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受欢迎的微积分 >

integral of-10csc^2(5x)cot^3(5x)

解答

\int - 10 csc^{2} (5 x) cot^{3} (5 x) d x

解答

\frac{1}{2} cot^{4} (5 x) + C

求解步骤

\int - 10 csc^{2} (5 x) cot^{3} (5 x) d x

提出常数:

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

= - 10 \cdot \int csc^{2} (5 x) cot^{3} (5 x) d x

使用换元积分法

= - 10 \cdot \int csc^{2} (u) cot^{3} (u) \frac{1}{5} d u

提出常数:

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

= - 10 \cdot \frac{1}{5} \cdot \int csc^{2} (u) cot^{3} (u) d u

使用换元积分法

= - 10 \cdot \frac{1}{5} \cdot \int - v^{3} d v

提出常数:

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

= - 10 \cdot \frac{1}{5} (- \int v^{3} d v)

使用幂法则

= - 10 \cdot \frac{1}{5} (- \frac{v ^{4}}{4})

代回

= - 10 \cdot \frac{1}{5} (- \frac{cot ^{4} ( 5 x )}{4})

化简

- 10 \cdot \frac{1}{5} (- \frac{cot ^{4} ( 5 x )}{4}) : \frac{1}{2} cot^{4} (5 x)

= \frac{1}{2} cot^{4} (5 x)

解答补常数

= \frac{1}{2} cot^{4} (5 x) + C

作图

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