integral from 0 to 1 of (e^x-1)/x

解答

\int_{0}^{1} \frac{e ^{x} - 1}{x} d x

发散

求解步骤

\int_{0}^{1} \frac{e ^{x} - 1}{x} d x

乘开

\frac{e ^{x} - 1}{x} : \frac{e ^{x}}{x} - \frac{1}{x}

= \int_{0}^{1} \frac{e ^{x}}{x} - \frac{1}{x} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{1} \frac{e ^{x}}{x} d x - \int_{0}^{1} \frac{1}{x} d x

\int_{0}^{1} \frac{e ^{x}}{x} d x = Ei (1) - Ei (0)

\int_{0}^{1} \frac{1}{x} d x =

发散

如果表达式有部分发散，则整个表达式发散

= 发散

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