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Math Help - Integration using Reduction formulae

  1. #1
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    Integration using Reduction formulae

    I've got an integration problem which my teachers can't solve and are telling me to ignore. However, I'd really like to figure out how to solve it so any help will be much appreciated.

    Given that In = INT [between 0 to 1] 1/[(1+x^2)^2] dx, show that, for n>/=2,

    2(n-1)In = 2^(1-n) + (2n-3)In-1

    Thanks.
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  2. #2
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    Please review you post. Have you dropped an n some where in the integral?
    Should it be (1+x^2)^{2n} instead of (1+x^2)^{2}?
    As it is you have a very simple integral with no need for reduction.
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  3. #3
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    Oops! You're right... I typed it wrong. It's supposed to be:

    Given that In = INT [between 0 to 1] 1/[(1+x^2)^n] dx, show that, for n>/=2,

    2(n-1)In = 2^(1-n) + (2n-3)In-1

    Cheers!
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