43.10 Problem number 1596

\[ \int \frac {e^{\frac {2}{5} \left (5 e^{\frac {-2 e^2+x \log ^2\left (\frac {2+3 x}{x}\right )}{x^2}}-x\right )} \left (-4 x^3-6 x^4+e^{\frac {-2 e^2+x \log ^2\left (\frac {2+3 x}{x}\right )}{x^2}} \left (e^2 (80+120 x)-40 x \log \left (\frac {2+3 x}{x}\right )+\left (-20 x-30 x^2\right ) \log ^2\left (\frac {2+3 x}{x}\right )\right )\right )}{10 x^3+15 x^4} \, dx \]

Optimal antiderivative \[ {\mathrm e}^{2 \,{\mathrm e}^{\frac {\ln \left (4-\frac {-2+x}{x}\right )^{2}-\frac {2 \,{\mathrm e}^{2}}{x}}{x}}-\frac {2 x}{5}} \]

command

integrate((((-30*x^2-20*x)*log((2+3*x)/x)^2-40*x*log((2+3*x)/x)+(120*x+80)*exp(2))*exp((x*log((2+3*x)/x)^2-2*exp(2))/x^2)-6*x^4-4*x^3)*exp(exp((x*log((2+3*x)/x)^2-2*exp(2))/x^2)-1/5*x)^2/(15*x^4+10*x^3),x, algorithm="giac")

Giac 1.9.0-11 via sagemath 9.6 output

\[ \text {could not integrate} \]

Giac 1.7.0 via sagemath 9.3 output

\[ e^{\left (-\frac {2}{5} \, x + 2 \, e^{\left (\frac {\log \left (\frac {2}{x} + 3\right )^{2}}{x} - \frac {2 \, e^{2}}{x^{2}}\right )}\right )} \]