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Math Help - Do I have to use Integration by Parts for this?

  1. #1
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    Do I have to use Integration by Parts for this?

    \int 2^3ln(x)dx

    What I did:

    u = ln(x) v = 2x^4/4
    du = 1/x dv = 2x^3*dx

    Then it becomes: \int ln(x)(2x^4/4) - \int (2x^4/4x)

    Next from \int (2x^4/4x)

    u = 1/x v = x^5/10
    du = -1/x^2 dv = 2x^4/4

    Thus becoming: (1/x)(2x^4/4)dx - \int x^5/10(-1/x^2)

    At this point it does not seem to be right because my teachers answer is x^4/(4ln(x) - 1)

    Can someone help me please? I have a test tomorrow and I need to know ASAP.
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Your u du v and dv are all correct

    Remember the formula for integration by parts is

    \int udv=uv-\int vdu

    So plugging in your info above I get

    \frac{x^4\ln(x)}{2}-\frac{1}{2}\int x^3dx

    You do not need integration by parts just use the power rule!
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  3. #3
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    I figured it out, thanks!
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