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Math Help - Integration by Parts with ln...

  1. #1
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    Integration by Parts with ln...

    Hi guys,

    Integrate:

    t^4*ln(4t)dt on the interval [2,7]

    I'm using substitution by parts so,

    u = t^4
    u' = 4t^3
    v = tln(4t) - t (i think so?!)
    v' = ln(4t)

    ∫t^4*ln(4t)dt = t^4(tln(4t) - t) - ∫(tln(4t) - t)4t^3

    and I don't know how to integrate the second term....Am I doing this right?

    Thank you!
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  2. #2
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    Re: Integration by Parts with ln...

    Hey UBCBOY.

    Hint: Try letting u = ln(4t) and dv = t^4 instead.
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  3. #3
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    Re: Integration by Parts with ln...

    Quote Originally Posted by chiro View Post
    Hey UBCBOY.

    Hint: Try letting u = ln(4t) and dv = t^4 instead.
    Alright, so then I would be left with:

    t^4*u du/4t is that right?
    Which becomes... 1/4 ∫t^3*u du ?

    But how would I be able to integrate that?
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  4. #4
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    Re: Integration by Parts with ln...

    Integration by Parts with ln...-integral.png
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