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 1/(49e^{-7x)+e^{7x}}

解答

\int \frac{1}{49 e ^{- 7 x} + e ^{7 x}} d x

解答

- \frac{1}{49} arctan (7 e^{- 7 x}) + C

求解步骤

\int \frac{1}{49 e ^{- 7 x} + e ^{7 x}} d x

使用换元积分法

= \int - \frac{1}{7 ( 49 u ^{2} + 1 )} d u

提出常数:

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

= - \frac{1}{7} \cdot \int \frac{1}{49 u ^{2} + 1} d u

使用换元积分法

= - \frac{1}{7} \cdot \int \frac{1}{7 ( v ^{2} + 1 )} d v

提出常数:

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

= - \frac{1}{7} \cdot \frac{1}{7} \cdot \int \frac{1}{v ^{2} + 1} d v

使用积分常见定则:

\int \frac{1}{v ^{2} + 1} d v = arctan (v)

= - \frac{1}{7} \cdot \frac{1}{7} arctan (v)

代回

= - \frac{1}{7} \cdot \frac{1}{7} arctan (7 e^{- 7 x})

化简

- \frac{1}{7} \cdot \frac{1}{7} arctan (7 e^{- 7 x}) : - \frac{1}{49} arctan (7 e^{- 7 x})

= - \frac{1}{49} arctan (7 e^{- 7 x})

解答补常数

= - \frac{1}{49} arctan (7 e^{- 7 x}) + C

作图

流行的例子

(dy)/(dx)=e^{x^2}

\frac{d y}{d x} = e^{x^{2}}

derivative (ln(x))^4

d er i v a t i v e (ln (x))^{4}

2xy(dy)/(dx)+y^2=2x^2

2 x y \frac{d y}{d x} + y^{2} = 2 x^{2}

derivative ln(8x)

d er i v a t i v e ln (8 x)

sum from n=1 to infinity of n/(2n^2+1)

n = 1 \sum \infty \frac{n}{2 n ^{2} + 1}