What is the integral of sin^3 theta?

[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.

 

[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:

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

 

[redshift]

Many thanks. I'll give it a shot.

 

[redshift]

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

 

[Fredrik]

Almost. It should be sin, not cos.