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受欢迎的微积分 >

integral of (sin((-5)/x))/(11x^2)

解答

\int \frac{sin ( \frac{- 5}{x} )}{11 x ^{2}} d x

解答

- \frac{1}{55} cos (\frac{5}{x}) + C

求解步骤

\int \frac{sin ( \frac{- 5}{x} )}{11 x ^{2}} d x

提出常数:

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

= \frac{1}{11} \cdot \int \frac{sin ( \frac{- 5}{x} )}{x ^{2}} d x

化简

\frac{sin ( \frac{- 5}{x} )}{x ^{2}} : - \frac{sin ( \frac{5}{x} )}{x ^{2}}

= \frac{1}{11} \cdot \int - \frac{sin ( \frac{5}{x} )}{x ^{2}} d x

提出常数:

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

= \frac{1}{11} (- \int \frac{sin ( \frac{5}{x} )}{x ^{2}} d x)

使用换元积分法

= \frac{1}{11} (- \int - \frac{sin ( u )}{5} d u)

提出常数:

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

= \frac{1}{11} (- (- \frac{1}{5} \cdot \int sin (u) d u))

使用积分常见定则:

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

= \frac{1}{11} (- (- \frac{1}{5} (- cos (u))))

u = \frac{5}{x}

代回

= \frac{1}{11} (- (- \frac{1}{5} (- cos (\frac{5}{x}))))

化简

\frac{1}{11} (- (- \frac{1}{5} (- cos (\frac{5}{x})))) : - \frac{1}{55} cos (\frac{5}{x})

= - \frac{1}{55} cos (\frac{5}{x})

解答补常数

= - \frac{1}{55} cos (\frac{5}{x}) + C

作图

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