What is the integral of e^{-x/3} ?

The integral of e^{-x/3} is -3e^{-x/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{-x/3}

\int e^{- \frac{x}{3}} d x

- 3 e^{- \frac{x}{3}} + C

Solution steps

\int e^{- \frac{x}{3}} d x

Apply u-substitution

= \int - 3 e^{u} d u

Take the constant out:

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

= - 3 \cdot \int e^{u} d u

Use the common integral:

\int e^{u} d u = e^{u}

= - 3 e^{u}

Substitute back

u = - \frac{x}{3}

= - 3 e^{- \frac{x}{3}}

Add a constant to the solution

= - 3 e^{- \frac{x}{3}} + C

s l o p e in t erce pt (4, 3), (- 2, 9)

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

\int 1 - 64 x^{2} d x

\frac{d}{d x} (\frac{x ln ( x )}{1 + ln ( x )})

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