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 (3x-1)^{-4}

解答

\int (3 x - 1)^{- 4} d x

解答

- \frac{1}{9 ( 3 x - 1 ) ^{3}} + C

求解步骤

\int (3 x - 1)^{- 4} d x

使用指数法则:

a^{- b} = \frac{1}{a ^{b}}

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

使用换元积分法

= \int \frac{1}{3 u ^{4}} d u

提出常数:

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

= \frac{1}{3} \cdot \int \frac{1}{u ^{4}} d u

使用幂法则

= \frac{1}{3} (- \frac{1}{3 u ^{3}})

u = 3 x - 1

代回

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

化简

\frac{1}{3} (- \frac{1}{3 ( 3 x - 1 ) ^{3}}) : - \frac{1}{9 ( 3 x - 1 ) ^{3}}

= - \frac{1}{9 ( 3 x - 1 ) ^{3}}

解答补常数

= - \frac{1}{9 ( 3 x - 1 ) ^{3}} + C

作图

流行的例子

y^'-7/(600+2t)y=6

y^{^{'}} - \frac{7}{600 + 2 t} y = 6

integral from 0 to 2 of 1/(x^2)

\int_{0}^{2} \frac{1}{x ^{2}} d x

(\partial)/(\partial x)(e^{xy}sin(xyz))

\frac{\partial}{\partial x} (e^{x y} sin (x yz))

t^2y^{''}-7ty^'+15y=0

t^{2} y^{^{''}} - 7 t y^{^{'}} + 15 y = 0

inverselaplace (s^2)/(s^3-1)

in v erse l a pl a ce \frac{s ^{2}}{s ^{3} - 1}