Integration of sin⁶θ cos θ using substitution

[SticksandStones]

[SOLVED] Integration using substitution

Problem: Find the integral of:
$$\int\sin^{6}\theta\cos\theta d\theta$$

My attempt:

Let $$u\equiv\cos\theta$$
so: $$du\equiv\sin\thetad\theta$$

Only I don't know where to go from there.

The book says it should $$\frac{1}{7}\sin^{7}\theta+C$$ but I have no idea how they got that.

I'm probably missing something obvious here.

 

[Office_Shredder]

Try letting $$u=sin \theta$$

 

[Dick]

Your are much better off letting u=sin(x).

 

[SticksandStones]

Your are much better off letting u=sin(x).

Ah, that was the totally obvious thing I was missing. For some reason, I decided that the derivative of Sin(x) was...Sin(x)...

Thanks guys.