zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral of (2u)/(u+2)

解答

\int \frac{2 u}{u + 2} d u

解答

2 (u + 2 - 2 ln ∣ u + 2 ∣) + C

求解步骤

\int \frac{2 u}{u + 2} d u

提出常数:

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

= 2 \cdot \int \frac{u}{u + 2} d u

使用换元积分法

= 2 \cdot \int \frac{v - 2}{v} d v

乘开

\frac{v - 2}{v} : 1 - \frac{2}{v}

= 2 \cdot \int 1 - \frac{2}{v} d v

使用积分加法定则:

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

= 2 (\int 1 d v - \int \frac{2}{v} d v)

\int 1 d v = v

\int \frac{2}{v} d v = 2 ln ∣ v ∣

= 2 (v - 2 ln ∣ v ∣)

v = u + 2

代回

= 2 (u + 2 - 2 ln ∣ u + 2 ∣)

解答补常数

= 2 (u + 2 - 2 ln ∣ u + 2 ∣) + C

作图

流行的例子

integral of 16x^3+1/x

\int 16 x^{3} + \frac{1}{x} d x

derivative of 3/(4x^3)

\frac{d}{d x} (\frac{3}{4 x ^{3}})

integral from 0 to 3 of sqrt(x^2-9)

\int_{0}^{3} x^{2} - 9 d x

integral of 30+(60)/(e^{0.06x)}

\int 30 + \frac{60}{e ^{0.06 x}} d x

\frac{d}{d y} (6 x y)