# Integral of (lnx)/(4x)

1. Dec 6, 2012

### 939

1. The problem statement, all variables and given/known data

I am lost as to what to do here.

2. Relevant equations

Integral of (lnx)/(4x)

3. The attempt at a solution

let u = lnx
let du = (1/x)dx

(u)/(4x) dx...

But then howdo you make 4x disappear in the equation? Typically I did it by making du = something in the equation I want to take out, but how can you make 1/x = 4x?

2. Dec 6, 2012

### Mute

$$\int dx~\frac{\ln x}{4x},$$
and you made the substitution u = ln x, so that du = dx/x, so you need to replace the dx in the integral with dx = x du. What happens to the 1/x in the integral then?

3. Dec 6, 2012

### Brown Arrow

du = 1/x dx sooo

u/4 du...........b/c.....(1/4)*(ln(x)/x) dx

4. Dec 6, 2012

### Dick

Sure, u/4 du. Integrate that.

5. Dec 6, 2012

### Staff: Mentor

And it would be a good idea to pull out that 1/4 right away so that you're working with this integral:
$$\frac{1}{4} \int \frac{ln(x) dx}{x}$$

6. Dec 7, 2012

### ross1219

u = lnx, du = (1/x) dx

$\frac{1}{4}$∫u du

Then apply power rule...