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Bierens de Haan (#17, Table 275) lists the incorrect result: $$\int_0^{\pi/2}\frac{\cosh[a \cos x]\cos[a\sin x]}{\cosh[2a\cos x]+\cos[a\sin x]}dx=\frac{\pi}{2}$$ What is the correct value?

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What leads you to conclude that it is incorrect? And why wouldn't this be an obvious piece of information to include? – Zev Chonoles Sep 2 '13 at 19:56

For $a=0$, the value of the integral is $\frac{\pi}4$, and the value is not independent of $a$.

Maple gives the following (graphical and numerical) dependence on $a$: enter image description here

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There is apparently a misprint in B de Haan; the 2 in the denominator should not be there. In this case, the integral can be written $$\frac{1}{2}Re\int_0^{\pi/2}\frac{dx}{\cosh(ae^{ix})}=\frac{\pi}{4}.$$

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