ja

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

人気のある微分積分 >

integral from 0 to 2 of (2x)/(3-x)

解

\int_{0}^{2} \frac{2 x}{3 - x} d x

解

2 (- 2 + 3 ln (3))

+1

十進法表記

2.59167 \dots

解答ステップ

\int_{0}^{2} \frac{2 x}{3 - x} d x

定数を除く:

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

= 2 \cdot \int_{0}^{2} \frac{x}{3 - x} d x

u置換積分法を適用する

= 2 \cdot \int_{3}^{1} - \frac{- u + 3}{u} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= 2 (- \int_{1}^{3} - \frac{- u + 3}{u} d u)

定数を除く:

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

= 2 (- (- \int_{1}^{3} \frac{- u + 3}{u} d u))

拡張

\frac{- u + 3}{u} : - 1 + \frac{3}{u}

= 2 (- (- \int_{1}^{3} - 1 + \frac{3}{u} d u))

総和規則を適用する:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (- (- (- \int_{1}^{3} 1 d u + \int_{1}^{3} \frac{3}{u} d u)))

\int_{1}^{3} 1 d u = 2

\int_{1}^{3} \frac{3}{u} d u = 3 ln (3)

= 2 (- (- (- 2 + 3 ln (3))))

簡素化

= 2 (- 2 + 3 ln (3))

グラフ

人気の例

integral from 1 to 25 of sqrt((11)/x)

\int_{1}^{25} \frac{11}{x} d x

integral from 1 to 3 of e^x-e

\int_{1}^{3} e^{x} - e d x

integral from 0 to a of 8xsqrt(a^2-x^2)

\int_{0}^{a} 8 x a^{2} - x^{2} d x

integral from 1 to 4 of (x^2+2)-3

\int_{1}^{4} (x^{2} + 2) - 3 d x

integral from 0 to pi of x^6sin(x)

\int_{0}^{π} x^{6} sin (x) d x