# How do you integrate int sinsqrtx by parts?

Jun 2, 2018

$2 \sqrt{x} \cdot \cos \left(\sqrt{x}\right) - 2 \sin \left(\sqrt{x}\right) + C$

#### Explanation:

Substituting $t = \sqrt{x}$ then we get
$\mathrm{dx} = 2 t \mathrm{dt}$
and we have to solve
$2 \int t \sin \left(t\right) \mathrm{dt}$
By partial Integration we get
$\int t \sin \left(t\right) \mathrm{dt} = t \cos \left(t\right) - \int \cos \left(t\right) \mathrm{dt}$
so we get
$2 t \cos \left(t\right) - 2 \sin \left(t\right) + C$
$2 \sqrt{x} \cos \left(\sqrt{x}\right) - 2 \sin \left(\sqrt{x}\right) + C$