# Thread: Inntegrate

1. ## Inntegrate

(cosx)^n
integrate please!!!!

2. Why?

Any Calculus text book has a recursive formula for this. Look it up.

3. You should specify your "n".
Is it a positive integer?
$\int cos^{n}(x) dx = \int cos^{n-1}(x) cos(x) dx$
Use integration by parts.

4. Originally Posted by bhuang
(cosx)^n
integrate please!!!!
$\int{\cos^n{x}\,dx} = \int{\cos^2{x}\cos^{n - 2}{x}\,dx}$

$= \int{(1 - \sin^2{x})\cos^{n - 2}{x}\,dx}$

$= \int{\cos^{n - 2}{x}\,dx} - \int{\sin^2{x}\cos^{n - 2}{x}\,dx}$.

Now use integration by parts on the second integral, with $u = \sin{x}$ and $dv = \sin{x}\cos^{n - 2}{x}$.