you get the gamma function which is an integral in the PDF of the gamma distribution.
How do you integrate the gamma PDF from x=0 to x=1; when you have the gamma function also in the PDF to integrate
Please help.
The gamma function taken at an integer value is just the factorial : Gamma(n)=(n-1)!
However, it's not the main problem. If you're looking for a general formula of the integral of this pdf between 0 and 1, you won't find it. It can only be expressed in terms of incomplete gamma function. I suggest you have a look at the wikipedia page about the gamma distribution !
The constants $\displaystyle \Gamma(\alpha)$ and $\displaystyle \beta^{\alpha}$ are in the density so that the density integrates to one.
$\displaystyle f(x)={1\over \Gamma(\alpha)\beta^{\alpha}}x^{\alpha-1}e^{-x/\beta}$ where x>0.
Do not confuse the gamma function $\displaystyle \Gamma(\alpha)$ with the gamma density $\displaystyle X\sim \Gamma(\alpha,\beta)$