The value of ∫0πecosxsinx1+cos2xecosx+e-cosxdx is equal to

Question

The value of

\int_{0}^{π} \frac{e^{\cos x} \sin x}{(1 + \cos^{2} x) (e^{\cos x} + e^{- \cos x})} d x

is equal to

\frac{π^{2}}{4}

\frac{π}{4}

\frac{π}{6}

\frac{π^{2}}{2}

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