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Math Help - Calc problem integrate

  1. #1
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    Calc problem integrate

    hi, i wasn't sure how to integrate the following expression by substitution so any help would be appreciated:

    1/[x(ln(x)]
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  2. #2
    MHF Contributor
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    Quote Originally Posted by clockingly View Post
    hi, i wasn't sure how to integrate the following expression by substitution so any help would be appreciated:

    1/[x(ln(x)]
    INT.[1 / [x*ln(x)]]dx

    Let u = ln(x)
    So, du = (1/x)dx

    INT.[1 / [x*ln(x)]]dx
    = INT.[1 / [ln(x)]] (1/x)dx
    = INT.[1/u]du
    = ln|u| +C
    = ln|ln(x)| +C ------------answer.
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