Wish \(e^{-2 x}\) wasn't there

Calculus Level 5

\[\large{\displaystyle \int^{\infty}_{0} \dfrac{\ln( \cos^2 t+ e^{-2x} \sin^2 t)}{\sinh x} dx=f(t)}\]

Find \(f(7)\) up to 4 decimal places.

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