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(9x-5)

解答

\int 9 x - 5 d x

解答

\frac{2}{27} (9 x - 5)^{\frac{3}{2}} + C

求解步骤

\int 9 x - 5 d x

使用换元积分法

= \int \frac{u}{9} d u

提出常数:

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

= \frac{1}{9} \cdot \int u d u

使用幂法则

= \frac{1}{9} \cdot \frac{2}{3} u^{\frac{3}{2}}

u = 9 x - 5

代回

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

化简

\frac{1}{9} \cdot \frac{2}{3} (9 x - 5)^{\frac{3}{2}} : \frac{2}{27} (9 x - 5)^{\frac{3}{2}}

= \frac{2}{27} (9 x - 5)^{\frac{3}{2}}

解答补常数

= \frac{2}{27} (9 x - 5)^{\frac{3}{2}} + C

作图

流行的例子

limit as x approaches-1 of 6x+5

x \to - 1 lim (6 x + 5)

derivative of arccos(x/(sqrt(1-x^2)))

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

f (x) = cos^{6} (x)

limit as x approaches 4 of x(x+5)(x+6)

x \to 4 lim (x (x + 5) (x + 6))

(d^4)/(dx^4)(3ln(x))

\frac{d ^{4}}{d x ^{4}} (3 ln (x))