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Math Help - integral 2

  1. #1
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    integral 2

    use substitution to evaluate the definite integral \int_e^e^2{dx\ x(lnx)^2}
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by fastman390 View Post
    use substitution to evaluate the definite integral \int_e^e^2{dx\ x(lnx)^2}
    huh? please clarify

    do you mean \int_e^{e^2} \frac {dx}{x (\ln x)^2} ??

    if so, the substitution you want is u = \ln x
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  3. #3
    Super Member redsoxfan325's Avatar
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    Assuming it is \int_e^{e^2} \frac {dx}{x (\ln x)^2}, use u = \ln x. Thus du = \frac{dx}{x}. The bounds become \ln(e)\to\ln(e^2) = 1\to 2

    Now you have \int_1^2\frac{du}{u^2}

    If you need it:
    Spoiler:

    \int_1^2\frac{du}{u^2} = \left(-\frac{1}{u}\right)\bigg|_1^2 = -\frac{1}{2}+1 = \frac{1}{2}
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