1) explicite ∫_0 ^∞ ((arctan(1+x(2+t^2 )))/(2+t^2 ))dt withx>0 2)determine values of ∫_0 ^∞ ((arctan(3+t^2 ))/(2+t^2 ))dt and ∫


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

$1) e x p l i c i t e \int_{0}^{\infty} \frac{a r c t a n (1 + x (2 + t^{2}))}{2 + t^{2}} d t$ $w i t h x > 0$ $2) d e t e r m i n e v a l u e s o f$ $\int_{0}^{\infty} \frac{a r c t a n (3 + t^{2})}{2 + t^{2}} d t a n d$ $\int_{0}^{\infty} \frac{a r c t a n (5 + 2 t^{2})}{2 + t^{2}} d t$
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