1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Integration by Parts - Substitution

  1. Sep 10, 2012 #1
    1. The problem statement, all variables and given/known data
    Evaluate the following indefinite integral:

    2. Relevant equations

    3. The attempt at a solution
    let u = ln16x
    therefore du=16/16x=1/x


    Why is this showing as the wrong answer?
  2. jcsd
  3. Sep 10, 2012 #2
    you need to substitute with two variables, u & v.

    [itex] ln(16x) [/itex] has a function within itself, therefore substituting that whole part with u wont work.

    keep in mind: [tex] \int u\, du = uv - \int v\, du [/tex]
  4. Sep 10, 2012 #3
    Sorry, stupid question - if there's both u and v, how do I choose which one goes with which?
  5. Sep 10, 2012 #4


    User Avatar
    Homework Helper

    Didn't you forget the arbitrary constant? The integral is -cos(ln16x))+C.

  6. Sep 10, 2012 #5


    User Avatar
    Science Advisor

    Yep, I can't see anything wrong except that you forgot the constant.:smile:
  7. Sep 10, 2012 #6
    Substitute for 16x and then further substitute for log(16x). You should end up with Int([e^a][sin(a)])/16

    At 1st I did it just like u did, then I saw sikrut's answer... Reworked it & verified with Matlab. Turns out Matlab agrees with Sikrut.
  8. Sep 10, 2012 #7


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    This problem is adequately handled by substitution, exactly as you did it --- of course, include the constant of integration.

    No need for integration by parts. I don't see how that would even be helpful.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook