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Math Help - How to you evaluate an indefinite integral with lnx?

  1. #1
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    How to you evaluate an indefinite integral with lnx?

    antiderivative(ln5x/x)dx

    i know ln5x(dx)=1/5x but not sure how to go about solving this
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  2. #2
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    This is hard to read, is it

    \displaystyle \int{\frac{\ln{(5x)}}{x}\,dx}?


    If so, \displaystyle \int{\frac{\ln{(5x)}}{x}\,dx} = \int{\ln{(5x)}\,\frac{1}{x}\,dx}.


    Now make the substitution \displaystyle u = \ln{(5x)} so that \displaystyle \frac{du}{dx} = \frac{1}{x}.
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