integral ln/sqroot of x dx?

2. Sub $u = \sqrt{x}$ and integrate by parts.

3. Originally Posted by andrewsx
integral ln/sqroot of x dx?
The obvious substitution is $u = \sqrt{x}$. Do it. Now use integration by parts.

4. $\int \ln \left(\sqrt{x}\right) dx$

You can use integration by parts: $\begin{array}{ll} u = \ln \left(\sqrt{x}\right) & dv = dx \\ du = \frac{1}{\sqrt{x}} \cdot \frac{1}{2\sqrt{x}} \ dx = \frac{1}{2x} \ dx& v = x \end{array}$

5. Alternatively, you can just rewrite the integral as:
$\frac{1}{2} \int \ln{x} dx$

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