\[ \int \frac {3 x^3+4^{25 x} \left (-2 x^2-25 x^3 \log (4)\right )+e^{2 \log ^2(x)} \left (x-25\ 4^{25 x} x \log (4)+\left (-4^{1+25 x}+4 x\right ) \log (x)\right )+e^{\log ^2(x)} \left (4 x^2+4^{25 x} \left (-2 x-50 x^2 \log (4)\right )+\left (-4^{1+25 x} x+4 x^2\right ) \log (x)\right )}{x} \, dx \]
Optimal antiderivative \[ -\left (x -{\mathrm e}^{50 x \ln \left (2\right )}\right ) \left (x +{\mathrm e}^{\ln \left (x \right )^{2}}\right ) \left (-x -{\mathrm e}^{\ln \left (x \right )^{2}}\right ) \]
command
integrate((((-4*exp(50*x*ln(2))+4*x)*ln(x)-50*x*ln(2)*exp(50*x*ln(2))+x)*exp(ln(x)**2)**2+((-4*x*exp(50*x*ln(2))+4*x**2)*ln(x)+(-100*x**2*ln(2)-2*x)*exp(50*x*ln(2))+4*x**2)*exp(ln(x)**2)+(-50*x**3*ln(2)-2*x**2)*exp(50*x*ln(2))+3*x**3)/x,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ x^{3} + 2 x^{2} e^{\log {\left (x \right )}^{2}} + x e^{2 \log {\left (x \right )}^{2}} + \left (- x^{2} - 2 x e^{\log {\left (x \right )}^{2}} - e^{2 \log {\left (x \right )}^{2}}\right ) e^{50 x \log {\left (2 \right )}} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________