let give F(x)=∫_0 ^∞ ((arctan(1+x(1+t^2 )))/(1+t^2 ))dt and x>0 calculate (dF/dx)(x).


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Question Number 28827 by abdo imad last updated on 30/Jan/18

$l e t g i v e F (x) = \int_{0}^{\infty} \frac{a r c t a n (1 + x (1 + t^{2}))}{1 + t^{2}} d t a n d x > 0$ $c a l c u l a t e \frac{d F}{d x} (x) .$
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