# Help with simple integration problem

1. Jul 1, 2007

### CaityAnn

Solve y'= Ln(12x)

2. Relevant equations
Integral of ln(x)= xlnx-x dx

3. The attempt at a solution
12x*ln(12x)-12x dx or even xlnx-x*1/12
But Im pretty sure these are wrong.

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

2. Jul 1, 2007

### bob1182006

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

3. Jul 1, 2007

### cristo

Staff Emeritus
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?

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

4. Jul 1, 2007

### Kurdt

Staff Emeritus
Try substituting 12x = u and work from there.

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

Last edited: Jul 1, 2007