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人気のある微分積分 >

integral from 4 to 6 of x/(4x^2+8)

解

\int_{4}^{6} \frac{x}{4 x ^{2} + 8} d x

解

\frac{1}{8} ln (\frac{19}{9})

+1

十進法表記

0.09340 \dots

解答ステップ

\int_{4}^{6} \frac{x}{4 x ^{2} + 8} d x

u置換積分法を適用する

= \int_{72}^{152} \frac{1}{8 u} d u

定数を除く:

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

= \frac{1}{8} \cdot \int_{72}^{152} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{8} [ln ∣ u ∣]_{72}^{152}

限度を計算する:

ln (152) - ln (72)

= \frac{1}{8} (ln (152) - ln (72))

簡素化

= \frac{1}{8} ln (\frac{19}{9})

グラフ

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