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 1/(3^{2x)}

解答

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

解答

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

求解步骤

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

使用指数法则:

\frac{1}{a ^{b}} = a^{- b}

\frac{1}{3 ^{2 x}} = 3^{- 2 x}

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

使用换元积分法

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

提出常数:

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

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

\int a^{x} d x = \frac{a ^{x}}{ln a}

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

u = - 2 x

代回

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

化简

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

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

解答补常数

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

作图

流行的例子

derivative of-1/(2x^{3/2})

\frac{d}{d x} (- \frac{1}{2 x ^{\frac{3}{2}}})

limit as x approaches 0 of tan^x(2x)

x \to 0 lim (tan^{x} (2 x))

derivative y=2x^2sqrt(25-x^2)

d er i v a t i v e y = 2 x^{2} 25 - x^{2}

y^{^{'}} = x y - y

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

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