integral from 1 to 2 of (e^x)/(x^2)

解答

\int_{1}^{2} \frac{e ^{x}}{x ^{2}} d x

- \frac{e ^{2}}{2} + Ei (2) + e - Ei (1)

求解步骤

\int_{1}^{2} \frac{e ^{x}}{x ^{2}} d x

使用分布积分法

= [- \frac{e ^{x}}{x} - \int - \frac{e ^{x}}{x} d x]_{1}^{2}

\int - \frac{e ^{x}}{x} d x = - Ei (x)

= [- \frac{e ^{x}}{x} - (- Ei (x))]_{1}^{2}

化简

= [- \frac{e ^{x}}{x} + Ei (x)]_{1}^{2}

带入上下限计算后得:

- \frac{e ^{2}}{2} + Ei (2) + e - Ei (1)

= - \frac{e ^{2}}{2} + Ei (2) + e - Ei (1)

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