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.

I tried to use WolframAlpha but no standard integral found.
So, you can approximate the function to an easier function.
cos(sin(x)) = a cos(bx)+c
if a = 0.25, b = 2, c = 0.75
then the approximation is almost inline with the function (I used a plotting program for this conclusion).
$$
\int f(x)dx = \int 0.25\cos(2x)+0.75\ dx \\= 0.5\sin(2x)\ +0.75x+C
$$
