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Math Help - Integration by Parts

  1. #1
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    Integration by Parts

    Hi all, I'm a little new here, but I hope you don't mind me joining your little community as I delve into Calculus II. I'd really like to learn to enjoy this class and be proficient in it. I hope you all will support me in this.

    Directions: In Exercises 11-38, find the integral. (Note: Solve by the simplest method--not all require integration by parts.)


    Integration by Parts-screen-shot-2013-02-22-6.25.45-pm.png

    I tried making
    dv=ln2x
    v=1/2x
    u=x^-2
    du=-2/x^3
    When plugging it into integral-calculator and Wolfphram Alpha I get nothing like my answer which was:

    1/2x^3 + -1/4x^3 + c
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  2. #2
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    Re: Integration by Parts

    Hey itshayley.

    The derivative of ln(2x) is 1/x and it isn't the integral.

    Try setting up dv = ln(2x) and u = x^(-2) [You have the v variables the wrong way around].
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  3. #3
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    Re: Integration by Parts

    Thank you chiro. But my understanding was that v = the integral of dv not the derivative.
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  4. #4
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    Re: Integration by Parts

    The integral of ln(2x) is not 1/2x.
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  5. #5
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    Re: Integration by Parts

    For \int\frac{\ln{2x}}{x^2}\,dx, you should let u=\ln{2x} and dv=\frac{1}{x^2}\,dx. Then du=\frac{1}{x}\,dx and v=-\frac{1}{x}. So:

    \int\frac{\ln{2x}}{x^2}\,dx =

    -\frac{1}{x}\ln{2x}+\int\frac{1}{x}\frac{1}{x}\,dx =

    -\frac{\ln{2x}}{x}-\frac{1}{x}

    There is a way to remember what to put in u and what to put in dv - it's "LIATE" - you choose for u whatever comes first in the list Logarithmic, Inverse trigonometric, Algebraic, Trigonometric, Exponential. It's not foolproof, but it's a pretty good rule of thumb.

    - Hollywood
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  6. #6
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    Re: Integration by Parts

    Integration by Parts-integration.png
    Last edited by ibdutt; February 24th 2013 at 01:46 AM.
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  7. #7
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    Re: Integration by Parts

    Wow, that was so much simpler than I was making it. Thanks Hollywood. I will keep that tip in mind.

    Thank you ibdutt for your input as well.

    I see now chiro, sorry for the miscommunication.
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