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Thread: improper integral of (2^(ln(n)))^-1

  1. August 27th 2010, 06:53 PM #1
    RedSwiss
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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)
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  2. August 27th 2010, 07:06 PM #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. August 27th 2010, 07:09 PM #3
    RedSwiss
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    is this some linearity of limits trick?
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  4. August 27th 2010, 07:20 PM #4
    RedSwiss
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    furthermore

    can someone tell me why 1^(1-ln(2)) = 1 ????
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  5. August 27th 2010, 07:23 PM #5
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    Because 1 to the power of anything is 1.
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