need help integrating x^2cos(x^2)dx

• Mar 26th 2008, 01:11 PM
ihaveamathproblem
need help integrating x^2cos(x^2)dx
i know that i need to use integration by parts but i am stuck on picking my u and dv

EDIT: the problem is the integral of 2xcos(x^2)dx sorry
• Mar 26th 2008, 01:28 PM
galactus
At first glance, I thought this was a Fresnel integral. Which is more difficult. But it is actually much easier than that.

Just use substitution instead of parts.

$2\int{xcos(x^{2})}dx$

Let $u=x^{2}, \;\ du=2xdx$

$\int{cos(u)}du=sin(u)$

$=sin(x^{2})$