\[ \int \frac {-80 e^{\frac {2}{5} (10-7 x)}+e^{\frac {2}{5} (10-7 x)} (-40-56 x) \log \left (x^2\right )}{5 x^3 \log ^3\left (x^2\right ) \log (\log (5))} \, dx \]
Optimal antiderivative \[ \frac {4 \,{\mathrm e}^{-\frac {14 x}{5}+4}}{\ln \left (x^{2}\right )^{2} \ln \left (\ln \left (5\right )\right ) x^{2}} \]
command
Int[(-80*E^((2*(10 - 7*x))/5) + E^((2*(10 - 7*x))/5)*(-40 - 56*x)*Log[x^2])/(5*x^3*Log[x^2]^3*Log[Log[5]]),x]
Rubi 4.17.3 under Mathematica 13.3.1 output
\[ \frac {4 e^{4-\frac {14 x}{5}}}{x^2 \log (\log (5)) \log ^2\left (x^2\right )} \]
Rubi 4.16.1 under Mathematica 13.3.1 output
\[ \int \frac {-80 e^{\frac {2}{5} (10-7 x)}+e^{\frac {2}{5} (10-7 x)} (-40-56 x) \log \left (x^2\right )}{5 x^3 \log ^3\left (x^2\right ) \log (\log (5))} \, dx \]________________________________________________________________________________________