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Math Help - integral of xlogx

  1. #1
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    integral of xlogx

    Hey all,

    i follow my notes from class to integrate x logx dx

    and i come up with the answer 1 - log x,

    however when i check my answer with Wolframs online integrator, it gets a different answer.

    can somebody show me step by step how to do it?

    heres what i did,

    x logx dx

    = x * 1/x - "int" 1/x * 1

    = 1 - logx

    our class example doesnt have the x on the front, it just has log x dx.

    thanks for any help,

    Mitch
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  2. #2
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    Quote Originally Posted by Mitch281008 View Post
    Hey all,

    i follow my notes from class to integrate x logx dx

    and i come up with the answer 1 - log x,

    however when i check my answer with Wolframs online integrator, it gets a different answer.

    can somebody show me step by step how to do it?

    heres what i did,

    x logx dx

    = x * 1/x - "int" 1/x * 1

    = 1 - logx

    our class example doesnt have the x on the front, it just has log x dx.

    thanks for any help,

    Mitch
    hi

    try integration by parts .

    \int x\ln x dx

    =\ln x\int x dx-\int [\int x dx]\frac{1}{x}dx

     <br />
=\frac{1}{2}x^2\ln x-\frac{1}{4}x^2+c<br />
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  3. #3
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    Quote Originally Posted by Mitch281008 View Post
    Hey all,

    i follow my notes from class to integrate x logx dx

    and i come up with the answer 1 - log x,

    however when i check my answer with Wolframs online integrator, it gets a different answer.

    can somebody show me step by step how to do it?

    heres what i did,

    x logx dx

    = x * 1/x - "int" 1/x * 1

    = 1 - logx

    our class example doesnt have the x on the front, it just has log x dx.

    thanks for any help,

    Mitch
    It would have helped if you showed the complete details of your working (your choice of u and dv etc.) because what little working you've posted is completely wrong.

    See here: integrate x Log&#x5b;x&#x5d; - Wolfram|Alpha (click on Show steps).
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