\[ \int \frac {3-x+e^x \left (-3-5 x-x^2+x^3\right ) \log (16)+\left (-x+e^x \left (1+x^2\right ) \log (16)\right ) \log \left (x+e^x \left (-1-x^2\right ) \log (16)\right ) \log \left (\log \left (x+e^x \left (-1-x^2\right ) \log (16)\right )\right )}{\left (-x+e^x \left (1+x^2\right ) \log (16)\right ) \log \left (x+e^x \left (-1-x^2\right ) \log (16)\right )} \, dx \]
Optimal antiderivative \[ \left (-3+x \right ) \ln \! \left (\ln \! \left (x -4 \ln \! \left (2\right ) \left ({\mathrm e}^{x} x^{2}+{\mathrm e}^{x}\right )\right )\right ) \]
command
integrate(((4*(x**2+1)*ln(2)*exp(x)-x)*ln(4*(-x**2-1)*ln(2)*exp(x)+x)*ln(ln(4*(-x**2-1)*ln(2)*exp(x)+x))+4*(x**3-x**2-5*x-3)*ln(2)*exp(x)+3-x)/(4*(x**2+1)*ln(2)*exp(x)-x)/ln(4*(-x**2-1)*ln(2)*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
\[ \left (x - 1\right ) \log {\left (\log {\left (x + \left (- 4 x^{2} - 4\right ) e^{x} \log {\left (2 \right )} \right )} \right )} - 2 \log {\left (\log {\left (x + \left (- 4 x^{2} - 4\right ) e^{x} \log {\left (2 \right )} \right )} \right )} \]