# Indefinite Integral

• Oct 13th 2012, 07:36 PM
Assassin0071
Indefinite Integral
I'm working out a problem and reached an integral of the following form. I'm not entirely sure how to evaluate it. I tried substitution and parts but ended up nowhere so far. Any help would be greatly apperciated.

$\int\sqrt{\frac{r}{hr+u}}\,dr$

Where u and h are constants.
• Oct 13th 2012, 07:47 PM
MaxJasper
Re: Indefinite Integral
A solution most likey looks like:

$\frac{1}{h^{3/2} \sqrt{r}}\sqrt{\frac{r}{h r+u}} \left(\sqrt{h} \sqrt{r} (h r+u)-u \sqrt{h r+u} \text{Log}\left[h \sqrt{r}+\sqrt{h} \sqrt{h r+u}\right]\right)$(Shake)
• Oct 13th 2012, 07:53 PM
Assassin0071
Re: Indefinite Integral
Thanks, but the problem is I'm not even sure how to start getting to that solution.
• Oct 13th 2012, 07:58 PM
MaxJasper
Re: Indefinite Integral
Is u or h a function of r?
• Oct 13th 2012, 08:01 PM
Assassin0071
Re: Indefinite Integral
Sorry I should have mentioned that u and h are constants.