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Math Help - Antiderivitive of natural log of xe^2x/x dx

  1. #1
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    Unhappy Antiderivitive of natural log of xe^2x/x dx

    This one has me all kinds of confused. I am the weakest at natural log and its base e. I was trying to use u substitution, but the /x is throwing me for a loop. Help please??

    the numerator is ln(xe^2x), denominator is x, I'm trying to find the indefinite integral
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by ceb0196 View Post
    This one has me all kinds of confused. I am the weakest at natural log and its base e. I was trying to use u substitution, but the /x is throwing me for a loop. Help please??

    the numerator is ln(xe^2x), denominator is x, I'm trying to find the indefinite integral
    First simplify:

    \frac{\ln\!\left(xe^{2x}\right)}{x}=\frac{\ln x+\ln\!\left(e^{2x}\right)}{x}=\frac{\ln x}{x}+2

    So \int\frac{\ln\!\left(xe^{2x}\right)}{x}\,dx=\int\f  rac{\ln x}{x}+2\,dx

    Can you continue from here?
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  3. #3
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    AH, yes I can finish. I just could not figure out how to split any of it up. THANKS!!
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