\[ \int \frac {e^{14 x/5} \left (-360-165 x-15 x^2\right )+\left (45 x+15 x^2+e^{14 x/5} \left (888 x+447 x^2+42 x^3\right )\right ) \log (x)+\left (-360-165 x-15 x^2+\left (-120 x-15 x^2\right ) \log (x)\right ) \log (8+x)}{\left (360 x+285 x^2+70 x^3+5 x^4\right ) \log ^2(x)} \, dx \]
Optimal antiderivative \[ \frac {3 \,{\mathrm e}^{2 x} {\mathrm e}^{\frac {4 x}{5}}+3 \ln \! \left (8+x \right )}{\left (3+x \right ) \ln \! \left (x \right )} \]
command
integrate((((-15*x**2-120*x)*ln(x)-15*x**2-165*x-360)*ln(x+8)+((42*x**3+447*x**2+888*x)*exp(2/5*x)**2*exp(x)**2+15*x**2+45*x)*ln(x)+(-15*x**2-165*x-360)*exp(2/5*x)**2*exp(x)**2)/(5*x**4+70*x**3+285*x**2+360*x)/ln(x)**2,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {Exception raised: TypeError} \]
Sympy 1.8 under Python 3.8.8 output
\[ \frac {3 e^{\frac {14 x}{5}}}{x \log {\left (x \right )} + 3 \log {\left (x \right )}} + \frac {3 \log {\left (x + 8 \right )}}{x \log {\left (x \right )} + 3 \log {\left (x \right )}} \]