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)/((x^2+6x)^3)

解答

\int \frac{x + 3}{( x ^{2} + 6 x ) ^{3}} d x

解答

- \frac{1}{4 ( x ^{2} + 6 x ) ^{2}} + C

求解步骤

\int \frac{x + 3}{( x ^{2} + 6 x ) ^{3}} d x

使用换元积分法

= \int \frac{u}{( u ^{2} - 9 ) ^{3}} d u

使用换元积分法

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

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}{v ^{3}} d v

使用幂法则

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

代回

= \frac{1}{2} - \frac{1}{2 ( ( x + 3 ) ^{2} - 9 ) ^{2}}

化简

\frac{1}{2} - \frac{1}{2 ( ( x + 3 ) ^{2} - 9 ) ^{2}} : - \frac{1}{4 ( x ^{2} + 6 x ) ^{2}}

= - \frac{1}{4 ( x ^{2} + 6 x ) ^{2}}

解答补常数

= - \frac{1}{4 ( x ^{2} + 6 x ) ^{2}} + C

作图

流行的例子

integral of (6(x+1))/(sqrt(2x+1))

\int \frac{6 ( x + 1 )}{2 x + 1} d x

integral of e^x(5-2e^x)^2

\int e^{x} (5 - 2 e^{x})^{2} d x

integral of ((x^2-3x+8))/((x^2-4x+7)^2)

\int \frac{( x ^{2} - 3 x + 8 )}{( x ^{2} - 4 x + 7 ) ^{2}} d x

integral of sqrt(200+200cos(x))

\int 200 + 200 cos (x) d x

integral of 1/(sqrt(h-19))

\int \frac{1}{h - 19} d h