# Thread: Need help with an integral

1. ## Need help with an integral

1 / sqrt(2x)

I tried splitting things up but I'm just running myself in circles at this point. Two methods I tried are:

pulling 1/sqrt(2) out so I get

1/sqrt(2) * 1/sqrt(x) <---But I can't integrate that

I also tried to rationalize by multiplying top and bottom by sqrt(2x) but I just end up with something I still can't integrate.

A really convoluted thing I did was change the sqrt(2x) to 2x^1/2

Separate 1/2 out of that so I get 1/2 * x^-1/2 and integrate from there. No luck, as I just end up with 2sqrt(x) / 2, which is not the right answer. Can anyone shed some light on this?

p.s. - sorry, I'm not quite sure how to use pretty print, u-sub is in the next section so i'm trying to do it the hard way first.

2. Hello,
Here's a clue
put $\displaystyle \sqrt{x} = t$
and go on

feel free to ask if there's is still trouble

3. ## Thanks

Thank you for your reply, but I'm not quite sure I'm catching on.

I thought 1 / sqrt(2) * 1 / sqrt(x) was the the way to go, but no so sure.

4. ## ..

put $\displaystyle \sqrt{x} = t$
differntiate both sides
$\displaystyle \frac{dx}{2\sqrt{x}}=dt$
$\displaystyle dx=2\sqrt{x}dt$
put this in
$\displaystyle \int{\frac{dx}{\sqrt{2x}}}$
you get
$\displaystyle \int{\sqrt{2}dt}$
$\displaystyle =\sqrt{2}t + c$
$\displaystyle =2\sqrt{x}+c$