simple u-du

[Whatupdoc]

how would i find the anti-derv. of (cos(2x)). im really confused with sub.

ok i'll use u-du

u = 2x
du = 2 dx
dx = 1/2 du

k so... cos(u)*dx

since the dx is there, you plug in the dx that i found right? so... sin(2x)1/2

ok so that's a simple integration problem, can someone give me a harder problem and show me how to find "dx", that's what im really confused about.

[plover]

So if in general:
u = f(x)
du = f'(x) dx
dx = du/f'(x)
Find the anti-derivative of:
cos(cos(x)) ⋅ sin(x)
and use:
u = cos(x)
as a substitution.