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人気のある微分積分 >

integral from 50 to 100 of x/(17+6x^2)

解

\int_{50}^{100} \frac{x}{17 + 6 x ^{2}} d x

解

\frac{1}{12} (ln (60017) - ln (15017))

+1

十進法表記

0.11545 \dots

解答ステップ

\int_{50}^{100} \frac{x}{17 + 6 x ^{2}} d x

u置換積分法を適用する

= \int_{15017}^{60017} \frac{1}{12 u} d u

定数を除く:

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

= \frac{1}{12} \cdot \int_{15017}^{60017} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{12} [ln ∣ u ∣]_{15017}^{60017}

限度を計算する:

ln (60017) - ln (15017)

= \frac{1}{12} (ln (60017) - ln (15017))

グラフ

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