# How do you integrate int tcosht using integration by parts?

Jan 12, 2017

$t \sinh t - \cosh t + C$

#### Explanation:

It is important to know the IBP formula

$I = \int u v ' \mathrm{dx} = u v - \int v u ' \mathrm{dx}$

$I = \int t \cosh t \mathrm{dt}$

$u = t \implies u ' = 1$

$v ' = \cosh t \implies v = \sinh t$

$I = t \sinh t - \int \sinh t \mathrm{dt}$

$I = t \sinh t - \cosh t + C$