Calculus (3rd Edition)

Given $$\int x\ \ \sinh x\ d x$$ Use integration by parts: $$u= x \Rightarrow du= dx$$ $$dv=\sinh x \ dx \Rightarrow v= \cosh x$$ So, we get \begin{aligned} I&=\int x\ \sinh x\ d x\\ &=uv - \int vdu\\ &= x \cosh x-\int \cosh x dx\\ &= x \cosh x- \sinh x +C \end{aligned}