integral ln/sqroot of x dx?

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- Sep 2nd 2008, 01:54 PMandrewsxplease help with this integral?
integral ln/sqroot of x dx?

- Sep 2nd 2008, 02:05 PMChop Suey
Sub $\displaystyle u = \sqrt{x}$ and integrate by parts.

- Sep 2nd 2008, 02:06 PMmr fantastic
- Sep 2nd 2008, 02:11 PMo_O
$\displaystyle \int \ln \left(\sqrt{x}\right) dx$

You can use integration by parts: $\displaystyle \begin{array}{ll} u = \ln \left(\sqrt{x}\right) & dv = dx \\ du = \frac{1}{\sqrt{x}} \cdot \frac{1}{2\sqrt{x}} \ dx = \frac{1}{2x} \ dx& v = x \end{array}$ - Sep 2nd 2008, 04:30 PMChop Suey
Alternatively, you can just rewrite the integral as:

$\displaystyle \frac{1}{2} \int \ln{x} dx$

I think it's obvious what u and dv should be in this case. ;)