43.25 Problem number 3083

\[ \int \frac {(80-20 x) \log \left (\frac {1}{3} e^{-16+8 x-x^2} \left (-1-15 e^{16-8 x+x^2}\right )\right )}{3+45 e^{16-8 x+x^2}} \, dx \]

Optimal antiderivative \[ \frac {5 \ln \! \left (-\frac {{\mathrm e}^{-\left (4-x \right )^{2}}}{3}-5\right )^{2}}{3} \]

command

integrate((-20*x+80)*log(1/3*(-15*exp(x^2-8*x+16)-1)/exp(x^2-8*x+16))/(45*exp(x^2-8*x+16)+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

\[ \frac {160}{3} \, x^{2} - \frac {1280}{3} \, x - \frac {160}{3} \, \log \left (15 \, e^{\left (x^{2} - 8 \, x + 16\right )} + 1\right ) \]