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Help with simple integration problem

  1. Jul 1, 2007 #1
    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. jcsd
  3. Jul 1, 2007 #2
    do you know how to do integration by parts?
    in order to solve this problem you need to use it.
  4. Jul 1, 2007 #3


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    Staff Emeritus
    Science Advisor

    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 [tex]\int \ln(12x) dx=\int 1\cdot\ln(12x) dx [/tex]. 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]
  5. Jul 1, 2007 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    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
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