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Math Help - One differentiation question and one integration question.

  1. #1
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    One differentiation question and one integration question.

    help with problem

     y = {e^x}{ln{x}}

    Find

     a)  \frac {dy}{dx}

     b)  \int_{e}^{e^2} \frac {1-ln{x}}{xln{x}}  dx
    Last edited by mr fantastic; June 20th 2010 at 11:59 PM. Reason: Re-titled.
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  2. #2
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    Quote Originally Posted by Beachball View Post
    help with problem

     y = {e^x}{ln{x}}

    Find

     a) \frac {dy}{dx}

     b) \int_{e}^{e^2} \frac {1-ln{x}}{xln{x}} dx
    a) Use the product rule.

    b) Substitute u = \ln x.

    If you need more help, please show all your work and say where you're stuck.
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  3. #3
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    im still having trouble with it.. ive tried the substitution but i couldnt quite get it.. would someone be able to post the step by step result?
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  4. #4
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    Here's a kick off for you

     \int_{e}^{e^2} \frac {1-\ln{x}}{x\ln{x}} ~dx

    u = \ln{x} \implies \frac{du}{dx}= \frac{1}{x}

    Now  \int\frac {1-\ln{x}}{x\ln{x}} ~dx = \int\frac{1}{x}\left(\frac {1-\ln{x}}{\ln{x}}\right) ~dx =\int \frac{1-u}{u}~du
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  5. #5
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    yea ive got that far.. but just stuck and dont know where togo after that. :/
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  6. #6
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    \frac{1-u}{u} = \frac{1}{u} - 1
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  7. #7
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    thankyou all so much
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