If replace the (1-x) by (a-x) in the Beta integral what the result will be?

[semigroups]

Once (1-x)^n-1 is replaced by (1-a)^n-1 where a>1, the form of the integral changed drastically (I can't find a proper substitution in order to transform the new integral to Beta), does anyone know how to compute the new integral then? (I presume the result will still involve Gamma functions, but in another form?)

 

[JJacquelin]

Incomplete Beta function instead of the Beta function :