# Help finding an indefinite integral

1. Nov 14, 2013

### AbsValue13

I am trying to find the following indefinite integral:
1. The problem statement, all variables and given/known data

∫$\sqrt{}x$/(x-1)dx

2. Relevant equations

None

3. The attempt at a solution

I tried to use substitution but got nowhere. I set u=$\sqrt{}x$ so du=1/(2$\sqrt{}x$)dx. However from here on on I got stuck. I also tried using substitution this way u=x-1 so du=dx. However, this doesn't help since we get ∫$\sqrt{}(u+1)$/(u)du.

2. Nov 14, 2013

### Staff: Mentor

The substitution u = √x will work.
So u2 = x => 2udu = dx.

You'll get an improper fraction that you can simplify using polynomial division.

LaTeX tip: Put the quantity that's inside the radical inside the braces {}. IOW, \sqrt{u + 1}.

3. Nov 14, 2013

### Ray Vickson

Or, you can use ASCII and write sqrt(x/(x-1)) or sqrt(x)/(x-1).

I cannot figure out whether your integrand is
$$\sqrt{\frac{x}{x-1}} \text{ or } \frac{\sqrt{x}}{x-1}$$
If you mean the first one, use "[t e x ] \sqrt{ \frac{x}{x-1} } [/t e x ]" (no spaces); if you mean the second one, use "[t e x ] \frac{ \sqrt{x} }{x-1} [/ t e x]" (no spaces).