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^2sqrt(5-2x^3)

解答

\int x^{2} 5 - 2 x^{3} d x

解答

- \frac{1}{9} (5 - 2 x^{3})^{\frac{3}{2}} + C

求解步骤

\int x^{2} 5 - 2 x^{3} d x

使用换元积分法

= \int \frac{5 - 2 u}{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 5 - 2 u d u

使用换元积分法

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

提出常数:

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

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

使用幂法则

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

代回

= \frac{1}{3} (- \frac{1}{2} \cdot \frac{2}{3} (5 - 2 x^{3})^{\frac{3}{2}})

化简

\frac{1}{3} (- \frac{1}{2} \cdot \frac{2}{3} (5 - 2 x^{3})^{\frac{3}{2}}) : - \frac{1}{9} (5 - 2 x^{3})^{\frac{3}{2}}

= - \frac{1}{9} (5 - 2 x^{3})^{\frac{3}{2}}

解答补常数

= - \frac{1}{9} (5 - 2 x^{3})^{\frac{3}{2}} + C

作图

流行的例子

integral of (x^{1.8}+11x^{4.5})

\int (x^{1.8} + 11 x^{4.5}) d x

(\partial)/(\partial y)(7e^xln(y))

\frac{\partial}{\partial y} (7 e^{x} ln (y))

limit as x approaches 6 of x(x-3)

x \to 6 lim (x (x - 3))

y^{''}-18y^'+130y=0,y(0)=0,y(pi/2)=1

y^{^{''}} - 18 y^{^{'}} + 130 y = 0, y (0) = 0, y (\frac{π}{2}) = 1

integral of (3x^2+3x+3)/(x^2+1)

\int \frac{3 x ^{2} + 3 x + 3}{x ^{2} + 1} d x