\[ \int \frac {\left (7 x+14 e^{2 x} x\right ) \log \left (-\frac {10}{x}\right )+\left (-7 e^{2 x}-7 x+\left (-7 e^{2 x} x-7 x^2\right ) \log \left (-\frac {10}{x}\right )\right ) \log \left (e^{2 x}+x\right )}{3 e^{3 x} x+3 e^x x^2} \, dx \]
Optimal antiderivative \[ \frac {7 \ln \! \left ({\mathrm e}^{2 x}+x \right ) \ln \! \left (-\frac {10}{x}\right ) {\mathrm e}^{-x}}{3} \]
command
integrate((((-7*x*exp(x)**2-7*x**2)*ln(-10/x)-7*exp(x)**2-7*x)*ln(exp(x)**2+x)+(14*x*exp(x)**2+7*x)*ln(-10/x))/(3*x*exp(x)**3+3*exp(x)*x**2),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Timed out} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {7 e^{- x} \log {\left (- \frac {10}{x} \right )} \log {\left (x + e^{2 x} \right )}}{3} \]