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 \sqrt[3]{2-5x^2}(-10x)

解答

\int 3 2 - 5 x^{2} (- 10 x) d x

解答

\frac{3}{4} (2 - 5 x^{2})^{\frac{4}{3}} + C

求解步骤

\int 3 2 - 5 x^{2} (- 10 x) d x

化简

= \int - 10 x 3 2 - 5 x^{2} d x

提出常数:

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

= - 10 \cdot \int x 3 2 - 5 x^{2} d x

使用换元积分法

= - 10 \cdot \int - \frac{3 u}{10} d u

提出常数:

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

= - 10 (- \frac{1}{10} \cdot \int 3 u d u)

使用幂法则

= - 10 (- \frac{1}{10} \cdot \frac{3}{4} u^{\frac{4}{3}})

u = 2 - 5 x^{2}

代回

= - 10 (- \frac{1}{10} \cdot \frac{3}{4} (2 - 5 x^{2})^{\frac{4}{3}})

化简

- 10 (- \frac{1}{10} \cdot \frac{3}{4} (2 - 5 x^{2})^{\frac{4}{3}}) : \frac{3}{4} (2 - 5 x^{2})^{\frac{4}{3}}

= \frac{3}{4} (2 - 5 x^{2})^{\frac{4}{3}}

解答补常数

= \frac{3}{4} (2 - 5 x^{2})^{\frac{4}{3}} + C

作图

流行的例子

integral from 1 to R of x^{-9/5}

\int_{1}^{R} x^{- \frac{9}{5}} d x

integral of 4/x-(4x)/(x^2+1)

\int \frac{4}{x} - \frac{4 x}{x ^{2} + 1} d x

(2 x + 1)^{^{'}}

integral of t^2sin(t)

\int t^{2} sin (t) d t

(x+2)^2y^'+3(x+2)y=4

(x + 2)^{2} y^{^{'}} + 3 (x + 2) y = 4