Question: > 
> Evaluate $\int \cos(\cos x)~dx$
> 
> 
> 

I tried to use chain rule but failed. Can anyone help me please?

Answer: 
The indefinite integral has no simpler form (known), but there are some definite integrals, like this
$$
\int\_0^{\pi/2} \cos(\cos x)\,dx = \frac{\pi}{2}\;J\_0(1)
$$
in terms of a Bessel function.
This integral doesn't have a nice closed-form solution in terms of elementary functions, so this question is impossible (assuming you're just supposed to find the antiderivative in a form simpler than $\int \cos(\cos(x)) dx$)