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Math Help - Integral involving lnx

  1. #1
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    Integral involving lnx

    I have an integral i cant seem to figure out how to do.

     \int \frac {2^\ln x} { x } dx


    would i use u - substition like:

    u = {2^\ln x}
    Then,

    du = {e^\ln 2x

    Do, i then assign K = ln2

    Then,

     \frac {e^k^x}{k}

    Then fill back in for k?
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  2. #2
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    Re: Integral involving lnx

    Quote Originally Posted by icelated View Post
    I have an integral i cant seem to figure out how to do.

     \int \frac {2^\ln x} { x } dx


    would i use u - substition like:

    u = {2^\ln x}
    Then,

    du = {e^\ln 2x

    Do, i then assign K = ln2

    Then,

     \frac {e^k^x}{k}

    Then fill back in for k?

     \int 2^{\ln x} \cdot \frac{1}{x} \, dx

    let u = \ln{x} ...
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  3. #3
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    Re: Integral involving lnx

    wolfram gives me an answer 2^lnx / lnx how did they get there?
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    Re: Integral involving lnx

    Quote Originally Posted by icelated View Post
    wolfram gives me an answer 2^lnx / lnx how did they get there?
    Are you sure you read that correctly?
    Could it be \frac{2^{\ln(x)}}{\ln(2)}~?
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    Re: Integral involving lnx

    yes , sorry thats what i meant. =(
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    Re: Integral involving lnx

    Quote Originally Posted by icelated View Post
    yes , sorry thats what i meant.
    Find the derivative of that to see how it works.
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  7. #7
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    Re: Integral involving lnx

    the dirivitive is 1/x dx would i need to solve for x?
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  8. #8
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    Re: Integral involving lnx

    I think i get it. Du = 1/x dx

    So, i would have 2^u du ?
    then, integrate
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  9. #9
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    Re: Integral involving lnx

    Quote Originally Posted by icelated View Post
    I think i get it. Du = 1/x dx

    So, i would have 2^u du ?
    then, integrate
    that's it
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