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人気のある微分積分 >

integral from 5 to 10 of (2x)/(x^2+1)

解

\int_{5}^{10} \frac{2 x}{x ^{2} + 1} d x

解

ln (101) - ln (26)

+1

十進法表記

1.35702 \dots

解答ステップ

\int_{5}^{10} \frac{2 x}{x ^{2} + 1} d x

定数を除く:

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

= 2 \cdot \int_{5}^{10} \frac{x}{x ^{2} + 1} d x

u置換積分法を適用する

= 2 \cdot \int_{26}^{101} \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

= 2 \cdot \frac{1}{2} \cdot \int_{26}^{101} \frac{1}{u} d u

共通積分を使用する:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 \cdot \frac{1}{2} [ln ∣ u ∣]_{26}^{101}

簡素化

2 \cdot \frac{1}{2} [ln ∣ u ∣]_{26}^{101} : [ln ∣ u ∣]_{26}^{101}

= [ln ∣ u ∣]_{26}^{101}

限度を計算する:

ln (101) - ln (26)

= ln (101) - ln (26)

グラフ

人気の例

integral from 0 to 3 of tsqrt(1+16t^2)

\int_{0}^{3} t 1 + 16 t^{2} d t

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

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

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

\int_{0}^{2} 3 t 4 - t^{2} d t

integral from 0 to pi/3 of (7sec^2(x))

\int_{0}^{\frac{π}{3}} (7 sec^{2} (x)) d x

integral from 2 to 3 of 2x+5

\int_{2}^{3} 2 x + 5 d x