\[ \int \frac {e^{4 x \log (5) \log \left (e^{3 x}-x\right )} \left (-100 x \log (5)+300 e^{3 x} x \log (5)+\left (100 e^{3 x} \log (5)-100 x \log (5)\right ) \log \left (e^{3 x}-x\right )\right )}{e^{3 x}-x} \, dx \]
Optimal antiderivative \[ 25 \,{\mathrm e}^{4 x \ln \left (5\right ) \ln \left ({\mathrm e}^{3 x}-x \right )} \]
command
integrate(((100*log(5)*exp(x)^3-100*x*log(5))*log(exp(x)^3-x)+300*x*log(5)*exp(x)^3-100*x*log(5))*exp(2*x*log(5)*log(exp(x)^3-x))^2/(exp(x)^3-x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {could not integrate} \]
Giac 1.7.0 via sagemath 9.3 output
\[ 25 \, e^{\left (4 \, x \log \left (5\right ) \log \left (-x + e^{\left (3 \, x\right )}\right )\right )} \]