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 (18)/(1-cos(6x))

解答

\int \frac{18}{1 - cos ( 6 x )} d x

解答

- 3 cot (3 x) + C

求解步骤

\int \frac{18}{1 - cos ( 6 x )} d x

提出常数:

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

= 18 \cdot \int \frac{1}{1 - cos ( 6 x )} d x

使用换元积分法

= 18 \cdot \int \frac{1}{6 ( 1 - cos ( u ) )} d u

提出常数:

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

= 18 \cdot \frac{1}{6} \cdot \int \frac{1}{1 - cos ( u )} d u

使用换元积分法

= 18 \cdot \frac{1}{6} \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

= 18 \cdot \frac{1}{6} (- \frac{1}{v})

代回

= 18 \cdot \frac{1}{6} (- \frac{1}{tan ( \frac{6 x}{2} )})

化简

18 \cdot \frac{1}{6} (- \frac{1}{tan ( \frac{6 x}{2} )}) : - 3 cot (3 x)

= - 3 cot (3 x)

解答补常数

= - 3 cot (3 x) + C

作图

流行的例子

laplacetransform sin(t-((2*pi))/3)

l a pl a ce t r an s f or m sin (t - \frac{( 2 \cdot π )}{3})

derivative (-3x+2)^4(-2x+3)^3

d er i v a t i v e (- 3 x + 2)^{4} (- 2 x + 3)^{3}

limit as x approaches 0 of (2tan(x/2))/x

x \to 0 lim (\frac{2 tan ( \frac{x}{2} )}{x})

integral of tan^5(6x)sec^2(6x)

\int tan^{5} (6 x) sec^{2} (6 x) d x

derivative of 1/(9x^{8/9})

\frac{d}{d x} (\frac{1}{9 x ^{\frac{8}{9}}})