Question

How do I start this?
\[\int\limits \cos^5(2x)\sqrt[7]{\sin(2x)}dx\]

Answer 1

realize that\[\sqrt[7]{\sin(2x)} = (\sin(2x))^{1/7}\]
and using the identity:\[\sin^2 \theta + \cos^2 \theta = 1\]\[\cos^2 \theta = 1 - \sin^2 \theta\]
we are now looking at:\[\int\limits_{}^{}(1- \sin^2(2x))^2(\sin(2x))^{1/7}\cos(2x) dx\]

expand and seperate as needed. use u = sin(2x) du = cos(2x)dx for each separation

let me knwo if i should continue ^_^

Answer 2

argh, du = 2cos(2x)dx

Answer 3

Thanks a lot. I think I know where to go now.