# Eliminating Gamma from result of integration

I think the following integration result can be shown without Gamma.

Can anyone explain

1. Why Mathematica Uses Gamma.
2. How to simplify the result to eliminate Gamma.

code:

Simplify[Integrate[(x/c)^(2/(1 - b)), {x, 0, 1/b}], Assumptions -> {1 > b > 0, c > 0}]

• Please do not post images of your work. Please post your actual Mathematica code in the form of text that can be copied and pasted into a Mathematica notebook. Without such, it will be difficult to reproduce your problem and to experiment with possible solutions. Sep 20 '18 at 15:52
• Your integral diverges for 0<b<1 and so Mathematica is returning the principal value. Sep 20 '18 at 15:56
• @ Carl Woll, if I change 2/(1-b) to 1/(1-b), the integral is also diverging? but there is no Gamma in the result, could you elaborate more on it? Sep 20 '18 at 16:42
• Try this: Assuming[{1 > b > 0, c > 0}, Integrate[(x/c)^(2/(1 - b)), {x, 0, 1/b}]] Sep 20 '18 at 16:45
• @ Mariusz Iwaniuk, thanks Sep 20 '18 at 16:48

Integrate[(x/c)^(2/(1 - b)), {x, 0, 1/b},