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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-x/a}

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

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

Solution steps

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

Apply u-substitution

: \int - a e^{u} d u

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

Take the constant out:

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

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

Use the common integral:

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

= - a e^{u}

Substitute back

u = - \frac{x}{a}

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

Add a constant to the solution

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

\int_{- 1}^{0} (x^{5} - 4 x^{3} + 4 x + 4) d x

\int \frac{4 x ^{2} - 8 x}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

\int x cos (n \cdot π \cdot \frac{x}{2}) d x

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

\int \frac{12 x}{2 x - 5} d x