How to go from this formula to F distribution I have the following formula.
$$\int_{0}^{\infty} x^{\frac{n-1}{2}-1} (a+x)^{\frac{1}{2} \frac{-n}{2} -v} dx.$$
The quantities $d1 ,d2$ appearing in the pdf of the F distribution are the following.
$$d1=n-1,\ d2=2v.$$
My problem is the term $a$ (which is a constant positive hyperparameter). I want to go from $(a+x)^{\frac{1}{2} \frac{-n}{2} -v}$ to something like $(1+\frac{d1}{d2}x)^{\frac{1}{2} \frac{-n}{2} -v}.$

Hint: For any $a>0$ you have:
$$(a+x)^b 
= \Big( a \Big( 1 + \frac{x}{a} \Big) \Big)^b
= a^b \Big( 1 + \frac{x}{a} \Big)^b.$$
