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人気のある微分積分 >

integral from 2 to e+1 of (x/(x-1))

解

\int_{2}^{e + 1} (\frac{x}{x - 1}) d x

解

e

+1

十進法表記

2.71828 \dots

解答ステップ

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

u置換積分法を適用する

= \int_{1}^{e} \frac{u + 1}{u} d u

拡張

\frac{u + 1}{u} : 1 + \frac{1}{u}

= \int_{1}^{e} 1 + \frac{1}{u} d u

総和規則を適用する:

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

= \int_{1}^{e} 1 d u + \int_{1}^{e} \frac{1}{u} d u

\int_{1}^{e} 1 d u = e - 1

\int_{1}^{e} \frac{1}{u} d u = 1

= e - 1 + 1

簡素化

= e

グラフ

人気の例

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\int_{0}^{t} sin (x^{2}) d x