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

解答

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

解答

\frac{1}{4 ( 3 - x ^{4} )} + C

求解步骤

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

使用换元积分法

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

使用幂法则

= - \frac{1}{4} (- \frac{1}{u})

u = 3 - x^{4}

代回

= - \frac{1}{4} (- \frac{1}{3 - x ^{4}})

化简

- \frac{1}{4} (- \frac{1}{3 - x ^{4}}) : \frac{1}{4 ( 3 - x ^{4} )}

= \frac{1}{4 ( 3 - x ^{4} )}

解答补常数

= \frac{1}{4 ( 3 - x ^{4} )} + C

作图

流行的例子

derivative y=2sin(4x)

d er i v a t i v e y = 2 sin (4 x)

y^'-8/x y=(y^3)/(x^{11)}

y^{^{'}} - \frac{8}{x} y = \frac{y ^{3}}{x ^{11}}

limit as x approaches 3-of |x-3|

x \to 3 - lim (∣ x - 3 ∣)

(dy)/(dt)=3y(y-2)

\frac{d y}{d t} = 3 y (y - 2)

x y^{^{'}} + y = 2 x^{2}