Integral of cos^3 theta

1. Oct 20, 2004

redshift

Would very much appreciate a hint on how to start this off.
So far I have cos theta = (1-t^2)/(1+t^2). After squaring this and doing various substitutions, I get (cos theta)^3, which can't be right.

2. Oct 20, 2004

Tide

I'm not sure what you're asking but if you want the integral indicated in the title of your post this may help:

$$\cos^3 \theta = \cos^2 \theta \cos \theta = \left(1-\sin^2 \theta \right) \frac {d \sin \theta}{d\theta}$$

3. Oct 20, 2004

redshift

Many thanks. I'll give it a shot.

4. Oct 20, 2004

redshift

I got cos theta - (1/3)cos^3 theta + C
Does this look right?

5. Oct 20, 2004

Fredrik

Staff Emeritus
Almost. It should be sin, not cos.