let I =∫_(−∞) ^(+∞) (dx/((x+i)^n )) and J =∫_(−∞) ^(+∞) (dx/((x−i)^n )) 1) calculate I and J interms of n 2) find thevalue of integral A_n =∫_(−∞) ^(+∞) (( cos(narctan((1/x))))/((1+x^2 )^(n/2) ))dx


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Question Number 61885 by maxmathsup by imad last updated on 10/Jun/19

$l e t I = \int_{- \infty}^{+ \infty} \frac{d x}{{(x + i)}^{n}} a n d J = \int_{- \infty}^{+ \infty} \frac{d x}{{(x - i)}^{n}}$ $1) c a l c u l a t e I a n d J i n t e r m s o f n$ $2) f i n d t h e v a l u e o f i n t e g r a l$ $A_{n} = \int_{- \infty}^{+ \infty} \frac{c o s (n a r c t a n (\frac{1}{x}))}{{(1 + x^{2})}^{\frac{n}{2}}} d x$
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