\[ \int \frac {e^{-9-\log ^2\left (\frac {1}{16} \left (4 x^2-\log (x)\right )\right )} \left (4 x^2-\log (x)\right )^6 \left (30-240 x^2+\left (-10+80 x^2\right ) \log \left (\frac {1}{16} \left (4 x^2-\log (x)\right )\right )\right )}{16777216 \left (-4 x^3+x \log (x)\right )} \, dx \]
Optimal antiderivative \[ 5 \,{\mathrm e}^{-\left (3-\ln \left (\frac {x^{2}}{4}+\ln \left (\frac {1}{x^{\frac {1}{16}}}\right )\right )\right )^{2}} \]
command
integrate(((80*x**2-10)*ln(1/4*x**2-1/16*ln(x))-240*x**2+30)/(x*ln(x)-4*x**3)/exp(ln(1/4*x**2-1/16*ln(x))**2-6*ln(1/4*x**2-1/16*ln(x))+9),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \frac {\left (20480 x^{12} - 30720 x^{10} \log {\left (x \right )} + 19200 x^{8} \log {\left (x \right )}^{2} - 6400 x^{6} \log {\left (x \right )}^{3} + 1200 x^{4} \log {\left (x \right )}^{4} - 120 x^{2} \log {\left (x \right )}^{5} + 5 \log {\left (x \right )}^{6}\right ) e^{- \log {\left (\frac {x^{2}}{4} - \frac {\log {\left (x \right )}}{16} \right )}^{2} - 9}}{16777216} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________