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人気のある微分積分 >

integral from 1 to 8 of (16x)/(x^2+6)

解

\int_{1}^{8} \frac{16 x}{x ^{2} + 6} d x

解

8 ln (10)

+1

十進法表記

18.42068 \dots

解答ステップ

\int_{1}^{8} \frac{16 x}{x ^{2} + 6} d x

定数を除く:

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

= 16 \cdot \int_{1}^{8} \frac{x}{x ^{2} + 6} d x

u置換積分法を適用する

= 16 \cdot \int_{7}^{70} \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

= 16 \cdot \frac{1}{2} \cdot \int_{7}^{70} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 16 \cdot \frac{1}{2} [ln ∣ u ∣]_{7}^{70}

簡素化

16 \cdot \frac{1}{2} [ln ∣ u ∣]_{7}^{70} : 8 [ln ∣ u ∣]_{7}^{70}

= 8 [ln ∣ u ∣]_{7}^{70}

限度を計算する:

ln (70) - ln (7)

= 8 (ln (70) - ln (7))

簡素化

= 8 ln (10)

グラフ

人気の例

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\int_{3}^{4.3} (12 x^{2} - 6 x + \frac{4}{x}) d x

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\int_{0}^{2} x 4 + x^{2} d x

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

integral from 0 to 4 of (x^2-3)

\int_{0}^{4} (x^{2} - 3) d x

integral from 2 to 5 of 4^{4x}

\int_{2}^{5} 4^{4 x} d x