Contour integration for $\int_0^\infty \frac{x^{\alpha -1}}{(x+\beta)(x+\gamma)}dx$

Question

I have been trying to compute the following integral using contour integration and the residue theorem for quite some time now and can't get it to work out: $$\int_0^\infty \frac{x^{\alpha -1}}{(x+\beta)(x+\gamma)}dx$$ for $0<\alpha<1$ and $\gamma,\beta>0$. I assume that we consider the function $f(z) = \frac{z^{\alpha -1}}{(z+\beta)(z+\gamma)}$, where $z^{\alpha -1}= e^{(\alpha-1)\log z}$. What should we choose our contour to be? I have tried things like a keyhole contour but they don't seem to work.