(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex] \int \frac {1}{\sqrt{x}(1+\sqrt{x})} dx [/tex]

3. The attempt at a solution

So let

[tex] u = 1 + \sqrt{x} [/tex]

then

[tex] du = \frac {1}{2}x^{-1/2} dx [/tex]

So dx should be this:

[tex] dx = 2x^{1/2} du[/tex]

right?

So now the Problem looks something like this:

[tex] \int \frac {2\sqrt{x}}{\sqrt{x}(u)} du [/tex]

[tex] \int \frac {\sqrt{x}}{(u)} du [/tex]

I am stuck here, I am just not sure where to go from here, the answer is suppose to be:

[tex] 2ln(1+\sqrt{x}) + C [/tex]

but I really don't know how to get there.

thanks!

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# Homework Help: Indefinite Integration by exchange of variables

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