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Homework Help: Integration of products.

  1. Mar 24, 2014 #1
    1. The problem statement, all variables and given/known data

    I'm not sure if this is pre calculus or calculus and beyond. If I've posted in the wrong section, please feel free to move this topic.

    ∫t2 * lnt dt

    2. Relevant equations

    3. The attempt at a solution

    I've tried using the integration by parts:

    ∫uv' dt = uv - ∫u'v dt

    u = lnt u' = 1/t

    v = t3 / 3 v' = t2

    I then get the following:

    lnt * t3 / 3 - ∫1/t * t3 / 3

    I'm not sure where to continue from this.
  2. jcsd
  3. Mar 24, 2014 #2

    Ray Vickson

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    What is preventing you from integrating ##(1/t)(t^3/3) = t^2 /3##?
    Last edited: Mar 24, 2014
  4. Mar 24, 2014 #3
    I thought I needed to do partial integration again for that one, since it's another set of products?
  5. Mar 24, 2014 #4


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    You've done the hard bit!
  6. Mar 24, 2014 #5
    The integral

    [tex]\int x^n dx [/tex]

    is a special case and you should have it memorized.
  7. Mar 24, 2014 #6


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    You are allowed to simplify things before integrating them.
  8. Mar 24, 2014 #7


    Staff: Mentor

    Problems involving integration or differentiation definitely should be posted in Calculus & Beyond, so this is the right forum section.
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