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

## Homework Statement

integral of x *sqrt( x/(x-1))

## 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

Related Calculus and Beyond Homework Help News on Phys.org
gabbagabbahey
Homework Helper
Gold Member

## Homework Statement

integral of x *sqrt( x/(x-1))

## 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
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 $x=1+\frac{1}{u-1}$

Mark44
Mentor

## Homework Statement

integral of x *sqrt( x/(x-1))

## 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
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).

vela
Staff Emeritus