I'm looking at a function (pdf) of the form
$f_X(x)=K \cdot \frac{x^{a-1}(1-x)^{b-1}}{(1+dx)^c}$ for $0<x<1$, $a,b>0$, $d>-1$ Also, K is the constant which makes this integral evaluate to 1 over $0<x<1$ Using the integral representation of the hypergeometric function, we get that
$\frac{1}{K}= B(a,b) \cdot _2F_1(c,a;a+b;-d)$
How do I find the cdf of such a function?
The cdf is supposed to be $F_X(x)= K \int_{0}^{x} \cdot \frac{y^{a-1}(1-y)^{b-1}dy}{(1+dx)^c}= \frac{Kx^a}{a} \cdot F_1(a,c,1-b,a+1;-dx,x) $$ where $F_1$ is the Appell function. I'm not sure why that is or how to show it.