1/ Montrer que ∫^( +∞) _( 0) (((1−x^2 )^(2p−1) )/(1−x^(4p) ))dx=((2^(2p−3) /p))π[1+2Σ_(k=1) ^(p−1) cos^(2p−1) (((kπ)/(2p)))] 2/ En de^� duire ∫^( 1)


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Question Number 195185 by Erico last updated on 26/Jul/23

$1 / Montrer que {\int_{0}}^{+ \infty} \frac{{(1 - x^{2})}^{2 p - 1}}{1 - x^{4 p}} d x = (\frac{2^{2 p - 3}}{p}) π [1 + 2 \underset{k = 1}{\sum^{p - 1}} {c o s}^{2 p - 1} (\frac{k π}{2 p})]$ $2 / En d \overset{´}{e d u i r e} {\int_{0}}^{1} \frac{{(1 - x^{2})}^{2 p - 1}}{1 - x^{4 p}} d x$
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