\[ \int \frac {5 e^{2 x/5} x^2 \log (16)+(-60+15 x) \log (16)+e^{2 x/5} \left (-8 x^2+2 x^3\right ) \log (16) \log (4-x)+(20-5 x) \log (16) \log \left (2 x^3\right )}{-20 x^2+5 x^3} \, dx \]
Optimal antiderivative \[ 4 \left ({\mathrm e}^{\frac {2 x}{5}} \ln \left (4-x \right )+\frac {\ln \left (2 x^{3}\right )}{x}\right ) \ln \left (2\right ) \]
command
integrate((4*(-5*x+20)*log(2)*log(2*x^3)+4*(2*x^3-8*x^2)*log(2)*exp(1/5*x)^2*log(-x+4)+20*x^2*log(2)*exp(1/5*x)^2+4*(15*x-60)*log(2))/(5*x^3-20*x^2),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ 4 \, e^{\left (\frac {2}{5} \, x\right )} \log \left (2\right ) \log \left (-x + 4\right ) + \frac {4 \, \log \left (2\right )^{2}}{x} + \frac {4 \, \log \left (2\right ) \log \left ({\left (x - 4\right )}^{3} + 12 \, {\left (x - 4\right )}^{2} + 48 \, x - 128\right )}{x} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Timed out} \]________________________________________________________________________________________