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/(1-sin(1/2 x))

解答

\int \frac{1}{1 - sin ( \frac{1}{2} x )} d x

解答

- \frac{4}{tan ( \frac{x}{4} ) - 1} + C

求解步骤

\int \frac{1}{1 - sin ( \frac{1}{2} x )} d x

使用换元积分法

= \int \frac{2}{1 - sin ( u )} d u

提出常数:

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

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

使用换元积分法

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

提出常数:

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

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

对

1 + v^{2} - 2 v

配方:

(v - 1)^{2}

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

使用换元积分法

= 2 \cdot 2 \cdot \int \frac{1}{w ^{2}} d w

使用幂法则

= 2 \cdot 2 (- \frac{1}{w})

代回

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

化简

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

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

解答补常数

= - \frac{4}{tan ( \frac{x}{4} ) - 1} + C

作图

流行的例子

t^2y^{''}+ty^'+4y=0

t^{2} y^{^{''}} + t y^{^{'}} + 4 y = 0

integral of 3x^3cos(5x)

\int 3 x^{3} cos (5 x) d x

limit as x approaches 5 of sqrt(x^2+11)

x \to 5 lim (x^{2} + 11)

limit as x approaches+(-3)-of 2x^2-6

x \to + (- 3) - lim (2 x^{2} - 6)

integral of (sqrt(100-x^2))/x

\int \frac{100 - x ^{2}}{x} d x