44.53 Problem number 3715

\[ \int \frac {-3 e^x x+e^{2 x} x^2+\left (12+4 e^x x^2\right ) \log \left (\frac {9-6 e^x x+e^{2 x} x^2}{e^{8/5} x^2}\right )+\left (3 x-e^x x^2\right ) \log ^2\left (\frac {9-6 e^x x+e^{2 x} x^2}{e^{8/5} x^2}\right )}{-3 e^x x+e^{2 x} x^2} \, dx \]

Optimal antiderivative \[ x +\ln \! \left (\left ({\mathrm e}^{x}-\frac {3}{x}\right )^{2} {\mathrm e}^{-\frac {8}{5}}\right )^{2} {\mathrm e}^{-x} \]

command

integrate(((-exp(x)*x**2+3*x)*ln((exp(x)**2*x**2-6*exp(x)*x+9)/x**2/exp(4/5)**2)**2+(4*exp(x)*x**2+12)*ln((exp(x)**2*x**2-6*exp(x)*x+9)/x**2/exp(4/5)**2)+exp(x)**2*x**2-3*exp(x)*x)/(exp(x)**2*x**2-3*exp(x)*x),x)

Sympy 1.10.1 under Python 3.10.4 output

\[ \text {Timed out} \]

Sympy 1.8 under Python 3.8.8 output

\[ x + e^{- x} \log {\left (\frac {x^{2} e^{2 x} - 6 x e^{x} + 9}{x^{2} e^{\frac {8}{5}}} \right )}^{2} \]