Answer
$$\frac{1}{8}x^8+\frac{1}{4}x^4 +\frac{1}{4}\ln|x^4-1|+C$$
Work Step by Step
Given $$\int \frac{x^{11}}{x^{4}-1} d x$$
Use long division
\begin{align*}
\int \frac{x^{11}}{x^{4}-1} d x&= \int \left(x^7+x^3+\frac{x^3}{x^4-1}\right)dx\\
&= \frac{1}{8}x^8+\frac{1}{4}x^4 +\frac{1}{4}\ln|x^4-1|+C
\end{align*}
