# Integration using substitution

1. Dec 7, 2007

### 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.

Last edited: Dec 7, 2007
2. Dec 7, 2007

### Office_Shredder

Staff Emeritus
Try letting $$u=sin \theta$$

3. Dec 7, 2007

### Dick

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

4. Dec 7, 2007

### SticksandStones

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.