\[ \int \frac {-240 x-48 x^2+\left (240 x+48 x^2\right ) \log (x)+\left (\left (240 x+96 x^2\right ) \log (x)+(45+18 x) \log ^2(x)\right ) \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right ) \log \left (2 \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right )\right )}{\left (16 x \log (x)+3 \log ^2(x)\right ) \log \left (\frac {16 x+3 \log (x)}{\log (x)}\right )} \, dx \]
Optimal antiderivative \[ 3 \ln \! \left (2 \ln \! \left (3+\frac {16 x}{\ln \! \left (x \right )}\right )\right ) \left (5+x \right ) x +\ln \! \left (5\right ) \]
command
integrate((((18*x+45)*ln(x)**2+(96*x**2+240*x)*ln(x))*ln((3*ln(x)+16*x)/ln(x))*ln(2*ln((3*ln(x)+16*x)/ln(x)))+(48*x**2+240*x)*ln(x)-48*x**2-240*x)/(3*ln(x)**2+16*x*ln(x))/ln((3*ln(x)+16*x)/ln(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
\[ \left (3 x^{2} + 15 x\right ) \log {\left (2 \log {\left (\frac {16 x + 3 \log {\left (x \right )}}{\log {\left (x \right )}} \right )} \right )} \]