zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的微积分 >

integral of x/((x^2-4)^3)

解答

\int \frac{x}{( x ^{2} - 4 ) ^{3}} d x

解答

- \frac{1}{4 ( x ^{2} - 4 ) ^{2}} + C

求解步骤

\int \frac{x}{( x ^{2} - 4 ) ^{3}} d x

使用换元积分法

= \int \frac{1}{2 u ^{3}} d u

提出常数:

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

= \frac{1}{2} \cdot \int \frac{1}{u ^{3}} d u

使用幂法则

= \frac{1}{2} (- \frac{1}{2 u ^{2}})

u = x^{2} - 4

代回

= \frac{1}{2} (- \frac{1}{2 ( x ^{2} - 4 ) ^{2}})

化简

\frac{1}{2} (- \frac{1}{2 ( x ^{2} - 4 ) ^{2}}) : - \frac{1}{4 ( x ^{2} - 4 ) ^{2}}

= - \frac{1}{4 ( x ^{2} - 4 ) ^{2}}

解答补常数

= - \frac{1}{4 ( x ^{2} - 4 ) ^{2}} + C

作图

流行的例子

derivative of (ax^2/(ln(x/4)))

\frac{d}{d x} (\frac{a x ^{2}}{ln ( \frac{x}{4} )})

y^{^{'}} = \frac{x - y}{x}

derivative e^{-(x+2)}-sin(x^2)+1

d er i v a t i v e e^{- (x + 2)} - sin (x^{2}) + 1

derivative (x^2)/4+x+1

d er i v a t i v e \frac{x ^{2}}{4} + x + 1

integral of 1/(sin(x)-2csc(x))

\int \frac{1}{sin ( x ) - 2 csc ( x )} d x