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受欢迎的微积分 >

integral of (sin(1/(x^4)))/(x^5)

解答

\int \frac{sin ( \frac{1}{x ^{4}} )}{x ^{5}} d x

解答

\frac{1}{4} cos (\frac{1}{x ^{4}}) + C

求解步骤

\int \frac{sin ( \frac{1}{x ^{4}} )}{x ^{5}} d x

使用换元积分法

= \int \frac{sin ( \frac{1}{u} )}{4 u ^{2}} 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{sin ( \frac{1}{u} )}{u ^{2}} d u

使用换元积分法

= \frac{1}{4} \cdot \int - sin (v) d v

提出常数:

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

= \frac{1}{4} (- \int sin (v) d v)

使用积分常见定则:

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

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

代回

= \frac{1}{4} (- (- cos (\frac{1}{x ^{4}})))

化简

= \frac{1}{4} cos (\frac{1}{x ^{4}})

解答补常数

= \frac{1}{4} cos (\frac{1}{x ^{4}}) + C

作图

流行的例子

integral from 0.2 to 0.4 of 150x

\int_{0.2}^{0.4} 150 x d x

derivative 5/(sqrt(x)+5)

d er i v a t i v e \frac{5}{x + 5}

y^{^{'}} - (2 x + 1) y = 0

integral of 1/(csc(x)(1+sin(x)))

\int \frac{1}{csc ( x ) ( 1 + sin ( x ) )} d x

integral from 0 to x of sqrt(1+36t)

\int_{0}^{x} 1 + 36 t d t