\[ \int \frac {4 x^5+x^3 \log (x)+\left (-32 x^3 \log \left (\frac {4}{x}\right )+64 x^3 \log \left (\frac {4}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )+\left (2 x^3 \log \left (\frac {4}{x}\right )-4 x^3 \log \left (\frac {4}{x}\right ) \log (x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )\right )}{\left (64 x^6 \log \left (\frac {4}{x}\right )+48 x^4 \log \left (\frac {4}{x}\right ) \log (x)+12 x^2 \log \left (\frac {4}{x}\right ) \log ^2(x)+\log \left (\frac {4}{x}\right ) \log ^3(x)\right ) \log \left (\log \left (\frac {4}{x}\right )\right ) \log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right ) \log \left (\log \left (\log \left (\log \left (\frac {4}{x}\right )\right )\right )\right )} \, dx \]
Optimal antiderivative \[ \frac {16-\ln \! \left (\ln \! \left (\ln \! \left (\ln \! \left (\ln \! \left (\frac {4}{x}\right )\right )\right )\right )\right )}{\left (4+\frac {\ln \left (x \right )}{x^{2}}\right )^{2}} \]
command
integrate(((-4*x**3*ln(4/x)*ln(x)+2*x**3*ln(4/x))*ln(ln(4/x))*ln(ln(ln(4/x)))*ln(ln(ln(ln(4/x))))*ln(ln(ln(ln(ln(4/x)))))+(64*x**3*ln(4/x)*ln(x)-32*x**3*ln(4/x))*ln(ln(4/x))*ln(ln(ln(4/x)))*ln(ln(ln(ln(4/x))))+x**3*ln(x)+4*x**5)/(ln(4/x)*ln(x)**3+12*x**2*ln(4/x)*ln(x)**2+48*x**4*ln(4/x)*ln(x)+64*x**6*ln(4/x))/ln(ln(4/x))/ln(ln(ln(4/x)))/ln(ln(ln(ln(4/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
\[ - \frac {x^{4} \log {\left (\log {\left (\log {\left (\log {\left (- \log {\left (x \right )} + \log {\left (4 \right )} \right )} \right )} \right )} \right )}}{16 x^{4} + 8 x^{2} \log {\left (x \right )} + \log {\left (x \right )}^{2}} + \frac {16 x^{4}}{16 x^{4} + 8 x^{2} \log {\left (x \right )} + \log {\left (x \right )}^{2}} \]