Question

Evaluate: given that b > a
\[ \int_0^\infty {x^{a-1} \over 1 + x^b}\; dx\]

Answer 1

*

Answer 2

man ... I stuck at finding the simple residue.

Answer 3

if my memory serves me, it is the numerator divided by the derivative of the denominator evaluated at the pole

Answer 4

yeah you are correct ... had trouble fixing.
\[ \huge \lim_{z \rightarrow e^{i \pi \over b}} {(z - e^{i{\pi }\over b}) z^{a-1} \over 1 + z^b} = \lim_{z \rightarrow e^{i \pi \over b}} {z^{a-1} \over -bz^{b-1}}\]

Answer 5

somehow it got this fixed. I had this Q on my exam paper ... Man i couldn't do it.