Help finding an indefinite integral

[AbsValue13]

I am trying to find the following indefinite integral:

Homework Statement

∫\sqrt{}x/(x-1)dx

Homework Equations

None

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.

 

[Mark44]

I am trying to find the following indefinite integral:

Homework Statement

∫\sqrt{}x/(x-1)dx

Homework Equations

None

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.

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}.

 

[Ray Vickson]

I am trying to find the following indefinite integral:

Homework Statement

∫\sqrt{}x/(x-1)dx

Homework Equations

None

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.

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).