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受欢迎的微积分 >

integral of cot(10x)csc^4(10x)

解答

\int cot (10 x) csc^{4} (10 x) d x

解答

- \frac{1}{40} csc^{4} (10 x) + C

求解步骤

\int cot (10 x) csc^{4} (10 x) d x

使用换元积分法

= \int cot (u) csc^{4} (u) \frac{1}{10} d u

提出常数:

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

= \frac{1}{10} \cdot \int cot (u) csc^{4} (u) d u

使用三角恒等式改写

= \frac{1}{10} \cdot \int \frac{cos ( u )}{sin ^{5} ( u )} d u

使用换元积分法

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

使用幂法则

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

代回

= \frac{1}{10} (- \frac{1}{4 sin ^{4} ( 10 x )})

化简

\frac{1}{10} (- \frac{1}{4 sin ^{4} ( 10 x )}) : - \frac{1}{40} csc^{4} (10 x)

= - \frac{1}{40} csc^{4} (10 x)

解答补常数

= - \frac{1}{40} csc^{4} (10 x) + C

作图

流行的例子

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\frac{d ^{2}}{d x ^{2}} ((x^{2} + 5)^{7})

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limit as x approaches-8 of |x|

x \to - 8 lim (∣ x ∣)

(dy)/(dx)=(sin(5x))

\frac{d y}{d x} = (sin (5 x))