\[ \int \frac {e^{16 x^8} (-839808-209952 x)+e^{16 x^8} \left (10917504 x^7+6718464 x^8+839808 x^9\right ) \log \left (13+8 x+x^2\right )+e^{12 x^8} (279936+69984 x) \log ^4\left (13+8 x+x^2\right )+e^{12 x^8} \left (-3639168 x^7-2239488 x^8-279936 x^9\right ) \log ^5\left (13+8 x+x^2\right )+e^{8 x^8} (-31104-7776 x) \log ^8\left (13+8 x+x^2\right )+e^{8 x^8} \left (404352 x^7+248832 x^8+31104 x^9\right ) \log ^9\left (13+8 x+x^2\right )+e^{4 x^8} (1152+288 x) \log ^{12}\left (13+8 x+x^2\right )+e^{4 x^8} \left (-14976 x^7-9216 x^8-1152 x^9\right ) \log ^{13}\left (13+8 x+x^2\right )}{\left (13+8 x+x^2\right ) \log ^{17}\left (13+8 x+x^2\right )} \, dx \]
Optimal antiderivative \[ \left (\frac {9 \,{\mathrm e}^{4 x^{8}}}{\ln \! \left (\left (4+x \right )^{2}-3\right )^{4}}-1\right )^{4} \]
command
integrate(((-1152*x^9-9216*x^8-14976*x^7)*exp(x^8)^4*log(x^2+8*x+13)^13+(288*x+1152)*exp(x^8)^4*log(x^2+8*x+13)^12+(31104*x^9+248832*x^8+404352*x^7)*exp(x^8)^8*log(x^2+8*x+13)^9+(-7776*x-31104)*exp(x^8)^8*log(x^2+8*x+13)^8+(-279936*x^9-2239488*x^8-3639168*x^7)*exp(x^8)^12*log(x^2+8*x+13)^5+(69984*x+279936)*exp(x^8)^12*log(x^2+8*x+13)^4+(839808*x^9+6718464*x^8+10917504*x^7)*exp(x^8)^16*log(x^2+8*x+13)+(-209952*x-839808)*exp(x^8)^16)/(x^2+8*x+13)/log(x^2+8*x+13)^17,x, algorithm="giac")
Giac 1.9.0-11 via sagemath 9.6 output
\[ \text {Timed out} \]
Giac 1.7.0 via sagemath 9.3 output
\[ -\frac {9 \, {\left (4 \, e^{\left (4 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{12} - 54 \, e^{\left (8 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{8} + 324 \, e^{\left (12 \, x^{8}\right )} \log \left (x^{2} + 8 \, x + 13\right )^{4} - 729 \, e^{\left (16 \, x^{8}\right )}\right )}}{\log \left (x^{2} + 8 \, x + 13\right )^{16}} \]