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Question Number 60264 by maxmathsup by imad last updated on 19/May/19

l e t f (t) = \int_{0}^{\infty} \frac{e^{- 3 [x^{2}]}}{x^{2} + t^{2}} d x w i t h t > 0

1 . d e t e r m i n e a e x p l i c i t f o r m o f f (t)

2 . f i n d a l s o g (t) = \int_{0}^{\infty} \frac{e^{- 3 [x^{2}]}}{{(x^{2} + t^{2})}^{2}} d x

3 . f i n d t h e v a l u e s o f i n t e g r a l s \int_{0}^{\infty} \frac{e^{- 3 [x^{2}]}}{x^{2} + 3} d x a n d \int_{0}^{\infty} \frac{e^{- 3 [x^{2}]}}{{(x^{2} + 4)}^{2}} d x .