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受欢迎的微积分 >

integral of (cos(pi/(x^5)))/(x^6)

解答

\int \frac{cos ( \frac{π}{x ^{5}} )}{x ^{6}} d x

解答

- \frac{1}{5 π} sin (\frac{π}{x ^{5}}) + C

求解步骤

\int \frac{cos ( \frac{π}{x ^{5}} )}{x ^{6}} d x

使用换元积分法

= \int \frac{cos ( \frac{π}{u} )}{5 u ^{2}} d u

提出常数:

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

= \frac{1}{5} \cdot \int \frac{cos ( \frac{π}{u} )}{u ^{2}} d u

使用换元积分法

= \frac{1}{5} \cdot \int - \frac{cos ( v )}{π} d v

提出常数:

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

= \frac{1}{5} (- \frac{1}{π} \cdot \int cos (v) d v)

使用积分常见定则:

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

= \frac{1}{5} (- \frac{1}{π} sin (v))

代回

= \frac{1}{5} (- \frac{1}{π} sin (\frac{π}{x ^{5}}))

化简

\frac{1}{5} (- \frac{1}{π} sin (\frac{π}{x ^{5}})) : - \frac{1}{5 π} sin (\frac{π}{x ^{5}})

= - \frac{1}{5 π} sin (\frac{π}{x ^{5}})

解答补常数

= - \frac{1}{5 π} sin (\frac{π}{x ^{5}}) + C

作图

流行的例子

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\int sin (ln (x)) d x

integral of 0.5x

\int 0.5 x d x

y^{''}+9y=cos(3x)

y^{^{''}} + 9 y = cos (3 x)

limit as x approaches-8 of x(8)

x \to - 8 lim (x (8))

derivative of 1/x-ln(x)

\frac{d}{d x} (\frac{1}{x} - ln (x))