\[ \int \frac {75+90 x+3 x^2+\left (120 x-24 x^2+\left (75-30 x+3 x^2\right ) \log \left (\frac {x}{e}\right )\right ) \log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right ) \log \left (-\log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right )\right )}{\left (40 x-8 x^2+\left (25-10 x+x^2\right ) \log \left (\frac {x}{e}\right )\right ) \log \left (\frac {-8 x+(-5+x) \log \left (\frac {x}{e}\right )}{-5+x}\right )} \, dx \]
Optimal antiderivative \[ 3 x \ln \! \left (-\ln \! \left (\ln \! \left ({\mathrm e}^{-1} x \right )+\frac {8 x}{5-x}\right )\right ) \]
command
integrate((((3*x**2-30*x+75)*ln(x/exp(1))-24*x**2+120*x)*ln(((-5+x)*ln(x/exp(1))-8*x)/(-5+x))*ln(-ln(((-5+x)*ln(x/exp(1))-8*x)/(-5+x)))+3*x**2+90*x+75)/((x**2-10*x+25)*ln(x/exp(1))-8*x**2+40*x)/ln(((-5+x)*ln(x/exp(1))-8*x)/(-5+x)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \left (3 x - \frac {5}{2}\right ) \log {\left (- \log {\left (\frac {- 8 x + \left (x - 5\right ) \log {\left (\frac {x}{e} \right )}}{x - 5} \right )} \right )} + \frac {5 \log {\left (\log {\left (\frac {- 8 x + \left (x - 5\right ) \log {\left (\frac {x}{e} \right )}}{x - 5} \right )} \right )}}{2} \]