Chapter 8 - Techniques of Integration - Chapter Review Exercises - Page 460: 60

$$\frac{1}{4} \sinh ^{4} x+C$$

Given $$\int \sinh ^{3} x \cosh x d x$$ Let $$ u= \sinh u\ \ \ \ \ \ du =\cosh udu$$ Then \begin{aligned} \int \sinh ^{3} x \cosh x d x &=\int u^{3} d u \\ &=\frac{u^{4}}{4}+C \\ &=\frac{1}{4} \sinh ^{4} x+C \end{aligned}