let-give-a-gt-0-1-find-the-value-of-F-a-0-lnt-t-2-a-2-dt-2-find-the-value-of-G-a-0-aln-t-t-2-a-2-2-dt-3-find-the-value-of-0-ln-t-t-2-3-2-dt-

Question Number 34260 by math khazana by abdo last updated on 03/May/18

l e t g i v e a > 0

1) f i n d t h e v a l u e o f F (a) = \int_{0}^{\infty} \frac{l n t}{t^{2} + a^{2}} d t

2) f i n d t h e v a l u e o f G (a) = \int_{0}^{\infty} \frac{a l n (t)}{{(t^{2} + a^{2})}^{2}} d t

3) f i n d t h e v a l u e o f \int_{0}^{\infty} \frac{l n (t)}{{(t^{2} + 3)}^{2}} d t