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人気のある微分積分 >

integral from 2 to 7 of (8x)/(x^2+1)

解

\int_{2}^{7} \frac{8 x}{x ^{2} + 1} d x

解

4 ln (10)

+1

十進法表記

9.21034 \dots

解答ステップ

\int_{2}^{7} \frac{8 x}{x ^{2} + 1} d x

定数を除く:

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

= 8 \cdot \int_{2}^{7} \frac{x}{x ^{2} + 1} d x

u置換積分法を適用する

= 8 \cdot \int_{5}^{50} \frac{1}{2 u} d u

定数を除く:

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

= 8 \cdot \frac{1}{2} \cdot \int_{5}^{50} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 8 \cdot \frac{1}{2} [ln ∣ u ∣]_{5}^{50}

簡素化

8 \cdot \frac{1}{2} [ln ∣ u ∣]_{5}^{50} : 4 [ln ∣ u ∣]_{5}^{50}

= 4 [ln ∣ u ∣]_{5}^{50}

限度を計算する:

ln (50) - ln (5)

= 4 (ln (50) - ln (5))

簡素化

= 4 ln (10)

グラフ

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