find the value of∫_0 ^∞ artan(2x)(1+x^2 )^(−1_ ) the key of slution put F(t)=∫_0 ^∞ artan(xt)(1+x^2 )^(−1) find ∂F/∂t first then F(t) and take t=2 you will of find find the value of integral..


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Question Number 25762 by abdo imad last updated on 14/Dec/17

$f i n d t h e v a l u e o f \int_{0}^{\infty} a r t a n (2 x) {(1 + x^{2})}^{- 1_{}} t h e k e y o f s l u t i o n p u t F (t) = \int_{0}^{\infty} a r t a n (x t) {(1 + x^{2})}^{- 1} f i n d \partial F / \partial t f i r s t t h e n F (t) a n d t a k e t = 2 y o u w i l l o f f i n d f i n d t h e v a l u e o f i n t e g r a l . .$
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