0385132人目の素数さん
2018/05/16(水) 18:21:33.74ID:wrcnERm0∫ x / (exp(x) - 1) dx from x = 0 to x = ∞
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∫ -log(t) / (1/t - 1) (-1/t) dt from t = 1 to t =0
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∫ log(t) / (t - 1) dt from t = 0 to t = 1
t = 1 + s とおく。
∫ log(t) / (t - 1) dt from t = 0 to t = 1
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∫ log(1 + s) / s ds from s = -1 to s = 0
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∫ [s - (1/2)*s^2 + (1/3)*s^3 - (1/4)*s^4 ± …] / s ds from s = -1 to s = 0
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∫ 1 - (1/2)*s + (1/3)*s^2 - (1/4)*s^3 ± … ds from s = -1 to s = 0
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[s - (1/2)^2*s^2 + (1/3)^2*s^3 - (1/4)^2*s^4 ± …] from s = -1 to s = 0
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0 - [(-1) - (1/2)^2*(-1)^2 + (1/3)^2*(-1)^3 - (1/4)^2*(-1)^4 ± … ]
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1 + 1/2^2 + 1/3^2 + …