1. integration

Thanks!

2. Originally Posted by turtle
Thanks!
You can write,
$\int (1+\cos x)(1-\cos x) dx$
By difference of two squares.
Now, use integration by parts.

3. There's nothing wrong with what TPH is doing :-),

I personally hate integration by parts. It's long and dreaful, personally:

$\int 1 - cos^2 x\,dx$
$=\int sin^2 x\,dx$, using double angle formula for cos2x,
$=\int \frac{1 - cos2x}{2}\,dx$
$=\int \frac{1}{2} - \frac{cos2x}{2}\,dx$
$=\frac{x}{2} - \frac{sin2x}{4} + C$