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-

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