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Homework Help: Integral of 1/(sqrt(x^2 *ln(x)) from e to e^2 No idea.

  1. Feb 3, 2013 #1
    Integral of 1/(sqrt(x^2 *ln(x)) from e to e^2... No idea. :(

    1. ∫e to e^2 of (1/(√x2ln(x)))dx


    2. So confused! :(

    Okay... So I tried something!

    ∫e to e^2 of [-2/3(x2*ln(x))-3/2 * 1/(x + 2xln(x))] |e to e^2


    I got the 1/(x+2xln(x)) because I was trying to think of some way to cancel out the
    x+2xln(x) that results from the chain rule...

    Don't think this is right... If not, what am I supposed to do here??? :confused:
     
  2. jcsd
  3. Feb 3, 2013 #2

    Ray Vickson

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    Re: Integral of 1/(sqrt(x^2 *ln(x)) from e to e^2... No idea. :(

    For x > 0 we have ##\sqrt{x^2 \ln(x)} = x \sqrt{\ln(x)},## because ##\sqrt{x^2} = x## for x > 0. Change variables to ln(x) = y.
     
  4. Feb 4, 2013 #3
    Re: Integral of 1/(sqrt(x^2 *ln(x)) from e to e^2... No idea. :(

    Oh. I think I know what you mean. It's not as hard as I thought it would be!

    ∫e to e^2 of [1/(xsqrt(ln(x)))]

    u = ln(x)
    du= (1/x)dx

    ∫e to e^2 [1/(sqrt(u))]du

    = ∫ u^(-1/2) du = 2(u)^1/2 |e to e^2

    = 2(ln(e^2))^1/2 - 2(ln(e))^1/2

    = 2(2)^1/2 - 2(1)^1/2

    = 2sqrt(2) - 2 <----Should be answer!

    Thanks, Ray Vickson! :D
     
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