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受欢迎的微积分 >

integral of (27)/(1-cos(9x))

解答

\int \frac{27}{1 - cos ( 9 x )} d x

解答

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

求解步骤

\int \frac{27}{1 - cos ( 9 x )} d x

提出常数:

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

= 27 \cdot \int \frac{1}{1 - cos ( 9 x )} d x

使用换元积分法

= 27 \cdot \int \frac{1}{9 ( 1 - cos ( u ) )} d u

提出常数:

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

= 27 \cdot \frac{1}{9} \cdot \int \frac{1}{1 - cos ( u )} d u

使用换元积分法

= 27 \cdot \frac{1}{9} \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

= 27 \cdot \frac{1}{9} (- \frac{1}{v})

代回

= 27 \cdot \frac{1}{9} (- \frac{1}{tan ( \frac{9 x}{2} )})

化简

27 \cdot \frac{1}{9} (- \frac{1}{tan ( \frac{9 x}{2} )}) : - 3 cot (\frac{9 x}{2})

= - 3 cot (\frac{9 x}{2})

解答补常数

= - 3 cot (\frac{9 x}{2}) + C

作图

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