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人気のある微分積分 >

integral from 1 to 3 of x/(3x^2+1)

解

\int_{1}^{3} \frac{x}{3 x ^{2} + 1} d x

解

\frac{1}{6} ln (7)

+1

十進法表記

0.32431 \dots

解答ステップ

\int_{1}^{3} \frac{x}{3 x ^{2} + 1} d x

u置換積分法を適用する

= \int_{4}^{28} \frac{1}{6 u} d u

定数を除く:

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

= \frac{1}{6} \cdot \int_{4}^{28} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{6} [ln ∣ u ∣]_{4}^{28}

限度を計算する:

ln (28) - 2 ln (2)

= \frac{1}{6} (ln (28) - 2 ln (2))

簡素化

= \frac{1}{6} ln (7)

グラフ

人気の例

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\int_{0}^{2} - 5 x^{2} d x

integral from 0 to 7/2 of 7x-2x^2

\int_{0}^{\frac{7}{2}} 7 x - 2 x^{2} d x

integral from 0 to 1 of 7/((3x+4)(5x+2))

\int_{0}^{1} \frac{7}{( 3 x + 4 ) ( 5 x + 2 )} d x

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