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 (28)/(1-cos(4x))

解答

\int \frac{28}{1 - cos ( 4 x )} d x

解答

- 7 cot (2 x) + C

求解步骤

\int \frac{28}{1 - cos ( 4 x )} d x

提出常数:

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

= 28 \cdot \int \frac{1}{1 - cos ( 4 x )} d x

使用换元积分法

= 28 \cdot \int \frac{1}{4 ( 1 - cos ( u ) )} d u

提出常数:

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

= 28 \cdot \frac{1}{4} \cdot \int \frac{1}{1 - cos ( u )} d u

使用换元积分法

= 28 \cdot \frac{1}{4} \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

= 28 \cdot \frac{1}{4} (- \frac{1}{v})

代回

= 28 \cdot \frac{1}{4} (- \frac{1}{tan ( \frac{4 x}{2} )})

化简

28 \cdot \frac{1}{4} (- \frac{1}{tan ( \frac{4 x}{2} )}) : - 7 cot (2 x)

= - 7 cot (2 x)

解答补常数

= - 7 cot (2 x) + C

作图

流行的例子

y^{^{'}} = y + x, y (0) = 1

(dy)/(dx)=(y^2-1)/(x^2-1),y(2)=2

\frac{d y}{d x} = \frac{y ^{2} - 1}{x ^{2} - 1}, y (2) = 2

integral of sin(t)e^{-2/3 t}

\int sin (t) e^{- \frac{2}{3} t} d t

integral from 1 to 2 of x^2e^{x^3-1}

\int_{1}^{2} x^{2} e^{x^{3} - 1} d x

sum from n=1 to infinity of 1/(\sqrt[n]{2)}

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