Integrating ln(x)/4x: Steps and Tips for Solving

[939]

Homework Statement

I am lost as to what to do here.

Homework Equations

Integral of (lnx)/(4x)

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?

 

[Mute]

Homework Statement

I am lost as to what to do here.

Homework Equations

Integral of (lnx)/(4x)

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?

Your integral is

$$\int dx~\frac{\ln x}{4x},$$
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?

 

[Brown Arrow]

du = 1/x dx sooo

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

 

[Dick]

du = 1/x dx sooo

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

Sure, u/4 du. Integrate that.

 

[Mark44]

du = 1/x dx sooo

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

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

 

[ross1219]

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

$\frac{1}{4}$∫u du

Then apply power rule...