Cosine Transform of Hyperbolic Functions

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Does anyone know a closed form of the integral:

$\int^{\infty}_{0}\text{d}x \cos(k x) \frac{\sinh(\frac{3\gamma-\pi}{4} x)}{\sinh(\frac{\gamma}{4} x)\cosh(\frac{2\gamma-\pi}{4} x)},$

where $\frac{\pi}{2}>\gamma>\frac{\pi}{4}$ k>0?

Best regards, CVJM