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) _( 0) (((1−x^2 )^(2p−1) )/(1−x^(4p) ))dx

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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) _( 0) (((1−x^2 )^(2p−1) )/(1−x^(4p) ))dx

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