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 (45)/(1-cos(5x))

解答

\int \frac{45}{1 - cos ( 5 x )} d x

解答

- 9 cot (\frac{5 x}{2}) + C

求解步骤

\int \frac{45}{1 - cos ( 5 x )} d x

提出常数:

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

= 45 \cdot \int \frac{1}{1 - cos ( 5 x )} d x

使用换元积分法

= 45 \cdot \int \frac{1}{5 ( 1 - cos ( u ) )} d u

提出常数:

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

= 45 \cdot \frac{1}{5} \cdot \int \frac{1}{1 - cos ( u )} d u

使用换元积分法

= 45 \cdot \frac{1}{5} \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

= 45 \cdot \frac{1}{5} (- \frac{1}{v})

代回

= 45 \cdot \frac{1}{5} (- \frac{1}{tan ( \frac{5 x}{2} )})

化简

45 \cdot \frac{1}{5} (- \frac{1}{tan ( \frac{5 x}{2} )}) : - 9 cot (\frac{5 x}{2})

= - 9 cot (\frac{5 x}{2})

解答补常数

= - 9 cot (\frac{5 x}{2}) + C

作图

流行的例子

s im pl i f y - 4

derivative f(-1)=-x^3

d er i v a t i v e f (- 1) = - x^{3}

tangent f(x)=x^3-3x+1,(4,53)

t an g e n t f (x) = x^{3} - 3 x + 1, (4, 53)

limit as h approaches 0 of-2x-h+6

h \to 0 lim (- 2 x - h + 6)

integral of 4sqrt(u)

\int 4 u d u