Help with simple integration problem

[CaityAnn]

Solve y'= Ln(12x)

Homework Equations

Integral of ln(x)= xlnx-x dx

The Attempt at a Solution

12x*ln(12x)-12x dx or even xlnx-x*1/12
But I am pretty sure these are wrong.

My calculator gives me xlnx+(ln(12)-1)x wth? Help!

 

[bob1182006]

do you know how to do integration by parts?
in order to solve this problem you need to use it.

 

[cristo]

Solve y'= Ln(12x)

Homework Equations

Integral of ln(x)= xlnx-x dx

The Attempt at a Solution

12x*ln(12x)-12x dx or even xlnx-x*1/12
But I am pretty sure these are wrong.

Yup, they are incorrect.

To do this, you should note why the integral of ln(x) is equal to xlnx-x dx. Namely, we use integration by parts, writing the integrand as 1.ln(x). So, for your question, we have $$\int \ln(12x) dx=\int 1\cdot\ln(12x) dx$$. Now, can you see a suitable choice for "u" and "dv" to enable you to perform integration by parts on this?

My calculator gives me xlnx+(ln(12)-1)x wth?

Your calculator is correct. [When you have the answer, check to see if yours is the same as this]

 

[Kurdt]

Try substituting 12x = u and work from there.

EDIT: Damn my slowness. And also cristo's method is better, mine is rather lazy.