Answer
$$\frac{1}{4}(\sinh x)^4+c$$
Work Step by Step
Let $u=\sinh x$, then $du=\cosh xdx$. Now, we have
$$\int (\sinh x)^3\cosh xdx=\int u^3du=\frac{1}{4}u^4+c\\
=\frac{1}{4}(\sinh x)^4+c$$
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