\[ \int \frac {a+b x^n}{\left (c+d x^n\right )^4} \, dx \]
Optimal antiderivative \[ -\frac {\left (-a d +b c \right ) x}{3 c d n \left (c +d \,x^{n}\right )^{3}}+\frac {\left (b c -a d \left (1-3 n \right )\right ) x \hypergeom \left (\left [3, \frac {1}{n}\right ], \left [1+\frac {1}{n}\right ], -\frac {d \,x^{n}}{c}\right )}{3 c^{4} d n} \]
command
integrate((a+b*x**n)/(c+d*x**n)**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 \[ \text {Timed out} \]_____________________________________________________