\[ \int \frac {e^{n \coth ^{-1}(a x)}}{(c-a c x)^3} \, dx \]
Optimal antiderivative \[ -\frac {\left (3+n \right ) \left (1-\frac {1}{a x}\right )^{-1-\frac {n}{2}} \left (1+\frac {1}{a x}\right )^{1+\frac {n}{2}}}{a \,c^{3} \left (n^{2}+6 n +8\right )}+\frac {\left (1-\frac {1}{a x}\right )^{-2-\frac {n}{2}} \left (1+\frac {1}{a x}\right )^{1+\frac {n}{2}}}{a \,c^{3} \left (4+n \right )} \]
command
integrate(exp(n*acoth(a*x))/(-a*c*x+c)**3,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 \[ \text {output too large to display} \]_____________________________________________________