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Math Help - improper integral of (2^(ln(n)))^-1

  1. #1
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    improper integral of (2^(ln(n)))^-1

    I don't understand how they get this boxed in quantity (shown in attachment)
    Attached Thumbnails Attached Thumbnails improper integral of (2^(ln(n)))^-1-help-.gif  
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  2. #2
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    \int{\frac{dx}{x^{\ln{2}}}} = \int{x^{-\ln{2}}\,dx}

     = \frac{x^{-\ln{2} + 1}}{-\ln{2} + 1}

    which gives you the required stuff inside the box.
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  3. #3
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    is this some linearity of limits trick?
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  4. #4
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    furthermore

    can someone tell me why 1^(1-ln(2)) = 1 ????
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  5. #5
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    Because 1 to the power of anything is 1.
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