# Thread: Find all primitives to root fraction

1. ## Find all primitives to root fraction

Find all primitives to f(x) by using substitution:
$$t=\sqrt(\frac{x-1}{x+1})$$
$$f(x)=\int\frac{3}{(x+1)^2}\sqrt(\frac{x-1}{x+1})dx$$

I have problem finding dt and dx.

2. ## Re: Find all primitives to root fraction

$t = \sqrt{\dfrac{x-1}{x+1}}$

$dt = \dfrac{1}{2}\left( \dfrac{x-1}{x+1} \right)^{-1/2}\dfrac{2}{(x+1)^2}dx$

So, you wind up with:

$\displaystyle \int 3t^2dt$

3. ## Re: Find all primitives to root fraction

Nice, just figured out how you did it.