\[ \int \frac {e^{n \tanh ^{-1}(a x)}}{(c-a c x)^4} \, dx \]
Optimal antiderivative \[ \frac {2 \left (-a x +1\right )^{-2-\frac {n}{2}} \left (a x +1\right )^{1+\frac {n}{2}}}{a \,c^{4} \left (n^{2}+10 n +24\right )}+\frac {2 \left (-a x +1\right )^{-1-\frac {n}{2}} \left (a x +1\right )^{1+\frac {n}{2}}}{a \,c^{4} \left (n^{3}+12 n^{2}+44 n +48\right )}+\frac {\left (-a x +1\right )^{-3-\frac {n}{2}} \left (a x +1\right )^{1+\frac {n}{2}}}{a \,c^{4} \left (6+n \right )} \]
command
integrate(exp(n*atanh(a*x))/(-a*c*x+c)**4,x)
Sympy 1.10.1 under Python 3.10.4 output
\[ \text {output too large to display} \]
Sympy 1.8 under Python 3.8.8 output \[ \text {Timed out} \]_____________________________________________________