let-f-t-0-arctan-e-tx-2-x-2-dx-with-t-gt-0-1-study-the-existence-of-f-t-2-calculate-f-t-

Question Number 35584 by abdo mathsup 649 cc last updated on 20/May/18

l e t f (t) = \int_{0}^{\infty} \frac{a r c t a n (e^{- {t x}^{2}})}{x^{2}} d x w i t h t > 0

1) s t u d y t h e e x i s t e n c e o f f (t)

2) c a l c u l a t e f^{^{'}} (t)