1-explicite-0-arctan-1-x-2-t-2-2-t-2-dt-withx-gt-0-2-determine-values-of-0-arctan-3-t-2-2-t-2-dt-and-0-arctan-5-2t-2-2-t-2-dt-

Question Number 116586 by Bird last updated on 05/Oct/20

1) e x p l i c i t e \int_{0}^{\infty} \frac{a r c t a n (1 + x (2 + t^{2}))}{2 + t^{2}} d t

w i t h x > 0

2) d e t e r m i n e v a l u e s o f

\int_{0}^{\infty} \frac{a r c t a n (3 + t^{2})}{2 + t^{2}} d t a n d

\int_{0}^{\infty} \frac{a r c t a n (5 + 2 t^{2})}{2 + t^{2}} d t