let-give-I-m-a-0-cos-mx-1-x-2-x-2-a-2-dx-1-verify-that-I-m-1-lim-a-1-I-m-a-2-find-the-value-of-0-x-sin-mx-1-x-2-2-dx-

Question Number 28985 by abdo imad last updated on 02/Feb/18

l e t g i v e I_{m, a} = \int_{0}^{\infty} \frac{c o s (m x)}{(1 + x^{2}) (x^{2} + a^{2})} d x

1) v e r i f y t h a t I_{m, 1} = {l i m}_{a \to 1} I_{m, a}

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