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Math Help - easy log integration question

  1. #1
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    the question is (integral) x log x dx

    i did integration by parts, and got it right with one exceptino....for the first term, i got 1/2 x^2 log x
    however, in the answers it says the x after the log should be in absolute value. why is this (or how do i show this in my work), i set my u to "log x" so i dont understand why it would change....

    any help as always is appreciated!

    would it be sufficient if i just threw the absolute value in the first step.. is this understood to be true without explanation?
    Last edited by mr fantastic; November 18th 2009 at 03:07 AM. Reason: Merged posts
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by twostep08 View Post
    the question is (integral) x log x dx

    i did integration by parts, and got it right with one exceptino....for the first term, i got 1/2 x^2 log x
    however, in the answers it says the x after the log should be in absolute value. why is this (or how do i show this in my work), i set my u to "log x" so i dont understand why it would change....

    any help as always is appreciated!

    would it be sufficient if i just threw the absolute value in the first step.. is this understood to be true without explanation?
    \int x \log x dx

    let u=\log x , dv= x \Rightarrow du=\frac{1}{x} , v=\frac{x^2}{2}

    \int x\log x dx =\frac{x^2}{2} \cdot \log x - \int \frac{x^2}{2x} dx

    \int x\log x dx = \frac{\log x \cdot x^2}{2} - \frac{x^2}{2\cdot 2}+C

    log(x) is defined for x positive values just (i,e x>0), for example log(-4) is not a real number
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