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受欢迎的微积分 >

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

解答

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

解答

- \frac{4}{tan ( \frac{x}{2} ) - 1} + C

求解步骤

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

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 ( x )} d x

使用换元积分法

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

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 + u ^{2} - 2 u} d u

对

1 + u^{2} - 2 u

配方:

(u - 1)^{2}

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

使用换元积分法

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

使用幂法则

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

代回

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

化简

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

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

解答补常数

= - \frac{4}{tan ( \frac{x}{2} ) - 1} + C

作图

流行的例子

integral of-0.01x

\int - 0.01 x d x

integral of ((x-2)sqrt(1-x^2))/(1-x^2)

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

derivative of (3x-4(5x+2))

\frac{d}{d x} ((3 x - 4) (5 x + 2))

(\partial)/(\partial x)(-y/(sqrt(x^2+y^2)))

\frac{\partial}{\partial x} (- \frac{y}{x ^{2} + y ^{2}})

tangent y= 1/(1+x^2),(1,0.5)

t an g e n t y = \frac{1}{1 + x ^{2}}, (1, 0.5)