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受欢迎的微积分 >

integral of xcsc(3x^2)cot(3x^2)

解答

\int x csc (3 x^{2}) cot (3 x^{2}) d x

解答

- \frac{1}{6} csc (3 x^{2}) + C

求解步骤

\int x csc (3 x^{2}) cot (3 x^{2}) d x

使用换元积分法

= \int \frac{csc ( u ) cot ( u )}{6} d u

提出常数:

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

= \frac{1}{6} \cdot \int csc (u) cot (u) d u

使用换元积分法

= \frac{1}{6} \cdot \int - 1 d v

常数积分:

\int a d x = a x

= \frac{1}{6} (- 1) v

代回

= \frac{1}{6} (- 1) csc (3 x^{2})

化简

= - \frac{1}{6} csc (3 x^{2})

解答补常数

= - \frac{1}{6} csc (3 x^{2}) + C

作图

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