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Math Help - Reduction formulae

  1. #1
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    Thumbs down Reduction formulae

    Given that In = integral between 1 and 0 of 1/(1+x^2)^n, show that for n>1, 2(n-1)In = 2^(1-n) + (2n-3)In-1
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  2. #2
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    Quote Originally Posted by Erghhh View Post
    Given that In = integral between 1 and 0 of 1/(1+x^2)^n, show that for n>1, 2(n-1)In = 2^(1-n) + (2n-3)In-1
    Start from I_{n-1} = \int_0^1\!\!\!1*(1+x^2)^{-(n-1)}dx and integrate by parts (integrating the 1 and differentiating the (1+x^2)^{-(n-1)}).
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