Inntegrate

**bhuang** · January 11th 2010, 04:20 AM

(cosx)^n
integrate please!!!!

**HallsofIvy** · January 11th 2010, 04:36 AM

Why?

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

**TWiX** · January 11th 2010, 05:44 AM

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.

**Prove It** · January 11th 2010, 05:48 AM

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 $dv = \sin{x}\cos^{n - 2}{x}$ .

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