How to solve this improper integral?

[salvomic]

(02-09-2015 08:10 AM)parisse Wrote:  ...
You can get the value of the integral by adding int(x^a/(1+x^2),x,-inf,0), replace -inf and inf by R large, add the upper half-circle integral of radius R and apply residue theorem, then take the limit as R->inf.
You can check for a=1/2 or a=1/3 like this
assume(t>0); simplify(eval(subst('int(x^(1/3)/(x^2+1),x,0,inf)',x=t^3)))

yes, thank you!
ir works well.
I'm trying to memorize this method, it's so useful.

Have a nice day