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受欢迎的微积分 >

integral of 7/(x^2)cos(7/x)

解答

\int \frac{7}{x ^{2}} cos (\frac{7}{x}) d x

解答

- sin (\frac{7}{x}) + C

求解步骤

\int \frac{7}{x ^{2}} cos (\frac{7}{x}) d x

提出常数:

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

= 7 \cdot \int \frac{1}{x ^{2}} cos (\frac{7}{x}) d x

使用换元积分法

= 7 \cdot \int - \frac{cos ( u )}{7} d u

提出常数:

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

= 7 (- \frac{1}{7} \cdot \int cos (u) d u)

使用积分常见定则:

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

= 7 (- \frac{1}{7} sin (u))

u = \frac{7}{x}

代回

= 7 (- \frac{1}{7} sin (\frac{7}{x}))

化简

7 (- \frac{1}{7} sin (\frac{7}{x})) : - sin (\frac{7}{x})

= - sin (\frac{7}{x})

解答补常数

= - sin (\frac{7}{x}) + C

作图

流行的例子

limit as h approaches 0 of x^2+2x+h-69

h \to 0 lim (x^{2} + 2 x + h - 69)

y^'(t)=(3+y)(1-y),y(0)=2

y^{^{'}} (t) = (3 + y) (1 - y), y (0) = 2

y^{^{'}} + 2 y = \frac{1}{x}

integral of (4w-11)/(2w^2+7w-4)

\int \frac{4 w - 11}{2 w ^{2} + 7 w - 4} d w

integral from-1 to 1 of 11^x

\int_{- 1}^{1} 1 1^{x} d x