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受欢迎的微积分 >

integral of 1/(csc(2x))csc(2x)cot(2x)

解答

\int \frac{1}{csc ( 2 x )} csc (2 x) cot (2 x) d x

解答

\frac{1}{2} ln ∣ sin (2 x) ∣ + C

求解步骤

\int \frac{1}{csc ( 2 x )} csc (2 x) cot (2 x) d x

化简

\frac{1}{csc ( 2 x )} csc (2 x) cot (2 x) : cot (2 x)

= \int cot (2 x) d x

使用三角恒等式改写

= \int \frac{cos ( 2 x )}{sin ( 2 x )} d x

使用换元积分法

= \int \frac{1}{2 u} d u

提出常数:

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

u = sin (2 x)

代回

= \frac{1}{2} ln ∣ sin (2 x) ∣

解答补常数

= \frac{1}{2} ln ∣ sin (2 x) ∣ + C

作图

流行的例子

(dy)/(dx)+3x^2y=sin(x)e^{-x^3},y(0)=1

\frac{d y}{d x} + 3 x^{2} y = sin (x) e^{- x^{3}}, y (0) = 1

integral of-9x^5e^{x^6}

\int - 9 x^{5} e^{x^{6}} d x

limit as x approaches 5-of (3x)/(2x+10)

x \to 5 - lim (\frac{3 x}{2 x + 10})

derivative of (arctan(3x)^2)

\frac{d}{d x} ((arctan (3 x))^{2})

泰勒 1/(x+5),0

t a y l or \frac{1}{x + 5}, 0