Integral of x sqrt( x/(x-1))

1. Aug 18, 2010

Sidthewall

1. The problem statement, all variables and given/known data
integral of x *sqrt( x/(x-1))

2. Relevant equations

3. The attempt at a solution
I honestly don't know how to approach this i dont see any type of trig substituions whatsover, I really need some kind of lead and an explnation y that method works

2. Aug 18, 2010

gabbagabbahey

Hmmm... I guess I'd start by making the substitution $u=\frac{x}{x-1}=1+\frac{1}{x-1}$ in order to get rid of the junk inside the square root. You'll probably find that doing this will allow you to split the integral into two easier integrals since $x=1+\frac{1}{u-1}$

3. Aug 18, 2010

Staff: Mentor

I haven't carried this all the way through, but I think it will work
$$\int x \sqrt{\frac{x}{x - 1}}dx = \int \frac{x^{3/2}}{\sqrt{x - 1}}dx$$

I believe that an ordinary substitution will work.
Let u = sqrt(x - 1).

4. Aug 18, 2010

mmmboh

5. Aug 18, 2010

vela

Staff Emeritus
You can integrate secn θ using integration by parts, letting u=secn-2 θ and dv=sec2 θ dθ. For sec5 θ, you'll have to do it twice. It's a bit tedious but straightforward.

6. Aug 18, 2010

gabbagabbahey

You don't actually need a trig sub. You can also use Partial Fraction Decomposition if you find that easier.