\[ \int \frac {-4-4 x+2 x^2+5 x^3+2 x^4+\left (7 x^2+6 x^3\right ) \log \left (\frac {3 e^{x+x^2}}{4}\right )+\left (-2+3 x+6 x^2\right ) \log ^2\left (\frac {3 e^{x+x^2}}{4}\right )+(1+2 x) \log ^3\left (\frac {3 e^{x+x^2}}{4}\right )}{x^3+3 x^2 \log \left (\frac {3 e^{x+x^2}}{4}\right )+3 x \log ^2\left (\frac {3 e^{x+x^2}}{4}\right )+\log ^3\left (\frac {3 e^{x+x^2}}{4}\right )} \, dx \]
Optimal antiderivative \[ \left (\frac {1}{\ln \left (\frac {3 \,{\mathrm e}^{x} {\mathrm e}^{x^{2}}}{4}\right )+x}-x \right )^{2}+x +1 \]
command
integrate(((1+2*x)*log(3/4*exp(x)*exp(x^2))^3+(6*x^2+3*x-2)*log(3/4*exp(x)*exp(x^2))^2+(6*x^3+7*x^2)*log(3/4*exp(x)*exp(x^2))+2*x^4+5*x^3+2*x^2-4*x-4)/(log(3/4*exp(x)*exp(x^2))^3+3*x*log(3/4*exp(x)*exp(x^2))^2+3*x^2*log(3/4*exp(x)*exp(x^2))+x^3),x, algorithm="maxima")
Maxima 5.46 SBCL 2.0.1.debian via sagemath 9.6 output
\[ \text {output too large to display} \]
Maxima 5.44 via sagemath 9.3 output \[ \text {Timed out} \]_____________________________________________________