Integrals

what is the integral of
(sin2x)^3
- working needed
also need integral of
(tan(x/2))^2 - book's hint: (sec(x/2))^2 - 1

ty in advance

If you don't do it yourself, how will you learn

You have sin(2x)^3 = sin(2x)(sin(2x)^2)=sin(2x)(1-cos(2x)^2)

Now try substitution and see if you can do it. I have to go to work so that's as far as i'm taking you.

OP here: <3 anon - figured out the second one with a hint in the book, thank's for the hint i got them both now

thanks*

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let u = sin2x
du/dx=2cos2x

The integral becomes int {u^3 * dx/du * du}
=1/4U^4*2cos2x
Put U back in terms of x

1/2*cos(2x)(sin(2x))^4