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 (2x^2)/(sqrt(7-6x^3))

解答

\int \frac{2 x ^{2}}{7 - 6 x ^{3}} d x

解答

- \frac{2}{9} 7 - 6 x^{3} + C

求解步骤

\int \frac{2 x ^{2}}{7 - 6 x ^{3}} d x

提出常数:

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

= 2 \cdot \int \frac{x ^{2}}{7 - 6 x ^{3}} d x

使用换元积分法

= 2 \cdot \int - \frac{1}{18 u} d u

提出常数:

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

= 2 (- \frac{1}{18} \cdot \int \frac{1}{u} d u)

使用幂法则

= 2 (- \frac{1}{18} \cdot 2 u^{\frac{1}{2}})

u = 7 - 6 x^{3}

代回

= 2 (- \frac{1}{18} \cdot 2 (7 - 6 x^{3})^{\frac{1}{2}})

化简

2 (- \frac{1}{18} \cdot 2 (7 - 6 x^{3})^{\frac{1}{2}}) : - \frac{2}{9} 7 - 6 x^{3}

= - \frac{2}{9} 7 - 6 x^{3}

解答补常数

= - \frac{2}{9} 7 - 6 x^{3} + C

作图

流行的例子

integral of x^2sin^2(x^3)

\int x^{2} sin^{2} (x^{3}) d x

integral of (4-3x)^6

\int (4 - 3 x)^{6} d x

integral of tcos(3t)

\int t cos (3 t) d t

integral of (2x+1)(3-x)

\int (2 x + 1) (3 - x) d x

integral of (x-2)^6

\int (x - 2)^{6} d x