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人気のある微分積分 >

integral from 50 to 100 of x/(23+9x^2)

解

\int_{50}^{100} \frac{x}{23 + 9 x ^{2}} d x

解

\frac{1}{18} (ln (90023) - ln (22523))

+1

十進法表記

0.07697 \dots

解答ステップ

\int_{50}^{100} \frac{x}{23 + 9 x ^{2}} d x

u置換積分法を適用する

= \int_{22523}^{90023} \frac{1}{18 u} d u

定数を除く:

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

= \frac{1}{18} \cdot \int_{22523}^{90023} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{18} [ln ∣ u ∣]_{22523}^{90023}

限度を計算する:

ln (90023) - ln (22523)

= \frac{1}{18} (ln (90023) - ln (22523))

グラフ

人気の例

integral from-4 to 7 of |x|

\int_{- 4}^{7} ∣ x ∣ d x

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

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

integral from 1 to 16 of sqrt(3/x)

\int_{1}^{16} \frac{3}{x} d x

integral from-2 to 1 of xarctan^2(x)

\int_{- 2}^{1} x arctan^{2} (x) d x

integral from 1 to 2 of 1/(x(ln(x))^2)

\int_{1}^{2} \frac{1}{x ( ln ( x ) ) ^{2}} d x