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受欢迎的微积分 >

integral of 4/(x^2)cos(4/x)

解答

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

解答

- sin (\frac{4}{x}) + C

求解步骤

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

提出常数:

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

= 4 \cdot \int \frac{1}{x ^{2}} cos (\frac{4}{x}) d x

使用换元积分法

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

提出常数:

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

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

使用积分常见定则:

\int cos (u) d u = sin (u)

= 4 (- \frac{1}{4} sin (u))

u = \frac{4}{x}

代回

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

化简

4 (- \frac{1}{4} sin (\frac{4}{x})) : - sin (\frac{4}{x})

= - sin (\frac{4}{x})

解答补常数

= - sin (\frac{4}{x}) + C

作图

流行的例子

integral from 0 to pi of sin(x)sin(nx)

\int_{0}^{π} sin (x) sin (n x) d x

integral of (4x-3)^6

\int (4 x - 3)^{6} d x

tangent f(x)= 6/x ,\at x=1

t an g e n t f (x) = \frac{6}{x}, at x = 1

limit as x approaches 4-of (x-4)/(x-1)

x \to 4 - lim (\frac{x - 4}{x - 1})

derivative y= 1/(sqrt(x))

d er i v a t i v e y = \frac{1}{x}