\[ \int \frac {\left (-x-16 e x^2-64 x^4\right ) \log (x)+\left (-e^2-x-8 e x^2-16 x^4+\left (e^2+x+8 e x^2+16 x^4\right ) \log (x)\right ) \log \left (e^2+x+8 e x^2+16 x^4\right )+\left (e^2+x+8 e x^2+16 x^4+\left (-e^2-x-8 e x^2-16 x^4\right ) \log (x)+\left (e^2+x+8 e x^2+16 x^4\right ) \log ^2(x)\right ) \log ^2\left (e^2+x+8 e x^2+16 x^4\right )}{\left (e^2+x+8 e x^2+16 x^4\right ) \log ^2(x) \log ^2\left (e^2+x+8 e x^2+16 x^4\right )} \, dx \]
Optimal antiderivative \[ x +\frac {\frac {x}{\ln \left (x +\left ({\mathrm e}+4 x^{2}\right )^{2}\right )}-x}{\ln \left (x \right )} \]
command
integrate((((exp(1)^2+8*x^2*exp(1)+16*x^4+x)*log(x)^2+(-exp(1)^2-8*x^2*exp(1)-16*x^4-x)*log(x)+exp(1)^2+8*x^2*exp(1)+16*x^4+x)*log(exp(1)^2+8*x^2*exp(1)+16*x^4+x)^2+((exp(1)^2+8*x^2*exp(1)+16*x^4+x)*log(x)-exp(1)^2-8*x^2*exp(1)-16*x^4-x)*log(exp(1)^2+8*x^2*exp(1)+16*x^4+x)+(-16*x^2*exp(1)-64*x^4-x)*log(x))/(exp(1)^2+8*x^2*exp(1)+16*x^4+x)/log(x)^2/log(exp(1)^2+8*x^2*exp(1)+16*x^4+x)^2,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \frac {x \log \left (16 \, x^{4} + 8 \, x^{2} e + x + e^{2}\right ) \log \left (x\right ) - x \log \left (16 \, x^{4} + 8 \, x^{2} e + x + e^{2}\right ) + x}{\log \left (16 \, x^{4} + 8 \, x^{2} e + x + e^{2}\right ) \log \left (x\right )} \]
Giac 1.7.0 via sagemath 9.3 output
\[ \text {Exception raised: TypeError} \]________________________________________________________________________________________