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^2(3-x^3)^{2/3}

解答

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

解答

- \frac{1}{5} (3 - x^{3})^{\frac{5}{3}} + C

求解步骤

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

使用换元积分法

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

使用换元积分法

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

提出常数:

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

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

使用幂法则

= \frac{1}{3} (- \frac{3}{5} v^{\frac{5}{3}})

代回

= \frac{1}{3} (- \frac{3}{5} (3 - x^{3})^{\frac{5}{3}})

化简

\frac{1}{3} (- \frac{3}{5} (3 - x^{3})^{\frac{5}{3}}) : - \frac{1}{5} (3 - x^{3})^{\frac{5}{3}}

= - \frac{1}{5} (3 - x^{3})^{\frac{5}{3}}

解答补常数

= - \frac{1}{5} (3 - x^{3})^{\frac{5}{3}} + C

作图

流行的例子

integral of 1/(4-v^2)

\int \frac{1}{4 - v ^{2}} d v

integral of (x^2+2x-1)/(x^2(x-1))

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

integral of 8x^5-5x^4-4x^3-6x^2-2x-3

\int 8 x^{5} - 5 x^{4} - 4 x^{3} - 6 x^{2} - 2 x - 3 d x

integral of (6x^2+1)ln(5x^3)

\int (6 x^{2} + 1) ln (5 x^{3}) d x

integral of-(e^x)/x

\int - \frac{e ^{x}}{x} d x