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Integration by Parts 5x ln(4x)dx

  1. Feb 19, 2014 #1
    1. The problem statement, all variables and given/known data

    Use integration by parts to evaluate the integral.
    ∫5x ln(4x)dx

    2. Relevant equations

    ∫udv = uv - ∫vdu

    3. The attempt at a solution
    So here's my solution:

    But the computer is telling me I'm wrong :( We haven't learned how to integrate lnx yet, so the only choice I have is to make u = ln(4x) (even our textbook does this). Any help would be really appreciated! Thanks :)
  2. jcsd
  3. Feb 19, 2014 #2


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    What is the derivative of ln(4x) ?
  4. Feb 19, 2014 #3
    Oh whoops! I can't believe I didn't notice such an obvious mistake. Thanks, I got the right answer now. :)
  5. Feb 20, 2014 #4


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    By the chain rule, the derivative of ln(4x) is (1/4x) times the derivative of 4x so (1/4x)(4)= 1/x.

    Even simpler: ln(4x)= ln(x)+ ln(4) so its derivative is 1/x.
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