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Evaluate the following integration

$$\int_{-2\pi}^{2\pi} \sin(2\sin x)+\cos(2\cos x) dx$$

klark
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    Done, what's next? – Jack D'Aurizio May 22 '17 at 19:00
  • In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. Also, please try to make the title more descriptive, there are a lot of questions about 'integration of trigonometric functions'. – projectilemotion May 22 '17 at 19:01
  • OK; I know that there is a solution using series form, but I was wondering if there is some solutions without using series idea! – klark May 22 '17 at 19:12
  • Just Bessel functions of integer order. – Jon May 22 '17 at 20:06
  • A related question. – Lucian Aug 21 '19 at 08:43

1 Answers1

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just a simplification

the first function is odd, thus the integral becomes $$4\int_0^{\pi}\cos (\cos (x))dx $$

hamam_Abdallah
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  • And a possible solution to it : https://math.stackexchange.com/questions/117536/evaluate-int-cos-cos-x-dx. But the second part doesn't seems to match the original integral. – zwim May 22 '17 at 19:28