What is the name of this integration?

[abcdefat]

What is the name of this integration?

. . . . .\(\displaystyle \displaystyle \int_0^{\infty}\,\)\(\displaystyle \dfrac{1}{1\,+\, x^u}\, dx\)

where u is an arbitrary number. I just know the result of this integration is a multiplication of Gamma functions. Does any body know the terminology of this integration?

 

[daon2]

It's an improper integral of an algebraic function (at least when u is rational). Don't know what else to call it. But note that u must be greater than 1 for it to converge.