What is the integral of ln|x|?

[bmed90]

What would the integral of ln|x| be.

 

[jakncoke]

Applying integration by parts which states

$$\int u\frac{dv}{dx}\,dx = uv - \int v \frac{du}{dx}\,dx$$
$$u=ln(x)$$ and $$v=x$$ So $$\int ln(x)\,dx = xln(x) - \int x\frac{1}{x}\,dx = xln(x)-x+c$$

 

[bmed90]

I wouldn't have thought to use parts. Thanks, I appreciate it