# Math Help - Insane Integrals

1. ## Insane Integrals

Stuff like this makes me want to drop out.

$\int\sin^5 (4x) \cos^2 (4x)dx$

I think I would be fine if it weren't for those coefficients in there.

Thanks

2. Originally Posted by Chicken Enchilada
Stuff like this makes me want to drop out.

$\int\sin^5 (4x) \cos^2 (4x)dx$

I think I would be fine if it weren't for those coefficients in there.

Thanks
Since sine is raise to an odd power, break off a factor of sine:

$\int\sin^5\!\left(4x\right)\cos^2\!\left(4x\right) \,dx=\int\left[\sin^2\!\left(4x\right)\right]^2\cos^2\!\left(4x\right)\sin\!\left(4x\right)\,dx$

Now apply the identity $\sin^2u=1-\cos^2u$ to get:

$\int\left[1-\cos^2\!\left(4x\right)\right]^2\cos^2\!\left(4x\right)\sin\!\left(4x\right)\,dx$.

Now let $u=\cos\!\left(4x\right)\implies -\tfrac{1}{4}\,du=\sin\!\left(4x\right)\,dx$.

Can you take it from here?