\[ \int \frac {e^{-\frac {-50 x+25 x^2}{-56 x+20 x^2+4 x^3+(7+x) \log (5)}} \left (3136 x^2-2240 x^3-48 x^4+160 x^5+16 x^6+\left (-784 x+168 x^2+96 x^3+8 x^4\right ) \log (5)+\left (49+14 x+x^2\right ) \log ^2(5)+\left (400 x^3-400 x^4+100 x^5+\left (350 x-350 x^2-25 x^3\right ) \log (5)\right ) \log (x)\right )}{3136 x^3-2240 x^4-48 x^5+160 x^6+16 x^7+\left (-784 x^2+168 x^3+96 x^4+8 x^5\right ) \log (5)+\left (49 x+14 x^2+x^3\right ) \log ^2(5)} \, dx \]
Optimal antiderivative \[ \ln \left (x \right ) {\mathrm e}^{-\frac {5 x}{4 \left (\frac {\ln \left (5\right )}{4 x -8}+x \right ) \left (\frac {7}{5}+\frac {x}{5}\right )}} \]
command
integrate((((-25*x**3-350*x**2+350*x)*ln(5)+100*x**5-400*x**4+400*x**3)*ln(x)+(x**2+14*x+49)*ln(5)**2+(8*x**4+96*x**3+168*x**2-784*x)*ln(5)+16*x**6+160*x**5-48*x**4-2240*x**3+3136*x**2)/((x**3+14*x**2+49*x)*ln(5)**2+(8*x**5+96*x**4+168*x**3-784*x**2)*ln(5)+16*x**7+160*x**6-48*x**5-2240*x**4+3136*x**3)/exp((25*x**2-50*x)/((x+7)*ln(5)+4*x**3+20*x**2-56*x)),x)
Sympy 1.10.1 under Python 3.10.4 output
\[ e^{- \frac {25 x^{2} - 50 x}{4 x^{3} + 20 x^{2} - 56 x + \left (x + 7\right ) \log {\left (5 \right )}}} \log {\left (x \right )} \]
Sympy 1.8 under Python 3.8.8 output
\[ \text {Timed out} \]________________________________________________________________________________________