Integrate[Log[(1/2) Sin[t]]^n Tan[t/2], {t, 0, Pi/2}] == (-(1/(n + 1))) Log[1/2]^(n + 1) + (1/2^(n + 1)) Limit[D[(1/p) (Gamma[1 + p]^2/Gamma[1 + 2 p] - 1), {p, n}], p -> 0] /; Element[n, Integers] && n > 0

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2001-10-29