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受欢迎的微积分 >

integral of csc((v-pi)/2)cot((v-pi)/2)

解答

\int csc (\frac{v - π}{2}) cot (\frac{v - π}{2}) d v

解答

- 2 csc (\frac{1}{2} (v - π)) + C

求解步骤

\int csc (\frac{v - π}{2}) cot (\frac{v - π}{2}) d v

\frac{v - π}{2} = \frac{1}{2} (v - π - 2) + 1

= \int csc (\frac{1}{2} (v - π - 2) + 1) cot (\frac{v - π}{2}) d v

使用换元积分法

= \int csc (\frac{u}{2}) cot (\frac{u}{2}) d u

使用换元积分法

= \int csc (w) cot (w) \cdot 2 d w

提出常数:

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

= 2 \cdot \int csc (w) cot (w) d w

使用换元积分法

= 2 \cdot \int - 1 d t

常数积分:

\int a d x = a x

= 2 (- 1) t

代回

= 2 (- 1) csc (\frac{v - π}{2})

化简

2 (- 1) csc (\frac{v - π}{2}) : - 2 csc (\frac{1}{2} (v - π))

= - 2 csc (\frac{1}{2} (v - π))

解答补常数

= - 2 csc (\frac{1}{2} (v - π)) + C

作图

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