43.5 Problem number 819

\[ \int \frac {10 x-3 e^{2 x} x-6 e^x x^3-3 x^5+\left (e^{3 x} (6+12 x)+e^{2 x} \left (36 x^2+12 x^3\right )+e^x \left (-20+30 x^4\right )\right ) \log \left (10 x-3 e^{2 x} x-6 e^x x^3-3 x^5\right )+\left (3 e^{3 x} x+6 e^{2 x} x^3+e^x \left (-10 x+3 x^5\right )\right ) \log ^2\left (10 x-3 e^{2 x} x-6 e^x x^3-3 x^5\right )}{-10 x+3 e^{2 x} x+6 e^x x^3+3 x^5} \, dx \]

Optimal antiderivative \[ {\mathrm e}^{x} \ln \! \left (x -3 x \left (\left ({\mathrm e}^{x}+x^{2}\right )^{2}-3\right )\right )^{2}-x \]

command

integrate(((3*x*exp(x)^3+6*exp(x)^2*x^3+(3*x^5-10*x)*exp(x))*log(-3*x*exp(x)^2-6*exp(x)*x^3-3*x^5+10*x)^2+((12*x+6)*exp(x)^3+(12*x^3+36*x^2)*exp(x)^2+(30*x^4-20)*exp(x))*log(-3*x*exp(x)^2-6*exp(x)*x^3-3*x^5+10*x)-3*x*exp(x)^2-6*exp(x)*x^3-3*x^5+10*x)/(3*x*exp(x)^2+6*exp(x)*x^3+3*x^5-10*x),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \text {Timed out} \]

Giac 1.7.0 via sagemath 9.3 output

\[ e^{x} \log \left (-3 \, x^{5} - 6 \, x^{3} e^{x} - 3 \, x e^{\left (2 \, x\right )} + 10 \, x\right )^{2} - x \]