Trig function within a trig function

[Audiophile]

I need some help with the problem

Integral (sin x cos (cos x)) dx

I've done it like this

u = cos x
du/dx = sin x
1/sin x du = dx
1/sin x (Integral (sin x cos u) du)
Integral cos u du
sin u
sin (cos x)

I'm pretty sure this isn't right, though.
Could anyone give me some pointers, please? Thanks.

 

[daon]

\(\displaystyle \L \int sinx \cdot cos(cos(x))dx\)

Let \(\displaystyle u=cosx\), then \(\displaystyle du=-sin(x)dx\)

Then you have:

\(\displaystyle \L -\int cos udu\)

 

[Audiophile]

Thank You! I feel sort of stupid that I missed such a little thing. Oh, well.
That's part of learning.