Forgot my trig integral tricks

[pergradus]

Homework Statement

∫[sin⁴(t)cos²(t) + cos⁴(t)sin²(t)]dt

The Attempt at a Solution

Is there any way to do this integral using a substitution, or do I need to just split it into two integrals and apply a very messy series of half-angle identities?

Thanks.

 

[Dick]

I would first factor cos(t)^2*sin(t)^2 out and look at what's left.

 

[pergradus]

DOH! That was stupid... finished. :)

Thanks a ton! BTW, this integral is involved in the area of a hypercycloid, which apparently is 3πa²/8.