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受欢迎的微积分 >

integral of 1/(1-cos(4x))

解答

\int \frac{1}{1 - cos ( 4 x )} d x

解答

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

求解步骤

\int \frac{1}{1 - cos ( 4 x )} d x

使用换元积分法

= \int \frac{1}{4 ( 1 - cos ( u ) )} d u

提出常数:

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

= \frac{1}{4} \cdot \int \frac{1}{1 - cos ( u )} d u

使用换元积分法

= \frac{1}{4} \cdot \int \frac{1}{v ^{2}} d v

使用幂法则

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

代回

= \frac{1}{4} (- \frac{1}{tan ( \frac{4 x}{2} )})

化简

\frac{1}{4} (- \frac{1}{tan ( \frac{4 x}{2} )}) : - \frac{1}{4} cot (2 x)

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

解答补常数

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

作图

流行的例子

integral of ((x^2))/(1-x^2)

\int \frac{( x ^{2} )}{1 - x ^{2}} d x

integral of x^3+3x

\int x^{3} + 3 x d x

integral of x^2-3sqrt(x)

\int x^{2} - 3 x d x

integral of 4(cos(x))^2

\int 4 (cos (x))^{2} d x

integral of 1/(sin(x)+2cos(x)+3)

\int \frac{1}{sin ( x ) + 2 cos ( x ) + 3} d x