# Math Help - Some trouble with trig integration.

1. ## Some trouble with trig integration.

∫sin^3(x)cos^2(x)dx.

I know you have to use the sin rule where you can change the sin into a 1-cos.

I'm not sure how to utilize that.

I've done u substitution where u=cos(x) and du=sin(x) but that's as far as I got before I was stuck.

Thanks!

2. Originally Posted by jelloish
∫sin^3(x)cos^2(x)dx.

I know you have to use the sin rule where you can change the sin into a 1-cos.

I'm not sure how to utilize that.

I've done u substitution where u=cos(x) and du=sin(x) but that's as far as I got before I was stuck.

Thanks!
$\int \sin^3(x)cos^2(x)dx$

$\int \sin(x)\sin^2(x)\cos^2(x)dx$

$\int \sin(x)(1-\cos^2(x))\cos^2(x)dx$

$\int \sin(x)(\cos^2(x)-\cos^4(x))dx$

$u = \cos(x)$

$-du = \sin(x)$

$-\int (u^2-u^4)du$

$\int (u^4-u^2)du$