integral from-7 to 0 of (e^{1/x})/(x^2)

解

\int_{- 7}^{0} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

\frac{1}{e ^{\frac{1}{7}}}

十進法表記

0.86687 \dots

解答ステップ

\int_{- 7}^{0} \frac{e ^{\frac{1}{x}}}{x ^{2}} d x

部分積分を適用する

= [\frac{e ^{\frac{1}{x}}}{x} - \int \frac{- e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x}{x ^{3}} d x]_{- 7}^{0}

\int \frac{- e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x}{x ^{3}} d x = \frac{e ^{\frac{1}{x}}}{x} + e^{\frac{1}{x}}

= [\frac{e ^{\frac{1}{x}}}{x} - (\frac{e ^{\frac{1}{x}}}{x} + e^{\frac{1}{x}})]_{- 7}^{0}

簡素化

= [- e^{\frac{1}{x}}]_{- 7}^{0}

限度を計算する:

\frac{1}{e ^{\frac{1}{7}}}

= \frac{1}{e ^{\frac{1}{7}}}