integral of sqrt(cot(y))csc^2(y)

解答

\int cot (y) csc^{2} (y) d y

- \frac{2}{3} cot^{\frac{3}{2}} (y) + C

求解步骤

\int cot (y) csc^{2} (y) d y

使用换元积分法

= \int - u d u

提出常数:

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

= - \int u d u

使用幂法则

= - \frac{2}{3} u^{\frac{3}{2}}

u = cot (y)

代回

= - \frac{2}{3} cot^{\frac{3}{2}} (y)

解答补常数

= - \frac{2}{3} cot^{\frac{3}{2}} (y) + C

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