\[ \int \frac {-4 \log (5) \log ^2\left (\frac {16}{x^2}\right )+e^{\frac {x}{\log \left (\frac {16}{x^2}\right )}} \left (8 x-8 x^2+\left (4 x-4 x^2\right ) \log \left (\frac {16}{x^2}\right )-4 \log ^2\left (\frac {16}{x^2}\right )\right )}{3 x^2 \log ^2\left (\frac {16}{x^2}\right )} \, dx \]
Optimal antiderivative \[ \frac {\left ({\mathrm e}^{\frac {x}{\ln \left (\frac {16}{x^{2}}\right )}}+\ln \! \left (5\right )\right ) \left (4-4 x \right )}{3 x} \]
command
integrate(1/3*((-4*ln(16/x**2)**2+(-4*x**2+4*x)*ln(16/x**2)-8*x**2+8*x)*exp(x/ln(16/x**2))-4*ln(5)*ln(16/x**2)**2)/x**2/ln(16/x**2)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {\left (4 - 4 x\right ) e^{\frac {x}{\log {\left (\frac {16}{x^{2}} \right )}}}}{3 x} + \frac {4 \log {\left (5 \right )}}{3 x} \]