Evaluate ∫0∞dxx2+2xcosα+1\int_0^{\infty} \frac{dx}{x^2 + 2x \cos \alpha + 1}∫0∞x2+2xcosα+1dx for 0<α<π0 < \alpha < \pi0<α<π.
αsinα\frac{\alpha}{\sin \alpha}sinαα
π−αsinα\frac{\pi - \alpha}{\sin \alpha}sinαπ−α
πsinα\frac{\pi}{\sin \alpha}sinαπ
αcosα\frac{\alpha}{\cos \alpha}cosαα