How to find the integral $\int_{0}^{\infty}\frac{\arctan{x}}{2+x^2}dx$? Find this integral
$$I=\int_{0}^{\infty}\dfrac{\arctan{x}}{2+x^2}dx$$
My try: since
let$$\arctan{x}=u$$
then
$$I=\int_{0}^{\frac{\pi}{2}}\dfrac{x}{1+\cos^2{x}}dx$$
the wolf <---
then I can't.Thank you

See my paper
Some Integrals of the Arctangent Function, M. L. Glasser, Mathematics of Computation, Vol. 22, No. 102 (Apr., 1968), pp. 445-447.
