Thread: Integration of powers of sin and cosine.

I suspect this is a simple problem and I'm just missing something obvious ... but I can't seem to figure it out. Here it is:

Integrate: sin^4(x/2) * cos (x/2)

I'm aware that the sine function is to an even power and cosine to an odd, and normally you'd use the substitution u=sinx in this case. It's the x/2 part that's throwing me off here. Any help appreciated, thank you.

So just let

Then , and go through from there as normal with the substitution.

Alternatively, use the rule that and manipulate slightly.

^ Ah of course, staring me in the face the whole time... many thanks pal!