How to integrate this function with $\ln(x)$ in the numerator?

Question

I have to integrate $$ \iint {\log \sqrt x \over xy} \, \mathrm dx \, \mathrm dy$$ I don't really care about integrating over $y$, I can't begin to integrate over $x$ because I don't know how. What rules do I use to do this, I'm a bit rusty.

It's actually a very simple substitution, because $d(\ln x) = dx/x$ — Dylan, Oct 29 '14 at 20:35

score 3 · Answer 1 · answered Oct 28 '14 at 18:13

3

$$\int\frac{\log\sqrt x}{xy}dx=\frac1{2y}\int\frac{\log x}xdx=\frac1{4y}\log^2x+C$$

answered Oct 28 '14 at 18:13

Timbuc

34,191

How to integrate this function with $\ln(x)$ in the numerator?

1 Answers1