\[ \int \frac {(16+20 x) \log \left (\frac {1}{8} \left (8 x+5 x^2\right )\right )}{8 x+5 x^2} \, dx \]
Optimal antiderivative \[ \ln \left (\frac {5}{8} x^{2}+x \right )^{2} \]
command
integrate((20*x+16)*log(5/8*x^2+x)/(5*x^2+8*x),x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \log \left (\frac {5}{8} \, x^{2} + x\right )^{2} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \int \frac {4 \, {\left (5 \, x + 4\right )} \log \left (\frac {5}{8} \, x^{2} + x\right )}{5 \, x^{2} + 8 \, x}\,{d x} \]________________________________________________________________________________________