Question

Evaluate:
\[ \huge \int_{-\infty}^\infty {e^{ax} \over 1 + e^x} \; dx\]

EDIT:: 0 < a < 1

Answer 1

IS your question right? @experimentX ... U sure that it is e^ax at one place and e^x at the other...??

Answer 2

mmm, \huge tags...

Answer 3

*

Answer 4

contour integrals ... complex analysis.

Answer 5

Okay..

Answer 6

*

Answer 7

let e^x = u,
-inf ->0
+inf -> +inf

dx = u^-1 du

the whole problem reduces to which is the special case of my previous problem
\[ \int_0^\infty {u^{a-1} \over 1 + u} \;du\]

Answer 8

interesting problem
http://math.stackexchange.com/questions/110494/possibility-to-simplify-sum-limits-k-infty-infty-frac-left