((-2*x^2+1)/(4*x^4+2*x^2+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{4 \, x^{4} + 6 \, x^{2} + 2 \, \sqrt{2} {\left(2 \, x^{3} + x\right)} + 1}{4 \, x^{4} + 2 \, x^{2} + 1}\right)"," ",0,"1/4*sqrt(2)*log((4*x^4 + 6*x^2 + 2*sqrt(2)*(2*x^3 + x) + 1)/(4*x^4 + 2*x^2 + 1))","A",0
60,1,43,0,0.809117," ","integrate((-2*x^2+1)/(4*x^4+x^2+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{4 \, x^{4} + 7 \, x^{2} + 2 \, \sqrt{3} {\left(2 \, x^{3} + x\right)} + 1}{4 \, x^{4} + x^{2} + 1}\right)"," ",0,"1/6*sqrt(3)*log((4*x^4 + 7*x^2 + 2*sqrt(3)*(2*x^3 + x) + 1)/(4*x^4 + x^2 + 1))","A",0
61,1,27,0,0.664099," ","integrate((-2*x^2+1)/(4*x^4+1),x, algorithm=""fricas"")","\frac{1}{4} \, \log\left(2 \, x^{2} + 2 \, x + 1\right) - \frac{1}{4} \, \log\left(2 \, x^{2} - 2 \, x + 1\right)"," ",0,"1/4*log(2*x^2 + 2*x + 1) - 1/4*log(2*x^2 - 2*x + 1)","A",0
62,1,45,0,0.989896," ","integrate((-2*x^2+1)/(4*x^4-x^2+1),x, algorithm=""fricas"")","\frac{1}{10} \, \sqrt{5} \log\left(\frac{4 \, x^{4} + 9 \, x^{2} + 2 \, \sqrt{5} {\left(2 \, x^{3} + x\right)} + 1}{4 \, x^{4} - x^{2} + 1}\right)"," ",0,"1/10*sqrt(5)*log((4*x^4 + 9*x^2 + 2*sqrt(5)*(2*x^3 + x) + 1)/(4*x^4 - x^2 + 1))","A",0
63,1,45,0,0.656432," ","integrate((-2*x^2+1)/(4*x^4-2*x^2+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{6} \log\left(\frac{4 \, x^{4} + 10 \, x^{2} + 2 \, \sqrt{6} {\left(2 \, x^{3} + x\right)} + 1}{4 \, x^{4} - 2 \, x^{2} + 1}\right)"," ",0,"1/12*sqrt(6)*log((4*x^4 + 10*x^2 + 2*sqrt(6)*(2*x^3 + x) + 1)/(4*x^4 - 2*x^2 + 1))","A",0
64,1,45,0,0.662471," ","integrate((-2*x^2+1)/(4*x^4-3*x^2+1),x, algorithm=""fricas"")","\frac{1}{14} \, \sqrt{7} \log\left(\frac{4 \, x^{4} + 11 \, x^{2} + 2 \, \sqrt{7} {\left(2 \, x^{3} + x\right)} + 1}{4 \, x^{4} - 3 \, x^{2} + 1}\right)"," ",0,"1/14*sqrt(7)*log((4*x^4 + 11*x^2 + 2*sqrt(7)*(2*x^3 + x) + 1)/(4*x^4 - 3*x^2 + 1))","A",0
65,1,29,0,0.606698," ","integrate((-2*x^2+1)/(4*x^4-4*x^2+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{2 \, x^{2} + 2 \, \sqrt{2} x + 1}{2 \, x^{2} - 1}\right)"," ",0,"1/4*sqrt(2)*log((2*x^2 + 2*sqrt(2)*x + 1)/(2*x^2 - 1))","B",0
66,1,27,0,0.471789," ","integrate((-2*x^2+1)/(4*x^4-5*x^2+1),x, algorithm=""fricas"")","\frac{1}{6} \, \log\left(2 \, x^{2} + 3 \, x + 1\right) - \frac{1}{6} \, \log\left(2 \, x^{2} - 3 \, x + 1\right)"," ",0,"1/6*log(2*x^2 + 3*x + 1) - 1/6*log(2*x^2 - 3*x + 1)","A",0
67,1,45,0,0.590130," ","integrate((-2*x^2+1)/(4*x^4-6*x^2+1),x, algorithm=""fricas"")","\frac{1}{20} \, \sqrt{10} \log\left(\frac{4 \, x^{4} + 14 \, x^{2} + 2 \, \sqrt{10} {\left(2 \, x^{3} + x\right)} + 1}{4 \, x^{4} - 6 \, x^{2} + 1}\right)"," ",0,"1/20*sqrt(10)*log((4*x^4 + 14*x^2 + 2*sqrt(10)*(2*x^3 + x) + 1)/(4*x^4 - 6*x^2 + 1))","A",0
68,1,101,0,1.663331," ","integrate((x^2+1)/(x^4+b*x^2+1),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b - 2} \log\left(\frac{x^{4} - {\left(b + 4\right)} x^{2} - 2 \, {\left(x^{3} - x\right)} \sqrt{-b - 2} + 1}{x^{4} + b x^{2} + 1}\right)}{2 \, {\left(b + 2\right)}}, \frac{\sqrt{b + 2} \arctan\left(\frac{x^{3} + {\left(b + 1\right)} x}{\sqrt{b + 2}}\right) + \sqrt{b + 2} \arctan\left(\frac{x}{\sqrt{b + 2}}\right)}{b + 2}\right]"," ",0,"[-1/2*sqrt(-b - 2)*log((x^4 - (b + 4)*x^2 - 2*(x^3 - x)*sqrt(-b - 2) + 1)/(x^4 + b*x^2 + 1))/(b + 2), (sqrt(b + 2)*arctan((x^3 + (b + 1)*x)/sqrt(b + 2)) + sqrt(b + 2)*arctan(x/sqrt(b + 2)))/(b + 2)]","A",0
69,1,31,0,0.812288," ","integrate((x^2+1)/(x^4+5*x^2+1),x, algorithm=""fricas"")","\frac{1}{7} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} {\left(x^{3} + 6 \, x\right)}\right) + \frac{1}{7} \, \sqrt{7} \arctan\left(\frac{1}{7} \, \sqrt{7} x\right)"," ",0,"1/7*sqrt(7)*arctan(1/7*sqrt(7)*(x^3 + 6*x)) + 1/7*sqrt(7)*arctan(1/7*sqrt(7)*x)","A",0
70,1,31,0,0.670005," ","integrate((x^2+1)/(x^4+4*x^2+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{6} \arctan\left(\frac{1}{6} \, \sqrt{6} {\left(x^{3} + 5 \, x\right)}\right) + \frac{1}{6} \, \sqrt{6} \arctan\left(\frac{1}{6} \, \sqrt{6} x\right)"," ",0,"1/6*sqrt(6)*arctan(1/6*sqrt(6)*(x^3 + 5*x)) + 1/6*sqrt(6)*arctan(1/6*sqrt(6)*x)","A",0
71,1,31,0,0.943148," ","integrate((x^2+1)/(x^4+3*x^2+1),x, algorithm=""fricas"")","\frac{1}{5} \, \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} {\left(x^{3} + 4 \, x\right)}\right) + \frac{1}{5} \, \sqrt{5} \arctan\left(\frac{1}{5} \, \sqrt{5} x\right)"," ",0,"1/5*sqrt(5)*arctan(1/5*sqrt(5)*(x^3 + 4*x)) + 1/5*sqrt(5)*arctan(1/5*sqrt(5)*x)","A",0
72,1,2,0,1.101075," ","integrate((x^2+1)/(x^4+2*x^2+1),x, algorithm=""fricas"")","\arctan\left(x\right)"," ",0,"arctan(x)","A",0
73,1,31,0,0.918210," ","integrate((x^2+1)/(x^4+x^2+1),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x^{3} + 2 \, x\right)}\right) + \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(x^3 + 2*x)) + 1/3*sqrt(3)*arctan(1/3*sqrt(3)*x)","A",0
74,1,29,0,1.221297," ","integrate((x^2+1)/(x^4+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{3} + x\right)}\right) + \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(x^3 + x)) + 1/2*sqrt(2)*arctan(1/2*sqrt(2)*x)","A",0
75,1,7,0,1.153875," ","integrate((x^2+1)/(x^4-x^2+1),x, algorithm=""fricas"")","\arctan\left(x^{3}\right) + \arctan\left(x\right)"," ",0,"arctan(x^3) + arctan(x)","A",0
76,1,10,0,1.211559," ","integrate((x^2+1)/(x^4-2*x^2+1),x, algorithm=""fricas"")","-\frac{x}{x^{2} - 1}"," ",0,"-x/(x^2 - 1)","A",0
77,1,21,0,1.203874," ","integrate((x^2+1)/(x^4-3*x^2+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(x^{2} + x - 1\right) + \frac{1}{2} \, \log\left(x^{2} - x - 1\right)"," ",0,"-1/2*log(x^2 + x - 1) + 1/2*log(x^2 - x - 1)","A",0
78,1,36,0,1.148839," ","integrate((x^2+1)/(x^4-4*x^2+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{x^{4} - 2 \, \sqrt{2} {\left(x^{3} - x\right)} + 1}{x^{4} - 4 \, x^{2} + 1}\right)"," ",0,"1/4*sqrt(2)*log((x^4 - 2*sqrt(2)*(x^3 - x) + 1)/(x^4 - 4*x^2 + 1))","A",0
79,1,39,0,1.007210," ","integrate((x^2+1)/(x^4-5*x^2+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{x^{4} + x^{2} - 2 \, \sqrt{3} {\left(x^{3} - x\right)} + 1}{x^{4} - 5 \, x^{2} + 1}\right)"," ",0,"1/6*sqrt(3)*log((x^4 + x^2 - 2*sqrt(3)*(x^3 - x) + 1)/(x^4 - 5*x^2 + 1))","A",0
80,1,100,0,1.207787," ","integrate((-x^2+1)/(x^4+b*x^2+1),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b + 2} \log\left(\frac{x^{4} - {\left(b - 4\right)} x^{2} + 2 \, {\left(x^{3} + x\right)} \sqrt{-b + 2} + 1}{x^{4} + b x^{2} + 1}\right)}{2 \, {\left(b - 2\right)}}, \frac{\sqrt{b - 2} \arctan\left(\frac{x^{3} + {\left(b - 1\right)} x}{\sqrt{b - 2}}\right) - \sqrt{b - 2} \arctan\left(\frac{x}{\sqrt{b - 2}}\right)}{b - 2}\right]"," ",0,"[-1/2*sqrt(-b + 2)*log((x^4 - (b - 4)*x^2 + 2*(x^3 + x)*sqrt(-b + 2) + 1)/(x^4 + b*x^2 + 1))/(b - 2), (sqrt(b - 2)*arctan((x^3 + (b - 1)*x)/sqrt(b - 2)) - sqrt(b - 2)*arctan(x/sqrt(b - 2)))/(b - 2)]","A",0
81,1,31,0,0.795977," ","integrate((-x^2+1)/(x^4+5*x^2+1),x, algorithm=""fricas"")","\frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(x^{3} + 4 \, x\right)}\right) - \frac{1}{3} \, \sqrt{3} \arctan\left(\frac{1}{3} \, \sqrt{3} x\right)"," ",0,"1/3*sqrt(3)*arctan(1/3*sqrt(3)*(x^3 + 4*x)) - 1/3*sqrt(3)*arctan(1/3*sqrt(3)*x)","A",0
82,1,31,0,0.933448," ","integrate((-x^2+1)/(x^4+4*x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} {\left(x^{3} + 3 \, x\right)}\right) - \frac{1}{2} \, \sqrt{2} \arctan\left(\frac{1}{2} \, \sqrt{2} x\right)"," ",0,"1/2*sqrt(2)*arctan(1/2*sqrt(2)*(x^3 + 3*x)) - 1/2*sqrt(2)*arctan(1/2*sqrt(2)*x)","A",0
83,1,13,0,0.893843," ","integrate((-x^2+1)/(x^4+3*x^2+1),x, algorithm=""fricas"")","\arctan\left(x^{3} + 2 \, x\right) - \arctan\left(x\right)"," ",0,"arctan(x^3 + 2*x) - arctan(x)","A",0
84,1,9,0,0.850129," ","integrate((-x^2+1)/(x^4+2*x^2+1),x, algorithm=""fricas"")","\frac{x}{x^{2} + 1}"," ",0,"x/(x^2 + 1)","A",0
85,1,21,0,1.557932," ","integrate((-x^2+1)/(x^4+x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x^{2} + x + 1\right) - \frac{1}{2} \, \log\left(x^{2} - x + 1\right)"," ",0,"1/2*log(x^2 + x + 1) - 1/2*log(x^2 - x + 1)","A",0
86,1,34,0,0.998501," ","integrate((-x^2+1)/(x^4+1),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(\frac{x^{4} + 4 \, x^{2} + 2 \, \sqrt{2} {\left(x^{3} + x\right)} + 1}{x^{4} + 1}\right)"," ",0,"1/4*sqrt(2)*log((x^4 + 4*x^2 + 2*sqrt(2)*(x^3 + x) + 1)/(x^4 + 1))","A",0
87,1,39,0,0.777680," ","integrate((-x^2+1)/(x^4-x^2+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} \log\left(\frac{x^{4} + 5 \, x^{2} + 2 \, \sqrt{3} {\left(x^{3} + x\right)} + 1}{x^{4} - x^{2} + 1}\right)"," ",0,"1/6*sqrt(3)*log((x^4 + 5*x^2 + 2*sqrt(3)*(x^3 + x) + 1)/(x^4 - x^2 + 1))","A",0
88,1,13,0,1.072730," ","integrate((-x^2+1)/(x^4-2*x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(x + 1\right) - \frac{1}{2} \, \log\left(x - 1\right)"," ",0,"1/2*log(x + 1) - 1/2*log(x - 1)","B",0
89,1,39,0,1.112560," ","integrate((-x^2+1)/(x^4-3*x^2+1),x, algorithm=""fricas"")","\frac{1}{10} \, \sqrt{5} \log\left(\frac{x^{4} + 7 \, x^{2} + 2 \, \sqrt{5} {\left(x^{3} + x\right)} + 1}{x^{4} - 3 \, x^{2} + 1}\right)"," ",0,"1/10*sqrt(5)*log((x^4 + 7*x^2 + 2*sqrt(5)*(x^3 + x) + 1)/(x^4 - 3*x^2 + 1))","A",0
90,1,39,0,1.262952," ","integrate((-x^2+1)/(x^4-4*x^2+1),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{6} \log\left(\frac{x^{4} + 8 \, x^{2} + 2 \, \sqrt{6} {\left(x^{3} + x\right)} + 1}{x^{4} - 4 \, x^{2} + 1}\right)"," ",0,"1/12*sqrt(6)*log((x^4 + 8*x^2 + 2*sqrt(6)*(x^3 + x) + 1)/(x^4 - 4*x^2 + 1))","A",0
91,1,39,0,0.779816," ","integrate((-x^2+1)/(x^4-5*x^2+1),x, algorithm=""fricas"")","\frac{1}{14} \, \sqrt{7} \log\left(\frac{x^{4} + 9 \, x^{2} + 2 \, \sqrt{7} {\left(x^{3} + x\right)} + 1}{x^{4} - 5 \, x^{2} + 1}\right)"," ",0,"1/14*sqrt(7)*log((x^4 + 9*x^2 + 2*sqrt(7)*(x^3 + x) + 1)/(x^4 - 5*x^2 + 1))","A",0
92,1,33,0,1.211581," ","integrate((-3*x^2-1)/(9*x^4+2*x^2+1),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{4} \, \sqrt{2} {\left(9 \, x^{3} + 5 \, x\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{3}{4} \, \sqrt{2} x\right)"," ",0,"-1/4*sqrt(2)*arctan(1/4*sqrt(2)*(9*x^3 + 5*x)) - 1/4*sqrt(2)*arctan(3/4*sqrt(2)*x)","A",0
93,1,33,0,0.924094," ","integrate((3*x^2+1)/(-9*x^4-2*x^2-1),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{2} \arctan\left(\frac{1}{4} \, \sqrt{2} {\left(9 \, x^{3} + 5 \, x\right)}\right) - \frac{1}{4} \, \sqrt{2} \arctan\left(\frac{3}{4} \, \sqrt{2} x\right)"," ",0,"-1/4*sqrt(2)*arctan(1/4*sqrt(2)*(9*x^3 + 5*x)) - 1/4*sqrt(2)*arctan(3/4*sqrt(2)*x)","A",0
94,1,34,0,1.031079," ","integrate((2*x^2+3)/(x^4-2*x^2+1),x, algorithm=""fricas"")","\frac{{\left(x^{2} - 1\right)} \log\left(x + 1\right) - {\left(x^{2} - 1\right)} \log\left(x - 1\right) - 10 \, x}{4 \, {\left(x^{2} - 1\right)}}"," ",0,"1/4*((x^2 - 1)*log(x + 1) - (x^2 - 1)*log(x - 1) - 10*x)/(x^2 - 1)","B",0
95,1,49,0,1.005212," ","integrate((3*x^2+2)/(3*x^4-8*x^2+5),x, algorithm=""fricas"")","\frac{7}{20} \, \sqrt{5} \sqrt{3} \log\left(-\frac{2 \, \sqrt{5} \sqrt{3} x - 3 \, x^{2} - 5}{3 \, x^{2} - 5}\right) + \frac{5}{4} \, \log\left(x + 1\right) - \frac{5}{4} \, \log\left(x - 1\right)"," ",0,"7/20*sqrt(5)*sqrt(3)*log(-(2*sqrt(5)*sqrt(3)*x - 3*x^2 - 5)/(3*x^2 - 5)) + 5/4*log(x + 1) - 5/4*log(x - 1)","B",0
96,1,55,0,0.996857," ","integrate((e*x^2+d)/(3*x^4-8*x^2+5),x, algorithm=""fricas"")","\frac{1}{60} \, \sqrt{15} {\left(3 \, d + 5 \, e\right)} \log\left(\frac{3 \, x^{2} - 2 \, \sqrt{15} x + 5}{3 \, x^{2} - 5}\right) + \frac{1}{4} \, {\left(d + e\right)} \log\left(x + 1\right) - \frac{1}{4} \, {\left(d + e\right)} \log\left(x - 1\right)"," ",0,"1/60*sqrt(15)*(3*d + 5*e)*log((3*x^2 - 2*sqrt(15)*x + 5)/(3*x^2 - 5)) + 1/4*(d + e)*log(x + 1) - 1/4*(d + e)*log(x - 1)","B",0
97,1,137,0,1.049458," ","integrate((x^2+3)/(x^4+3*x^2+1),x, algorithm=""fricas"")","\frac{2}{5} \, \sqrt{5} \sqrt{-4 \, \sqrt{5} + 9} \arctan\left(\frac{1}{4} \, \sqrt{2 \, x^{2} + \sqrt{5} + 3} {\left(\sqrt{5} \sqrt{2} + 3 \, \sqrt{2}\right)} \sqrt{-4 \, \sqrt{5} + 9} - \frac{1}{2} \, {\left(\sqrt{5} x + 3 \, x\right)} \sqrt{-4 \, \sqrt{5} + 9}\right) + \frac{2}{5} \, \sqrt{5} \sqrt{4 \, \sqrt{5} + 9} \arctan\left(\frac{1}{4} \, {\left(\sqrt{2 \, x^{2} - \sqrt{5} + 3} {\left(\sqrt{5} \sqrt{2} - 3 \, \sqrt{2}\right)} - 2 \, \sqrt{5} x + 6 \, x\right)} \sqrt{4 \, \sqrt{5} + 9}\right)"," ",0,"2/5*sqrt(5)*sqrt(-4*sqrt(5) + 9)*arctan(1/4*sqrt(2*x^2 + sqrt(5) + 3)*(sqrt(5)*sqrt(2) + 3*sqrt(2))*sqrt(-4*sqrt(5) + 9) - 1/2*(sqrt(5)*x + 3*x)*sqrt(-4*sqrt(5) + 9)) + 2/5*sqrt(5)*sqrt(4*sqrt(5) + 9)*arctan(1/4*(sqrt(2*x^2 - sqrt(5) + 3)*(sqrt(5)*sqrt(2) - 3*sqrt(2)) - 2*sqrt(5)*x + 6*x)*sqrt(4*sqrt(5) + 9))","B",0
98,1,69,0,1.039254," ","integrate((b*x^2+a)/(x^4+x^2+1),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{3} {\left(a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) + \frac{1}{6} \, \sqrt{3} {\left(a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) + \frac{1}{4} \, {\left(a - b\right)} \log\left(x^{2} + x + 1\right) - \frac{1}{4} \, {\left(a - b\right)} \log\left(x^{2} - x + 1\right)"," ",0,"1/6*sqrt(3)*(a + b)*arctan(1/3*sqrt(3)*(2*x + 1)) + 1/6*sqrt(3)*(a + b)*arctan(1/3*sqrt(3)*(2*x - 1)) + 1/4*(a - b)*log(x^2 + x + 1) - 1/4*(a - b)*log(x^2 - x + 1)","A",0
99,1,185,0,0.803243," ","integrate((b*x^2+a)/(x^4+x^2+1)^2,x, algorithm=""fricas"")","-\frac{12 \, {\left(a - 2 \, b\right)} x^{3} - 2 \, \sqrt{3} {\left({\left(4 \, a + b\right)} x^{4} + {\left(4 \, a + b\right)} x^{2} + 4 \, a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x + 1\right)}\right) - 2 \, \sqrt{3} {\left({\left(4 \, a + b\right)} x^{4} + {\left(4 \, a + b\right)} x^{2} + 4 \, a + b\right)} \arctan\left(\frac{1}{3} \, \sqrt{3} {\left(2 \, x - 1\right)}\right) - 12 \, {\left(a + b\right)} x - 9 \, {\left({\left(2 \, a - b\right)} x^{4} + {\left(2 \, a - b\right)} x^{2} + 2 \, a - b\right)} \log\left(x^{2} + x + 1\right) + 9 \, {\left({\left(2 \, a - b\right)} x^{4} + {\left(2 \, a - b\right)} x^{2} + 2 \, a - b\right)} \log\left(x^{2} - x + 1\right)}{72 \, {\left(x^{4} + x^{2} + 1\right)}}"," ",0,"-1/72*(12*(a - 2*b)*x^3 - 2*sqrt(3)*((4*a + b)*x^4 + (4*a + b)*x^2 + 4*a + b)*arctan(1/3*sqrt(3)*(2*x + 1)) - 2*sqrt(3)*((4*a + b)*x^4 + (4*a + b)*x^2 + 4*a + b)*arctan(1/3*sqrt(3)*(2*x - 1)) - 12*(a + b)*x - 9*((2*a - b)*x^4 + (2*a - b)*x^2 + 2*a - b)*log(x^2 + x + 1) + 9*((2*a - b)*x^4 + (2*a - b)*x^2 + 2*a - b)*log(x^2 - x + 1))/(x^4 + x^2 + 1)","A",0
100,1,3406,0,1.284841," ","integrate((b*x^2+a)/(x^4+x^2+2),x, algorithm=""fricas"")","\frac{28 \, \sqrt{2} \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{1}{4}} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} \arctan\left(-\frac{7 \, \sqrt{\frac{1}{2}} \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{3}{4}} {\left(\sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} a - 2 \, \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} {\left(a^{2} b - a b^{2} + 2 \, b^{3}\right)}\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} \sqrt{\frac{2 \, {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)} x^{2} + \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} b x - \sqrt{7} {\left(a^{3} - a^{2} b + 2 \, a b^{2}\right)} x\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} + 2 \, \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - a b + 2 \, b^{2}\right)}}{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}}} + 8 \, \sqrt{7} \sqrt{2} {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)}^{\frac{3}{2}} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} - 7 \, \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{3}{4}} {\left(\sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} a x - 2 \, \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} {\left(a^{2} b - a b^{2} + 2 \, b^{3}\right)} x\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} - 4 \, \sqrt{7} {\left(a^{6} - 3 \, a^{5} b + 9 \, a^{4} b^{2} - 13 \, a^{3} b^{3} + 18 \, a^{2} b^{4} - 12 \, a b^{5} + 8 \, b^{6}\right)} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}}{28 \, {\left(a^{8} - 3 \, a^{7} b + 7 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} - 28 \, a^{2} b^{6} + 24 \, a b^{7} - 16 \, b^{8}\right)}}\right) + 28 \, \sqrt{2} \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{1}{4}} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} \arctan\left(-\frac{7 \, \sqrt{\frac{1}{2}} \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{3}{4}} {\left(\sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} a - 2 \, \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} {\left(a^{2} b - a b^{2} + 2 \, b^{3}\right)}\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} \sqrt{\frac{2 \, {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)} x^{2} - \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} b x - \sqrt{7} {\left(a^{3} - a^{2} b + 2 \, a b^{2}\right)} x\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} + 2 \, \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - a b + 2 \, b^{2}\right)}}{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}}} - 8 \, \sqrt{7} \sqrt{2} {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)}^{\frac{3}{2}} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} - 7 \, \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{3}{4}} {\left(\sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} a x - 2 \, \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}} {\left(a^{2} b - a b^{2} + 2 \, b^{3}\right)} x\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} + 4 \, \sqrt{7} {\left(a^{6} - 3 \, a^{5} b + 9 \, a^{4} b^{2} - 13 \, a^{3} b^{3} + 18 \, a^{2} b^{4} - 12 \, a b^{5} + 8 \, b^{6}\right)} \sqrt{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}}{28 \, {\left(a^{8} - 3 \, a^{7} b + 7 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 14 \, a^{3} b^{5} - 28 \, a^{2} b^{6} + 24 \, a b^{7} - 16 \, b^{8}\right)}}\right) - \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)} + 4 \, \sqrt{7} {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)}\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} \log\left(8 \, {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)} x^{2} + 4 \, \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} b x - \sqrt{7} {\left(a^{3} - a^{2} b + 2 \, a b^{2}\right)} x\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} + 8 \, \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - a b + 2 \, b^{2}\right)}\right) + \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)} + 4 \, \sqrt{7} {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)}\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} \log\left(8 \, {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)} x^{2} - 4 \, \sqrt{\frac{1}{7}} {\left(8 \, a^{4} - 16 \, a^{3} b + 40 \, a^{2} b^{2} - 32 \, a b^{3} + 32 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} b x - \sqrt{7} {\left(a^{3} - a^{2} b + 2 \, a b^{2}\right)} x\right)} \sqrt{\frac{4 \, a^{4} - 8 \, a^{3} b + 20 \, a^{2} b^{2} - 16 \, a b^{3} + 16 \, b^{4} - \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - 8 \, a b + 2 \, b^{2}\right)}}{a^{4} - 4 \, a^{2} b^{2} + 4 \, b^{4}}} + 8 \, \sqrt{2} \sqrt{a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}} {\left(a^{2} - a b + 2 \, b^{2}\right)}\right)}{112 \, {\left(a^{4} - 2 \, a^{3} b + 5 \, a^{2} b^{2} - 4 \, a b^{3} + 4 \, b^{4}\right)}}"," ",0,"1/112*(28*sqrt(2)*sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(1/4)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4))*arctan(-1/28*(7*sqrt(1/2)*sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(3/4)*(sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*a - 2*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*(a^2*b - a*b^2 + 2*b^3))*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4))*sqrt((2*(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*x^2 + sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*b*x - sqrt(7)*(a^3 - a^2*b + 2*a*b^2)*x)*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4)) + 2*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - a*b + 2*b^2))/(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)) + 8*sqrt(7)*sqrt(2)*(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)^(3/2)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4) - 7*sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(3/4)*(sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*a*x - 2*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*(a^2*b - a*b^2 + 2*b^3)*x)*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4)) - 4*sqrt(7)*(a^6 - 3*a^5*b + 9*a^4*b^2 - 13*a^3*b^3 + 18*a^2*b^4 - 12*a*b^5 + 8*b^6)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4))/(a^8 - 3*a^7*b + 7*a^6*b^2 - 7*a^5*b^3 + 14*a^3*b^5 - 28*a^2*b^6 + 24*a*b^7 - 16*b^8)) + 28*sqrt(2)*sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(1/4)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4))*arctan(-1/28*(7*sqrt(1/2)*sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(3/4)*(sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*a - 2*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*(a^2*b - a*b^2 + 2*b^3))*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4))*sqrt((2*(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*x^2 - sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*b*x - sqrt(7)*(a^3 - a^2*b + 2*a*b^2)*x)*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4)) + 2*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - a*b + 2*b^2))/(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)) - 8*sqrt(7)*sqrt(2)*(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)^(3/2)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4) - 7*sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(3/4)*(sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*a*x - 2*sqrt(a^4 - 4*a^2*b^2 + 4*b^4)*(a^2*b - a*b^2 + 2*b^3)*x)*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4)) + 4*sqrt(7)*(a^6 - 3*a^5*b + 9*a^4*b^2 - 13*a^3*b^3 + 18*a^2*b^4 - 12*a*b^5 + 8*b^6)*sqrt(a^4 - 4*a^2*b^2 + 4*b^4))/(a^8 - 3*a^7*b + 7*a^6*b^2 - 7*a^5*b^3 + 14*a^3*b^5 - 28*a^2*b^6 + 24*a*b^7 - 16*b^8)) - sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2) + 4*sqrt(7)*(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4))*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4))*log(8*(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*x^2 + 4*sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*b*x - sqrt(7)*(a^3 - a^2*b + 2*a*b^2)*x)*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4)) + 8*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - a*b + 2*b^2)) + sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2) + 4*sqrt(7)*(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4))*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4))*log(8*(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*x^2 - 4*sqrt(1/7)*(8*a^4 - 16*a^3*b + 40*a^2*b^2 - 32*a*b^3 + 32*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*b*x - sqrt(7)*(a^3 - a^2*b + 2*a*b^2)*x)*sqrt((4*a^4 - 8*a^3*b + 20*a^2*b^2 - 16*a*b^3 + 16*b^4 - sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - 8*a*b + 2*b^2))/(a^4 - 4*a^2*b^2 + 4*b^4)) + 8*sqrt(2)*sqrt(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)*(a^2 - a*b + 2*b^2)))/(a^4 - 2*a^3*b + 5*a^2*b^2 - 4*a*b^3 + 4*b^4)","B",0
101,1,4346,0,1.148897," ","integrate((b*x^2+a)/(x^4+x^2+2)^2,x, algorithm=""fricas"")","-\frac{196 \cdot 2^{\frac{3}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{3}{4}} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(x^{4} + x^{2} + 2\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} \arctan\left(\frac{2^{\frac{3}{4}} \sqrt{\frac{2}{7}} \sqrt{\frac{1}{14}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{3}{4}} {\left(\sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(11 \, a - 2 \, b\right)} + 2 \, \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(67 \, a^{3} - 321 \, a^{2} b + 234 \, a b^{2} - 88 \, b^{3}\right)}\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} \sqrt{\frac{14 \, {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{2} + 2^{\frac{1}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(a - 4 \, b\right)} x + \sqrt{7} {\left(737 \, a^{3} - 717 \, a^{2} b + 348 \, a b^{2} - 44 \, b^{3}\right)} x\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} + 14 \, \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(67 \, a^{2} - 53 \, a b + 22 \, b^{2}\right)}}{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}}} - 2^{\frac{3}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{3}{4}} {\left(\sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(11 \, a - 2 \, b\right)} x + 2 \, \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(67 \, a^{3} - 321 \, a^{2} b + 234 \, a b^{2} - 88 \, b^{3}\right)} x\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} - 4 \, \sqrt{7} \sqrt{2} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{3}{2}} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} + 2 \, \sqrt{7} {\left(300763 \, a^{6} - 713751 \, a^{5} b + 860883 \, a^{4} b^{2} - 617609 \, a^{3} b^{3} + 282678 \, a^{2} b^{4} - 76956 \, a b^{5} + 10648 \, b^{6}\right)} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}}{14 \, {\left(5112971 \, a^{8} - 13336819 \, a^{7} b + 16286963 \, a^{6} b^{2} - 11087881 \, a^{5} b^{3} + 3832430 \, a^{4} b^{4} + 31472 \, a^{3} b^{5} - 641872 \, a^{2} b^{6} + 265232 \, a b^{7} - 42592 \, b^{8}\right)}}\right) + 196 \cdot 2^{\frac{3}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{3}{4}} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(x^{4} + x^{2} + 2\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} \arctan\left(\frac{2^{\frac{3}{4}} \sqrt{\frac{2}{7}} \sqrt{\frac{1}{14}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{3}{4}} {\left(\sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(11 \, a - 2 \, b\right)} + 2 \, \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(67 \, a^{3} - 321 \, a^{2} b + 234 \, a b^{2} - 88 \, b^{3}\right)}\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} \sqrt{\frac{14 \, {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{2} - 2^{\frac{1}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(a - 4 \, b\right)} x + \sqrt{7} {\left(737 \, a^{3} - 717 \, a^{2} b + 348 \, a b^{2} - 44 \, b^{3}\right)} x\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} + 14 \, \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(67 \, a^{2} - 53 \, a b + 22 \, b^{2}\right)}}{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}}} - 2^{\frac{3}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{3}{4}} {\left(\sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(11 \, a - 2 \, b\right)} x + 2 \, \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} {\left(67 \, a^{3} - 321 \, a^{2} b + 234 \, a b^{2} - 88 \, b^{3}\right)} x\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} + 4 \, \sqrt{7} \sqrt{2} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{3}{2}} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}} - 2 \, \sqrt{7} {\left(300763 \, a^{6} - 713751 \, a^{5} b + 860883 \, a^{4} b^{2} - 617609 \, a^{3} b^{3} + 282678 \, a^{2} b^{4} - 76956 \, a b^{5} + 10648 \, b^{6}\right)} \sqrt{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}}{14 \, {\left(5112971 \, a^{8} - 13336819 \, a^{7} b + 16286963 \, a^{6} b^{2} - 11087881 \, a^{5} b^{3} + 3832430 \, a^{4} b^{4} + 31472 \, a^{3} b^{5} - 641872 \, a^{2} b^{6} + 265232 \, a b^{7} - 42592 \, b^{8}\right)}}\right) + 784 \, {\left(4489 \, a^{5} - 25058 \, a^{4} b + 34165 \, a^{3} b^{2} - 25360 \, a^{2} b^{3} + 9812 \, a b^{4} - 1936 \, b^{5}\right)} x^{3} - 2^{\frac{1}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} {\left({\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)} x^{4} + {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)} x^{2} + 422 \, a^{2} - 856 \, a b + 200 \, b^{2}\right)} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} + 8 \, \sqrt{7} {\left({\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{4} + 8978 \, a^{4} - 14204 \, a^{3} b + 11514 \, a^{2} b^{2} - 4664 \, a b^{3} + 968 \, b^{4} + {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{2}\right)}\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} \log\left(32 \, {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{2} + \frac{16}{7} \cdot 2^{\frac{1}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(a - 4 \, b\right)} x + \sqrt{7} {\left(737 \, a^{3} - 717 \, a^{2} b + 348 \, a b^{2} - 44 \, b^{3}\right)} x\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} + 32 \, \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(67 \, a^{2} - 53 \, a b + 22 \, b^{2}\right)}\right) + 2^{\frac{1}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} {\left({\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)} x^{4} + {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)} x^{2} + 422 \, a^{2} - 856 \, a b + 200 \, b^{2}\right)} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} + 8 \, \sqrt{7} {\left({\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{4} + 8978 \, a^{4} - 14204 \, a^{3} b + 11514 \, a^{2} b^{2} - 4664 \, a b^{3} + 968 \, b^{4} + {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{2}\right)}\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} \log\left(32 \, {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{2} - \frac{16}{7} \cdot 2^{\frac{1}{4}} \sqrt{\frac{2}{7}} {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)}^{\frac{1}{4}} {\left(\sqrt{7} \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(a - 4 \, b\right)} x + \sqrt{7} {\left(737 \, a^{3} - 717 \, a^{2} b + 348 \, a b^{2} - 44 \, b^{3}\right)} x\right)} \sqrt{\frac{35912 \, a^{4} - 56816 \, a^{3} b + 46056 \, a^{2} b^{2} - 18656 \, a b^{3} + 3872 \, b^{4} - \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(211 \, a^{2} - 428 \, a b + 100 \, b^{2}\right)}}{289 \, a^{4} - 136 \, a^{3} b - 120 \, a^{2} b^{2} + 32 \, a b^{3} + 16 \, b^{4}}} + 32 \, \sqrt{2} \sqrt{4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}} {\left(67 \, a^{2} - 53 \, a b + 22 \, b^{2}\right)}\right) - 784 \, {\left(13467 \, a^{5} - 12328 \, a^{4} b + 3067 \, a^{3} b^{2} + 4518 \, a^{2} b^{3} - 3212 \, a b^{4} + 968 \, b^{5}\right)} x}{21952 \, {\left({\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{4} + 8978 \, a^{4} - 14204 \, a^{3} b + 11514 \, a^{2} b^{2} - 4664 \, a b^{3} + 968 \, b^{4} + {\left(4489 \, a^{4} - 7102 \, a^{3} b + 5757 \, a^{2} b^{2} - 2332 \, a b^{3} + 484 \, b^{4}\right)} x^{2}\right)}}"," ",0,"-1/21952*(196*2^(3/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(3/4)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(x^4 + x^2 + 2)*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4))*arctan(1/14*(2^(3/4)*sqrt(2/7)*sqrt(1/14)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(3/4)*(sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(11*a - 2*b) + 2*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(67*a^3 - 321*a^2*b + 234*a*b^2 - 88*b^3))*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4))*sqrt((14*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^2 + 2^(1/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(a - 4*b)*x + sqrt(7)*(737*a^3 - 717*a^2*b + 348*a*b^2 - 44*b^3)*x)*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)) + 14*sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(67*a^2 - 53*a*b + 22*b^2))/(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)) - 2^(3/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(3/4)*(sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(11*a - 2*b)*x + 2*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(67*a^3 - 321*a^2*b + 234*a*b^2 - 88*b^3)*x)*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)) - 4*sqrt(7)*sqrt(2)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(3/2)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4) + 2*sqrt(7)*(300763*a^6 - 713751*a^5*b + 860883*a^4*b^2 - 617609*a^3*b^3 + 282678*a^2*b^4 - 76956*a*b^5 + 10648*b^6)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4))/(5112971*a^8 - 13336819*a^7*b + 16286963*a^6*b^2 - 11087881*a^5*b^3 + 3832430*a^4*b^4 + 31472*a^3*b^5 - 641872*a^2*b^6 + 265232*a*b^7 - 42592*b^8)) + 196*2^(3/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(3/4)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(x^4 + x^2 + 2)*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4))*arctan(1/14*(2^(3/4)*sqrt(2/7)*sqrt(1/14)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(3/4)*(sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(11*a - 2*b) + 2*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(67*a^3 - 321*a^2*b + 234*a*b^2 - 88*b^3))*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4))*sqrt((14*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^2 - 2^(1/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(a - 4*b)*x + sqrt(7)*(737*a^3 - 717*a^2*b + 348*a*b^2 - 44*b^3)*x)*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)) + 14*sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(67*a^2 - 53*a*b + 22*b^2))/(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)) - 2^(3/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(3/4)*(sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(11*a - 2*b)*x + 2*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)*(67*a^3 - 321*a^2*b + 234*a*b^2 - 88*b^3)*x)*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)) + 4*sqrt(7)*sqrt(2)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(3/2)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4) - 2*sqrt(7)*(300763*a^6 - 713751*a^5*b + 860883*a^4*b^2 - 617609*a^3*b^3 + 282678*a^2*b^4 - 76956*a*b^5 + 10648*b^6)*sqrt(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4))/(5112971*a^8 - 13336819*a^7*b + 16286963*a^6*b^2 - 11087881*a^5*b^3 + 3832430*a^4*b^4 + 31472*a^3*b^5 - 641872*a^2*b^6 + 265232*a*b^7 - 42592*b^8)) + 784*(4489*a^5 - 25058*a^4*b + 34165*a^3*b^2 - 25360*a^2*b^3 + 9812*a*b^4 - 1936*b^5)*x^3 - 2^(1/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(1/4)*(sqrt(7)*sqrt(2)*((211*a^2 - 428*a*b + 100*b^2)*x^4 + (211*a^2 - 428*a*b + 100*b^2)*x^2 + 422*a^2 - 856*a*b + 200*b^2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4) + 8*sqrt(7)*((4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^4 + 8978*a^4 - 14204*a^3*b + 11514*a^2*b^2 - 4664*a*b^3 + 968*b^4 + (4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^2))*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4))*log(32*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^2 + 16/7*2^(1/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(a - 4*b)*x + sqrt(7)*(737*a^3 - 717*a^2*b + 348*a*b^2 - 44*b^3)*x)*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)) + 32*sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(67*a^2 - 53*a*b + 22*b^2)) + 2^(1/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(1/4)*(sqrt(7)*sqrt(2)*((211*a^2 - 428*a*b + 100*b^2)*x^4 + (211*a^2 - 428*a*b + 100*b^2)*x^2 + 422*a^2 - 856*a*b + 200*b^2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4) + 8*sqrt(7)*((4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^4 + 8978*a^4 - 14204*a^3*b + 11514*a^2*b^2 - 4664*a*b^3 + 968*b^4 + (4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^2))*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4))*log(32*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^2 - 16/7*2^(1/4)*sqrt(2/7)*(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)^(1/4)*(sqrt(7)*sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(a - 4*b)*x + sqrt(7)*(737*a^3 - 717*a^2*b + 348*a*b^2 - 44*b^3)*x)*sqrt((35912*a^4 - 56816*a^3*b + 46056*a^2*b^2 - 18656*a*b^3 + 3872*b^4 - sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(211*a^2 - 428*a*b + 100*b^2))/(289*a^4 - 136*a^3*b - 120*a^2*b^2 + 32*a*b^3 + 16*b^4)) + 32*sqrt(2)*sqrt(4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*(67*a^2 - 53*a*b + 22*b^2)) - 784*(13467*a^5 - 12328*a^4*b + 3067*a^3*b^2 + 4518*a^2*b^3 - 3212*a*b^4 + 968*b^5)*x)/((4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^4 + 8978*a^4 - 14204*a^3*b + 11514*a^2*b^2 - 4664*a*b^3 + 968*b^4 + (4489*a^4 - 7102*a^3*b + 5757*a^2*b^2 - 2332*a*b^3 + 484*b^4)*x^2)","B",0
102,1,97,0,1.008367," ","integrate((-x^2+2^(1/2))/(1+x^4-x^2*2^(1/2)),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\left(i + 1\right) \, \sqrt{2}} \log\left(x + \frac{1}{2} \, \sqrt{2} \sqrt{\left(i + 1\right) \, \sqrt{2}}\right) - \frac{1}{4} \, \sqrt{\left(i + 1\right) \, \sqrt{2}} \log\left(x - \frac{1}{2} \, \sqrt{2} \sqrt{\left(i + 1\right) \, \sqrt{2}}\right) + \frac{1}{4} \, \sqrt{-\left(i - 1\right) \, \sqrt{2}} \log\left(x + \frac{1}{2} \, \sqrt{2} \sqrt{-\left(i - 1\right) \, \sqrt{2}}\right) - \frac{1}{4} \, \sqrt{-\left(i - 1\right) \, \sqrt{2}} \log\left(x - \frac{1}{2} \, \sqrt{2} \sqrt{-\left(i - 1\right) \, \sqrt{2}}\right)"," ",0,"1/4*sqrt((I + 1)*sqrt(2))*log(x + 1/2*sqrt(2)*sqrt((I + 1)*sqrt(2))) - 1/4*sqrt((I + 1)*sqrt(2))*log(x - 1/2*sqrt(2)*sqrt((I + 1)*sqrt(2))) + 1/4*sqrt(-(I - 1)*sqrt(2))*log(x + 1/2*sqrt(2)*sqrt(-(I - 1)*sqrt(2))) - 1/4*sqrt(-(I - 1)*sqrt(2))*log(x - 1/2*sqrt(2)*sqrt(-(I - 1)*sqrt(2)))","C",0
103,1,97,0,1.129237," ","integrate((x^2+2^(1/2))/(1+x^4+x^2*2^(1/2)),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{\left(i - 1\right) \, \sqrt{2}} \log\left(x + \frac{1}{2} \, \sqrt{2} \sqrt{\left(i - 1\right) \, \sqrt{2}}\right) - \frac{1}{4} \, \sqrt{\left(i - 1\right) \, \sqrt{2}} \log\left(x - \frac{1}{2} \, \sqrt{2} \sqrt{\left(i - 1\right) \, \sqrt{2}}\right) + \frac{1}{4} \, \sqrt{-\left(i + 1\right) \, \sqrt{2}} \log\left(x + \frac{1}{2} \, \sqrt{2} \sqrt{-\left(i + 1\right) \, \sqrt{2}}\right) - \frac{1}{4} \, \sqrt{-\left(i + 1\right) \, \sqrt{2}} \log\left(x - \frac{1}{2} \, \sqrt{2} \sqrt{-\left(i + 1\right) \, \sqrt{2}}\right)"," ",0,"1/4*sqrt((I - 1)*sqrt(2))*log(x + 1/2*sqrt(2)*sqrt((I - 1)*sqrt(2))) - 1/4*sqrt((I - 1)*sqrt(2))*log(x - 1/2*sqrt(2)*sqrt((I - 1)*sqrt(2))) + 1/4*sqrt(-(I + 1)*sqrt(2))*log(x + 1/2*sqrt(2)*sqrt(-(I + 1)*sqrt(2))) - 1/4*sqrt(-(I + 1)*sqrt(2))*log(x - 1/2*sqrt(2)*sqrt(-(I + 1)*sqrt(2)))","C",0
104,1,451,0,1.216092," ","integrate((-x^2+2^(1/2))/(x^4+b*x^2+1),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{3 \, b + 4 \, \sqrt{2} + \sqrt{b^{2} - 4}}{b^{2} - 4}} \log\left(\frac{1}{2} \, {\left(2 \, b + 3 \, \sqrt{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - \frac{b^{3} + \sqrt{2} b^{2} - 4 \, b - 4 \, \sqrt{2}}{\sqrt{b^{2} - 4}} - 4\right)} \sqrt{-\frac{3 \, b + 4 \, \sqrt{2} + \sqrt{b^{2} - 4}}{b^{2} - 4}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{3 \, b + 4 \, \sqrt{2} + \sqrt{b^{2} - 4}}{b^{2} - 4}} \log\left(\frac{1}{2} \, {\left(2 \, b + 3 \, \sqrt{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - \frac{b^{3} + \sqrt{2} b^{2} - 4 \, b - 4 \, \sqrt{2}}{\sqrt{b^{2} - 4}} - 4\right)} \sqrt{-\frac{3 \, b + 4 \, \sqrt{2} + \sqrt{b^{2} - 4}}{b^{2} - 4}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{3 \, b + 4 \, \sqrt{2} - \sqrt{b^{2} - 4}}{b^{2} - 4}} \log\left(\frac{1}{2} \, {\left(2 \, b + 3 \, \sqrt{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} + \frac{b^{3} + \sqrt{2} b^{2} - 4 \, b - 4 \, \sqrt{2}}{\sqrt{b^{2} - 4}} - 4\right)} \sqrt{-\frac{3 \, b + 4 \, \sqrt{2} - \sqrt{b^{2} - 4}}{b^{2} - 4}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{3 \, b + 4 \, \sqrt{2} - \sqrt{b^{2} - 4}}{b^{2} - 4}} \log\left(\frac{1}{2} \, {\left(2 \, b + 3 \, \sqrt{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} + \frac{b^{3} + \sqrt{2} b^{2} - 4 \, b - 4 \, \sqrt{2}}{\sqrt{b^{2} - 4}} - 4\right)} \sqrt{-\frac{3 \, b + 4 \, \sqrt{2} - \sqrt{b^{2} - 4}}{b^{2} - 4}}\right)"," ",0,"-1/2*sqrt(1/2)*sqrt(-(3*b + 4*sqrt(2) + sqrt(b^2 - 4))/(b^2 - 4))*log(1/2*(2*b + 3*sqrt(2))*x + 1/2*sqrt(1/2)*(b^2 - (b^3 + sqrt(2)*b^2 - 4*b - 4*sqrt(2))/sqrt(b^2 - 4) - 4)*sqrt(-(3*b + 4*sqrt(2) + sqrt(b^2 - 4))/(b^2 - 4))) + 1/2*sqrt(1/2)*sqrt(-(3*b + 4*sqrt(2) + sqrt(b^2 - 4))/(b^2 - 4))*log(1/2*(2*b + 3*sqrt(2))*x - 1/2*sqrt(1/2)*(b^2 - (b^3 + sqrt(2)*b^2 - 4*b - 4*sqrt(2))/sqrt(b^2 - 4) - 4)*sqrt(-(3*b + 4*sqrt(2) + sqrt(b^2 - 4))/(b^2 - 4))) - 1/2*sqrt(1/2)*sqrt(-(3*b + 4*sqrt(2) - sqrt(b^2 - 4))/(b^2 - 4))*log(1/2*(2*b + 3*sqrt(2))*x + 1/2*sqrt(1/2)*(b^2 + (b^3 + sqrt(2)*b^2 - 4*b - 4*sqrt(2))/sqrt(b^2 - 4) - 4)*sqrt(-(3*b + 4*sqrt(2) - sqrt(b^2 - 4))/(b^2 - 4))) + 1/2*sqrt(1/2)*sqrt(-(3*b + 4*sqrt(2) - sqrt(b^2 - 4))/(b^2 - 4))*log(1/2*(2*b + 3*sqrt(2))*x - 1/2*sqrt(1/2)*(b^2 + (b^3 + sqrt(2)*b^2 - 4*b - 4*sqrt(2))/sqrt(b^2 - 4) - 4)*sqrt(-(3*b + 4*sqrt(2) - sqrt(b^2 - 4))/(b^2 - 4)))","B",0
105,1,455,0,1.102057," ","integrate((x^2+2^(1/2))/(x^4+b*x^2+1),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{3 \, b - 4 \, \sqrt{2} + \sqrt{b^{2} - 4}}{b^{2} - 4}} \log\left(\frac{1}{2} \, {\left(2 \, b - 3 \, \sqrt{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - \frac{b^{3} - \sqrt{2} b^{2} - 4 \, b + 4 \, \sqrt{2}}{\sqrt{b^{2} - 4}} - 4\right)} \sqrt{-\frac{3 \, b - 4 \, \sqrt{2} + \sqrt{b^{2} - 4}}{b^{2} - 4}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{3 \, b - 4 \, \sqrt{2} + \sqrt{b^{2} - 4}}{b^{2} - 4}} \log\left(\frac{1}{2} \, {\left(2 \, b - 3 \, \sqrt{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} - \frac{b^{3} - \sqrt{2} b^{2} - 4 \, b + 4 \, \sqrt{2}}{\sqrt{b^{2} - 4}} - 4\right)} \sqrt{-\frac{3 \, b - 4 \, \sqrt{2} + \sqrt{b^{2} - 4}}{b^{2} - 4}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{3 \, b - 4 \, \sqrt{2} - \sqrt{b^{2} - 4}}{b^{2} - 4}} \log\left(\frac{1}{2} \, {\left(2 \, b - 3 \, \sqrt{2}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} + \frac{b^{3} - \sqrt{2} b^{2} - 4 \, b + 4 \, \sqrt{2}}{\sqrt{b^{2} - 4}} - 4\right)} \sqrt{-\frac{3 \, b - 4 \, \sqrt{2} - \sqrt{b^{2} - 4}}{b^{2} - 4}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{3 \, b - 4 \, \sqrt{2} - \sqrt{b^{2} - 4}}{b^{2} - 4}} \log\left(\frac{1}{2} \, {\left(2 \, b - 3 \, \sqrt{2}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{2} + \frac{b^{3} - \sqrt{2} b^{2} - 4 \, b + 4 \, \sqrt{2}}{\sqrt{b^{2} - 4}} - 4\right)} \sqrt{-\frac{3 \, b - 4 \, \sqrt{2} - \sqrt{b^{2} - 4}}{b^{2} - 4}}\right)"," ",0,"1/2*sqrt(1/2)*sqrt(-(3*b - 4*sqrt(2) + sqrt(b^2 - 4))/(b^2 - 4))*log(1/2*(2*b - 3*sqrt(2))*x + 1/2*sqrt(1/2)*(b^2 - (b^3 - sqrt(2)*b^2 - 4*b + 4*sqrt(2))/sqrt(b^2 - 4) - 4)*sqrt(-(3*b - 4*sqrt(2) + sqrt(b^2 - 4))/(b^2 - 4))) - 1/2*sqrt(1/2)*sqrt(-(3*b - 4*sqrt(2) + sqrt(b^2 - 4))/(b^2 - 4))*log(1/2*(2*b - 3*sqrt(2))*x - 1/2*sqrt(1/2)*(b^2 - (b^3 - sqrt(2)*b^2 - 4*b + 4*sqrt(2))/sqrt(b^2 - 4) - 4)*sqrt(-(3*b - 4*sqrt(2) + sqrt(b^2 - 4))/(b^2 - 4))) + 1/2*sqrt(1/2)*sqrt(-(3*b - 4*sqrt(2) - sqrt(b^2 - 4))/(b^2 - 4))*log(1/2*(2*b - 3*sqrt(2))*x + 1/2*sqrt(1/2)*(b^2 + (b^3 - sqrt(2)*b^2 - 4*b + 4*sqrt(2))/sqrt(b^2 - 4) - 4)*sqrt(-(3*b - 4*sqrt(2) - sqrt(b^2 - 4))/(b^2 - 4))) - 1/2*sqrt(1/2)*sqrt(-(3*b - 4*sqrt(2) - sqrt(b^2 - 4))/(b^2 - 4))*log(1/2*(2*b - 3*sqrt(2))*x - 1/2*sqrt(1/2)*(b^2 + (b^3 - sqrt(2)*b^2 - 4*b + 4*sqrt(2))/sqrt(b^2 - 4) - 4)*sqrt(-(3*b - 4*sqrt(2) - sqrt(b^2 - 4))/(b^2 - 4)))","B",0
106,1,517,0,0.845866," ","integrate((-x^2+2*a)/(x^4-a*x^2+a^2),x, algorithm=""fricas"")","\frac{1}{24} \, {\left(\sqrt{3} a \sqrt{\frac{1}{a^{2}}} + 2 \, \sqrt{3}\right)} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{1}{4}} \log\left(6 \, a^{2} \sqrt{\frac{1}{a^{2}}} + 6 \, x^{2} + {\left(\sqrt{3} a^{2} \sqrt{\frac{1}{a^{2}}} x + 2 \, \sqrt{3} a x\right)} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{1}{4}}\right) - \frac{1}{24} \, {\left(\sqrt{3} a \sqrt{\frac{1}{a^{2}}} + 2 \, \sqrt{3}\right)} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{1}{4}} \log\left(6 \, a^{2} \sqrt{\frac{1}{a^{2}}} + 6 \, x^{2} - {\left(\sqrt{3} a^{2} \sqrt{\frac{1}{a^{2}}} x + 2 \, \sqrt{3} a x\right)} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{1}{4}}\right) - \frac{1}{2} \, \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{1}{4}} \arctan\left(\frac{1}{18} \, {\left(\sqrt{6} a^{2} \sqrt{\frac{1}{a^{2}}} + 2 \, \sqrt{6} a\right)} \sqrt{6 \, a^{2} \sqrt{\frac{1}{a^{2}}} + 6 \, x^{2} + {\left(\sqrt{3} a^{2} \sqrt{\frac{1}{a^{2}}} x + 2 \, \sqrt{3} a x\right)} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{1}{4}}} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{3}{4}} - \frac{1}{3} \, {\left(a^{2} \sqrt{\frac{1}{a^{2}}} x + 2 \, a x\right)} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{3}{4}} - \frac{1}{3} \, \sqrt{3} a \sqrt{\frac{1}{a^{2}}} - \frac{2}{3} \, \sqrt{3}\right) - \frac{1}{2} \, \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{1}{4}} \arctan\left(\frac{1}{18} \, {\left(\sqrt{6} a^{2} \sqrt{\frac{1}{a^{2}}} + 2 \, \sqrt{6} a\right)} \sqrt{6 \, a^{2} \sqrt{\frac{1}{a^{2}}} + 6 \, x^{2} - {\left(\sqrt{3} a^{2} \sqrt{\frac{1}{a^{2}}} x + 2 \, \sqrt{3} a x\right)} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{1}{4}}} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{3}{4}} - \frac{1}{3} \, {\left(a^{2} \sqrt{\frac{1}{a^{2}}} x + 2 \, a x\right)} \sqrt{-4 \, a \sqrt{\frac{1}{a^{2}}} + 8} \frac{1}{a^{2}}^{\frac{3}{4}} + \frac{1}{3} \, \sqrt{3} a \sqrt{\frac{1}{a^{2}}} + \frac{2}{3} \, \sqrt{3}\right)"," ",0,"1/24*(sqrt(3)*a*sqrt(a^(-2)) + 2*sqrt(3))*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(1/4)*log(6*a^2*sqrt(a^(-2)) + 6*x^2 + (sqrt(3)*a^2*sqrt(a^(-2))*x + 2*sqrt(3)*a*x)*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(1/4)) - 1/24*(sqrt(3)*a*sqrt(a^(-2)) + 2*sqrt(3))*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(1/4)*log(6*a^2*sqrt(a^(-2)) + 6*x^2 - (sqrt(3)*a^2*sqrt(a^(-2))*x + 2*sqrt(3)*a*x)*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(1/4)) - 1/2*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(1/4)*arctan(1/18*(sqrt(6)*a^2*sqrt(a^(-2)) + 2*sqrt(6)*a)*sqrt(6*a^2*sqrt(a^(-2)) + 6*x^2 + (sqrt(3)*a^2*sqrt(a^(-2))*x + 2*sqrt(3)*a*x)*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(1/4))*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(3/4) - 1/3*(a^2*sqrt(a^(-2))*x + 2*a*x)*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(3/4) - 1/3*sqrt(3)*a*sqrt(a^(-2)) - 2/3*sqrt(3)) - 1/2*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(1/4)*arctan(1/18*(sqrt(6)*a^2*sqrt(a^(-2)) + 2*sqrt(6)*a)*sqrt(6*a^2*sqrt(a^(-2)) + 6*x^2 - (sqrt(3)*a^2*sqrt(a^(-2))*x + 2*sqrt(3)*a*x)*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(1/4))*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(3/4) - 1/3*(a^2*sqrt(a^(-2))*x + 2*a*x)*sqrt(-4*a*sqrt(a^(-2)) + 8)*(a^(-2))^(3/4) + 1/3*sqrt(3)*a*sqrt(a^(-2)) + 2/3*sqrt(3))","B",0
107,1,251,0,1.065913," ","integrate((-x^2+2*a^(1/2))/(a+x^4-x^2*a^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{\sqrt{3} a \sqrt{-\frac{1}{a}} + \sqrt{a}}{a}} \log\left(\sqrt{\frac{1}{2}} \sqrt{a} \sqrt{\frac{\sqrt{3} a \sqrt{-\frac{1}{a}} + \sqrt{a}}{a}} + x\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{\frac{\sqrt{3} a \sqrt{-\frac{1}{a}} + \sqrt{a}}{a}} \log\left(-\sqrt{\frac{1}{2}} \sqrt{a} \sqrt{\frac{\sqrt{3} a \sqrt{-\frac{1}{a}} + \sqrt{a}}{a}} + x\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{\sqrt{3} a \sqrt{-\frac{1}{a}} - \sqrt{a}}{a}} \log\left(\sqrt{\frac{1}{2}} \sqrt{a} \sqrt{-\frac{\sqrt{3} a \sqrt{-\frac{1}{a}} - \sqrt{a}}{a}} + x\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{\sqrt{3} a \sqrt{-\frac{1}{a}} - \sqrt{a}}{a}} \log\left(-\sqrt{\frac{1}{2}} \sqrt{a} \sqrt{-\frac{\sqrt{3} a \sqrt{-\frac{1}{a}} - \sqrt{a}}{a}} + x\right)"," ",0,"1/2*sqrt(1/2)*sqrt((sqrt(3)*a*sqrt(-1/a) + sqrt(a))/a)*log(sqrt(1/2)*sqrt(a)*sqrt((sqrt(3)*a*sqrt(-1/a) + sqrt(a))/a) + x) - 1/2*sqrt(1/2)*sqrt((sqrt(3)*a*sqrt(-1/a) + sqrt(a))/a)*log(-sqrt(1/2)*sqrt(a)*sqrt((sqrt(3)*a*sqrt(-1/a) + sqrt(a))/a) + x) + 1/2*sqrt(1/2)*sqrt(-(sqrt(3)*a*sqrt(-1/a) - sqrt(a))/a)*log(sqrt(1/2)*sqrt(a)*sqrt(-(sqrt(3)*a*sqrt(-1/a) - sqrt(a))/a) + x) - 1/2*sqrt(1/2)*sqrt(-(sqrt(3)*a*sqrt(-1/a) - sqrt(a))/a)*log(-sqrt(1/2)*sqrt(a)*sqrt(-(sqrt(3)*a*sqrt(-1/a) - sqrt(a))/a) + x)","B",0
108,1,264,0,1.287507," ","integrate((2*b^(2/3)+x^2)/(b^(4/3)+b^(2/3)*x^2+x^4),x, algorithm=""fricas"")","\left[\frac{\sqrt{3} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(\frac{2 \, x^{3} + \sqrt{3} {\left(2 \, b^{\frac{2}{3}} x^{2} + b x - b^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 3 \, b^{\frac{2}{3}} x - b}{x^{3} + b}\right) + \sqrt{3} b \sqrt{-\frac{1}{b^{\frac{2}{3}}}} \log\left(\frac{2 \, x^{3} + \sqrt{3} {\left(2 \, b^{\frac{2}{3}} x^{2} - b x - b^{\frac{4}{3}}\right)} \sqrt{-\frac{1}{b^{\frac{2}{3}}}} - 3 \, b^{\frac{2}{3}} x + b}{x^{3} - b}\right) + b^{\frac{2}{3}} \log\left(x^{2} + b^{\frac{1}{3}} x + b^{\frac{2}{3}}\right) - b^{\frac{2}{3}} \log\left(x^{2} - b^{\frac{1}{3}} x + b^{\frac{2}{3}}\right)}{4 \, b}, \frac{2 \, \sqrt{3} b^{\frac{2}{3}} \arctan\left(\frac{\sqrt{3} {\left(2 \, x + b^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right) - 2 \, \sqrt{3} b^{\frac{2}{3}} \arctan\left(-\frac{\sqrt{3} {\left(2 \, x - b^{\frac{1}{3}}\right)}}{3 \, b^{\frac{1}{3}}}\right) + b^{\frac{2}{3}} \log\left(x^{2} + b^{\frac{1}{3}} x + b^{\frac{2}{3}}\right) - b^{\frac{2}{3}} \log\left(x^{2} - b^{\frac{1}{3}} x + b^{\frac{2}{3}}\right)}{4 \, b}\right]"," ",0,"[1/4*(sqrt(3)*b*sqrt(-1/b^(2/3))*log((2*x^3 + sqrt(3)*(2*b^(2/3)*x^2 + b*x - b^(4/3))*sqrt(-1/b^(2/3)) - 3*b^(2/3)*x - b)/(x^3 + b)) + sqrt(3)*b*sqrt(-1/b^(2/3))*log((2*x^3 + sqrt(3)*(2*b^(2/3)*x^2 - b*x - b^(4/3))*sqrt(-1/b^(2/3)) - 3*b^(2/3)*x + b)/(x^3 - b)) + b^(2/3)*log(x^2 + b^(1/3)*x + b^(2/3)) - b^(2/3)*log(x^2 - b^(1/3)*x + b^(2/3)))/b, 1/4*(2*sqrt(3)*b^(2/3)*arctan(1/3*sqrt(3)*(2*x + b^(1/3))/b^(1/3)) - 2*sqrt(3)*b^(2/3)*arctan(-1/3*sqrt(3)*(2*x - b^(1/3))/b^(1/3)) + b^(2/3)*log(x^2 + b^(1/3)*x + b^(2/3)) - b^(2/3)*log(x^2 - b^(1/3)*x + b^(2/3)))/b]","A",0
109,1,4551,0,2.411841," ","integrate((B*x^2+A)/(x^4-a*x^2+a^2),x, algorithm=""fricas"")","\frac{4 \, \left(\frac{1}{9}\right)^{\frac{1}{4}} a^{6} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}} \arctan\left(\frac{18 \, \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{3}{4}} {\left(\sqrt{\frac{1}{3}} A a^{10} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}} - \sqrt{\frac{1}{3}} {\left(B^{3} a^{10} + A B^{2} a^{9} + A^{2} B a^{8}\right)} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}}\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \sqrt{\frac{{\left(B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}\right)} x^{2} + 3 \, \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{1}{4}} {\left(B a^{6} x \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} - {\left(A B^{2} a^{4} + A^{2} B a^{3} + A^{3} a^{2}\right)} x\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{1}{4}} + {\left(B^{2} a^{6} + A B a^{5} + A^{2} a^{4}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{3}{4}} - 18 \, \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{3}{4}} {\left(\sqrt{\frac{1}{3}} A a^{10} x \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}} - \sqrt{\frac{1}{3}} {\left(B^{3} a^{10} + A B^{2} a^{9} + A^{2} B a^{8}\right)} x \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}}\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{3}{4}} + 2 \, \sqrt{\frac{1}{3}} {\left(B^{4} a^{10} + 2 \, A B^{3} a^{9} + 3 \, A^{2} B^{2} a^{8} + 2 \, A^{3} B a^{7} + A^{4} a^{6}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}} + \sqrt{\frac{1}{3}} {\left(B^{6} a^{9} + 3 \, A B^{5} a^{8} + 6 \, A^{2} B^{4} a^{7} + 7 \, A^{3} B^{3} a^{6} + 6 \, A^{4} B^{2} a^{5} + 3 \, A^{5} B a^{4} + A^{6} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}}}{B^{8} a^{8} + 3 \, A B^{7} a^{7} + 5 \, A^{2} B^{6} a^{6} + 4 \, A^{3} B^{5} a^{5} - 4 \, A^{5} B^{3} a^{3} - 5 \, A^{6} B^{2} a^{2} - 3 \, A^{7} B a - A^{8}}\right) + 4 \, \left(\frac{1}{9}\right)^{\frac{1}{4}} a^{6} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{3}{4}} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}} \arctan\left(\frac{18 \, \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{3}{4}} {\left(\sqrt{\frac{1}{3}} A a^{10} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}} - \sqrt{\frac{1}{3}} {\left(B^{3} a^{10} + A B^{2} a^{9} + A^{2} B a^{8}\right)} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}}\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \sqrt{\frac{{\left(B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}\right)} x^{2} - 3 \, \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{1}{4}} {\left(B a^{6} x \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} - {\left(A B^{2} a^{4} + A^{2} B a^{3} + A^{3} a^{2}\right)} x\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{1}{4}} + {\left(B^{2} a^{6} + A B a^{5} + A^{2} a^{4}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{3}{4}} - 18 \, \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{3}{4}} {\left(\sqrt{\frac{1}{3}} A a^{10} x \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}} - \sqrt{\frac{1}{3}} {\left(B^{3} a^{10} + A B^{2} a^{9} + A^{2} B a^{8}\right)} x \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}}\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{3}{4}} - 2 \, \sqrt{\frac{1}{3}} {\left(B^{4} a^{10} + 2 \, A B^{3} a^{9} + 3 \, A^{2} B^{2} a^{8} + 2 \, A^{3} B a^{7} + A^{4} a^{6}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}} - \sqrt{\frac{1}{3}} {\left(B^{6} a^{9} + 3 \, A B^{5} a^{8} + 6 \, A^{2} B^{4} a^{7} + 7 \, A^{3} B^{3} a^{6} + 6 \, A^{4} B^{2} a^{5} + 3 \, A^{5} B a^{4} + A^{6} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}{a^{6}}}}{B^{8} a^{8} + 3 \, A B^{7} a^{7} + 5 \, A^{2} B^{6} a^{6} + 4 \, A^{3} B^{5} a^{5} - 4 \, A^{5} B^{3} a^{3} - 5 \, A^{6} B^{2} a^{2} - 3 \, A^{7} B a - A^{8}}\right) - \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{1}{4}} {\left(2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} - {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{1}{4}} \log\left(2 \, {\left(B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}\right)} x^{2} + 6 \, \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{1}{4}} {\left(B a^{6} x \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} - {\left(A B^{2} a^{4} + A^{2} B a^{3} + A^{3} a^{2}\right)} x\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{1}{4}} + 2 \, {\left(B^{2} a^{6} + A B a^{5} + A^{2} a^{4}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}\right) + \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{1}{4}} {\left(2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} - {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{1}{4}} \log\left(2 \, {\left(B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}\right)} x^{2} - 6 \, \sqrt{\frac{1}{3}} \left(\frac{1}{9}\right)^{\frac{1}{4}} {\left(B a^{6} x \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}} - {\left(A B^{2} a^{4} + A^{2} B a^{3} + A^{3} a^{2}\right)} x\right)} \sqrt{\frac{2 \, B^{4} a^{4} + 4 \, A B^{3} a^{3} + 6 \, A^{2} B^{2} a^{2} + 4 \, A^{3} B a + 2 \, A^{4} + {\left(B^{2} a^{5} + 4 \, A B a^{4} + A^{2} a^{3}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}}{B^{4} a^{4} - 2 \, A^{2} B^{2} a^{2} + A^{4}}} \left(\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}\right)^{\frac{1}{4}} + 2 \, {\left(B^{2} a^{6} + A B a^{5} + A^{2} a^{4}\right)} \sqrt{\frac{B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}}{a^{6}}}\right)}{4 \, {\left(B^{4} a^{4} + 2 \, A B^{3} a^{3} + 3 \, A^{2} B^{2} a^{2} + 2 \, A^{3} B a + A^{4}\right)}}"," ",0,"1/4*(4*(1/9)^(1/4)*a^6*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(3/4)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6)*arctan((18*sqrt(1/3)*(1/9)^(3/4)*(sqrt(1/3)*A*a^10*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6) - sqrt(1/3)*(B^3*a^10 + A*B^2*a^9 + A^2*B*a^8)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6))*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*sqrt(((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)*x^2 + 3*sqrt(1/3)*(1/9)^(1/4)*(B*a^6*x*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6) - (A*B^2*a^4 + A^2*B*a^3 + A^3*a^2)*x)*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(1/4) + (B^2*a^6 + A*B*a^5 + A^2*a^4)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(3/4) - 18*sqrt(1/3)*(1/9)^(3/4)*(sqrt(1/3)*A*a^10*x*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6) - sqrt(1/3)*(B^3*a^10 + A*B^2*a^9 + A^2*B*a^8)*x*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6))*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(3/4) + 2*sqrt(1/3)*(B^4*a^10 + 2*A*B^3*a^9 + 3*A^2*B^2*a^8 + 2*A^3*B*a^7 + A^4*a^6)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6) + sqrt(1/3)*(B^6*a^9 + 3*A*B^5*a^8 + 6*A^2*B^4*a^7 + 7*A^3*B^3*a^6 + 6*A^4*B^2*a^5 + 3*A^5*B*a^4 + A^6*a^3)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6))/(B^8*a^8 + 3*A*B^7*a^7 + 5*A^2*B^6*a^6 + 4*A^3*B^5*a^5 - 4*A^5*B^3*a^3 - 5*A^6*B^2*a^2 - 3*A^7*B*a - A^8)) + 4*(1/9)^(1/4)*a^6*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(3/4)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6)*arctan((18*sqrt(1/3)*(1/9)^(3/4)*(sqrt(1/3)*A*a^10*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6) - sqrt(1/3)*(B^3*a^10 + A*B^2*a^9 + A^2*B*a^8)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6))*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*sqrt(((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)*x^2 - 3*sqrt(1/3)*(1/9)^(1/4)*(B*a^6*x*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6) - (A*B^2*a^4 + A^2*B*a^3 + A^3*a^2)*x)*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(1/4) + (B^2*a^6 + A*B*a^5 + A^2*a^4)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(3/4) - 18*sqrt(1/3)*(1/9)^(3/4)*(sqrt(1/3)*A*a^10*x*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6) - sqrt(1/3)*(B^3*a^10 + A*B^2*a^9 + A^2*B*a^8)*x*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6))*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(3/4) - 2*sqrt(1/3)*(B^4*a^10 + 2*A*B^3*a^9 + 3*A^2*B^2*a^8 + 2*A^3*B*a^7 + A^4*a^6)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6) - sqrt(1/3)*(B^6*a^9 + 3*A*B^5*a^8 + 6*A^2*B^4*a^7 + 7*A^3*B^3*a^6 + 6*A^4*B^2*a^5 + 3*A^5*B*a^4 + A^6*a^3)*sqrt((B^4*a^4 - 2*A^2*B^2*a^2 + A^4)/a^6))/(B^8*a^8 + 3*A*B^7*a^7 + 5*A^2*B^6*a^6 + 4*A^3*B^5*a^5 - 4*A^5*B^3*a^3 - 5*A^6*B^2*a^2 - 3*A^7*B*a - A^8)) - sqrt(1/3)*(1/9)^(1/4)*(2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 - (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(1/4)*log(2*(B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)*x^2 + 6*sqrt(1/3)*(1/9)^(1/4)*(B*a^6*x*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6) - (A*B^2*a^4 + A^2*B*a^3 + A^3*a^2)*x)*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(1/4) + 2*(B^2*a^6 + A*B*a^5 + A^2*a^4)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)) + sqrt(1/3)*(1/9)^(1/4)*(2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 - (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(1/4)*log(2*(B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)*x^2 - 6*sqrt(1/3)*(1/9)^(1/4)*(B*a^6*x*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6) - (A*B^2*a^4 + A^2*B*a^3 + A^3*a^2)*x)*sqrt((2*B^4*a^4 + 4*A*B^3*a^3 + 6*A^2*B^2*a^2 + 4*A^3*B*a + 2*A^4 + (B^2*a^5 + 4*A*B*a^4 + A^2*a^3)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6))/(B^4*a^4 - 2*A^2*B^2*a^2 + A^4))*((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)^(1/4) + 2*(B^2*a^6 + A*B*a^5 + A^2*a^4)*sqrt((B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)/a^6)))/(B^4*a^4 + 2*A*B^3*a^3 + 3*A^2*B^2*a^2 + 2*A^3*B*a + A^4)","B",0
110,1,1141,0,1.677726," ","integrate((B*x^2+A)/(a+x^4-x^2*a^(1/2)),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{-\frac{4 \, A B a + 3 \, \sqrt{\frac{1}{3}} a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} + {\left(B^{2} a + A^{2}\right)} \sqrt{a}}{a^{2}}} \log\left(2 \, {\left(B^{6} a^{3} - A^{6}\right)} x + 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} - A^{5} a - \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} + A^{2} B a^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} - {\left(A^{2} B^{3} a^{2} - A^{4} B a - \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} - A^{3} a^{2}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}}\right)} \sqrt{a}\right)} \sqrt{-\frac{4 \, A B a + 3 \, \sqrt{\frac{1}{3}} a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} + {\left(B^{2} a + A^{2}\right)} \sqrt{a}}{a^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{-\frac{4 \, A B a + 3 \, \sqrt{\frac{1}{3}} a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} + {\left(B^{2} a + A^{2}\right)} \sqrt{a}}{a^{2}}} \log\left(2 \, {\left(B^{6} a^{3} - A^{6}\right)} x - 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} - A^{5} a - \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} + A^{2} B a^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} - {\left(A^{2} B^{3} a^{2} - A^{4} B a - \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} - A^{3} a^{2}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}}\right)} \sqrt{a}\right)} \sqrt{-\frac{4 \, A B a + 3 \, \sqrt{\frac{1}{3}} a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} + {\left(B^{2} a + A^{2}\right)} \sqrt{a}}{a^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{-\frac{4 \, A B a - 3 \, \sqrt{\frac{1}{3}} a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} + {\left(B^{2} a + A^{2}\right)} \sqrt{a}}{a^{2}}} \log\left(2 \, {\left(B^{6} a^{3} - A^{6}\right)} x + 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} - A^{5} a + \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} + A^{2} B a^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} - {\left(A^{2} B^{3} a^{2} - A^{4} B a + \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} - A^{3} a^{2}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}}\right)} \sqrt{a}\right)} \sqrt{-\frac{4 \, A B a - 3 \, \sqrt{\frac{1}{3}} a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} + {\left(B^{2} a + A^{2}\right)} \sqrt{a}}{a^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{-\frac{4 \, A B a - 3 \, \sqrt{\frac{1}{3}} a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} + {\left(B^{2} a + A^{2}\right)} \sqrt{a}}{a^{2}}} \log\left(2 \, {\left(B^{6} a^{3} - A^{6}\right)} x - 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} - A^{5} a + \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} + A^{2} B a^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} - {\left(A^{2} B^{3} a^{2} - A^{4} B a + \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} - A^{3} a^{2}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}}\right)} \sqrt{a}\right)} \sqrt{-\frac{4 \, A B a - 3 \, \sqrt{\frac{1}{3}} a^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a + A^{4}}{a^{3}}} + {\left(B^{2} a + A^{2}\right)} \sqrt{a}}{a^{2}}}\right)"," ",0,"1/2*sqrt(1/6)*sqrt(-(4*A*B*a + 3*sqrt(1/3)*a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) + (B^2*a + A^2)*sqrt(a))/a^2)*log(2*(B^6*a^3 - A^6)*x + 3*sqrt(1/6)*(A*B^4*a^3 - A^5*a - sqrt(1/3)*(2*B^3*a^4 + A^2*B*a^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) - (A^2*B^3*a^2 - A^4*B*a - sqrt(1/3)*(A*B^2*a^3 - A^3*a^2)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3))*sqrt(a))*sqrt(-(4*A*B*a + 3*sqrt(1/3)*a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) + (B^2*a + A^2)*sqrt(a))/a^2)) - 1/2*sqrt(1/6)*sqrt(-(4*A*B*a + 3*sqrt(1/3)*a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) + (B^2*a + A^2)*sqrt(a))/a^2)*log(2*(B^6*a^3 - A^6)*x - 3*sqrt(1/6)*(A*B^4*a^3 - A^5*a - sqrt(1/3)*(2*B^3*a^4 + A^2*B*a^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) - (A^2*B^3*a^2 - A^4*B*a - sqrt(1/3)*(A*B^2*a^3 - A^3*a^2)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3))*sqrt(a))*sqrt(-(4*A*B*a + 3*sqrt(1/3)*a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) + (B^2*a + A^2)*sqrt(a))/a^2)) + 1/2*sqrt(1/6)*sqrt(-(4*A*B*a - 3*sqrt(1/3)*a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) + (B^2*a + A^2)*sqrt(a))/a^2)*log(2*(B^6*a^3 - A^6)*x + 3*sqrt(1/6)*(A*B^4*a^3 - A^5*a + sqrt(1/3)*(2*B^3*a^4 + A^2*B*a^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) - (A^2*B^3*a^2 - A^4*B*a + sqrt(1/3)*(A*B^2*a^3 - A^3*a^2)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3))*sqrt(a))*sqrt(-(4*A*B*a - 3*sqrt(1/3)*a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) + (B^2*a + A^2)*sqrt(a))/a^2)) - 1/2*sqrt(1/6)*sqrt(-(4*A*B*a - 3*sqrt(1/3)*a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) + (B^2*a + A^2)*sqrt(a))/a^2)*log(2*(B^6*a^3 - A^6)*x - 3*sqrt(1/6)*(A*B^4*a^3 - A^5*a + sqrt(1/3)*(2*B^3*a^4 + A^2*B*a^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) - (A^2*B^3*a^2 - A^4*B*a + sqrt(1/3)*(A*B^2*a^3 - A^3*a^2)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3))*sqrt(a))*sqrt(-(4*A*B*a - 3*sqrt(1/3)*a^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a + A^4)/a^3) + (B^2*a + A^2)*sqrt(a))/a^2))","B",0
111,1,1457,0,1.513667," ","integrate((B*x^2+A)/(a+c*x^4-x^2*(a*c)^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{-\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 4 \, A B a c + {\left(B^{2} a + A^{2} c\right)} \sqrt{a c}}{a^{2} c^{2}}} \log\left(-2 \, {\left(B^{6} a^{3} - A^{6} c^{3}\right)} x + 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} c - A^{5} a c^{3} - \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} c^{2} + A^{2} B a^{3} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - {\left(A^{2} B^{3} a^{2} c - A^{4} B a c^{2} - \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{a c}\right)} \sqrt{-\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 4 \, A B a c + {\left(B^{2} a + A^{2} c\right)} \sqrt{a c}}{a^{2} c^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{-\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 4 \, A B a c + {\left(B^{2} a + A^{2} c\right)} \sqrt{a c}}{a^{2} c^{2}}} \log\left(-2 \, {\left(B^{6} a^{3} - A^{6} c^{3}\right)} x - 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} c - A^{5} a c^{3} - \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} c^{2} + A^{2} B a^{3} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - {\left(A^{2} B^{3} a^{2} c - A^{4} B a c^{2} - \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{a c}\right)} \sqrt{-\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 4 \, A B a c + {\left(B^{2} a + A^{2} c\right)} \sqrt{a c}}{a^{2} c^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 4 \, A B a c - {\left(B^{2} a + A^{2} c\right)} \sqrt{a c}}{a^{2} c^{2}}} \log\left(-2 \, {\left(B^{6} a^{3} - A^{6} c^{3}\right)} x + 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} c - A^{5} a c^{3} + \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} c^{2} + A^{2} B a^{3} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - {\left(A^{2} B^{3} a^{2} c - A^{4} B a c^{2} + \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{a c}\right)} \sqrt{\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 4 \, A B a c - {\left(B^{2} a + A^{2} c\right)} \sqrt{a c}}{a^{2} c^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 4 \, A B a c - {\left(B^{2} a + A^{2} c\right)} \sqrt{a c}}{a^{2} c^{2}}} \log\left(-2 \, {\left(B^{6} a^{3} - A^{6} c^{3}\right)} x - 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} c - A^{5} a c^{3} + \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} c^{2} + A^{2} B a^{3} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - {\left(A^{2} B^{3} a^{2} c - A^{4} B a c^{2} + \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{a c}\right)} \sqrt{\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 4 \, A B a c - {\left(B^{2} a + A^{2} c\right)} \sqrt{a c}}{a^{2} c^{2}}}\right)"," ",0,"-1/2*sqrt(1/6)*sqrt(-(3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 4*A*B*a*c + (B^2*a + A^2*c)*sqrt(a*c))/(a^2*c^2))*log(-2*(B^6*a^3 - A^6*c^3)*x + 3*sqrt(1/6)*(A*B^4*a^3*c - A^5*a*c^3 - sqrt(1/3)*(2*B^3*a^4*c^2 + A^2*B*a^3*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - (A^2*B^3*a^2*c - A^4*B*a*c^2 - sqrt(1/3)*(A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(a*c))*sqrt(-(3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 4*A*B*a*c + (B^2*a + A^2*c)*sqrt(a*c))/(a^2*c^2))) + 1/2*sqrt(1/6)*sqrt(-(3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 4*A*B*a*c + (B^2*a + A^2*c)*sqrt(a*c))/(a^2*c^2))*log(-2*(B^6*a^3 - A^6*c^3)*x - 3*sqrt(1/6)*(A*B^4*a^3*c - A^5*a*c^3 - sqrt(1/3)*(2*B^3*a^4*c^2 + A^2*B*a^3*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - (A^2*B^3*a^2*c - A^4*B*a*c^2 - sqrt(1/3)*(A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(a*c))*sqrt(-(3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 4*A*B*a*c + (B^2*a + A^2*c)*sqrt(a*c))/(a^2*c^2))) - 1/2*sqrt(1/6)*sqrt((3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 4*A*B*a*c - (B^2*a + A^2*c)*sqrt(a*c))/(a^2*c^2))*log(-2*(B^6*a^3 - A^6*c^3)*x + 3*sqrt(1/6)*(A*B^4*a^3*c - A^5*a*c^3 + sqrt(1/3)*(2*B^3*a^4*c^2 + A^2*B*a^3*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - (A^2*B^3*a^2*c - A^4*B*a*c^2 + sqrt(1/3)*(A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(a*c))*sqrt((3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 4*A*B*a*c - (B^2*a + A^2*c)*sqrt(a*c))/(a^2*c^2))) + 1/2*sqrt(1/6)*sqrt((3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 4*A*B*a*c - (B^2*a + A^2*c)*sqrt(a*c))/(a^2*c^2))*log(-2*(B^6*a^3 - A^6*c^3)*x - 3*sqrt(1/6)*(A*B^4*a^3*c - A^5*a*c^3 + sqrt(1/3)*(2*B^3*a^4*c^2 + A^2*B*a^3*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - (A^2*B^3*a^2*c - A^4*B*a*c^2 + sqrt(1/3)*(A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(a*c))*sqrt((3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 4*A*B*a*c - (B^2*a + A^2*c)*sqrt(a*c))/(a^2*c^2)))","B",0
112,1,1469,0,2.805661," ","integrate((B*x^2+A)/(a+c*x^4-x^2*a^(1/2)*c^(1/2)),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{-\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 4 \, A B a c + {\left(B^{2} a + A^{2} c\right)} \sqrt{a} \sqrt{c}}{a^{2} c^{2}}} \log\left(-2 \, {\left(B^{6} a^{3} - A^{6} c^{3}\right)} x + 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} c - A^{5} a c^{3} - {\left(A^{2} B^{3} a^{2} c - A^{4} B a c^{2} - \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{a} \sqrt{c} - \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} c^{2} + A^{2} B a^{3} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{-\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 4 \, A B a c + {\left(B^{2} a + A^{2} c\right)} \sqrt{a} \sqrt{c}}{a^{2} c^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{-\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 4 \, A B a c + {\left(B^{2} a + A^{2} c\right)} \sqrt{a} \sqrt{c}}{a^{2} c^{2}}} \log\left(-2 \, {\left(B^{6} a^{3} - A^{6} c^{3}\right)} x - 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} c - A^{5} a c^{3} - {\left(A^{2} B^{3} a^{2} c - A^{4} B a c^{2} - \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{a} \sqrt{c} - \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} c^{2} + A^{2} B a^{3} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{-\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} + 4 \, A B a c + {\left(B^{2} a + A^{2} c\right)} \sqrt{a} \sqrt{c}}{a^{2} c^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 4 \, A B a c - {\left(B^{2} a + A^{2} c\right)} \sqrt{a} \sqrt{c}}{a^{2} c^{2}}} \log\left(-2 \, {\left(B^{6} a^{3} - A^{6} c^{3}\right)} x + 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} c - A^{5} a c^{3} - {\left(A^{2} B^{3} a^{2} c - A^{4} B a c^{2} + \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{a} \sqrt{c} + \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} c^{2} + A^{2} B a^{3} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 4 \, A B a c - {\left(B^{2} a + A^{2} c\right)} \sqrt{a} \sqrt{c}}{a^{2} c^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{6}} \sqrt{\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 4 \, A B a c - {\left(B^{2} a + A^{2} c\right)} \sqrt{a} \sqrt{c}}{a^{2} c^{2}}} \log\left(-2 \, {\left(B^{6} a^{3} - A^{6} c^{3}\right)} x - 3 \, \sqrt{\frac{1}{6}} {\left(A B^{4} a^{3} c - A^{5} a c^{3} - {\left(A^{2} B^{3} a^{2} c - A^{4} B a c^{2} + \sqrt{\frac{1}{3}} {\left(A B^{2} a^{3} c^{2} - A^{3} a^{2} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{a} \sqrt{c} + \sqrt{\frac{1}{3}} {\left(2 \, B^{3} a^{4} c^{2} + A^{2} B a^{3} c^{3}\right)} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}}\right)} \sqrt{\frac{3 \, \sqrt{\frac{1}{3}} a^{2} c^{2} \sqrt{-\frac{B^{4} a^{2} - 2 \, A^{2} B^{2} a c + A^{4} c^{2}}{a^{3} c^{3}}} - 4 \, A B a c - {\left(B^{2} a + A^{2} c\right)} \sqrt{a} \sqrt{c}}{a^{2} c^{2}}}\right)"," ",0,"-1/2*sqrt(1/6)*sqrt(-(3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 4*A*B*a*c + (B^2*a + A^2*c)*sqrt(a)*sqrt(c))/(a^2*c^2))*log(-2*(B^6*a^3 - A^6*c^3)*x + 3*sqrt(1/6)*(A*B^4*a^3*c - A^5*a*c^3 - (A^2*B^3*a^2*c - A^4*B*a*c^2 - sqrt(1/3)*(A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(a)*sqrt(c) - sqrt(1/3)*(2*B^3*a^4*c^2 + A^2*B*a^3*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(-(3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 4*A*B*a*c + (B^2*a + A^2*c)*sqrt(a)*sqrt(c))/(a^2*c^2))) + 1/2*sqrt(1/6)*sqrt(-(3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 4*A*B*a*c + (B^2*a + A^2*c)*sqrt(a)*sqrt(c))/(a^2*c^2))*log(-2*(B^6*a^3 - A^6*c^3)*x - 3*sqrt(1/6)*(A*B^4*a^3*c - A^5*a*c^3 - (A^2*B^3*a^2*c - A^4*B*a*c^2 - sqrt(1/3)*(A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(a)*sqrt(c) - sqrt(1/3)*(2*B^3*a^4*c^2 + A^2*B*a^3*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(-(3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) + 4*A*B*a*c + (B^2*a + A^2*c)*sqrt(a)*sqrt(c))/(a^2*c^2))) - 1/2*sqrt(1/6)*sqrt((3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 4*A*B*a*c - (B^2*a + A^2*c)*sqrt(a)*sqrt(c))/(a^2*c^2))*log(-2*(B^6*a^3 - A^6*c^3)*x + 3*sqrt(1/6)*(A*B^4*a^3*c - A^5*a*c^3 - (A^2*B^3*a^2*c - A^4*B*a*c^2 + sqrt(1/3)*(A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(a)*sqrt(c) + sqrt(1/3)*(2*B^3*a^4*c^2 + A^2*B*a^3*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt((3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 4*A*B*a*c - (B^2*a + A^2*c)*sqrt(a)*sqrt(c))/(a^2*c^2))) + 1/2*sqrt(1/6)*sqrt((3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 4*A*B*a*c - (B^2*a + A^2*c)*sqrt(a)*sqrt(c))/(a^2*c^2))*log(-2*(B^6*a^3 - A^6*c^3)*x - 3*sqrt(1/6)*(A*B^4*a^3*c - A^5*a*c^3 - (A^2*B^3*a^2*c - A^4*B*a*c^2 + sqrt(1/3)*(A*B^2*a^3*c^2 - A^3*a^2*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt(a)*sqrt(c) + sqrt(1/3)*(2*B^3*a^4*c^2 + A^2*B*a^3*c^3)*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)))*sqrt((3*sqrt(1/3)*a^2*c^2*sqrt(-(B^4*a^2 - 2*A^2*B^2*a*c + A^4*c^2)/(a^3*c^3)) - 4*A*B*a*c - (B^2*a + A^2*c)*sqrt(a)*sqrt(c))/(a^2*c^2)))","B",0
113,0,0,0,0.753612," ","integrate((-x^2+3)/(-x^4+x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 3} {\left(x^{2} - 3\right)}}{x^{4} - x^{2} - 3}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 3)*(x^2 - 3)/(x^4 - x^2 - 3), x)","F",0
114,0,0,0,0.837741," ","integrate((-x^2+3)/(-x^4+2*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 2 \, x^{2} + 3}}{x^{2} + 1}, x\right)"," ",0,"integral(sqrt(-x^4 + 2*x^2 + 3)/(x^2 + 1), x)","F",0
115,0,0,0,0.871991," ","integrate((-x^2+3)/(-x^4+3*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + 3 \, x^{2} + 3} {\left(x^{2} - 3\right)}}{x^{4} - 3 \, x^{2} - 3}, x\right)"," ",0,"integral(sqrt(-x^4 + 3*x^2 + 3)*(x^2 - 3)/(x^4 - 3*x^2 - 3), x)","F",0
116,0,0,0,0.836873," ","integrate((-x^2+3)/(-x^4-x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} - x^{2} + 3} {\left(x^{2} - 3\right)}}{x^{4} + x^{2} - 3}, x\right)"," ",0,"integral(sqrt(-x^4 - x^2 + 3)*(x^2 - 3)/(x^4 + x^2 - 3), x)","F",0
117,0,0,0,0.657910," ","integrate((-x^2+3)/(-x^4-2*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} - 2 \, x^{2} + 3} {\left(x^{2} - 3\right)}}{x^{4} + 2 \, x^{2} - 3}, x\right)"," ",0,"integral(sqrt(-x^4 - 2*x^2 + 3)*(x^2 - 3)/(x^4 + 2*x^2 - 3), x)","F",0
118,0,0,0,1.005117," ","integrate((-x^2+3)/(-x^4-3*x^2+3)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} - 3 \, x^{2} + 3} {\left(x^{2} - 3\right)}}{x^{4} + 3 \, x^{2} - 3}, x\right)"," ",0,"integral(sqrt(-x^4 - 3*x^2 + 3)*(x^2 - 3)/(x^4 + 3*x^2 - 3), x)","F",0
119,0,0,0,1.703825," ","integrate((2*c*x^2-(-4*a*c+b^2)^(1/2)+b)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{2 \, c x^{2} + b - \sqrt{b^{2} - 4 \, a c}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((2*c*x^2 + b - sqrt(b^2 - 4*a*c))/sqrt(c*x^4 + b*x^2 + a), x)","F",0
120,1,98,0,0.868007," ","integrate((e*x^2+d)^4*(c*x^4+a),x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{4} c + \frac{4}{11} x^{11} e^{3} d c + \frac{2}{3} x^{9} e^{2} d^{2} c + \frac{1}{9} x^{9} e^{4} a + \frac{4}{7} x^{7} e d^{3} c + \frac{4}{7} x^{7} e^{3} d a + \frac{1}{5} x^{5} d^{4} c + \frac{6}{5} x^{5} e^{2} d^{2} a + \frac{4}{3} x^{3} e d^{3} a + x d^{4} a"," ",0,"1/13*x^13*e^4*c + 4/11*x^11*e^3*d*c + 2/3*x^9*e^2*d^2*c + 1/9*x^9*e^4*a + 4/7*x^7*e*d^3*c + 4/7*x^7*e^3*d*a + 1/5*x^5*d^4*c + 6/5*x^5*e^2*d^2*a + 4/3*x^3*e*d^3*a + x*d^4*a","A",0
121,1,73,0,0.872644," ","integrate((e*x^2+d)^3*(c*x^4+a),x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{3} c + \frac{1}{3} x^{9} e^{2} d c + \frac{3}{7} x^{7} e d^{2} c + \frac{1}{7} x^{7} e^{3} a + \frac{1}{5} x^{5} d^{3} c + \frac{3}{5} x^{5} e^{2} d a + x^{3} e d^{2} a + x d^{3} a"," ",0,"1/11*x^11*e^3*c + 1/3*x^9*e^2*d*c + 3/7*x^7*e*d^2*c + 1/7*x^7*e^3*a + 1/5*x^5*d^3*c + 3/5*x^5*e^2*d*a + x^3*e*d^2*a + x*d^3*a","A",0
122,1,50,0,0.570307," ","integrate((e*x^2+d)^2*(c*x^4+a),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{2} c + \frac{2}{7} x^{7} e d c + \frac{1}{5} x^{5} d^{2} c + \frac{1}{5} x^{5} e^{2} a + \frac{2}{3} x^{3} e d a + x d^{2} a"," ",0,"1/9*x^9*e^2*c + 2/7*x^7*e*d*c + 1/5*x^5*d^2*c + 1/5*x^5*e^2*a + 2/3*x^3*e*d*a + x*d^2*a","A",0
123,1,26,0,0.807352," ","integrate((e*x^2+d)*(c*x^4+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e c + \frac{1}{5} x^{5} d c + \frac{1}{3} x^{3} e a + x d a"," ",0,"1/7*x^7*e*c + 1/5*x^5*d*c + 1/3*x^3*e*a + x*d*a","A",0
124,1,131,0,1.106422," ","integrate((c*x^4+a)/(e*x^2+d),x, algorithm=""fricas"")","\left[\frac{2 \, c d e^{2} x^{3} - 6 \, c d^{2} e x - 3 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{6 \, d e^{3}}, \frac{c d e^{2} x^{3} - 3 \, c d^{2} e x + 3 \, {\left(c d^{2} + a e^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right)}{3 \, d e^{3}}\right]"," ",0,"[1/6*(2*c*d*e^2*x^3 - 6*c*d^2*e*x - 3*(c*d^2 + a*e^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(d*e^3), 1/3*(c*d*e^2*x^3 - 3*c*d^2*e*x + 3*(c*d^2 + a*e^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d))/(d*e^3)]","A",0
125,1,222,0,1.108802," ","integrate((c*x^4+a)/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c d^{2} e^{2} x^{3} + {\left(3 \, c d^{3} - a d e^{2} + {\left(3 \, c d^{2} e - a e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(3 \, c d^{3} e + a d e^{3}\right)} x}{4 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}, \frac{2 \, c d^{2} e^{2} x^{3} - {\left(3 \, c d^{3} - a d e^{2} + {\left(3 \, c d^{2} e - a e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(3 \, c d^{3} e + a d e^{3}\right)} x}{2 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}\right]"," ",0,"[1/4*(4*c*d^2*e^2*x^3 + (3*c*d^3 - a*d*e^2 + (3*c*d^2*e - a*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(3*c*d^3*e + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3), 1/2*(2*c*d^2*e^2*x^3 - (3*c*d^3 - a*d*e^2 + (3*c*d^2*e - a*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (3*c*d^3*e + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3)]","A",0
126,1,306,0,0.894192," ","integrate((c*x^4+a)/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, c d^{3} e^{2} - 3 \, a d e^{4}\right)} x^{3} + 3 \, {\left(c d^{4} + a d^{2} e^{2} + {\left(c d^{2} e^{2} + a e^{4}\right)} x^{4} + 2 \, {\left(c d^{3} e + a d e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(3 \, c d^{4} e - 5 \, a d^{2} e^{3}\right)} x}{16 \, {\left(d^{3} e^{5} x^{4} + 2 \, d^{4} e^{4} x^{2} + d^{5} e^{3}\right)}}, -\frac{{\left(5 \, c d^{3} e^{2} - 3 \, a d e^{4}\right)} x^{3} - 3 \, {\left(c d^{4} + a d^{2} e^{2} + {\left(c d^{2} e^{2} + a e^{4}\right)} x^{4} + 2 \, {\left(c d^{3} e + a d e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(3 \, c d^{4} e - 5 \, a d^{2} e^{3}\right)} x}{8 \, {\left(d^{3} e^{5} x^{4} + 2 \, d^{4} e^{4} x^{2} + d^{5} e^{3}\right)}}\right]"," ",0,"[-1/16*(2*(5*c*d^3*e^2 - 3*a*d*e^4)*x^3 + 3*(c*d^4 + a*d^2*e^2 + (c*d^2*e^2 + a*e^4)*x^4 + 2*(c*d^3*e + a*d*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(3*c*d^4*e - 5*a*d^2*e^3)*x)/(d^3*e^5*x^4 + 2*d^4*e^4*x^2 + d^5*e^3), -1/8*((5*c*d^3*e^2 - 3*a*d*e^4)*x^3 - 3*(c*d^4 + a*d^2*e^2 + (c*d^2*e^2 + a*e^4)*x^4 + 2*(c*d^3*e + a*d*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (3*c*d^4*e - 5*a*d^2*e^3)*x)/(d^3*e^5*x^4 + 2*d^4*e^4*x^2 + d^5*e^3)]","A",0
127,1,424,0,0.998561," ","integrate((c*x^4+a)/(e*x^2+d)^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(c d^{3} e^{3} + 5 \, a d e^{5}\right)} x^{5} - 16 \, {\left(c d^{4} e^{2} - 5 \, a d^{2} e^{4}\right)} x^{3} - 3 \, {\left({\left(c d^{2} e^{3} + 5 \, a e^{5}\right)} x^{6} + c d^{5} + 5 \, a d^{3} e^{2} + 3 \, {\left(c d^{3} e^{2} + 5 \, a d e^{4}\right)} x^{4} + 3 \, {\left(c d^{4} e + 5 \, a d^{2} e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 6 \, {\left(c d^{5} e - 11 \, a d^{3} e^{3}\right)} x}{96 \, {\left(d^{4} e^{6} x^{6} + 3 \, d^{5} e^{5} x^{4} + 3 \, d^{6} e^{4} x^{2} + d^{7} e^{3}\right)}}, \frac{3 \, {\left(c d^{3} e^{3} + 5 \, a d e^{5}\right)} x^{5} - 8 \, {\left(c d^{4} e^{2} - 5 \, a d^{2} e^{4}\right)} x^{3} + 3 \, {\left({\left(c d^{2} e^{3} + 5 \, a e^{5}\right)} x^{6} + c d^{5} + 5 \, a d^{3} e^{2} + 3 \, {\left(c d^{3} e^{2} + 5 \, a d e^{4}\right)} x^{4} + 3 \, {\left(c d^{4} e + 5 \, a d^{2} e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 3 \, {\left(c d^{5} e - 11 \, a d^{3} e^{3}\right)} x}{48 \, {\left(d^{4} e^{6} x^{6} + 3 \, d^{5} e^{5} x^{4} + 3 \, d^{6} e^{4} x^{2} + d^{7} e^{3}\right)}}\right]"," ",0,"[1/96*(6*(c*d^3*e^3 + 5*a*d*e^5)*x^5 - 16*(c*d^4*e^2 - 5*a*d^2*e^4)*x^3 - 3*((c*d^2*e^3 + 5*a*e^5)*x^6 + c*d^5 + 5*a*d^3*e^2 + 3*(c*d^3*e^2 + 5*a*d*e^4)*x^4 + 3*(c*d^4*e + 5*a*d^2*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 6*(c*d^5*e - 11*a*d^3*e^3)*x)/(d^4*e^6*x^6 + 3*d^5*e^5*x^4 + 3*d^6*e^4*x^2 + d^7*e^3), 1/48*(3*(c*d^3*e^3 + 5*a*d*e^5)*x^5 - 8*(c*d^4*e^2 - 5*a*d^2*e^4)*x^3 + 3*((c*d^2*e^3 + 5*a*e^5)*x^6 + c*d^5 + 5*a*d^3*e^2 + 3*(c*d^3*e^2 + 5*a*d*e^4)*x^4 + 3*(c*d^4*e + 5*a*d^2*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 3*(c*d^5*e - 11*a*d^3*e^3)*x)/(d^4*e^6*x^6 + 3*d^5*e^5*x^4 + 3*d^6*e^4*x^2 + d^7*e^3)]","A",0
128,1,131,0,0.786436," ","integrate((e*x^2+d)^3*(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{15} x^{15} e^{3} c^{2} + \frac{3}{13} x^{13} e^{2} d c^{2} + \frac{3}{11} x^{11} e d^{2} c^{2} + \frac{2}{11} x^{11} e^{3} c a + \frac{1}{9} x^{9} d^{3} c^{2} + \frac{2}{3} x^{9} e^{2} d c a + \frac{6}{7} x^{7} e d^{2} c a + \frac{1}{7} x^{7} e^{3} a^{2} + \frac{2}{5} x^{5} d^{3} c a + \frac{3}{5} x^{5} e^{2} d a^{2} + x^{3} e d^{2} a^{2} + x d^{3} a^{2}"," ",0,"1/15*x^15*e^3*c^2 + 3/13*x^13*e^2*d*c^2 + 3/11*x^11*e*d^2*c^2 + 2/11*x^11*e^3*c*a + 1/9*x^9*d^3*c^2 + 2/3*x^9*e^2*d*c*a + 6/7*x^7*e*d^2*c*a + 1/7*x^7*e^3*a^2 + 2/5*x^5*d^3*c*a + 3/5*x^5*e^2*d*a^2 + x^3*e*d^2*a^2 + x*d^3*a^2","A",0
129,1,91,0,0.750582," ","integrate((e*x^2+d)^2*(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{2} c^{2} + \frac{2}{11} x^{11} e d c^{2} + \frac{1}{9} x^{9} d^{2} c^{2} + \frac{2}{9} x^{9} e^{2} c a + \frac{4}{7} x^{7} e d c a + \frac{2}{5} x^{5} d^{2} c a + \frac{1}{5} x^{5} e^{2} a^{2} + \frac{2}{3} x^{3} e d a^{2} + x d^{2} a^{2}"," ",0,"1/13*x^13*e^2*c^2 + 2/11*x^11*e*d*c^2 + 1/9*x^9*d^2*c^2 + 2/9*x^9*e^2*c*a + 4/7*x^7*e*d*c*a + 2/5*x^5*d^2*c*a + 1/5*x^5*e^2*a^2 + 2/3*x^3*e*d*a^2 + x*d^2*a^2","A",0
130,1,50,0,1.273934," ","integrate((e*x^2+d)*(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e c^{2} + \frac{1}{9} x^{9} d c^{2} + \frac{2}{7} x^{7} e c a + \frac{2}{5} x^{5} d c a + \frac{1}{3} x^{3} e a^{2} + x d a^{2}"," ",0,"1/11*x^11*e*c^2 + 1/9*x^9*d*c^2 + 2/7*x^7*e*c*a + 2/5*x^5*d*c*a + 1/3*x^3*e*a^2 + x*d*a^2","A",0
131,1,21,0,0.369370," ","integrate((c*x^4+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{2} + \frac{2}{5} x^{5} c a + x a^{2}"," ",0,"1/9*x^9*c^2 + 2/5*x^5*c*a + x*a^2","A",0
132,1,268,0,1.268149," ","integrate((c*x^4+a)^2/(e*x^2+d),x, algorithm=""fricas"")","\left[\frac{30 \, c^{2} d e^{4} x^{7} - 42 \, c^{2} d^{2} e^{3} x^{5} + 70 \, {\left(c^{2} d^{3} e^{2} + 2 \, a c d e^{4}\right)} x^{3} - 105 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 210 \, {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3}\right)} x}{210 \, d e^{5}}, \frac{15 \, c^{2} d e^{4} x^{7} - 21 \, c^{2} d^{2} e^{3} x^{5} + 35 \, {\left(c^{2} d^{3} e^{2} + 2 \, a c d e^{4}\right)} x^{3} + 105 \, {\left(c^{2} d^{4} + 2 \, a c d^{2} e^{2} + a^{2} e^{4}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 105 \, {\left(c^{2} d^{4} e + 2 \, a c d^{2} e^{3}\right)} x}{105 \, d e^{5}}\right]"," ",0,"[1/210*(30*c^2*d*e^4*x^7 - 42*c^2*d^2*e^3*x^5 + 70*(c^2*d^3*e^2 + 2*a*c*d*e^4)*x^3 - 105*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 210*(c^2*d^4*e + 2*a*c*d^2*e^3)*x)/(d*e^5), 1/105*(15*c^2*d*e^4*x^7 - 21*c^2*d^2*e^3*x^5 + 35*(c^2*d^3*e^2 + 2*a*c*d*e^4)*x^3 + 105*(c^2*d^4 + 2*a*c*d^2*e^2 + a^2*e^4)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 105*(c^2*d^4*e + 2*a*c*d^2*e^3)*x)/(d*e^5)]","A",0
133,1,394,0,1.602309," ","integrate((c*x^4+a)^2/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{12 \, c^{2} d^{2} e^{4} x^{7} - 28 \, c^{2} d^{3} e^{3} x^{5} + 20 \, {\left(7 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4}\right)} x^{3} + 15 \, {\left(7 \, c^{2} d^{5} + 6 \, a c d^{3} e^{2} - a^{2} d e^{4} + {\left(7 \, c^{2} d^{4} e + 6 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 30 \, {\left(7 \, c^{2} d^{5} e + 6 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x}{60 \, {\left(d^{2} e^{6} x^{2} + d^{3} e^{5}\right)}}, \frac{6 \, c^{2} d^{2} e^{4} x^{7} - 14 \, c^{2} d^{3} e^{3} x^{5} + 10 \, {\left(7 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4}\right)} x^{3} - 15 \, {\left(7 \, c^{2} d^{5} + 6 \, a c d^{3} e^{2} - a^{2} d e^{4} + {\left(7 \, c^{2} d^{4} e + 6 \, a c d^{2} e^{3} - a^{2} e^{5}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + 15 \, {\left(7 \, c^{2} d^{5} e + 6 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x}{30 \, {\left(d^{2} e^{6} x^{2} + d^{3} e^{5}\right)}}\right]"," ",0,"[1/60*(12*c^2*d^2*e^4*x^7 - 28*c^2*d^3*e^3*x^5 + 20*(7*c^2*d^4*e^2 + 6*a*c*d^2*e^4)*x^3 + 15*(7*c^2*d^5 + 6*a*c*d^3*e^2 - a^2*d*e^4 + (7*c^2*d^4*e + 6*a*c*d^2*e^3 - a^2*e^5)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 30*(7*c^2*d^5*e + 6*a*c*d^3*e^3 + a^2*d*e^5)*x)/(d^2*e^6*x^2 + d^3*e^5), 1/30*(6*c^2*d^2*e^4*x^7 - 14*c^2*d^3*e^3*x^5 + 10*(7*c^2*d^4*e^2 + 6*a*c*d^2*e^4)*x^3 - 15*(7*c^2*d^5 + 6*a*c*d^3*e^2 - a^2*d*e^4 + (7*c^2*d^4*e + 6*a*c*d^2*e^3 - a^2*e^5)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + 15*(7*c^2*d^5*e + 6*a*c*d^3*e^3 + a^2*d*e^5)*x)/(d^2*e^6*x^2 + d^3*e^5)]","A",0
134,1,516,0,0.884797," ","integrate((c*x^4+a)^2/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[\frac{16 \, c^{2} d^{3} e^{4} x^{7} - 112 \, c^{2} d^{4} e^{3} x^{5} - 2 \, {\left(175 \, c^{2} d^{5} e^{2} + 30 \, a c d^{3} e^{4} - 9 \, a^{2} d e^{6}\right)} x^{3} - 3 \, {\left(35 \, c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 3 \, a^{2} d^{2} e^{4} + {\left(35 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + 3 \, a^{2} e^{6}\right)} x^{4} + 2 \, {\left(35 \, c^{2} d^{5} e + 6 \, a c d^{3} e^{3} + 3 \, a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 6 \, {\left(35 \, c^{2} d^{6} e + 6 \, a c d^{4} e^{3} - 5 \, a^{2} d^{2} e^{5}\right)} x}{48 \, {\left(d^{3} e^{7} x^{4} + 2 \, d^{4} e^{6} x^{2} + d^{5} e^{5}\right)}}, \frac{8 \, c^{2} d^{3} e^{4} x^{7} - 56 \, c^{2} d^{4} e^{3} x^{5} - {\left(175 \, c^{2} d^{5} e^{2} + 30 \, a c d^{3} e^{4} - 9 \, a^{2} d e^{6}\right)} x^{3} + 3 \, {\left(35 \, c^{2} d^{6} + 6 \, a c d^{4} e^{2} + 3 \, a^{2} d^{2} e^{4} + {\left(35 \, c^{2} d^{4} e^{2} + 6 \, a c d^{2} e^{4} + 3 \, a^{2} e^{6}\right)} x^{4} + 2 \, {\left(35 \, c^{2} d^{5} e + 6 \, a c d^{3} e^{3} + 3 \, a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 3 \, {\left(35 \, c^{2} d^{6} e + 6 \, a c d^{4} e^{3} - 5 \, a^{2} d^{2} e^{5}\right)} x}{24 \, {\left(d^{3} e^{7} x^{4} + 2 \, d^{4} e^{6} x^{2} + d^{5} e^{5}\right)}}\right]"," ",0,"[1/48*(16*c^2*d^3*e^4*x^7 - 112*c^2*d^4*e^3*x^5 - 2*(175*c^2*d^5*e^2 + 30*a*c*d^3*e^4 - 9*a^2*d*e^6)*x^3 - 3*(35*c^2*d^6 + 6*a*c*d^4*e^2 + 3*a^2*d^2*e^4 + (35*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + 3*a^2*e^6)*x^4 + 2*(35*c^2*d^5*e + 6*a*c*d^3*e^3 + 3*a^2*d*e^5)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 6*(35*c^2*d^6*e + 6*a*c*d^4*e^3 - 5*a^2*d^2*e^5)*x)/(d^3*e^7*x^4 + 2*d^4*e^6*x^2 + d^5*e^5), 1/24*(8*c^2*d^3*e^4*x^7 - 56*c^2*d^4*e^3*x^5 - (175*c^2*d^5*e^2 + 30*a*c*d^3*e^4 - 9*a^2*d*e^6)*x^3 + 3*(35*c^2*d^6 + 6*a*c*d^4*e^2 + 3*a^2*d^2*e^4 + (35*c^2*d^4*e^2 + 6*a*c*d^2*e^4 + 3*a^2*e^6)*x^4 + 2*(35*c^2*d^5*e + 6*a*c*d^3*e^3 + 3*a^2*d*e^5)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 3*(35*c^2*d^6*e + 6*a*c*d^4*e^3 - 5*a^2*d^2*e^5)*x)/(d^3*e^7*x^4 + 2*d^4*e^6*x^2 + d^5*e^5)]","A",0
135,1,662,0,0.868123," ","integrate((c*x^4+a)^2/(e*x^2+d)^4,x, algorithm=""fricas"")","\left[\frac{96 \, c^{2} d^{4} e^{4} x^{7} + 6 \, {\left(77 \, c^{2} d^{5} e^{3} + 2 \, a c d^{3} e^{5} + 5 \, a^{2} d e^{7}\right)} x^{5} + 16 \, {\left(35 \, c^{2} d^{6} e^{2} - 2 \, a c d^{4} e^{4} + 5 \, a^{2} d^{2} e^{6}\right)} x^{3} + 3 \, {\left(35 \, c^{2} d^{7} - 2 \, a c d^{5} e^{2} - 5 \, a^{2} d^{3} e^{4} + {\left(35 \, c^{2} d^{4} e^{3} - 2 \, a c d^{2} e^{5} - 5 \, a^{2} e^{7}\right)} x^{6} + 3 \, {\left(35 \, c^{2} d^{5} e^{2} - 2 \, a c d^{3} e^{4} - 5 \, a^{2} d e^{6}\right)} x^{4} + 3 \, {\left(35 \, c^{2} d^{6} e - 2 \, a c d^{4} e^{3} - 5 \, a^{2} d^{2} e^{5}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 6 \, {\left(35 \, c^{2} d^{7} e - 2 \, a c d^{5} e^{3} + 11 \, a^{2} d^{3} e^{5}\right)} x}{96 \, {\left(d^{4} e^{8} x^{6} + 3 \, d^{5} e^{7} x^{4} + 3 \, d^{6} e^{6} x^{2} + d^{7} e^{5}\right)}}, \frac{48 \, c^{2} d^{4} e^{4} x^{7} + 3 \, {\left(77 \, c^{2} d^{5} e^{3} + 2 \, a c d^{3} e^{5} + 5 \, a^{2} d e^{7}\right)} x^{5} + 8 \, {\left(35 \, c^{2} d^{6} e^{2} - 2 \, a c d^{4} e^{4} + 5 \, a^{2} d^{2} e^{6}\right)} x^{3} - 3 \, {\left(35 \, c^{2} d^{7} - 2 \, a c d^{5} e^{2} - 5 \, a^{2} d^{3} e^{4} + {\left(35 \, c^{2} d^{4} e^{3} - 2 \, a c d^{2} e^{5} - 5 \, a^{2} e^{7}\right)} x^{6} + 3 \, {\left(35 \, c^{2} d^{5} e^{2} - 2 \, a c d^{3} e^{4} - 5 \, a^{2} d e^{6}\right)} x^{4} + 3 \, {\left(35 \, c^{2} d^{6} e - 2 \, a c d^{4} e^{3} - 5 \, a^{2} d^{2} e^{5}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + 3 \, {\left(35 \, c^{2} d^{7} e - 2 \, a c d^{5} e^{3} + 11 \, a^{2} d^{3} e^{5}\right)} x}{48 \, {\left(d^{4} e^{8} x^{6} + 3 \, d^{5} e^{7} x^{4} + 3 \, d^{6} e^{6} x^{2} + d^{7} e^{5}\right)}}\right]"," ",0,"[1/96*(96*c^2*d^4*e^4*x^7 + 6*(77*c^2*d^5*e^3 + 2*a*c*d^3*e^5 + 5*a^2*d*e^7)*x^5 + 16*(35*c^2*d^6*e^2 - 2*a*c*d^4*e^4 + 5*a^2*d^2*e^6)*x^3 + 3*(35*c^2*d^7 - 2*a*c*d^5*e^2 - 5*a^2*d^3*e^4 + (35*c^2*d^4*e^3 - 2*a*c*d^2*e^5 - 5*a^2*e^7)*x^6 + 3*(35*c^2*d^5*e^2 - 2*a*c*d^3*e^4 - 5*a^2*d*e^6)*x^4 + 3*(35*c^2*d^6*e - 2*a*c*d^4*e^3 - 5*a^2*d^2*e^5)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 6*(35*c^2*d^7*e - 2*a*c*d^5*e^3 + 11*a^2*d^3*e^5)*x)/(d^4*e^8*x^6 + 3*d^5*e^7*x^4 + 3*d^6*e^6*x^2 + d^7*e^5), 1/48*(48*c^2*d^4*e^4*x^7 + 3*(77*c^2*d^5*e^3 + 2*a*c*d^3*e^5 + 5*a^2*d*e^7)*x^5 + 8*(35*c^2*d^6*e^2 - 2*a*c*d^4*e^4 + 5*a^2*d^2*e^6)*x^3 - 3*(35*c^2*d^7 - 2*a*c*d^5*e^2 - 5*a^2*d^3*e^4 + (35*c^2*d^4*e^3 - 2*a*c*d^2*e^5 - 5*a^2*e^7)*x^6 + 3*(35*c^2*d^5*e^2 - 2*a*c*d^3*e^4 - 5*a^2*d*e^6)*x^4 + 3*(35*c^2*d^6*e - 2*a*c*d^4*e^3 - 5*a^2*d^2*e^5)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + 3*(35*c^2*d^7*e - 2*a*c*d^5*e^3 + 11*a^2*d^3*e^5)*x)/(d^4*e^8*x^6 + 3*d^5*e^7*x^4 + 3*d^6*e^6*x^2 + d^7*e^5)]","A",0
136,1,806,0,0.958171," ","integrate((c*x^4+a)^2/(e*x^2+d)^5,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(93 \, c^{2} d^{5} e^{4} - 6 \, a c d^{3} e^{6} - 35 \, a^{2} d e^{8}\right)} x^{7} + 2 \, {\left(511 \, c^{2} d^{6} e^{3} - 66 \, a c d^{4} e^{5} - 385 \, a^{2} d^{2} e^{7}\right)} x^{5} + 2 \, {\left(385 \, c^{2} d^{7} e^{2} + 66 \, a c d^{5} e^{4} - 511 \, a^{2} d^{3} e^{6}\right)} x^{3} + 3 \, {\left(35 \, c^{2} d^{8} + 6 \, a c d^{6} e^{2} + 35 \, a^{2} d^{4} e^{4} + {\left(35 \, c^{2} d^{4} e^{4} + 6 \, a c d^{2} e^{6} + 35 \, a^{2} e^{8}\right)} x^{8} + 4 \, {\left(35 \, c^{2} d^{5} e^{3} + 6 \, a c d^{3} e^{5} + 35 \, a^{2} d e^{7}\right)} x^{6} + 6 \, {\left(35 \, c^{2} d^{6} e^{2} + 6 \, a c d^{4} e^{4} + 35 \, a^{2} d^{2} e^{6}\right)} x^{4} + 4 \, {\left(35 \, c^{2} d^{7} e + 6 \, a c d^{5} e^{3} + 35 \, a^{2} d^{3} e^{5}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 6 \, {\left(35 \, c^{2} d^{8} e + 6 \, a c d^{6} e^{3} - 93 \, a^{2} d^{4} e^{5}\right)} x}{768 \, {\left(d^{5} e^{9} x^{8} + 4 \, d^{6} e^{8} x^{6} + 6 \, d^{7} e^{7} x^{4} + 4 \, d^{8} e^{6} x^{2} + d^{9} e^{5}\right)}}, -\frac{3 \, {\left(93 \, c^{2} d^{5} e^{4} - 6 \, a c d^{3} e^{6} - 35 \, a^{2} d e^{8}\right)} x^{7} + {\left(511 \, c^{2} d^{6} e^{3} - 66 \, a c d^{4} e^{5} - 385 \, a^{2} d^{2} e^{7}\right)} x^{5} + {\left(385 \, c^{2} d^{7} e^{2} + 66 \, a c d^{5} e^{4} - 511 \, a^{2} d^{3} e^{6}\right)} x^{3} - 3 \, {\left(35 \, c^{2} d^{8} + 6 \, a c d^{6} e^{2} + 35 \, a^{2} d^{4} e^{4} + {\left(35 \, c^{2} d^{4} e^{4} + 6 \, a c d^{2} e^{6} + 35 \, a^{2} e^{8}\right)} x^{8} + 4 \, {\left(35 \, c^{2} d^{5} e^{3} + 6 \, a c d^{3} e^{5} + 35 \, a^{2} d e^{7}\right)} x^{6} + 6 \, {\left(35 \, c^{2} d^{6} e^{2} + 6 \, a c d^{4} e^{4} + 35 \, a^{2} d^{2} e^{6}\right)} x^{4} + 4 \, {\left(35 \, c^{2} d^{7} e + 6 \, a c d^{5} e^{3} + 35 \, a^{2} d^{3} e^{5}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + 3 \, {\left(35 \, c^{2} d^{8} e + 6 \, a c d^{6} e^{3} - 93 \, a^{2} d^{4} e^{5}\right)} x}{384 \, {\left(d^{5} e^{9} x^{8} + 4 \, d^{6} e^{8} x^{6} + 6 \, d^{7} e^{7} x^{4} + 4 \, d^{8} e^{6} x^{2} + d^{9} e^{5}\right)}}\right]"," ",0,"[-1/768*(6*(93*c^2*d^5*e^4 - 6*a*c*d^3*e^6 - 35*a^2*d*e^8)*x^7 + 2*(511*c^2*d^6*e^3 - 66*a*c*d^4*e^5 - 385*a^2*d^2*e^7)*x^5 + 2*(385*c^2*d^7*e^2 + 66*a*c*d^5*e^4 - 511*a^2*d^3*e^6)*x^3 + 3*(35*c^2*d^8 + 6*a*c*d^6*e^2 + 35*a^2*d^4*e^4 + (35*c^2*d^4*e^4 + 6*a*c*d^2*e^6 + 35*a^2*e^8)*x^8 + 4*(35*c^2*d^5*e^3 + 6*a*c*d^3*e^5 + 35*a^2*d*e^7)*x^6 + 6*(35*c^2*d^6*e^2 + 6*a*c*d^4*e^4 + 35*a^2*d^2*e^6)*x^4 + 4*(35*c^2*d^7*e + 6*a*c*d^5*e^3 + 35*a^2*d^3*e^5)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 6*(35*c^2*d^8*e + 6*a*c*d^6*e^3 - 93*a^2*d^4*e^5)*x)/(d^5*e^9*x^8 + 4*d^6*e^8*x^6 + 6*d^7*e^7*x^4 + 4*d^8*e^6*x^2 + d^9*e^5), -1/384*(3*(93*c^2*d^5*e^4 - 6*a*c*d^3*e^6 - 35*a^2*d*e^8)*x^7 + (511*c^2*d^6*e^3 - 66*a*c*d^4*e^5 - 385*a^2*d^2*e^7)*x^5 + (385*c^2*d^7*e^2 + 66*a*c*d^5*e^4 - 511*a^2*d^3*e^6)*x^3 - 3*(35*c^2*d^8 + 6*a*c*d^6*e^2 + 35*a^2*d^4*e^4 + (35*c^2*d^4*e^4 + 6*a*c*d^2*e^6 + 35*a^2*e^8)*x^8 + 4*(35*c^2*d^5*e^3 + 6*a*c*d^3*e^5 + 35*a^2*d*e^7)*x^6 + 6*(35*c^2*d^6*e^2 + 6*a*c*d^4*e^4 + 35*a^2*d^2*e^6)*x^4 + 4*(35*c^2*d^7*e + 6*a*c*d^5*e^3 + 35*a^2*d^3*e^5)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + 3*(35*c^2*d^8*e + 6*a*c*d^6*e^3 - 93*a^2*d^4*e^5)*x)/(d^5*e^9*x^8 + 4*d^6*e^8*x^6 + 6*d^7*e^7*x^4 + 4*d^8*e^6*x^2 + d^9*e^5)]","A",0
137,1,2878,0,11.044736," ","integrate((e*x^2+d)^4/(c*x^4+a),x, algorithm=""fricas"")","\frac{12 \, c e^{4} x^{5} + 80 \, c d e^{3} x^{3} + 15 \, c^{2} \sqrt{-\frac{8 \, c^{3} d^{7} e - 56 \, a c^{2} d^{5} e^{3} + 56 \, a^{2} c d^{3} e^{5} - 8 \, a^{3} d e^{7} + a c^{4} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}}{a c^{4}}} \log\left({\left(c^{8} d^{16} - 24 \, a c^{7} d^{14} e^{2} - 36 \, a^{2} c^{6} d^{12} e^{4} + 88 \, a^{3} c^{5} d^{10} e^{6} + 198 \, a^{4} c^{4} d^{8} e^{8} + 88 \, a^{5} c^{3} d^{6} e^{10} - 36 \, a^{6} c^{2} d^{4} e^{12} - 24 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}\right)} x + {\left(a c^{8} d^{12} - 34 \, a^{2} c^{7} d^{10} e^{2} + 239 \, a^{3} c^{6} d^{8} e^{4} - 476 \, a^{4} c^{5} d^{6} e^{6} + 239 \, a^{5} c^{4} d^{4} e^{8} - 34 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12} + 4 \, {\left(a^{3} c^{8} d^{3} e - a^{4} c^{7} d e^{3}\right)} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}\right)} \sqrt{-\frac{8 \, c^{3} d^{7} e - 56 \, a c^{2} d^{5} e^{3} + 56 \, a^{2} c d^{3} e^{5} - 8 \, a^{3} d e^{7} + a c^{4} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}}{a c^{4}}}\right) - 15 \, c^{2} \sqrt{-\frac{8 \, c^{3} d^{7} e - 56 \, a c^{2} d^{5} e^{3} + 56 \, a^{2} c d^{3} e^{5} - 8 \, a^{3} d e^{7} + a c^{4} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}}{a c^{4}}} \log\left({\left(c^{8} d^{16} - 24 \, a c^{7} d^{14} e^{2} - 36 \, a^{2} c^{6} d^{12} e^{4} + 88 \, a^{3} c^{5} d^{10} e^{6} + 198 \, a^{4} c^{4} d^{8} e^{8} + 88 \, a^{5} c^{3} d^{6} e^{10} - 36 \, a^{6} c^{2} d^{4} e^{12} - 24 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}\right)} x - {\left(a c^{8} d^{12} - 34 \, a^{2} c^{7} d^{10} e^{2} + 239 \, a^{3} c^{6} d^{8} e^{4} - 476 \, a^{4} c^{5} d^{6} e^{6} + 239 \, a^{5} c^{4} d^{4} e^{8} - 34 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12} + 4 \, {\left(a^{3} c^{8} d^{3} e - a^{4} c^{7} d e^{3}\right)} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}\right)} \sqrt{-\frac{8 \, c^{3} d^{7} e - 56 \, a c^{2} d^{5} e^{3} + 56 \, a^{2} c d^{3} e^{5} - 8 \, a^{3} d e^{7} + a c^{4} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}}{a c^{4}}}\right) + 15 \, c^{2} \sqrt{-\frac{8 \, c^{3} d^{7} e - 56 \, a c^{2} d^{5} e^{3} + 56 \, a^{2} c d^{3} e^{5} - 8 \, a^{3} d e^{7} - a c^{4} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}}{a c^{4}}} \log\left({\left(c^{8} d^{16} - 24 \, a c^{7} d^{14} e^{2} - 36 \, a^{2} c^{6} d^{12} e^{4} + 88 \, a^{3} c^{5} d^{10} e^{6} + 198 \, a^{4} c^{4} d^{8} e^{8} + 88 \, a^{5} c^{3} d^{6} e^{10} - 36 \, a^{6} c^{2} d^{4} e^{12} - 24 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}\right)} x + {\left(a c^{8} d^{12} - 34 \, a^{2} c^{7} d^{10} e^{2} + 239 \, a^{3} c^{6} d^{8} e^{4} - 476 \, a^{4} c^{5} d^{6} e^{6} + 239 \, a^{5} c^{4} d^{4} e^{8} - 34 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12} - 4 \, {\left(a^{3} c^{8} d^{3} e - a^{4} c^{7} d e^{3}\right)} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}\right)} \sqrt{-\frac{8 \, c^{3} d^{7} e - 56 \, a c^{2} d^{5} e^{3} + 56 \, a^{2} c d^{3} e^{5} - 8 \, a^{3} d e^{7} - a c^{4} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}}{a c^{4}}}\right) - 15 \, c^{2} \sqrt{-\frac{8 \, c^{3} d^{7} e - 56 \, a c^{2} d^{5} e^{3} + 56 \, a^{2} c d^{3} e^{5} - 8 \, a^{3} d e^{7} - a c^{4} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}}{a c^{4}}} \log\left({\left(c^{8} d^{16} - 24 \, a c^{7} d^{14} e^{2} - 36 \, a^{2} c^{6} d^{12} e^{4} + 88 \, a^{3} c^{5} d^{10} e^{6} + 198 \, a^{4} c^{4} d^{8} e^{8} + 88 \, a^{5} c^{3} d^{6} e^{10} - 36 \, a^{6} c^{2} d^{4} e^{12} - 24 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}\right)} x - {\left(a c^{8} d^{12} - 34 \, a^{2} c^{7} d^{10} e^{2} + 239 \, a^{3} c^{6} d^{8} e^{4} - 476 \, a^{4} c^{5} d^{6} e^{6} + 239 \, a^{5} c^{4} d^{4} e^{8} - 34 \, a^{6} c^{3} d^{2} e^{10} + a^{7} c^{2} e^{12} - 4 \, {\left(a^{3} c^{8} d^{3} e - a^{4} c^{7} d e^{3}\right)} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}\right)} \sqrt{-\frac{8 \, c^{3} d^{7} e - 56 \, a c^{2} d^{5} e^{3} + 56 \, a^{2} c d^{3} e^{5} - 8 \, a^{3} d e^{7} - a c^{4} \sqrt{-\frac{c^{8} d^{16} - 56 \, a c^{7} d^{14} e^{2} + 924 \, a^{2} c^{6} d^{12} e^{4} - 3976 \, a^{3} c^{5} d^{10} e^{6} + 6470 \, a^{4} c^{4} d^{8} e^{8} - 3976 \, a^{5} c^{3} d^{6} e^{10} + 924 \, a^{6} c^{2} d^{4} e^{12} - 56 \, a^{7} c d^{2} e^{14} + a^{8} e^{16}}{a^{3} c^{9}}}}{a c^{4}}}\right) + 60 \, {\left(6 \, c d^{2} e^{2} - a e^{4}\right)} x}{60 \, c^{2}}"," ",0,"1/60*(12*c*e^4*x^5 + 80*c*d*e^3*x^3 + 15*c^2*sqrt(-(8*c^3*d^7*e - 56*a*c^2*d^5*e^3 + 56*a^2*c*d^3*e^5 - 8*a^3*d*e^7 + a*c^4*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))/(a*c^4))*log((c^8*d^16 - 24*a*c^7*d^14*e^2 - 36*a^2*c^6*d^12*e^4 + 88*a^3*c^5*d^10*e^6 + 198*a^4*c^4*d^8*e^8 + 88*a^5*c^3*d^6*e^10 - 36*a^6*c^2*d^4*e^12 - 24*a^7*c*d^2*e^14 + a^8*e^16)*x + (a*c^8*d^12 - 34*a^2*c^7*d^10*e^2 + 239*a^3*c^6*d^8*e^4 - 476*a^4*c^5*d^6*e^6 + 239*a^5*c^4*d^4*e^8 - 34*a^6*c^3*d^2*e^10 + a^7*c^2*e^12 + 4*(a^3*c^8*d^3*e - a^4*c^7*d*e^3)*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))*sqrt(-(8*c^3*d^7*e - 56*a*c^2*d^5*e^3 + 56*a^2*c*d^3*e^5 - 8*a^3*d*e^7 + a*c^4*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))/(a*c^4))) - 15*c^2*sqrt(-(8*c^3*d^7*e - 56*a*c^2*d^5*e^3 + 56*a^2*c*d^3*e^5 - 8*a^3*d*e^7 + a*c^4*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))/(a*c^4))*log((c^8*d^16 - 24*a*c^7*d^14*e^2 - 36*a^2*c^6*d^12*e^4 + 88*a^3*c^5*d^10*e^6 + 198*a^4*c^4*d^8*e^8 + 88*a^5*c^3*d^6*e^10 - 36*a^6*c^2*d^4*e^12 - 24*a^7*c*d^2*e^14 + a^8*e^16)*x - (a*c^8*d^12 - 34*a^2*c^7*d^10*e^2 + 239*a^3*c^6*d^8*e^4 - 476*a^4*c^5*d^6*e^6 + 239*a^5*c^4*d^4*e^8 - 34*a^6*c^3*d^2*e^10 + a^7*c^2*e^12 + 4*(a^3*c^8*d^3*e - a^4*c^7*d*e^3)*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))*sqrt(-(8*c^3*d^7*e - 56*a*c^2*d^5*e^3 + 56*a^2*c*d^3*e^5 - 8*a^3*d*e^7 + a*c^4*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))/(a*c^4))) + 15*c^2*sqrt(-(8*c^3*d^7*e - 56*a*c^2*d^5*e^3 + 56*a^2*c*d^3*e^5 - 8*a^3*d*e^7 - a*c^4*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))/(a*c^4))*log((c^8*d^16 - 24*a*c^7*d^14*e^2 - 36*a^2*c^6*d^12*e^4 + 88*a^3*c^5*d^10*e^6 + 198*a^4*c^4*d^8*e^8 + 88*a^5*c^3*d^6*e^10 - 36*a^6*c^2*d^4*e^12 - 24*a^7*c*d^2*e^14 + a^8*e^16)*x + (a*c^8*d^12 - 34*a^2*c^7*d^10*e^2 + 239*a^3*c^6*d^8*e^4 - 476*a^4*c^5*d^6*e^6 + 239*a^5*c^4*d^4*e^8 - 34*a^6*c^3*d^2*e^10 + a^7*c^2*e^12 - 4*(a^3*c^8*d^3*e - a^4*c^7*d*e^3)*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))*sqrt(-(8*c^3*d^7*e - 56*a*c^2*d^5*e^3 + 56*a^2*c*d^3*e^5 - 8*a^3*d*e^7 - a*c^4*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))/(a*c^4))) - 15*c^2*sqrt(-(8*c^3*d^7*e - 56*a*c^2*d^5*e^3 + 56*a^2*c*d^3*e^5 - 8*a^3*d*e^7 - a*c^4*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))/(a*c^4))*log((c^8*d^16 - 24*a*c^7*d^14*e^2 - 36*a^2*c^6*d^12*e^4 + 88*a^3*c^5*d^10*e^6 + 198*a^4*c^4*d^8*e^8 + 88*a^5*c^3*d^6*e^10 - 36*a^6*c^2*d^4*e^12 - 24*a^7*c*d^2*e^14 + a^8*e^16)*x - (a*c^8*d^12 - 34*a^2*c^7*d^10*e^2 + 239*a^3*c^6*d^8*e^4 - 476*a^4*c^5*d^6*e^6 + 239*a^5*c^4*d^4*e^8 - 34*a^6*c^3*d^2*e^10 + a^7*c^2*e^12 - 4*(a^3*c^8*d^3*e - a^4*c^7*d*e^3)*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))*sqrt(-(8*c^3*d^7*e - 56*a*c^2*d^5*e^3 + 56*a^2*c*d^3*e^5 - 8*a^3*d*e^7 - a*c^4*sqrt(-(c^8*d^16 - 56*a*c^7*d^14*e^2 + 924*a^2*c^6*d^12*e^4 - 3976*a^3*c^5*d^10*e^6 + 6470*a^4*c^4*d^8*e^8 - 3976*a^5*c^3*d^6*e^10 + 924*a^6*c^2*d^4*e^12 - 56*a^7*c*d^2*e^14 + a^8*e^16)/(a^3*c^9)))/(a*c^4))) + 60*(6*c*d^2*e^2 - a*e^4)*x)/c^2","B",0
138,1,2133,0,2.980026," ","integrate((e*x^2+d)^3/(c*x^4+a),x, algorithm=""fricas"")","\frac{4 \, e^{3} x^{3} + 36 \, d e^{2} x - 3 \, c \sqrt{-\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + a c^{3} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}}{a c^{3}}} \log\left(-{\left(c^{6} d^{12} - 12 \, a c^{5} d^{10} e^{2} - 27 \, a^{2} c^{4} d^{8} e^{4} + 27 \, a^{4} c^{2} d^{4} e^{8} + 12 \, a^{5} c d^{2} e^{10} - a^{6} e^{12}\right)} x + {\left(a c^{6} d^{9} - 18 \, a^{2} c^{5} d^{7} e^{2} + 60 \, a^{3} c^{4} d^{5} e^{4} - 46 \, a^{4} c^{3} d^{3} e^{6} + 3 \, a^{5} c^{2} d e^{8} + {\left(3 \, a^{3} c^{6} d^{2} e - a^{4} c^{5} e^{3}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}\right)} \sqrt{-\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + a c^{3} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}}{a c^{3}}}\right) + 3 \, c \sqrt{-\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + a c^{3} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}}{a c^{3}}} \log\left(-{\left(c^{6} d^{12} - 12 \, a c^{5} d^{10} e^{2} - 27 \, a^{2} c^{4} d^{8} e^{4} + 27 \, a^{4} c^{2} d^{4} e^{8} + 12 \, a^{5} c d^{2} e^{10} - a^{6} e^{12}\right)} x - {\left(a c^{6} d^{9} - 18 \, a^{2} c^{5} d^{7} e^{2} + 60 \, a^{3} c^{4} d^{5} e^{4} - 46 \, a^{4} c^{3} d^{3} e^{6} + 3 \, a^{5} c^{2} d e^{8} + {\left(3 \, a^{3} c^{6} d^{2} e - a^{4} c^{5} e^{3}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}\right)} \sqrt{-\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} + a c^{3} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}}{a c^{3}}}\right) - 3 \, c \sqrt{-\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - a c^{3} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}}{a c^{3}}} \log\left(-{\left(c^{6} d^{12} - 12 \, a c^{5} d^{10} e^{2} - 27 \, a^{2} c^{4} d^{8} e^{4} + 27 \, a^{4} c^{2} d^{4} e^{8} + 12 \, a^{5} c d^{2} e^{10} - a^{6} e^{12}\right)} x + {\left(a c^{6} d^{9} - 18 \, a^{2} c^{5} d^{7} e^{2} + 60 \, a^{3} c^{4} d^{5} e^{4} - 46 \, a^{4} c^{3} d^{3} e^{6} + 3 \, a^{5} c^{2} d e^{8} - {\left(3 \, a^{3} c^{6} d^{2} e - a^{4} c^{5} e^{3}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}\right)} \sqrt{-\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - a c^{3} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}}{a c^{3}}}\right) + 3 \, c \sqrt{-\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - a c^{3} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}}{a c^{3}}} \log\left(-{\left(c^{6} d^{12} - 12 \, a c^{5} d^{10} e^{2} - 27 \, a^{2} c^{4} d^{8} e^{4} + 27 \, a^{4} c^{2} d^{4} e^{8} + 12 \, a^{5} c d^{2} e^{10} - a^{6} e^{12}\right)} x - {\left(a c^{6} d^{9} - 18 \, a^{2} c^{5} d^{7} e^{2} + 60 \, a^{3} c^{4} d^{5} e^{4} - 46 \, a^{4} c^{3} d^{3} e^{6} + 3 \, a^{5} c^{2} d e^{8} - {\left(3 \, a^{3} c^{6} d^{2} e - a^{4} c^{5} e^{3}\right)} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}\right)} \sqrt{-\frac{6 \, c^{2} d^{5} e - 20 \, a c d^{3} e^{3} + 6 \, a^{2} d e^{5} - a c^{3} \sqrt{-\frac{c^{6} d^{12} - 30 \, a c^{5} d^{10} e^{2} + 255 \, a^{2} c^{4} d^{8} e^{4} - 452 \, a^{3} c^{3} d^{6} e^{6} + 255 \, a^{4} c^{2} d^{4} e^{8} - 30 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{3} c^{7}}}}{a c^{3}}}\right)}{12 \, c}"," ",0,"1/12*(4*e^3*x^3 + 36*d*e^2*x - 3*c*sqrt(-(6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + a*c^3*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))/(a*c^3))*log(-(c^6*d^12 - 12*a*c^5*d^10*e^2 - 27*a^2*c^4*d^8*e^4 + 27*a^4*c^2*d^4*e^8 + 12*a^5*c*d^2*e^10 - a^6*e^12)*x + (a*c^6*d^9 - 18*a^2*c^5*d^7*e^2 + 60*a^3*c^4*d^5*e^4 - 46*a^4*c^3*d^3*e^6 + 3*a^5*c^2*d*e^8 + (3*a^3*c^6*d^2*e - a^4*c^5*e^3)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))*sqrt(-(6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + a*c^3*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))/(a*c^3))) + 3*c*sqrt(-(6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + a*c^3*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))/(a*c^3))*log(-(c^6*d^12 - 12*a*c^5*d^10*e^2 - 27*a^2*c^4*d^8*e^4 + 27*a^4*c^2*d^4*e^8 + 12*a^5*c*d^2*e^10 - a^6*e^12)*x - (a*c^6*d^9 - 18*a^2*c^5*d^7*e^2 + 60*a^3*c^4*d^5*e^4 - 46*a^4*c^3*d^3*e^6 + 3*a^5*c^2*d*e^8 + (3*a^3*c^6*d^2*e - a^4*c^5*e^3)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))*sqrt(-(6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 + a*c^3*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))/(a*c^3))) - 3*c*sqrt(-(6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - a*c^3*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))/(a*c^3))*log(-(c^6*d^12 - 12*a*c^5*d^10*e^2 - 27*a^2*c^4*d^8*e^4 + 27*a^4*c^2*d^4*e^8 + 12*a^5*c*d^2*e^10 - a^6*e^12)*x + (a*c^6*d^9 - 18*a^2*c^5*d^7*e^2 + 60*a^3*c^4*d^5*e^4 - 46*a^4*c^3*d^3*e^6 + 3*a^5*c^2*d*e^8 - (3*a^3*c^6*d^2*e - a^4*c^5*e^3)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))*sqrt(-(6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - a*c^3*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))/(a*c^3))) + 3*c*sqrt(-(6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - a*c^3*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))/(a*c^3))*log(-(c^6*d^12 - 12*a*c^5*d^10*e^2 - 27*a^2*c^4*d^8*e^4 + 27*a^4*c^2*d^4*e^8 + 12*a^5*c*d^2*e^10 - a^6*e^12)*x - (a*c^6*d^9 - 18*a^2*c^5*d^7*e^2 + 60*a^3*c^4*d^5*e^4 - 46*a^4*c^3*d^3*e^6 + 3*a^5*c^2*d*e^8 - (3*a^3*c^6*d^2*e - a^4*c^5*e^3)*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))*sqrt(-(6*c^2*d^5*e - 20*a*c*d^3*e^3 + 6*a^2*d*e^5 - a*c^3*sqrt(-(c^6*d^12 - 30*a*c^5*d^10*e^2 + 255*a^2*c^4*d^8*e^4 - 452*a^3*c^3*d^6*e^6 + 255*a^4*c^2*d^4*e^8 - 30*a^5*c*d^2*e^10 + a^6*e^12)/(a^3*c^7)))/(a*c^3))))/c","B",0
139,1,1480,0,1.361540," ","integrate((e*x^2+d)^2/(c*x^4+a),x, algorithm=""fricas"")","\frac{4 \, e^{2} x + c \sqrt{-\frac{4 \, c d^{3} e - 4 \, a d e^{3} + a 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^{3} c^{5}}}}{a c^{2}}} \log\left({\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 + {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} + 2 \, a^{3} 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^{3} c^{5}}}\right)} \sqrt{-\frac{4 \, c d^{3} e - 4 \, a d e^{3} + a 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^{3} c^{5}}}}{a c^{2}}}\right) - c \sqrt{-\frac{4 \, c d^{3} e - 4 \, a d e^{3} + a 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^{3} c^{5}}}}{a c^{2}}} \log\left({\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 - {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} + 2 \, a^{3} 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^{3} c^{5}}}\right)} \sqrt{-\frac{4 \, c d^{3} e - 4 \, a d e^{3} + a 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^{3} c^{5}}}}{a c^{2}}}\right) + c \sqrt{-\frac{4 \, c d^{3} e - 4 \, a d e^{3} - a 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^{3} c^{5}}}}{a c^{2}}} \log\left({\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 + {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} - 2 \, a^{3} 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^{3} c^{5}}}\right)} \sqrt{-\frac{4 \, c d^{3} e - 4 \, a d e^{3} - a 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^{3} c^{5}}}}{a c^{2}}}\right) - c \sqrt{-\frac{4 \, c d^{3} e - 4 \, a d e^{3} - a 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^{3} c^{5}}}}{a c^{2}}} \log\left({\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 - {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} - 2 \, a^{3} 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^{3} c^{5}}}\right)} \sqrt{-\frac{4 \, c d^{3} e - 4 \, a d e^{3} - a 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^{3} c^{5}}}}{a c^{2}}}\right)}{4 \, c}"," ",0,"1/4*(4*e^2*x + c*sqrt(-(4*c*d^3*e - 4*a*d*e^3 + a*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^3*c^5)))/(a*c^2))*log((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 + (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 + 2*a^3*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^3*c^5)))*sqrt(-(4*c*d^3*e - 4*a*d*e^3 + a*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^3*c^5)))/(a*c^2))) - c*sqrt(-(4*c*d^3*e - 4*a*d*e^3 + a*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^3*c^5)))/(a*c^2))*log((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 - (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 + 2*a^3*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^3*c^5)))*sqrt(-(4*c*d^3*e - 4*a*d*e^3 + a*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^3*c^5)))/(a*c^2))) + c*sqrt(-(4*c*d^3*e - 4*a*d*e^3 - a*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^3*c^5)))/(a*c^2))*log((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 + (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 - 2*a^3*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^3*c^5)))*sqrt(-(4*c*d^3*e - 4*a*d*e^3 - a*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^3*c^5)))/(a*c^2))) - c*sqrt(-(4*c*d^3*e - 4*a*d*e^3 - a*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^3*c^5)))/(a*c^2))*log((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 - (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 - 2*a^3*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^3*c^5)))*sqrt(-(4*c*d^3*e - 4*a*d*e^3 - a*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^3*c^5)))/(a*c^2))))/c","B",0
140,1,767,0,0.982117," ","integrate((e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-\frac{a c \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} + 2 \, d e}{a c}} \log\left(-{\left(c^{2} d^{4} - a^{2} e^{4}\right)} x + {\left(a^{3} c^{2} e \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} + a c^{2} d^{3} - a^{2} c d e^{2}\right)} \sqrt{-\frac{a c \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} + 2 \, d e}{a c}}\right) + \frac{1}{4} \, \sqrt{-\frac{a c \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} + 2 \, d e}{a c}} \log\left(-{\left(c^{2} d^{4} - a^{2} e^{4}\right)} x - {\left(a^{3} c^{2} e \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} + a c^{2} d^{3} - a^{2} c d e^{2}\right)} \sqrt{-\frac{a c \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} + 2 \, d e}{a c}}\right) + \frac{1}{4} \, \sqrt{\frac{a c \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} - 2 \, d e}{a c}} \log\left(-{\left(c^{2} d^{4} - a^{2} e^{4}\right)} x + {\left(a^{3} c^{2} e \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} - a c^{2} d^{3} + a^{2} c d e^{2}\right)} \sqrt{\frac{a c \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} - 2 \, d e}{a c}}\right) - \frac{1}{4} \, \sqrt{\frac{a c \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} - 2 \, d e}{a c}} \log\left(-{\left(c^{2} d^{4} - a^{2} e^{4}\right)} x - {\left(a^{3} c^{2} e \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} - a c^{2} d^{3} + a^{2} c d e^{2}\right)} \sqrt{\frac{a c \sqrt{-\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{3} c^{3}}} - 2 \, d e}{a c}}\right)"," ",0,"-1/4*sqrt(-(a*c*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) + 2*d*e)/(a*c))*log(-(c^2*d^4 - a^2*e^4)*x + (a^3*c^2*e*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) + a*c^2*d^3 - a^2*c*d*e^2)*sqrt(-(a*c*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) + 2*d*e)/(a*c))) + 1/4*sqrt(-(a*c*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) + 2*d*e)/(a*c))*log(-(c^2*d^4 - a^2*e^4)*x - (a^3*c^2*e*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) + a*c^2*d^3 - a^2*c*d*e^2)*sqrt(-(a*c*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) + 2*d*e)/(a*c))) + 1/4*sqrt((a*c*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) - 2*d*e)/(a*c))*log(-(c^2*d^4 - a^2*e^4)*x + (a^3*c^2*e*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) - a*c^2*d^3 + a^2*c*d*e^2)*sqrt((a*c*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) - 2*d*e)/(a*c))) - 1/4*sqrt((a*c*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) - 2*d*e)/(a*c))*log(-(c^2*d^4 - a^2*e^4)*x - (a^3*c^2*e*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) - a*c^2*d^3 + a^2*c*d*e^2)*sqrt((a*c*sqrt(-(c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^3*c^3)) - 2*d*e)/(a*c)))","B",0
141,1,121,0,1.759237," ","integrate(1/(c*x^4+a),x, algorithm=""fricas"")","\left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \arctan\left(-a^{2} c x \left(-\frac{1}{a^{3} c}\right)^{\frac{3}{4}} + \sqrt{a^{2} \sqrt{-\frac{1}{a^{3} c}} + x^{2}} a^{2} c \left(-\frac{1}{a^{3} c}\right)^{\frac{3}{4}}\right) + \frac{1}{4} \, \left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \log\left(a \left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} + x\right) - \frac{1}{4} \, \left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} \log\left(-a \left(-\frac{1}{a^{3} c}\right)^{\frac{1}{4}} + x\right)"," ",0,"(-1/(a^3*c))^(1/4)*arctan(-a^2*c*x*(-1/(a^3*c))^(3/4) + sqrt(a^2*sqrt(-1/(a^3*c)) + x^2)*a^2*c*(-1/(a^3*c))^(3/4)) + 1/4*(-1/(a^3*c))^(1/4)*log(a*(-1/(a^3*c))^(1/4) + x) - 1/4*(-1/(a^3*c))^(1/4)*log(-a*(-1/(a^3*c))^(1/4) + x)","A",0
142,1,4084,0,2.563640," ","integrate(1/(e*x^2+d)/(c*x^4+a),x, algorithm=""fricas"")","\left[-\frac{{\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x + {\left(a c^{2} d^{3} - a^{2} c d e^{2} + {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x - {\left(a c^{2} d^{3} - a^{2} c d e^{2} + {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x + {\left(a c^{2} d^{3} - a^{2} c d e^{2} - {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x - {\left(a c^{2} d^{3} - a^{2} c d e^{2} - {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) - 2 \, e \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}, \frac{4 \, e \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x + {\left(a c^{2} d^{3} - a^{2} c d e^{2} + {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x - {\left(a c^{2} d^{3} - a^{2} c d e^{2} + {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e + {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) - {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x + {\left(a c^{2} d^{3} - a^{2} c d e^{2} - {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right) + {\left(c d^{2} + a e^{2}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}} \log\left(-{\left(c^{2} d^{2} - a c e^{2}\right)} x - {\left(a c^{2} d^{3} - a^{2} c d e^{2} - {\left(a^{3} c^{2} d^{4} e + 2 \, a^{4} c d^{2} e^{3} + a^{5} e^{5}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right)} \sqrt{\frac{2 \, c d e - {\left(a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}\right)} \sqrt{-\frac{c^{3} d^{4} - 2 \, a c^{2} d^{2} e^{2} + a^{2} c e^{4}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}}{a c^{2} d^{4} + 2 \, a^{2} c d^{2} e^{2} + a^{3} e^{4}}}\right)}{4 \, {\left(c d^{2} + a e^{2}\right)}}\right]"," ",0,"[-1/4*((c*d^2 + a*e^2)*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x + (a*c^2*d^3 - a^2*c*d*e^2 + (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) - (c*d^2 + a*e^2)*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x - (a*c^2*d^3 - a^2*c*d*e^2 + (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) + (c*d^2 + a*e^2)*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x + (a*c^2*d^3 - a^2*c*d*e^2 - (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) - (c*d^2 + a*e^2)*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x - (a*c^2*d^3 - a^2*c*d*e^2 - (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) - 2*e*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)))/(c*d^2 + a*e^2), 1/4*(4*e*sqrt(e/d)*arctan(x*sqrt(e/d)) - (c*d^2 + a*e^2)*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x + (a*c^2*d^3 - a^2*c*d*e^2 + (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) + (c*d^2 + a*e^2)*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x - (a*c^2*d^3 - a^2*c*d*e^2 + (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e + (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) - (c*d^2 + a*e^2)*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x + (a*c^2*d^3 - a^2*c*d*e^2 - (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))) + (c*d^2 + a*e^2)*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))*log(-(c^2*d^2 - a*c*e^2)*x - (a*c^2*d^3 - a^2*c*d*e^2 - (a^3*c^2*d^4*e + 2*a^4*c*d^2*e^3 + a^5*e^5)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))*sqrt((2*c*d*e - (a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4)*sqrt(-(c^3*d^4 - 2*a*c^2*d^2*e^2 + a^2*c*e^4)/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)))/(a*c^2*d^4 + 2*a^2*c*d^2*e^2 + a^3*e^4))))/(c*d^2 + a*e^2)]","B",0
143,1,8409,0,42.204865," ","integrate(1/(e*x^2+d)^2/(c*x^4+a),x, algorithm=""fricas"")","\left[\frac{{\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}} \log\left({\left(c^{4} d^{4} - 6 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x + {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} + 2 \, {\left(a^{3} c^{4} d^{9} e + 4 \, a^{4} c^{3} d^{7} e^{3} + 6 \, a^{5} c^{2} d^{5} e^{5} + 4 \, a^{6} c d^{3} e^{7} + a^{7} d e^{9}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}}\right) - {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}} \log\left({\left(c^{4} d^{4} - 6 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x - {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} + 2 \, {\left(a^{3} c^{4} d^{9} e + 4 \, a^{4} c^{3} d^{7} e^{3} + 6 \, a^{5} c^{2} d^{5} e^{5} + 4 \, a^{6} c d^{3} e^{7} + a^{7} d e^{9}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}}\right) + {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}} \log\left({\left(c^{4} d^{4} - 6 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x + {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} - 2 \, {\left(a^{3} c^{4} d^{9} e + 4 \, a^{4} c^{3} d^{7} e^{3} + 6 \, a^{5} c^{2} d^{5} e^{5} + 4 \, a^{6} c d^{3} e^{7} + a^{7} d e^{9}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}}\right) - {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}} \log\left({\left(c^{4} d^{4} - 6 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x - {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} - 2 \, {\left(a^{3} c^{4} d^{9} e + 4 \, a^{4} c^{3} d^{7} e^{3} + 6 \, a^{5} c^{2} d^{5} e^{5} + 4 \, a^{6} c d^{3} e^{7} + a^{7} d e^{9}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}}\right) + {\left(5 \, c d^{3} e + a d e^{3} + {\left(5 \, c d^{2} e^{2} + a e^{4}\right)} x^{2}\right)} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) + 2 \, {\left(c d^{2} e^{2} + a e^{4}\right)} x}{4 \, {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)}}, \frac{2 \, {\left(5 \, c d^{3} e + a d e^{3} + {\left(5 \, c d^{2} e^{2} + a e^{4}\right)} x^{2}\right)} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) + {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}} \log\left({\left(c^{4} d^{4} - 6 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x + {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} + 2 \, {\left(a^{3} c^{4} d^{9} e + 4 \, a^{4} c^{3} d^{7} e^{3} + 6 \, a^{5} c^{2} d^{5} e^{5} + 4 \, a^{6} c d^{3} e^{7} + a^{7} d e^{9}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}}\right) - {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}} \log\left({\left(c^{4} d^{4} - 6 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x - {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} + 2 \, {\left(a^{3} c^{4} d^{9} e + 4 \, a^{4} c^{3} d^{7} e^{3} + 6 \, a^{5} c^{2} d^{5} e^{5} + 4 \, a^{6} c d^{3} e^{7} + a^{7} d e^{9}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} + {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}}\right) + {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}} \log\left({\left(c^{4} d^{4} - 6 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x + {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} - 2 \, {\left(a^{3} c^{4} d^{9} e + 4 \, a^{4} c^{3} d^{7} e^{3} + 6 \, a^{5} c^{2} d^{5} e^{5} + 4 \, a^{6} c d^{3} e^{7} + a^{7} d e^{9}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}}\right) - {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}} \log\left({\left(c^{4} d^{4} - 6 \, a c^{3} d^{2} e^{2} + a^{2} c^{2} e^{4}\right)} x - {\left(a c^{4} d^{6} - 7 \, a^{2} c^{3} d^{4} e^{2} + 7 \, a^{3} c^{2} d^{2} e^{4} - a^{4} c e^{6} - 2 \, {\left(a^{3} c^{4} d^{9} e + 4 \, a^{4} c^{3} d^{7} e^{3} + 6 \, a^{5} c^{2} d^{5} e^{5} + 4 \, a^{6} c d^{3} e^{7} + a^{7} d e^{9}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}\right)} \sqrt{\frac{4 \, c^{3} d^{3} e - 4 \, a c^{2} d e^{3} - {\left(a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}\right)} \sqrt{-\frac{c^{7} d^{8} - 12 \, a c^{6} d^{6} e^{2} + 38 \, a^{2} c^{5} d^{4} e^{4} - 12 \, a^{3} c^{4} d^{2} e^{6} + a^{4} c^{3} e^{8}}{a^{3} c^{8} d^{16} + 8 \, a^{4} c^{7} d^{14} e^{2} + 28 \, a^{5} c^{6} d^{12} e^{4} + 56 \, a^{6} c^{5} d^{10} e^{6} + 70 \, a^{7} c^{4} d^{8} e^{8} + 56 \, a^{8} c^{3} d^{6} e^{10} + 28 \, a^{9} c^{2} d^{4} e^{12} + 8 \, a^{10} c d^{2} e^{14} + a^{11} e^{16}}}}{a c^{4} d^{8} + 4 \, a^{2} c^{3} d^{6} e^{2} + 6 \, a^{3} c^{2} d^{4} e^{4} + 4 \, a^{4} c d^{2} e^{6} + a^{5} e^{8}}}\right) + 2 \, {\left(c d^{2} e^{2} + a e^{4}\right)} x}{4 \, {\left(c^{2} d^{6} + 2 \, a c d^{4} e^{2} + a^{2} d^{2} e^{4} + {\left(c^{2} d^{5} e + 2 \, a c d^{3} e^{3} + a^{2} d e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*((c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))*log((c^4*d^4 - 6*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x + (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 + 2*(a^3*c^4*d^9*e + 4*a^4*c^3*d^7*e^3 + 6*a^5*c^2*d^5*e^5 + 4*a^6*c*d^3*e^7 + a^7*d*e^9)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))) - (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))*log((c^4*d^4 - 6*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x - (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 + 2*(a^3*c^4*d^9*e + 4*a^4*c^3*d^7*e^3 + 6*a^5*c^2*d^5*e^5 + 4*a^6*c*d^3*e^7 + a^7*d*e^9)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))) + (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))*log((c^4*d^4 - 6*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x + (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 - 2*(a^3*c^4*d^9*e + 4*a^4*c^3*d^7*e^3 + 6*a^5*c^2*d^5*e^5 + 4*a^6*c*d^3*e^7 + a^7*d*e^9)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))) - (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))*log((c^4*d^4 - 6*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x - (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 - 2*(a^3*c^4*d^9*e + 4*a^4*c^3*d^7*e^3 + 6*a^5*c^2*d^5*e^5 + 4*a^6*c*d^3*e^7 + a^7*d*e^9)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))) + (5*c*d^3*e + a*d*e^3 + (5*c*d^2*e^2 + a*e^4)*x^2)*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) + 2*(c*d^2*e^2 + a*e^4)*x)/(c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2), 1/4*(2*(5*c*d^3*e + a*d*e^3 + (5*c*d^2*e^2 + a*e^4)*x^2)*sqrt(e/d)*arctan(x*sqrt(e/d)) + (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))*log((c^4*d^4 - 6*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x + (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 + 2*(a^3*c^4*d^9*e + 4*a^4*c^3*d^7*e^3 + 6*a^5*c^2*d^5*e^5 + 4*a^6*c*d^3*e^7 + a^7*d*e^9)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))) - (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))*log((c^4*d^4 - 6*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x - (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 + 2*(a^3*c^4*d^9*e + 4*a^4*c^3*d^7*e^3 + 6*a^5*c^2*d^5*e^5 + 4*a^6*c*d^3*e^7 + a^7*d*e^9)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 + (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))) + (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))*log((c^4*d^4 - 6*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x + (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 - 2*(a^3*c^4*d^9*e + 4*a^4*c^3*d^7*e^3 + 6*a^5*c^2*d^5*e^5 + 4*a^6*c*d^3*e^7 + a^7*d*e^9)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))) - (c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))*log((c^4*d^4 - 6*a*c^3*d^2*e^2 + a^2*c^2*e^4)*x - (a*c^4*d^6 - 7*a^2*c^3*d^4*e^2 + 7*a^3*c^2*d^2*e^4 - a^4*c*e^6 - 2*(a^3*c^4*d^9*e + 4*a^4*c^3*d^7*e^3 + 6*a^5*c^2*d^5*e^5 + 4*a^6*c*d^3*e^7 + a^7*d*e^9)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))*sqrt((4*c^3*d^3*e - 4*a*c^2*d*e^3 - (a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8)*sqrt(-(c^7*d^8 - 12*a*c^6*d^6*e^2 + 38*a^2*c^5*d^4*e^4 - 12*a^3*c^4*d^2*e^6 + a^4*c^3*e^8)/(a^3*c^8*d^16 + 8*a^4*c^7*d^14*e^2 + 28*a^5*c^6*d^12*e^4 + 56*a^6*c^5*d^10*e^6 + 70*a^7*c^4*d^8*e^8 + 56*a^8*c^3*d^6*e^10 + 28*a^9*c^2*d^4*e^12 + 8*a^10*c*d^2*e^14 + a^11*e^16)))/(a*c^4*d^8 + 4*a^2*c^3*d^6*e^2 + 6*a^3*c^2*d^4*e^4 + 4*a^4*c*d^2*e^6 + a^5*e^8))) + 2*(c*d^2*e^2 + a*e^4)*x)/(c^2*d^6 + 2*a*c*d^4*e^2 + a^2*d^2*e^4 + (c^2*d^5*e + 2*a*c*d^3*e^3 + a^2*d*e^5)*x^2)]","B",0
144,1,2116,0,1.132469," ","integrate((e*x^2+d)^3/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{4 \, {\left(3 \, c d^{2} e - a e^{3}\right)} x^{3} - 3 \, {\left(a c^{2} x^{4} + a^{2} c\right)} \sqrt{-\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5} + a^{3} c^{3} \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}}{a^{3} c^{3}}} \log\left(-27 \, {\left(c^{5} d^{10} + 3 \, a c^{4} d^{8} e^{2} + 2 \, a^{2} c^{3} d^{6} e^{4} - 2 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} x + 27 \, {\left(a^{2} c^{5} d^{7} + a^{3} c^{4} d^{5} e^{2} - a^{4} c^{3} d^{3} e^{4} - a^{5} c^{2} d e^{6} + a^{6} c^{5} e \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}\right)} \sqrt{-\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5} + a^{3} c^{3} \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}}{a^{3} c^{3}}}\right) + 3 \, {\left(a c^{2} x^{4} + a^{2} c\right)} \sqrt{-\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5} + a^{3} c^{3} \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}}{a^{3} c^{3}}} \log\left(-27 \, {\left(c^{5} d^{10} + 3 \, a c^{4} d^{8} e^{2} + 2 \, a^{2} c^{3} d^{6} e^{4} - 2 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} x - 27 \, {\left(a^{2} c^{5} d^{7} + a^{3} c^{4} d^{5} e^{2} - a^{4} c^{3} d^{3} e^{4} - a^{5} c^{2} d e^{6} + a^{6} c^{5} e \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}\right)} \sqrt{-\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5} + a^{3} c^{3} \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}}{a^{3} c^{3}}}\right) - 3 \, {\left(a c^{2} x^{4} + a^{2} c\right)} \sqrt{-\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5} - a^{3} c^{3} \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}}{a^{3} c^{3}}} \log\left(-27 \, {\left(c^{5} d^{10} + 3 \, a c^{4} d^{8} e^{2} + 2 \, a^{2} c^{3} d^{6} e^{4} - 2 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} x + 27 \, {\left(a^{2} c^{5} d^{7} + a^{3} c^{4} d^{5} e^{2} - a^{4} c^{3} d^{3} e^{4} - a^{5} c^{2} d e^{6} - a^{6} c^{5} e \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}\right)} \sqrt{-\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5} - a^{3} c^{3} \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}}{a^{3} c^{3}}}\right) + 3 \, {\left(a c^{2} x^{4} + a^{2} c\right)} \sqrt{-\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5} - a^{3} c^{3} \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}}{a^{3} c^{3}}} \log\left(-27 \, {\left(c^{5} d^{10} + 3 \, a c^{4} d^{8} e^{2} + 2 \, a^{2} c^{3} d^{6} e^{4} - 2 \, a^{3} c^{2} d^{4} e^{6} - 3 \, a^{4} c d^{2} e^{8} - a^{5} e^{10}\right)} x - 27 \, {\left(a^{2} c^{5} d^{7} + a^{3} c^{4} d^{5} e^{2} - a^{4} c^{3} d^{3} e^{4} - a^{5} c^{2} d e^{6} - a^{6} c^{5} e \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}\right)} \sqrt{-\frac{2 \, c^{2} d^{5} e + 4 \, a c d^{3} e^{3} + 2 \, a^{2} d e^{5} - a^{3} c^{3} \sqrt{-\frac{c^{6} d^{12} + 2 \, a c^{5} d^{10} e^{2} - a^{2} c^{4} d^{8} e^{4} - 4 \, a^{3} c^{3} d^{6} e^{6} - a^{4} c^{2} d^{4} e^{8} + 2 \, a^{5} c d^{2} e^{10} + a^{6} e^{12}}{a^{7} c^{7}}}}{a^{3} c^{3}}}\right) + 4 \, {\left(c d^{3} - 3 \, a d e^{2}\right)} x}{16 \, {\left(a c^{2} x^{4} + a^{2} c\right)}}"," ",0,"1/16*(4*(3*c*d^2*e - a*e^3)*x^3 - 3*(a*c^2*x^4 + a^2*c)*sqrt(-(2*c^2*d^5*e + 4*a*c*d^3*e^3 + 2*a^2*d*e^5 + a^3*c^3*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))/(a^3*c^3))*log(-27*(c^5*d^10 + 3*a*c^4*d^8*e^2 + 2*a^2*c^3*d^6*e^4 - 2*a^3*c^2*d^4*e^6 - 3*a^4*c*d^2*e^8 - a^5*e^10)*x + 27*(a^2*c^5*d^7 + a^3*c^4*d^5*e^2 - a^4*c^3*d^3*e^4 - a^5*c^2*d*e^6 + a^6*c^5*e*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))*sqrt(-(2*c^2*d^5*e + 4*a*c*d^3*e^3 + 2*a^2*d*e^5 + a^3*c^3*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))/(a^3*c^3))) + 3*(a*c^2*x^4 + a^2*c)*sqrt(-(2*c^2*d^5*e + 4*a*c*d^3*e^3 + 2*a^2*d*e^5 + a^3*c^3*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))/(a^3*c^3))*log(-27*(c^5*d^10 + 3*a*c^4*d^8*e^2 + 2*a^2*c^3*d^6*e^4 - 2*a^3*c^2*d^4*e^6 - 3*a^4*c*d^2*e^8 - a^5*e^10)*x - 27*(a^2*c^5*d^7 + a^3*c^4*d^5*e^2 - a^4*c^3*d^3*e^4 - a^5*c^2*d*e^6 + a^6*c^5*e*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))*sqrt(-(2*c^2*d^5*e + 4*a*c*d^3*e^3 + 2*a^2*d*e^5 + a^3*c^3*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))/(a^3*c^3))) - 3*(a*c^2*x^4 + a^2*c)*sqrt(-(2*c^2*d^5*e + 4*a*c*d^3*e^3 + 2*a^2*d*e^5 - a^3*c^3*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))/(a^3*c^3))*log(-27*(c^5*d^10 + 3*a*c^4*d^8*e^2 + 2*a^2*c^3*d^6*e^4 - 2*a^3*c^2*d^4*e^6 - 3*a^4*c*d^2*e^8 - a^5*e^10)*x + 27*(a^2*c^5*d^7 + a^3*c^4*d^5*e^2 - a^4*c^3*d^3*e^4 - a^5*c^2*d*e^6 - a^6*c^5*e*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))*sqrt(-(2*c^2*d^5*e + 4*a*c*d^3*e^3 + 2*a^2*d*e^5 - a^3*c^3*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))/(a^3*c^3))) + 3*(a*c^2*x^4 + a^2*c)*sqrt(-(2*c^2*d^5*e + 4*a*c*d^3*e^3 + 2*a^2*d*e^5 - a^3*c^3*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))/(a^3*c^3))*log(-27*(c^5*d^10 + 3*a*c^4*d^8*e^2 + 2*a^2*c^3*d^6*e^4 - 2*a^3*c^2*d^4*e^6 - 3*a^4*c*d^2*e^8 - a^5*e^10)*x - 27*(a^2*c^5*d^7 + a^3*c^4*d^5*e^2 - a^4*c^3*d^3*e^4 - a^5*c^2*d*e^6 - a^6*c^5*e*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))*sqrt(-(2*c^2*d^5*e + 4*a*c*d^3*e^3 + 2*a^2*d*e^5 - a^3*c^3*sqrt(-(c^6*d^12 + 2*a*c^5*d^10*e^2 - a^2*c^4*d^8*e^4 - 4*a^3*c^3*d^6*e^6 - a^4*c^2*d^4*e^8 + 2*a^5*c*d^2*e^10 + a^6*e^12)/(a^7*c^7)))/(a^3*c^3))) + 4*(c*d^3 - 3*a*d*e^2)*x)/(a*c^2*x^4 + a^2*c)","B",0
145,1,1596,0,1.773293," ","integrate((e*x^2+d)^2/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{8 \, c d e x^{3} + {\left(a c^{2} x^{4} + a^{2} c\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 12 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}} \log\left({\left(81 \, c^{4} d^{8} + 108 \, 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}\right)} x + {\left(2 \, a^{6} c^{4} d e \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 27 \, a^{2} c^{4} d^{6} + 15 \, a^{3} c^{3} d^{4} e^{2} + 5 \, a^{4} c^{2} d^{2} e^{4} + a^{5} c e^{6}\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 12 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}}\right) - {\left(a c^{2} x^{4} + a^{2} c\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 12 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}} \log\left({\left(81 \, c^{4} d^{8} + 108 \, 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}\right)} x - {\left(2 \, a^{6} c^{4} d e \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 27 \, a^{2} c^{4} d^{6} + 15 \, a^{3} c^{3} d^{4} e^{2} + 5 \, a^{4} c^{2} d^{2} e^{4} + a^{5} c e^{6}\right)} \sqrt{-\frac{a^{3} c^{2} \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} + 12 \, c d^{3} e + 4 \, a d e^{3}}{a^{3} c^{2}}}\right) - {\left(a c^{2} x^{4} + a^{2} c\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 12 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}} \log\left({\left(81 \, c^{4} d^{8} + 108 \, 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}\right)} x + {\left(2 \, a^{6} c^{4} d e \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 27 \, a^{2} c^{4} d^{6} - 15 \, a^{3} c^{3} d^{4} e^{2} - 5 \, a^{4} c^{2} d^{2} e^{4} - a^{5} c e^{6}\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 12 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}}\right) + {\left(a c^{2} x^{4} + a^{2} c\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 12 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}} \log\left({\left(81 \, c^{4} d^{8} + 108 \, 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}\right)} x - {\left(2 \, a^{6} c^{4} d e \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 27 \, a^{2} c^{4} d^{6} - 15 \, a^{3} c^{3} d^{4} e^{2} - 5 \, a^{4} c^{2} d^{2} e^{4} - a^{5} c e^{6}\right)} \sqrt{\frac{a^{3} c^{2} \sqrt{-\frac{81 \, c^{4} d^{8} + 36 \, a c^{3} d^{6} e^{2} + 22 \, a^{2} c^{2} d^{4} e^{4} + 4 \, a^{3} c d^{2} e^{6} + a^{4} e^{8}}{a^{7} c^{5}}} - 12 \, c d^{3} e - 4 \, a d e^{3}}{a^{3} c^{2}}}\right) + 4 \, {\left(c d^{2} - a e^{2}\right)} x}{16 \, {\left(a c^{2} x^{4} + a^{2} c\right)}}"," ",0,"1/16*(8*c*d*e*x^3 + (a*c^2*x^4 + a^2*c)*sqrt(-(a^3*c^2*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 12*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))*log((81*c^4*d^8 + 108*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)*x + (2*a^6*c^4*d*e*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 27*a^2*c^4*d^6 + 15*a^3*c^3*d^4*e^2 + 5*a^4*c^2*d^2*e^4 + a^5*c*e^6)*sqrt(-(a^3*c^2*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 12*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))) - (a*c^2*x^4 + a^2*c)*sqrt(-(a^3*c^2*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 12*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))*log((81*c^4*d^8 + 108*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)*x - (2*a^6*c^4*d*e*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 27*a^2*c^4*d^6 + 15*a^3*c^3*d^4*e^2 + 5*a^4*c^2*d^2*e^4 + a^5*c*e^6)*sqrt(-(a^3*c^2*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) + 12*c*d^3*e + 4*a*d*e^3)/(a^3*c^2))) - (a*c^2*x^4 + a^2*c)*sqrt((a^3*c^2*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 12*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))*log((81*c^4*d^8 + 108*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)*x + (2*a^6*c^4*d*e*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 27*a^2*c^4*d^6 - 15*a^3*c^3*d^4*e^2 - 5*a^4*c^2*d^2*e^4 - a^5*c*e^6)*sqrt((a^3*c^2*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 12*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))) + (a*c^2*x^4 + a^2*c)*sqrt((a^3*c^2*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 12*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))*log((81*c^4*d^8 + 108*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)*x - (2*a^6*c^4*d*e*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 27*a^2*c^4*d^6 - 15*a^3*c^3*d^4*e^2 - 5*a^4*c^2*d^2*e^4 - a^5*c*e^6)*sqrt((a^3*c^2*sqrt(-(81*c^4*d^8 + 36*a*c^3*d^6*e^2 + 22*a^2*c^2*d^4*e^4 + 4*a^3*c*d^2*e^6 + a^4*e^8)/(a^7*c^5)) - 12*c*d^3*e - 4*a*d*e^3)/(a^3*c^2))) + 4*(c*d^2 - a*e^2)*x)/(a*c^2*x^4 + a^2*c)","B",0
146,1,873,0,1.102875," ","integrate((e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{4 \, e x^{3} - {\left(a c x^{4} + a^{2}\right)} \sqrt{-\frac{a^{3} c \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} + 6 \, d e}{a^{3} c}} \log\left(-{\left(81 \, c^{2} d^{4} - a^{2} e^{4}\right)} x + {\left(a^{6} c^{2} e \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} + 27 \, a^{2} c^{2} d^{3} - 3 \, a^{3} c d e^{2}\right)} \sqrt{-\frac{a^{3} c \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} + 6 \, d e}{a^{3} c}}\right) + {\left(a c x^{4} + a^{2}\right)} \sqrt{-\frac{a^{3} c \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} + 6 \, d e}{a^{3} c}} \log\left(-{\left(81 \, c^{2} d^{4} - a^{2} e^{4}\right)} x - {\left(a^{6} c^{2} e \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} + 27 \, a^{2} c^{2} d^{3} - 3 \, a^{3} c d e^{2}\right)} \sqrt{-\frac{a^{3} c \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} + 6 \, d e}{a^{3} c}}\right) + {\left(a c x^{4} + a^{2}\right)} \sqrt{\frac{a^{3} c \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} - 6 \, d e}{a^{3} c}} \log\left(-{\left(81 \, c^{2} d^{4} - a^{2} e^{4}\right)} x + {\left(a^{6} c^{2} e \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} - 27 \, a^{2} c^{2} d^{3} + 3 \, a^{3} c d e^{2}\right)} \sqrt{\frac{a^{3} c \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} - 6 \, d e}{a^{3} c}}\right) - {\left(a c x^{4} + a^{2}\right)} \sqrt{\frac{a^{3} c \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} - 6 \, d e}{a^{3} c}} \log\left(-{\left(81 \, c^{2} d^{4} - a^{2} e^{4}\right)} x - {\left(a^{6} c^{2} e \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} - 27 \, a^{2} c^{2} d^{3} + 3 \, a^{3} c d e^{2}\right)} \sqrt{\frac{a^{3} c \sqrt{-\frac{81 \, c^{2} d^{4} - 18 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{7} c^{3}}} - 6 \, d e}{a^{3} c}}\right) + 4 \, d x}{16 \, {\left(a c x^{4} + a^{2}\right)}}"," ",0,"1/16*(4*e*x^3 - (a*c*x^4 + a^2)*sqrt(-(a^3*c*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) + 6*d*e)/(a^3*c))*log(-(81*c^2*d^4 - a^2*e^4)*x + (a^6*c^2*e*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) + 27*a^2*c^2*d^3 - 3*a^3*c*d*e^2)*sqrt(-(a^3*c*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) + 6*d*e)/(a^3*c))) + (a*c*x^4 + a^2)*sqrt(-(a^3*c*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) + 6*d*e)/(a^3*c))*log(-(81*c^2*d^4 - a^2*e^4)*x - (a^6*c^2*e*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) + 27*a^2*c^2*d^3 - 3*a^3*c*d*e^2)*sqrt(-(a^3*c*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) + 6*d*e)/(a^3*c))) + (a*c*x^4 + a^2)*sqrt((a^3*c*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) - 6*d*e)/(a^3*c))*log(-(81*c^2*d^4 - a^2*e^4)*x + (a^6*c^2*e*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) - 27*a^2*c^2*d^3 + 3*a^3*c*d*e^2)*sqrt((a^3*c*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) - 6*d*e)/(a^3*c))) - (a*c*x^4 + a^2)*sqrt((a^3*c*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) - 6*d*e)/(a^3*c))*log(-(81*c^2*d^4 - a^2*e^4)*x - (a^6*c^2*e*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) - 27*a^2*c^2*d^3 + 3*a^3*c*d*e^2)*sqrt((a^3*c*sqrt(-(81*c^2*d^4 - 18*a*c*d^2*e^2 + a^2*e^4)/(a^7*c^3)) - 6*d*e)/(a^3*c))) + 4*d*x)/(a*c*x^4 + a^2)","B",0
147,1,173,0,1.091142," ","integrate(1/(c*x^4+a)^2,x, algorithm=""fricas"")","\frac{12 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} \arctan\left(-a^{5} c x \left(-\frac{1}{a^{7} c}\right)^{\frac{3}{4}} + \sqrt{a^{4} \sqrt{-\frac{1}{a^{7} c}} + x^{2}} a^{5} c \left(-\frac{1}{a^{7} c}\right)^{\frac{3}{4}}\right) + 3 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} \log\left(a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} + x\right) - 3 \, {\left(a c x^{4} + a^{2}\right)} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} \log\left(-a^{2} \left(-\frac{1}{a^{7} c}\right)^{\frac{1}{4}} + x\right) + 4 \, x}{16 \, {\left(a c x^{4} + a^{2}\right)}}"," ",0,"1/16*(12*(a*c*x^4 + a^2)*(-1/(a^7*c))^(1/4)*arctan(-a^5*c*x*(-1/(a^7*c))^(3/4) + sqrt(a^4*sqrt(-1/(a^7*c)) + x^2)*a^5*c*(-1/(a^7*c))^(3/4)) + 3*(a*c*x^4 + a^2)*(-1/(a^7*c))^(1/4)*log(a^2*(-1/(a^7*c))^(1/4) + x) - 3*(a*c*x^4 + a^2)*(-1/(a^7*c))^(1/4)*log(-a^2*(-1/(a^7*c))^(1/4) + x) + 4*x)/(a*c*x^4 + a^2)","A",0
148,1,9892,0,45.346770," ","integrate(1/(e*x^2+d)/(c*x^4+a)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(c^{2} d^{2} e + a c e^{3}\right)} x^{3} + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x + {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} + {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x - {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} + {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x + {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} - {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x - {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} - {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - 8 \, {\left(a c e^{3} x^{4} + a^{2} e^{3}\right)} \sqrt{-\frac{e}{d}} \log\left(\frac{e x^{2} + 2 \, d x \sqrt{-\frac{e}{d}} - d}{e x^{2} + d}\right) - 4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x}{16 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)}}, -\frac{4 \, {\left(c^{2} d^{2} e + a c e^{3}\right)} x^{3} - 16 \, {\left(a c e^{3} x^{4} + a^{2} e^{3}\right)} \sqrt{\frac{e}{d}} \arctan\left(x \sqrt{\frac{e}{d}}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x + {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} + {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x - {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} + {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} + {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) + {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x + {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} - {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}} \log\left(-{\left(81 \, c^{5} d^{8} + 594 \, a c^{4} d^{6} e^{2} + 1376 \, a^{2} c^{3} d^{4} e^{4} + 750 \, a^{3} c^{2} d^{2} e^{6} - 625 \, a^{4} c e^{8}\right)} x - {\left(27 \, a^{2} c^{5} d^{9} + 186 \, a^{3} c^{4} d^{7} e^{2} + 404 \, a^{4} c^{3} d^{5} e^{4} + 198 \, a^{5} c^{2} d^{3} e^{6} - 175 \, a^{6} c d e^{8} - {\left(a^{6} c^{5} d^{10} e + 9 \, a^{7} c^{4} d^{8} e^{3} + 26 \, a^{8} c^{3} d^{6} e^{5} + 34 \, a^{9} c^{2} d^{4} e^{7} + 21 \, a^{10} c d^{2} e^{9} + 5 \, a^{11} e^{11}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}\right)} \sqrt{\frac{6 \, c^{3} d^{5} e + 44 \, a c^{2} d^{3} e^{3} + 70 \, a^{2} c d e^{5} - {\left(a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}\right)} \sqrt{-\frac{81 \, c^{7} d^{12} + 738 \, a c^{6} d^{10} e^{2} + 2383 \, a^{2} c^{5} d^{8} e^{4} + 2748 \, a^{3} c^{4} d^{6} e^{6} - 529 \, a^{4} c^{3} d^{4} e^{8} - 1950 \, a^{5} c^{2} d^{2} e^{10} + 625 \, a^{6} c e^{12}}{a^{7} c^{8} d^{16} + 8 \, a^{8} c^{7} d^{14} e^{2} + 28 \, a^{9} c^{6} d^{12} e^{4} + 56 \, a^{10} c^{5} d^{10} e^{6} + 70 \, a^{11} c^{4} d^{8} e^{8} + 56 \, a^{12} c^{3} d^{6} e^{10} + 28 \, a^{13} c^{2} d^{4} e^{12} + 8 \, a^{14} c d^{2} e^{14} + a^{15} e^{16}}}}{a^{3} c^{4} d^{8} + 4 \, a^{4} c^{3} d^{6} e^{2} + 6 \, a^{5} c^{2} d^{4} e^{4} + 4 \, a^{6} c d^{2} e^{6} + a^{7} e^{8}}}\right) - 4 \, {\left(c^{2} d^{3} + a c d e^{2}\right)} x}{16 \, {\left(a^{2} c^{2} d^{4} + 2 \, a^{3} c d^{2} e^{2} + a^{4} e^{4} + {\left(a c^{3} d^{4} + 2 \, a^{2} c^{2} d^{2} e^{2} + a^{3} c e^{4}\right)} x^{4}\right)}}\right]"," ",0,"[-1/16*(4*(c^2*d^2*e + a*c*e^3)*x^3 + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x + (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 + (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x - (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 + (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x + (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 - (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x - (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 - (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - 8*(a*c*e^3*x^4 + a^2*e^3)*sqrt(-e/d)*log((e*x^2 + 2*d*x*sqrt(-e/d) - d)/(e*x^2 + d)) - 4*(c^2*d^3 + a*c*d*e^2)*x)/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4), -1/16*(4*(c^2*d^2*e + a*c*e^3)*x^3 - 16*(a*c*e^3*x^4 + a^2*e^3)*sqrt(e/d)*arctan(x*sqrt(e/d)) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x + (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 + (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x - (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 + (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 + (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) + (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x + (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 - (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - (a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))*log(-(81*c^5*d^8 + 594*a*c^4*d^6*e^2 + 1376*a^2*c^3*d^4*e^4 + 750*a^3*c^2*d^2*e^6 - 625*a^4*c*e^8)*x - (27*a^2*c^5*d^9 + 186*a^3*c^4*d^7*e^2 + 404*a^4*c^3*d^5*e^4 + 198*a^5*c^2*d^3*e^6 - 175*a^6*c*d*e^8 - (a^6*c^5*d^10*e + 9*a^7*c^4*d^8*e^3 + 26*a^8*c^3*d^6*e^5 + 34*a^9*c^2*d^4*e^7 + 21*a^10*c*d^2*e^9 + 5*a^11*e^11)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))*sqrt((6*c^3*d^5*e + 44*a*c^2*d^3*e^3 + 70*a^2*c*d*e^5 - (a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8)*sqrt(-(81*c^7*d^12 + 738*a*c^6*d^10*e^2 + 2383*a^2*c^5*d^8*e^4 + 2748*a^3*c^4*d^6*e^6 - 529*a^4*c^3*d^4*e^8 - 1950*a^5*c^2*d^2*e^10 + 625*a^6*c*e^12)/(a^7*c^8*d^16 + 8*a^8*c^7*d^14*e^2 + 28*a^9*c^6*d^12*e^4 + 56*a^10*c^5*d^10*e^6 + 70*a^11*c^4*d^8*e^8 + 56*a^12*c^3*d^6*e^10 + 28*a^13*c^2*d^4*e^12 + 8*a^14*c*d^2*e^14 + a^15*e^16)))/(a^3*c^4*d^8 + 4*a^4*c^3*d^6*e^2 + 6*a^5*c^2*d^4*e^4 + 4*a^6*c*d^2*e^6 + a^7*e^8))) - 4*(c^2*d^3 + a*c*d*e^2)*x)/(a^2*c^2*d^4 + 2*a^3*c*d^2*e^2 + a^4*e^4 + (a*c^3*d^4 + 2*a^2*c^2*d^2*e^2 + a^3*c*e^4)*x^4)]","B",0
149,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*x^4+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
150,0,0,0,1.358368," ","integrate((e*x^2+d)^4/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{4} x^{8} + 4 \, d e^{3} x^{6} + 6 \, d^{2} e^{2} x^{4} + 4 \, d^{3} e x^{2} + d^{4}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((e^4*x^8 + 4*d*e^3*x^6 + 6*d^2*e^2*x^4 + 4*d^3*e*x^2 + d^4)/sqrt(c*x^4 + a), x)","F",0
151,0,0,0,1.709366," ","integrate((e*x^2+d)^3/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3)/sqrt(c*x^4 + a), x)","F",0
152,0,0,0,1.061691," ","integrate((e*x^2+d)^2/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((e^2*x^4 + 2*d*e*x^2 + d^2)/sqrt(c*x^4 + a), x)","F",0
153,0,0,0,1.039938," ","integrate((e*x^2+d)/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{2} + d}{\sqrt{c x^{4} + a}}, x\right)"," ",0,"integral((e*x^2 + d)/sqrt(c*x^4 + a), x)","F",0
154,0,0,0,17.423089," ","integrate(1/(e*x^2+d)/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + a}}{c e x^{6} + c d x^{4} + a e x^{2} + a d}, x\right)"," ",0,"integral(sqrt(c*x^4 + a)/(c*e*x^6 + c*d*x^4 + a*e*x^2 + a*d), x)","F",0
155,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
156,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^3/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
157,0,0,0,1.039482," ","integrate((e*x^2+d)^3/(-c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}\right)} \sqrt{-c x^{4} + a}}{c x^{4} - a}, x\right)"," ",0,"integral(-(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3)*sqrt(-c*x^4 + a)/(c*x^4 - a), x)","F",0
158,0,0,0,1.154912," ","integrate((e*x^2+d)^2/(-c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{-c x^{4} + a}}{c x^{4} - a}, x\right)"," ",0,"integral(-(e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(-c*x^4 + a)/(c*x^4 - a), x)","F",0
159,0,0,0,1.347386," ","integrate((e*x^2+d)/(-c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + a} {\left(e x^{2} + d\right)}}{c x^{4} - a}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + a)*(e*x^2 + d)/(c*x^4 - a), x)","F",0
160,0,0,0,18.764016," ","integrate(1/(e*x^2+d)/(-c*x^4+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + a}}{c e x^{6} + c d x^{4} - a e x^{2} - a d}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + a)/(c*e*x^6 + c*d*x^4 - a*e*x^2 - a*d), x)","F",0
161,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(-c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
162,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^3/(-c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
163,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^4/(-c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
164,0,0,0,1.224654," ","integrate((e*x^2+d)/(c*x^4-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{2} + d}{\sqrt{c x^{4} - a}}, x\right)"," ",0,"integral((e*x^2 + d)/sqrt(c*x^4 - a), x)","F",0
165,0,0,0,15.980957," ","integrate(1/(e*x^2+d)/(c*x^4-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} - a}}{c e x^{6} + c d x^{4} - a e x^{2} - a d}, x\right)"," ",0,"integral(sqrt(c*x^4 - a)/(c*e*x^6 + c*d*x^4 - a*e*x^2 - a*d), x)","F",0
166,0,0,0,0.711637," ","integrate((a^(1/2)+x^2*c^(1/2))/(c*x^4-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c} x^{2} + \sqrt{a}}{\sqrt{c x^{4} - a}}, x\right)"," ",0,"integral((sqrt(c)*x^2 + sqrt(a))/sqrt(c*x^4 - a), x)","F",0
167,0,0,0,1.190126," ","integrate((1+x^2*(c/a)^(1/2))/(c*x^4-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} \sqrt{\frac{c}{a}} + 1}{\sqrt{c x^{4} - a}}, x\right)"," ",0,"integral((x^2*sqrt(c/a) + 1)/sqrt(c*x^4 - a), x)","F",0
168,0,0,0,0.839574," ","integrate((e*x^2+d)/(-c*x^4-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} - a} {\left(e x^{2} + d\right)}}{c x^{4} + a}, x\right)"," ",0,"integral(-sqrt(-c*x^4 - a)*(e*x^2 + d)/(c*x^4 + a), x)","F",0
169,0,0,0,16.187870," ","integrate(1/(e*x^2+d)/(-c*x^4-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} - a}}{c e x^{6} + c d x^{4} + a e x^{2} + a d}, x\right)"," ",0,"integral(-sqrt(-c*x^4 - a)/(c*e*x^6 + c*d*x^4 + a*e*x^2 + a*d), x)","F",0
170,0,0,0,9.277338," ","integrate(1/(b*x^2+a)/(-5*x^4+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-5 \, x^{4} + 4}}{5 \, b x^{6} + 5 \, a x^{4} - 4 \, b x^{2} - 4 \, a}, x\right)"," ",0,"integral(-sqrt(-5*x^4 + 4)/(5*b*x^6 + 5*a*x^4 - 4*b*x^2 - 4*a), x)","F",0
171,0,0,0,9.340731," ","integrate(1/(b*x^2+a)/(5*x^4+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{5 \, x^{4} + 4}}{5 \, b x^{6} + 5 \, a x^{4} + 4 \, b x^{2} + 4 \, a}, x\right)"," ",0,"integral(sqrt(5*x^4 + 4)/(5*b*x^6 + 5*a*x^4 + 4*b*x^2 + 4*a), x)","F",0
172,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(-d*x^4+4)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate(1/(b*x^2+a)/(d*x^4+4)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,0,0,0,1.491205," ","integrate((b*x^2+a)^(1/2)/(-x^4+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + 1} \sqrt{b x^{2} + a}}{x^{4} - 1}, x\right)"," ",0,"integral(-sqrt(-x^4 + 1)*sqrt(b*x^2 + a)/(x^4 - 1), x)","F",0
175,0,0,0,0.945248," ","integrate((e*x^2+c)^q*(b*x^4+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{p} {\left(e x^{2} + c\right)}^{q}, x\right)"," ",0,"integral((b*x^4 + a)^p*(e*x^2 + c)^q, x)","F",0
176,0,0,0,1.032346," ","integrate((e*x^2+c)^3*(b*x^4+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{6} + 3 \, c e^{2} x^{4} + 3 \, c^{2} e x^{2} + c^{3}\right)} {\left(b x^{4} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^6 + 3*c*e^2*x^4 + 3*c^2*e*x^2 + c^3)*(b*x^4 + a)^p, x)","F",0
177,0,0,0,1.088224," ","integrate((e*x^2+c)^2*(b*x^4+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{4} + 2 \, c e x^{2} + c^{2}\right)} {\left(b x^{4} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^4 + 2*c*e*x^2 + c^2)*(b*x^4 + a)^p, x)","F",0
178,0,0,0,0.885031," ","integrate((e*x^2+c)*(b*x^4+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{2} + c\right)} {\left(b x^{4} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^2 + c)*(b*x^4 + a)^p, x)","F",0
179,0,0,0,0.860180," ","integrate((b*x^4+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + a\right)}^{p}, x\right)"," ",0,"integral((b*x^4 + a)^p, x)","F",0
180,0,0,0,1.055504," ","integrate((b*x^4+a)^p/(e*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{p}}{e x^{2} + c}, x\right)"," ",0,"integral((b*x^4 + a)^p/(e*x^2 + c), x)","F",0
181,0,0,0,1.150923," ","integrate((b*x^4+a)^p/(e*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + a\right)}^{p}}{e^{2} x^{4} + 2 \, c e x^{2} + c^{2}}, x\right)"," ",0,"integral((b*x^4 + a)^p/(e^2*x^4 + 2*c*e*x^2 + c^2), x)","F",0
182,0,0,0,1.018800," ","integrate((-x^2+1)^3*(b*x^4+1)^p,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1\right)} {\left(b x^{4} + 1\right)}^{p}, x\right)"," ",0,"integral(-(x^6 - 3*x^4 + 3*x^2 - 1)*(b*x^4 + 1)^p, x)","F",0
183,0,0,0,0.700952," ","integrate((-x^2+1)^2*(b*x^4+1)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{4} - 2 \, x^{2} + 1\right)} {\left(b x^{4} + 1\right)}^{p}, x\right)"," ",0,"integral((x^4 - 2*x^2 + 1)*(b*x^4 + 1)^p, x)","F",0
184,0,0,0,0.734942," ","integrate((-x^2+1)*(b*x^4+1)^p,x, algorithm=""fricas"")","{\rm integral}\left(-{\left(x^{2} - 1\right)} {\left(b x^{4} + 1\right)}^{p}, x\right)"," ",0,"integral(-(x^2 - 1)*(b*x^4 + 1)^p, x)","F",0
185,0,0,0,0.878067," ","integrate((b*x^4+1)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + 1\right)}^{p}, x\right)"," ",0,"integral((b*x^4 + 1)^p, x)","F",0
186,0,0,0,1.009942," ","integrate((b*x^4+1)^p/(-x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{4} + 1\right)}^{p}}{x^{2} - 1}, x\right)"," ",0,"integral(-(b*x^4 + 1)^p/(x^2 - 1), x)","F",0
187,0,0,0,1.161687," ","integrate((b*x^4+1)^p/(-x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + 1\right)}^{p}}{x^{4} - 2 \, x^{2} + 1}, x\right)"," ",0,"integral((b*x^4 + 1)^p/(x^4 - 2*x^2 + 1), x)","F",0
188,0,0,0,0.949031," ","integrate((b*x^4+1)^p/(-x^2+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(b x^{4} + 1\right)}^{p}}{x^{6} - 3 \, x^{4} + 3 \, x^{2} - 1}, x\right)"," ",0,"integral(-(b*x^4 + 1)^p/(x^6 - 3*x^4 + 3*x^2 - 1), x)","F",0
189,1,116,0,0.832053," ","integrate((e*x^2+d)^4/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[-\frac{1}{5} \, e^{2} x^{5} - \frac{4}{3} \, d e x^{3} + 4 \, d^{2} \sqrt{\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{\frac{d}{e}} + d}{e x^{2} - d}\right) - 7 \, d^{2} x, -\frac{1}{5} \, e^{2} x^{5} - \frac{4}{3} \, d e x^{3} - 8 \, d^{2} \sqrt{-\frac{d}{e}} \arctan\left(\frac{e x \sqrt{-\frac{d}{e}}}{d}\right) - 7 \, d^{2} x\right]"," ",0,"[-1/5*e^2*x^5 - 4/3*d*e*x^3 + 4*d^2*sqrt(d/e)*log((e*x^2 + 2*e*x*sqrt(d/e) + d)/(e*x^2 - d)) - 7*d^2*x, -1/5*e^2*x^5 - 4/3*d*e*x^3 - 8*d^2*sqrt(-d/e)*arctan(e*x*sqrt(-d/e)/d) - 7*d^2*x]","A",0
190,1,90,0,0.867715," ","integrate((e*x^2+d)^3/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[-\frac{1}{3} \, e x^{3} + 2 \, d \sqrt{\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{\frac{d}{e}} + d}{e x^{2} - d}\right) - 3 \, d x, -\frac{1}{3} \, e x^{3} - 4 \, d \sqrt{-\frac{d}{e}} \arctan\left(\frac{e x \sqrt{-\frac{d}{e}}}{d}\right) - 3 \, d x\right]"," ",0,"[-1/3*e*x^3 + 2*d*sqrt(d/e)*log((e*x^2 + 2*e*x*sqrt(d/e) + d)/(e*x^2 - d)) - 3*d*x, -1/3*e*x^3 - 4*d*sqrt(-d/e)*arctan(e*x*sqrt(-d/e)/d) - 3*d*x]","A",0
191,1,73,0,1.675805," ","integrate((e*x^2+d)^2/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\sqrt{\frac{d}{e}} \log\left(\frac{e x^{2} + 2 \, e x \sqrt{\frac{d}{e}} + d}{e x^{2} - d}\right) - x, -2 \, \sqrt{-\frac{d}{e}} \arctan\left(\frac{e x \sqrt{-\frac{d}{e}}}{d}\right) - x\right]"," ",0,"[sqrt(d/e)*log((e*x^2 + 2*e*x*sqrt(d/e) + d)/(e*x^2 - d)) - x, -2*sqrt(-d/e)*arctan(e*x*sqrt(-d/e)/d) - x]","A",0
192,1,68,0,1.094141," ","integrate((e*x^2+d)/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{d e} \log\left(\frac{e x^{2} + 2 \, \sqrt{d e} x + d}{e x^{2} - d}\right)}{2 \, d e}, -\frac{\sqrt{-d e} \arctan\left(\frac{\sqrt{-d e} x}{d}\right)}{d e}\right]"," ",0,"[1/2*sqrt(d*e)*log((e*x^2 + 2*sqrt(d*e)*x + d)/(e*x^2 - d))/(d*e), -sqrt(-d*e)*arctan(sqrt(-d*e)*x/d)/(d*e)]","A",0
193,1,189,0,0.882555," ","integrate(1/(e*x^2+d)/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\frac{2 \, d e x + 4 \, {\left(e x^{2} + d\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(e x^{2} + d\right)} \sqrt{d e} \log\left(\frac{e x^{2} + 2 \, \sqrt{d e} x + d}{e x^{2} - d}\right)}{8 \, {\left(d^{3} e^{2} x^{2} + d^{4} e\right)}}, \frac{d e x - {\left(e x^{2} + d\right)} \sqrt{-d e} \arctan\left(\frac{\sqrt{-d e} x}{d}\right) - {\left(e x^{2} + d\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{4 \, {\left(d^{3} e^{2} x^{2} + d^{4} e\right)}}\right]"," ",0,"[1/8*(2*d*e*x + 4*(e*x^2 + d)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (e*x^2 + d)*sqrt(d*e)*log((e*x^2 + 2*sqrt(d*e)*x + d)/(e*x^2 - d)))/(d^3*e^2*x^2 + d^4*e), 1/4*(d*e*x - (e*x^2 + d)*sqrt(-d*e)*arctan(sqrt(-d*e)*x/d) - (e*x^2 + d)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(d^3*e^2*x^2 + d^4*e)]","A",0
194,1,278,0,1.235181," ","integrate(1/(e*x^2+d)^2/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\frac{5 \, d e^{2} x^{3} + 7 \, d^{2} e x + 7 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{d e} \log\left(\frac{e x^{2} + 2 \, \sqrt{d e} x + d}{e x^{2} - d}\right)}{16 \, {\left(d^{4} e^{3} x^{4} + 2 \, d^{5} e^{2} x^{2} + d^{6} e\right)}}, \frac{10 \, d e^{2} x^{3} + 14 \, d^{2} e x - 4 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{-d e} \arctan\left(\frac{\sqrt{-d e} x}{d}\right) - 7 \, {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right)}{32 \, {\left(d^{4} e^{3} x^{4} + 2 \, d^{5} e^{2} x^{2} + d^{6} e\right)}}\right]"," ",0,"[1/16*(5*d*e^2*x^3 + 7*d^2*e*x + 7*(e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(d*e)*log((e*x^2 + 2*sqrt(d*e)*x + d)/(e*x^2 - d)))/(d^4*e^3*x^4 + 2*d^5*e^2*x^2 + d^6*e), 1/32*(10*d*e^2*x^3 + 14*d^2*e*x - 4*(e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(-d*e)*arctan(sqrt(-d*e)*x/d) - 7*(e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)))/(d^4*e^3*x^4 + 2*d^5*e^2*x^2 + d^6*e)]","B",0
195,1,199,0,0.853681," ","integrate((e*x^2+d)^(3/2)/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \sqrt{e} \log\left(\frac{17 \, e^{2} x^{4} + 14 \, d e x^{2} + d^{2} + \frac{4 \, \sqrt{2} {\left(3 \, e^{2} x^{3} + d e x\right)} \sqrt{e x^{2} + d}}{\sqrt{e}}}{e^{2} x^{4} - 2 \, d e x^{2} + d^{2}}\right) + 2 \, \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right)}{4 \, e}, -\frac{\sqrt{2} e \sqrt{-\frac{1}{e}} \arctan\left(\frac{\sqrt{2} {\left(3 \, e x^{2} + d\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{1}{e}}}{4 \, {\left(e x^{3} + d x\right)}}\right) - 2 \, \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{2 \, e}\right]"," ",0,"[1/4*(sqrt(2)*sqrt(e)*log((17*e^2*x^4 + 14*d*e*x^2 + d^2 + 4*sqrt(2)*(3*e^2*x^3 + d*e*x)*sqrt(e*x^2 + d)/sqrt(e))/(e^2*x^4 - 2*d*e*x^2 + d^2)) + 2*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d))/e, -1/2*(sqrt(2)*e*sqrt(-1/e)*arctan(1/4*sqrt(2)*(3*e*x^2 + d)*sqrt(e*x^2 + d)*sqrt(-1/e)/(e*x^3 + d*x)) - 2*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/e]","A",0
196,1,138,0,0.557468," ","integrate((e*x^2+d)^(1/2)/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(\frac{17 \, e^{2} x^{4} + 14 \, d e x^{2} + 4 \, \sqrt{2} {\left(3 \, e x^{3} + d x\right)} \sqrt{e x^{2} + d} \sqrt{e} + d^{2}}{e^{2} x^{4} - 2 \, d e x^{2} + d^{2}}\right)}{8 \, d \sqrt{e}}, -\frac{\sqrt{2} \sqrt{-e} \arctan\left(\frac{\sqrt{2} {\left(3 \, e x^{2} + d\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{4 \, {\left(e^{2} x^{3} + d e x\right)}}\right)}{4 \, d e}\right]"," ",0,"[1/8*sqrt(2)*log((17*e^2*x^4 + 14*d*e*x^2 + 4*sqrt(2)*(3*e*x^3 + d*x)*sqrt(e*x^2 + d)*sqrt(e) + d^2)/(e^2*x^4 - 2*d*e*x^2 + d^2))/(d*sqrt(e)), -1/4*sqrt(2)*sqrt(-e)*arctan(1/4*sqrt(2)*(3*e*x^2 + d)*sqrt(e*x^2 + d)*sqrt(-e)/(e^2*x^3 + d*e*x))/(d*e)]","A",0
197,1,209,0,1.082038," ","integrate(1/(e*x^2+d)^(1/2)/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} {\left(e x^{2} + d\right)} \sqrt{e} \log\left(\frac{17 \, e^{2} x^{4} + 14 \, d e x^{2} + 4 \, \sqrt{2} {\left(3 \, e x^{3} + d x\right)} \sqrt{e x^{2} + d} \sqrt{e} + d^{2}}{e^{2} x^{4} - 2 \, d e x^{2} + d^{2}}\right) + 8 \, \sqrt{e x^{2} + d} e x}{16 \, {\left(d^{2} e^{2} x^{2} + d^{3} e\right)}}, -\frac{\sqrt{2} {\left(e x^{2} + d\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{2} {\left(3 \, e x^{2} + d\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{4 \, {\left(e^{2} x^{3} + d e x\right)}}\right) - 4 \, \sqrt{e x^{2} + d} e x}{8 \, {\left(d^{2} e^{2} x^{2} + d^{3} e\right)}}\right]"," ",0,"[1/16*(sqrt(2)*(e*x^2 + d)*sqrt(e)*log((17*e^2*x^4 + 14*d*e*x^2 + 4*sqrt(2)*(3*e*x^3 + d*x)*sqrt(e*x^2 + d)*sqrt(e) + d^2)/(e^2*x^4 - 2*d*e*x^2 + d^2)) + 8*sqrt(e*x^2 + d)*e*x)/(d^2*e^2*x^2 + d^3*e), -1/8*(sqrt(2)*(e*x^2 + d)*sqrt(-e)*arctan(1/4*sqrt(2)*(3*e*x^2 + d)*sqrt(e*x^2 + d)*sqrt(-e)/(e^2*x^3 + d*e*x)) - 4*sqrt(e*x^2 + d)*e*x)/(d^2*e^2*x^2 + d^3*e)]","B",0
198,1,279,0,1.740664," ","integrate(1/(e*x^2+d)^(3/2)/(-e^2*x^4+d^2),x, algorithm=""fricas"")","\left[\frac{3 \, \sqrt{2} {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{e} \log\left(\frac{17 \, e^{2} x^{4} + 14 \, d e x^{2} + 4 \, \sqrt{2} {\left(3 \, e x^{3} + d x\right)} \sqrt{e x^{2} + d} \sqrt{e} + d^{2}}{e^{2} x^{4} - 2 \, d e x^{2} + d^{2}}\right) + 8 \, {\left(7 \, e^{2} x^{3} + 9 \, d e x\right)} \sqrt{e x^{2} + d}}{96 \, {\left(d^{3} e^{3} x^{4} + 2 \, d^{4} e^{2} x^{2} + d^{5} e\right)}}, -\frac{3 \, \sqrt{2} {\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{2} {\left(3 \, e x^{2} + d\right)} \sqrt{e x^{2} + d} \sqrt{-e}}{4 \, {\left(e^{2} x^{3} + d e x\right)}}\right) - 4 \, {\left(7 \, e^{2} x^{3} + 9 \, d e x\right)} \sqrt{e x^{2} + d}}{48 \, {\left(d^{3} e^{3} x^{4} + 2 \, d^{4} e^{2} x^{2} + d^{5} e\right)}}\right]"," ",0,"[1/96*(3*sqrt(2)*(e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(e)*log((17*e^2*x^4 + 14*d*e*x^2 + 4*sqrt(2)*(3*e*x^3 + d*x)*sqrt(e*x^2 + d)*sqrt(e) + d^2)/(e^2*x^4 - 2*d*e*x^2 + d^2)) + 8*(7*e^2*x^3 + 9*d*e*x)*sqrt(e*x^2 + d))/(d^3*e^3*x^4 + 2*d^4*e^2*x^2 + d^5*e), -1/48*(3*sqrt(2)*(e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(-e)*arctan(1/4*sqrt(2)*(3*e*x^2 + d)*sqrt(e*x^2 + d)*sqrt(-e)/(e^2*x^3 + d*e*x)) - 4*(7*e^2*x^3 + 9*d*e*x)*sqrt(e*x^2 + d))/(d^3*e^3*x^4 + 2*d^4*e^2*x^2 + d^5*e)]","B",0
199,1,251,0,1.134500," ","integrate((b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{19 \, {\left(a^{2} b x^{2} + a^{3}\right)} \sqrt{-b} \log\left(-\frac{2 \, b^{2} x^{4} + a b x^{2} - 2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{-b} x - a^{2}}{b x^{2} + a}\right) + 2 \, \sqrt{-b^{2} x^{4} + a^{2}} {\left(2 \, b^{2} x^{3} + 11 \, a b x\right)} \sqrt{b x^{2} + a}}{16 \, {\left(b^{2} x^{2} + a b\right)}}, -\frac{19 \, {\left(a^{2} b x^{2} + a^{3}\right)} \sqrt{b} \arctan\left(\frac{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{b}}{b^{2} x^{3} + a b x}\right) + \sqrt{-b^{2} x^{4} + a^{2}} {\left(2 \, b^{2} x^{3} + 11 \, a b x\right)} \sqrt{b x^{2} + a}}{8 \, {\left(b^{2} x^{2} + a b\right)}}\right]"," ",0,"[-1/16*(19*(a^2*b*x^2 + a^3)*sqrt(-b)*log(-(2*b^2*x^4 + a*b*x^2 - 2*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(-b)*x - a^2)/(b*x^2 + a)) + 2*sqrt(-b^2*x^4 + a^2)*(2*b^2*x^3 + 11*a*b*x)*sqrt(b*x^2 + a))/(b^2*x^2 + a*b), -1/8*(19*(a^2*b*x^2 + a^3)*sqrt(b)*arctan(sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(b)/(b^2*x^3 + a*b*x)) + sqrt(-b^2*x^4 + a^2)*(2*b^2*x^3 + 11*a*b*x)*sqrt(b*x^2 + a))/(b^2*x^2 + a*b)]","A",0
200,1,223,0,1.085312," ","integrate((b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} b x + 3 \, {\left(a b x^{2} + a^{2}\right)} \sqrt{-b} \log\left(-\frac{2 \, b^{2} x^{4} + a b x^{2} - 2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{-b} x - a^{2}}{b x^{2} + a}\right)}{4 \, {\left(b^{2} x^{2} + a b\right)}}, -\frac{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} b x + 3 \, {\left(a b x^{2} + a^{2}\right)} \sqrt{b} \arctan\left(\frac{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{b}}{b^{2} x^{3} + a b x}\right)}{2 \, {\left(b^{2} x^{2} + a b\right)}}\right]"," ",0,"[-1/4*(2*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*b*x + 3*(a*b*x^2 + a^2)*sqrt(-b)*log(-(2*b^2*x^4 + a*b*x^2 - 2*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(-b)*x - a^2)/(b*x^2 + a)))/(b^2*x^2 + a*b), -1/2*(sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*b*x + 3*(a*b*x^2 + a^2)*sqrt(b)*arctan(sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(b)/(b^2*x^3 + a*b*x)))/(b^2*x^2 + a*b)]","A",0
201,1,121,0,1.023318," ","integrate((b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-b} \log\left(-\frac{2 \, b^{2} x^{4} + a b x^{2} - 2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{-b} x - a^{2}}{b x^{2} + a}\right)}{2 \, b}, -\frac{\arctan\left(\frac{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{b}}{b^{2} x^{3} + a b x}\right)}{\sqrt{b}}\right]"," ",0,"[-1/2*sqrt(-b)*log(-(2*b^2*x^4 + a*b*x^2 - 2*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(-b)*x - a^2)/(b*x^2 + a))/b, -arctan(sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(b)/(b^2*x^3 + a*b*x))/sqrt(b)]","A",0
202,1,152,0,0.848375," ","integrate(1/(b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{2} \sqrt{-b} \log\left(-\frac{3 \, b^{2} x^{4} + 2 \, a b x^{2} - 2 \, \sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{-b} x - a^{2}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{4 \, a b}, -\frac{\sqrt{2} \arctan\left(\frac{\sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{b}}{2 \, {\left(b^{2} x^{3} + a b x\right)}}\right)}{2 \, a \sqrt{b}}\right]"," ",0,"[-1/4*sqrt(2)*sqrt(-b)*log(-(3*b^2*x^4 + 2*a*b*x^2 - 2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(-b)*x - a^2)/(b^2*x^4 + 2*a*b*x^2 + a^2))/(a*b), -1/2*sqrt(2)*arctan(1/2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(b)/(b^2*x^3 + a*b*x))/(a*sqrt(b))]","A",0
203,1,297,0,0.889326," ","integrate(1/(b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} b x - 3 \, \sqrt{2} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{-b} \log\left(-\frac{3 \, b^{2} x^{4} + 2 \, a b x^{2} - 2 \, \sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{-b} x - a^{2}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right)}{16 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}, \frac{2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} b x - 3 \, \sqrt{2} {\left(b^{2} x^{4} + 2 \, a b x^{2} + a^{2}\right)} \sqrt{b} \arctan\left(\frac{\sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{b}}{2 \, {\left(b^{2} x^{3} + a b x\right)}}\right)}{8 \, {\left(a^{2} b^{3} x^{4} + 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}\right]"," ",0,"[1/16*(4*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*b*x - 3*sqrt(2)*(b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(-b)*log(-(3*b^2*x^4 + 2*a*b*x^2 - 2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(-b)*x - a^2)/(b^2*x^4 + 2*a*b*x^2 + a^2)))/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b), 1/8*(2*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*b*x - 3*sqrt(2)*(b^2*x^4 + 2*a*b*x^2 + a^2)*sqrt(b)*arctan(1/2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(b)/(b^2*x^3 + a*b*x)))/(a^2*b^3*x^4 + 2*a^3*b^2*x^2 + a^4*b)]","A",0
204,1,365,0,0.736931," ","integrate(1/(b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{19 \, \sqrt{2} {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{-b} \log\left(-\frac{3 \, b^{2} x^{4} + 2 \, a b x^{2} - 2 \, \sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{-b} x - a^{2}}{b^{2} x^{4} + 2 \, a b x^{2} + a^{2}}\right) - 4 \, \sqrt{-b^{2} x^{4} + a^{2}} {\left(9 \, b^{2} x^{3} + 13 \, a b x\right)} \sqrt{b x^{2} + a}}{128 \, {\left(a^{3} b^{4} x^{6} + 3 \, a^{4} b^{3} x^{4} + 3 \, a^{5} b^{2} x^{2} + a^{6} b\right)}}, -\frac{19 \, \sqrt{2} {\left(b^{3} x^{6} + 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} + a^{3}\right)} \sqrt{b} \arctan\left(\frac{\sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{b x^{2} + a} \sqrt{b}}{2 \, {\left(b^{2} x^{3} + a b x\right)}}\right) - 2 \, \sqrt{-b^{2} x^{4} + a^{2}} {\left(9 \, b^{2} x^{3} + 13 \, a b x\right)} \sqrt{b x^{2} + a}}{64 \, {\left(a^{3} b^{4} x^{6} + 3 \, a^{4} b^{3} x^{4} + 3 \, a^{5} b^{2} x^{2} + a^{6} b\right)}}\right]"," ",0,"[-1/128*(19*sqrt(2)*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(-b)*log(-(3*b^2*x^4 + 2*a*b*x^2 - 2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(-b)*x - a^2)/(b^2*x^4 + 2*a*b*x^2 + a^2)) - 4*sqrt(-b^2*x^4 + a^2)*(9*b^2*x^3 + 13*a*b*x)*sqrt(b*x^2 + a))/(a^3*b^4*x^6 + 3*a^4*b^3*x^4 + 3*a^5*b^2*x^2 + a^6*b), -1/64*(19*sqrt(2)*(b^3*x^6 + 3*a*b^2*x^4 + 3*a^2*b*x^2 + a^3)*sqrt(b)*arctan(1/2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(b*x^2 + a)*sqrt(b)/(b^2*x^3 + a*b*x)) - 2*sqrt(-b^2*x^4 + a^2)*(9*b^2*x^3 + 13*a*b*x)*sqrt(b*x^2 + a))/(a^3*b^4*x^6 + 3*a^4*b^3*x^4 + 3*a^5*b^2*x^2 + a^6*b)]","A",0
205,1,265,0,1.317949," ","integrate((-b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{19 \, {\left(a^{2} b x^{2} - a^{3}\right)} \sqrt{b} \log\left(\frac{2 \, b^{2} x^{4} - a b x^{2} - 2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{b} x - a^{2}}{b x^{2} - a}\right) - 2 \, \sqrt{-b^{2} x^{4} + a^{2}} {\left(2 \, b^{2} x^{3} - 11 \, a b x\right)} \sqrt{-b x^{2} + a}}{16 \, {\left(b^{2} x^{2} - a b\right)}}, \frac{19 \, {\left(a^{2} b x^{2} - a^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{-b}}{b^{2} x^{3} - a b x}\right) - \sqrt{-b^{2} x^{4} + a^{2}} {\left(2 \, b^{2} x^{3} - 11 \, a b x\right)} \sqrt{-b x^{2} + a}}{8 \, {\left(b^{2} x^{2} - a b\right)}}\right]"," ",0,"[1/16*(19*(a^2*b*x^2 - a^3)*sqrt(b)*log((2*b^2*x^4 - a*b*x^2 - 2*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(b)*x - a^2)/(b*x^2 - a)) - 2*sqrt(-b^2*x^4 + a^2)*(2*b^2*x^3 - 11*a*b*x)*sqrt(-b*x^2 + a))/(b^2*x^2 - a*b), 1/8*(19*(a^2*b*x^2 - a^3)*sqrt(-b)*arctan(sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(-b)/(b^2*x^3 - a*b*x)) - sqrt(-b^2*x^4 + a^2)*(2*b^2*x^3 - 11*a*b*x)*sqrt(-b*x^2 + a))/(b^2*x^2 - a*b)]","A",0
206,1,236,0,1.037871," ","integrate((-b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} b x + 3 \, {\left(a b x^{2} - a^{2}\right)} \sqrt{b} \log\left(\frac{2 \, b^{2} x^{4} - a b x^{2} - 2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{b} x - a^{2}}{b x^{2} - a}\right)}{4 \, {\left(b^{2} x^{2} - a b\right)}}, \frac{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} b x + 3 \, {\left(a b x^{2} - a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{-b}}{b^{2} x^{3} - a b x}\right)}{2 \, {\left(b^{2} x^{2} - a b\right)}}\right]"," ",0,"[1/4*(2*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*b*x + 3*(a*b*x^2 - a^2)*sqrt(b)*log((2*b^2*x^4 - a*b*x^2 - 2*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(b)*x - a^2)/(b*x^2 - a)))/(b^2*x^2 - a*b), 1/2*(sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*b*x + 3*(a*b*x^2 - a^2)*sqrt(-b)*arctan(sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(-b)/(b^2*x^3 - a*b*x)))/(b^2*x^2 - a*b)]","A",0
207,1,125,0,1.066869," ","integrate((-b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{2 \, b^{2} x^{4} - a b x^{2} - 2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{b} x - a^{2}}{b x^{2} - a}\right)}{2 \, \sqrt{b}}, \frac{\sqrt{-b} \arctan\left(\frac{\sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{-b}}{b^{2} x^{3} - a b x}\right)}{b}\right]"," ",0,"[1/2*log((2*b^2*x^4 - a*b*x^2 - 2*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(b)*x - a^2)/(b*x^2 - a))/sqrt(b), sqrt(-b)*arctan(sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(-b)/(b^2*x^3 - a*b*x))/b]","A",0
208,1,155,0,1.080863," ","integrate(1/(-b*x^2+a)^(1/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{2} \log\left(-\frac{3 \, b^{2} x^{4} - 2 \, a b x^{2} - 2 \, \sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{b} x - a^{2}}{b^{2} x^{4} - 2 \, a b x^{2} + a^{2}}\right)}{4 \, a \sqrt{b}}, \frac{\sqrt{2} \sqrt{-b} \arctan\left(\frac{\sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{-b}}{2 \, {\left(b^{2} x^{3} - a b x\right)}}\right)}{2 \, a b}\right]"," ",0,"[1/4*sqrt(2)*log(-(3*b^2*x^4 - 2*a*b*x^2 - 2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(b)*x - a^2)/(b^2*x^4 - 2*a*b*x^2 + a^2))/(a*sqrt(b)), 1/2*sqrt(2)*sqrt(-b)*arctan(1/2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(-b)/(b^2*x^3 - a*b*x))/(a*b)]","A",0
209,1,302,0,1.139057," ","integrate(1/(-b*x^2+a)^(3/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} b x + 3 \, \sqrt{2} {\left(b^{2} x^{4} - 2 \, a b x^{2} + a^{2}\right)} \sqrt{b} \log\left(-\frac{3 \, b^{2} x^{4} - 2 \, a b x^{2} - 2 \, \sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{b} x - a^{2}}{b^{2} x^{4} - 2 \, a b x^{2} + a^{2}}\right)}{16 \, {\left(a^{2} b^{3} x^{4} - 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}, \frac{2 \, \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} b x + 3 \, \sqrt{2} {\left(b^{2} x^{4} - 2 \, a b x^{2} + a^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{-b}}{2 \, {\left(b^{2} x^{3} - a b x\right)}}\right)}{8 \, {\left(a^{2} b^{3} x^{4} - 2 \, a^{3} b^{2} x^{2} + a^{4} b\right)}}\right]"," ",0,"[1/16*(4*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*b*x + 3*sqrt(2)*(b^2*x^4 - 2*a*b*x^2 + a^2)*sqrt(b)*log(-(3*b^2*x^4 - 2*a*b*x^2 - 2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(b)*x - a^2)/(b^2*x^4 - 2*a*b*x^2 + a^2)))/(a^2*b^3*x^4 - 2*a^3*b^2*x^2 + a^4*b), 1/8*(2*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*b*x + 3*sqrt(2)*(b^2*x^4 - 2*a*b*x^2 + a^2)*sqrt(-b)*arctan(1/2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(-b)/(b^2*x^3 - a*b*x)))/(a^2*b^3*x^4 - 2*a^3*b^2*x^2 + a^4*b)]","A",0
210,1,376,0,1.156775," ","integrate(1/(-b*x^2+a)^(5/2)/(-b^2*x^4+a^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{19 \, \sqrt{2} {\left(b^{3} x^{6} - 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} - a^{3}\right)} \sqrt{b} \log\left(-\frac{3 \, b^{2} x^{4} - 2 \, a b x^{2} - 2 \, \sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{b} x - a^{2}}{b^{2} x^{4} - 2 \, a b x^{2} + a^{2}}\right) + 4 \, \sqrt{-b^{2} x^{4} + a^{2}} {\left(9 \, b^{2} x^{3} - 13 \, a b x\right)} \sqrt{-b x^{2} + a}}{128 \, {\left(a^{3} b^{4} x^{6} - 3 \, a^{4} b^{3} x^{4} + 3 \, a^{5} b^{2} x^{2} - a^{6} b\right)}}, \frac{19 \, \sqrt{2} {\left(b^{3} x^{6} - 3 \, a b^{2} x^{4} + 3 \, a^{2} b x^{2} - a^{3}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} \sqrt{-b^{2} x^{4} + a^{2}} \sqrt{-b x^{2} + a} \sqrt{-b}}{2 \, {\left(b^{2} x^{3} - a b x\right)}}\right) + 2 \, \sqrt{-b^{2} x^{4} + a^{2}} {\left(9 \, b^{2} x^{3} - 13 \, a b x\right)} \sqrt{-b x^{2} + a}}{64 \, {\left(a^{3} b^{4} x^{6} - 3 \, a^{4} b^{3} x^{4} + 3 \, a^{5} b^{2} x^{2} - a^{6} b\right)}}\right]"," ",0,"[1/128*(19*sqrt(2)*(b^3*x^6 - 3*a*b^2*x^4 + 3*a^2*b*x^2 - a^3)*sqrt(b)*log(-(3*b^2*x^4 - 2*a*b*x^2 - 2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(b)*x - a^2)/(b^2*x^4 - 2*a*b*x^2 + a^2)) + 4*sqrt(-b^2*x^4 + a^2)*(9*b^2*x^3 - 13*a*b*x)*sqrt(-b*x^2 + a))/(a^3*b^4*x^6 - 3*a^4*b^3*x^4 + 3*a^5*b^2*x^2 - a^6*b), 1/64*(19*sqrt(2)*(b^3*x^6 - 3*a*b^2*x^4 + 3*a^2*b*x^2 - a^3)*sqrt(-b)*arctan(1/2*sqrt(2)*sqrt(-b^2*x^4 + a^2)*sqrt(-b*x^2 + a)*sqrt(-b)/(b^2*x^3 - a*b*x)) + 2*sqrt(-b^2*x^4 + a^2)*(9*b^2*x^3 - 13*a*b*x)*sqrt(-b*x^2 + a))/(a^3*b^4*x^6 - 3*a^4*b^3*x^4 + 3*a^5*b^2*x^2 - a^6*b)]","A",0
211,1,73,0,0.690036," ","integrate((x^2-1)^(1/2)/(x^4-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\frac{x^{3} + \sqrt{x^{4} - 1} \sqrt{x^{2} - 1} - x}{x^{3} - x}\right) - \frac{1}{2} \, \log\left(-\frac{x^{3} - \sqrt{x^{4} - 1} \sqrt{x^{2} - 1} - x}{x^{3} - x}\right)"," ",0,"1/2*log((x^3 + sqrt(x^4 - 1)*sqrt(x^2 - 1) - x)/(x^3 - x)) - 1/2*log(-(x^3 - sqrt(x^4 - 1)*sqrt(x^2 - 1) - x)/(x^3 - x))","B",0
212,1,65,0,1.028254," ","integrate((x^2+1)^(1/2)/(x^4-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\frac{x^{3} + \sqrt{x^{4} - 1} \sqrt{x^{2} + 1} + x}{x^{3} + x}\right) - \frac{1}{2} \, \log\left(-\frac{x^{3} - \sqrt{x^{4} - 1} \sqrt{x^{2} + 1} + x}{x^{3} + x}\right)"," ",0,"1/2*log((x^3 + sqrt(x^4 - 1)*sqrt(x^2 + 1) + x)/(x^3 + x)) - 1/2*log(-(x^3 - sqrt(x^4 - 1)*sqrt(x^2 + 1) + x)/(x^3 + x))","B",0
213,1,137,0,1.418978," ","integrate((-(x^2-1)^(1/2)+(x^2+1)^(1/2))/(x^4-1)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, \log\left(\frac{x^{3} + \sqrt{x^{4} - 1} \sqrt{x^{2} + 1} + x}{x^{3} + x}\right) - \frac{1}{2} \, \log\left(-\frac{x^{3} - \sqrt{x^{4} - 1} \sqrt{x^{2} + 1} + x}{x^{3} + x}\right) - \frac{1}{2} \, \log\left(\frac{x^{3} + \sqrt{x^{4} - 1} \sqrt{x^{2} - 1} - x}{x^{3} - x}\right) + \frac{1}{2} \, \log\left(-\frac{x^{3} - \sqrt{x^{4} - 1} \sqrt{x^{2} - 1} - x}{x^{3} - x}\right)"," ",0,"1/2*log((x^3 + sqrt(x^4 - 1)*sqrt(x^2 + 1) + x)/(x^3 + x)) - 1/2*log(-(x^3 - sqrt(x^4 - 1)*sqrt(x^2 + 1) + x)/(x^3 + x)) - 1/2*log((x^3 + sqrt(x^4 - 1)*sqrt(x^2 - 1) - x)/(x^3 - x)) + 1/2*log(-(x^3 - sqrt(x^4 - 1)*sqrt(x^2 - 1) - x)/(x^3 - x))","B",0
214,1,446,0,0.482058," ","integrate((e*x^2+d)^4/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(c^{4} d e^{3} - b c^{3} e^{4}\right)} x^{5} + 10 \, {\left(4 \, c^{4} d^{2} e^{2} - 5 \, b c^{3} d e^{3} + b^{2} c^{2} e^{4}\right)} x^{3} - 15 \, {\left(8 \, c^{3} d^{3} - 12 \, b c^{2} d^{2} e + 6 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \sqrt{c^{2} d e - b c e^{2}} \log\left(\frac{c e x^{2} + c d - b e + 2 \, \sqrt{c^{2} d e - b c e^{2}} x}{c e x^{2} - c d + b e}\right) + 30 \, {\left(7 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} x}{30 \, {\left(c^{5} d e - b c^{4} e^{2}\right)}}, \frac{3 \, {\left(c^{4} d e^{3} - b c^{3} e^{4}\right)} x^{5} + 5 \, {\left(4 \, c^{4} d^{2} e^{2} - 5 \, b c^{3} d e^{3} + b^{2} c^{2} e^{4}\right)} x^{3} - 15 \, {\left(8 \, c^{3} d^{3} - 12 \, b c^{2} d^{2} e + 6 \, b^{2} c d e^{2} - b^{3} e^{3}\right)} \sqrt{-c^{2} d e + b c e^{2}} \arctan\left(-\frac{\sqrt{-c^{2} d e + b c e^{2}} x}{c d - b e}\right) + 15 \, {\left(7 \, c^{4} d^{3} e - 12 \, b c^{3} d^{2} e^{2} + 6 \, b^{2} c^{2} d e^{3} - b^{3} c e^{4}\right)} x}{15 \, {\left(c^{5} d e - b c^{4} e^{2}\right)}}\right]"," ",0,"[1/30*(6*(c^4*d*e^3 - b*c^3*e^4)*x^5 + 10*(4*c^4*d^2*e^2 - 5*b*c^3*d*e^3 + b^2*c^2*e^4)*x^3 - 15*(8*c^3*d^3 - 12*b*c^2*d^2*e + 6*b^2*c*d*e^2 - b^3*e^3)*sqrt(c^2*d*e - b*c*e^2)*log((c*e*x^2 + c*d - b*e + 2*sqrt(c^2*d*e - b*c*e^2)*x)/(c*e*x^2 - c*d + b*e)) + 30*(7*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*x)/(c^5*d*e - b*c^4*e^2), 1/15*(3*(c^4*d*e^3 - b*c^3*e^4)*x^5 + 5*(4*c^4*d^2*e^2 - 5*b*c^3*d*e^3 + b^2*c^2*e^4)*x^3 - 15*(8*c^3*d^3 - 12*b*c^2*d^2*e + 6*b^2*c*d*e^2 - b^3*e^3)*sqrt(-c^2*d*e + b*c*e^2)*arctan(-sqrt(-c^2*d*e + b*c*e^2)*x/(c*d - b*e)) + 15*(7*c^4*d^3*e - 12*b*c^3*d^2*e^2 + 6*b^2*c^2*d*e^3 - b^3*c*e^4)*x)/(c^5*d*e - b*c^4*e^2)]","B",0
215,1,311,0,1.697434," ","integrate((e*x^2+d)^3/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(c^{3} d e^{2} - b c^{2} e^{3}\right)} x^{3} + 3 \, {\left(4 \, c^{2} d^{2} - 4 \, b c d e + b^{2} e^{2}\right)} \sqrt{c^{2} d e - b c e^{2}} \log\left(\frac{c e x^{2} + c d - b e - 2 \, \sqrt{c^{2} d e - b c e^{2}} x}{c e x^{2} - c d + b e}\right) + 6 \, {\left(3 \, c^{3} d^{2} e - 4 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} x}{6 \, {\left(c^{4} d e - b c^{3} e^{2}\right)}}, \frac{{\left(c^{3} d e^{2} - b c^{2} e^{3}\right)} x^{3} - 3 \, {\left(4 \, c^{2} d^{2} - 4 \, b c d e + b^{2} e^{2}\right)} \sqrt{-c^{2} d e + b c e^{2}} \arctan\left(-\frac{\sqrt{-c^{2} d e + b c e^{2}} x}{c d - b e}\right) + 3 \, {\left(3 \, c^{3} d^{2} e - 4 \, b c^{2} d e^{2} + b^{2} c e^{3}\right)} x}{3 \, {\left(c^{4} d e - b c^{3} e^{2}\right)}}\right]"," ",0,"[1/6*(2*(c^3*d*e^2 - b*c^2*e^3)*x^3 + 3*(4*c^2*d^2 - 4*b*c*d*e + b^2*e^2)*sqrt(c^2*d*e - b*c*e^2)*log((c*e*x^2 + c*d - b*e - 2*sqrt(c^2*d*e - b*c*e^2)*x)/(c*e*x^2 - c*d + b*e)) + 6*(3*c^3*d^2*e - 4*b*c^2*d*e^2 + b^2*c*e^3)*x)/(c^4*d*e - b*c^3*e^2), 1/3*((c^3*d*e^2 - b*c^2*e^3)*x^3 - 3*(4*c^2*d^2 - 4*b*c*d*e + b^2*e^2)*sqrt(-c^2*d*e + b*c*e^2)*arctan(-sqrt(-c^2*d*e + b*c*e^2)*x/(c*d - b*e)) + 3*(3*c^3*d^2*e - 4*b*c^2*d*e^2 + b^2*c*e^3)*x)/(c^4*d*e - b*c^3*e^2)]","A",0
216,1,210,0,1.111873," ","integrate((e*x^2+d)^2/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{c^{2} d e - b c e^{2}} {\left(2 \, c d - b e\right)} \log\left(\frac{c e x^{2} + c d - b e + 2 \, \sqrt{c^{2} d e - b c e^{2}} x}{c e x^{2} - c d + b e}\right) - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x}{2 \, {\left(c^{3} d e - b c^{2} e^{2}\right)}}, -\frac{\sqrt{-c^{2} d e + b c e^{2}} {\left(2 \, c d - b e\right)} \arctan\left(-\frac{\sqrt{-c^{2} d e + b c e^{2}} x}{c d - b e}\right) - {\left(c^{2} d e - b c e^{2}\right)} x}{c^{3} d e - b c^{2} e^{2}}\right]"," ",0,"[-1/2*(sqrt(c^2*d*e - b*c*e^2)*(2*c*d - b*e)*log((c*e*x^2 + c*d - b*e + 2*sqrt(c^2*d*e - b*c*e^2)*x)/(c*e*x^2 - c*d + b*e)) - 2*(c^2*d*e - b*c*e^2)*x)/(c^3*d*e - b*c^2*e^2), -(sqrt(-c^2*d*e + b*c*e^2)*(2*c*d - b*e)*arctan(-sqrt(-c^2*d*e + b*c*e^2)*x/(c*d - b*e)) - (c^2*d*e - b*c*e^2)*x)/(c^3*d*e - b*c^2*e^2)]","A",0
217,1,134,0,0.626013," ","integrate((e*x^2+d)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{c e x^{2} + c d - b e - 2 \, \sqrt{c^{2} d e - b c e^{2}} x}{c e x^{2} - c d + b e}\right)}{2 \, \sqrt{c^{2} d e - b c e^{2}}}, -\frac{\sqrt{-c^{2} d e + b c e^{2}} \arctan\left(-\frac{\sqrt{-c^{2} d e + b c e^{2}} x}{c d - b e}\right)}{c^{2} d e - b c e^{2}}\right]"," ",0,"[1/2*log((c*e*x^2 + c*d - b*e - 2*sqrt(c^2*d*e - b*c*e^2)*x)/(c*e*x^2 - c*d + b*e))/sqrt(c^2*d*e - b*c*e^2), -sqrt(-c^2*d*e + b*c*e^2)*arctan(-sqrt(-c^2*d*e + b*c*e^2)*x/(c*d - b*e))/(c^2*d*e - b*c*e^2)]","A",0
218,1,895,0,1.286660," ","integrate(1/(e*x^2+d)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(c d^{2} e^{2} x^{2} + c d^{3} e\right)} \sqrt{\frac{c}{c d e - b e^{2}}} \log\left(\frac{c e x^{2} - 2 \, {\left(c d e - b e^{2}\right)} x \sqrt{\frac{c}{c d e - b e^{2}}} + c d - b e}{c e x^{2} - c d + b e}\right) + {\left(4 \, c d^{2} - b d e + {\left(4 \, c d e - b e^{2}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} x}{4 \, {\left(4 \, c^{2} d^{5} e - 4 \, b c d^{4} e^{2} + b^{2} d^{3} e^{3} + {\left(4 \, c^{2} d^{4} e^{2} - 4 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} x^{2}\right)}}, -\frac{{\left(4 \, c d^{2} - b d e + {\left(4 \, c d e - b e^{2}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - {\left(c d^{2} e^{2} x^{2} + c d^{3} e\right)} \sqrt{\frac{c}{c d e - b e^{2}}} \log\left(\frac{c e x^{2} - 2 \, {\left(c d e - b e^{2}\right)} x \sqrt{\frac{c}{c d e - b e^{2}}} + c d - b e}{c e x^{2} - c d + b e}\right) + {\left(2 \, c d^{2} e - b d e^{2}\right)} x}{2 \, {\left(4 \, c^{2} d^{5} e - 4 \, b c d^{4} e^{2} + b^{2} d^{3} e^{3} + {\left(4 \, c^{2} d^{4} e^{2} - 4 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} x^{2}\right)}}, \frac{4 \, {\left(c d^{2} e^{2} x^{2} + c d^{3} e\right)} \sqrt{-\frac{c}{c d e - b e^{2}}} \arctan\left(e x \sqrt{-\frac{c}{c d e - b e^{2}}}\right) + {\left(4 \, c d^{2} - b d e + {\left(4 \, c d e - b e^{2}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 2 \, {\left(2 \, c d^{2} e - b d e^{2}\right)} x}{4 \, {\left(4 \, c^{2} d^{5} e - 4 \, b c d^{4} e^{2} + b^{2} d^{3} e^{3} + {\left(4 \, c^{2} d^{4} e^{2} - 4 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} x^{2}\right)}}, \frac{2 \, {\left(c d^{2} e^{2} x^{2} + c d^{3} e\right)} \sqrt{-\frac{c}{c d e - b e^{2}}} \arctan\left(e x \sqrt{-\frac{c}{c d e - b e^{2}}}\right) - {\left(4 \, c d^{2} - b d e + {\left(4 \, c d e - b e^{2}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - {\left(2 \, c d^{2} e - b d e^{2}\right)} x}{2 \, {\left(4 \, c^{2} d^{5} e - 4 \, b c d^{4} e^{2} + b^{2} d^{3} e^{3} + {\left(4 \, c^{2} d^{4} e^{2} - 4 \, b c d^{3} e^{3} + b^{2} d^{2} e^{4}\right)} x^{2}\right)}}\right]"," ",0,"[1/4*(2*(c*d^2*e^2*x^2 + c*d^3*e)*sqrt(c/(c*d*e - b*e^2))*log((c*e*x^2 - 2*(c*d*e - b*e^2)*x*sqrt(c/(c*d*e - b*e^2)) + c*d - b*e)/(c*e*x^2 - c*d + b*e)) + (4*c*d^2 - b*d*e + (4*c*d*e - b*e^2)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 2*(2*c*d^2*e - b*d*e^2)*x)/(4*c^2*d^5*e - 4*b*c*d^4*e^2 + b^2*d^3*e^3 + (4*c^2*d^4*e^2 - 4*b*c*d^3*e^3 + b^2*d^2*e^4)*x^2), -1/2*((4*c*d^2 - b*d*e + (4*c*d*e - b*e^2)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - (c*d^2*e^2*x^2 + c*d^3*e)*sqrt(c/(c*d*e - b*e^2))*log((c*e*x^2 - 2*(c*d*e - b*e^2)*x*sqrt(c/(c*d*e - b*e^2)) + c*d - b*e)/(c*e*x^2 - c*d + b*e)) + (2*c*d^2*e - b*d*e^2)*x)/(4*c^2*d^5*e - 4*b*c*d^4*e^2 + b^2*d^3*e^3 + (4*c^2*d^4*e^2 - 4*b*c*d^3*e^3 + b^2*d^2*e^4)*x^2), 1/4*(4*(c*d^2*e^2*x^2 + c*d^3*e)*sqrt(-c/(c*d*e - b*e^2))*arctan(e*x*sqrt(-c/(c*d*e - b*e^2))) + (4*c*d^2 - b*d*e + (4*c*d*e - b*e^2)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 2*(2*c*d^2*e - b*d*e^2)*x)/(4*c^2*d^5*e - 4*b*c*d^4*e^2 + b^2*d^3*e^3 + (4*c^2*d^4*e^2 - 4*b*c*d^3*e^3 + b^2*d^2*e^4)*x^2), 1/2*(2*(c*d^2*e^2*x^2 + c*d^3*e)*sqrt(-c/(c*d*e - b*e^2))*arctan(e*x*sqrt(-c/(c*d*e - b*e^2))) - (4*c*d^2 - b*d*e + (4*c*d*e - b*e^2)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - (2*c*d^2*e - b*d*e^2)*x)/(4*c^2*d^5*e - 4*b*c*d^4*e^2 + b^2*d^3*e^3 + (4*c^2*d^4*e^2 - 4*b*c*d^3*e^3 + b^2*d^2*e^4)*x^2)]","A",0
219,1,1765,0,3.708233," ","integrate(1/(e*x^2+d)^2/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(20 \, c^{2} d^{3} e^{2} - 16 \, b c d^{2} e^{3} + 3 \, b^{2} d e^{4}\right)} x^{3} + 8 \, {\left(c^{2} d^{3} e^{3} x^{4} + 2 \, c^{2} d^{4} e^{2} x^{2} + c^{2} d^{5} e\right)} \sqrt{\frac{c}{c d e - b e^{2}}} \log\left(\frac{c e x^{2} + 2 \, {\left(c d e - b e^{2}\right)} x \sqrt{\frac{c}{c d e - b e^{2}}} + c d - b e}{c e x^{2} - c d + b e}\right) - {\left(28 \, c^{2} d^{4} - 16 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + {\left(28 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 3 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(28 \, c^{2} d^{3} e - 16 \, b c d^{2} e^{2} + 3 \, b^{2} d e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(28 \, c^{2} d^{4} e - 24 \, b c d^{3} e^{2} + 5 \, b^{2} d^{2} e^{3}\right)} x}{16 \, {\left(8 \, c^{3} d^{8} e - 12 \, b c^{2} d^{7} e^{2} + 6 \, b^{2} c d^{6} e^{3} - b^{3} d^{5} e^{4} + {\left(8 \, c^{3} d^{6} e^{3} - 12 \, b c^{2} d^{5} e^{4} + 6 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x^{4} + 2 \, {\left(8 \, c^{3} d^{7} e^{2} - 12 \, b c^{2} d^{6} e^{3} + 6 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5}\right)} x^{2}\right)}}, -\frac{{\left(20 \, c^{2} d^{3} e^{2} - 16 \, b c d^{2} e^{3} + 3 \, b^{2} d e^{4}\right)} x^{3} + {\left(28 \, c^{2} d^{4} - 16 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + {\left(28 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 3 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(28 \, c^{2} d^{3} e - 16 \, b c d^{2} e^{2} + 3 \, b^{2} d e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + 4 \, {\left(c^{2} d^{3} e^{3} x^{4} + 2 \, c^{2} d^{4} e^{2} x^{2} + c^{2} d^{5} e\right)} \sqrt{\frac{c}{c d e - b e^{2}}} \log\left(\frac{c e x^{2} + 2 \, {\left(c d e - b e^{2}\right)} x \sqrt{\frac{c}{c d e - b e^{2}}} + c d - b e}{c e x^{2} - c d + b e}\right) + {\left(28 \, c^{2} d^{4} e - 24 \, b c d^{3} e^{2} + 5 \, b^{2} d^{2} e^{3}\right)} x}{8 \, {\left(8 \, c^{3} d^{8} e - 12 \, b c^{2} d^{7} e^{2} + 6 \, b^{2} c d^{6} e^{3} - b^{3} d^{5} e^{4} + {\left(8 \, c^{3} d^{6} e^{3} - 12 \, b c^{2} d^{5} e^{4} + 6 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x^{4} + 2 \, {\left(8 \, c^{3} d^{7} e^{2} - 12 \, b c^{2} d^{6} e^{3} + 6 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5}\right)} x^{2}\right)}}, -\frac{2 \, {\left(20 \, c^{2} d^{3} e^{2} - 16 \, b c d^{2} e^{3} + 3 \, b^{2} d e^{4}\right)} x^{3} - 16 \, {\left(c^{2} d^{3} e^{3} x^{4} + 2 \, c^{2} d^{4} e^{2} x^{2} + c^{2} d^{5} e\right)} \sqrt{-\frac{c}{c d e - b e^{2}}} \arctan\left(e x \sqrt{-\frac{c}{c d e - b e^{2}}}\right) - {\left(28 \, c^{2} d^{4} - 16 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + {\left(28 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 3 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(28 \, c^{2} d^{3} e - 16 \, b c d^{2} e^{2} + 3 \, b^{2} d e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(28 \, c^{2} d^{4} e - 24 \, b c d^{3} e^{2} + 5 \, b^{2} d^{2} e^{3}\right)} x}{16 \, {\left(8 \, c^{3} d^{8} e - 12 \, b c^{2} d^{7} e^{2} + 6 \, b^{2} c d^{6} e^{3} - b^{3} d^{5} e^{4} + {\left(8 \, c^{3} d^{6} e^{3} - 12 \, b c^{2} d^{5} e^{4} + 6 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x^{4} + 2 \, {\left(8 \, c^{3} d^{7} e^{2} - 12 \, b c^{2} d^{6} e^{3} + 6 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5}\right)} x^{2}\right)}}, -\frac{{\left(20 \, c^{2} d^{3} e^{2} - 16 \, b c d^{2} e^{3} + 3 \, b^{2} d e^{4}\right)} x^{3} - 8 \, {\left(c^{2} d^{3} e^{3} x^{4} + 2 \, c^{2} d^{4} e^{2} x^{2} + c^{2} d^{5} e\right)} \sqrt{-\frac{c}{c d e - b e^{2}}} \arctan\left(e x \sqrt{-\frac{c}{c d e - b e^{2}}}\right) + {\left(28 \, c^{2} d^{4} - 16 \, b c d^{3} e + 3 \, b^{2} d^{2} e^{2} + {\left(28 \, c^{2} d^{2} e^{2} - 16 \, b c d e^{3} + 3 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(28 \, c^{2} d^{3} e - 16 \, b c d^{2} e^{2} + 3 \, b^{2} d e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(28 \, c^{2} d^{4} e - 24 \, b c d^{3} e^{2} + 5 \, b^{2} d^{2} e^{3}\right)} x}{8 \, {\left(8 \, c^{3} d^{8} e - 12 \, b c^{2} d^{7} e^{2} + 6 \, b^{2} c d^{6} e^{3} - b^{3} d^{5} e^{4} + {\left(8 \, c^{3} d^{6} e^{3} - 12 \, b c^{2} d^{5} e^{4} + 6 \, b^{2} c d^{4} e^{5} - b^{3} d^{3} e^{6}\right)} x^{4} + 2 \, {\left(8 \, c^{3} d^{7} e^{2} - 12 \, b c^{2} d^{6} e^{3} + 6 \, b^{2} c d^{5} e^{4} - b^{3} d^{4} e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/16*(2*(20*c^2*d^3*e^2 - 16*b*c*d^2*e^3 + 3*b^2*d*e^4)*x^3 + 8*(c^2*d^3*e^3*x^4 + 2*c^2*d^4*e^2*x^2 + c^2*d^5*e)*sqrt(c/(c*d*e - b*e^2))*log((c*e*x^2 + 2*(c*d*e - b*e^2)*x*sqrt(c/(c*d*e - b*e^2)) + c*d - b*e)/(c*e*x^2 - c*d + b*e)) - (28*c^2*d^4 - 16*b*c*d^3*e + 3*b^2*d^2*e^2 + (28*c^2*d^2*e^2 - 16*b*c*d*e^3 + 3*b^2*e^4)*x^4 + 2*(28*c^2*d^3*e - 16*b*c*d^2*e^2 + 3*b^2*d*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(28*c^2*d^4*e - 24*b*c*d^3*e^2 + 5*b^2*d^2*e^3)*x)/(8*c^3*d^8*e - 12*b*c^2*d^7*e^2 + 6*b^2*c*d^6*e^3 - b^3*d^5*e^4 + (8*c^3*d^6*e^3 - 12*b*c^2*d^5*e^4 + 6*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x^4 + 2*(8*c^3*d^7*e^2 - 12*b*c^2*d^6*e^3 + 6*b^2*c*d^5*e^4 - b^3*d^4*e^5)*x^2), -1/8*((20*c^2*d^3*e^2 - 16*b*c*d^2*e^3 + 3*b^2*d*e^4)*x^3 + (28*c^2*d^4 - 16*b*c*d^3*e + 3*b^2*d^2*e^2 + (28*c^2*d^2*e^2 - 16*b*c*d*e^3 + 3*b^2*e^4)*x^4 + 2*(28*c^2*d^3*e - 16*b*c*d^2*e^2 + 3*b^2*d*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + 4*(c^2*d^3*e^3*x^4 + 2*c^2*d^4*e^2*x^2 + c^2*d^5*e)*sqrt(c/(c*d*e - b*e^2))*log((c*e*x^2 + 2*(c*d*e - b*e^2)*x*sqrt(c/(c*d*e - b*e^2)) + c*d - b*e)/(c*e*x^2 - c*d + b*e)) + (28*c^2*d^4*e - 24*b*c*d^3*e^2 + 5*b^2*d^2*e^3)*x)/(8*c^3*d^8*e - 12*b*c^2*d^7*e^2 + 6*b^2*c*d^6*e^3 - b^3*d^5*e^4 + (8*c^3*d^6*e^3 - 12*b*c^2*d^5*e^4 + 6*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x^4 + 2*(8*c^3*d^7*e^2 - 12*b*c^2*d^6*e^3 + 6*b^2*c*d^5*e^4 - b^3*d^4*e^5)*x^2), -1/16*(2*(20*c^2*d^3*e^2 - 16*b*c*d^2*e^3 + 3*b^2*d*e^4)*x^3 - 16*(c^2*d^3*e^3*x^4 + 2*c^2*d^4*e^2*x^2 + c^2*d^5*e)*sqrt(-c/(c*d*e - b*e^2))*arctan(e*x*sqrt(-c/(c*d*e - b*e^2))) - (28*c^2*d^4 - 16*b*c*d^3*e + 3*b^2*d^2*e^2 + (28*c^2*d^2*e^2 - 16*b*c*d*e^3 + 3*b^2*e^4)*x^4 + 2*(28*c^2*d^3*e - 16*b*c*d^2*e^2 + 3*b^2*d*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(28*c^2*d^4*e - 24*b*c*d^3*e^2 + 5*b^2*d^2*e^3)*x)/(8*c^3*d^8*e - 12*b*c^2*d^7*e^2 + 6*b^2*c*d^6*e^3 - b^3*d^5*e^4 + (8*c^3*d^6*e^3 - 12*b*c^2*d^5*e^4 + 6*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x^4 + 2*(8*c^3*d^7*e^2 - 12*b*c^2*d^6*e^3 + 6*b^2*c*d^5*e^4 - b^3*d^4*e^5)*x^2), -1/8*((20*c^2*d^3*e^2 - 16*b*c*d^2*e^3 + 3*b^2*d*e^4)*x^3 - 8*(c^2*d^3*e^3*x^4 + 2*c^2*d^4*e^2*x^2 + c^2*d^5*e)*sqrt(-c/(c*d*e - b*e^2))*arctan(e*x*sqrt(-c/(c*d*e - b*e^2))) + (28*c^2*d^4 - 16*b*c*d^3*e + 3*b^2*d^2*e^2 + (28*c^2*d^2*e^2 - 16*b*c*d*e^3 + 3*b^2*e^4)*x^4 + 2*(28*c^2*d^3*e - 16*b*c*d^2*e^2 + 3*b^2*d*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (28*c^2*d^4*e - 24*b*c*d^3*e^2 + 5*b^2*d^2*e^3)*x)/(8*c^3*d^8*e - 12*b*c^2*d^7*e^2 + 6*b^2*c*d^6*e^3 - b^3*d^5*e^4 + (8*c^3*d^6*e^3 - 12*b*c^2*d^5*e^4 + 6*b^2*c*d^4*e^5 - b^3*d^3*e^6)*x^4 + 2*(8*c^3*d^7*e^2 - 12*b*c^2*d^6*e^3 + 6*b^2*c*d^5*e^4 - b^3*d^4*e^5)*x^2)]","B",0
220,1,1079,0,2.744593," ","integrate((e*x^2+d)^(5/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[\frac{2 \, \sqrt{e x^{2} + d} c e x - {\left(5 \, c d - 2 \, b e\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) - {\left(2 \, c d e - b e^{2}\right)} \sqrt{\frac{2 \, c d - b e}{c d e - b e^{2}}} \log\left(\frac{c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(17 \, c^{2} d^{2} e^{2} - 24 \, b c d e^{3} + 8 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 11 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} x^{2} + 4 \, {\left({\left(3 \, c^{2} d^{2} e^{2} - 5 \, b c d e^{3} + 2 \, b^{2} e^{4}\right)} x^{3} + {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{\frac{2 \, c d - b e}{c d e - b e^{2}}}}{c^{2} e^{2} x^{4} + c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x^{2}}\right)}{4 \, c^{2} e}, \frac{2 \, \sqrt{e x^{2} + d} c e x - 2 \, {\left(5 \, c d - 2 \, b e\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(2 \, c d e - b e^{2}\right)} \sqrt{\frac{2 \, c d - b e}{c d e - b e^{2}}} \log\left(\frac{c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(17 \, c^{2} d^{2} e^{2} - 24 \, b c d e^{3} + 8 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 11 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} x^{2} + 4 \, {\left({\left(3 \, c^{2} d^{2} e^{2} - 5 \, b c d e^{3} + 2 \, b^{2} e^{4}\right)} x^{3} + {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{\frac{2 \, c d - b e}{c d e - b e^{2}}}}{c^{2} e^{2} x^{4} + c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x^{2}}\right)}{4 \, c^{2} e}, \frac{2 \, \sqrt{e x^{2} + d} c e x + 2 \, {\left(2 \, c d e - b e^{2}\right)} \sqrt{-\frac{2 \, c d - b e}{c d e - b e^{2}}} \arctan\left(\frac{{\left(c d^{2} - b d e + {\left(3 \, c d e - 2 \, b e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{2 \, c d - b e}{c d e - b e^{2}}}}{2 \, {\left({\left(2 \, c d e - b e^{2}\right)} x^{3} + {\left(2 \, c d^{2} - b d e\right)} x\right)}}\right) - {\left(5 \, c d - 2 \, b e\right)} \sqrt{e} \log\left(-2 \, e x^{2} + 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right)}{4 \, c^{2} e}, \frac{\sqrt{e x^{2} + d} c e x - {\left(5 \, c d - 2 \, b e\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left(2 \, c d e - b e^{2}\right)} \sqrt{-\frac{2 \, c d - b e}{c d e - b e^{2}}} \arctan\left(\frac{{\left(c d^{2} - b d e + {\left(3 \, c d e - 2 \, b e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{2 \, c d - b e}{c d e - b e^{2}}}}{2 \, {\left({\left(2 \, c d e - b e^{2}\right)} x^{3} + {\left(2 \, c d^{2} - b d e\right)} x\right)}}\right)}{2 \, c^{2} e}\right]"," ",0,"[1/4*(2*sqrt(e*x^2 + d)*c*e*x - (5*c*d - 2*b*e)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) - (2*c*d*e - b*e^2)*sqrt((2*c*d - b*e)/(c*d*e - b*e^2))*log((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (17*c^2*d^2*e^2 - 24*b*c*d*e^3 + 8*b^2*e^4)*x^4 + 2*(7*c^2*d^3*e - 11*b*c*d^2*e^2 + 4*b^2*d*e^3)*x^2 + 4*((3*c^2*d^2*e^2 - 5*b*c*d*e^3 + 2*b^2*e^4)*x^3 + (c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(e*x^2 + d)*sqrt((2*c*d - b*e)/(c*d*e - b*e^2)))/(c^2*e^2*x^4 + c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*(c^2*d*e - b*c*e^2)*x^2)))/(c^2*e), 1/4*(2*sqrt(e*x^2 + d)*c*e*x - 2*(5*c*d - 2*b*e)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (2*c*d*e - b*e^2)*sqrt((2*c*d - b*e)/(c*d*e - b*e^2))*log((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (17*c^2*d^2*e^2 - 24*b*c*d*e^3 + 8*b^2*e^4)*x^4 + 2*(7*c^2*d^3*e - 11*b*c*d^2*e^2 + 4*b^2*d*e^3)*x^2 + 4*((3*c^2*d^2*e^2 - 5*b*c*d*e^3 + 2*b^2*e^4)*x^3 + (c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(e*x^2 + d)*sqrt((2*c*d - b*e)/(c*d*e - b*e^2)))/(c^2*e^2*x^4 + c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*(c^2*d*e - b*c*e^2)*x^2)))/(c^2*e), 1/4*(2*sqrt(e*x^2 + d)*c*e*x + 2*(2*c*d*e - b*e^2)*sqrt(-(2*c*d - b*e)/(c*d*e - b*e^2))*arctan(1/2*(c*d^2 - b*d*e + (3*c*d*e - 2*b*e^2)*x^2)*sqrt(e*x^2 + d)*sqrt(-(2*c*d - b*e)/(c*d*e - b*e^2))/((2*c*d*e - b*e^2)*x^3 + (2*c*d^2 - b*d*e)*x)) - (5*c*d - 2*b*e)*sqrt(e)*log(-2*e*x^2 + 2*sqrt(e*x^2 + d)*sqrt(e)*x - d))/(c^2*e), 1/2*(sqrt(e*x^2 + d)*c*e*x - (5*c*d - 2*b*e)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + (2*c*d*e - b*e^2)*sqrt(-(2*c*d - b*e)/(c*d*e - b*e^2))*arctan(1/2*(c*d^2 - b*d*e + (3*c*d*e - 2*b*e^2)*x^2)*sqrt(e*x^2 + d)*sqrt(-(2*c*d - b*e)/(c*d*e - b*e^2))/((2*c*d*e - b*e^2)*x^3 + (2*c*d^2 - b*d*e)*x)))/(c^2*e)]","A",0
221,1,940,0,1.040534," ","integrate((e*x^2+d)^(3/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[\frac{e \sqrt{\frac{2 \, c d - b e}{c d e - b e^{2}}} \log\left(\frac{c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(17 \, c^{2} d^{2} e^{2} - 24 \, b c d e^{3} + 8 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 11 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} x^{2} - 4 \, {\left({\left(3 \, c^{2} d^{2} e^{2} - 5 \, b c d e^{3} + 2 \, b^{2} e^{4}\right)} x^{3} + {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{\frac{2 \, c d - b e}{c d e - b e^{2}}}}{c^{2} e^{2} x^{4} + c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x^{2}}\right) + 2 \, \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right)}{4 \, c e}, \frac{e \sqrt{\frac{2 \, c d - b e}{c d e - b e^{2}}} \log\left(\frac{c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(17 \, c^{2} d^{2} e^{2} - 24 \, b c d e^{3} + 8 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 11 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} x^{2} - 4 \, {\left({\left(3 \, c^{2} d^{2} e^{2} - 5 \, b c d e^{3} + 2 \, b^{2} e^{4}\right)} x^{3} + {\left(c^{2} d^{3} e - 2 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)} \sqrt{e x^{2} + d} \sqrt{\frac{2 \, c d - b e}{c d e - b e^{2}}}}{c^{2} e^{2} x^{4} + c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x^{2}}\right) - 4 \, \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{4 \, c e}, \frac{e \sqrt{-\frac{2 \, c d - b e}{c d e - b e^{2}}} \arctan\left(\frac{{\left(c d^{2} - b d e + {\left(3 \, c d e - 2 \, b e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{2 \, c d - b e}{c d e - b e^{2}}}}{2 \, {\left({\left(2 \, c d e - b e^{2}\right)} x^{3} + {\left(2 \, c d^{2} - b d e\right)} x\right)}}\right) + \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right)}{2 \, c e}, \frac{e \sqrt{-\frac{2 \, c d - b e}{c d e - b e^{2}}} \arctan\left(\frac{{\left(c d^{2} - b d e + {\left(3 \, c d e - 2 \, b e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d} \sqrt{-\frac{2 \, c d - b e}{c d e - b e^{2}}}}{2 \, {\left({\left(2 \, c d e - b e^{2}\right)} x^{3} + {\left(2 \, c d^{2} - b d e\right)} x\right)}}\right) - 2 \, \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right)}{2 \, c e}\right]"," ",0,"[1/4*(e*sqrt((2*c*d - b*e)/(c*d*e - b*e^2))*log((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (17*c^2*d^2*e^2 - 24*b*c*d*e^3 + 8*b^2*e^4)*x^4 + 2*(7*c^2*d^3*e - 11*b*c*d^2*e^2 + 4*b^2*d*e^3)*x^2 - 4*((3*c^2*d^2*e^2 - 5*b*c*d*e^3 + 2*b^2*e^4)*x^3 + (c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(e*x^2 + d)*sqrt((2*c*d - b*e)/(c*d*e - b*e^2)))/(c^2*e^2*x^4 + c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*(c^2*d*e - b*c*e^2)*x^2)) + 2*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d))/(c*e), 1/4*(e*sqrt((2*c*d - b*e)/(c*d*e - b*e^2))*log((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (17*c^2*d^2*e^2 - 24*b*c*d*e^3 + 8*b^2*e^4)*x^4 + 2*(7*c^2*d^3*e - 11*b*c*d^2*e^2 + 4*b^2*d*e^3)*x^2 - 4*((3*c^2*d^2*e^2 - 5*b*c*d*e^3 + 2*b^2*e^4)*x^3 + (c^2*d^3*e - 2*b*c*d^2*e^2 + b^2*d*e^3)*x)*sqrt(e*x^2 + d)*sqrt((2*c*d - b*e)/(c*d*e - b*e^2)))/(c^2*e^2*x^4 + c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*(c^2*d*e - b*c*e^2)*x^2)) - 4*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/(c*e), 1/2*(e*sqrt(-(2*c*d - b*e)/(c*d*e - b*e^2))*arctan(1/2*(c*d^2 - b*d*e + (3*c*d*e - 2*b*e^2)*x^2)*sqrt(e*x^2 + d)*sqrt(-(2*c*d - b*e)/(c*d*e - b*e^2))/((2*c*d*e - b*e^2)*x^3 + (2*c*d^2 - b*d*e)*x)) + sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d))/(c*e), 1/2*(e*sqrt(-(2*c*d - b*e)/(c*d*e - b*e^2))*arctan(1/2*(c*d^2 - b*d*e + (3*c*d*e - 2*b*e^2)*x^2)*sqrt(e*x^2 + d)*sqrt(-(2*c*d - b*e)/(c*d*e - b*e^2))/((2*c*d*e - b*e^2)*x^3 + (2*c*d^2 - b*d*e)*x)) - 2*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)))/(c*e)]","A",0
222,1,432,0,1.094262," ","integrate((e*x^2+d)^(1/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(17 \, c^{2} d^{2} e^{2} - 24 \, b c d e^{3} + 8 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 11 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} x^{2} - 4 \, \sqrt{2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}} {\left({\left(3 \, c d e - 2 \, b e^{2}\right)} x^{3} + {\left(c d^{2} - b d e\right)} x\right)} \sqrt{e x^{2} + d}}{c^{2} e^{2} x^{4} + c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x^{2}}\right)}{4 \, \sqrt{2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}}}, -\frac{\sqrt{-2 \, c^{2} d^{2} e + 3 \, b c d e^{2} - b^{2} e^{3}} \arctan\left(-\frac{\sqrt{-2 \, c^{2} d^{2} e + 3 \, b c d e^{2} - b^{2} e^{3}} {\left(c d^{2} - b d e + {\left(3 \, c d e - 2 \, b e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(2 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + b^{2} e^{4}\right)} x^{3} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)}}\right)}{2 \, {\left(2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}\right)}}\right]"," ",0,"[1/4*log((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (17*c^2*d^2*e^2 - 24*b*c*d*e^3 + 8*b^2*e^4)*x^4 + 2*(7*c^2*d^3*e - 11*b*c*d^2*e^2 + 4*b^2*d*e^3)*x^2 - 4*sqrt(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)*((3*c*d*e - 2*b*e^2)*x^3 + (c*d^2 - b*d*e)*x)*sqrt(e*x^2 + d))/(c^2*e^2*x^4 + c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*(c^2*d*e - b*c*e^2)*x^2))/sqrt(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3), -1/2*sqrt(-2*c^2*d^2*e + 3*b*c*d*e^2 - b^2*e^3)*arctan(-1/2*sqrt(-2*c^2*d^2*e + 3*b*c*d*e^2 - b^2*e^3)*(c*d^2 - b*d*e + (3*c*d*e - 2*b*e^2)*x^2)*sqrt(e*x^2 + d)/((2*c^2*d^2*e^2 - 3*b*c*d*e^3 + b^2*e^4)*x^3 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 + b^2*d*e^3)*x))/(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)]","B",0
223,1,701,0,1.270324," ","integrate(1/(e*x^2+d)^(1/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}\right)} \sqrt{e x^{2} + d} x + \sqrt{2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}} {\left(c d e x^{2} + c d^{2}\right)} \log\left(\frac{c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(17 \, c^{2} d^{2} e^{2} - 24 \, b c d e^{3} + 8 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 11 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} x^{2} + 4 \, \sqrt{2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}} {\left({\left(3 \, c d e - 2 \, b e^{2}\right)} x^{3} + {\left(c d^{2} - b d e\right)} x\right)} \sqrt{e x^{2} + d}}{c^{2} e^{2} x^{4} + c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x^{2}}\right)}{4 \, {\left(4 \, c^{3} d^{5} e - 8 \, b c^{2} d^{4} e^{2} + 5 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4} + {\left(4 \, c^{3} d^{4} e^{2} - 8 \, b c^{2} d^{3} e^{3} + 5 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2}\right)}}, -\frac{2 \, {\left(2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}\right)} \sqrt{e x^{2} + d} x + \sqrt{-2 \, c^{2} d^{2} e + 3 \, b c d e^{2} - b^{2} e^{3}} {\left(c d e x^{2} + c d^{2}\right)} \arctan\left(-\frac{\sqrt{-2 \, c^{2} d^{2} e + 3 \, b c d e^{2} - b^{2} e^{3}} {\left(c d^{2} - b d e + {\left(3 \, c d e - 2 \, b e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(2 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + b^{2} e^{4}\right)} x^{3} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)}}\right)}{2 \, {\left(4 \, c^{3} d^{5} e - 8 \, b c^{2} d^{4} e^{2} + 5 \, b^{2} c d^{3} e^{3} - b^{3} d^{2} e^{4} + {\left(4 \, c^{3} d^{4} e^{2} - 8 \, b c^{2} d^{3} e^{3} + 5 \, b^{2} c d^{2} e^{4} - b^{3} d e^{5}\right)} x^{2}\right)}}\right]"," ",0,"[-1/4*(4*(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)*sqrt(e*x^2 + d)*x + sqrt(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)*(c*d*e*x^2 + c*d^2)*log((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (17*c^2*d^2*e^2 - 24*b*c*d*e^3 + 8*b^2*e^4)*x^4 + 2*(7*c^2*d^3*e - 11*b*c*d^2*e^2 + 4*b^2*d*e^3)*x^2 + 4*sqrt(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)*((3*c*d*e - 2*b*e^2)*x^3 + (c*d^2 - b*d*e)*x)*sqrt(e*x^2 + d))/(c^2*e^2*x^4 + c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*(c^2*d*e - b*c*e^2)*x^2)))/(4*c^3*d^5*e - 8*b*c^2*d^4*e^2 + 5*b^2*c*d^3*e^3 - b^3*d^2*e^4 + (4*c^3*d^4*e^2 - 8*b*c^2*d^3*e^3 + 5*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2), -1/2*(2*(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)*sqrt(e*x^2 + d)*x + sqrt(-2*c^2*d^2*e + 3*b*c*d*e^2 - b^2*e^3)*(c*d*e*x^2 + c*d^2)*arctan(-1/2*sqrt(-2*c^2*d^2*e + 3*b*c*d*e^2 - b^2*e^3)*(c*d^2 - b*d*e + (3*c*d*e - 2*b*e^2)*x^2)*sqrt(e*x^2 + d)/((2*c^2*d^2*e^2 - 3*b*c*d*e^3 + b^2*e^4)*x^3 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 + b^2*d*e^3)*x)))/(4*c^3*d^5*e - 8*b*c^2*d^4*e^2 + 5*b^2*c*d^3*e^3 - b^3*d^2*e^4 + (4*c^3*d^4*e^2 - 8*b*c^2*d^3*e^3 + 5*b^2*c*d^2*e^4 - b^3*d*e^5)*x^2)]","B",0
224,1,1063,0,2.645125," ","integrate(1/(e*x^2+d)^(3/2)/(c*e^2*x^4+b*e^2*x^2+b*d*e-c*d^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c^{2} d^{2} e^{2} x^{4} + 2 \, c^{2} d^{3} e x^{2} + c^{2} d^{4}\right)} \sqrt{2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}} \log\left(\frac{c^{2} d^{4} - 2 \, b c d^{3} e + b^{2} d^{2} e^{2} + {\left(17 \, c^{2} d^{2} e^{2} - 24 \, b c d e^{3} + 8 \, b^{2} e^{4}\right)} x^{4} + 2 \, {\left(7 \, c^{2} d^{3} e - 11 \, b c d^{2} e^{2} + 4 \, b^{2} d e^{3}\right)} x^{2} - 4 \, \sqrt{2 \, c^{2} d^{2} e - 3 \, b c d e^{2} + b^{2} e^{3}} {\left({\left(3 \, c d e - 2 \, b e^{2}\right)} x^{3} + {\left(c d^{2} - b d e\right)} x\right)} \sqrt{e x^{2} + d}}{c^{2} e^{2} x^{4} + c^{2} d^{2} - 2 \, b c d e + b^{2} e^{2} - 2 \, {\left(c^{2} d e - b c e^{2}\right)} x^{2}}\right) - 4 \, {\left({\left(14 \, c^{3} d^{3} e^{2} - 25 \, b c^{2} d^{2} e^{3} + 13 \, b^{2} c d e^{4} - 2 \, b^{3} e^{5}\right)} x^{3} + 3 \, {\left(6 \, c^{3} d^{4} e - 11 \, b c^{2} d^{3} e^{2} + 6 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4}\right)} x\right)} \sqrt{e x^{2} + d}}{12 \, {\left(8 \, c^{4} d^{8} e - 20 \, b c^{3} d^{7} e^{2} + 18 \, b^{2} c^{2} d^{6} e^{3} - 7 \, b^{3} c d^{5} e^{4} + b^{4} d^{4} e^{5} + {\left(8 \, c^{4} d^{6} e^{3} - 20 \, b c^{3} d^{5} e^{4} + 18 \, b^{2} c^{2} d^{4} e^{5} - 7 \, b^{3} c d^{3} e^{6} + b^{4} d^{2} e^{7}\right)} x^{4} + 2 \, {\left(8 \, c^{4} d^{7} e^{2} - 20 \, b c^{3} d^{6} e^{3} + 18 \, b^{2} c^{2} d^{5} e^{4} - 7 \, b^{3} c d^{4} e^{5} + b^{4} d^{3} e^{6}\right)} x^{2}\right)}}, -\frac{3 \, {\left(c^{2} d^{2} e^{2} x^{4} + 2 \, c^{2} d^{3} e x^{2} + c^{2} d^{4}\right)} \sqrt{-2 \, c^{2} d^{2} e + 3 \, b c d e^{2} - b^{2} e^{3}} \arctan\left(-\frac{\sqrt{-2 \, c^{2} d^{2} e + 3 \, b c d e^{2} - b^{2} e^{3}} {\left(c d^{2} - b d e + {\left(3 \, c d e - 2 \, b e^{2}\right)} x^{2}\right)} \sqrt{e x^{2} + d}}{2 \, {\left({\left(2 \, c^{2} d^{2} e^{2} - 3 \, b c d e^{3} + b^{2} e^{4}\right)} x^{3} + {\left(2 \, c^{2} d^{3} e - 3 \, b c d^{2} e^{2} + b^{2} d e^{3}\right)} x\right)}}\right) + 2 \, {\left({\left(14 \, c^{3} d^{3} e^{2} - 25 \, b c^{2} d^{2} e^{3} + 13 \, b^{2} c d e^{4} - 2 \, b^{3} e^{5}\right)} x^{3} + 3 \, {\left(6 \, c^{3} d^{4} e - 11 \, b c^{2} d^{3} e^{2} + 6 \, b^{2} c d^{2} e^{3} - b^{3} d e^{4}\right)} x\right)} \sqrt{e x^{2} + d}}{6 \, {\left(8 \, c^{4} d^{8} e - 20 \, b c^{3} d^{7} e^{2} + 18 \, b^{2} c^{2} d^{6} e^{3} - 7 \, b^{3} c d^{5} e^{4} + b^{4} d^{4} e^{5} + {\left(8 \, c^{4} d^{6} e^{3} - 20 \, b c^{3} d^{5} e^{4} + 18 \, b^{2} c^{2} d^{4} e^{5} - 7 \, b^{3} c d^{3} e^{6} + b^{4} d^{2} e^{7}\right)} x^{4} + 2 \, {\left(8 \, c^{4} d^{7} e^{2} - 20 \, b c^{3} d^{6} e^{3} + 18 \, b^{2} c^{2} d^{5} e^{4} - 7 \, b^{3} c d^{4} e^{5} + b^{4} d^{3} e^{6}\right)} x^{2}\right)}}\right]"," ",0,"[1/12*(3*(c^2*d^2*e^2*x^4 + 2*c^2*d^3*e*x^2 + c^2*d^4)*sqrt(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)*log((c^2*d^4 - 2*b*c*d^3*e + b^2*d^2*e^2 + (17*c^2*d^2*e^2 - 24*b*c*d*e^3 + 8*b^2*e^4)*x^4 + 2*(7*c^2*d^3*e - 11*b*c*d^2*e^2 + 4*b^2*d*e^3)*x^2 - 4*sqrt(2*c^2*d^2*e - 3*b*c*d*e^2 + b^2*e^3)*((3*c*d*e - 2*b*e^2)*x^3 + (c*d^2 - b*d*e)*x)*sqrt(e*x^2 + d))/(c^2*e^2*x^4 + c^2*d^2 - 2*b*c*d*e + b^2*e^2 - 2*(c^2*d*e - b*c*e^2)*x^2)) - 4*((14*c^3*d^3*e^2 - 25*b*c^2*d^2*e^3 + 13*b^2*c*d*e^4 - 2*b^3*e^5)*x^3 + 3*(6*c^3*d^4*e - 11*b*c^2*d^3*e^2 + 6*b^2*c*d^2*e^3 - b^3*d*e^4)*x)*sqrt(e*x^2 + d))/(8*c^4*d^8*e - 20*b*c^3*d^7*e^2 + 18*b^2*c^2*d^6*e^3 - 7*b^3*c*d^5*e^4 + b^4*d^4*e^5 + (8*c^4*d^6*e^3 - 20*b*c^3*d^5*e^4 + 18*b^2*c^2*d^4*e^5 - 7*b^3*c*d^3*e^6 + b^4*d^2*e^7)*x^4 + 2*(8*c^4*d^7*e^2 - 20*b*c^3*d^6*e^3 + 18*b^2*c^2*d^5*e^4 - 7*b^3*c*d^4*e^5 + b^4*d^3*e^6)*x^2), -1/6*(3*(c^2*d^2*e^2*x^4 + 2*c^2*d^3*e*x^2 + c^2*d^4)*sqrt(-2*c^2*d^2*e + 3*b*c*d*e^2 - b^2*e^3)*arctan(-1/2*sqrt(-2*c^2*d^2*e + 3*b*c*d*e^2 - b^2*e^3)*(c*d^2 - b*d*e + (3*c*d*e - 2*b*e^2)*x^2)*sqrt(e*x^2 + d)/((2*c^2*d^2*e^2 - 3*b*c*d*e^3 + b^2*e^4)*x^3 + (2*c^2*d^3*e - 3*b*c*d^2*e^2 + b^2*d*e^3)*x)) + 2*((14*c^3*d^3*e^2 - 25*b*c^2*d^2*e^3 + 13*b^2*c*d*e^4 - 2*b^3*e^5)*x^3 + 3*(6*c^3*d^4*e - 11*b*c^2*d^3*e^2 + 6*b^2*c*d^2*e^3 - b^3*d*e^4)*x)*sqrt(e*x^2 + d))/(8*c^4*d^8*e - 20*b*c^3*d^7*e^2 + 18*b^2*c^2*d^6*e^3 - 7*b^3*c*d^5*e^4 + b^4*d^4*e^5 + (8*c^4*d^6*e^3 - 20*b*c^3*d^5*e^4 + 18*b^2*c^2*d^4*e^5 - 7*b^3*c*d^3*e^6 + b^4*d^2*e^7)*x^4 + 2*(8*c^4*d^7*e^2 - 20*b*c^3*d^6*e^3 + 18*b^2*c^2*d^5*e^4 - 7*b^3*c*d^4*e^5 + b^4*d^3*e^6)*x^2)]","B",0
225,0,0,0,2.124104," ","integrate((x^2+1)^3*(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{6} + 3 \, x^{4} + 3 \, x^{2} + 1\right)} \sqrt{x^{4} + x^{2} + 1}, x\right)"," ",0,"integral((x^6 + 3*x^4 + 3*x^2 + 1)*sqrt(x^4 + x^2 + 1), x)","F",0
226,0,0,0,1.112049," ","integrate((x^2+1)^2*(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{4} + 2 \, x^{2} + 1\right)} \sqrt{x^{4} + x^{2} + 1}, x\right)"," ",0,"integral((x^4 + 2*x^2 + 1)*sqrt(x^4 + x^2 + 1), x)","F",0
227,0,0,0,1.035324," ","integrate((x^2+1)*(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)*(x^2 + 1), x)","F",0
228,0,0,0,1.105595," ","integrate((x^4+x^2+1)^(1/2)/(x^2+1),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^2 + 1), x)","F",0
229,0,0,0,0.786149," ","integrate((x^4+x^2+1)^(1/2)/(x^2+1)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{4} + 2 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^4 + 2*x^2 + 1), x)","F",0
230,0,0,0,0.975184," ","integrate((x^4+x^2+1)^(1/2)/(x^2+1)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{6} + 3 \, x^{4} + 3 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^6 + 3*x^4 + 3*x^2 + 1), x)","F",0
231,0,0,0,1.102839," ","integrate((x^4+x^2+1)^(1/2)/(x^2+1)^4,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{8} + 4 \, x^{6} + 6 \, x^{4} + 4 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^8 + 4*x^6 + 6*x^4 + 4*x^2 + 1), x)","F",0
232,0,0,0,1.121581," ","integrate((x^2+1)^3/(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{6} + 3 \, x^{4} + 3 \, x^{2} + 1}{\sqrt{x^{4} + x^{2} + 1}}, x\right)"," ",0,"integral((x^6 + 3*x^4 + 3*x^2 + 1)/sqrt(x^4 + x^2 + 1), x)","F",0
233,0,0,0,0.533090," ","integrate((x^2+1)^2/(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{4} + 2 \, x^{2} + 1}{\sqrt{x^{4} + x^{2} + 1}}, x\right)"," ",0,"integral((x^4 + 2*x^2 + 1)/sqrt(x^4 + x^2 + 1), x)","F",0
234,0,0,0,1.053656," ","integrate((x^2+1)/(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{x^{2} + 1}{\sqrt{x^{4} + x^{2} + 1}}, x\right)"," ",0,"integral((x^2 + 1)/sqrt(x^4 + x^2 + 1), x)","F",0
235,0,0,0,1.097128," ","integrate(1/(x^2+1)/(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{6} + 2 \, x^{4} + 2 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^6 + 2*x^4 + 2*x^2 + 1), x)","F",0
236,0,0,0,1.108783," ","integrate(1/(x^2+1)^2/(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{8} + 3 \, x^{6} + 4 \, x^{4} + 3 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^8 + 3*x^6 + 4*x^4 + 3*x^2 + 1), x)","F",0
237,0,0,0,0.953938," ","integrate(1/(x^2+1)^3/(x^4+x^2+1)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{10} + 4 \, x^{8} + 7 \, x^{6} + 7 \, x^{4} + 4 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^10 + 4*x^8 + 7*x^6 + 7*x^4 + 4*x^2 + 1), x)","F",0
238,0,0,0,1.224184," ","integrate((x^2+1)^3/(x^4+x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{6} + 3 \, x^{4} + 3 \, x^{2} + 1\right)} \sqrt{x^{4} + x^{2} + 1}}{x^{8} + 2 \, x^{6} + 3 \, x^{4} + 2 \, x^{2} + 1}, x\right)"," ",0,"integral((x^6 + 3*x^4 + 3*x^2 + 1)*sqrt(x^4 + x^2 + 1)/(x^8 + 2*x^6 + 3*x^4 + 2*x^2 + 1), x)","F",0
239,0,0,0,1.322153," ","integrate((x^2+1)^2/(x^4+x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{4} + 2 \, x^{2} + 1\right)} \sqrt{x^{4} + x^{2} + 1}}{x^{8} + 2 \, x^{6} + 3 \, x^{4} + 2 \, x^{2} + 1}, x\right)"," ",0,"integral((x^4 + 2*x^2 + 1)*sqrt(x^4 + x^2 + 1)/(x^8 + 2*x^6 + 3*x^4 + 2*x^2 + 1), x)","F",0
240,0,0,0,0.780103," ","integrate((x^2+1)/(x^4+x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1} {\left(x^{2} + 1\right)}}{x^{8} + 2 \, x^{6} + 3 \, x^{4} + 2 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)*(x^2 + 1)/(x^8 + 2*x^6 + 3*x^4 + 2*x^2 + 1), x)","F",0
241,0,0,0,1.118973," ","integrate(1/(x^2+1)/(x^4+x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{10} + 3 \, x^{8} + 5 \, x^{6} + 5 \, x^{4} + 3 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^10 + 3*x^8 + 5*x^6 + 5*x^4 + 3*x^2 + 1), x)","F",0
242,0,0,0,1.238581," ","integrate(1/(x^2+1)^2/(x^4+x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{12} + 4 \, x^{10} + 8 \, x^{8} + 10 \, x^{6} + 8 \, x^{4} + 4 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^12 + 4*x^10 + 8*x^8 + 10*x^6 + 8*x^4 + 4*x^2 + 1), x)","F",0
243,0,0,0,0.934813," ","integrate(1/(x^2+1)^3/(x^4+x^2+1)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + x^{2} + 1}}{x^{14} + 5 \, x^{12} + 12 \, x^{10} + 18 \, x^{8} + 18 \, x^{6} + 12 \, x^{4} + 5 \, x^{2} + 1}, x\right)"," ",0,"integral(sqrt(x^4 + x^2 + 1)/(x^14 + 5*x^12 + 12*x^10 + 18*x^8 + 18*x^6 + 12*x^4 + 5*x^2 + 1), x)","F",0
244,1,148,0,0.869428," ","integrate((e*x^2+d)^4*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{4} c + \frac{4}{11} x^{11} e^{3} d c + \frac{1}{11} x^{11} e^{4} b + \frac{2}{3} x^{9} e^{2} d^{2} c + \frac{4}{9} x^{9} e^{3} d b + \frac{1}{9} x^{9} e^{4} a + \frac{4}{7} x^{7} e d^{3} c + \frac{6}{7} x^{7} e^{2} d^{2} b + \frac{4}{7} x^{7} e^{3} d a + \frac{1}{5} x^{5} d^{4} c + \frac{4}{5} x^{5} e d^{3} b + \frac{6}{5} x^{5} e^{2} d^{2} a + \frac{1}{3} x^{3} d^{4} b + \frac{4}{3} x^{3} e d^{3} a + x d^{4} a"," ",0,"1/13*x^13*e^4*c + 4/11*x^11*e^3*d*c + 1/11*x^11*e^4*b + 2/3*x^9*e^2*d^2*c + 4/9*x^9*e^3*d*b + 1/9*x^9*e^4*a + 4/7*x^7*e*d^3*c + 6/7*x^7*e^2*d^2*b + 4/7*x^7*e^3*d*a + 1/5*x^5*d^4*c + 4/5*x^5*e*d^3*b + 6/5*x^5*e^2*d^2*a + 1/3*x^3*d^4*b + 4/3*x^3*e*d^3*a + x*d^4*a","A",0
245,1,111,0,0.600122," ","integrate((e*x^2+d)^3*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{11} x^{11} e^{3} c + \frac{1}{3} x^{9} e^{2} d c + \frac{1}{9} x^{9} e^{3} b + \frac{3}{7} x^{7} e d^{2} c + \frac{3}{7} x^{7} e^{2} d b + \frac{1}{7} x^{7} e^{3} a + \frac{1}{5} x^{5} d^{3} c + \frac{3}{5} x^{5} e d^{2} b + \frac{3}{5} x^{5} e^{2} d a + \frac{1}{3} x^{3} d^{3} b + x^{3} e d^{2} a + x d^{3} a"," ",0,"1/11*x^11*e^3*c + 1/3*x^9*e^2*d*c + 1/9*x^9*e^3*b + 3/7*x^7*e*d^2*c + 3/7*x^7*e^2*d*b + 1/7*x^7*e^3*a + 1/5*x^5*d^3*c + 3/5*x^5*e*d^2*b + 3/5*x^5*e^2*d*a + 1/3*x^3*d^3*b + x^3*e*d^2*a + x*d^3*a","A",0
246,1,76,0,0.792349," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{9} x^{9} e^{2} c + \frac{2}{7} x^{7} e d c + \frac{1}{7} x^{7} e^{2} b + \frac{1}{5} x^{5} d^{2} c + \frac{2}{5} x^{5} e d b + \frac{1}{5} x^{5} e^{2} a + \frac{1}{3} x^{3} d^{2} b + \frac{2}{3} x^{3} e d a + x d^{2} a"," ",0,"1/9*x^9*e^2*c + 2/7*x^7*e*d*c + 1/7*x^7*e^2*b + 1/5*x^5*d^2*c + 2/5*x^5*e*d*b + 1/5*x^5*e^2*a + 1/3*x^3*d^2*b + 2/3*x^3*e*d*a + x*d^2*a","A",0
247,1,40,0,0.928230," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{7} x^{7} e c + \frac{1}{5} x^{5} d c + \frac{1}{5} x^{5} e b + \frac{1}{3} x^{3} d b + \frac{1}{3} x^{3} e a + x d a"," ",0,"1/7*x^7*e*c + 1/5*x^5*d*c + 1/5*x^5*e*b + 1/3*x^3*d*b + 1/3*x^3*e*a + x*d*a","A",0
248,1,159,0,1.005273," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d),x, algorithm=""fricas"")","\left[\frac{2 \, c d e^{2} x^{3} - 3 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 6 \, {\left(c d^{2} e - b d e^{2}\right)} x}{6 \, d e^{3}}, \frac{c d e^{2} x^{3} + 3 \, {\left(c d^{2} - b d e + a e^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 3 \, {\left(c d^{2} e - b d e^{2}\right)} x}{3 \, d e^{3}}\right]"," ",0,"[1/6*(2*c*d*e^2*x^3 - 3*(c*d^2 - b*d*e + a*e^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 6*(c*d^2*e - b*d*e^2)*x)/(d*e^3), 1/3*(c*d*e^2*x^3 + 3*(c*d^2 - b*d*e + a*e^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 3*(c*d^2*e - b*d*e^2)*x)/(d*e^3)]","A",0
249,1,268,0,1.024925," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c d^{2} e^{2} x^{3} + {\left(3 \, c d^{3} - b d^{2} e - a d e^{2} + {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} x}{4 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}, \frac{2 \, c d^{2} e^{2} x^{3} - {\left(3 \, c d^{3} - b d^{2} e - a d e^{2} + {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} x}{2 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}\right]"," ",0,"[1/4*(4*c*d^2*e^2*x^3 + (3*c*d^3 - b*d^2*e - a*d*e^2 + (3*c*d^2*e - b*d*e^2 - a*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3), 1/2*(2*c*d^2*e^2*x^3 - (3*c*d^3 - b*d^2*e - a*d*e^2 + (3*c*d^2*e - b*d*e^2 - a*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3)]","A",0
250,1,391,0,1.369286," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[-\frac{2 \, {\left(5 \, c d^{3} e^{2} - b d^{2} e^{3} - 3 \, a d e^{4}\right)} x^{3} + {\left(3 \, c d^{4} + b d^{3} e + 3 \, a d^{2} e^{2} + {\left(3 \, c d^{2} e^{2} + b d e^{3} + 3 \, a e^{4}\right)} x^{4} + 2 \, {\left(3 \, c d^{3} e + b d^{2} e^{2} + 3 \, a d e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(3 \, c d^{4} e + b d^{3} e^{2} - 5 \, a d^{2} e^{3}\right)} x}{16 \, {\left(d^{3} e^{5} x^{4} + 2 \, d^{4} e^{4} x^{2} + d^{5} e^{3}\right)}}, -\frac{{\left(5 \, c d^{3} e^{2} - b d^{2} e^{3} - 3 \, a d e^{4}\right)} x^{3} - {\left(3 \, c d^{4} + b d^{3} e + 3 \, a d^{2} e^{2} + {\left(3 \, c d^{2} e^{2} + b d e^{3} + 3 \, a e^{4}\right)} x^{4} + 2 \, {\left(3 \, c d^{3} e + b d^{2} e^{2} + 3 \, a d e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(3 \, c d^{4} e + b d^{3} e^{2} - 5 \, a d^{2} e^{3}\right)} x}{8 \, {\left(d^{3} e^{5} x^{4} + 2 \, d^{4} e^{4} x^{2} + d^{5} e^{3}\right)}}\right]"," ",0,"[-1/16*(2*(5*c*d^3*e^2 - b*d^2*e^3 - 3*a*d*e^4)*x^3 + (3*c*d^4 + b*d^3*e + 3*a*d^2*e^2 + (3*c*d^2*e^2 + b*d*e^3 + 3*a*e^4)*x^4 + 2*(3*c*d^3*e + b*d^2*e^2 + 3*a*d*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(3*c*d^4*e + b*d^3*e^2 - 5*a*d^2*e^3)*x)/(d^3*e^5*x^4 + 2*d^4*e^4*x^2 + d^5*e^3), -1/8*((5*c*d^3*e^2 - b*d^2*e^3 - 3*a*d*e^4)*x^3 - (3*c*d^4 + b*d^3*e + 3*a*d^2*e^2 + (3*c*d^2*e^2 + b*d*e^3 + 3*a*e^4)*x^4 + 2*(3*c*d^3*e + b*d^2*e^2 + 3*a*d*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (3*c*d^4*e + b*d^3*e^2 - 5*a*d^2*e^3)*x)/(d^3*e^5*x^4 + 2*d^4*e^4*x^2 + d^5*e^3)]","A",0
251,1,530,0,0.596276," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^4,x, algorithm=""fricas"")","\left[\frac{6 \, {\left(c d^{3} e^{3} + b d^{2} e^{4} + 5 \, a d e^{5}\right)} x^{5} - 16 \, {\left(c d^{4} e^{2} - b d^{3} e^{3} - 5 \, a d^{2} e^{4}\right)} x^{3} - 3 \, {\left({\left(c d^{2} e^{3} + b d e^{4} + 5 \, a e^{5}\right)} x^{6} + c d^{5} + b d^{4} e + 5 \, a d^{3} e^{2} + 3 \, {\left(c d^{3} e^{2} + b d^{2} e^{3} + 5 \, a d e^{4}\right)} x^{4} + 3 \, {\left(c d^{4} e + b d^{3} e^{2} + 5 \, a d^{2} e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 6 \, {\left(c d^{5} e + b d^{4} e^{2} - 11 \, a d^{3} e^{3}\right)} x}{96 \, {\left(d^{4} e^{6} x^{6} + 3 \, d^{5} e^{5} x^{4} + 3 \, d^{6} e^{4} x^{2} + d^{7} e^{3}\right)}}, \frac{3 \, {\left(c d^{3} e^{3} + b d^{2} e^{4} + 5 \, a d e^{5}\right)} x^{5} - 8 \, {\left(c d^{4} e^{2} - b d^{3} e^{3} - 5 \, a d^{2} e^{4}\right)} x^{3} + 3 \, {\left({\left(c d^{2} e^{3} + b d e^{4} + 5 \, a e^{5}\right)} x^{6} + c d^{5} + b d^{4} e + 5 \, a d^{3} e^{2} + 3 \, {\left(c d^{3} e^{2} + b d^{2} e^{3} + 5 \, a d e^{4}\right)} x^{4} + 3 \, {\left(c d^{4} e + b d^{3} e^{2} + 5 \, a d^{2} e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 3 \, {\left(c d^{5} e + b d^{4} e^{2} - 11 \, a d^{3} e^{3}\right)} x}{48 \, {\left(d^{4} e^{6} x^{6} + 3 \, d^{5} e^{5} x^{4} + 3 \, d^{6} e^{4} x^{2} + d^{7} e^{3}\right)}}\right]"," ",0,"[1/96*(6*(c*d^3*e^3 + b*d^2*e^4 + 5*a*d*e^5)*x^5 - 16*(c*d^4*e^2 - b*d^3*e^3 - 5*a*d^2*e^4)*x^3 - 3*((c*d^2*e^3 + b*d*e^4 + 5*a*e^5)*x^6 + c*d^5 + b*d^4*e + 5*a*d^3*e^2 + 3*(c*d^3*e^2 + b*d^2*e^3 + 5*a*d*e^4)*x^4 + 3*(c*d^4*e + b*d^3*e^2 + 5*a*d^2*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 6*(c*d^5*e + b*d^4*e^2 - 11*a*d^3*e^3)*x)/(d^4*e^6*x^6 + 3*d^5*e^5*x^4 + 3*d^6*e^4*x^2 + d^7*e^3), 1/48*(3*(c*d^3*e^3 + b*d^2*e^4 + 5*a*d*e^5)*x^5 - 8*(c*d^4*e^2 - b*d^3*e^3 - 5*a*d^2*e^4)*x^3 + 3*((c*d^2*e^3 + b*d*e^4 + 5*a*e^5)*x^6 + c*d^5 + b*d^4*e + 5*a*d^3*e^2 + 3*(c*d^3*e^2 + b*d^2*e^3 + 5*a*d*e^4)*x^4 + 3*(c*d^4*e + b*d^3*e^2 + 5*a*d^2*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 3*(c*d^5*e + b*d^4*e^2 - 11*a*d^3*e^3)*x)/(d^4*e^6*x^6 + 3*d^5*e^5*x^4 + 3*d^6*e^4*x^2 + d^7*e^3)]","A",0
252,1,261,0,0.667606," ","integrate((e*x^2+d)^3*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{15} x^{15} e^{3} c^{2} + \frac{3}{13} x^{13} e^{2} d c^{2} + \frac{2}{13} x^{13} e^{3} c b + \frac{3}{11} x^{11} e d^{2} c^{2} + \frac{6}{11} x^{11} e^{2} d c b + \frac{1}{11} x^{11} e^{3} b^{2} + \frac{2}{11} x^{11} e^{3} c a + \frac{1}{9} x^{9} d^{3} c^{2} + \frac{2}{3} x^{9} e d^{2} c b + \frac{1}{3} x^{9} e^{2} d b^{2} + \frac{2}{3} x^{9} e^{2} d c a + \frac{2}{9} x^{9} e^{3} b a + \frac{2}{7} x^{7} d^{3} c b + \frac{3}{7} x^{7} e d^{2} b^{2} + \frac{6}{7} x^{7} e d^{2} c a + \frac{6}{7} x^{7} e^{2} d b a + \frac{1}{7} x^{7} e^{3} a^{2} + \frac{1}{5} x^{5} d^{3} b^{2} + \frac{2}{5} x^{5} d^{3} c a + \frac{6}{5} x^{5} e d^{2} b a + \frac{3}{5} x^{5} e^{2} d a^{2} + \frac{2}{3} x^{3} d^{3} b a + x^{3} e d^{2} a^{2} + x d^{3} a^{2}"," ",0,"1/15*x^15*e^3*c^2 + 3/13*x^13*e^2*d*c^2 + 2/13*x^13*e^3*c*b + 3/11*x^11*e*d^2*c^2 + 6/11*x^11*e^2*d*c*b + 1/11*x^11*e^3*b^2 + 2/11*x^11*e^3*c*a + 1/9*x^9*d^3*c^2 + 2/3*x^9*e*d^2*c*b + 1/3*x^9*e^2*d*b^2 + 2/3*x^9*e^2*d*c*a + 2/9*x^9*e^3*b*a + 2/7*x^7*d^3*c*b + 3/7*x^7*e*d^2*b^2 + 6/7*x^7*e*d^2*c*a + 6/7*x^7*e^2*d*b*a + 1/7*x^7*e^3*a^2 + 1/5*x^5*d^3*b^2 + 2/5*x^5*d^3*c*a + 6/5*x^5*e*d^2*b*a + 3/5*x^5*e^2*d*a^2 + 2/3*x^3*d^3*b*a + x^3*e*d^2*a^2 + x*d^3*a^2","A",0
253,1,181,0,0.557251," ","integrate((e*x^2+d)^2*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{13} x^{13} e^{2} c^{2} + \frac{2}{11} x^{11} e d c^{2} + \frac{2}{11} x^{11} e^{2} c b + \frac{1}{9} x^{9} d^{2} c^{2} + \frac{4}{9} x^{9} e d c b + \frac{1}{9} x^{9} e^{2} b^{2} + \frac{2}{9} x^{9} e^{2} c a + \frac{2}{7} x^{7} d^{2} c b + \frac{2}{7} x^{7} e d b^{2} + \frac{4}{7} x^{7} e d c a + \frac{2}{7} x^{7} e^{2} b a + \frac{1}{5} x^{5} d^{2} b^{2} + \frac{2}{5} x^{5} d^{2} c a + \frac{4}{5} x^{5} e d b a + \frac{1}{5} x^{5} e^{2} a^{2} + \frac{2}{3} x^{3} d^{2} b a + \frac{2}{3} x^{3} e d a^{2} + x d^{2} a^{2}"," ",0,"1/13*x^13*e^2*c^2 + 2/11*x^11*e*d*c^2 + 2/11*x^11*e^2*c*b + 1/9*x^9*d^2*c^2 + 4/9*x^9*e*d*c*b + 1/9*x^9*e^2*b^2 + 2/9*x^9*e^2*c*a + 2/7*x^7*d^2*c*b + 2/7*x^7*e*d*b^2 + 4/7*x^7*e*d*c*a + 2/7*x^7*e^2*b*a + 1/5*x^5*d^2*b^2 + 2/5*x^5*d^2*c*a + 4/5*x^5*e*d*b*a + 1/5*x^5*e^2*a^2 + 2/3*x^3*d^2*b*a + 2/3*x^3*e*d*a^2 + x*d^2*a^2","A",0
254,1,100,0,0.767499," ","integrate((e*x^2+d)*(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{11} x^{11} e c^{2} + \frac{1}{9} x^{9} d c^{2} + \frac{2}{9} x^{9} e c b + \frac{2}{7} x^{7} d c b + \frac{1}{7} x^{7} e b^{2} + \frac{2}{7} x^{7} e c a + \frac{1}{5} x^{5} d b^{2} + \frac{2}{5} x^{5} d c a + \frac{2}{5} x^{5} e b a + \frac{2}{3} x^{3} d b a + \frac{1}{3} x^{3} e a^{2} + x d a^{2}"," ",0,"1/11*x^11*e*c^2 + 1/9*x^9*d*c^2 + 2/9*x^9*e*c*b + 2/7*x^7*d*c*b + 1/7*x^7*e*b^2 + 2/7*x^7*e*c*a + 1/5*x^5*d*b^2 + 2/5*x^5*d*c*a + 2/5*x^5*e*b*a + 2/3*x^3*d*b*a + 1/3*x^3*e*a^2 + x*d*a^2","A",0
255,1,43,0,0.749593," ","integrate((c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{1}{9} x^{9} c^{2} + \frac{2}{7} x^{7} c b + \frac{1}{5} x^{5} b^{2} + \frac{2}{5} x^{5} c a + \frac{2}{3} x^{3} b a + x a^{2}"," ",0,"1/9*x^9*c^2 + 2/7*x^7*c*b + 1/5*x^5*b^2 + 2/5*x^5*c*a + 2/3*x^3*b*a + x*a^2","A",0
256,1,406,0,0.679580," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d),x, algorithm=""fricas"")","\left[\frac{30 \, c^{2} d e^{4} x^{7} - 42 \, {\left(c^{2} d^{2} e^{3} - 2 \, b c d e^{4}\right)} x^{5} + 70 \, {\left(c^{2} d^{3} e^{2} - 2 \, b c d^{2} e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x^{3} - 105 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 210 \, {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x}{210 \, d e^{5}}, \frac{15 \, c^{2} d e^{4} x^{7} - 21 \, {\left(c^{2} d^{2} e^{3} - 2 \, b c d e^{4}\right)} x^{5} + 35 \, {\left(c^{2} d^{3} e^{2} - 2 \, b c d^{2} e^{3} + {\left(b^{2} + 2 \, a c\right)} d e^{4}\right)} x^{3} + 105 \, {\left(c^{2} d^{4} - 2 \, b c d^{3} e - 2 \, a b d e^{3} + a^{2} e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 105 \, {\left(c^{2} d^{4} e - 2 \, b c d^{3} e^{2} - 2 \, a b d e^{4} + {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x}{105 \, d e^{5}}\right]"," ",0,"[1/210*(30*c^2*d*e^4*x^7 - 42*(c^2*d^2*e^3 - 2*b*c*d*e^4)*x^5 + 70*(c^2*d^3*e^2 - 2*b*c*d^2*e^3 + (b^2 + 2*a*c)*d*e^4)*x^3 - 105*(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 210*(c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + (b^2 + 2*a*c)*d^2*e^3)*x)/(d*e^5), 1/105*(15*c^2*d*e^4*x^7 - 21*(c^2*d^2*e^3 - 2*b*c*d*e^4)*x^5 + 35*(c^2*d^3*e^2 - 2*b*c*d^2*e^3 + (b^2 + 2*a*c)*d*e^4)*x^3 + 105*(c^2*d^4 - 2*b*c*d^3*e - 2*a*b*d*e^3 + a^2*e^4 + (b^2 + 2*a*c)*d^2*e^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 105*(c^2*d^4*e - 2*b*c*d^3*e^2 - 2*a*b*d*e^4 + (b^2 + 2*a*c)*d^2*e^3)*x)/(d*e^5)]","A",0
257,1,600,0,0.914744," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{12 \, c^{2} d^{2} e^{4} x^{7} - 4 \, {\left(7 \, c^{2} d^{3} e^{3} - 10 \, b c d^{2} e^{4}\right)} x^{5} + 20 \, {\left(7 \, c^{2} d^{4} e^{2} - 10 \, b c d^{3} e^{3} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} x^{3} + 15 \, {\left(7 \, c^{2} d^{5} - 10 \, b c d^{4} e - 2 \, a b d^{2} e^{3} - a^{2} d e^{4} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(7 \, c^{2} d^{4} e - 10 \, b c d^{3} e^{2} - 2 \, a b d e^{4} - a^{2} e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 30 \, {\left(7 \, c^{2} d^{5} e - 10 \, b c d^{4} e^{2} - 2 \, a b d^{2} e^{4} + a^{2} d e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} x}{60 \, {\left(d^{2} e^{6} x^{2} + d^{3} e^{5}\right)}}, \frac{6 \, c^{2} d^{2} e^{4} x^{7} - 2 \, {\left(7 \, c^{2} d^{3} e^{3} - 10 \, b c d^{2} e^{4}\right)} x^{5} + 10 \, {\left(7 \, c^{2} d^{4} e^{2} - 10 \, b c d^{3} e^{3} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} x^{3} - 15 \, {\left(7 \, c^{2} d^{5} - 10 \, b c d^{4} e - 2 \, a b d^{2} e^{3} - a^{2} d e^{4} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{2} + {\left(7 \, c^{2} d^{4} e - 10 \, b c d^{3} e^{2} - 2 \, a b d e^{4} - a^{2} e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + 15 \, {\left(7 \, c^{2} d^{5} e - 10 \, b c d^{4} e^{2} - 2 \, a b d^{2} e^{4} + a^{2} d e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} x}{30 \, {\left(d^{2} e^{6} x^{2} + d^{3} e^{5}\right)}}\right]"," ",0,"[1/60*(12*c^2*d^2*e^4*x^7 - 4*(7*c^2*d^3*e^3 - 10*b*c*d^2*e^4)*x^5 + 20*(7*c^2*d^4*e^2 - 10*b*c*d^3*e^3 + 3*(b^2 + 2*a*c)*d^2*e^4)*x^3 + 15*(7*c^2*d^5 - 10*b*c*d^4*e - 2*a*b*d^2*e^3 - a^2*d*e^4 + 3*(b^2 + 2*a*c)*d^3*e^2 + (7*c^2*d^4*e - 10*b*c*d^3*e^2 - 2*a*b*d*e^4 - a^2*e^5 + 3*(b^2 + 2*a*c)*d^2*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 30*(7*c^2*d^5*e - 10*b*c*d^4*e^2 - 2*a*b*d^2*e^4 + a^2*d*e^5 + 3*(b^2 + 2*a*c)*d^3*e^3)*x)/(d^2*e^6*x^2 + d^3*e^5), 1/30*(6*c^2*d^2*e^4*x^7 - 2*(7*c^2*d^3*e^3 - 10*b*c*d^2*e^4)*x^5 + 10*(7*c^2*d^4*e^2 - 10*b*c*d^3*e^3 + 3*(b^2 + 2*a*c)*d^2*e^4)*x^3 - 15*(7*c^2*d^5 - 10*b*c*d^4*e - 2*a*b*d^2*e^3 - a^2*d*e^4 + 3*(b^2 + 2*a*c)*d^3*e^2 + (7*c^2*d^4*e - 10*b*c*d^3*e^2 - 2*a*b*d*e^4 - a^2*e^5 + 3*(b^2 + 2*a*c)*d^2*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + 15*(7*c^2*d^5*e - 10*b*c*d^4*e^2 - 2*a*b*d^2*e^4 + a^2*d*e^5 + 3*(b^2 + 2*a*c)*d^3*e^3)*x)/(d^2*e^6*x^2 + d^3*e^5)]","A",0
258,1,794,0,0.712106," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d)^3,x, algorithm=""fricas"")","\left[\frac{16 \, c^{2} d^{3} e^{4} x^{7} - 16 \, {\left(7 \, c^{2} d^{4} e^{3} - 6 \, b c d^{3} e^{4}\right)} x^{5} - 2 \, {\left(175 \, c^{2} d^{5} e^{2} - 150 \, b c d^{4} e^{3} - 6 \, a b d^{2} e^{5} - 9 \, a^{2} d e^{6} + 15 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} x^{3} - 3 \, {\left(35 \, c^{2} d^{6} - 30 \, b c d^{5} e + 2 \, a b d^{3} e^{3} + 3 \, a^{2} d^{2} e^{4} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2} + {\left(35 \, c^{2} d^{4} e^{2} - 30 \, b c d^{3} e^{3} + 2 \, a b d e^{5} + 3 \, a^{2} e^{6} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} x^{4} + 2 \, {\left(35 \, c^{2} d^{5} e - 30 \, b c d^{4} e^{2} + 2 \, a b d^{2} e^{4} + 3 \, a^{2} d e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) - 6 \, {\left(35 \, c^{2} d^{6} e - 30 \, b c d^{5} e^{2} + 2 \, a b d^{3} e^{4} - 5 \, a^{2} d^{2} e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} x}{48 \, {\left(d^{3} e^{7} x^{4} + 2 \, d^{4} e^{6} x^{2} + d^{5} e^{5}\right)}}, \frac{8 \, c^{2} d^{3} e^{4} x^{7} - 8 \, {\left(7 \, c^{2} d^{4} e^{3} - 6 \, b c d^{3} e^{4}\right)} x^{5} - {\left(175 \, c^{2} d^{5} e^{2} - 150 \, b c d^{4} e^{3} - 6 \, a b d^{2} e^{5} - 9 \, a^{2} d e^{6} + 15 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} x^{3} + 3 \, {\left(35 \, c^{2} d^{6} - 30 \, b c d^{5} e + 2 \, a b d^{3} e^{3} + 3 \, a^{2} d^{2} e^{4} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{2} + {\left(35 \, c^{2} d^{4} e^{2} - 30 \, b c d^{3} e^{3} + 2 \, a b d e^{5} + 3 \, a^{2} e^{6} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{4}\right)} x^{4} + 2 \, {\left(35 \, c^{2} d^{5} e - 30 \, b c d^{4} e^{2} + 2 \, a b d^{2} e^{4} + 3 \, a^{2} d e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) - 3 \, {\left(35 \, c^{2} d^{6} e - 30 \, b c d^{5} e^{2} + 2 \, a b d^{3} e^{4} - 5 \, a^{2} d^{2} e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} x}{24 \, {\left(d^{3} e^{7} x^{4} + 2 \, d^{4} e^{6} x^{2} + d^{5} e^{5}\right)}}\right]"," ",0,"[1/48*(16*c^2*d^3*e^4*x^7 - 16*(7*c^2*d^4*e^3 - 6*b*c*d^3*e^4)*x^5 - 2*(175*c^2*d^5*e^2 - 150*b*c*d^4*e^3 - 6*a*b*d^2*e^5 - 9*a^2*d*e^6 + 15*(b^2 + 2*a*c)*d^3*e^4)*x^3 - 3*(35*c^2*d^6 - 30*b*c*d^5*e + 2*a*b*d^3*e^3 + 3*a^2*d^2*e^4 + 3*(b^2 + 2*a*c)*d^4*e^2 + (35*c^2*d^4*e^2 - 30*b*c*d^3*e^3 + 2*a*b*d*e^5 + 3*a^2*e^6 + 3*(b^2 + 2*a*c)*d^2*e^4)*x^4 + 2*(35*c^2*d^5*e - 30*b*c*d^4*e^2 + 2*a*b*d^2*e^4 + 3*a^2*d*e^5 + 3*(b^2 + 2*a*c)*d^3*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) - 6*(35*c^2*d^6*e - 30*b*c*d^5*e^2 + 2*a*b*d^3*e^4 - 5*a^2*d^2*e^5 + 3*(b^2 + 2*a*c)*d^4*e^3)*x)/(d^3*e^7*x^4 + 2*d^4*e^6*x^2 + d^5*e^5), 1/24*(8*c^2*d^3*e^4*x^7 - 8*(7*c^2*d^4*e^3 - 6*b*c*d^3*e^4)*x^5 - (175*c^2*d^5*e^2 - 150*b*c*d^4*e^3 - 6*a*b*d^2*e^5 - 9*a^2*d*e^6 + 15*(b^2 + 2*a*c)*d^3*e^4)*x^3 + 3*(35*c^2*d^6 - 30*b*c*d^5*e + 2*a*b*d^3*e^3 + 3*a^2*d^2*e^4 + 3*(b^2 + 2*a*c)*d^4*e^2 + (35*c^2*d^4*e^2 - 30*b*c*d^3*e^3 + 2*a*b*d*e^5 + 3*a^2*e^6 + 3*(b^2 + 2*a*c)*d^2*e^4)*x^4 + 2*(35*c^2*d^5*e - 30*b*c*d^4*e^2 + 2*a*b*d^2*e^4 + 3*a^2*d*e^5 + 3*(b^2 + 2*a*c)*d^3*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) - 3*(35*c^2*d^6*e - 30*b*c*d^5*e^2 + 2*a*b*d^3*e^4 - 5*a^2*d^2*e^5 + 3*(b^2 + 2*a*c)*d^4*e^3)*x)/(d^3*e^7*x^4 + 2*d^4*e^6*x^2 + d^5*e^5)]","B",0
259,1,1016,0,0.805431," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d)^4,x, algorithm=""fricas"")","\left[\frac{96 \, c^{2} d^{4} e^{4} x^{7} + 6 \, {\left(77 \, c^{2} d^{5} e^{3} - 22 \, b c d^{4} e^{4} + 2 \, a b d^{2} e^{6} + 5 \, a^{2} d e^{7} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{5}\right)} x^{5} + 16 \, {\left(35 \, c^{2} d^{6} e^{2} - 10 \, b c d^{5} e^{3} + 2 \, a b d^{3} e^{5} + 5 \, a^{2} d^{2} e^{6} - {\left(b^{2} + 2 \, a c\right)} d^{4} e^{4}\right)} x^{3} + 3 \, {\left(35 \, c^{2} d^{7} - 10 \, b c d^{6} e - 2 \, a b d^{4} e^{3} - 5 \, a^{2} d^{3} e^{4} - {\left(b^{2} + 2 \, a c\right)} d^{5} e^{2} + {\left(35 \, c^{2} d^{4} e^{3} - 10 \, b c d^{3} e^{4} - 2 \, a b d e^{6} - 5 \, a^{2} e^{7} - {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} x^{6} + 3 \, {\left(35 \, c^{2} d^{5} e^{2} - 10 \, b c d^{4} e^{3} - 2 \, a b d^{2} e^{5} - 5 \, a^{2} d e^{6} - {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} x^{4} + 3 \, {\left(35 \, c^{2} d^{6} e - 10 \, b c d^{5} e^{2} - 2 \, a b d^{3} e^{4} - 5 \, a^{2} d^{2} e^{5} - {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 6 \, {\left(35 \, c^{2} d^{7} e - 10 \, b c d^{6} e^{2} - 2 \, a b d^{4} e^{4} + 11 \, a^{2} d^{3} e^{5} - {\left(b^{2} + 2 \, a c\right)} d^{5} e^{3}\right)} x}{96 \, {\left(d^{4} e^{8} x^{6} + 3 \, d^{5} e^{7} x^{4} + 3 \, d^{6} e^{6} x^{2} + d^{7} e^{5}\right)}}, \frac{48 \, c^{2} d^{4} e^{4} x^{7} + 3 \, {\left(77 \, c^{2} d^{5} e^{3} - 22 \, b c d^{4} e^{4} + 2 \, a b d^{2} e^{6} + 5 \, a^{2} d e^{7} + {\left(b^{2} + 2 \, a c\right)} d^{3} e^{5}\right)} x^{5} + 8 \, {\left(35 \, c^{2} d^{6} e^{2} - 10 \, b c d^{5} e^{3} + 2 \, a b d^{3} e^{5} + 5 \, a^{2} d^{2} e^{6} - {\left(b^{2} + 2 \, a c\right)} d^{4} e^{4}\right)} x^{3} - 3 \, {\left(35 \, c^{2} d^{7} - 10 \, b c d^{6} e - 2 \, a b d^{4} e^{3} - 5 \, a^{2} d^{3} e^{4} - {\left(b^{2} + 2 \, a c\right)} d^{5} e^{2} + {\left(35 \, c^{2} d^{4} e^{3} - 10 \, b c d^{3} e^{4} - 2 \, a b d e^{6} - 5 \, a^{2} e^{7} - {\left(b^{2} + 2 \, a c\right)} d^{2} e^{5}\right)} x^{6} + 3 \, {\left(35 \, c^{2} d^{5} e^{2} - 10 \, b c d^{4} e^{3} - 2 \, a b d^{2} e^{5} - 5 \, a^{2} d e^{6} - {\left(b^{2} + 2 \, a c\right)} d^{3} e^{4}\right)} x^{4} + 3 \, {\left(35 \, c^{2} d^{6} e - 10 \, b c d^{5} e^{2} - 2 \, a b d^{3} e^{4} - 5 \, a^{2} d^{2} e^{5} - {\left(b^{2} + 2 \, a c\right)} d^{4} e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + 3 \, {\left(35 \, c^{2} d^{7} e - 10 \, b c d^{6} e^{2} - 2 \, a b d^{4} e^{4} + 11 \, a^{2} d^{3} e^{5} - {\left(b^{2} + 2 \, a c\right)} d^{5} e^{3}\right)} x}{48 \, {\left(d^{4} e^{8} x^{6} + 3 \, d^{5} e^{7} x^{4} + 3 \, d^{6} e^{6} x^{2} + d^{7} e^{5}\right)}}\right]"," ",0,"[1/96*(96*c^2*d^4*e^4*x^7 + 6*(77*c^2*d^5*e^3 - 22*b*c*d^4*e^4 + 2*a*b*d^2*e^6 + 5*a^2*d*e^7 + (b^2 + 2*a*c)*d^3*e^5)*x^5 + 16*(35*c^2*d^6*e^2 - 10*b*c*d^5*e^3 + 2*a*b*d^3*e^5 + 5*a^2*d^2*e^6 - (b^2 + 2*a*c)*d^4*e^4)*x^3 + 3*(35*c^2*d^7 - 10*b*c*d^6*e - 2*a*b*d^4*e^3 - 5*a^2*d^3*e^4 - (b^2 + 2*a*c)*d^5*e^2 + (35*c^2*d^4*e^3 - 10*b*c*d^3*e^4 - 2*a*b*d*e^6 - 5*a^2*e^7 - (b^2 + 2*a*c)*d^2*e^5)*x^6 + 3*(35*c^2*d^5*e^2 - 10*b*c*d^4*e^3 - 2*a*b*d^2*e^5 - 5*a^2*d*e^6 - (b^2 + 2*a*c)*d^3*e^4)*x^4 + 3*(35*c^2*d^6*e - 10*b*c*d^5*e^2 - 2*a*b*d^3*e^4 - 5*a^2*d^2*e^5 - (b^2 + 2*a*c)*d^4*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 6*(35*c^2*d^7*e - 10*b*c*d^6*e^2 - 2*a*b*d^4*e^4 + 11*a^2*d^3*e^5 - (b^2 + 2*a*c)*d^5*e^3)*x)/(d^4*e^8*x^6 + 3*d^5*e^7*x^4 + 3*d^6*e^6*x^2 + d^7*e^5), 1/48*(48*c^2*d^4*e^4*x^7 + 3*(77*c^2*d^5*e^3 - 22*b*c*d^4*e^4 + 2*a*b*d^2*e^6 + 5*a^2*d*e^7 + (b^2 + 2*a*c)*d^3*e^5)*x^5 + 8*(35*c^2*d^6*e^2 - 10*b*c*d^5*e^3 + 2*a*b*d^3*e^5 + 5*a^2*d^2*e^6 - (b^2 + 2*a*c)*d^4*e^4)*x^3 - 3*(35*c^2*d^7 - 10*b*c*d^6*e - 2*a*b*d^4*e^3 - 5*a^2*d^3*e^4 - (b^2 + 2*a*c)*d^5*e^2 + (35*c^2*d^4*e^3 - 10*b*c*d^3*e^4 - 2*a*b*d*e^6 - 5*a^2*e^7 - (b^2 + 2*a*c)*d^2*e^5)*x^6 + 3*(35*c^2*d^5*e^2 - 10*b*c*d^4*e^3 - 2*a*b*d^2*e^5 - 5*a^2*d*e^6 - (b^2 + 2*a*c)*d^3*e^4)*x^4 + 3*(35*c^2*d^6*e - 10*b*c*d^5*e^2 - 2*a*b*d^3*e^4 - 5*a^2*d^2*e^5 - (b^2 + 2*a*c)*d^4*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + 3*(35*c^2*d^7*e - 10*b*c*d^6*e^2 - 2*a*b*d^4*e^4 + 11*a^2*d^3*e^5 - (b^2 + 2*a*c)*d^5*e^3)*x)/(d^4*e^8*x^6 + 3*d^5*e^7*x^4 + 3*d^6*e^6*x^2 + d^7*e^5)]","B",0
260,1,1266,0,0.641481," ","integrate((c*x^4+b*x^2+a)^2/(e*x^2+d)^5,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left(93 \, c^{2} d^{5} e^{4} - 10 \, b c d^{4} e^{5} - 10 \, a b d^{2} e^{7} - 35 \, a^{2} d e^{8} - 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{6}\right)} x^{7} + 2 \, {\left(511 \, c^{2} d^{6} e^{3} + 146 \, b c d^{5} e^{4} - 110 \, a b d^{3} e^{6} - 385 \, a^{2} d^{2} e^{7} - 33 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{5}\right)} x^{5} + 2 \, {\left(385 \, c^{2} d^{7} e^{2} + 110 \, b c d^{6} e^{3} - 146 \, a b d^{4} e^{5} - 511 \, a^{2} d^{3} e^{6} + 33 \, {\left(b^{2} + 2 \, a c\right)} d^{5} e^{4}\right)} x^{3} + 3 \, {\left(35 \, c^{2} d^{8} + 10 \, b c d^{7} e + 10 \, a b d^{5} e^{3} + 35 \, a^{2} d^{4} e^{4} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{6} e^{2} + {\left(35 \, c^{2} d^{4} e^{4} + 10 \, b c d^{3} e^{5} + 10 \, a b d e^{7} + 35 \, a^{2} e^{8} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{6}\right)} x^{8} + 4 \, {\left(35 \, c^{2} d^{5} e^{3} + 10 \, b c d^{4} e^{4} + 10 \, a b d^{2} e^{6} + 35 \, a^{2} d e^{7} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{5}\right)} x^{6} + 6 \, {\left(35 \, c^{2} d^{6} e^{2} + 10 \, b c d^{5} e^{3} + 10 \, a b d^{3} e^{5} + 35 \, a^{2} d^{2} e^{6} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{4}\right)} x^{4} + 4 \, {\left(35 \, c^{2} d^{7} e + 10 \, b c d^{6} e^{2} + 10 \, a b d^{4} e^{4} + 35 \, a^{2} d^{3} e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{5} e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 6 \, {\left(35 \, c^{2} d^{8} e + 10 \, b c d^{7} e^{2} + 10 \, a b d^{5} e^{4} - 93 \, a^{2} d^{4} e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{6} e^{3}\right)} x}{768 \, {\left(d^{5} e^{9} x^{8} + 4 \, d^{6} e^{8} x^{6} + 6 \, d^{7} e^{7} x^{4} + 4 \, d^{8} e^{6} x^{2} + d^{9} e^{5}\right)}}, -\frac{3 \, {\left(93 \, c^{2} d^{5} e^{4} - 10 \, b c d^{4} e^{5} - 10 \, a b d^{2} e^{7} - 35 \, a^{2} d e^{8} - 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{6}\right)} x^{7} + {\left(511 \, c^{2} d^{6} e^{3} + 146 \, b c d^{5} e^{4} - 110 \, a b d^{3} e^{6} - 385 \, a^{2} d^{2} e^{7} - 33 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{5}\right)} x^{5} + {\left(385 \, c^{2} d^{7} e^{2} + 110 \, b c d^{6} e^{3} - 146 \, a b d^{4} e^{5} - 511 \, a^{2} d^{3} e^{6} + 33 \, {\left(b^{2} + 2 \, a c\right)} d^{5} e^{4}\right)} x^{3} - 3 \, {\left(35 \, c^{2} d^{8} + 10 \, b c d^{7} e + 10 \, a b d^{5} e^{3} + 35 \, a^{2} d^{4} e^{4} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{6} e^{2} + {\left(35 \, c^{2} d^{4} e^{4} + 10 \, b c d^{3} e^{5} + 10 \, a b d e^{7} + 35 \, a^{2} e^{8} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{2} e^{6}\right)} x^{8} + 4 \, {\left(35 \, c^{2} d^{5} e^{3} + 10 \, b c d^{4} e^{4} + 10 \, a b d^{2} e^{6} + 35 \, a^{2} d e^{7} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{3} e^{5}\right)} x^{6} + 6 \, {\left(35 \, c^{2} d^{6} e^{2} + 10 \, b c d^{5} e^{3} + 10 \, a b d^{3} e^{5} + 35 \, a^{2} d^{2} e^{6} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{4} e^{4}\right)} x^{4} + 4 \, {\left(35 \, c^{2} d^{7} e + 10 \, b c d^{6} e^{2} + 10 \, a b d^{4} e^{4} + 35 \, a^{2} d^{3} e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{5} e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + 3 \, {\left(35 \, c^{2} d^{8} e + 10 \, b c d^{7} e^{2} + 10 \, a b d^{5} e^{4} - 93 \, a^{2} d^{4} e^{5} + 3 \, {\left(b^{2} + 2 \, a c\right)} d^{6} e^{3}\right)} x}{384 \, {\left(d^{5} e^{9} x^{8} + 4 \, d^{6} e^{8} x^{6} + 6 \, d^{7} e^{7} x^{4} + 4 \, d^{8} e^{6} x^{2} + d^{9} e^{5}\right)}}\right]"," ",0,"[-1/768*(6*(93*c^2*d^5*e^4 - 10*b*c*d^4*e^5 - 10*a*b*d^2*e^7 - 35*a^2*d*e^8 - 3*(b^2 + 2*a*c)*d^3*e^6)*x^7 + 2*(511*c^2*d^6*e^3 + 146*b*c*d^5*e^4 - 110*a*b*d^3*e^6 - 385*a^2*d^2*e^7 - 33*(b^2 + 2*a*c)*d^4*e^5)*x^5 + 2*(385*c^2*d^7*e^2 + 110*b*c*d^6*e^3 - 146*a*b*d^4*e^5 - 511*a^2*d^3*e^6 + 33*(b^2 + 2*a*c)*d^5*e^4)*x^3 + 3*(35*c^2*d^8 + 10*b*c*d^7*e + 10*a*b*d^5*e^3 + 35*a^2*d^4*e^4 + 3*(b^2 + 2*a*c)*d^6*e^2 + (35*c^2*d^4*e^4 + 10*b*c*d^3*e^5 + 10*a*b*d*e^7 + 35*a^2*e^8 + 3*(b^2 + 2*a*c)*d^2*e^6)*x^8 + 4*(35*c^2*d^5*e^3 + 10*b*c*d^4*e^4 + 10*a*b*d^2*e^6 + 35*a^2*d*e^7 + 3*(b^2 + 2*a*c)*d^3*e^5)*x^6 + 6*(35*c^2*d^6*e^2 + 10*b*c*d^5*e^3 + 10*a*b*d^3*e^5 + 35*a^2*d^2*e^6 + 3*(b^2 + 2*a*c)*d^4*e^4)*x^4 + 4*(35*c^2*d^7*e + 10*b*c*d^6*e^2 + 10*a*b*d^4*e^4 + 35*a^2*d^3*e^5 + 3*(b^2 + 2*a*c)*d^5*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 6*(35*c^2*d^8*e + 10*b*c*d^7*e^2 + 10*a*b*d^5*e^4 - 93*a^2*d^4*e^5 + 3*(b^2 + 2*a*c)*d^6*e^3)*x)/(d^5*e^9*x^8 + 4*d^6*e^8*x^6 + 6*d^7*e^7*x^4 + 4*d^8*e^6*x^2 + d^9*e^5), -1/384*(3*(93*c^2*d^5*e^4 - 10*b*c*d^4*e^5 - 10*a*b*d^2*e^7 - 35*a^2*d*e^8 - 3*(b^2 + 2*a*c)*d^3*e^6)*x^7 + (511*c^2*d^6*e^3 + 146*b*c*d^5*e^4 - 110*a*b*d^3*e^6 - 385*a^2*d^2*e^7 - 33*(b^2 + 2*a*c)*d^4*e^5)*x^5 + (385*c^2*d^7*e^2 + 110*b*c*d^6*e^3 - 146*a*b*d^4*e^5 - 511*a^2*d^3*e^6 + 33*(b^2 + 2*a*c)*d^5*e^4)*x^3 - 3*(35*c^2*d^8 + 10*b*c*d^7*e + 10*a*b*d^5*e^3 + 35*a^2*d^4*e^4 + 3*(b^2 + 2*a*c)*d^6*e^2 + (35*c^2*d^4*e^4 + 10*b*c*d^3*e^5 + 10*a*b*d*e^7 + 35*a^2*e^8 + 3*(b^2 + 2*a*c)*d^2*e^6)*x^8 + 4*(35*c^2*d^5*e^3 + 10*b*c*d^4*e^4 + 10*a*b*d^2*e^6 + 35*a^2*d*e^7 + 3*(b^2 + 2*a*c)*d^3*e^5)*x^6 + 6*(35*c^2*d^6*e^2 + 10*b*c*d^5*e^3 + 10*a*b*d^3*e^5 + 35*a^2*d^2*e^6 + 3*(b^2 + 2*a*c)*d^4*e^4)*x^4 + 4*(35*c^2*d^7*e + 10*b*c*d^6*e^2 + 10*a*b*d^4*e^4 + 35*a^2*d^3*e^5 + 3*(b^2 + 2*a*c)*d^5*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + 3*(35*c^2*d^8*e + 10*b*c*d^7*e^2 + 10*a*b*d^5*e^4 - 93*a^2*d^4*e^5 + 3*(b^2 + 2*a*c)*d^6*e^3)*x)/(d^5*e^9*x^8 + 4*d^6*e^8*x^6 + 6*d^7*e^7*x^4 + 4*d^8*e^6*x^2 + d^9*e^5)]","B",0
261,1,268,0,0.686900," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c d^{2} e^{2} x^{3} + {\left(3 \, c d^{3} - b d^{2} e - a d e^{2} + {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} x}{4 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}, \frac{2 \, c d^{2} e^{2} x^{3} - {\left(3 \, c d^{3} - b d^{2} e - a d e^{2} + {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} x}{2 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}\right]"," ",0,"[1/4*(4*c*d^2*e^2*x^3 + (3*c*d^3 - b*d^2*e - a*d*e^2 + (3*c*d^2*e - b*d*e^2 - a*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3), 1/2*(2*c*d^2*e^2*x^3 - (3*c*d^3 - b*d^2*e - a*d*e^2 + (3*c*d^2*e - b*d*e^2 - a*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3)]","A",0
262,1,268,0,0.619281," ","integrate((a+x^2*(c*x^2+b))/(e*x^2+d)^2,x, algorithm=""fricas"")","\left[\frac{4 \, c d^{2} e^{2} x^{3} + {\left(3 \, c d^{3} - b d^{2} e - a d e^{2} + {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} x^{2}\right)} \sqrt{-d e} \log\left(\frac{e x^{2} - 2 \, \sqrt{-d e} x - d}{e x^{2} + d}\right) + 2 \, {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} x}{4 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}, \frac{2 \, c d^{2} e^{2} x^{3} - {\left(3 \, c d^{3} - b d^{2} e - a d e^{2} + {\left(3 \, c d^{2} e - b d e^{2} - a e^{3}\right)} x^{2}\right)} \sqrt{d e} \arctan\left(\frac{\sqrt{d e} x}{d}\right) + {\left(3 \, c d^{3} e - b d^{2} e^{2} + a d e^{3}\right)} x}{2 \, {\left(d^{2} e^{4} x^{2} + d^{3} e^{3}\right)}}\right]"," ",0,"[1/4*(4*c*d^2*e^2*x^3 + (3*c*d^3 - b*d^2*e - a*d*e^2 + (3*c*d^2*e - b*d*e^2 - a*e^3)*x^2)*sqrt(-d*e)*log((e*x^2 - 2*sqrt(-d*e)*x - d)/(e*x^2 + d)) + 2*(3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3), 1/2*(2*c*d^2*e^2*x^3 - (3*c*d^3 - b*d^2*e - a*d*e^2 + (3*c*d^2*e - b*d*e^2 - a*e^3)*x^2)*sqrt(d*e)*arctan(sqrt(d*e)*x/d) + (3*c*d^3*e - b*d^2*e^2 + a*d*e^3)*x)/(d^2*e^4*x^2 + d^3*e^3)]","A",0
263,-1,0,0,0.000000," ","integrate((e*x^2+d)^4/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,1,9584,0,34.094819," ","integrate((e*x^2+d)^3/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, c e^{3} x^{3} + 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b c^{5} d^{6} - 12 \, a c^{5} d^{5} e + 15 \, a b c^{4} d^{4} e^{2} - 20 \, {\left(a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{3} e^{3} + 15 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a b^{4} c - 4 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{5} + {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e^{6} + {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}}{a b^{2} c^{5} - 4 \, a^{2} c^{6}}} \log\left(-2 \, {\left(c^{8} d^{12} - 3 \, b c^{7} d^{11} e + 3 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{10} e^{2} - {\left(b^{3} c^{5} - 59 \, a b c^{6}\right)} d^{9} e^{3} - 9 \, {\left(13 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{8} e^{4} + 18 \, {\left(7 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)} d^{7} e^{5} - 42 \, {\left(2 \, a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d^{6} e^{6} + 18 \, {\left(2 \, a b^{5} c^{2} + 6 \, a^{2} b^{3} c^{3} - a^{3} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(a b^{6} c + 7 \, a^{2} b^{4} c^{2} - 2 \, a^{3} b^{2} c^{3} - 3 \, a^{4} c^{4}\right)} d^{4} e^{8} + {\left(a b^{7} + 21 \, a^{2} b^{5} c + 10 \, a^{3} b^{3} c^{2} - 55 \, a^{4} b c^{3}\right)} d^{3} e^{9} - 3 \, {\left(a^{2} b^{6} + 4 \, a^{3} b^{4} c - 9 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{2} e^{10} + 3 \, {\left(a^{3} b^{5} - a^{4} b^{3} c - 3 \, a^{5} b c^{2}\right)} d e^{11} - {\left(a^{4} b^{4} - 3 \, a^{5} b^{2} c + a^{6} c^{2}\right)} e^{12}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{9} - 18 \, {\left(a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} d^{7} e^{2} + 21 \, {\left(a b^{3} c^{5} - 4 \, a^{2} b c^{6}\right)} d^{6} e^{3} - 15 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{5} e^{4} + 3 \, {\left(2 \, a b^{5} c^{3} - 37 \, a^{2} b^{3} c^{4} + 116 \, a^{3} b c^{5}\right)} d^{4} e^{5} - {\left(a b^{6} c^{2} - 72 \, a^{2} b^{4} c^{3} + 318 \, a^{3} b^{2} c^{4} - 184 \, a^{4} c^{5}\right)} d^{3} e^{6} - 3 \, {\left(11 \, a^{2} b^{5} c^{2} - 61 \, a^{3} b^{3} c^{3} + 68 \, a^{4} b c^{4}\right)} d^{2} e^{7} + 3 \, {\left(3 \, a^{2} b^{6} c - 19 \, a^{3} b^{4} c^{2} + 29 \, a^{4} b^{2} c^{3} - 4 \, a^{5} c^{4}\right)} d e^{8} - {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 13 \, a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} e^{9} - {\left({\left(a b^{3} c^{7} - 4 \, a^{2} b c^{8}\right)} d^{3} - 6 \, {\left(a^{2} b^{2} c^{7} - 4 \, a^{3} c^{8}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} c^{6} - 4 \, a^{3} b c^{7}\right)} d e^{2} - {\left(a^{2} b^{4} c^{5} - 6 \, a^{3} b^{2} c^{6} + 8 \, a^{4} c^{7}\right)} e^{3}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}\right)} \sqrt{-\frac{b c^{5} d^{6} - 12 \, a c^{5} d^{5} e + 15 \, a b c^{4} d^{4} e^{2} - 20 \, {\left(a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{3} e^{3} + 15 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a b^{4} c - 4 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{5} + {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e^{6} + {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}}{a b^{2} c^{5} - 4 \, a^{2} c^{6}}}\right) - 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b c^{5} d^{6} - 12 \, a c^{5} d^{5} e + 15 \, a b c^{4} d^{4} e^{2} - 20 \, {\left(a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{3} e^{3} + 15 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a b^{4} c - 4 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{5} + {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e^{6} + {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}}{a b^{2} c^{5} - 4 \, a^{2} c^{6}}} \log\left(-2 \, {\left(c^{8} d^{12} - 3 \, b c^{7} d^{11} e + 3 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{10} e^{2} - {\left(b^{3} c^{5} - 59 \, a b c^{6}\right)} d^{9} e^{3} - 9 \, {\left(13 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{8} e^{4} + 18 \, {\left(7 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)} d^{7} e^{5} - 42 \, {\left(2 \, a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d^{6} e^{6} + 18 \, {\left(2 \, a b^{5} c^{2} + 6 \, a^{2} b^{3} c^{3} - a^{3} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(a b^{6} c + 7 \, a^{2} b^{4} c^{2} - 2 \, a^{3} b^{2} c^{3} - 3 \, a^{4} c^{4}\right)} d^{4} e^{8} + {\left(a b^{7} + 21 \, a^{2} b^{5} c + 10 \, a^{3} b^{3} c^{2} - 55 \, a^{4} b c^{3}\right)} d^{3} e^{9} - 3 \, {\left(a^{2} b^{6} + 4 \, a^{3} b^{4} c - 9 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{2} e^{10} + 3 \, {\left(a^{3} b^{5} - a^{4} b^{3} c - 3 \, a^{5} b c^{2}\right)} d e^{11} - {\left(a^{4} b^{4} - 3 \, a^{5} b^{2} c + a^{6} c^{2}\right)} e^{12}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{9} - 18 \, {\left(a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} d^{7} e^{2} + 21 \, {\left(a b^{3} c^{5} - 4 \, a^{2} b c^{6}\right)} d^{6} e^{3} - 15 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{5} e^{4} + 3 \, {\left(2 \, a b^{5} c^{3} - 37 \, a^{2} b^{3} c^{4} + 116 \, a^{3} b c^{5}\right)} d^{4} e^{5} - {\left(a b^{6} c^{2} - 72 \, a^{2} b^{4} c^{3} + 318 \, a^{3} b^{2} c^{4} - 184 \, a^{4} c^{5}\right)} d^{3} e^{6} - 3 \, {\left(11 \, a^{2} b^{5} c^{2} - 61 \, a^{3} b^{3} c^{3} + 68 \, a^{4} b c^{4}\right)} d^{2} e^{7} + 3 \, {\left(3 \, a^{2} b^{6} c - 19 \, a^{3} b^{4} c^{2} + 29 \, a^{4} b^{2} c^{3} - 4 \, a^{5} c^{4}\right)} d e^{8} - {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 13 \, a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} e^{9} - {\left({\left(a b^{3} c^{7} - 4 \, a^{2} b c^{8}\right)} d^{3} - 6 \, {\left(a^{2} b^{2} c^{7} - 4 \, a^{3} c^{8}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} c^{6} - 4 \, a^{3} b c^{7}\right)} d e^{2} - {\left(a^{2} b^{4} c^{5} - 6 \, a^{3} b^{2} c^{6} + 8 \, a^{4} c^{7}\right)} e^{3}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}\right)} \sqrt{-\frac{b c^{5} d^{6} - 12 \, a c^{5} d^{5} e + 15 \, a b c^{4} d^{4} e^{2} - 20 \, {\left(a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{3} e^{3} + 15 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a b^{4} c - 4 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{5} + {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e^{6} + {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}}{a b^{2} c^{5} - 4 \, a^{2} c^{6}}}\right) + 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b c^{5} d^{6} - 12 \, a c^{5} d^{5} e + 15 \, a b c^{4} d^{4} e^{2} - 20 \, {\left(a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{3} e^{3} + 15 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a b^{4} c - 4 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{5} + {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e^{6} - {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}}{a b^{2} c^{5} - 4 \, a^{2} c^{6}}} \log\left(-2 \, {\left(c^{8} d^{12} - 3 \, b c^{7} d^{11} e + 3 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{10} e^{2} - {\left(b^{3} c^{5} - 59 \, a b c^{6}\right)} d^{9} e^{3} - 9 \, {\left(13 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{8} e^{4} + 18 \, {\left(7 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)} d^{7} e^{5} - 42 \, {\left(2 \, a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d^{6} e^{6} + 18 \, {\left(2 \, a b^{5} c^{2} + 6 \, a^{2} b^{3} c^{3} - a^{3} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(a b^{6} c + 7 \, a^{2} b^{4} c^{2} - 2 \, a^{3} b^{2} c^{3} - 3 \, a^{4} c^{4}\right)} d^{4} e^{8} + {\left(a b^{7} + 21 \, a^{2} b^{5} c + 10 \, a^{3} b^{3} c^{2} - 55 \, a^{4} b c^{3}\right)} d^{3} e^{9} - 3 \, {\left(a^{2} b^{6} + 4 \, a^{3} b^{4} c - 9 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{2} e^{10} + 3 \, {\left(a^{3} b^{5} - a^{4} b^{3} c - 3 \, a^{5} b c^{2}\right)} d e^{11} - {\left(a^{4} b^{4} - 3 \, a^{5} b^{2} c + a^{6} c^{2}\right)} e^{12}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{9} - 18 \, {\left(a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} d^{7} e^{2} + 21 \, {\left(a b^{3} c^{5} - 4 \, a^{2} b c^{6}\right)} d^{6} e^{3} - 15 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{5} e^{4} + 3 \, {\left(2 \, a b^{5} c^{3} - 37 \, a^{2} b^{3} c^{4} + 116 \, a^{3} b c^{5}\right)} d^{4} e^{5} - {\left(a b^{6} c^{2} - 72 \, a^{2} b^{4} c^{3} + 318 \, a^{3} b^{2} c^{4} - 184 \, a^{4} c^{5}\right)} d^{3} e^{6} - 3 \, {\left(11 \, a^{2} b^{5} c^{2} - 61 \, a^{3} b^{3} c^{3} + 68 \, a^{4} b c^{4}\right)} d^{2} e^{7} + 3 \, {\left(3 \, a^{2} b^{6} c - 19 \, a^{3} b^{4} c^{2} + 29 \, a^{4} b^{2} c^{3} - 4 \, a^{5} c^{4}\right)} d e^{8} - {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 13 \, a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} e^{9} + {\left({\left(a b^{3} c^{7} - 4 \, a^{2} b c^{8}\right)} d^{3} - 6 \, {\left(a^{2} b^{2} c^{7} - 4 \, a^{3} c^{8}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} c^{6} - 4 \, a^{3} b c^{7}\right)} d e^{2} - {\left(a^{2} b^{4} c^{5} - 6 \, a^{3} b^{2} c^{6} + 8 \, a^{4} c^{7}\right)} e^{3}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}\right)} \sqrt{-\frac{b c^{5} d^{6} - 12 \, a c^{5} d^{5} e + 15 \, a b c^{4} d^{4} e^{2} - 20 \, {\left(a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{3} e^{3} + 15 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a b^{4} c - 4 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{5} + {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e^{6} - {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}}{a b^{2} c^{5} - 4 \, a^{2} c^{6}}}\right) - 3 \, \sqrt{\frac{1}{2}} c^{2} \sqrt{-\frac{b c^{5} d^{6} - 12 \, a c^{5} d^{5} e + 15 \, a b c^{4} d^{4} e^{2} - 20 \, {\left(a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{3} e^{3} + 15 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a b^{4} c - 4 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{5} + {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e^{6} - {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}}{a b^{2} c^{5} - 4 \, a^{2} c^{6}}} \log\left(-2 \, {\left(c^{8} d^{12} - 3 \, b c^{7} d^{11} e + 3 \, {\left(b^{2} c^{6} - 4 \, a c^{7}\right)} d^{10} e^{2} - {\left(b^{3} c^{5} - 59 \, a b c^{6}\right)} d^{9} e^{3} - 9 \, {\left(13 \, a b^{2} c^{5} + 3 \, a^{2} c^{6}\right)} d^{8} e^{4} + 18 \, {\left(7 \, a b^{3} c^{4} + 5 \, a^{2} b c^{5}\right)} d^{7} e^{5} - 42 \, {\left(2 \, a b^{4} c^{3} + 3 \, a^{2} b^{2} c^{4}\right)} d^{6} e^{6} + 18 \, {\left(2 \, a b^{5} c^{2} + 6 \, a^{2} b^{3} c^{3} - a^{3} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(a b^{6} c + 7 \, a^{2} b^{4} c^{2} - 2 \, a^{3} b^{2} c^{3} - 3 \, a^{4} c^{4}\right)} d^{4} e^{8} + {\left(a b^{7} + 21 \, a^{2} b^{5} c + 10 \, a^{3} b^{3} c^{2} - 55 \, a^{4} b c^{3}\right)} d^{3} e^{9} - 3 \, {\left(a^{2} b^{6} + 4 \, a^{3} b^{4} c - 9 \, a^{4} b^{2} c^{2} - 4 \, a^{5} c^{3}\right)} d^{2} e^{10} + 3 \, {\left(a^{3} b^{5} - a^{4} b^{3} c - 3 \, a^{5} b c^{2}\right)} d e^{11} - {\left(a^{4} b^{4} - 3 \, a^{5} b^{2} c + a^{6} c^{2}\right)} e^{12}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{7} - 4 \, a c^{8}\right)} d^{9} - 18 \, {\left(a b^{2} c^{6} - 4 \, a^{2} c^{7}\right)} d^{7} e^{2} + 21 \, {\left(a b^{3} c^{5} - 4 \, a^{2} b c^{6}\right)} d^{6} e^{3} - 15 \, {\left(a b^{4} c^{4} - 8 \, a^{2} b^{2} c^{5} + 16 \, a^{3} c^{6}\right)} d^{5} e^{4} + 3 \, {\left(2 \, a b^{5} c^{3} - 37 \, a^{2} b^{3} c^{4} + 116 \, a^{3} b c^{5}\right)} d^{4} e^{5} - {\left(a b^{6} c^{2} - 72 \, a^{2} b^{4} c^{3} + 318 \, a^{3} b^{2} c^{4} - 184 \, a^{4} c^{5}\right)} d^{3} e^{6} - 3 \, {\left(11 \, a^{2} b^{5} c^{2} - 61 \, a^{3} b^{3} c^{3} + 68 \, a^{4} b c^{4}\right)} d^{2} e^{7} + 3 \, {\left(3 \, a^{2} b^{6} c - 19 \, a^{3} b^{4} c^{2} + 29 \, a^{4} b^{2} c^{3} - 4 \, a^{5} c^{4}\right)} d e^{8} - {\left(a^{2} b^{7} - 7 \, a^{3} b^{5} c + 13 \, a^{4} b^{3} c^{2} - 4 \, a^{5} b c^{3}\right)} e^{9} + {\left({\left(a b^{3} c^{7} - 4 \, a^{2} b c^{8}\right)} d^{3} - 6 \, {\left(a^{2} b^{2} c^{7} - 4 \, a^{3} c^{8}\right)} d^{2} e + 3 \, {\left(a^{2} b^{3} c^{6} - 4 \, a^{3} b c^{7}\right)} d e^{2} - {\left(a^{2} b^{4} c^{5} - 6 \, a^{3} b^{2} c^{6} + 8 \, a^{4} c^{7}\right)} e^{3}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}\right)} \sqrt{-\frac{b c^{5} d^{6} - 12 \, a c^{5} d^{5} e + 15 \, a b c^{4} d^{4} e^{2} - 20 \, {\left(a b^{2} c^{3} - 2 \, a^{2} c^{4}\right)} d^{3} e^{3} + 15 \, {\left(a b^{3} c^{2} - 3 \, a^{2} b c^{3}\right)} d^{2} e^{4} - 6 \, {\left(a b^{4} c - 4 \, a^{2} b^{2} c^{2} + 2 \, a^{3} c^{3}\right)} d e^{5} + {\left(a b^{5} - 5 \, a^{2} b^{3} c + 5 \, a^{3} b c^{2}\right)} e^{6} - {\left(a b^{2} c^{5} - 4 \, a^{2} c^{6}\right)} \sqrt{\frac{c^{10} d^{12} - 30 \, a c^{9} d^{10} e^{2} + 40 \, a b c^{8} d^{9} e^{3} - 15 \, {\left(2 \, a b^{2} c^{7} - 17 \, a^{2} c^{8}\right)} d^{8} e^{4} + 12 \, {\left(a b^{3} c^{6} - 52 \, a^{2} b c^{7}\right)} d^{7} e^{5} - 2 \, {\left(a b^{4} c^{5} - 428 \, a^{2} b^{2} c^{6} + 226 \, a^{3} c^{7}\right)} d^{6} e^{6} - 60 \, {\left(13 \, a^{2} b^{3} c^{5} - 16 \, a^{3} b c^{6}\right)} d^{5} e^{7} + 15 \, {\left(33 \, a^{2} b^{4} c^{4} - 68 \, a^{3} b^{2} c^{5} + 17 \, a^{4} c^{6}\right)} d^{4} e^{8} - 20 \, {\left(11 \, a^{2} b^{5} c^{3} - 33 \, a^{3} b^{3} c^{4} + 20 \, a^{4} b c^{5}\right)} d^{3} e^{9} + 6 \, {\left(11 \, a^{2} b^{6} c^{2} - 44 \, a^{3} b^{4} c^{3} + 44 \, a^{4} b^{2} c^{4} - 5 \, a^{5} c^{5}\right)} d^{2} e^{10} - 12 \, {\left(a^{2} b^{7} c - 5 \, a^{3} b^{5} c^{2} + 7 \, a^{4} b^{3} c^{3} - 2 \, a^{5} b c^{4}\right)} d e^{11} + {\left(a^{2} b^{8} - 6 \, a^{3} b^{6} c + 11 \, a^{4} b^{4} c^{2} - 6 \, a^{5} b^{2} c^{3} + a^{6} c^{4}\right)} e^{12}}{a^{2} b^{2} c^{10} - 4 \, a^{3} c^{11}}}}{a b^{2} c^{5} - 4 \, a^{2} c^{6}}}\right) + 6 \, {\left(3 \, c d e^{2} - b e^{3}\right)} x}{6 \, c^{2}}"," ",0,"1/6*(2*c*e^3*x^3 + 3*sqrt(1/2)*c^2*sqrt(-(b*c^5*d^6 - 12*a*c^5*d^5*e + 15*a*b*c^4*d^4*e^2 - 20*(a*b^2*c^3 - 2*a^2*c^4)*d^3*e^3 + 15*(a*b^3*c^2 - 3*a^2*b*c^3)*d^2*e^4 - 6*(a*b^4*c - 4*a^2*b^2*c^2 + 2*a^3*c^3)*d*e^5 + (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e^6 + (a*b^2*c^5 - 4*a^2*c^6)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))/(a*b^2*c^5 - 4*a^2*c^6))*log(-2*(c^8*d^12 - 3*b*c^7*d^11*e + 3*(b^2*c^6 - 4*a*c^7)*d^10*e^2 - (b^3*c^5 - 59*a*b*c^6)*d^9*e^3 - 9*(13*a*b^2*c^5 + 3*a^2*c^6)*d^8*e^4 + 18*(7*a*b^3*c^4 + 5*a^2*b*c^5)*d^7*e^5 - 42*(2*a*b^4*c^3 + 3*a^2*b^2*c^4)*d^6*e^6 + 18*(2*a*b^5*c^2 + 6*a^2*b^3*c^3 - a^3*b*c^4)*d^5*e^7 - 9*(a*b^6*c + 7*a^2*b^4*c^2 - 2*a^3*b^2*c^3 - 3*a^4*c^4)*d^4*e^8 + (a*b^7 + 21*a^2*b^5*c + 10*a^3*b^3*c^2 - 55*a^4*b*c^3)*d^3*e^9 - 3*(a^2*b^6 + 4*a^3*b^4*c - 9*a^4*b^2*c^2 - 4*a^5*c^3)*d^2*e^10 + 3*(a^3*b^5 - a^4*b^3*c - 3*a^5*b*c^2)*d*e^11 - (a^4*b^4 - 3*a^5*b^2*c + a^6*c^2)*e^12)*x + sqrt(1/2)*((b^2*c^7 - 4*a*c^8)*d^9 - 18*(a*b^2*c^6 - 4*a^2*c^7)*d^7*e^2 + 21*(a*b^3*c^5 - 4*a^2*b*c^6)*d^6*e^3 - 15*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^5*e^4 + 3*(2*a*b^5*c^3 - 37*a^2*b^3*c^4 + 116*a^3*b*c^5)*d^4*e^5 - (a*b^6*c^2 - 72*a^2*b^4*c^3 + 318*a^3*b^2*c^4 - 184*a^4*c^5)*d^3*e^6 - 3*(11*a^2*b^5*c^2 - 61*a^3*b^3*c^3 + 68*a^4*b*c^4)*d^2*e^7 + 3*(3*a^2*b^6*c - 19*a^3*b^4*c^2 + 29*a^4*b^2*c^3 - 4*a^5*c^4)*d*e^8 - (a^2*b^7 - 7*a^3*b^5*c + 13*a^4*b^3*c^2 - 4*a^5*b*c^3)*e^9 - ((a*b^3*c^7 - 4*a^2*b*c^8)*d^3 - 6*(a^2*b^2*c^7 - 4*a^3*c^8)*d^2*e + 3*(a^2*b^3*c^6 - 4*a^3*b*c^7)*d*e^2 - (a^2*b^4*c^5 - 6*a^3*b^2*c^6 + 8*a^4*c^7)*e^3)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))*sqrt(-(b*c^5*d^6 - 12*a*c^5*d^5*e + 15*a*b*c^4*d^4*e^2 - 20*(a*b^2*c^3 - 2*a^2*c^4)*d^3*e^3 + 15*(a*b^3*c^2 - 3*a^2*b*c^3)*d^2*e^4 - 6*(a*b^4*c - 4*a^2*b^2*c^2 + 2*a^3*c^3)*d*e^5 + (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e^6 + (a*b^2*c^5 - 4*a^2*c^6)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))/(a*b^2*c^5 - 4*a^2*c^6))) - 3*sqrt(1/2)*c^2*sqrt(-(b*c^5*d^6 - 12*a*c^5*d^5*e + 15*a*b*c^4*d^4*e^2 - 20*(a*b^2*c^3 - 2*a^2*c^4)*d^3*e^3 + 15*(a*b^3*c^2 - 3*a^2*b*c^3)*d^2*e^4 - 6*(a*b^4*c - 4*a^2*b^2*c^2 + 2*a^3*c^3)*d*e^5 + (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e^6 + (a*b^2*c^5 - 4*a^2*c^6)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))/(a*b^2*c^5 - 4*a^2*c^6))*log(-2*(c^8*d^12 - 3*b*c^7*d^11*e + 3*(b^2*c^6 - 4*a*c^7)*d^10*e^2 - (b^3*c^5 - 59*a*b*c^6)*d^9*e^3 - 9*(13*a*b^2*c^5 + 3*a^2*c^6)*d^8*e^4 + 18*(7*a*b^3*c^4 + 5*a^2*b*c^5)*d^7*e^5 - 42*(2*a*b^4*c^3 + 3*a^2*b^2*c^4)*d^6*e^6 + 18*(2*a*b^5*c^2 + 6*a^2*b^3*c^3 - a^3*b*c^4)*d^5*e^7 - 9*(a*b^6*c + 7*a^2*b^4*c^2 - 2*a^3*b^2*c^3 - 3*a^4*c^4)*d^4*e^8 + (a*b^7 + 21*a^2*b^5*c + 10*a^3*b^3*c^2 - 55*a^4*b*c^3)*d^3*e^9 - 3*(a^2*b^6 + 4*a^3*b^4*c - 9*a^4*b^2*c^2 - 4*a^5*c^3)*d^2*e^10 + 3*(a^3*b^5 - a^4*b^3*c - 3*a^5*b*c^2)*d*e^11 - (a^4*b^4 - 3*a^5*b^2*c + a^6*c^2)*e^12)*x - sqrt(1/2)*((b^2*c^7 - 4*a*c^8)*d^9 - 18*(a*b^2*c^6 - 4*a^2*c^7)*d^7*e^2 + 21*(a*b^3*c^5 - 4*a^2*b*c^6)*d^6*e^3 - 15*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^5*e^4 + 3*(2*a*b^5*c^3 - 37*a^2*b^3*c^4 + 116*a^3*b*c^5)*d^4*e^5 - (a*b^6*c^2 - 72*a^2*b^4*c^3 + 318*a^3*b^2*c^4 - 184*a^4*c^5)*d^3*e^6 - 3*(11*a^2*b^5*c^2 - 61*a^3*b^3*c^3 + 68*a^4*b*c^4)*d^2*e^7 + 3*(3*a^2*b^6*c - 19*a^3*b^4*c^2 + 29*a^4*b^2*c^3 - 4*a^5*c^4)*d*e^8 - (a^2*b^7 - 7*a^3*b^5*c + 13*a^4*b^3*c^2 - 4*a^5*b*c^3)*e^9 - ((a*b^3*c^7 - 4*a^2*b*c^8)*d^3 - 6*(a^2*b^2*c^7 - 4*a^3*c^8)*d^2*e + 3*(a^2*b^3*c^6 - 4*a^3*b*c^7)*d*e^2 - (a^2*b^4*c^5 - 6*a^3*b^2*c^6 + 8*a^4*c^7)*e^3)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))*sqrt(-(b*c^5*d^6 - 12*a*c^5*d^5*e + 15*a*b*c^4*d^4*e^2 - 20*(a*b^2*c^3 - 2*a^2*c^4)*d^3*e^3 + 15*(a*b^3*c^2 - 3*a^2*b*c^3)*d^2*e^4 - 6*(a*b^4*c - 4*a^2*b^2*c^2 + 2*a^3*c^3)*d*e^5 + (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e^6 + (a*b^2*c^5 - 4*a^2*c^6)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))/(a*b^2*c^5 - 4*a^2*c^6))) + 3*sqrt(1/2)*c^2*sqrt(-(b*c^5*d^6 - 12*a*c^5*d^5*e + 15*a*b*c^4*d^4*e^2 - 20*(a*b^2*c^3 - 2*a^2*c^4)*d^3*e^3 + 15*(a*b^3*c^2 - 3*a^2*b*c^3)*d^2*e^4 - 6*(a*b^4*c - 4*a^2*b^2*c^2 + 2*a^3*c^3)*d*e^5 + (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e^6 - (a*b^2*c^5 - 4*a^2*c^6)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))/(a*b^2*c^5 - 4*a^2*c^6))*log(-2*(c^8*d^12 - 3*b*c^7*d^11*e + 3*(b^2*c^6 - 4*a*c^7)*d^10*e^2 - (b^3*c^5 - 59*a*b*c^6)*d^9*e^3 - 9*(13*a*b^2*c^5 + 3*a^2*c^6)*d^8*e^4 + 18*(7*a*b^3*c^4 + 5*a^2*b*c^5)*d^7*e^5 - 42*(2*a*b^4*c^3 + 3*a^2*b^2*c^4)*d^6*e^6 + 18*(2*a*b^5*c^2 + 6*a^2*b^3*c^3 - a^3*b*c^4)*d^5*e^7 - 9*(a*b^6*c + 7*a^2*b^4*c^2 - 2*a^3*b^2*c^3 - 3*a^4*c^4)*d^4*e^8 + (a*b^7 + 21*a^2*b^5*c + 10*a^3*b^3*c^2 - 55*a^4*b*c^3)*d^3*e^9 - 3*(a^2*b^6 + 4*a^3*b^4*c - 9*a^4*b^2*c^2 - 4*a^5*c^3)*d^2*e^10 + 3*(a^3*b^5 - a^4*b^3*c - 3*a^5*b*c^2)*d*e^11 - (a^4*b^4 - 3*a^5*b^2*c + a^6*c^2)*e^12)*x + sqrt(1/2)*((b^2*c^7 - 4*a*c^8)*d^9 - 18*(a*b^2*c^6 - 4*a^2*c^7)*d^7*e^2 + 21*(a*b^3*c^5 - 4*a^2*b*c^6)*d^6*e^3 - 15*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^5*e^4 + 3*(2*a*b^5*c^3 - 37*a^2*b^3*c^4 + 116*a^3*b*c^5)*d^4*e^5 - (a*b^6*c^2 - 72*a^2*b^4*c^3 + 318*a^3*b^2*c^4 - 184*a^4*c^5)*d^3*e^6 - 3*(11*a^2*b^5*c^2 - 61*a^3*b^3*c^3 + 68*a^4*b*c^4)*d^2*e^7 + 3*(3*a^2*b^6*c - 19*a^3*b^4*c^2 + 29*a^4*b^2*c^3 - 4*a^5*c^4)*d*e^8 - (a^2*b^7 - 7*a^3*b^5*c + 13*a^4*b^3*c^2 - 4*a^5*b*c^3)*e^9 + ((a*b^3*c^7 - 4*a^2*b*c^8)*d^3 - 6*(a^2*b^2*c^7 - 4*a^3*c^8)*d^2*e + 3*(a^2*b^3*c^6 - 4*a^3*b*c^7)*d*e^2 - (a^2*b^4*c^5 - 6*a^3*b^2*c^6 + 8*a^4*c^7)*e^3)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))*sqrt(-(b*c^5*d^6 - 12*a*c^5*d^5*e + 15*a*b*c^4*d^4*e^2 - 20*(a*b^2*c^3 - 2*a^2*c^4)*d^3*e^3 + 15*(a*b^3*c^2 - 3*a^2*b*c^3)*d^2*e^4 - 6*(a*b^4*c - 4*a^2*b^2*c^2 + 2*a^3*c^3)*d*e^5 + (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e^6 - (a*b^2*c^5 - 4*a^2*c^6)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))/(a*b^2*c^5 - 4*a^2*c^6))) - 3*sqrt(1/2)*c^2*sqrt(-(b*c^5*d^6 - 12*a*c^5*d^5*e + 15*a*b*c^4*d^4*e^2 - 20*(a*b^2*c^3 - 2*a^2*c^4)*d^3*e^3 + 15*(a*b^3*c^2 - 3*a^2*b*c^3)*d^2*e^4 - 6*(a*b^4*c - 4*a^2*b^2*c^2 + 2*a^3*c^3)*d*e^5 + (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e^6 - (a*b^2*c^5 - 4*a^2*c^6)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))/(a*b^2*c^5 - 4*a^2*c^6))*log(-2*(c^8*d^12 - 3*b*c^7*d^11*e + 3*(b^2*c^6 - 4*a*c^7)*d^10*e^2 - (b^3*c^5 - 59*a*b*c^6)*d^9*e^3 - 9*(13*a*b^2*c^5 + 3*a^2*c^6)*d^8*e^4 + 18*(7*a*b^3*c^4 + 5*a^2*b*c^5)*d^7*e^5 - 42*(2*a*b^4*c^3 + 3*a^2*b^2*c^4)*d^6*e^6 + 18*(2*a*b^5*c^2 + 6*a^2*b^3*c^3 - a^3*b*c^4)*d^5*e^7 - 9*(a*b^6*c + 7*a^2*b^4*c^2 - 2*a^3*b^2*c^3 - 3*a^4*c^4)*d^4*e^8 + (a*b^7 + 21*a^2*b^5*c + 10*a^3*b^3*c^2 - 55*a^4*b*c^3)*d^3*e^9 - 3*(a^2*b^6 + 4*a^3*b^4*c - 9*a^4*b^2*c^2 - 4*a^5*c^3)*d^2*e^10 + 3*(a^3*b^5 - a^4*b^3*c - 3*a^5*b*c^2)*d*e^11 - (a^4*b^4 - 3*a^5*b^2*c + a^6*c^2)*e^12)*x - sqrt(1/2)*((b^2*c^7 - 4*a*c^8)*d^9 - 18*(a*b^2*c^6 - 4*a^2*c^7)*d^7*e^2 + 21*(a*b^3*c^5 - 4*a^2*b*c^6)*d^6*e^3 - 15*(a*b^4*c^4 - 8*a^2*b^2*c^5 + 16*a^3*c^6)*d^5*e^4 + 3*(2*a*b^5*c^3 - 37*a^2*b^3*c^4 + 116*a^3*b*c^5)*d^4*e^5 - (a*b^6*c^2 - 72*a^2*b^4*c^3 + 318*a^3*b^2*c^4 - 184*a^4*c^5)*d^3*e^6 - 3*(11*a^2*b^5*c^2 - 61*a^3*b^3*c^3 + 68*a^4*b*c^4)*d^2*e^7 + 3*(3*a^2*b^6*c - 19*a^3*b^4*c^2 + 29*a^4*b^2*c^3 - 4*a^5*c^4)*d*e^8 - (a^2*b^7 - 7*a^3*b^5*c + 13*a^4*b^3*c^2 - 4*a^5*b*c^3)*e^9 + ((a*b^3*c^7 - 4*a^2*b*c^8)*d^3 - 6*(a^2*b^2*c^7 - 4*a^3*c^8)*d^2*e + 3*(a^2*b^3*c^6 - 4*a^3*b*c^7)*d*e^2 - (a^2*b^4*c^5 - 6*a^3*b^2*c^6 + 8*a^4*c^7)*e^3)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))*sqrt(-(b*c^5*d^6 - 12*a*c^5*d^5*e + 15*a*b*c^4*d^4*e^2 - 20*(a*b^2*c^3 - 2*a^2*c^4)*d^3*e^3 + 15*(a*b^3*c^2 - 3*a^2*b*c^3)*d^2*e^4 - 6*(a*b^4*c - 4*a^2*b^2*c^2 + 2*a^3*c^3)*d*e^5 + (a*b^5 - 5*a^2*b^3*c + 5*a^3*b*c^2)*e^6 - (a*b^2*c^5 - 4*a^2*c^6)*sqrt((c^10*d^12 - 30*a*c^9*d^10*e^2 + 40*a*b*c^8*d^9*e^3 - 15*(2*a*b^2*c^7 - 17*a^2*c^8)*d^8*e^4 + 12*(a*b^3*c^6 - 52*a^2*b*c^7)*d^7*e^5 - 2*(a*b^4*c^5 - 428*a^2*b^2*c^6 + 226*a^3*c^7)*d^6*e^6 - 60*(13*a^2*b^3*c^5 - 16*a^3*b*c^6)*d^5*e^7 + 15*(33*a^2*b^4*c^4 - 68*a^3*b^2*c^5 + 17*a^4*c^6)*d^4*e^8 - 20*(11*a^2*b^5*c^3 - 33*a^3*b^3*c^4 + 20*a^4*b*c^5)*d^3*e^9 + 6*(11*a^2*b^6*c^2 - 44*a^3*b^4*c^3 + 44*a^4*b^2*c^4 - 5*a^5*c^5)*d^2*e^10 - 12*(a^2*b^7*c - 5*a^3*b^5*c^2 + 7*a^4*b^3*c^3 - 2*a^5*b*c^4)*d*e^11 + (a^2*b^8 - 6*a^3*b^6*c + 11*a^4*b^4*c^2 - 6*a^5*b^2*c^3 + a^6*c^4)*e^12)/(a^2*b^2*c^10 - 4*a^3*c^11)))/(a*b^2*c^5 - 4*a^2*c^6))) + 6*(3*c*d*e^2 - b*e^3)*x)/c^2","B",0
265,1,4690,0,3.220604," ","integrate((e*x^2+d)^2/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{2 \, e^{2} x - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}}{a b^{2} c^{3} - 4 \, a^{2} c^{4}}} \log\left(2 \, {\left(c^{5} d^{8} - 2 \, b c^{4} d^{7} e + 14 \, a b c^{3} d^{5} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{5} - {\left(a b^{4} + 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e^{6} + 2 \, {\left(a^{2} b^{3} + a^{3} b c\right)} d e^{7} - {\left(a^{3} b^{2} - a^{4} c\right)} e^{8}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} - 7 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{2} + 4 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{3} - {\left(a b^{4} c - 11 \, a^{2} b^{2} c^{2} + 28 \, a^{3} c^{3}\right)} d^{2} e^{4} - 4 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6} - {\left({\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} - 4 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d e + {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} e^{2}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}\right)} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}}{a b^{2} c^{3} - 4 \, a^{2} c^{4}}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}}{a b^{2} c^{3} - 4 \, a^{2} c^{4}}} \log\left(2 \, {\left(c^{5} d^{8} - 2 \, b c^{4} d^{7} e + 14 \, a b c^{3} d^{5} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{5} - {\left(a b^{4} + 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e^{6} + 2 \, {\left(a^{2} b^{3} + a^{3} b c\right)} d e^{7} - {\left(a^{3} b^{2} - a^{4} c\right)} e^{8}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} - 7 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{2} + 4 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{3} - {\left(a b^{4} c - 11 \, a^{2} b^{2} c^{2} + 28 \, a^{3} c^{3}\right)} d^{2} e^{4} - 4 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6} - {\left({\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} - 4 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d e + {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} e^{2}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}\right)} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} + {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}}{a b^{2} c^{3} - 4 \, a^{2} c^{4}}}\right) - \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}}{a b^{2} c^{3} - 4 \, a^{2} c^{4}}} \log\left(2 \, {\left(c^{5} d^{8} - 2 \, b c^{4} d^{7} e + 14 \, a b c^{3} d^{5} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{5} - {\left(a b^{4} + 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e^{6} + 2 \, {\left(a^{2} b^{3} + a^{3} b c\right)} d e^{7} - {\left(a^{3} b^{2} - a^{4} c\right)} e^{8}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} - 7 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{2} + 4 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{3} - {\left(a b^{4} c - 11 \, a^{2} b^{2} c^{2} + 28 \, a^{3} c^{3}\right)} d^{2} e^{4} - 4 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6} + {\left({\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} - 4 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d e + {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} e^{2}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}\right)} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}}{a b^{2} c^{3} - 4 \, a^{2} c^{4}}}\right) + \sqrt{\frac{1}{2}} c \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}}{a b^{2} c^{3} - 4 \, a^{2} c^{4}}} \log\left(2 \, {\left(c^{5} d^{8} - 2 \, b c^{4} d^{7} e + 14 \, a b c^{3} d^{5} e^{3} + {\left(b^{2} c^{3} - 4 \, a c^{4}\right)} d^{6} e^{2} - 5 \, {\left(3 \, a b^{2} c^{2} + 2 \, a^{2} c^{3}\right)} d^{4} e^{4} + 6 \, {\left(a b^{3} c + 3 \, a^{2} b c^{2}\right)} d^{3} e^{5} - {\left(a b^{4} + 9 \, a^{2} b^{2} c + 4 \, a^{3} c^{2}\right)} d^{2} e^{6} + 2 \, {\left(a^{2} b^{3} + a^{3} b c\right)} d e^{7} - {\left(a^{3} b^{2} - a^{4} c\right)} e^{8}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c^{4} - 4 \, a c^{5}\right)} d^{6} - 7 \, {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} d^{4} e^{2} + 4 \, {\left(a b^{3} c^{2} - 4 \, a^{2} b c^{3}\right)} d^{3} e^{3} - {\left(a b^{4} c - 11 \, a^{2} b^{2} c^{2} + 28 \, a^{3} c^{3}\right)} d^{2} e^{4} - 4 \, {\left(a^{2} b^{3} c - 4 \, a^{3} b c^{2}\right)} d e^{5} + {\left(a^{2} b^{4} - 5 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{6} + {\left({\left(a b^{3} c^{4} - 4 \, a^{2} b c^{5}\right)} d^{2} - 4 \, {\left(a^{2} b^{2} c^{4} - 4 \, a^{3} c^{5}\right)} d e + {\left(a^{2} b^{3} c^{3} - 4 \, a^{3} b c^{4}\right)} e^{2}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}\right)} \sqrt{-\frac{b c^{3} d^{4} - 8 \, a c^{3} d^{3} e + 6 \, a b c^{2} d^{2} e^{2} - 4 \, {\left(a b^{2} c - 2 \, a^{2} c^{2}\right)} d e^{3} + {\left(a b^{3} - 3 \, a^{2} b c\right)} e^{4} - {\left(a b^{2} c^{3} - 4 \, a^{2} c^{4}\right)} \sqrt{\frac{c^{6} d^{8} - 12 \, a c^{5} d^{6} e^{2} + 8 \, a b c^{4} d^{5} e^{3} - 48 \, a^{2} b c^{3} d^{3} e^{5} - 2 \, {\left(a b^{2} c^{3} - 19 \, a^{2} c^{4}\right)} d^{4} e^{4} + 4 \, {\left(7 \, a^{2} b^{2} c^{2} - 3 \, a^{3} c^{3}\right)} d^{2} e^{6} - 8 \, {\left(a^{2} b^{3} c - a^{3} b c^{2}\right)} d e^{7} + {\left(a^{2} b^{4} - 2 \, a^{3} b^{2} c + a^{4} c^{2}\right)} e^{8}}{a^{2} b^{2} c^{6} - 4 \, a^{3} c^{7}}}}{a b^{2} c^{3} - 4 \, a^{2} c^{4}}}\right)}{2 \, c}"," ",0,"1/2*(2*e^2*x - sqrt(1/2)*c*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^2*c^3 - 4*a^2*c^4)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))/(a*b^2*c^3 - 4*a^2*c^4))*log(2*(c^5*d^8 - 2*b*c^4*d^7*e + 14*a*b*c^3*d^5*e^3 + (b^2*c^3 - 4*a*c^4)*d^6*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^4 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^5 - (a*b^4 + 9*a^2*b^2*c + 4*a^3*c^2)*d^2*e^6 + 2*(a^2*b^3 + a^3*b*c)*d*e^7 - (a^3*b^2 - a^4*c)*e^8)*x + sqrt(1/2)*((b^2*c^4 - 4*a*c^5)*d^6 - 7*(a*b^2*c^3 - 4*a^2*c^4)*d^4*e^2 + 4*(a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^3 - (a*b^4*c - 11*a^2*b^2*c^2 + 28*a^3*c^3)*d^2*e^4 - 4*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*e^6 - ((a*b^3*c^4 - 4*a^2*b*c^5)*d^2 - 4*(a^2*b^2*c^4 - 4*a^3*c^5)*d*e + (a^2*b^3*c^3 - 4*a^3*b*c^4)*e^2)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^2*c^3 - 4*a^2*c^4)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))/(a*b^2*c^3 - 4*a^2*c^4))) + sqrt(1/2)*c*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^2*c^3 - 4*a^2*c^4)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))/(a*b^2*c^3 - 4*a^2*c^4))*log(2*(c^5*d^8 - 2*b*c^4*d^7*e + 14*a*b*c^3*d^5*e^3 + (b^2*c^3 - 4*a*c^4)*d^6*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^4 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^5 - (a*b^4 + 9*a^2*b^2*c + 4*a^3*c^2)*d^2*e^6 + 2*(a^2*b^3 + a^3*b*c)*d*e^7 - (a^3*b^2 - a^4*c)*e^8)*x - sqrt(1/2)*((b^2*c^4 - 4*a*c^5)*d^6 - 7*(a*b^2*c^3 - 4*a^2*c^4)*d^4*e^2 + 4*(a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^3 - (a*b^4*c - 11*a^2*b^2*c^2 + 28*a^3*c^3)*d^2*e^4 - 4*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*e^6 - ((a*b^3*c^4 - 4*a^2*b*c^5)*d^2 - 4*(a^2*b^2*c^4 - 4*a^3*c^5)*d*e + (a^2*b^3*c^3 - 4*a^3*b*c^4)*e^2)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 + (a*b^2*c^3 - 4*a^2*c^4)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))/(a*b^2*c^3 - 4*a^2*c^4))) - sqrt(1/2)*c*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^2*c^3 - 4*a^2*c^4)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))/(a*b^2*c^3 - 4*a^2*c^4))*log(2*(c^5*d^8 - 2*b*c^4*d^7*e + 14*a*b*c^3*d^5*e^3 + (b^2*c^3 - 4*a*c^4)*d^6*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^4 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^5 - (a*b^4 + 9*a^2*b^2*c + 4*a^3*c^2)*d^2*e^6 + 2*(a^2*b^3 + a^3*b*c)*d*e^7 - (a^3*b^2 - a^4*c)*e^8)*x + sqrt(1/2)*((b^2*c^4 - 4*a*c^5)*d^6 - 7*(a*b^2*c^3 - 4*a^2*c^4)*d^4*e^2 + 4*(a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^3 - (a*b^4*c - 11*a^2*b^2*c^2 + 28*a^3*c^3)*d^2*e^4 - 4*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*e^6 + ((a*b^3*c^4 - 4*a^2*b*c^5)*d^2 - 4*(a^2*b^2*c^4 - 4*a^3*c^5)*d*e + (a^2*b^3*c^3 - 4*a^3*b*c^4)*e^2)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^2*c^3 - 4*a^2*c^4)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))/(a*b^2*c^3 - 4*a^2*c^4))) + sqrt(1/2)*c*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^2*c^3 - 4*a^2*c^4)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))/(a*b^2*c^3 - 4*a^2*c^4))*log(2*(c^5*d^8 - 2*b*c^4*d^7*e + 14*a*b*c^3*d^5*e^3 + (b^2*c^3 - 4*a*c^4)*d^6*e^2 - 5*(3*a*b^2*c^2 + 2*a^2*c^3)*d^4*e^4 + 6*(a*b^3*c + 3*a^2*b*c^2)*d^3*e^5 - (a*b^4 + 9*a^2*b^2*c + 4*a^3*c^2)*d^2*e^6 + 2*(a^2*b^3 + a^3*b*c)*d*e^7 - (a^3*b^2 - a^4*c)*e^8)*x - sqrt(1/2)*((b^2*c^4 - 4*a*c^5)*d^6 - 7*(a*b^2*c^3 - 4*a^2*c^4)*d^4*e^2 + 4*(a*b^3*c^2 - 4*a^2*b*c^3)*d^3*e^3 - (a*b^4*c - 11*a^2*b^2*c^2 + 28*a^3*c^3)*d^2*e^4 - 4*(a^2*b^3*c - 4*a^3*b*c^2)*d*e^5 + (a^2*b^4 - 5*a^3*b^2*c + 4*a^4*c^2)*e^6 + ((a*b^3*c^4 - 4*a^2*b*c^5)*d^2 - 4*(a^2*b^2*c^4 - 4*a^3*c^5)*d*e + (a^2*b^3*c^3 - 4*a^3*b*c^4)*e^2)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))*sqrt(-(b*c^3*d^4 - 8*a*c^3*d^3*e + 6*a*b*c^2*d^2*e^2 - 4*(a*b^2*c - 2*a^2*c^2)*d*e^3 + (a*b^3 - 3*a^2*b*c)*e^4 - (a*b^2*c^3 - 4*a^2*c^4)*sqrt((c^6*d^8 - 12*a*c^5*d^6*e^2 + 8*a*b*c^4*d^5*e^3 - 48*a^2*b*c^3*d^3*e^5 - 2*(a*b^2*c^3 - 19*a^2*c^4)*d^4*e^4 + 4*(7*a^2*b^2*c^2 - 3*a^3*c^3)*d^2*e^6 - 8*(a^2*b^3*c - a^3*b*c^2)*d*e^7 + (a^2*b^4 - 2*a^3*b^2*c + a^4*c^2)*e^8)/(a^2*b^2*c^6 - 4*a^3*c^7)))/(a*b^2*c^3 - 4*a^2*c^4))))/c","B",0
266,1,1525,0,0.880593," ","integrate((e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-2 \, {\left(c^{2} d^{4} - b c d^{3} e + a b d e^{3} - a^{2} e^{4}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} - {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-2 \, {\left(c^{2} d^{4} - b c d^{3} e + a b d e^{3} - a^{2} e^{4}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} - {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} + {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-2 \, {\left(c^{2} d^{4} - b c d^{3} e + a b d e^{3} - a^{2} e^{4}\right)} x + \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} + {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}} \log\left(-2 \, {\left(c^{2} d^{4} - b c d^{3} e + a b d e^{3} - a^{2} e^{4}\right)} x - \sqrt{\frac{1}{2}} {\left({\left(b^{2} c - 4 \, a c^{2}\right)} d^{3} - {\left(a b^{2} - 4 \, a^{2} c\right)} d e^{2} + {\left({\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} d - 2 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2}\right)} e\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}\right)} \sqrt{-\frac{b c d^{2} - 4 \, a c d e + a b e^{2} - {\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} \sqrt{\frac{c^{2} d^{4} - 2 \, a c d^{2} e^{2} + a^{2} e^{4}}{a^{2} b^{2} c^{2} - 4 \, a^{3} c^{3}}}}{a b^{2} c - 4 \, a^{2} c^{2}}}\right)"," ",0,"1/2*sqrt(1/2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-2*(c^2*d^4 - b*c*d^3*e + a*b*d*e^3 - a^2*e^4)*x + sqrt(1/2)*((b^2*c - 4*a*c^2)*d^3 - (a*b^2 - 4*a^2*c)*d*e^2 - ((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) - 1/2*sqrt(1/2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-2*(c^2*d^4 - b*c*d^3*e + a*b*d*e^3 - a^2*e^4)*x - sqrt(1/2)*((b^2*c - 4*a*c^2)*d^3 - (a*b^2 - 4*a^2*c)*d*e^2 - ((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 + (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) + 1/2*sqrt(1/2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-2*(c^2*d^4 - b*c*d^3*e + a*b*d*e^3 - a^2*e^4)*x + sqrt(1/2)*((b^2*c - 4*a*c^2)*d^3 - (a*b^2 - 4*a^2*c)*d*e^2 + ((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))) - 1/2*sqrt(1/2)*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2))*log(-2*(c^2*d^4 - b*c*d^3*e + a*b*d*e^3 - a^2*e^4)*x - sqrt(1/2)*((b^2*c - 4*a*c^2)*d^3 - (a*b^2 - 4*a^2*c)*d*e^2 + ((a*b^3*c - 4*a^2*b*c^2)*d - 2*(a^2*b^2*c - 4*a^3*c^2)*e)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))*sqrt(-(b*c*d^2 - 4*a*c*d*e + a*b*e^2 - (a*b^2*c - 4*a^2*c^2)*sqrt((c^2*d^4 - 2*a*c*d^2*e^2 + a^2*e^4)/(a^2*b^2*c^2 - 4*a^3*c^3)))/(a*b^2*c - 4*a^2*c^2)))","B",0
267,1,613,0,0.407346," ","integrate(1/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","-\frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(2 \, c x + \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c - \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(2 \, c x - \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c - \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{b + \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}\right) - \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(2 \, c x + \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c + \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}\right) + \frac{1}{2} \, \sqrt{\frac{1}{2}} \sqrt{-\frac{b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}} \log\left(2 \, c x - \sqrt{\frac{1}{2}} {\left(b^{2} - 4 \, a c + \frac{a b^{3} - 4 \, a^{2} b c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}\right)} \sqrt{-\frac{b - \frac{a b^{2} - 4 \, a^{2} c}{\sqrt{a^{2} b^{2} - 4 \, a^{3} c}}}{a b^{2} - 4 \, a^{2} c}}\right)"," ",0,"-1/2*sqrt(1/2)*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(2*c*x + sqrt(1/2)*(b^2 - 4*a*c - (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) + 1/2*sqrt(1/2)*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(2*c*x - sqrt(1/2)*(b^2 - 4*a*c - (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b + (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) - 1/2*sqrt(1/2)*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(2*c*x + sqrt(1/2)*(b^2 - 4*a*c + (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))) + 1/2*sqrt(1/2)*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c))*log(2*c*x - sqrt(1/2)*(b^2 - 4*a*c + (a*b^3 - 4*a^2*b*c)/sqrt(a^2*b^2 - 4*a^3*c))*sqrt(-(b - (a*b^2 - 4*a^2*c)/sqrt(a^2*b^2 - 4*a^3*c))/(a*b^2 - 4*a^2*c)))","B",0
268,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,1,12117,0,111.889825," ","integrate((e*x^2+d)^3/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(b c^{2} d^{3} - 6 \, a c^{2} d^{2} e + 3 \, a b c d e^{2} - {\left(a b^{2} - 2 \, a^{2} c\right)} e^{3}\right)} x^{3} - \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} x^{4} + {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} c^{3} - 15 \, a b^{3} c^{4} + 60 \, a^{2} b c^{5}\right)} d^{6} + 6 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{5} e - 3 \, {\left(3 \, a^{2} b^{3} c^{3} - 92 \, a^{3} b c^{4}\right)} d^{4} e^{2} - 8 \, {\left(11 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} d^{3} e^{3} - 3 \, {\left(3 \, a^{3} b^{3} c^{2} - 92 \, a^{4} b c^{3}\right)} d^{2} e^{4} + 6 \, {\left(a^{3} b^{4} c - 6 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} - 15 \, a^{4} b^{3} c + 60 \, a^{5} b c^{2}\right)} e^{6} + {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}}{a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}}} \log\left(-{\left({\left(5 \, b^{4} c^{6} - 81 \, a b^{2} c^{7} + 324 \, a^{2} c^{8}\right)} d^{12} - 3 \, {\left(3 \, b^{5} c^{5} - 65 \, a b^{3} c^{6} + 324 \, a^{2} b c^{7}\right)} d^{11} e + 3 \, {\left(b^{6} c^{4} - 42 \, a b^{4} c^{5} + 252 \, a^{2} b^{2} c^{6} + 432 \, a^{3} c^{7}\right)} d^{10} e^{2} + {\left(b^{7} c^{3} + 3 \, a b^{5} c^{4} + 33 \, a^{2} b^{3} c^{5} - 2916 \, a^{3} b c^{6}\right)} d^{9} e^{3} + 9 \, {\left(a b^{6} c^{3} - 15 \, a^{2} b^{4} c^{4} + 195 \, a^{3} b^{2} c^{5} + 180 \, a^{4} c^{6}\right)} d^{8} e^{4} - 162 \, {\left(a^{3} b^{3} c^{4} + 12 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 162 \, {\left(a^{4} b^{3} c^{3} + 12 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(a^{3} b^{6} c - 15 \, a^{4} b^{4} c^{2} + 195 \, a^{5} b^{2} c^{3} + 180 \, a^{6} c^{4}\right)} d^{4} e^{8} - {\left(a^{3} b^{7} + 3 \, a^{4} b^{5} c + 33 \, a^{5} b^{3} c^{2} - 2916 \, a^{6} b c^{3}\right)} d^{3} e^{9} - 3 \, {\left(a^{4} b^{6} - 42 \, a^{5} b^{4} c + 252 \, a^{6} b^{2} c^{2} + 432 \, a^{7} c^{3}\right)} d^{2} e^{10} + 3 \, {\left(3 \, a^{5} b^{5} - 65 \, a^{6} b^{3} c + 324 \, a^{7} b c^{2}\right)} d e^{11} - {\left(5 \, a^{6} b^{4} - 81 \, a^{7} b^{2} c + 324 \, a^{8} c^{2}\right)} e^{12}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} c^{4} - 23 \, a b^{6} c^{5} + 190 \, a^{2} b^{4} c^{6} - 672 \, a^{3} b^{2} c^{7} + 864 \, a^{4} c^{8}\right)} d^{9} + 9 \, {\left(a b^{7} c^{4} - 15 \, a^{2} b^{5} c^{5} + 72 \, a^{3} b^{3} c^{6} - 112 \, a^{4} b c^{7}\right)} d^{8} e + 3 \, {\left(a^{2} b^{6} c^{4} + 28 \, a^{3} b^{4} c^{5} - 272 \, a^{4} b^{2} c^{6} + 576 \, a^{5} c^{7}\right)} d^{7} e^{2} + {\left(a^{2} b^{7} c^{3} - 80 \, a^{3} b^{5} c^{4} + 592 \, a^{4} b^{3} c^{5} - 1152 \, a^{5} b c^{6}\right)} d^{6} e^{3} + 15 \, {\left(a^{3} b^{6} c^{3} - 8 \, a^{4} b^{4} c^{4} + 16 \, a^{5} b^{2} c^{5}\right)} d^{5} e^{4} - 6 \, {\left(a^{3} b^{7} c^{2} - 17 \, a^{4} b^{5} c^{3} + 88 \, a^{5} b^{3} c^{4} - 144 \, a^{6} b c^{5}\right)} d^{4} e^{5} - {\left(a^{3} b^{8} c - 5 \, a^{4} b^{6} c^{2} + 100 \, a^{5} b^{4} c^{3} - 816 \, a^{6} b^{2} c^{4} + 1728 \, a^{7} c^{5}\right)} d^{3} e^{6} - 3 \, {\left(a^{4} b^{7} c - 32 \, a^{5} b^{5} c^{2} + 208 \, a^{6} b^{3} c^{3} - 384 \, a^{7} b c^{4}\right)} d^{2} e^{7} - 54 \, {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)} d e^{8} - {\left(a^{5} b^{7} - 17 \, a^{6} b^{5} c + 88 \, a^{7} b^{3} c^{2} - 144 \, a^{8} b c^{3}\right)} e^{9} - {\left({\left(a^{3} b^{9} c^{4} - 20 \, a^{4} b^{7} c^{5} + 144 \, a^{5} b^{5} c^{6} - 448 \, a^{6} b^{3} c^{7} + 512 \, a^{7} b c^{8}\right)} d^{3} + 3 \, {\left(a^{4} b^{8} c^{4} - 8 \, a^{5} b^{6} c^{5} + 128 \, a^{7} b^{2} c^{7} - 256 \, a^{8} c^{8}\right)} d^{2} e - 12 \, {\left(a^{5} b^{7} c^{4} - 12 \, a^{6} b^{5} c^{5} + 48 \, a^{7} b^{3} c^{6} - 64 \, a^{8} b c^{7}\right)} d e^{2} - {\left(a^{5} b^{8} c^{3} - 24 \, a^{6} b^{6} c^{4} + 192 \, a^{7} b^{4} c^{5} - 640 \, a^{8} b^{2} c^{6} + 768 \, a^{9} c^{7}\right)} e^{3}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}\right)} \sqrt{-\frac{{\left(b^{5} c^{3} - 15 \, a b^{3} c^{4} + 60 \, a^{2} b c^{5}\right)} d^{6} + 6 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{5} e - 3 \, {\left(3 \, a^{2} b^{3} c^{3} - 92 \, a^{3} b c^{4}\right)} d^{4} e^{2} - 8 \, {\left(11 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} d^{3} e^{3} - 3 \, {\left(3 \, a^{3} b^{3} c^{2} - 92 \, a^{4} b c^{3}\right)} d^{2} e^{4} + 6 \, {\left(a^{3} b^{4} c - 6 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} - 15 \, a^{4} b^{3} c + 60 \, a^{5} b c^{2}\right)} e^{6} + {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}}{a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}}}\right) + \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} x^{4} + {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} c^{3} - 15 \, a b^{3} c^{4} + 60 \, a^{2} b c^{5}\right)} d^{6} + 6 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{5} e - 3 \, {\left(3 \, a^{2} b^{3} c^{3} - 92 \, a^{3} b c^{4}\right)} d^{4} e^{2} - 8 \, {\left(11 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} d^{3} e^{3} - 3 \, {\left(3 \, a^{3} b^{3} c^{2} - 92 \, a^{4} b c^{3}\right)} d^{2} e^{4} + 6 \, {\left(a^{3} b^{4} c - 6 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} - 15 \, a^{4} b^{3} c + 60 \, a^{5} b c^{2}\right)} e^{6} + {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}}{a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}}} \log\left(-{\left({\left(5 \, b^{4} c^{6} - 81 \, a b^{2} c^{7} + 324 \, a^{2} c^{8}\right)} d^{12} - 3 \, {\left(3 \, b^{5} c^{5} - 65 \, a b^{3} c^{6} + 324 \, a^{2} b c^{7}\right)} d^{11} e + 3 \, {\left(b^{6} c^{4} - 42 \, a b^{4} c^{5} + 252 \, a^{2} b^{2} c^{6} + 432 \, a^{3} c^{7}\right)} d^{10} e^{2} + {\left(b^{7} c^{3} + 3 \, a b^{5} c^{4} + 33 \, a^{2} b^{3} c^{5} - 2916 \, a^{3} b c^{6}\right)} d^{9} e^{3} + 9 \, {\left(a b^{6} c^{3} - 15 \, a^{2} b^{4} c^{4} + 195 \, a^{3} b^{2} c^{5} + 180 \, a^{4} c^{6}\right)} d^{8} e^{4} - 162 \, {\left(a^{3} b^{3} c^{4} + 12 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 162 \, {\left(a^{4} b^{3} c^{3} + 12 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(a^{3} b^{6} c - 15 \, a^{4} b^{4} c^{2} + 195 \, a^{5} b^{2} c^{3} + 180 \, a^{6} c^{4}\right)} d^{4} e^{8} - {\left(a^{3} b^{7} + 3 \, a^{4} b^{5} c + 33 \, a^{5} b^{3} c^{2} - 2916 \, a^{6} b c^{3}\right)} d^{3} e^{9} - 3 \, {\left(a^{4} b^{6} - 42 \, a^{5} b^{4} c + 252 \, a^{6} b^{2} c^{2} + 432 \, a^{7} c^{3}\right)} d^{2} e^{10} + 3 \, {\left(3 \, a^{5} b^{5} - 65 \, a^{6} b^{3} c + 324 \, a^{7} b c^{2}\right)} d e^{11} - {\left(5 \, a^{6} b^{4} - 81 \, a^{7} b^{2} c + 324 \, a^{8} c^{2}\right)} e^{12}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} c^{4} - 23 \, a b^{6} c^{5} + 190 \, a^{2} b^{4} c^{6} - 672 \, a^{3} b^{2} c^{7} + 864 \, a^{4} c^{8}\right)} d^{9} + 9 \, {\left(a b^{7} c^{4} - 15 \, a^{2} b^{5} c^{5} + 72 \, a^{3} b^{3} c^{6} - 112 \, a^{4} b c^{7}\right)} d^{8} e + 3 \, {\left(a^{2} b^{6} c^{4} + 28 \, a^{3} b^{4} c^{5} - 272 \, a^{4} b^{2} c^{6} + 576 \, a^{5} c^{7}\right)} d^{7} e^{2} + {\left(a^{2} b^{7} c^{3} - 80 \, a^{3} b^{5} c^{4} + 592 \, a^{4} b^{3} c^{5} - 1152 \, a^{5} b c^{6}\right)} d^{6} e^{3} + 15 \, {\left(a^{3} b^{6} c^{3} - 8 \, a^{4} b^{4} c^{4} + 16 \, a^{5} b^{2} c^{5}\right)} d^{5} e^{4} - 6 \, {\left(a^{3} b^{7} c^{2} - 17 \, a^{4} b^{5} c^{3} + 88 \, a^{5} b^{3} c^{4} - 144 \, a^{6} b c^{5}\right)} d^{4} e^{5} - {\left(a^{3} b^{8} c - 5 \, a^{4} b^{6} c^{2} + 100 \, a^{5} b^{4} c^{3} - 816 \, a^{6} b^{2} c^{4} + 1728 \, a^{7} c^{5}\right)} d^{3} e^{6} - 3 \, {\left(a^{4} b^{7} c - 32 \, a^{5} b^{5} c^{2} + 208 \, a^{6} b^{3} c^{3} - 384 \, a^{7} b c^{4}\right)} d^{2} e^{7} - 54 \, {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)} d e^{8} - {\left(a^{5} b^{7} - 17 \, a^{6} b^{5} c + 88 \, a^{7} b^{3} c^{2} - 144 \, a^{8} b c^{3}\right)} e^{9} - {\left({\left(a^{3} b^{9} c^{4} - 20 \, a^{4} b^{7} c^{5} + 144 \, a^{5} b^{5} c^{6} - 448 \, a^{6} b^{3} c^{7} + 512 \, a^{7} b c^{8}\right)} d^{3} + 3 \, {\left(a^{4} b^{8} c^{4} - 8 \, a^{5} b^{6} c^{5} + 128 \, a^{7} b^{2} c^{7} - 256 \, a^{8} c^{8}\right)} d^{2} e - 12 \, {\left(a^{5} b^{7} c^{4} - 12 \, a^{6} b^{5} c^{5} + 48 \, a^{7} b^{3} c^{6} - 64 \, a^{8} b c^{7}\right)} d e^{2} - {\left(a^{5} b^{8} c^{3} - 24 \, a^{6} b^{6} c^{4} + 192 \, a^{7} b^{4} c^{5} - 640 \, a^{8} b^{2} c^{6} + 768 \, a^{9} c^{7}\right)} e^{3}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}\right)} \sqrt{-\frac{{\left(b^{5} c^{3} - 15 \, a b^{3} c^{4} + 60 \, a^{2} b c^{5}\right)} d^{6} + 6 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{5} e - 3 \, {\left(3 \, a^{2} b^{3} c^{3} - 92 \, a^{3} b c^{4}\right)} d^{4} e^{2} - 8 \, {\left(11 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} d^{3} e^{3} - 3 \, {\left(3 \, a^{3} b^{3} c^{2} - 92 \, a^{4} b c^{3}\right)} d^{2} e^{4} + 6 \, {\left(a^{3} b^{4} c - 6 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} - 15 \, a^{4} b^{3} c + 60 \, a^{5} b c^{2}\right)} e^{6} + {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}}{a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}}}\right) - \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} x^{4} + {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} c^{3} - 15 \, a b^{3} c^{4} + 60 \, a^{2} b c^{5}\right)} d^{6} + 6 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{5} e - 3 \, {\left(3 \, a^{2} b^{3} c^{3} - 92 \, a^{3} b c^{4}\right)} d^{4} e^{2} - 8 \, {\left(11 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} d^{3} e^{3} - 3 \, {\left(3 \, a^{3} b^{3} c^{2} - 92 \, a^{4} b c^{3}\right)} d^{2} e^{4} + 6 \, {\left(a^{3} b^{4} c - 6 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} - 15 \, a^{4} b^{3} c + 60 \, a^{5} b c^{2}\right)} e^{6} - {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}}{a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}}} \log\left(-{\left({\left(5 \, b^{4} c^{6} - 81 \, a b^{2} c^{7} + 324 \, a^{2} c^{8}\right)} d^{12} - 3 \, {\left(3 \, b^{5} c^{5} - 65 \, a b^{3} c^{6} + 324 \, a^{2} b c^{7}\right)} d^{11} e + 3 \, {\left(b^{6} c^{4} - 42 \, a b^{4} c^{5} + 252 \, a^{2} b^{2} c^{6} + 432 \, a^{3} c^{7}\right)} d^{10} e^{2} + {\left(b^{7} c^{3} + 3 \, a b^{5} c^{4} + 33 \, a^{2} b^{3} c^{5} - 2916 \, a^{3} b c^{6}\right)} d^{9} e^{3} + 9 \, {\left(a b^{6} c^{3} - 15 \, a^{2} b^{4} c^{4} + 195 \, a^{3} b^{2} c^{5} + 180 \, a^{4} c^{6}\right)} d^{8} e^{4} - 162 \, {\left(a^{3} b^{3} c^{4} + 12 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 162 \, {\left(a^{4} b^{3} c^{3} + 12 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(a^{3} b^{6} c - 15 \, a^{4} b^{4} c^{2} + 195 \, a^{5} b^{2} c^{3} + 180 \, a^{6} c^{4}\right)} d^{4} e^{8} - {\left(a^{3} b^{7} + 3 \, a^{4} b^{5} c + 33 \, a^{5} b^{3} c^{2} - 2916 \, a^{6} b c^{3}\right)} d^{3} e^{9} - 3 \, {\left(a^{4} b^{6} - 42 \, a^{5} b^{4} c + 252 \, a^{6} b^{2} c^{2} + 432 \, a^{7} c^{3}\right)} d^{2} e^{10} + 3 \, {\left(3 \, a^{5} b^{5} - 65 \, a^{6} b^{3} c + 324 \, a^{7} b c^{2}\right)} d e^{11} - {\left(5 \, a^{6} b^{4} - 81 \, a^{7} b^{2} c + 324 \, a^{8} c^{2}\right)} e^{12}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} c^{4} - 23 \, a b^{6} c^{5} + 190 \, a^{2} b^{4} c^{6} - 672 \, a^{3} b^{2} c^{7} + 864 \, a^{4} c^{8}\right)} d^{9} + 9 \, {\left(a b^{7} c^{4} - 15 \, a^{2} b^{5} c^{5} + 72 \, a^{3} b^{3} c^{6} - 112 \, a^{4} b c^{7}\right)} d^{8} e + 3 \, {\left(a^{2} b^{6} c^{4} + 28 \, a^{3} b^{4} c^{5} - 272 \, a^{4} b^{2} c^{6} + 576 \, a^{5} c^{7}\right)} d^{7} e^{2} + {\left(a^{2} b^{7} c^{3} - 80 \, a^{3} b^{5} c^{4} + 592 \, a^{4} b^{3} c^{5} - 1152 \, a^{5} b c^{6}\right)} d^{6} e^{3} + 15 \, {\left(a^{3} b^{6} c^{3} - 8 \, a^{4} b^{4} c^{4} + 16 \, a^{5} b^{2} c^{5}\right)} d^{5} e^{4} - 6 \, {\left(a^{3} b^{7} c^{2} - 17 \, a^{4} b^{5} c^{3} + 88 \, a^{5} b^{3} c^{4} - 144 \, a^{6} b c^{5}\right)} d^{4} e^{5} - {\left(a^{3} b^{8} c - 5 \, a^{4} b^{6} c^{2} + 100 \, a^{5} b^{4} c^{3} - 816 \, a^{6} b^{2} c^{4} + 1728 \, a^{7} c^{5}\right)} d^{3} e^{6} - 3 \, {\left(a^{4} b^{7} c - 32 \, a^{5} b^{5} c^{2} + 208 \, a^{6} b^{3} c^{3} - 384 \, a^{7} b c^{4}\right)} d^{2} e^{7} - 54 \, {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)} d e^{8} - {\left(a^{5} b^{7} - 17 \, a^{6} b^{5} c + 88 \, a^{7} b^{3} c^{2} - 144 \, a^{8} b c^{3}\right)} e^{9} + {\left({\left(a^{3} b^{9} c^{4} - 20 \, a^{4} b^{7} c^{5} + 144 \, a^{5} b^{5} c^{6} - 448 \, a^{6} b^{3} c^{7} + 512 \, a^{7} b c^{8}\right)} d^{3} + 3 \, {\left(a^{4} b^{8} c^{4} - 8 \, a^{5} b^{6} c^{5} + 128 \, a^{7} b^{2} c^{7} - 256 \, a^{8} c^{8}\right)} d^{2} e - 12 \, {\left(a^{5} b^{7} c^{4} - 12 \, a^{6} b^{5} c^{5} + 48 \, a^{7} b^{3} c^{6} - 64 \, a^{8} b c^{7}\right)} d e^{2} - {\left(a^{5} b^{8} c^{3} - 24 \, a^{6} b^{6} c^{4} + 192 \, a^{7} b^{4} c^{5} - 640 \, a^{8} b^{2} c^{6} + 768 \, a^{9} c^{7}\right)} e^{3}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}\right)} \sqrt{-\frac{{\left(b^{5} c^{3} - 15 \, a b^{3} c^{4} + 60 \, a^{2} b c^{5}\right)} d^{6} + 6 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{5} e - 3 \, {\left(3 \, a^{2} b^{3} c^{3} - 92 \, a^{3} b c^{4}\right)} d^{4} e^{2} - 8 \, {\left(11 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} d^{3} e^{3} - 3 \, {\left(3 \, a^{3} b^{3} c^{2} - 92 \, a^{4} b c^{3}\right)} d^{2} e^{4} + 6 \, {\left(a^{3} b^{4} c - 6 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} - 15 \, a^{4} b^{3} c + 60 \, a^{5} b c^{2}\right)} e^{6} - {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}}{a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}}}\right) + \sqrt{\frac{1}{2}} {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} x^{4} + {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} c^{3} - 15 \, a b^{3} c^{4} + 60 \, a^{2} b c^{5}\right)} d^{6} + 6 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{5} e - 3 \, {\left(3 \, a^{2} b^{3} c^{3} - 92 \, a^{3} b c^{4}\right)} d^{4} e^{2} - 8 \, {\left(11 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} d^{3} e^{3} - 3 \, {\left(3 \, a^{3} b^{3} c^{2} - 92 \, a^{4} b c^{3}\right)} d^{2} e^{4} + 6 \, {\left(a^{3} b^{4} c - 6 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} - 15 \, a^{4} b^{3} c + 60 \, a^{5} b c^{2}\right)} e^{6} - {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}}{a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}}} \log\left(-{\left({\left(5 \, b^{4} c^{6} - 81 \, a b^{2} c^{7} + 324 \, a^{2} c^{8}\right)} d^{12} - 3 \, {\left(3 \, b^{5} c^{5} - 65 \, a b^{3} c^{6} + 324 \, a^{2} b c^{7}\right)} d^{11} e + 3 \, {\left(b^{6} c^{4} - 42 \, a b^{4} c^{5} + 252 \, a^{2} b^{2} c^{6} + 432 \, a^{3} c^{7}\right)} d^{10} e^{2} + {\left(b^{7} c^{3} + 3 \, a b^{5} c^{4} + 33 \, a^{2} b^{3} c^{5} - 2916 \, a^{3} b c^{6}\right)} d^{9} e^{3} + 9 \, {\left(a b^{6} c^{3} - 15 \, a^{2} b^{4} c^{4} + 195 \, a^{3} b^{2} c^{5} + 180 \, a^{4} c^{6}\right)} d^{8} e^{4} - 162 \, {\left(a^{3} b^{3} c^{4} + 12 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 162 \, {\left(a^{4} b^{3} c^{3} + 12 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(a^{3} b^{6} c - 15 \, a^{4} b^{4} c^{2} + 195 \, a^{5} b^{2} c^{3} + 180 \, a^{6} c^{4}\right)} d^{4} e^{8} - {\left(a^{3} b^{7} + 3 \, a^{4} b^{5} c + 33 \, a^{5} b^{3} c^{2} - 2916 \, a^{6} b c^{3}\right)} d^{3} e^{9} - 3 \, {\left(a^{4} b^{6} - 42 \, a^{5} b^{4} c + 252 \, a^{6} b^{2} c^{2} + 432 \, a^{7} c^{3}\right)} d^{2} e^{10} + 3 \, {\left(3 \, a^{5} b^{5} - 65 \, a^{6} b^{3} c + 324 \, a^{7} b c^{2}\right)} d e^{11} - {\left(5 \, a^{6} b^{4} - 81 \, a^{7} b^{2} c + 324 \, a^{8} c^{2}\right)} e^{12}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} c^{4} - 23 \, a b^{6} c^{5} + 190 \, a^{2} b^{4} c^{6} - 672 \, a^{3} b^{2} c^{7} + 864 \, a^{4} c^{8}\right)} d^{9} + 9 \, {\left(a b^{7} c^{4} - 15 \, a^{2} b^{5} c^{5} + 72 \, a^{3} b^{3} c^{6} - 112 \, a^{4} b c^{7}\right)} d^{8} e + 3 \, {\left(a^{2} b^{6} c^{4} + 28 \, a^{3} b^{4} c^{5} - 272 \, a^{4} b^{2} c^{6} + 576 \, a^{5} c^{7}\right)} d^{7} e^{2} + {\left(a^{2} b^{7} c^{3} - 80 \, a^{3} b^{5} c^{4} + 592 \, a^{4} b^{3} c^{5} - 1152 \, a^{5} b c^{6}\right)} d^{6} e^{3} + 15 \, {\left(a^{3} b^{6} c^{3} - 8 \, a^{4} b^{4} c^{4} + 16 \, a^{5} b^{2} c^{5}\right)} d^{5} e^{4} - 6 \, {\left(a^{3} b^{7} c^{2} - 17 \, a^{4} b^{5} c^{3} + 88 \, a^{5} b^{3} c^{4} - 144 \, a^{6} b c^{5}\right)} d^{4} e^{5} - {\left(a^{3} b^{8} c - 5 \, a^{4} b^{6} c^{2} + 100 \, a^{5} b^{4} c^{3} - 816 \, a^{6} b^{2} c^{4} + 1728 \, a^{7} c^{5}\right)} d^{3} e^{6} - 3 \, {\left(a^{4} b^{7} c - 32 \, a^{5} b^{5} c^{2} + 208 \, a^{6} b^{3} c^{3} - 384 \, a^{7} b c^{4}\right)} d^{2} e^{7} - 54 \, {\left(a^{6} b^{4} c^{2} - 8 \, a^{7} b^{2} c^{3} + 16 \, a^{8} c^{4}\right)} d e^{8} - {\left(a^{5} b^{7} - 17 \, a^{6} b^{5} c + 88 \, a^{7} b^{3} c^{2} - 144 \, a^{8} b c^{3}\right)} e^{9} + {\left({\left(a^{3} b^{9} c^{4} - 20 \, a^{4} b^{7} c^{5} + 144 \, a^{5} b^{5} c^{6} - 448 \, a^{6} b^{3} c^{7} + 512 \, a^{7} b c^{8}\right)} d^{3} + 3 \, {\left(a^{4} b^{8} c^{4} - 8 \, a^{5} b^{6} c^{5} + 128 \, a^{7} b^{2} c^{7} - 256 \, a^{8} c^{8}\right)} d^{2} e - 12 \, {\left(a^{5} b^{7} c^{4} - 12 \, a^{6} b^{5} c^{5} + 48 \, a^{7} b^{3} c^{6} - 64 \, a^{8} b c^{7}\right)} d e^{2} - {\left(a^{5} b^{8} c^{3} - 24 \, a^{6} b^{6} c^{4} + 192 \, a^{7} b^{4} c^{5} - 640 \, a^{8} b^{2} c^{6} + 768 \, a^{9} c^{7}\right)} e^{3}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}\right)} \sqrt{-\frac{{\left(b^{5} c^{3} - 15 \, a b^{3} c^{4} + 60 \, a^{2} b c^{5}\right)} d^{6} + 6 \, {\left(a b^{4} c^{3} - 6 \, a^{2} b^{2} c^{4} - 24 \, a^{3} c^{5}\right)} d^{5} e - 3 \, {\left(3 \, a^{2} b^{3} c^{3} - 92 \, a^{3} b c^{4}\right)} d^{4} e^{2} - 8 \, {\left(11 \, a^{3} b^{2} c^{3} + 36 \, a^{4} c^{4}\right)} d^{3} e^{3} - 3 \, {\left(3 \, a^{3} b^{3} c^{2} - 92 \, a^{4} b c^{3}\right)} d^{2} e^{4} + 6 \, {\left(a^{3} b^{4} c - 6 \, a^{4} b^{2} c^{2} - 24 \, a^{5} c^{3}\right)} d e^{5} + {\left(a^{3} b^{5} - 15 \, a^{4} b^{3} c + 60 \, a^{5} b c^{2}\right)} e^{6} - {\left(a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}\right)} \sqrt{-\frac{108 \, a^{3} b c^{6} d^{9} e^{3} + 108 \, a^{6} b c^{3} d^{3} e^{9} - {\left(b^{4} c^{6} - 18 \, a b^{2} c^{7} + 81 \, a^{2} c^{8}\right)} d^{12} - 12 \, {\left(a b^{3} c^{6} - 9 \, a^{2} b c^{7}\right)} d^{11} e - 18 \, {\left(a^{2} b^{2} c^{6} + 9 \, a^{3} c^{7}\right)} d^{10} e^{2} - 9 \, {\left(2 \, a^{3} b^{2} c^{5} - 9 \, a^{4} c^{6}\right)} d^{8} e^{4} + 12 \, {\left(a^{3} b^{3} c^{4} - 18 \, a^{4} b c^{5}\right)} d^{7} e^{5} + 2 \, {\left(a^{3} b^{4} c^{3} + 18 \, a^{4} b^{2} c^{4} + 162 \, a^{5} c^{5}\right)} d^{6} e^{6} + 12 \, {\left(a^{4} b^{3} c^{3} - 18 \, a^{5} b c^{4}\right)} d^{5} e^{7} - 9 \, {\left(2 \, a^{5} b^{2} c^{3} - 9 \, a^{6} c^{4}\right)} d^{4} e^{8} - 18 \, {\left(a^{6} b^{2} c^{2} + 9 \, a^{7} c^{3}\right)} d^{2} e^{10} - 12 \, {\left(a^{6} b^{3} c - 9 \, a^{7} b c^{2}\right)} d e^{11} - {\left(a^{6} b^{4} - 18 \, a^{7} b^{2} c + 81 \, a^{8} c^{2}\right)} e^{12}}{a^{6} b^{6} c^{6} - 12 \, a^{7} b^{4} c^{7} + 48 \, a^{8} b^{2} c^{8} - 64 \, a^{9} c^{9}}}}{a^{3} b^{6} c^{3} - 12 \, a^{4} b^{4} c^{4} + 48 \, a^{5} b^{2} c^{5} - 64 \, a^{6} c^{6}}}\right) - 2 \, {\left(3 \, a b c d^{2} e - 6 \, a^{2} c d e^{2} + a^{2} b e^{3} - {\left(b^{2} c - 2 \, a c^{2}\right)} d^{3}\right)} x}{4 \, {\left(a^{2} b^{2} c - 4 \, a^{3} c^{2} + {\left(a b^{2} c^{2} - 4 \, a^{2} c^{3}\right)} x^{4} + {\left(a b^{3} c - 4 \, a^{2} b c^{2}\right)} x^{2}\right)}}"," ",0,"1/4*(2*(b*c^2*d^3 - 6*a*c^2*d^2*e + 3*a*b*c*d*e^2 - (a*b^2 - 2*a^2*c)*e^3)*x^3 - sqrt(1/2)*(a^2*b^2*c - 4*a^3*c^2 + (a*b^2*c^2 - 4*a^2*c^3)*x^4 + (a*b^3*c - 4*a^2*b*c^2)*x^2)*sqrt(-((b^5*c^3 - 15*a*b^3*c^4 + 60*a^2*b*c^5)*d^6 + 6*(a*b^4*c^3 - 6*a^2*b^2*c^4 - 24*a^3*c^5)*d^5*e - 3*(3*a^2*b^3*c^3 - 92*a^3*b*c^4)*d^4*e^2 - 8*(11*a^3*b^2*c^3 + 36*a^4*c^4)*d^3*e^3 - 3*(3*a^3*b^3*c^2 - 92*a^4*b*c^3)*d^2*e^4 + 6*(a^3*b^4*c - 6*a^4*b^2*c^2 - 24*a^5*c^3)*d*e^5 + (a^3*b^5 - 15*a^4*b^3*c + 60*a^5*b*c^2)*e^6 + (a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))/(a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6))*log(-((5*b^4*c^6 - 81*a*b^2*c^7 + 324*a^2*c^8)*d^12 - 3*(3*b^5*c^5 - 65*a*b^3*c^6 + 324*a^2*b*c^7)*d^11*e + 3*(b^6*c^4 - 42*a*b^4*c^5 + 252*a^2*b^2*c^6 + 432*a^3*c^7)*d^10*e^2 + (b^7*c^3 + 3*a*b^5*c^4 + 33*a^2*b^3*c^5 - 2916*a^3*b*c^6)*d^9*e^3 + 9*(a*b^6*c^3 - 15*a^2*b^4*c^4 + 195*a^3*b^2*c^5 + 180*a^4*c^6)*d^8*e^4 - 162*(a^3*b^3*c^4 + 12*a^4*b*c^5)*d^7*e^5 + 162*(a^4*b^3*c^3 + 12*a^5*b*c^4)*d^5*e^7 - 9*(a^3*b^6*c - 15*a^4*b^4*c^2 + 195*a^5*b^2*c^3 + 180*a^6*c^4)*d^4*e^8 - (a^3*b^7 + 3*a^4*b^5*c + 33*a^5*b^3*c^2 - 2916*a^6*b*c^3)*d^3*e^9 - 3*(a^4*b^6 - 42*a^5*b^4*c + 252*a^6*b^2*c^2 + 432*a^7*c^3)*d^2*e^10 + 3*(3*a^5*b^5 - 65*a^6*b^3*c + 324*a^7*b*c^2)*d*e^11 - (5*a^6*b^4 - 81*a^7*b^2*c + 324*a^8*c^2)*e^12)*x + 1/2*sqrt(1/2)*((b^8*c^4 - 23*a*b^6*c^5 + 190*a^2*b^4*c^6 - 672*a^3*b^2*c^7 + 864*a^4*c^8)*d^9 + 9*(a*b^7*c^4 - 15*a^2*b^5*c^5 + 72*a^3*b^3*c^6 - 112*a^4*b*c^7)*d^8*e + 3*(a^2*b^6*c^4 + 28*a^3*b^4*c^5 - 272*a^4*b^2*c^6 + 576*a^5*c^7)*d^7*e^2 + (a^2*b^7*c^3 - 80*a^3*b^5*c^4 + 592*a^4*b^3*c^5 - 1152*a^5*b*c^6)*d^6*e^3 + 15*(a^3*b^6*c^3 - 8*a^4*b^4*c^4 + 16*a^5*b^2*c^5)*d^5*e^4 - 6*(a^3*b^7*c^2 - 17*a^4*b^5*c^3 + 88*a^5*b^3*c^4 - 144*a^6*b*c^5)*d^4*e^5 - (a^3*b^8*c - 5*a^4*b^6*c^2 + 100*a^5*b^4*c^3 - 816*a^6*b^2*c^4 + 1728*a^7*c^5)*d^3*e^6 - 3*(a^4*b^7*c - 32*a^5*b^5*c^2 + 208*a^6*b^3*c^3 - 384*a^7*b*c^4)*d^2*e^7 - 54*(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)*d*e^8 - (a^5*b^7 - 17*a^6*b^5*c + 88*a^7*b^3*c^2 - 144*a^8*b*c^3)*e^9 - ((a^3*b^9*c^4 - 20*a^4*b^7*c^5 + 144*a^5*b^5*c^6 - 448*a^6*b^3*c^7 + 512*a^7*b*c^8)*d^3 + 3*(a^4*b^8*c^4 - 8*a^5*b^6*c^5 + 128*a^7*b^2*c^7 - 256*a^8*c^8)*d^2*e - 12*(a^5*b^7*c^4 - 12*a^6*b^5*c^5 + 48*a^7*b^3*c^6 - 64*a^8*b*c^7)*d*e^2 - (a^5*b^8*c^3 - 24*a^6*b^6*c^4 + 192*a^7*b^4*c^5 - 640*a^8*b^2*c^6 + 768*a^9*c^7)*e^3)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))*sqrt(-((b^5*c^3 - 15*a*b^3*c^4 + 60*a^2*b*c^5)*d^6 + 6*(a*b^4*c^3 - 6*a^2*b^2*c^4 - 24*a^3*c^5)*d^5*e - 3*(3*a^2*b^3*c^3 - 92*a^3*b*c^4)*d^4*e^2 - 8*(11*a^3*b^2*c^3 + 36*a^4*c^4)*d^3*e^3 - 3*(3*a^3*b^3*c^2 - 92*a^4*b*c^3)*d^2*e^4 + 6*(a^3*b^4*c - 6*a^4*b^2*c^2 - 24*a^5*c^3)*d*e^5 + (a^3*b^5 - 15*a^4*b^3*c + 60*a^5*b*c^2)*e^6 + (a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))/(a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6))) + sqrt(1/2)*(a^2*b^2*c - 4*a^3*c^2 + (a*b^2*c^2 - 4*a^2*c^3)*x^4 + (a*b^3*c - 4*a^2*b*c^2)*x^2)*sqrt(-((b^5*c^3 - 15*a*b^3*c^4 + 60*a^2*b*c^5)*d^6 + 6*(a*b^4*c^3 - 6*a^2*b^2*c^4 - 24*a^3*c^5)*d^5*e - 3*(3*a^2*b^3*c^3 - 92*a^3*b*c^4)*d^4*e^2 - 8*(11*a^3*b^2*c^3 + 36*a^4*c^4)*d^3*e^3 - 3*(3*a^3*b^3*c^2 - 92*a^4*b*c^3)*d^2*e^4 + 6*(a^3*b^4*c - 6*a^4*b^2*c^2 - 24*a^5*c^3)*d*e^5 + (a^3*b^5 - 15*a^4*b^3*c + 60*a^5*b*c^2)*e^6 + (a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))/(a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6))*log(-((5*b^4*c^6 - 81*a*b^2*c^7 + 324*a^2*c^8)*d^12 - 3*(3*b^5*c^5 - 65*a*b^3*c^6 + 324*a^2*b*c^7)*d^11*e + 3*(b^6*c^4 - 42*a*b^4*c^5 + 252*a^2*b^2*c^6 + 432*a^3*c^7)*d^10*e^2 + (b^7*c^3 + 3*a*b^5*c^4 + 33*a^2*b^3*c^5 - 2916*a^3*b*c^6)*d^9*e^3 + 9*(a*b^6*c^3 - 15*a^2*b^4*c^4 + 195*a^3*b^2*c^5 + 180*a^4*c^6)*d^8*e^4 - 162*(a^3*b^3*c^4 + 12*a^4*b*c^5)*d^7*e^5 + 162*(a^4*b^3*c^3 + 12*a^5*b*c^4)*d^5*e^7 - 9*(a^3*b^6*c - 15*a^4*b^4*c^2 + 195*a^5*b^2*c^3 + 180*a^6*c^4)*d^4*e^8 - (a^3*b^7 + 3*a^4*b^5*c + 33*a^5*b^3*c^2 - 2916*a^6*b*c^3)*d^3*e^9 - 3*(a^4*b^6 - 42*a^5*b^4*c + 252*a^6*b^2*c^2 + 432*a^7*c^3)*d^2*e^10 + 3*(3*a^5*b^5 - 65*a^6*b^3*c + 324*a^7*b*c^2)*d*e^11 - (5*a^6*b^4 - 81*a^7*b^2*c + 324*a^8*c^2)*e^12)*x - 1/2*sqrt(1/2)*((b^8*c^4 - 23*a*b^6*c^5 + 190*a^2*b^4*c^6 - 672*a^3*b^2*c^7 + 864*a^4*c^8)*d^9 + 9*(a*b^7*c^4 - 15*a^2*b^5*c^5 + 72*a^3*b^3*c^6 - 112*a^4*b*c^7)*d^8*e + 3*(a^2*b^6*c^4 + 28*a^3*b^4*c^5 - 272*a^4*b^2*c^6 + 576*a^5*c^7)*d^7*e^2 + (a^2*b^7*c^3 - 80*a^3*b^5*c^4 + 592*a^4*b^3*c^5 - 1152*a^5*b*c^6)*d^6*e^3 + 15*(a^3*b^6*c^3 - 8*a^4*b^4*c^4 + 16*a^5*b^2*c^5)*d^5*e^4 - 6*(a^3*b^7*c^2 - 17*a^4*b^5*c^3 + 88*a^5*b^3*c^4 - 144*a^6*b*c^5)*d^4*e^5 - (a^3*b^8*c - 5*a^4*b^6*c^2 + 100*a^5*b^4*c^3 - 816*a^6*b^2*c^4 + 1728*a^7*c^5)*d^3*e^6 - 3*(a^4*b^7*c - 32*a^5*b^5*c^2 + 208*a^6*b^3*c^3 - 384*a^7*b*c^4)*d^2*e^7 - 54*(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)*d*e^8 - (a^5*b^7 - 17*a^6*b^5*c + 88*a^7*b^3*c^2 - 144*a^8*b*c^3)*e^9 - ((a^3*b^9*c^4 - 20*a^4*b^7*c^5 + 144*a^5*b^5*c^6 - 448*a^6*b^3*c^7 + 512*a^7*b*c^8)*d^3 + 3*(a^4*b^8*c^4 - 8*a^5*b^6*c^5 + 128*a^7*b^2*c^7 - 256*a^8*c^8)*d^2*e - 12*(a^5*b^7*c^4 - 12*a^6*b^5*c^5 + 48*a^7*b^3*c^6 - 64*a^8*b*c^7)*d*e^2 - (a^5*b^8*c^3 - 24*a^6*b^6*c^4 + 192*a^7*b^4*c^5 - 640*a^8*b^2*c^6 + 768*a^9*c^7)*e^3)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))*sqrt(-((b^5*c^3 - 15*a*b^3*c^4 + 60*a^2*b*c^5)*d^6 + 6*(a*b^4*c^3 - 6*a^2*b^2*c^4 - 24*a^3*c^5)*d^5*e - 3*(3*a^2*b^3*c^3 - 92*a^3*b*c^4)*d^4*e^2 - 8*(11*a^3*b^2*c^3 + 36*a^4*c^4)*d^3*e^3 - 3*(3*a^3*b^3*c^2 - 92*a^4*b*c^3)*d^2*e^4 + 6*(a^3*b^4*c - 6*a^4*b^2*c^2 - 24*a^5*c^3)*d*e^5 + (a^3*b^5 - 15*a^4*b^3*c + 60*a^5*b*c^2)*e^6 + (a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))/(a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6))) - sqrt(1/2)*(a^2*b^2*c - 4*a^3*c^2 + (a*b^2*c^2 - 4*a^2*c^3)*x^4 + (a*b^3*c - 4*a^2*b*c^2)*x^2)*sqrt(-((b^5*c^3 - 15*a*b^3*c^4 + 60*a^2*b*c^5)*d^6 + 6*(a*b^4*c^3 - 6*a^2*b^2*c^4 - 24*a^3*c^5)*d^5*e - 3*(3*a^2*b^3*c^3 - 92*a^3*b*c^4)*d^4*e^2 - 8*(11*a^3*b^2*c^3 + 36*a^4*c^4)*d^3*e^3 - 3*(3*a^3*b^3*c^2 - 92*a^4*b*c^3)*d^2*e^4 + 6*(a^3*b^4*c - 6*a^4*b^2*c^2 - 24*a^5*c^3)*d*e^5 + (a^3*b^5 - 15*a^4*b^3*c + 60*a^5*b*c^2)*e^6 - (a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))/(a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6))*log(-((5*b^4*c^6 - 81*a*b^2*c^7 + 324*a^2*c^8)*d^12 - 3*(3*b^5*c^5 - 65*a*b^3*c^6 + 324*a^2*b*c^7)*d^11*e + 3*(b^6*c^4 - 42*a*b^4*c^5 + 252*a^2*b^2*c^6 + 432*a^3*c^7)*d^10*e^2 + (b^7*c^3 + 3*a*b^5*c^4 + 33*a^2*b^3*c^5 - 2916*a^3*b*c^6)*d^9*e^3 + 9*(a*b^6*c^3 - 15*a^2*b^4*c^4 + 195*a^3*b^2*c^5 + 180*a^4*c^6)*d^8*e^4 - 162*(a^3*b^3*c^4 + 12*a^4*b*c^5)*d^7*e^5 + 162*(a^4*b^3*c^3 + 12*a^5*b*c^4)*d^5*e^7 - 9*(a^3*b^6*c - 15*a^4*b^4*c^2 + 195*a^5*b^2*c^3 + 180*a^6*c^4)*d^4*e^8 - (a^3*b^7 + 3*a^4*b^5*c + 33*a^5*b^3*c^2 - 2916*a^6*b*c^3)*d^3*e^9 - 3*(a^4*b^6 - 42*a^5*b^4*c + 252*a^6*b^2*c^2 + 432*a^7*c^3)*d^2*e^10 + 3*(3*a^5*b^5 - 65*a^6*b^3*c + 324*a^7*b*c^2)*d*e^11 - (5*a^6*b^4 - 81*a^7*b^2*c + 324*a^8*c^2)*e^12)*x + 1/2*sqrt(1/2)*((b^8*c^4 - 23*a*b^6*c^5 + 190*a^2*b^4*c^6 - 672*a^3*b^2*c^7 + 864*a^4*c^8)*d^9 + 9*(a*b^7*c^4 - 15*a^2*b^5*c^5 + 72*a^3*b^3*c^6 - 112*a^4*b*c^7)*d^8*e + 3*(a^2*b^6*c^4 + 28*a^3*b^4*c^5 - 272*a^4*b^2*c^6 + 576*a^5*c^7)*d^7*e^2 + (a^2*b^7*c^3 - 80*a^3*b^5*c^4 + 592*a^4*b^3*c^5 - 1152*a^5*b*c^6)*d^6*e^3 + 15*(a^3*b^6*c^3 - 8*a^4*b^4*c^4 + 16*a^5*b^2*c^5)*d^5*e^4 - 6*(a^3*b^7*c^2 - 17*a^4*b^5*c^3 + 88*a^5*b^3*c^4 - 144*a^6*b*c^5)*d^4*e^5 - (a^3*b^8*c - 5*a^4*b^6*c^2 + 100*a^5*b^4*c^3 - 816*a^6*b^2*c^4 + 1728*a^7*c^5)*d^3*e^6 - 3*(a^4*b^7*c - 32*a^5*b^5*c^2 + 208*a^6*b^3*c^3 - 384*a^7*b*c^4)*d^2*e^7 - 54*(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)*d*e^8 - (a^5*b^7 - 17*a^6*b^5*c + 88*a^7*b^3*c^2 - 144*a^8*b*c^3)*e^9 + ((a^3*b^9*c^4 - 20*a^4*b^7*c^5 + 144*a^5*b^5*c^6 - 448*a^6*b^3*c^7 + 512*a^7*b*c^8)*d^3 + 3*(a^4*b^8*c^4 - 8*a^5*b^6*c^5 + 128*a^7*b^2*c^7 - 256*a^8*c^8)*d^2*e - 12*(a^5*b^7*c^4 - 12*a^6*b^5*c^5 + 48*a^7*b^3*c^6 - 64*a^8*b*c^7)*d*e^2 - (a^5*b^8*c^3 - 24*a^6*b^6*c^4 + 192*a^7*b^4*c^5 - 640*a^8*b^2*c^6 + 768*a^9*c^7)*e^3)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))*sqrt(-((b^5*c^3 - 15*a*b^3*c^4 + 60*a^2*b*c^5)*d^6 + 6*(a*b^4*c^3 - 6*a^2*b^2*c^4 - 24*a^3*c^5)*d^5*e - 3*(3*a^2*b^3*c^3 - 92*a^3*b*c^4)*d^4*e^2 - 8*(11*a^3*b^2*c^3 + 36*a^4*c^4)*d^3*e^3 - 3*(3*a^3*b^3*c^2 - 92*a^4*b*c^3)*d^2*e^4 + 6*(a^3*b^4*c - 6*a^4*b^2*c^2 - 24*a^5*c^3)*d*e^5 + (a^3*b^5 - 15*a^4*b^3*c + 60*a^5*b*c^2)*e^6 - (a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))/(a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6))) + sqrt(1/2)*(a^2*b^2*c - 4*a^3*c^2 + (a*b^2*c^2 - 4*a^2*c^3)*x^4 + (a*b^3*c - 4*a^2*b*c^2)*x^2)*sqrt(-((b^5*c^3 - 15*a*b^3*c^4 + 60*a^2*b*c^5)*d^6 + 6*(a*b^4*c^3 - 6*a^2*b^2*c^4 - 24*a^3*c^5)*d^5*e - 3*(3*a^2*b^3*c^3 - 92*a^3*b*c^4)*d^4*e^2 - 8*(11*a^3*b^2*c^3 + 36*a^4*c^4)*d^3*e^3 - 3*(3*a^3*b^3*c^2 - 92*a^4*b*c^3)*d^2*e^4 + 6*(a^3*b^4*c - 6*a^4*b^2*c^2 - 24*a^5*c^3)*d*e^5 + (a^3*b^5 - 15*a^4*b^3*c + 60*a^5*b*c^2)*e^6 - (a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))/(a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6))*log(-((5*b^4*c^6 - 81*a*b^2*c^7 + 324*a^2*c^8)*d^12 - 3*(3*b^5*c^5 - 65*a*b^3*c^6 + 324*a^2*b*c^7)*d^11*e + 3*(b^6*c^4 - 42*a*b^4*c^5 + 252*a^2*b^2*c^6 + 432*a^3*c^7)*d^10*e^2 + (b^7*c^3 + 3*a*b^5*c^4 + 33*a^2*b^3*c^5 - 2916*a^3*b*c^6)*d^9*e^3 + 9*(a*b^6*c^3 - 15*a^2*b^4*c^4 + 195*a^3*b^2*c^5 + 180*a^4*c^6)*d^8*e^4 - 162*(a^3*b^3*c^4 + 12*a^4*b*c^5)*d^7*e^5 + 162*(a^4*b^3*c^3 + 12*a^5*b*c^4)*d^5*e^7 - 9*(a^3*b^6*c - 15*a^4*b^4*c^2 + 195*a^5*b^2*c^3 + 180*a^6*c^4)*d^4*e^8 - (a^3*b^7 + 3*a^4*b^5*c + 33*a^5*b^3*c^2 - 2916*a^6*b*c^3)*d^3*e^9 - 3*(a^4*b^6 - 42*a^5*b^4*c + 252*a^6*b^2*c^2 + 432*a^7*c^3)*d^2*e^10 + 3*(3*a^5*b^5 - 65*a^6*b^3*c + 324*a^7*b*c^2)*d*e^11 - (5*a^6*b^4 - 81*a^7*b^2*c + 324*a^8*c^2)*e^12)*x - 1/2*sqrt(1/2)*((b^8*c^4 - 23*a*b^6*c^5 + 190*a^2*b^4*c^6 - 672*a^3*b^2*c^7 + 864*a^4*c^8)*d^9 + 9*(a*b^7*c^4 - 15*a^2*b^5*c^5 + 72*a^3*b^3*c^6 - 112*a^4*b*c^7)*d^8*e + 3*(a^2*b^6*c^4 + 28*a^3*b^4*c^5 - 272*a^4*b^2*c^6 + 576*a^5*c^7)*d^7*e^2 + (a^2*b^7*c^3 - 80*a^3*b^5*c^4 + 592*a^4*b^3*c^5 - 1152*a^5*b*c^6)*d^6*e^3 + 15*(a^3*b^6*c^3 - 8*a^4*b^4*c^4 + 16*a^5*b^2*c^5)*d^5*e^4 - 6*(a^3*b^7*c^2 - 17*a^4*b^5*c^3 + 88*a^5*b^3*c^4 - 144*a^6*b*c^5)*d^4*e^5 - (a^3*b^8*c - 5*a^4*b^6*c^2 + 100*a^5*b^4*c^3 - 816*a^6*b^2*c^4 + 1728*a^7*c^5)*d^3*e^6 - 3*(a^4*b^7*c - 32*a^5*b^5*c^2 + 208*a^6*b^3*c^3 - 384*a^7*b*c^4)*d^2*e^7 - 54*(a^6*b^4*c^2 - 8*a^7*b^2*c^3 + 16*a^8*c^4)*d*e^8 - (a^5*b^7 - 17*a^6*b^5*c + 88*a^7*b^3*c^2 - 144*a^8*b*c^3)*e^9 + ((a^3*b^9*c^4 - 20*a^4*b^7*c^5 + 144*a^5*b^5*c^6 - 448*a^6*b^3*c^7 + 512*a^7*b*c^8)*d^3 + 3*(a^4*b^8*c^4 - 8*a^5*b^6*c^5 + 128*a^7*b^2*c^7 - 256*a^8*c^8)*d^2*e - 12*(a^5*b^7*c^4 - 12*a^6*b^5*c^5 + 48*a^7*b^3*c^6 - 64*a^8*b*c^7)*d*e^2 - (a^5*b^8*c^3 - 24*a^6*b^6*c^4 + 192*a^7*b^4*c^5 - 640*a^8*b^2*c^6 + 768*a^9*c^7)*e^3)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))*sqrt(-((b^5*c^3 - 15*a*b^3*c^4 + 60*a^2*b*c^5)*d^6 + 6*(a*b^4*c^3 - 6*a^2*b^2*c^4 - 24*a^3*c^5)*d^5*e - 3*(3*a^2*b^3*c^3 - 92*a^3*b*c^4)*d^4*e^2 - 8*(11*a^3*b^2*c^3 + 36*a^4*c^4)*d^3*e^3 - 3*(3*a^3*b^3*c^2 - 92*a^4*b*c^3)*d^2*e^4 + 6*(a^3*b^4*c - 6*a^4*b^2*c^2 - 24*a^5*c^3)*d*e^5 + (a^3*b^5 - 15*a^4*b^3*c + 60*a^5*b*c^2)*e^6 - (a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6)*sqrt(-(108*a^3*b*c^6*d^9*e^3 + 108*a^6*b*c^3*d^3*e^9 - (b^4*c^6 - 18*a*b^2*c^7 + 81*a^2*c^8)*d^12 - 12*(a*b^3*c^6 - 9*a^2*b*c^7)*d^11*e - 18*(a^2*b^2*c^6 + 9*a^3*c^7)*d^10*e^2 - 9*(2*a^3*b^2*c^5 - 9*a^4*c^6)*d^8*e^4 + 12*(a^3*b^3*c^4 - 18*a^4*b*c^5)*d^7*e^5 + 2*(a^3*b^4*c^3 + 18*a^4*b^2*c^4 + 162*a^5*c^5)*d^6*e^6 + 12*(a^4*b^3*c^3 - 18*a^5*b*c^4)*d^5*e^7 - 9*(2*a^5*b^2*c^3 - 9*a^6*c^4)*d^4*e^8 - 18*(a^6*b^2*c^2 + 9*a^7*c^3)*d^2*e^10 - 12*(a^6*b^3*c - 9*a^7*b*c^2)*d*e^11 - (a^6*b^4 - 18*a^7*b^2*c + 81*a^8*c^2)*e^12)/(a^6*b^6*c^6 - 12*a^7*b^4*c^7 + 48*a^8*b^2*c^8 - 64*a^9*c^9)))/(a^3*b^6*c^3 - 12*a^4*b^4*c^4 + 48*a^5*b^2*c^5 - 64*a^6*c^6))) - 2*(3*a*b*c*d^2*e - 6*a^2*c*d*e^2 + a^2*b*e^3 - (b^2*c - 2*a*c^2)*d^3)*x)/(a^2*b^2*c - 4*a^3*c^2 + (a*b^2*c^2 - 4*a^2*c^3)*x^4 + (a*b^3*c - 4*a^2*b*c^2)*x^2)","B",0
271,1,7338,0,13.151578," ","integrate((e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(b c d^{2} - 4 \, a c d e + a b e^{2}\right)} x^{3} + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} c - 15 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{4} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{3} e - 2 \, {\left(a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{2} - 8 \, {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} + 12 \, a^{4} b c\right)} e^{4} + {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}}} \log\left({\left({\left(5 \, b^{4} c^{3} - 81 \, a b^{2} c^{4} + 324 \, a^{2} c^{5}\right)} d^{8} - 2 \, {\left(3 \, b^{5} c^{2} - 65 \, a b^{3} c^{3} + 324 \, a^{2} b c^{4}\right)} d^{7} e + {\left(b^{6} c - 51 \, a b^{4} c^{2} + 336 \, a^{2} b^{2} c^{3} + 432 \, a^{3} c^{4}\right)} d^{6} e^{2} + 2 \, {\left(3 \, a b^{5} c - 27 \, a^{2} b^{3} c^{2} - 244 \, a^{3} b c^{3}\right)} d^{5} e^{3} + {\left(3 \, a^{2} b^{4} c + 150 \, a^{3} b^{2} c^{2} + 152 \, a^{4} c^{3}\right)} d^{4} e^{4} - 10 \, {\left(a^{3} b^{3} c + 12 \, a^{4} b c^{2}\right)} d^{3} e^{5} - {\left(a^{3} b^{4} - 24 \, a^{4} b^{2} c - 48 \, a^{5} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a^{4} b^{3} + 12 \, a^{5} b c\right)} d e^{7} + {\left(3 \, a^{5} b^{2} + 4 \, a^{6} c\right)} e^{8}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} c - 23 \, a b^{6} c^{2} + 190 \, a^{2} b^{4} c^{3} - 672 \, a^{3} b^{2} c^{4} + 864 \, a^{4} c^{5}\right)} d^{6} + 6 \, {\left(a b^{7} c - 15 \, a^{2} b^{5} c^{2} + 72 \, a^{3} b^{3} c^{3} - 112 \, a^{4} b c^{4}\right)} d^{5} e + 2 \, {\left(2 \, a^{2} b^{6} c - a^{3} b^{4} c^{2} - 88 \, a^{4} b^{2} c^{3} + 240 \, a^{5} c^{4}\right)} d^{4} e^{2} - 12 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} e^{3} - {\left(a^{3} b^{6} - 18 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 160 \, a^{6} c^{3}\right)} d^{2} e^{4} - 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + 2 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} - {\left({\left(a^{3} b^{9} c - 20 \, a^{4} b^{7} c^{2} + 144 \, a^{5} b^{5} c^{3} - 448 \, a^{6} b^{3} c^{4} + 512 \, a^{7} b c^{5}\right)} d^{2} + 2 \, {\left(a^{4} b^{8} c - 8 \, a^{5} b^{6} c^{2} + 128 \, a^{7} b^{2} c^{4} - 256 \, a^{8} c^{5}\right)} d e - 4 \, {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} e^{2}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{-\frac{{\left(b^{5} c - 15 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{4} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{3} e - 2 \, {\left(a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{2} - 8 \, {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} + 12 \, a^{4} b c\right)} e^{4} + {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} c - 15 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{4} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{3} e - 2 \, {\left(a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{2} - 8 \, {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} + 12 \, a^{4} b c\right)} e^{4} + {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}}} \log\left({\left({\left(5 \, b^{4} c^{3} - 81 \, a b^{2} c^{4} + 324 \, a^{2} c^{5}\right)} d^{8} - 2 \, {\left(3 \, b^{5} c^{2} - 65 \, a b^{3} c^{3} + 324 \, a^{2} b c^{4}\right)} d^{7} e + {\left(b^{6} c - 51 \, a b^{4} c^{2} + 336 \, a^{2} b^{2} c^{3} + 432 \, a^{3} c^{4}\right)} d^{6} e^{2} + 2 \, {\left(3 \, a b^{5} c - 27 \, a^{2} b^{3} c^{2} - 244 \, a^{3} b c^{3}\right)} d^{5} e^{3} + {\left(3 \, a^{2} b^{4} c + 150 \, a^{3} b^{2} c^{2} + 152 \, a^{4} c^{3}\right)} d^{4} e^{4} - 10 \, {\left(a^{3} b^{3} c + 12 \, a^{4} b c^{2}\right)} d^{3} e^{5} - {\left(a^{3} b^{4} - 24 \, a^{4} b^{2} c - 48 \, a^{5} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a^{4} b^{3} + 12 \, a^{5} b c\right)} d e^{7} + {\left(3 \, a^{5} b^{2} + 4 \, a^{6} c\right)} e^{8}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} c - 23 \, a b^{6} c^{2} + 190 \, a^{2} b^{4} c^{3} - 672 \, a^{3} b^{2} c^{4} + 864 \, a^{4} c^{5}\right)} d^{6} + 6 \, {\left(a b^{7} c - 15 \, a^{2} b^{5} c^{2} + 72 \, a^{3} b^{3} c^{3} - 112 \, a^{4} b c^{4}\right)} d^{5} e + 2 \, {\left(2 \, a^{2} b^{6} c - a^{3} b^{4} c^{2} - 88 \, a^{4} b^{2} c^{3} + 240 \, a^{5} c^{4}\right)} d^{4} e^{2} - 12 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} e^{3} - {\left(a^{3} b^{6} - 18 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 160 \, a^{6} c^{3}\right)} d^{2} e^{4} - 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + 2 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} - {\left({\left(a^{3} b^{9} c - 20 \, a^{4} b^{7} c^{2} + 144 \, a^{5} b^{5} c^{3} - 448 \, a^{6} b^{3} c^{4} + 512 \, a^{7} b c^{5}\right)} d^{2} + 2 \, {\left(a^{4} b^{8} c - 8 \, a^{5} b^{6} c^{2} + 128 \, a^{7} b^{2} c^{4} - 256 \, a^{8} c^{5}\right)} d e - 4 \, {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} e^{2}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{-\frac{{\left(b^{5} c - 15 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{4} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{3} e - 2 \, {\left(a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{2} - 8 \, {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} + 12 \, a^{4} b c\right)} e^{4} + {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} c - 15 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{4} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{3} e - 2 \, {\left(a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{2} - 8 \, {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} + 12 \, a^{4} b c\right)} e^{4} - {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}}} \log\left({\left({\left(5 \, b^{4} c^{3} - 81 \, a b^{2} c^{4} + 324 \, a^{2} c^{5}\right)} d^{8} - 2 \, {\left(3 \, b^{5} c^{2} - 65 \, a b^{3} c^{3} + 324 \, a^{2} b c^{4}\right)} d^{7} e + {\left(b^{6} c - 51 \, a b^{4} c^{2} + 336 \, a^{2} b^{2} c^{3} + 432 \, a^{3} c^{4}\right)} d^{6} e^{2} + 2 \, {\left(3 \, a b^{5} c - 27 \, a^{2} b^{3} c^{2} - 244 \, a^{3} b c^{3}\right)} d^{5} e^{3} + {\left(3 \, a^{2} b^{4} c + 150 \, a^{3} b^{2} c^{2} + 152 \, a^{4} c^{3}\right)} d^{4} e^{4} - 10 \, {\left(a^{3} b^{3} c + 12 \, a^{4} b c^{2}\right)} d^{3} e^{5} - {\left(a^{3} b^{4} - 24 \, a^{4} b^{2} c - 48 \, a^{5} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a^{4} b^{3} + 12 \, a^{5} b c\right)} d e^{7} + {\left(3 \, a^{5} b^{2} + 4 \, a^{6} c\right)} e^{8}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} c - 23 \, a b^{6} c^{2} + 190 \, a^{2} b^{4} c^{3} - 672 \, a^{3} b^{2} c^{4} + 864 \, a^{4} c^{5}\right)} d^{6} + 6 \, {\left(a b^{7} c - 15 \, a^{2} b^{5} c^{2} + 72 \, a^{3} b^{3} c^{3} - 112 \, a^{4} b c^{4}\right)} d^{5} e + 2 \, {\left(2 \, a^{2} b^{6} c - a^{3} b^{4} c^{2} - 88 \, a^{4} b^{2} c^{3} + 240 \, a^{5} c^{4}\right)} d^{4} e^{2} - 12 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} e^{3} - {\left(a^{3} b^{6} - 18 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 160 \, a^{6} c^{3}\right)} d^{2} e^{4} - 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + 2 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} + {\left({\left(a^{3} b^{9} c - 20 \, a^{4} b^{7} c^{2} + 144 \, a^{5} b^{5} c^{3} - 448 \, a^{6} b^{3} c^{4} + 512 \, a^{7} b c^{5}\right)} d^{2} + 2 \, {\left(a^{4} b^{8} c - 8 \, a^{5} b^{6} c^{2} + 128 \, a^{7} b^{2} c^{4} - 256 \, a^{8} c^{5}\right)} d e - 4 \, {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} e^{2}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{-\frac{{\left(b^{5} c - 15 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{4} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{3} e - 2 \, {\left(a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{2} - 8 \, {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} + 12 \, a^{4} b c\right)} e^{4} - {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} c - 15 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{4} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{3} e - 2 \, {\left(a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{2} - 8 \, {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} + 12 \, a^{4} b c\right)} e^{4} - {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}}} \log\left({\left({\left(5 \, b^{4} c^{3} - 81 \, a b^{2} c^{4} + 324 \, a^{2} c^{5}\right)} d^{8} - 2 \, {\left(3 \, b^{5} c^{2} - 65 \, a b^{3} c^{3} + 324 \, a^{2} b c^{4}\right)} d^{7} e + {\left(b^{6} c - 51 \, a b^{4} c^{2} + 336 \, a^{2} b^{2} c^{3} + 432 \, a^{3} c^{4}\right)} d^{6} e^{2} + 2 \, {\left(3 \, a b^{5} c - 27 \, a^{2} b^{3} c^{2} - 244 \, a^{3} b c^{3}\right)} d^{5} e^{3} + {\left(3 \, a^{2} b^{4} c + 150 \, a^{3} b^{2} c^{2} + 152 \, a^{4} c^{3}\right)} d^{4} e^{4} - 10 \, {\left(a^{3} b^{3} c + 12 \, a^{4} b c^{2}\right)} d^{3} e^{5} - {\left(a^{3} b^{4} - 24 \, a^{4} b^{2} c - 48 \, a^{5} c^{2}\right)} d^{2} e^{6} - 2 \, {\left(a^{4} b^{3} + 12 \, a^{5} b c\right)} d e^{7} + {\left(3 \, a^{5} b^{2} + 4 \, a^{6} c\right)} e^{8}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} c - 23 \, a b^{6} c^{2} + 190 \, a^{2} b^{4} c^{3} - 672 \, a^{3} b^{2} c^{4} + 864 \, a^{4} c^{5}\right)} d^{6} + 6 \, {\left(a b^{7} c - 15 \, a^{2} b^{5} c^{2} + 72 \, a^{3} b^{3} c^{3} - 112 \, a^{4} b c^{4}\right)} d^{5} e + 2 \, {\left(2 \, a^{2} b^{6} c - a^{3} b^{4} c^{2} - 88 \, a^{4} b^{2} c^{3} + 240 \, a^{5} c^{4}\right)} d^{4} e^{2} - 12 \, {\left(a^{3} b^{5} c - 8 \, a^{4} b^{3} c^{2} + 16 \, a^{5} b c^{3}\right)} d^{3} e^{3} - {\left(a^{3} b^{6} - 18 \, a^{4} b^{4} c + 96 \, a^{5} b^{2} c^{2} - 160 \, a^{6} c^{3}\right)} d^{2} e^{4} - 2 \, {\left(a^{4} b^{5} - 8 \, a^{5} b^{3} c + 16 \, a^{6} b c^{2}\right)} d e^{5} + 2 \, {\left(a^{5} b^{4} - 8 \, a^{6} b^{2} c + 16 \, a^{7} c^{2}\right)} e^{6} + {\left({\left(a^{3} b^{9} c - 20 \, a^{4} b^{7} c^{2} + 144 \, a^{5} b^{5} c^{3} - 448 \, a^{6} b^{3} c^{4} + 512 \, a^{7} b c^{5}\right)} d^{2} + 2 \, {\left(a^{4} b^{8} c - 8 \, a^{5} b^{6} c^{2} + 128 \, a^{7} b^{2} c^{4} - 256 \, a^{8} c^{5}\right)} d e - 4 \, {\left(a^{5} b^{7} c - 12 \, a^{6} b^{5} c^{2} + 48 \, a^{7} b^{3} c^{3} - 64 \, a^{8} b c^{4}\right)} e^{2}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}\right)} \sqrt{-\frac{{\left(b^{5} c - 15 \, a b^{3} c^{2} + 60 \, a^{2} b c^{3}\right)} d^{4} + 4 \, {\left(a b^{4} c - 6 \, a^{2} b^{2} c^{2} - 24 \, a^{3} c^{3}\right)} d^{3} e - 2 \, {\left(a^{2} b^{3} c - 52 \, a^{3} b c^{2}\right)} d^{2} e^{2} - 8 \, {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} d e^{3} + {\left(a^{3} b^{3} + 12 \, a^{4} b c\right)} e^{4} - {\left(a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}\right)} \sqrt{-\frac{16 \, a^{3} b c^{2} d^{5} e^{3} + 8 \, a^{4} b c d^{3} e^{5} - 4 \, a^{5} c d^{2} e^{6} - a^{6} e^{8} - {\left(b^{4} c^{2} - 18 \, a b^{2} c^{3} + 81 \, a^{2} c^{4}\right)} d^{8} - 8 \, {\left(a b^{3} c^{2} - 9 \, a^{2} b c^{3}\right)} d^{7} e - 12 \, {\left(a^{2} b^{2} c^{2} + 3 \, a^{3} c^{3}\right)} d^{6} e^{2} + 2 \, {\left(a^{3} b^{2} c - 11 \, a^{4} c^{2}\right)} d^{4} e^{4}}{a^{6} b^{6} c^{2} - 12 \, a^{7} b^{4} c^{3} + 48 \, a^{8} b^{2} c^{4} - 64 \, a^{9} c^{5}}}}{a^{3} b^{6} c - 12 \, a^{4} b^{4} c^{2} + 48 \, a^{5} b^{2} c^{3} - 64 \, a^{6} c^{4}}}\right) - 2 \, {\left(2 \, a b d e - 2 \, a^{2} e^{2} - {\left(b^{2} - 2 \, a c\right)} d^{2}\right)} x}{4 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}}"," ",0,"1/4*(2*(b*c*d^2 - 4*a*c*d*e + a*b*e^2)*x^3 + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-((b^5*c - 15*a*b^3*c^2 + 60*a^2*b*c^3)*d^4 + 4*(a*b^4*c - 6*a^2*b^2*c^2 - 24*a^3*c^3)*d^3*e - 2*(a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^2 - 8*(3*a^3*b^2*c + 4*a^4*c^2)*d*e^3 + (a^3*b^3 + 12*a^4*b*c)*e^4 + (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4))*log(((5*b^4*c^3 - 81*a*b^2*c^4 + 324*a^2*c^5)*d^8 - 2*(3*b^5*c^2 - 65*a*b^3*c^3 + 324*a^2*b*c^4)*d^7*e + (b^6*c - 51*a*b^4*c^2 + 336*a^2*b^2*c^3 + 432*a^3*c^4)*d^6*e^2 + 2*(3*a*b^5*c - 27*a^2*b^3*c^2 - 244*a^3*b*c^3)*d^5*e^3 + (3*a^2*b^4*c + 150*a^3*b^2*c^2 + 152*a^4*c^3)*d^4*e^4 - 10*(a^3*b^3*c + 12*a^4*b*c^2)*d^3*e^5 - (a^3*b^4 - 24*a^4*b^2*c - 48*a^5*c^2)*d^2*e^6 - 2*(a^4*b^3 + 12*a^5*b*c)*d*e^7 + (3*a^5*b^2 + 4*a^6*c)*e^8)*x + 1/2*sqrt(1/2)*((b^8*c - 23*a*b^6*c^2 + 190*a^2*b^4*c^3 - 672*a^3*b^2*c^4 + 864*a^4*c^5)*d^6 + 6*(a*b^7*c - 15*a^2*b^5*c^2 + 72*a^3*b^3*c^3 - 112*a^4*b*c^4)*d^5*e + 2*(2*a^2*b^6*c - a^3*b^4*c^2 - 88*a^4*b^2*c^3 + 240*a^5*c^4)*d^4*e^2 - 12*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3*e^3 - (a^3*b^6 - 18*a^4*b^4*c + 96*a^5*b^2*c^2 - 160*a^6*c^3)*d^2*e^4 - 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + 2*(a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 - ((a^3*b^9*c - 20*a^4*b^7*c^2 + 144*a^5*b^5*c^3 - 448*a^6*b^3*c^4 + 512*a^7*b*c^5)*d^2 + 2*(a^4*b^8*c - 8*a^5*b^6*c^2 + 128*a^7*b^2*c^4 - 256*a^8*c^5)*d*e - 4*(a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*e^2)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(-((b^5*c - 15*a*b^3*c^2 + 60*a^2*b*c^3)*d^4 + 4*(a*b^4*c - 6*a^2*b^2*c^2 - 24*a^3*c^3)*d^3*e - 2*(a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^2 - 8*(3*a^3*b^2*c + 4*a^4*c^2)*d*e^3 + (a^3*b^3 + 12*a^4*b*c)*e^4 + (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-((b^5*c - 15*a*b^3*c^2 + 60*a^2*b*c^3)*d^4 + 4*(a*b^4*c - 6*a^2*b^2*c^2 - 24*a^3*c^3)*d^3*e - 2*(a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^2 - 8*(3*a^3*b^2*c + 4*a^4*c^2)*d*e^3 + (a^3*b^3 + 12*a^4*b*c)*e^4 + (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4))*log(((5*b^4*c^3 - 81*a*b^2*c^4 + 324*a^2*c^5)*d^8 - 2*(3*b^5*c^2 - 65*a*b^3*c^3 + 324*a^2*b*c^4)*d^7*e + (b^6*c - 51*a*b^4*c^2 + 336*a^2*b^2*c^3 + 432*a^3*c^4)*d^6*e^2 + 2*(3*a*b^5*c - 27*a^2*b^3*c^2 - 244*a^3*b*c^3)*d^5*e^3 + (3*a^2*b^4*c + 150*a^3*b^2*c^2 + 152*a^4*c^3)*d^4*e^4 - 10*(a^3*b^3*c + 12*a^4*b*c^2)*d^3*e^5 - (a^3*b^4 - 24*a^4*b^2*c - 48*a^5*c^2)*d^2*e^6 - 2*(a^4*b^3 + 12*a^5*b*c)*d*e^7 + (3*a^5*b^2 + 4*a^6*c)*e^8)*x - 1/2*sqrt(1/2)*((b^8*c - 23*a*b^6*c^2 + 190*a^2*b^4*c^3 - 672*a^3*b^2*c^4 + 864*a^4*c^5)*d^6 + 6*(a*b^7*c - 15*a^2*b^5*c^2 + 72*a^3*b^3*c^3 - 112*a^4*b*c^4)*d^5*e + 2*(2*a^2*b^6*c - a^3*b^4*c^2 - 88*a^4*b^2*c^3 + 240*a^5*c^4)*d^4*e^2 - 12*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3*e^3 - (a^3*b^6 - 18*a^4*b^4*c + 96*a^5*b^2*c^2 - 160*a^6*c^3)*d^2*e^4 - 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + 2*(a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 - ((a^3*b^9*c - 20*a^4*b^7*c^2 + 144*a^5*b^5*c^3 - 448*a^6*b^3*c^4 + 512*a^7*b*c^5)*d^2 + 2*(a^4*b^8*c - 8*a^5*b^6*c^2 + 128*a^7*b^2*c^4 - 256*a^8*c^5)*d*e - 4*(a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*e^2)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(-((b^5*c - 15*a*b^3*c^2 + 60*a^2*b*c^3)*d^4 + 4*(a*b^4*c - 6*a^2*b^2*c^2 - 24*a^3*c^3)*d^3*e - 2*(a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^2 - 8*(3*a^3*b^2*c + 4*a^4*c^2)*d*e^3 + (a^3*b^3 + 12*a^4*b*c)*e^4 + (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-((b^5*c - 15*a*b^3*c^2 + 60*a^2*b*c^3)*d^4 + 4*(a*b^4*c - 6*a^2*b^2*c^2 - 24*a^3*c^3)*d^3*e - 2*(a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^2 - 8*(3*a^3*b^2*c + 4*a^4*c^2)*d*e^3 + (a^3*b^3 + 12*a^4*b*c)*e^4 - (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4))*log(((5*b^4*c^3 - 81*a*b^2*c^4 + 324*a^2*c^5)*d^8 - 2*(3*b^5*c^2 - 65*a*b^3*c^3 + 324*a^2*b*c^4)*d^7*e + (b^6*c - 51*a*b^4*c^2 + 336*a^2*b^2*c^3 + 432*a^3*c^4)*d^6*e^2 + 2*(3*a*b^5*c - 27*a^2*b^3*c^2 - 244*a^3*b*c^3)*d^5*e^3 + (3*a^2*b^4*c + 150*a^3*b^2*c^2 + 152*a^4*c^3)*d^4*e^4 - 10*(a^3*b^3*c + 12*a^4*b*c^2)*d^3*e^5 - (a^3*b^4 - 24*a^4*b^2*c - 48*a^5*c^2)*d^2*e^6 - 2*(a^4*b^3 + 12*a^5*b*c)*d*e^7 + (3*a^5*b^2 + 4*a^6*c)*e^8)*x + 1/2*sqrt(1/2)*((b^8*c - 23*a*b^6*c^2 + 190*a^2*b^4*c^3 - 672*a^3*b^2*c^4 + 864*a^4*c^5)*d^6 + 6*(a*b^7*c - 15*a^2*b^5*c^2 + 72*a^3*b^3*c^3 - 112*a^4*b*c^4)*d^5*e + 2*(2*a^2*b^6*c - a^3*b^4*c^2 - 88*a^4*b^2*c^3 + 240*a^5*c^4)*d^4*e^2 - 12*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3*e^3 - (a^3*b^6 - 18*a^4*b^4*c + 96*a^5*b^2*c^2 - 160*a^6*c^3)*d^2*e^4 - 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + 2*(a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 + ((a^3*b^9*c - 20*a^4*b^7*c^2 + 144*a^5*b^5*c^3 - 448*a^6*b^3*c^4 + 512*a^7*b*c^5)*d^2 + 2*(a^4*b^8*c - 8*a^5*b^6*c^2 + 128*a^7*b^2*c^4 - 256*a^8*c^5)*d*e - 4*(a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*e^2)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(-((b^5*c - 15*a*b^3*c^2 + 60*a^2*b*c^3)*d^4 + 4*(a*b^4*c - 6*a^2*b^2*c^2 - 24*a^3*c^3)*d^3*e - 2*(a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^2 - 8*(3*a^3*b^2*c + 4*a^4*c^2)*d*e^3 + (a^3*b^3 + 12*a^4*b*c)*e^4 - (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-((b^5*c - 15*a*b^3*c^2 + 60*a^2*b*c^3)*d^4 + 4*(a*b^4*c - 6*a^2*b^2*c^2 - 24*a^3*c^3)*d^3*e - 2*(a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^2 - 8*(3*a^3*b^2*c + 4*a^4*c^2)*d*e^3 + (a^3*b^3 + 12*a^4*b*c)*e^4 - (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4))*log(((5*b^4*c^3 - 81*a*b^2*c^4 + 324*a^2*c^5)*d^8 - 2*(3*b^5*c^2 - 65*a*b^3*c^3 + 324*a^2*b*c^4)*d^7*e + (b^6*c - 51*a*b^4*c^2 + 336*a^2*b^2*c^3 + 432*a^3*c^4)*d^6*e^2 + 2*(3*a*b^5*c - 27*a^2*b^3*c^2 - 244*a^3*b*c^3)*d^5*e^3 + (3*a^2*b^4*c + 150*a^3*b^2*c^2 + 152*a^4*c^3)*d^4*e^4 - 10*(a^3*b^3*c + 12*a^4*b*c^2)*d^3*e^5 - (a^3*b^4 - 24*a^4*b^2*c - 48*a^5*c^2)*d^2*e^6 - 2*(a^4*b^3 + 12*a^5*b*c)*d*e^7 + (3*a^5*b^2 + 4*a^6*c)*e^8)*x - 1/2*sqrt(1/2)*((b^8*c - 23*a*b^6*c^2 + 190*a^2*b^4*c^3 - 672*a^3*b^2*c^4 + 864*a^4*c^5)*d^6 + 6*(a*b^7*c - 15*a^2*b^5*c^2 + 72*a^3*b^3*c^3 - 112*a^4*b*c^4)*d^5*e + 2*(2*a^2*b^6*c - a^3*b^4*c^2 - 88*a^4*b^2*c^3 + 240*a^5*c^4)*d^4*e^2 - 12*(a^3*b^5*c - 8*a^4*b^3*c^2 + 16*a^5*b*c^3)*d^3*e^3 - (a^3*b^6 - 18*a^4*b^4*c + 96*a^5*b^2*c^2 - 160*a^6*c^3)*d^2*e^4 - 2*(a^4*b^5 - 8*a^5*b^3*c + 16*a^6*b*c^2)*d*e^5 + 2*(a^5*b^4 - 8*a^6*b^2*c + 16*a^7*c^2)*e^6 + ((a^3*b^9*c - 20*a^4*b^7*c^2 + 144*a^5*b^5*c^3 - 448*a^6*b^3*c^4 + 512*a^7*b*c^5)*d^2 + 2*(a^4*b^8*c - 8*a^5*b^6*c^2 + 128*a^7*b^2*c^4 - 256*a^8*c^5)*d*e - 4*(a^5*b^7*c - 12*a^6*b^5*c^2 + 48*a^7*b^3*c^3 - 64*a^8*b*c^4)*e^2)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))*sqrt(-((b^5*c - 15*a*b^3*c^2 + 60*a^2*b*c^3)*d^4 + 4*(a*b^4*c - 6*a^2*b^2*c^2 - 24*a^3*c^3)*d^3*e - 2*(a^2*b^3*c - 52*a^3*b*c^2)*d^2*e^2 - 8*(3*a^3*b^2*c + 4*a^4*c^2)*d*e^3 + (a^3*b^3 + 12*a^4*b*c)*e^4 - (a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4)*sqrt(-(16*a^3*b*c^2*d^5*e^3 + 8*a^4*b*c*d^3*e^5 - 4*a^5*c*d^2*e^6 - a^6*e^8 - (b^4*c^2 - 18*a*b^2*c^3 + 81*a^2*c^4)*d^8 - 8*(a*b^3*c^2 - 9*a^2*b*c^3)*d^7*e - 12*(a^2*b^2*c^2 + 3*a^3*c^3)*d^6*e^2 + 2*(a^3*b^2*c - 11*a^4*c^2)*d^4*e^4)/(a^6*b^6*c^2 - 12*a^7*b^4*c^3 + 48*a^8*b^2*c^4 - 64*a^9*c^5)))/(a^3*b^6*c - 12*a^4*b^4*c^2 + 48*a^5*b^2*c^3 - 64*a^6*c^4))) - 2*(2*a*b*d*e - 2*a^2*e^2 - (b^2 - 2*a*c)*d^2)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)","B",0
272,1,4573,0,3.548615," ","integrate((e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(b c d - 2 \, a c e\right)} x^{3} - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} + 12 \, a^{3} b c\right)} e^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left(-{\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} d^{4} - {\left(3 \, b^{5} c - 65 \, a b^{3} c^{2} + 324 \, a^{2} b c^{3}\right)} d^{3} e - 3 \, {\left(3 \, a b^{4} c - 28 \, a^{2} b^{2} c^{2}\right)} d^{2} e^{2} - {\left(9 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} d e^{3} - {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{4}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a b^{7} - 15 \, a^{2} b^{5} c + 72 \, a^{3} b^{3} c^{2} - 112 \, a^{4} b c^{3}\right)} d^{2} e + 3 \, {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 32 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} d e^{2} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} e^{3} - {\left({\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} d + {\left(a^{4} b^{8} - 8 \, a^{5} b^{6} c + 128 \, a^{7} b^{2} c^{3} - 256 \, a^{8} c^{4}\right)} e\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{{\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} + 12 \, a^{3} b c\right)} e^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} + 12 \, a^{3} b c\right)} e^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left(-{\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} d^{4} - {\left(3 \, b^{5} c - 65 \, a b^{3} c^{2} + 324 \, a^{2} b c^{3}\right)} d^{3} e - 3 \, {\left(3 \, a b^{4} c - 28 \, a^{2} b^{2} c^{2}\right)} d^{2} e^{2} - {\left(9 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} d e^{3} - {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{4}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a b^{7} - 15 \, a^{2} b^{5} c + 72 \, a^{3} b^{3} c^{2} - 112 \, a^{4} b c^{3}\right)} d^{2} e + 3 \, {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 32 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} d e^{2} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} e^{3} - {\left({\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} d + {\left(a^{4} b^{8} - 8 \, a^{5} b^{6} c + 128 \, a^{7} b^{2} c^{3} - 256 \, a^{8} c^{4}\right)} e\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{{\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} + 12 \, a^{3} b c\right)} e^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} + 12 \, a^{3} b c\right)} e^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left(-{\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} d^{4} - {\left(3 \, b^{5} c - 65 \, a b^{3} c^{2} + 324 \, a^{2} b c^{3}\right)} d^{3} e - 3 \, {\left(3 \, a b^{4} c - 28 \, a^{2} b^{2} c^{2}\right)} d^{2} e^{2} - {\left(9 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} d e^{3} - {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{4}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a b^{7} - 15 \, a^{2} b^{5} c + 72 \, a^{3} b^{3} c^{2} - 112 \, a^{4} b c^{3}\right)} d^{2} e + 3 \, {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 32 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} d e^{2} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} e^{3} + {\left({\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} d + {\left(a^{4} b^{8} - 8 \, a^{5} b^{6} c + 128 \, a^{7} b^{2} c^{3} - 256 \, a^{8} c^{4}\right)} e\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{{\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} + 12 \, a^{3} b c\right)} e^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{{\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} + 12 \, a^{3} b c\right)} e^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left(-{\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} d^{4} - {\left(3 \, b^{5} c - 65 \, a b^{3} c^{2} + 324 \, a^{2} b c^{3}\right)} d^{3} e - 3 \, {\left(3 \, a b^{4} c - 28 \, a^{2} b^{2} c^{2}\right)} d^{2} e^{2} - {\left(9 \, a^{2} b^{3} c - 20 \, a^{3} b c^{2}\right)} d e^{3} - {\left(3 \, a^{3} b^{2} c + 4 \, a^{4} c^{2}\right)} e^{4}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left({\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4}\right)} d^{3} + 3 \, {\left(a b^{7} - 15 \, a^{2} b^{5} c + 72 \, a^{3} b^{3} c^{2} - 112 \, a^{4} b c^{3}\right)} d^{2} e + 3 \, {\left(a^{2} b^{6} - 10 \, a^{3} b^{4} c + 32 \, a^{4} b^{2} c^{2} - 32 \, a^{5} c^{3}\right)} d e^{2} + {\left(a^{3} b^{5} - 8 \, a^{4} b^{3} c + 16 \, a^{5} b c^{2}\right)} e^{3} + {\left({\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} d + {\left(a^{4} b^{8} - 8 \, a^{5} b^{6} c + 128 \, a^{7} b^{2} c^{3} - 256 \, a^{8} c^{4}\right)} e\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{{\left(b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2}\right)} d^{2} + 2 \, {\left(a b^{4} - 6 \, a^{2} b^{2} c - 24 \, a^{3} c^{2}\right)} d e + {\left(a^{2} b^{3} + 12 \, a^{3} b c\right)} e^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{4 \, a^{3} b d e^{3} + a^{4} e^{4} + {\left(b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}\right)} d^{4} + 4 \, {\left(a b^{3} - 9 \, a^{2} b c\right)} d^{3} e + 6 \, {\left(a^{2} b^{2} - 3 \, a^{3} c\right)} d^{2} e^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) - 2 \, {\left(a b e - {\left(b^{2} - 2 \, a c\right)} d\right)} x}{4 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}}"," ",0,"1/4*(2*(b*c*d - 2*a*c*e)*x^3 - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-((b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*d^2 + 2*(a*b^4 - 6*a^2*b^2*c - 24*a^3*c^2)*d*e + (a^2*b^3 + 12*a^3*b*c)*e^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log(-((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*d^4 - (3*b^5*c - 65*a*b^3*c^2 + 324*a^2*b*c^3)*d^3*e - 3*(3*a*b^4*c - 28*a^2*b^2*c^2)*d^2*e^2 - (9*a^2*b^3*c - 20*a^3*b*c^2)*d*e^3 - (3*a^3*b^2*c + 4*a^4*c^2)*e^4)*x + 1/2*sqrt(1/2)*((b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4)*d^3 + 3*(a*b^7 - 15*a^2*b^5*c + 72*a^3*b^3*c^2 - 112*a^4*b*c^3)*d^2*e + 3*(a^2*b^6 - 10*a^3*b^4*c + 32*a^4*b^2*c^2 - 32*a^5*c^3)*d*e^2 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*e^3 - ((a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*d + (a^4*b^8 - 8*a^5*b^6*c + 128*a^7*b^2*c^3 - 256*a^8*c^4)*e)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-((b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*d^2 + 2*(a*b^4 - 6*a^2*b^2*c - 24*a^3*c^2)*d*e + (a^2*b^3 + 12*a^3*b*c)*e^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-((b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*d^2 + 2*(a*b^4 - 6*a^2*b^2*c - 24*a^3*c^2)*d*e + (a^2*b^3 + 12*a^3*b*c)*e^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log(-((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*d^4 - (3*b^5*c - 65*a*b^3*c^2 + 324*a^2*b*c^3)*d^3*e - 3*(3*a*b^4*c - 28*a^2*b^2*c^2)*d^2*e^2 - (9*a^2*b^3*c - 20*a^3*b*c^2)*d*e^3 - (3*a^3*b^2*c + 4*a^4*c^2)*e^4)*x - 1/2*sqrt(1/2)*((b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4)*d^3 + 3*(a*b^7 - 15*a^2*b^5*c + 72*a^3*b^3*c^2 - 112*a^4*b*c^3)*d^2*e + 3*(a^2*b^6 - 10*a^3*b^4*c + 32*a^4*b^2*c^2 - 32*a^5*c^3)*d*e^2 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*e^3 - ((a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*d + (a^4*b^8 - 8*a^5*b^6*c + 128*a^7*b^2*c^3 - 256*a^8*c^4)*e)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-((b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*d^2 + 2*(a*b^4 - 6*a^2*b^2*c - 24*a^3*c^2)*d*e + (a^2*b^3 + 12*a^3*b*c)*e^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-((b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*d^2 + 2*(a*b^4 - 6*a^2*b^2*c - 24*a^3*c^2)*d*e + (a^2*b^3 + 12*a^3*b*c)*e^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log(-((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*d^4 - (3*b^5*c - 65*a*b^3*c^2 + 324*a^2*b*c^3)*d^3*e - 3*(3*a*b^4*c - 28*a^2*b^2*c^2)*d^2*e^2 - (9*a^2*b^3*c - 20*a^3*b*c^2)*d*e^3 - (3*a^3*b^2*c + 4*a^4*c^2)*e^4)*x + 1/2*sqrt(1/2)*((b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4)*d^3 + 3*(a*b^7 - 15*a^2*b^5*c + 72*a^3*b^3*c^2 - 112*a^4*b*c^3)*d^2*e + 3*(a^2*b^6 - 10*a^3*b^4*c + 32*a^4*b^2*c^2 - 32*a^5*c^3)*d*e^2 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*e^3 + ((a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*d + (a^4*b^8 - 8*a^5*b^6*c + 128*a^7*b^2*c^3 - 256*a^8*c^4)*e)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-((b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*d^2 + 2*(a*b^4 - 6*a^2*b^2*c - 24*a^3*c^2)*d*e + (a^2*b^3 + 12*a^3*b*c)*e^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-((b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*d^2 + 2*(a*b^4 - 6*a^2*b^2*c - 24*a^3*c^2)*d*e + (a^2*b^3 + 12*a^3*b*c)*e^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log(-((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*d^4 - (3*b^5*c - 65*a*b^3*c^2 + 324*a^2*b*c^3)*d^3*e - 3*(3*a*b^4*c - 28*a^2*b^2*c^2)*d^2*e^2 - (9*a^2*b^3*c - 20*a^3*b*c^2)*d*e^3 - (3*a^3*b^2*c + 4*a^4*c^2)*e^4)*x - 1/2*sqrt(1/2)*((b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4)*d^3 + 3*(a*b^7 - 15*a^2*b^5*c + 72*a^3*b^3*c^2 - 112*a^4*b*c^3)*d^2*e + 3*(a^2*b^6 - 10*a^3*b^4*c + 32*a^4*b^2*c^2 - 32*a^5*c^3)*d*e^2 + (a^3*b^5 - 8*a^4*b^3*c + 16*a^5*b*c^2)*e^3 + ((a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*d + (a^4*b^8 - 8*a^5*b^6*c + 128*a^7*b^2*c^3 - 256*a^8*c^4)*e)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-((b^5 - 15*a*b^3*c + 60*a^2*b*c^2)*d^2 + 2*(a*b^4 - 6*a^2*b^2*c - 24*a^3*c^2)*d*e + (a^2*b^3 + 12*a^3*b*c)*e^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((4*a^3*b*d*e^3 + a^4*e^4 + (b^4 - 18*a*b^2*c + 81*a^2*c^2)*d^4 + 4*(a*b^3 - 9*a^2*b*c)*d^3*e + 6*(a^2*b^2 - 3*a^3*c)*d^2*e^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) - 2*(a*b*e - (b^2 - 2*a*c)*d)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)","B",0
273,1,2309,0,0.845014," ","integrate(1/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\frac{2 \, b c x^{3} + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4} - {\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4} - {\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} + {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} x + \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4} + {\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) - \sqrt{\frac{1}{2}} {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}} \log\left({\left(5 \, b^{4} c^{2} - 81 \, a b^{2} c^{3} + 324 \, a^{2} c^{4}\right)} x - \frac{1}{2} \, \sqrt{\frac{1}{2}} {\left(b^{8} - 23 \, a b^{6} c + 190 \, a^{2} b^{4} c^{2} - 672 \, a^{3} b^{2} c^{3} + 864 \, a^{4} c^{4} + {\left(a^{3} b^{9} - 20 \, a^{4} b^{7} c + 144 \, a^{5} b^{5} c^{2} - 448 \, a^{6} b^{3} c^{3} + 512 \, a^{7} b c^{4}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}\right)} \sqrt{-\frac{b^{5} - 15 \, a b^{3} c + 60 \, a^{2} b c^{2} - {\left(a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}\right)} \sqrt{\frac{b^{4} - 18 \, a b^{2} c + 81 \, a^{2} c^{2}}{a^{6} b^{6} - 12 \, a^{7} b^{4} c + 48 \, a^{8} b^{2} c^{2} - 64 \, a^{9} c^{3}}}}{a^{3} b^{6} - 12 \, a^{4} b^{4} c + 48 \, a^{5} b^{2} c^{2} - 64 \, a^{6} c^{3}}}\right) + 2 \, {\left(b^{2} - 2 \, a c\right)} x}{4 \, {\left({\left(a b^{2} c - 4 \, a^{2} c^{2}\right)} x^{4} + a^{2} b^{2} - 4 \, a^{3} c + {\left(a b^{3} - 4 \, a^{2} b c\right)} x^{2}\right)}}"," ",0,"1/4*(2*b*c*x^3 + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*x + 1/2*sqrt(1/2)*(b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4 - (a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*x - 1/2*sqrt(1/2)*(b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4 - (a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 + (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*x + 1/2*sqrt(1/2)*(b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4 + (a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) - sqrt(1/2)*((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))*log((5*b^4*c^2 - 81*a*b^2*c^3 + 324*a^2*c^4)*x - 1/2*sqrt(1/2)*(b^8 - 23*a*b^6*c + 190*a^2*b^4*c^2 - 672*a^3*b^2*c^3 + 864*a^4*c^4 + (a^3*b^9 - 20*a^4*b^7*c + 144*a^5*b^5*c^2 - 448*a^6*b^3*c^3 + 512*a^7*b*c^4)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))*sqrt(-(b^5 - 15*a*b^3*c + 60*a^2*b*c^2 - (a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3)*sqrt((b^4 - 18*a*b^2*c + 81*a^2*c^2)/(a^6*b^6 - 12*a^7*b^4*c + 48*a^8*b^2*c^2 - 64*a^9*c^3)))/(a^3*b^6 - 12*a^4*b^4*c + 48*a^5*b^2*c^2 - 64*a^6*c^3))) + 2*(b^2 - 2*a*c)*x)/((a*b^2*c - 4*a^2*c^2)*x^4 + a^2*b^2 - 4*a^3*c + (a*b^3 - 4*a^2*b*c)*x^2)","B",0
274,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
275,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
276,1,370,0,1.645158," ","integrate((e*x^2+d)^(5/2)*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{15 \, {\left(3 \, c d^{5} - 10 \, b d^{4} e + 80 \, a d^{3} e^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 2 \, {\left(384 \, c e^{5} x^{9} + 48 \, {\left(21 \, c d e^{4} + 10 \, b e^{5}\right)} x^{7} + 8 \, {\left(93 \, c d^{2} e^{3} + 170 \, b d e^{4} + 80 \, a e^{5}\right)} x^{5} + 10 \, {\left(3 \, c d^{3} e^{2} + 118 \, b d^{2} e^{3} + 208 \, a d e^{4}\right)} x^{3} - 15 \, {\left(3 \, c d^{4} e - 10 \, b d^{3} e^{2} - 176 \, a d^{2} e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{7680 \, e^{3}}, -\frac{15 \, {\left(3 \, c d^{5} - 10 \, b d^{4} e + 80 \, a d^{3} e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(384 \, c e^{5} x^{9} + 48 \, {\left(21 \, c d e^{4} + 10 \, b e^{5}\right)} x^{7} + 8 \, {\left(93 \, c d^{2} e^{3} + 170 \, b d e^{4} + 80 \, a e^{5}\right)} x^{5} + 10 \, {\left(3 \, c d^{3} e^{2} + 118 \, b d^{2} e^{3} + 208 \, a d e^{4}\right)} x^{3} - 15 \, {\left(3 \, c d^{4} e - 10 \, b d^{3} e^{2} - 176 \, a d^{2} e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{3840 \, e^{3}}\right]"," ",0,"[1/7680*(15*(3*c*d^5 - 10*b*d^4*e + 80*a*d^3*e^2)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 2*(384*c*e^5*x^9 + 48*(21*c*d*e^4 + 10*b*e^5)*x^7 + 8*(93*c*d^2*e^3 + 170*b*d*e^4 + 80*a*e^5)*x^5 + 10*(3*c*d^3*e^2 + 118*b*d^2*e^3 + 208*a*d*e^4)*x^3 - 15*(3*c*d^4*e - 10*b*d^3*e^2 - 176*a*d^2*e^3)*x)*sqrt(e*x^2 + d))/e^3, -1/3840*(15*(3*c*d^5 - 10*b*d^4*e + 80*a*d^3*e^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (384*c*e^5*x^9 + 48*(21*c*d*e^4 + 10*b*e^5)*x^7 + 8*(93*c*d^2*e^3 + 170*b*d*e^4 + 80*a*e^5)*x^5 + 10*(3*c*d^3*e^2 + 118*b*d^2*e^3 + 208*a*d*e^4)*x^3 - 15*(3*c*d^4*e - 10*b*d^3*e^2 - 176*a*d^2*e^3)*x)*sqrt(e*x^2 + d))/e^3]","A",0
277,1,304,0,0.980948," ","integrate((e*x^2+d)^(3/2)*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(3 \, c d^{4} - 8 \, b d^{3} e + 48 \, a d^{2} e^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 2 \, {\left(48 \, c e^{4} x^{7} + 8 \, {\left(9 \, c d e^{3} + 8 \, b e^{4}\right)} x^{5} + 2 \, {\left(3 \, c d^{2} e^{2} + 56 \, b d e^{3} + 48 \, a e^{4}\right)} x^{3} - 3 \, {\left(3 \, c d^{3} e - 8 \, b d^{2} e^{2} - 80 \, a d e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{768 \, e^{3}}, -\frac{3 \, {\left(3 \, c d^{4} - 8 \, b d^{3} e + 48 \, a d^{2} e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(48 \, c e^{4} x^{7} + 8 \, {\left(9 \, c d e^{3} + 8 \, b e^{4}\right)} x^{5} + 2 \, {\left(3 \, c d^{2} e^{2} + 56 \, b d e^{3} + 48 \, a e^{4}\right)} x^{3} - 3 \, {\left(3 \, c d^{3} e - 8 \, b d^{2} e^{2} - 80 \, a d e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{384 \, e^{3}}\right]"," ",0,"[1/768*(3*(3*c*d^4 - 8*b*d^3*e + 48*a*d^2*e^2)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 2*(48*c*e^4*x^7 + 8*(9*c*d*e^3 + 8*b*e^4)*x^5 + 2*(3*c*d^2*e^2 + 56*b*d*e^3 + 48*a*e^4)*x^3 - 3*(3*c*d^3*e - 8*b*d^2*e^2 - 80*a*d*e^3)*x)*sqrt(e*x^2 + d))/e^3, -1/384*(3*(3*c*d^4 - 8*b*d^3*e + 48*a*d^2*e^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (48*c*e^4*x^7 + 8*(9*c*d*e^3 + 8*b*e^4)*x^5 + 2*(3*c*d^2*e^2 + 56*b*d*e^3 + 48*a*e^4)*x^3 - 3*(3*c*d^3*e - 8*b*d^2*e^2 - 80*a*d*e^3)*x)*sqrt(e*x^2 + d))/e^3]","A",0
278,1,232,0,0.996514," ","integrate((e*x^2+d)^(1/2)*(c*x^4+b*x^2+a),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d^{3} - 2 \, b d^{2} e + 8 \, a d e^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 2 \, {\left(8 \, c e^{3} x^{5} + 2 \, {\left(c d e^{2} + 6 \, b e^{3}\right)} x^{3} - 3 \, {\left(c d^{2} e - 2 \, b d e^{2} - 8 \, a e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{96 \, e^{3}}, -\frac{3 \, {\left(c d^{3} - 2 \, b d^{2} e + 8 \, a d e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(8 \, c e^{3} x^{5} + 2 \, {\left(c d e^{2} + 6 \, b e^{3}\right)} x^{3} - 3 \, {\left(c d^{2} e - 2 \, b d e^{2} - 8 \, a e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{48 \, e^{3}}\right]"," ",0,"[1/96*(3*(c*d^3 - 2*b*d^2*e + 8*a*d*e^2)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 2*(8*c*e^3*x^5 + 2*(c*d*e^2 + 6*b*e^3)*x^3 - 3*(c*d^2*e - 2*b*d*e^2 - 8*a*e^3)*x)*sqrt(e*x^2 + d))/e^3, -1/48*(3*(c*d^3 - 2*b*d^2*e + 8*a*d*e^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (8*c*e^3*x^5 + 2*(c*d*e^2 + 6*b*e^3)*x^3 - 3*(c*d^2*e - 2*b*d*e^2 - 8*a*e^3)*x)*sqrt(e*x^2 + d))/e^3]","A",0
279,1,174,0,1.297373," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, c d^{2} - 4 \, b d e + 8 \, a e^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) + 2 \, {\left(2 \, c e^{2} x^{3} - {\left(3 \, c d e - 4 \, b e^{2}\right)} x\right)} \sqrt{e x^{2} + d}}{16 \, e^{3}}, -\frac{{\left(3 \, c d^{2} - 4 \, b d e + 8 \, a e^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) - {\left(2 \, c e^{2} x^{3} - {\left(3 \, c d e - 4 \, b e^{2}\right)} x\right)} \sqrt{e x^{2} + d}}{8 \, e^{3}}\right]"," ",0,"[1/16*((3*c*d^2 - 4*b*d*e + 8*a*e^2)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) + 2*(2*c*e^2*x^3 - (3*c*d*e - 4*b*e^2)*x)*sqrt(e*x^2 + d))/e^3, -1/8*((3*c*d^2 - 4*b*d*e + 8*a*e^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) - (2*c*e^2*x^3 - (3*c*d*e - 4*b*e^2)*x)*sqrt(e*x^2 + d))/e^3]","A",0
280,1,249,0,0.847264," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(3 \, c d^{3} - 2 \, b d^{2} e + {\left(3 \, c d^{2} e - 2 \, b d e^{2}\right)} x^{2}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) - 2 \, {\left(c d e^{2} x^{3} + {\left(3 \, c d^{2} e - 2 \, b d e^{2} + 2 \, a e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{4 \, {\left(d e^{4} x^{2} + d^{2} e^{3}\right)}}, \frac{{\left(3 \, c d^{3} - 2 \, b d^{2} e + {\left(3 \, c d^{2} e - 2 \, b d e^{2}\right)} x^{2}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left(c d e^{2} x^{3} + {\left(3 \, c d^{2} e - 2 \, b d e^{2} + 2 \, a e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{2 \, {\left(d e^{4} x^{2} + d^{2} e^{3}\right)}}\right]"," ",0,"[-1/4*((3*c*d^3 - 2*b*d^2*e + (3*c*d^2*e - 2*b*d*e^2)*x^2)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) - 2*(c*d*e^2*x^3 + (3*c*d^2*e - 2*b*d*e^2 + 2*a*e^3)*x)*sqrt(e*x^2 + d))/(d*e^4*x^2 + d^2*e^3), 1/2*((3*c*d^3 - 2*b*d^2*e + (3*c*d^2*e - 2*b*d*e^2)*x^2)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + (c*d*e^2*x^3 + (3*c*d^2*e - 2*b*d*e^2 + 2*a*e^3)*x)*sqrt(e*x^2 + d))/(d*e^4*x^2 + d^2*e^3)]","A",0
281,1,289,0,0.851288," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(c d^{2} e^{2} x^{4} + 2 \, c d^{3} e x^{2} + c d^{4}\right)} \sqrt{e} \log\left(-2 \, e x^{2} - 2 \, \sqrt{e x^{2} + d} \sqrt{e} x - d\right) - 2 \, {\left({\left(4 \, c d^{2} e^{2} - b d e^{3} - 2 \, a e^{4}\right)} x^{3} + 3 \, {\left(c d^{3} e - a d e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{6 \, {\left(d^{2} e^{5} x^{4} + 2 \, d^{3} e^{4} x^{2} + d^{4} e^{3}\right)}}, -\frac{3 \, {\left(c d^{2} e^{2} x^{4} + 2 \, c d^{3} e x^{2} + c d^{4}\right)} \sqrt{-e} \arctan\left(\frac{\sqrt{-e} x}{\sqrt{e x^{2} + d}}\right) + {\left({\left(4 \, c d^{2} e^{2} - b d e^{3} - 2 \, a e^{4}\right)} x^{3} + 3 \, {\left(c d^{3} e - a d e^{3}\right)} x\right)} \sqrt{e x^{2} + d}}{3 \, {\left(d^{2} e^{5} x^{4} + 2 \, d^{3} e^{4} x^{2} + d^{4} e^{3}\right)}}\right]"," ",0,"[1/6*(3*(c*d^2*e^2*x^4 + 2*c*d^3*e*x^2 + c*d^4)*sqrt(e)*log(-2*e*x^2 - 2*sqrt(e*x^2 + d)*sqrt(e)*x - d) - 2*((4*c*d^2*e^2 - b*d*e^3 - 2*a*e^4)*x^3 + 3*(c*d^3*e - a*d*e^3)*x)*sqrt(e*x^2 + d))/(d^2*e^5*x^4 + 2*d^3*e^4*x^2 + d^4*e^3), -1/3*(3*(c*d^2*e^2*x^4 + 2*c*d^3*e*x^2 + c*d^4)*sqrt(-e)*arctan(sqrt(-e)*x/sqrt(e*x^2 + d)) + ((4*c*d^2*e^2 - b*d*e^3 - 2*a*e^4)*x^3 + 3*(c*d^3*e - a*d*e^3)*x)*sqrt(e*x^2 + d))/(d^2*e^5*x^4 + 2*d^3*e^4*x^2 + d^4*e^3)]","A",0
282,1,93,0,1.066158," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(7/2),x, algorithm=""fricas"")","\frac{{\left({\left(3 \, c d^{2} + 2 \, b d e + 8 \, a e^{2}\right)} x^{5} + 15 \, a d^{2} x + 5 \, {\left(b d^{2} + 4 \, a d e\right)} x^{3}\right)} \sqrt{e x^{2} + d}}{15 \, {\left(d^{3} e^{3} x^{6} + 3 \, d^{4} e^{2} x^{4} + 3 \, d^{5} e x^{2} + d^{6}\right)}}"," ",0,"1/15*((3*c*d^2 + 2*b*d*e + 8*a*e^2)*x^5 + 15*a*d^2*x + 5*(b*d^2 + 4*a*d*e)*x^3)*sqrt(e*x^2 + d)/(d^3*e^3*x^6 + 3*d^4*e^2*x^4 + 3*d^5*e*x^2 + d^6)","A",0
283,1,136,0,0.952380," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(9/2),x, algorithm=""fricas"")","\frac{{\left(2 \, {\left(3 \, c d^{2} e + 4 \, b d e^{2} + 24 \, a e^{3}\right)} x^{7} + 7 \, {\left(3 \, c d^{3} + 4 \, b d^{2} e + 24 \, a d e^{2}\right)} x^{5} + 105 \, a d^{3} x + 35 \, {\left(b d^{3} + 6 \, a d^{2} e\right)} x^{3}\right)} \sqrt{e x^{2} + d}}{105 \, {\left(d^{4} e^{4} x^{8} + 4 \, d^{5} e^{3} x^{6} + 6 \, d^{6} e^{2} x^{4} + 4 \, d^{7} e x^{2} + d^{8}\right)}}"," ",0,"1/105*(2*(3*c*d^2*e + 4*b*d*e^2 + 24*a*e^3)*x^7 + 7*(3*c*d^3 + 4*b*d^2*e + 24*a*d*e^2)*x^5 + 105*a*d^3*x + 35*(b*d^3 + 6*a*d^2*e)*x^3)*sqrt(e*x^2 + d)/(d^4*e^4*x^8 + 4*d^5*e^3*x^6 + 6*d^6*e^2*x^4 + 4*d^7*e*x^2 + d^8)","A",0
284,1,177,0,1.148320," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(11/2),x, algorithm=""fricas"")","\frac{{\left(8 \, {\left(c d^{2} e^{2} + 2 \, b d e^{3} + 16 \, a e^{4}\right)} x^{9} + 36 \, {\left(c d^{3} e + 2 \, b d^{2} e^{2} + 16 \, a d e^{3}\right)} x^{7} + 315 \, a d^{4} x + 63 \, {\left(c d^{4} + 2 \, b d^{3} e + 16 \, a d^{2} e^{2}\right)} x^{5} + 105 \, {\left(b d^{4} + 8 \, a d^{3} e\right)} x^{3}\right)} \sqrt{e x^{2} + d}}{315 \, {\left(d^{5} e^{5} x^{10} + 5 \, d^{6} e^{4} x^{8} + 10 \, d^{7} e^{3} x^{6} + 10 \, d^{8} e^{2} x^{4} + 5 \, d^{9} e x^{2} + d^{10}\right)}}"," ",0,"1/315*(8*(c*d^2*e^2 + 2*b*d*e^3 + 16*a*e^4)*x^9 + 36*(c*d^3*e + 2*b*d^2*e^2 + 16*a*d*e^3)*x^7 + 315*a*d^4*x + 63*(c*d^4 + 2*b*d^3*e + 16*a*d^2*e^2)*x^5 + 105*(b*d^4 + 8*a*d^3*e)*x^3)*sqrt(e*x^2 + d)/(d^5*e^5*x^10 + 5*d^6*e^4*x^8 + 10*d^7*e^3*x^6 + 10*d^8*e^2*x^4 + 5*d^9*e*x^2 + d^10)","A",0
285,1,224,0,1.310247," ","integrate((c*x^4+b*x^2+a)/(e*x^2+d)^(13/2),x, algorithm=""fricas"")","\frac{{\left(16 \, {\left(3 \, c d^{2} e^{3} + 8 \, b d e^{4} + 80 \, a e^{5}\right)} x^{11} + 88 \, {\left(3 \, c d^{3} e^{2} + 8 \, b d^{2} e^{3} + 80 \, a d e^{4}\right)} x^{9} + 198 \, {\left(3 \, c d^{4} e + 8 \, b d^{3} e^{2} + 80 \, a d^{2} e^{3}\right)} x^{7} + 3465 \, a d^{5} x + 231 \, {\left(3 \, c d^{5} + 8 \, b d^{4} e + 80 \, a d^{3} e^{2}\right)} x^{5} + 1155 \, {\left(b d^{5} + 10 \, a d^{4} e\right)} x^{3}\right)} \sqrt{e x^{2} + d}}{3465 \, {\left(d^{6} e^{6} x^{12} + 6 \, d^{7} e^{5} x^{10} + 15 \, d^{8} e^{4} x^{8} + 20 \, d^{9} e^{3} x^{6} + 15 \, d^{10} e^{2} x^{4} + 6 \, d^{11} e x^{2} + d^{12}\right)}}"," ",0,"1/3465*(16*(3*c*d^2*e^3 + 8*b*d*e^4 + 80*a*e^5)*x^11 + 88*(3*c*d^3*e^2 + 8*b*d^2*e^3 + 80*a*d*e^4)*x^9 + 198*(3*c*d^4*e + 8*b*d^3*e^2 + 80*a*d^2*e^3)*x^7 + 3465*a*d^5*x + 231*(3*c*d^5 + 8*b*d^4*e + 80*a*d^3*e^2)*x^5 + 1155*(b*d^5 + 10*a*d^4*e)*x^3)*sqrt(e*x^2 + d)/(d^6*e^6*x^12 + 6*d^7*e^5*x^10 + 15*d^8*e^4*x^8 + 20*d^9*e^3*x^6 + 15*d^10*e^2*x^4 + 6*d^11*e*x^2 + d^12)","A",0
286,0,0,0,0.956243," ","integrate((5*x^2+7)^3*(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral((125*x^6 + 525*x^4 + 735*x^2 + 343)*sqrt(x^4 + 3*x^2 + 2), x)","F",0
287,0,0,0,0.609376," ","integrate((5*x^2+7)^2*(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(25 \, x^{4} + 70 \, x^{2} + 49\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral((25*x^4 + 70*x^2 + 49)*sqrt(x^4 + 3*x^2 + 2), x)","F",0
288,0,0,0,1.213635," ","integrate((5*x^2+7)*(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{4} + 3 \, x^{2} + 2} {\left(5 \, x^{2} + 7\right)}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)*(5*x^2 + 7), x)","F",0
289,0,0,0,1.165303," ","integrate((x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2), x)","F",0
290,0,0,0,0.992121," ","integrate((x^4+3*x^2+2)^(1/2)/(5*x^2+7),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{5 \, x^{2} + 7}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(5*x^2 + 7), x)","F",0
291,0,0,0,1.361872," ","integrate((x^4+3*x^2+2)^(1/2)/(5*x^2+7)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{25 \, x^{4} + 70 \, x^{2} + 49}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(25*x^4 + 70*x^2 + 49), x)","F",0
292,0,0,0,1.042498," ","integrate((x^4+3*x^2+2)^(1/2)/(5*x^2+7)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(125*x^6 + 525*x^4 + 735*x^2 + 343), x)","F",0
293,0,0,0,0.672272," ","integrate((5*x^2+7)^3*(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(125 \, x^{10} + 900 \, x^{8} + 2560 \, x^{6} + 3598 \, x^{4} + 2499 \, x^{2} + 686\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral((125*x^10 + 900*x^8 + 2560*x^6 + 3598*x^4 + 2499*x^2 + 686)*sqrt(x^4 + 3*x^2 + 2), x)","F",0
294,0,0,0,1.013669," ","integrate((5*x^2+7)^2*(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(25 \, x^{8} + 145 \, x^{6} + 309 \, x^{4} + 287 \, x^{2} + 98\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral((25*x^8 + 145*x^6 + 309*x^4 + 287*x^2 + 98)*sqrt(x^4 + 3*x^2 + 2), x)","F",0
295,0,0,0,0.602387," ","integrate((5*x^2+7)*(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(5 \, x^{6} + 22 \, x^{4} + 31 \, x^{2} + 14\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}, x\right)"," ",0,"integral((5*x^6 + 22*x^4 + 31*x^2 + 14)*sqrt(x^4 + 3*x^2 + 2), x)","F",0
296,0,0,0,0.654831," ","integrate((x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((x^4 + 3*x^2 + 2)^(3/2), x)","F",0
297,0,0,0,1.138233," ","integrate((x^4+3*x^2+2)^(3/2)/(5*x^2+7),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}{5 \, x^{2} + 7}, x\right)"," ",0,"integral((x^4 + 3*x^2 + 2)^(3/2)/(5*x^2 + 7), x)","F",0
298,0,0,0,1.008687," ","integrate((x^4+3*x^2+2)^(3/2)/(5*x^2+7)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}{25 \, x^{4} + 70 \, x^{2} + 49}, x\right)"," ",0,"integral((x^4 + 3*x^2 + 2)^(3/2)/(25*x^4 + 70*x^2 + 49), x)","F",0
299,0,0,0,1.115958," ","integrate((x^4+3*x^2+2)^(3/2)/(5*x^2+7)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{4} + 3 \, x^{2} + 2\right)}^{\frac{3}{2}}}{125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343}, x\right)"," ",0,"integral((x^4 + 3*x^2 + 2)^(3/2)/(125*x^6 + 525*x^4 + 735*x^2 + 343), x)","F",0
300,0,0,0,0.818943," ","integrate((5*x^2+7)^3/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343}{\sqrt{x^{4} + 3 \, x^{2} + 2}}, x\right)"," ",0,"integral((125*x^6 + 525*x^4 + 735*x^2 + 343)/sqrt(x^4 + 3*x^2 + 2), x)","F",0
301,0,0,0,0.892714," ","integrate((5*x^2+7)^2/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{25 \, x^{4} + 70 \, x^{2} + 49}{\sqrt{x^{4} + 3 \, x^{2} + 2}}, x\right)"," ",0,"integral((25*x^4 + 70*x^2 + 49)/sqrt(x^4 + 3*x^2 + 2), x)","F",0
302,0,0,0,0.814962," ","integrate((5*x^2+7)/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{5 \, x^{2} + 7}{\sqrt{x^{4} + 3 \, x^{2} + 2}}, x\right)"," ",0,"integral((5*x^2 + 7)/sqrt(x^4 + 3*x^2 + 2), x)","F",0
303,0,0,0,0.925225," ","integrate(1/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 2}}, x\right)"," ",0,"integral(1/sqrt(x^4 + 3*x^2 + 2), x)","F",0
304,0,0,0,0.719563," ","integrate(1/(5*x^2+7)/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{5 \, x^{6} + 22 \, x^{4} + 31 \, x^{2} + 14}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(5*x^6 + 22*x^4 + 31*x^2 + 14), x)","F",0
305,0,0,0,0.936447," ","integrate(1/(5*x^2+7)^2/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{25 \, x^{8} + 145 \, x^{6} + 309 \, x^{4} + 287 \, x^{2} + 98}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(25*x^8 + 145*x^6 + 309*x^4 + 287*x^2 + 98), x)","F",0
306,0,0,0,1.290759," ","integrate(1/(5*x^2+7)^3/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{125 \, x^{10} + 900 \, x^{8} + 2560 \, x^{6} + 3598 \, x^{4} + 2499 \, x^{2} + 686}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(125*x^10 + 900*x^8 + 2560*x^6 + 3598*x^4 + 2499*x^2 + 686), x)","F",0
307,0,0,0,0.986838," ","integrate((5*x^2+7)^5/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3125 \, x^{10} + 21875 \, x^{8} + 61250 \, x^{6} + 85750 \, x^{4} + 60025 \, x^{2} + 16807\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}}{x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4}, x\right)"," ",0,"integral((3125*x^10 + 21875*x^8 + 61250*x^6 + 85750*x^4 + 60025*x^2 + 16807)*sqrt(x^4 + 3*x^2 + 2)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4), x)","F",0
308,0,0,0,0.812193," ","integrate((5*x^2+7)^4/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(625 \, x^{8} + 3500 \, x^{6} + 7350 \, x^{4} + 6860 \, x^{2} + 2401\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}}{x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4}, x\right)"," ",0,"integral((625*x^8 + 3500*x^6 + 7350*x^4 + 6860*x^2 + 2401)*sqrt(x^4 + 3*x^2 + 2)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4), x)","F",0
309,0,0,0,1.142100," ","integrate((5*x^2+7)^3/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}}{x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4}, x\right)"," ",0,"integral((125*x^6 + 525*x^4 + 735*x^2 + 343)*sqrt(x^4 + 3*x^2 + 2)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4), x)","F",0
310,0,0,0,1.044518," ","integrate((5*x^2+7)^2/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{4} + 70 \, x^{2} + 49\right)} \sqrt{x^{4} + 3 \, x^{2} + 2}}{x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4}, x\right)"," ",0,"integral((25*x^4 + 70*x^2 + 49)*sqrt(x^4 + 3*x^2 + 2)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4), x)","F",0
311,0,0,0,0.572304," ","integrate((5*x^2+7)/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2} {\left(5 \, x^{2} + 7\right)}}{x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)*(5*x^2 + 7)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4), x)","F",0
312,0,0,0,0.933262," ","integrate(1/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{x^{8} + 6 \, x^{6} + 13 \, x^{4} + 12 \, x^{2} + 4}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(x^8 + 6*x^6 + 13*x^4 + 12*x^2 + 4), x)","F",0
313,0,0,0,1.193709," ","integrate(1/(5*x^2+7)/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{5 \, x^{10} + 37 \, x^{8} + 107 \, x^{6} + 151 \, x^{4} + 104 \, x^{2} + 28}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(5*x^10 + 37*x^8 + 107*x^6 + 151*x^4 + 104*x^2 + 28), x)","F",0
314,0,0,0,1.090620," ","integrate(1/(5*x^2+7)^2/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{25 \, x^{12} + 220 \, x^{10} + 794 \, x^{8} + 1504 \, x^{6} + 1577 \, x^{4} + 868 \, x^{2} + 196}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(25*x^12 + 220*x^10 + 794*x^8 + 1504*x^6 + 1577*x^4 + 868*x^2 + 196), x)","F",0
315,0,0,0,1.138355," ","integrate(1/(5*x^2+7)^3/(x^4+3*x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{125 \, x^{14} + 1275 \, x^{12} + 5510 \, x^{10} + 13078 \, x^{8} + 18413 \, x^{6} + 15379 \, x^{4} + 7056 \, x^{2} + 1372}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(125*x^14 + 1275*x^12 + 5510*x^10 + 13078*x^8 + 18413*x^6 + 15379*x^4 + 7056*x^2 + 1372), x)","F",0
316,0,0,0,1.056598," ","integrate((5*x^2+7)^4*(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(625 \, x^{8} + 3500 \, x^{6} + 7350 \, x^{4} + 6860 \, x^{2} + 2401\right)} \sqrt{-x^{4} + x^{2} + 2}, x\right)"," ",0,"integral((625*x^8 + 3500*x^6 + 7350*x^4 + 6860*x^2 + 2401)*sqrt(-x^4 + x^2 + 2), x)","F",0
317,0,0,0,1.162060," ","integrate((5*x^2+7)^3*(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right)} \sqrt{-x^{4} + x^{2} + 2}, x\right)"," ",0,"integral((125*x^6 + 525*x^4 + 735*x^2 + 343)*sqrt(-x^4 + x^2 + 2), x)","F",0
318,0,0,0,0.981431," ","integrate((5*x^2+7)^2*(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(25 \, x^{4} + 70 \, x^{2} + 49\right)} \sqrt{-x^{4} + x^{2} + 2}, x\right)"," ",0,"integral((25*x^4 + 70*x^2 + 49)*sqrt(-x^4 + x^2 + 2), x)","F",0
319,0,0,0,0.806920," ","integrate((5*x^2+7)*(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7), x)","F",0
320,0,0,0,1.074986," ","integrate((-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-x^{4} + x^{2} + 2}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2), x)","F",0
321,0,0,0,0.665212," ","integrate((-x^4+x^2+2)^(1/2)/(5*x^2+7),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 2}}{5 \, x^{2} + 7}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)/(5*x^2 + 7), x)","F",0
322,0,0,0,0.738849," ","integrate((-x^4+x^2+2)^(1/2)/(5*x^2+7)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 2}}{25 \, x^{4} + 70 \, x^{2} + 49}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)/(25*x^4 + 70*x^2 + 49), x)","F",0
323,0,0,0,0.941200," ","integrate((-x^4+x^2+2)^(1/2)/(5*x^2+7)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 2}}{125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)/(125*x^6 + 525*x^4 + 735*x^2 + 343), x)","F",0
324,0,0,0,0.726234," ","integrate((5*x^2+7)^4*(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(625 \, x^{12} + 2875 \, x^{10} + 2600 \, x^{8} - 7490 \, x^{6} - 19159 \, x^{4} - 16121 \, x^{2} - 4802\right)} \sqrt{-x^{4} + x^{2} + 2}, x\right)"," ",0,"integral(-(625*x^12 + 2875*x^10 + 2600*x^8 - 7490*x^6 - 19159*x^4 - 16121*x^2 - 4802)*sqrt(-x^4 + x^2 + 2), x)","F",0
325,0,0,0,0.838310," ","integrate((5*x^2+7)^3*(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(125 \, x^{10} + 400 \, x^{8} - 40 \, x^{6} - 1442 \, x^{4} - 1813 \, x^{2} - 686\right)} \sqrt{-x^{4} + x^{2} + 2}, x\right)"," ",0,"integral(-(125*x^10 + 400*x^8 - 40*x^6 - 1442*x^4 - 1813*x^2 - 686)*sqrt(-x^4 + x^2 + 2), x)","F",0
326,0,0,0,0.550266," ","integrate((5*x^2+7)^2*(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(25 \, x^{8} + 45 \, x^{6} - 71 \, x^{4} - 189 \, x^{2} - 98\right)} \sqrt{-x^{4} + x^{2} + 2}, x\right)"," ",0,"integral(-(25*x^8 + 45*x^6 - 71*x^4 - 189*x^2 - 98)*sqrt(-x^4 + x^2 + 2), x)","F",0
327,0,0,0,0.807791," ","integrate((5*x^2+7)*(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(-{\left(5 \, x^{6} + 2 \, x^{4} - 17 \, x^{2} - 14\right)} \sqrt{-x^{4} + x^{2} + 2}, x\right)"," ",0,"integral(-(5*x^6 + 2*x^4 - 17*x^2 - 14)*sqrt(-x^4 + x^2 + 2), x)","F",0
328,0,0,0,0.681226," ","integrate((-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((-x^4 + x^2 + 2)^(3/2), x)","F",0
329,0,0,0,1.198729," ","integrate((-x^4+x^2+2)^(3/2)/(5*x^2+7),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}{5 \, x^{2} + 7}, x\right)"," ",0,"integral((-x^4 + x^2 + 2)^(3/2)/(5*x^2 + 7), x)","F",0
330,0,0,0,0.970216," ","integrate((-x^4+x^2+2)^(3/2)/(5*x^2+7)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}{25 \, x^{4} + 70 \, x^{2} + 49}, x\right)"," ",0,"integral((-x^4 + x^2 + 2)^(3/2)/(25*x^4 + 70*x^2 + 49), x)","F",0
331,0,0,0,1.120264," ","integrate((-x^4+x^2+2)^(3/2)/(5*x^2+7)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(-x^{4} + x^{2} + 2\right)}^{\frac{3}{2}}}{125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343}, x\right)"," ",0,"integral((-x^4 + x^2 + 2)^(3/2)/(125*x^6 + 525*x^4 + 735*x^2 + 343), x)","F",0
332,0,0,0,0.814136," ","integrate((5*x^2+7)^3/(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right)} \sqrt{-x^{4} + x^{2} + 2}}{x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(-(125*x^6 + 525*x^4 + 735*x^2 + 343)*sqrt(-x^4 + x^2 + 2)/(x^4 - x^2 - 2), x)","F",0
333,0,0,0,0.568297," ","integrate((5*x^2+7)^2/(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(25 \, x^{4} + 70 \, x^{2} + 49\right)} \sqrt{-x^{4} + x^{2} + 2}}{x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(-(25*x^4 + 70*x^2 + 49)*sqrt(-x^4 + x^2 + 2)/(x^4 - x^2 - 2), x)","F",0
334,0,0,0,0.785756," ","integrate((5*x^2+7)/(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}}{x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7)/(x^4 - x^2 - 2), x)","F",0
335,0,0,0,0.805558," ","integrate(1/(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + x^{2} + 2}}{x^{4} - x^{2} - 2}, x\right)"," ",0,"integral(-sqrt(-x^4 + x^2 + 2)/(x^4 - x^2 - 2), x)","F",0
336,0,0,0,0.961213," ","integrate(1/(5*x^2+7)/(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + x^{2} + 2}}{5 \, x^{6} + 2 \, x^{4} - 17 \, x^{2} - 14}, x\right)"," ",0,"integral(-sqrt(-x^4 + x^2 + 2)/(5*x^6 + 2*x^4 - 17*x^2 - 14), x)","F",0
337,0,0,0,0.648114," ","integrate(1/(5*x^2+7)^2/(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + x^{2} + 2}}{25 \, x^{8} + 45 \, x^{6} - 71 \, x^{4} - 189 \, x^{2} - 98}, x\right)"," ",0,"integral(-sqrt(-x^4 + x^2 + 2)/(25*x^8 + 45*x^6 - 71*x^4 - 189*x^2 - 98), x)","F",0
338,0,0,0,0.913394," ","integrate(1/(5*x^2+7)^3/(-x^4+x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-x^{4} + x^{2} + 2}}{125 \, x^{10} + 400 \, x^{8} - 40 \, x^{6} - 1442 \, x^{4} - 1813 \, x^{2} - 686}, x\right)"," ",0,"integral(-sqrt(-x^4 + x^2 + 2)/(125*x^10 + 400*x^8 - 40*x^6 - 1442*x^4 - 1813*x^2 - 686), x)","F",0
339,0,0,0,0.795027," ","integrate((5*x^2+7)^5/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3125 \, x^{10} + 21875 \, x^{8} + 61250 \, x^{6} + 85750 \, x^{4} + 60025 \, x^{2} + 16807\right)} \sqrt{-x^{4} + x^{2} + 2}}{x^{8} - 2 \, x^{6} - 3 \, x^{4} + 4 \, x^{2} + 4}, x\right)"," ",0,"integral((3125*x^10 + 21875*x^8 + 61250*x^6 + 85750*x^4 + 60025*x^2 + 16807)*sqrt(-x^4 + x^2 + 2)/(x^8 - 2*x^6 - 3*x^4 + 4*x^2 + 4), x)","F",0
340,0,0,0,0.709135," ","integrate((5*x^2+7)^4/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(625 \, x^{8} + 3500 \, x^{6} + 7350 \, x^{4} + 6860 \, x^{2} + 2401\right)} \sqrt{-x^{4} + x^{2} + 2}}{x^{8} - 2 \, x^{6} - 3 \, x^{4} + 4 \, x^{2} + 4}, x\right)"," ",0,"integral((625*x^8 + 3500*x^6 + 7350*x^4 + 6860*x^2 + 2401)*sqrt(-x^4 + x^2 + 2)/(x^8 - 2*x^6 - 3*x^4 + 4*x^2 + 4), x)","F",0
341,0,0,0,0.653715," ","integrate((5*x^2+7)^3/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right)} \sqrt{-x^{4} + x^{2} + 2}}{x^{8} - 2 \, x^{6} - 3 \, x^{4} + 4 \, x^{2} + 4}, x\right)"," ",0,"integral((125*x^6 + 525*x^4 + 735*x^2 + 343)*sqrt(-x^4 + x^2 + 2)/(x^8 - 2*x^6 - 3*x^4 + 4*x^2 + 4), x)","F",0
342,0,0,0,0.833024," ","integrate((5*x^2+7)^2/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{4} + 70 \, x^{2} + 49\right)} \sqrt{-x^{4} + x^{2} + 2}}{x^{8} - 2 \, x^{6} - 3 \, x^{4} + 4 \, x^{2} + 4}, x\right)"," ",0,"integral((25*x^4 + 70*x^2 + 49)*sqrt(-x^4 + x^2 + 2)/(x^8 - 2*x^6 - 3*x^4 + 4*x^2 + 4), x)","F",0
343,0,0,0,0.783744," ","integrate((5*x^2+7)/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 2} {\left(5 \, x^{2} + 7\right)}}{x^{8} - 2 \, x^{6} - 3 \, x^{4} + 4 \, x^{2} + 4}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)*(5*x^2 + 7)/(x^8 - 2*x^6 - 3*x^4 + 4*x^2 + 4), x)","F",0
344,0,0,0,0.787537," ","integrate(1/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 2}}{x^{8} - 2 \, x^{6} - 3 \, x^{4} + 4 \, x^{2} + 4}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)/(x^8 - 2*x^6 - 3*x^4 + 4*x^2 + 4), x)","F",0
345,0,0,0,0.949238," ","integrate(1/(5*x^2+7)/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 2}}{5 \, x^{10} - 3 \, x^{8} - 29 \, x^{6} - x^{4} + 48 \, x^{2} + 28}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)/(5*x^10 - 3*x^8 - 29*x^6 - x^4 + 48*x^2 + 28), x)","F",0
346,0,0,0,1.114871," ","integrate(1/(5*x^2+7)^2/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 2}}{25 \, x^{12} + 20 \, x^{10} - 166 \, x^{8} - 208 \, x^{6} + 233 \, x^{4} + 476 \, x^{2} + 196}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)/(25*x^12 + 20*x^10 - 166*x^8 - 208*x^6 + 233*x^4 + 476*x^2 + 196), x)","F",0
347,0,0,0,0.765883," ","integrate(1/(5*x^2+7)^3/(-x^4+x^2+2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{-x^{4} + x^{2} + 2}}{125 \, x^{14} + 275 \, x^{12} - 690 \, x^{10} - 2202 \, x^{8} - 291 \, x^{6} + 4011 \, x^{4} + 4312 \, x^{2} + 1372}, x\right)"," ",0,"integral(sqrt(-x^4 + x^2 + 2)/(125*x^14 + 275*x^12 - 690*x^10 - 2202*x^8 - 291*x^6 + 4011*x^4 + 4312*x^2 + 1372), x)","F",0
348,0,0,0,0.895037," ","integrate((5*x^2+7)^4*(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(625 \, x^{8} + 3500 \, x^{6} + 7350 \, x^{4} + 6860 \, x^{2} + 2401\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}, x\right)"," ",0,"integral((625*x^8 + 3500*x^6 + 7350*x^4 + 6860*x^2 + 2401)*sqrt(x^4 + 3*x^2 + 4), x)","F",0
349,0,0,0,0.821604," ","integrate((5*x^2+7)^3*(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}, x\right)"," ",0,"integral((125*x^6 + 525*x^4 + 735*x^2 + 343)*sqrt(x^4 + 3*x^2 + 4), x)","F",0
350,0,0,0,0.866396," ","integrate((5*x^2+7)^2*(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(25 \, x^{4} + 70 \, x^{2} + 49\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}, x\right)"," ",0,"integral((25*x^4 + 70*x^2 + 49)*sqrt(x^4 + 3*x^2 + 4), x)","F",0
351,0,0,0,0.799185," ","integrate((5*x^2+7)*(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7), x)","F",0
352,0,0,0,0.799718," ","integrate((x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{x^{4} + 3 \, x^{2} + 4}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4), x)","F",0
353,0,0,0,1.178787," ","integrate((x^4+3*x^2+4)^(1/2)/(5*x^2+7),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{5 \, x^{2} + 7}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(5*x^2 + 7), x)","F",0
354,0,0,0,0.770011," ","integrate((x^4+3*x^2+4)^(1/2)/(5*x^2+7)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{25 \, x^{4} + 70 \, x^{2} + 49}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(25*x^4 + 70*x^2 + 49), x)","F",0
355,0,0,0,0.783977," ","integrate((x^4+3*x^2+4)^(1/2)/(5*x^2+7)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(125*x^6 + 525*x^4 + 735*x^2 + 343), x)","F",0
356,0,0,0,0.793170," ","integrate((5*x^2+7)^4*(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(625 \, x^{12} + 5375 \, x^{10} + 20350 \, x^{8} + 42910 \, x^{6} + 52381 \, x^{4} + 34643 \, x^{2} + 9604\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}, x\right)"," ",0,"integral((625*x^12 + 5375*x^10 + 20350*x^8 + 42910*x^6 + 52381*x^4 + 34643*x^2 + 9604)*sqrt(x^4 + 3*x^2 + 4), x)","F",0
357,0,0,0,0.777292," ","integrate((5*x^2+7)^3*(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(125 \, x^{10} + 900 \, x^{8} + 2810 \, x^{6} + 4648 \, x^{4} + 3969 \, x^{2} + 1372\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}, x\right)"," ",0,"integral((125*x^10 + 900*x^8 + 2810*x^6 + 4648*x^4 + 3969*x^2 + 1372)*sqrt(x^4 + 3*x^2 + 4), x)","F",0
358,0,0,0,1.023292," ","integrate((5*x^2+7)^2*(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(25 \, x^{8} + 145 \, x^{6} + 359 \, x^{4} + 427 \, x^{2} + 196\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}, x\right)"," ",0,"integral((25*x^8 + 145*x^6 + 359*x^4 + 427*x^2 + 196)*sqrt(x^4 + 3*x^2 + 4), x)","F",0
359,0,0,0,0.791987," ","integrate((5*x^2+7)*(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(5 \, x^{6} + 22 \, x^{4} + 41 \, x^{2} + 28\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}, x\right)"," ",0,"integral((5*x^6 + 22*x^4 + 41*x^2 + 28)*sqrt(x^4 + 3*x^2 + 4), x)","F",0
360,0,0,0,0.883267," ","integrate((x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((x^4 + 3*x^2 + 4)^(3/2), x)","F",0
361,0,0,0,0.931724," ","integrate((x^4+3*x^2+4)^(3/2)/(5*x^2+7),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}{5 \, x^{2} + 7}, x\right)"," ",0,"integral((x^4 + 3*x^2 + 4)^(3/2)/(5*x^2 + 7), x)","F",0
362,0,0,0,1.098673," ","integrate((x^4+3*x^2+4)^(3/2)/(5*x^2+7)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}{25 \, x^{4} + 70 \, x^{2} + 49}, x\right)"," ",0,"integral((x^4 + 3*x^2 + 4)^(3/2)/(25*x^4 + 70*x^2 + 49), x)","F",0
363,0,0,0,0.912361," ","integrate((x^4+3*x^2+4)^(3/2)/(5*x^2+7)^3,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(x^{4} + 3 \, x^{2} + 4\right)}^{\frac{3}{2}}}{125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343}, x\right)"," ",0,"integral((x^4 + 3*x^2 + 4)^(3/2)/(125*x^6 + 525*x^4 + 735*x^2 + 343), x)","F",0
364,0,0,0,0.797613," ","integrate((5*x^2+7)^3/(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343}{\sqrt{x^{4} + 3 \, x^{2} + 4}}, x\right)"," ",0,"integral((125*x^6 + 525*x^4 + 735*x^2 + 343)/sqrt(x^4 + 3*x^2 + 4), x)","F",0
365,0,0,0,1.072540," ","integrate((5*x^2+7)^2/(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{25 \, x^{4} + 70 \, x^{2} + 49}{\sqrt{x^{4} + 3 \, x^{2} + 4}}, x\right)"," ",0,"integral((25*x^4 + 70*x^2 + 49)/sqrt(x^4 + 3*x^2 + 4), x)","F",0
366,0,0,0,0.643024," ","integrate((5*x^2+7)/(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{5 \, x^{2} + 7}{\sqrt{x^{4} + 3 \, x^{2} + 4}}, x\right)"," ",0,"integral((5*x^2 + 7)/sqrt(x^4 + 3*x^2 + 4), x)","F",0
367,0,0,0,0.929684," ","integrate(1/(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{x^{4} + 3 \, x^{2} + 4}}, x\right)"," ",0,"integral(1/sqrt(x^4 + 3*x^2 + 4), x)","F",0
368,0,0,0,0.830076," ","integrate(1/(5*x^2+7)/(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{5 \, x^{6} + 22 \, x^{4} + 41 \, x^{2} + 28}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(5*x^6 + 22*x^4 + 41*x^2 + 28), x)","F",0
369,0,0,0,0.708076," ","integrate(1/(5*x^2+7)^2/(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{25 \, x^{8} + 145 \, x^{6} + 359 \, x^{4} + 427 \, x^{2} + 196}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(25*x^8 + 145*x^6 + 359*x^4 + 427*x^2 + 196), x)","F",0
370,0,0,0,0.859879," ","integrate(1/(5*x^2+7)^3/(x^4+3*x^2+4)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{125 \, x^{10} + 900 \, x^{8} + 2810 \, x^{6} + 4648 \, x^{4} + 3969 \, x^{2} + 1372}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(125*x^10 + 900*x^8 + 2810*x^6 + 4648*x^4 + 3969*x^2 + 1372), x)","F",0
371,0,0,0,0.745364," ","integrate((5*x^2+7)^5/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(3125 \, x^{10} + 21875 \, x^{8} + 61250 \, x^{6} + 85750 \, x^{4} + 60025 \, x^{2} + 16807\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}}{x^{8} + 6 \, x^{6} + 17 \, x^{4} + 24 \, x^{2} + 16}, x\right)"," ",0,"integral((3125*x^10 + 21875*x^8 + 61250*x^6 + 85750*x^4 + 60025*x^2 + 16807)*sqrt(x^4 + 3*x^2 + 4)/(x^8 + 6*x^6 + 17*x^4 + 24*x^2 + 16), x)","F",0
372,0,0,0,0.833245," ","integrate((5*x^2+7)^4/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(625 \, x^{8} + 3500 \, x^{6} + 7350 \, x^{4} + 6860 \, x^{2} + 2401\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}}{x^{8} + 6 \, x^{6} + 17 \, x^{4} + 24 \, x^{2} + 16}, x\right)"," ",0,"integral((625*x^8 + 3500*x^6 + 7350*x^4 + 6860*x^2 + 2401)*sqrt(x^4 + 3*x^2 + 4)/(x^8 + 6*x^6 + 17*x^4 + 24*x^2 + 16), x)","F",0
373,0,0,0,0.853917," ","integrate((5*x^2+7)^3/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(125 \, x^{6} + 525 \, x^{4} + 735 \, x^{2} + 343\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}}{x^{8} + 6 \, x^{6} + 17 \, x^{4} + 24 \, x^{2} + 16}, x\right)"," ",0,"integral((125*x^6 + 525*x^4 + 735*x^2 + 343)*sqrt(x^4 + 3*x^2 + 4)/(x^8 + 6*x^6 + 17*x^4 + 24*x^2 + 16), x)","F",0
374,0,0,0,1.007668," ","integrate((5*x^2+7)^2/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(25 \, x^{4} + 70 \, x^{2} + 49\right)} \sqrt{x^{4} + 3 \, x^{2} + 4}}{x^{8} + 6 \, x^{6} + 17 \, x^{4} + 24 \, x^{2} + 16}, x\right)"," ",0,"integral((25*x^4 + 70*x^2 + 49)*sqrt(x^4 + 3*x^2 + 4)/(x^8 + 6*x^6 + 17*x^4 + 24*x^2 + 16), x)","F",0
375,0,0,0,0.738014," ","integrate((5*x^2+7)/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4} {\left(5 \, x^{2} + 7\right)}}{x^{8} + 6 \, x^{6} + 17 \, x^{4} + 24 \, x^{2} + 16}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)*(5*x^2 + 7)/(x^8 + 6*x^6 + 17*x^4 + 24*x^2 + 16), x)","F",0
376,0,0,0,0.963964," ","integrate(1/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{x^{8} + 6 \, x^{6} + 17 \, x^{4} + 24 \, x^{2} + 16}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(x^8 + 6*x^6 + 17*x^4 + 24*x^2 + 16), x)","F",0
377,0,0,0,1.001091," ","integrate(1/(5*x^2+7)/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{5 \, x^{10} + 37 \, x^{8} + 127 \, x^{6} + 239 \, x^{4} + 248 \, x^{2} + 112}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(5*x^10 + 37*x^8 + 127*x^6 + 239*x^4 + 248*x^2 + 112), x)","F",0
378,0,0,0,0.876348," ","integrate(1/(5*x^2+7)^2/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{25 \, x^{12} + 220 \, x^{10} + 894 \, x^{8} + 2084 \, x^{6} + 2913 \, x^{4} + 2296 \, x^{2} + 784}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(25*x^12 + 220*x^10 + 894*x^8 + 2084*x^6 + 2913*x^4 + 2296*x^2 + 784), x)","F",0
379,0,0,0,1.010198," ","integrate(1/(5*x^2+7)^3/(x^4+3*x^2+4)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 4}}{125 \, x^{14} + 1275 \, x^{12} + 6010 \, x^{10} + 16678 \, x^{8} + 29153 \, x^{6} + 31871 \, x^{4} + 19992 \, x^{2} + 5488}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 4)/(125*x^14 + 1275*x^12 + 6010*x^10 + 16678*x^8 + 29153*x^6 + 31871*x^4 + 19992*x^2 + 5488), x)","F",0
380,0,0,0,0.832650," ","integrate((e*x^2+d)^3/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
381,0,0,0,1.062234," ","integrate((e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((e^2*x^4 + 2*d*e*x^2 + d^2)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
382,0,0,0,0.639693," ","integrate((e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{2} + d}{\sqrt{c x^{4} + b x^{2} + a}}, x\right)"," ",0,"integral((e*x^2 + d)/sqrt(c*x^4 + b*x^2 + a), x)","F",0
383,0,0,0,96.217825," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} + a}}{c e x^{6} + {\left(c d + b e\right)} x^{4} + {\left(b d + a e\right)} x^{2} + a d}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 + a)/(c*e*x^6 + (c*d + b*e)*x^4 + (b*d + a*e)*x^2 + a*d), x)","F",0
384,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
385,0,0,0,0.790454," ","integrate((e*x^2+d)^3/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}\right)} \sqrt{-c x^{4} + b x^{2} + a}}{c x^{4} - b x^{2} - a}, x\right)"," ",0,"integral(-(e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3)*sqrt(-c*x^4 + b*x^2 + a)/(c*x^4 - b*x^2 - a), x)","F",0
386,0,0,0,0.757755," ","integrate((e*x^2+d)^2/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{{\left(e^{2} x^{4} + 2 \, d e x^{2} + d^{2}\right)} \sqrt{-c x^{4} + b x^{2} + a}}{c x^{4} - b x^{2} - a}, x\right)"," ",0,"integral(-(e^2*x^4 + 2*d*e*x^2 + d^2)*sqrt(-c*x^4 + b*x^2 + a)/(c*x^4 - b*x^2 - a), x)","F",0
387,0,0,0,0.786012," ","integrate((e*x^2+d)/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + b x^{2} + a} {\left(e x^{2} + d\right)}}{c x^{4} - b x^{2} - a}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + b*x^2 + a)*(e*x^2 + d)/(c*x^4 - b*x^2 - a), x)","F",0
388,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
389,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)^2/(-c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
390,0,0,0,0.976536," ","integrate((e*x^2+d)/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{2} + d}{\sqrt{c x^{4} + b x^{2} - a}}, x\right)"," ",0,"integral((e*x^2 + d)/sqrt(c*x^4 + b*x^2 - a), x)","F",0
391,0,0,0,86.135738," ","integrate(1/(e*x^2+d)/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{c x^{4} + b x^{2} - a}}{c e x^{6} + {\left(c d + b e\right)} x^{4} + {\left(b d - a e\right)} x^{2} - a d}, x\right)"," ",0,"integral(sqrt(c*x^4 + b*x^2 - a)/(c*e*x^6 + (c*d + b*e)*x^4 + (b*d - a*e)*x^2 - a*d), x)","F",0
392,0,0,0,0.885340," ","integrate((e*x^2+d)/(-c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-c x^{4} + b x^{2} - a} {\left(e x^{2} + d\right)}}{c x^{4} - b x^{2} + a}, x\right)"," ",0,"integral(-sqrt(-c*x^4 + b*x^2 - a)*(e*x^2 + d)/(c*x^4 - b*x^2 + a), x)","F",0
393,-1,0,0,0.000000," ","integrate(1/(e*x^2+d)/(-c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
394,0,0,0,0.949120," ","integrate((e*x^2+d)^3/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{3} x^{6} + 3 \, d e^{2} x^{4} + 3 \, d^{2} e x^{2} + d^{3}}{\sqrt{x^{4} + 3 \, x^{2} + 2}}, x\right)"," ",0,"integral((e^3*x^6 + 3*d*e^2*x^4 + 3*d^2*e*x^2 + d^3)/sqrt(x^4 + 3*x^2 + 2), x)","F",0
395,0,0,0,0.952747," ","integrate((e*x^2+d)^2/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e^{2} x^{4} + 2 \, d e x^{2} + d^{2}}{\sqrt{x^{4} + 3 \, x^{2} + 2}}, x\right)"," ",0,"integral((e^2*x^4 + 2*d*e*x^2 + d^2)/sqrt(x^4 + 3*x^2 + 2), x)","F",0
396,0,0,0,1.053696," ","integrate((e*x^2+d)/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{e x^{2} + d}{\sqrt{x^{4} + 3 \, x^{2} + 2}}, x\right)"," ",0,"integral((e*x^2 + d)/sqrt(x^4 + 3*x^2 + 2), x)","F",0
397,0,0,0,1.654828," ","integrate(1/(e*x^2+d)/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{e x^{6} + {\left(d + 3 \, e\right)} x^{4} + {\left(3 \, d + 2 \, e\right)} x^{2} + 2 \, d}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(e*x^6 + (d + 3*e)*x^4 + (3*d + 2*e)*x^2 + 2*d), x)","F",0
398,0,0,0,1.790263," ","integrate(1/(e*x^2+d)^2/(x^4+3*x^2+2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{x^{4} + 3 \, x^{2} + 2}}{e^{2} x^{8} + {\left(2 \, d e + 3 \, e^{2}\right)} x^{6} + {\left(d^{2} + 6 \, d e + 2 \, e^{2}\right)} x^{4} + {\left(3 \, d^{2} + 4 \, d e\right)} x^{2} + 2 \, d^{2}}, x\right)"," ",0,"integral(sqrt(x^4 + 3*x^2 + 2)/(e^2*x^8 + (2*d*e + 3*e^2)*x^6 + (d^2 + 6*d*e + 2*e^2)*x^4 + (3*d^2 + 4*d*e)*x^2 + 2*d^2), x)","F",0
399,0,0,0,1.470257," ","integrate((e*x^2+c)^q*(b*x^4+c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + c x^{2} + a\right)}^{p} {\left(e x^{2} + c\right)}^{q}, x\right)"," ",0,"integral((b*x^4 + c*x^2 + a)^p*(e*x^2 + c)^q, x)","F",0
400,0,0,0,0.665077," ","integrate((e*x^2+c)^3*(b*x^4+c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{3} x^{6} + 3 \, c e^{2} x^{4} + 3 \, c^{2} e x^{2} + c^{3}\right)} {\left(b x^{4} + c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^3*x^6 + 3*c*e^2*x^4 + 3*c^2*e*x^2 + c^3)*(b*x^4 + c*x^2 + a)^p, x)","F",0
401,0,0,0,0.575644," ","integrate((e*x^2+c)^2*(b*x^4+c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e^{2} x^{4} + 2 \, c e x^{2} + c^{2}\right)} {\left(b x^{4} + c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e^2*x^4 + 2*c*e*x^2 + c^2)*(b*x^4 + c*x^2 + a)^p, x)","F",0
402,0,0,0,0.725066," ","integrate((e*x^2+c)*(b*x^4+c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(e x^{2} + c\right)} {\left(b x^{4} + c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((e*x^2 + c)*(b*x^4 + c*x^2 + a)^p, x)","F",0
403,0,0,0,0.878787," ","integrate((b*x^4+c*x^2+a)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b x^{4} + c x^{2} + a\right)}^{p}, x\right)"," ",0,"integral((b*x^4 + c*x^2 + a)^p, x)","F",0
404,0,0,0,0.675349," ","integrate((b*x^4+c*x^2+a)^p/(e*x^2+c),x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + c x^{2} + a\right)}^{p}}{e x^{2} + c}, x\right)"," ",0,"integral((b*x^4 + c*x^2 + a)^p/(e*x^2 + c), x)","F",0
405,0,0,0,0.772497," ","integrate((b*x^4+c*x^2+a)^p/(e*x^2+c)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{{\left(b x^{4} + c x^{2} + a\right)}^{p}}{e^{2} x^{4} + 2 \, c e x^{2} + c^{2}}, x\right)"," ",0,"integral((b*x^4 + c*x^2 + a)^p/(e^2*x^4 + 2*c*e*x^2 + c^2), x)","F",0
406,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^4+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
407,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^4-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
408,1,323,0,1.641481," ","integrate((1+x-3^(1/2))/(1+x+3^(1/2))/(-4+x^4+4*3^(1/2)*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{2 \, \sqrt{3} - 3} \log\left(-\frac{37 \, x^{12} - 204 \, x^{11} + 804 \, x^{10} - 2408 \, x^{9} + 3708 \, x^{8} - 5472 \, x^{7} + 6432 \, x^{6} + 10944 \, x^{5} + 14832 \, x^{4} + 19264 \, x^{3} + 12864 \, x^{2} + {\left(54 \, x^{10} - 300 \, x^{9} + 1026 \, x^{8} - 2232 \, x^{7} + 3024 \, x^{6} - 3024 \, x^{5} - 1008 \, x^{4} - 2016 \, x^{3} - 2592 \, x^{2} + \sqrt{3} {\left(31 \, x^{10} - 176 \, x^{9} + 576 \, x^{8} - 1320 \, x^{7} + 1848 \, x^{6} - 1008 \, x^{5} + 1344 \, x^{4} + 1632 \, x^{3} + 1008 \, x^{2} + 832 \, x + 256\right)} - 1152 \, x - 480\right)} \sqrt{x^{4} + 4 \, \sqrt{3} x^{2} - 4} \sqrt{2 \, \sqrt{3} - 3} + 3 \, \sqrt{3} {\left(7 \, x^{12} - 40 \, x^{11} + 160 \, x^{10} - 400 \, x^{9} + 924 \, x^{8} - 960 \, x^{7} - 1920 \, x^{5} - 3696 \, x^{4} - 3200 \, x^{3} - 2560 \, x^{2} - 1280 \, x - 448\right)} + 6528 \, x + 2368}{x^{12} + 12 \, x^{11} + 48 \, x^{10} + 40 \, x^{9} - 180 \, x^{8} - 288 \, x^{7} + 384 \, x^{6} + 576 \, x^{5} - 720 \, x^{4} - 320 \, x^{3} + 768 \, x^{2} - 384 \, x + 64}\right)"," ",0,"1/12*sqrt(2*sqrt(3) - 3)*log(-(37*x^12 - 204*x^11 + 804*x^10 - 2408*x^9 + 3708*x^8 - 5472*x^7 + 6432*x^6 + 10944*x^5 + 14832*x^4 + 19264*x^3 + 12864*x^2 + (54*x^10 - 300*x^9 + 1026*x^8 - 2232*x^7 + 3024*x^6 - 3024*x^5 - 1008*x^4 - 2016*x^3 - 2592*x^2 + sqrt(3)*(31*x^10 - 176*x^9 + 576*x^8 - 1320*x^7 + 1848*x^6 - 1008*x^5 + 1344*x^4 + 1632*x^3 + 1008*x^2 + 832*x + 256) - 1152*x - 480)*sqrt(x^4 + 4*sqrt(3)*x^2 - 4)*sqrt(2*sqrt(3) - 3) + 3*sqrt(3)*(7*x^12 - 40*x^11 + 160*x^10 - 400*x^9 + 924*x^8 - 960*x^7 - 1920*x^5 - 3696*x^4 - 3200*x^3 - 2560*x^2 - 1280*x - 448) + 6528*x + 2368)/(x^12 + 12*x^11 + 48*x^10 + 40*x^9 - 180*x^8 - 288*x^7 + 384*x^6 + 576*x^5 - 720*x^4 - 320*x^3 + 768*x^2 - 384*x + 64))","B",0
409,1,112,0,1.360789," ","integrate((1+x+3^(1/2))/(1+x-3^(1/2))/(-4+x^4-4*3^(1/2)*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{2 \, \sqrt{3} + 3} \arctan\left(-\frac{{\left(9 \, x^{4} - 30 \, x^{3} + 18 \, x^{2} - 2 \, \sqrt{3} {\left(2 \, x^{4} - 10 \, x^{3} + 3 \, x^{2} - 10 \, x + 2\right)} + 24\right)} \sqrt{x^{4} - 4 \, \sqrt{3} x^{2} - 4} \sqrt{2 \, \sqrt{3} + 3}}{11 \, x^{6} - 42 \, x^{5} + 66 \, x^{4} - 176 \, x^{3} - 132 \, x^{2} - 168 \, x - 88}\right)"," ",0,"1/6*sqrt(2*sqrt(3) + 3)*arctan(-(9*x^4 - 30*x^3 + 18*x^2 - 2*sqrt(3)*(2*x^4 - 10*x^3 + 3*x^2 - 10*x + 2) + 24)*sqrt(x^4 - 4*sqrt(3)*x^2 - 4)*sqrt(2*sqrt(3) + 3)/(11*x^6 - 42*x^5 + 66*x^4 - 176*x^3 - 132*x^2 - 168*x - 88))","B",0
410,1,328,0,1.289201," ","integrate((1+2*x-3^(1/2))/(1+2*x+3^(1/2))/(-1+4*x^4+4*3^(1/2)*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sqrt{2 \, \sqrt{3} - 3} \log\left(-\frac{2368 \, x^{12} - 6528 \, x^{11} + 12864 \, x^{10} - 19264 \, x^{9} + 14832 \, x^{8} - 10944 \, x^{7} + 6432 \, x^{6} + 5472 \, x^{5} + 3708 \, x^{4} + 2408 \, x^{3} + 804 \, x^{2} + {\left(1728 \, x^{10} - 4800 \, x^{9} + 8208 \, x^{8} - 8928 \, x^{7} + 6048 \, x^{6} - 3024 \, x^{5} - 504 \, x^{4} - 504 \, x^{3} - 324 \, x^{2} + 2 \, \sqrt{3} {\left(496 \, x^{10} - 1408 \, x^{9} + 2304 \, x^{8} - 2640 \, x^{7} + 1848 \, x^{6} - 504 \, x^{5} + 336 \, x^{4} + 204 \, x^{3} + 63 \, x^{2} + 26 \, x + 4\right)} - 72 \, x - 15\right)} \sqrt{4 \, x^{4} + 4 \, \sqrt{3} x^{2} - 1} \sqrt{2 \, \sqrt{3} - 3} + 3 \, \sqrt{3} {\left(448 \, x^{12} - 1280 \, x^{11} + 2560 \, x^{10} - 3200 \, x^{9} + 3696 \, x^{8} - 1920 \, x^{7} - 960 \, x^{5} - 924 \, x^{4} - 400 \, x^{3} - 160 \, x^{2} - 40 \, x - 7\right)} + 204 \, x + 37}{64 \, x^{12} + 384 \, x^{11} + 768 \, x^{10} + 320 \, x^{9} - 720 \, x^{8} - 576 \, x^{7} + 384 \, x^{6} + 288 \, x^{5} - 180 \, x^{4} - 40 \, x^{3} + 48 \, x^{2} - 12 \, x + 1}\right)"," ",0,"1/12*sqrt(2*sqrt(3) - 3)*log(-(2368*x^12 - 6528*x^11 + 12864*x^10 - 19264*x^9 + 14832*x^8 - 10944*x^7 + 6432*x^6 + 5472*x^5 + 3708*x^4 + 2408*x^3 + 804*x^2 + (1728*x^10 - 4800*x^9 + 8208*x^8 - 8928*x^7 + 6048*x^6 - 3024*x^5 - 504*x^4 - 504*x^3 - 324*x^2 + 2*sqrt(3)*(496*x^10 - 1408*x^9 + 2304*x^8 - 2640*x^7 + 1848*x^6 - 504*x^5 + 336*x^4 + 204*x^3 + 63*x^2 + 26*x + 4) - 72*x - 15)*sqrt(4*x^4 + 4*sqrt(3)*x^2 - 1)*sqrt(2*sqrt(3) - 3) + 3*sqrt(3)*(448*x^12 - 1280*x^11 + 2560*x^10 - 3200*x^9 + 3696*x^8 - 1920*x^7 - 960*x^5 - 924*x^4 - 400*x^3 - 160*x^2 - 40*x - 7) + 204*x + 37)/(64*x^12 + 384*x^11 + 768*x^10 + 320*x^9 - 720*x^8 - 576*x^7 + 384*x^6 + 288*x^5 - 180*x^4 - 40*x^3 + 48*x^2 - 12*x + 1))","B",0
411,1,114,0,1.273212," ","integrate((1+2*x+3^(1/2))/(1+2*x-3^(1/2))/(-1+4*x^4-4*3^(1/2)*x^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{6} \, \sqrt{2 \, \sqrt{3} + 3} \arctan\left(-\frac{{\left(36 \, x^{4} - 60 \, x^{3} + 18 \, x^{2} - \sqrt{3} {\left(16 \, x^{4} - 40 \, x^{3} + 6 \, x^{2} - 10 \, x + 1\right)} + 6\right)} \sqrt{4 \, x^{4} - 4 \, \sqrt{3} x^{2} - 1} \sqrt{2 \, \sqrt{3} + 3}}{88 \, x^{6} - 168 \, x^{5} + 132 \, x^{4} - 176 \, x^{3} - 66 \, x^{2} - 42 \, x - 11}\right)"," ",0,"1/6*sqrt(2*sqrt(3) + 3)*arctan(-(36*x^4 - 60*x^3 + 18*x^2 - sqrt(3)*(16*x^4 - 40*x^3 + 6*x^2 - 10*x + 1) + 6)*sqrt(4*x^4 - 4*sqrt(3)*x^2 - 1)*sqrt(2*sqrt(3) + 3)/(88*x^6 - 168*x^5 + 132*x^4 - 176*x^3 - 66*x^2 - 42*x - 11))","B",0
412,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^4+b*x^2+a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
413,-1,0,0,0.000000," ","integrate((g*x+f)/(e*x+d)/(c*x^4+b*x^2-a)^(1/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
