by-using-residus-theorem-prove-that-0-t-a-1-1-t-dt-pi-sin-pia-with-0-lt-a-lt-1-

Question Number 33069 by abdo imad last updated on 09/Apr/18

b y u s i n g r e s i d u s t h e o r e m p r o v e t h a t

\int_{0}^{\infty} \frac{t^{a - 1}}{1 + t} d t = \frac{π}{s i n (π a)} w i t h 0 < a < 1 .