# Thread: Integration of powers of sin and cosine.

1. ## 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.

2. So just let $u=Sin(\frac{x}{2})$

Then $du=\frac{1}{2} Cos(\frac{x}{2}) dx$, and go through from there as normal with the substitution.

Alternatively, use the rule that $\int f'(x)[f(x)]^n dx=\frac{f(x)^{n+1}}{n+1}+C$ and manipulate slightly.

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