# ∫cos(x)^2 * tan(x)^3dx

1. Feb 5, 2012

### NWeid1

1. The problem statement, all variables and given/known data
∫cos(x)^2*tan(x)^3dx

2. Relevant equations

3. The attempt at a solution

Were learning Integration by parts and u substitution but this one I can't figure out. I tried making it ∫cos(x)*(sin(x)^3)/(cos(x)^3)dx and then ∫tan(x)*sin(x)^2 but I don't know if I'm going in the right direction because I don't know how to solve from here.

2. Feb 6, 2012

### SammyS

Staff Emeritus
Re: ∫cos(x)^2*tan(x)^3dx

That should be $\displaystyle \int\frac{\cos^2(x)\sin^3(x)}{\cos^3(x)}\,dx$

The integrand can be simplified to:
$\displaystyle \frac{\sin^3(x)}{\cos(x)}$​
Then change sin3(x) to (sin(x))(1-cos2(x))

The integrand becomes:
$\displaystyle \frac{\sin(x)}{\cos(x)}-\sin(x)\cos(x)$​