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 (a^2x^2)/(sqrt(x^3+a))

解答

\int \frac{a ^{2} x ^{2}}{x ^{3} + a} d x

解答

\frac{2}{3} a^{2} x^{3} + a + C

求解步骤

\int \frac{a ^{2} x ^{2}}{x ^{3} + a} d x

提出常数:

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

= a^{2} \cdot \int \frac{x ^{2}}{x ^{3} + a} d x

使用换元积分法

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

提出常数:

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

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

使用换元积分法

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

使用幂法则

= a^{2} \frac{1}{3} \cdot 2 v^{\frac{1}{2}}

代回

= a^{2} \frac{1}{3} \cdot 2 (x^{3} + a)^{\frac{1}{2}}

化简

a^{2} \frac{1}{3} \cdot 2 (x^{3} + a)^{\frac{1}{2}} : \frac{2}{3} a^{2} x^{3} + a

= \frac{2}{3} a^{2} x^{3} + a

解答补常数

= \frac{2}{3} a^{2} x^{3} + a + C

作图

流行的例子

integral of (x+1)^2-1

\int (x + 1)^{2} - 1 d x

integral of 1/(x(2sqrt(x-1)))

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

integral of x^{1/8}

\int x^{\frac{1}{8}} d x

integral of (2900)/(1+0.25t)

\int \frac{2900}{1 + 0.25 t} d t

integral of 12x+2

\int 12 x + 2 d x