$\int_0^\infty\:\frac{x}{(x^2+\omega^2)(1+e^{2{\pi}x})}\:dx$ integralini çözün

Question

$$\large\int_0^\infty\:\frac{x}{(x^2+\omega^2)(1+e^{2{\pi}x})}\:dx\:\:\:,\:\:\:\omega\in\mathbb{R}$$

İntegralini çözün