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Use residues to evaluate $\int_0^\infty \frac{\cosh(ax)}{\cosh(x)}\,\mathrm{d}x$, where $|a|<1$
Use residues to evaluate $$
\int_0^\infty \frac{\cosh(ax)}{\cosh(x)}\,\mathrm{d}x
$$
where $|a|<1$.
Try considering the integral of the form
$$
\int_C \frac{\exp(az)}{\cosh(z)}\,\mathrm dz,
$$
...
