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Math Help - Evaluating the integral of natural log of the absolute value of x

  1. #1
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    Evaluating the integral of natural log of the absolute value of x

    Evaluate : *integral sign* ln (abs(x)) dx
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  2. #2
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    Quote Originally Posted by soccerballboy20 View Post
    Evaluate : *integral sign* ln (abs(x)) dx
    integration by parts ...

    u = \ln|x| ... du = \frac{1}{x} \, dx

    dv = dx ... v = x

    \int \ln|x| \, dx = x\ln|x| - \int x \cdot \frac{1}{x} \, dx

    finish up ...
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  3. #3
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    what do you mean finish up?
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  4. #4
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    He gave you x\ln|x| - \int x \cdot \frac{1}{x} \, dx

    You need to finish integrating
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  5. #5
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    so would that then result in the answer:

    = x ln|x| -(x/2)(ln|x|)

    ??
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  6. #6
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    x * \frac{1}{x} = 1

    xlnx - \int dx

    xlnx - x is your answer
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