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Math Help - Indefinite Integration Using Substitution

  1. #1
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    Indefinite Integration Using Substitution

    Find \int \frac{(lnx)^7}{x} dx.

    Let u = lnx

    Let du = \frac{1}{x} dx => dx = x du

    = \int \frac{1}{x} (lnx)^7 dx

    = \int (\frac{1}{x}) ((lnx)^7) (x) (du)

    = \frac{u^8}{8} + c

    ... I stopped right here because I'm not getting the right answer... which is...

    = \frac{1}{4}u^4 + c

    I don't get where \frac{1}{4} and u^4 comes from??? I thought I'm following the antiderivative rules???
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  2. #2
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    Quote Originally Posted by Macleef View Post
    Find \int \frac{(lnx)^7}{x} dx.

    Let u = lnx

    Let du = \frac{1}{x} dx => dx = x du

    = \int \frac{1}{x} (lnx)^7 dx

    = \int (\frac{1}{x}) ((lnx)^7) (x) (du)

    = \frac{u^8}{8} + c

    ... I stopped right here because I'm not getting the right answer... which is...

    = \frac{1}{4}u^4 + c

    I don't get where \frac{1}{4} and u^4 comes from??? I thought I'm following the antiderivative rules???
    0.25u^4+C is wrong, your solution is absolutely correct.
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    don't forget to back-substitute, the solution is \frac 18 ( \ln x)^8 + C
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