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受欢迎的微积分 >

integral of cot(mx)csc^2(mx)

解答

\int cot (m x) csc^{2} (m x) d x

解答

- \frac{1}{2 m} csc^{2} (m x) + C

求解步骤

\int cot (m x) csc^{2} (m x) d x

使用换元积分法

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

提出常数:

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

= \frac{1}{m} \cdot \int csc^{2} (u) cot (u) d u

使用换元积分法

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

常数积分:

\int a d x = a x

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

代回

= \frac{1}{m} (- \frac{1}{2}) csc^{2} (m x)

化简

\frac{1}{m} (- \frac{1}{2}) csc^{2} (m x) : - \frac{1}{2 m} csc^{2} (m x)

= - \frac{1}{2 m} csc^{2} (m x)

解答补常数

= - \frac{1}{2 m} csc^{2} (m x) + C

作图

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