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人気のある微分積分 >

integral from-1 to 1 of ((3e^x))/(1+e^x)

解

\int_{- 1}^{1} \frac{( 3 e ^{x} )}{1 + e ^{x}} d x

解

3

解答ステップ

\int_{- 1}^{1} \frac{3 e ^{x}}{1 + e ^{x}} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{- 1}^{1} \frac{e ^{x}}{1 + e ^{x}} d x

u置換積分法を適用する

= 3 \cdot \int_{1 + \frac{1}{e}}^{1 + e} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 [ln ∣ u ∣]_{1 + \frac{1}{e}}^{1 + e}

限度を計算する:

ln (1 + e) - ln (1 + \frac{1}{e})

= 3 (ln (1 + e) - ln (1 + \frac{1}{e}))

簡素化

= 3

グラフ

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