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 4/(sqrt(e^t))

解答

\int \frac{4}{e ^{t}} d t

解答

- \frac{8}{e ^{\frac{t}{2}}} + C

求解步骤

\int \frac{4}{e ^{t}} d t

提出常数:

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

= 4 \cdot \int \frac{1}{e ^{t}} d t

使用换元积分法

= 4 \cdot \int \frac{1}{u u} d u

化简

u u : u^{\frac{3}{2}}

= 4 \cdot \int \frac{1}{u ^{\frac{3}{2}}} d u

使用幂法则

= 4 (- \frac{2}{u})

u = e^{t}

代回

= 4 (- \frac{2}{e ^{t}})

化简

4 (- \frac{2}{e ^{t}}) : - \frac{8}{e ^{\frac{t}{2}}}

= - \frac{8}{e ^{\frac{t}{2}}}

解答补常数

= - \frac{8}{e ^{\frac{t}{2}}} + C

作图

流行的例子

integral of 1/(4sin(x)+3cos(x))

\int \frac{1}{4 sin ( x ) + 3 cos ( x )} d x

derivative of e^{-x^2-y^2}cos(xy)

\frac{d}{d x} (e^{- x^{2} - y^{2}} cos (x y))

sum from n=1 to infinity of n^2e^{-n^3}

n = 1 \sum \infty n^{2} e^{- n^{3}}

inverselaplace 6/(s^2+9)

in v erse l a pl a ce \frac{6}{s ^{2} + 9}

limit as x approaches 3-of 2/((x-3))

x \to 3 - lim (\frac{2}{( x - 3 )})