# How do you integrate int (2x+3)sin(x^2+3x) by integration by parts method?

Feb 8, 2017

The integrand is perfect for $u$-substitution.

I think using I.B.P would get really messy; especially if you're familiar with the L.I.A.T.E mnemonic . . .

You'd end up having to find the antiderivative of $\sin \left({x}^{2} + 3 x\right)$ which is REALLY ugly.

#### Explanation:

Just by looking at the integrand, we should let:

$u = {x}^{2} + 3 x$
$\mathrm{du} = 2 x + 3 \mathrm{dx}$

$\int \sin \left(u\right) \mathrm{du}$

$= - \cos \left(u\right) + C$

Plug $u$ back in:

$= - \cos \left({x}^{2} + 3 x\right) + C$