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experimentX

  • 3 years ago

Evaluate: given that b > a \[ \int_0^\infty {x^{a-1} \over 1 + x^b}\; dx\]

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  1. mukushla
    • 3 years ago
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    *

  2. experimentX
    • 3 years ago
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    man ... I stuck at finding the simple residue.

  3. anonymous
    • 3 years ago
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    if my memory serves me, it is the numerator divided by the derivative of the denominator evaluated at the pole

  4. experimentX
    • 3 years ago
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    yeah you are correct ... had trouble fixing. \[ \huge \lim_{z \rightarrow e^{i \pi \over b}} {(z - e^{i{\pi }\over b}) z^{a-1} \over 1 + z^b} = \lim_{z \rightarrow e^{i \pi \over b}} {z^{a-1} \over -bz^{b-1}}\]

  5. experimentX
    • 3 years ago
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    |dw:1346858176216:dw| somehow it got this fixed. I had this Q on my exam paper ... Man i couldn't do it.

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