A very challenging integral

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Tolaso J Kos: Administrator; Posts: 867; Joined: Sat Nov 07, 2015 6:12 pm; Location: Larisa; Contact:
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A very challenging integral

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Post by Tolaso J Kos » Sat Jul 09, 2016 5:18 am

This comes from Sweden.

Prove that:
$$ \int_{25\pi/4}^{53\pi/4}\frac{{\rm d}x}{\left ( 1+2^{\sin x} \right )\left ( 1+2^{\cos x} \right )}=\frac{7\pi}{4}$$

Imagination is much more important than knowledge.