Double substitution when integrating. I need to integrate
$$f(x) = \cos(\sin x)$$
my first thought was substituting so that $u = \cos(x)$, but that doesn't seem to do the trick. Is there any way to do a double substitution on this?
Any ways on how to proceed would be appreciated.

Or you also can solve it numerically by expand the function (e.g. use Taylor expansion) 
and then integrate each of its terms (e.g. first 5 terms).
