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 (-2x)/(1+x^2)

解答

\int \frac{- 2 x}{1 + x ^{2}} d x

解答

- ln 1 + x^{2} + C

求解步骤

\int \frac{- 2 x}{1 + x ^{2}} d x

提出常数:

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

= - 2 \cdot \int \frac{x}{1 + x ^{2}} d x

使用换元积分法

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

提出常数:

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

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

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 2 \cdot \frac{1}{2} ln ∣ u ∣

u = 1 + x^{2}

代回

= - 2 \cdot \frac{1}{2} ln 1 + x^{2}

化简

- 2 \cdot \frac{1}{2} ln 1 + x^{2} : - ln 1 + x^{2}

= - ln 1 + x^{2}

解答补常数

= - ln 1 + x^{2} + C

作图

流行的例子

(\partial)/(\partial x)(e^{-8x})

\frac{\partial}{\partial x} (e^{- 8 x})

d/(dy)(cos(2y))

\frac{d}{d y} (cos (2 y))

limit as x approaches 0-of 5x^3-7x^2+2^x-2

x \to 0 - lim (5 x^{3} - 7 x^{2} + 2^{x} - 2)

integral of 1/(sqrt(t^2-6t+34))

\int \frac{1}{t ^{2} - 6 t + 34} d t

tangent f(x)=8(x-1/x)^2

t an g e n t f (x) = 8 (x - \frac{1}{x})^{2}