What is the integral of 1/5 e^{-x/5} ?

The integral of 1/5 e^{-x/5} is -e^{-x/5}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/5 e^{-x/5}

\int \frac{1}{5} e^{- \frac{x}{5}} d x

- e^{- \frac{x}{5}} + C

Solution steps

\int \frac{1}{5} e^{- \frac{x}{5}} d x

Take the constant out:

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

= \frac{1}{5} \cdot \int e^{- \frac{x}{5}} d x

Apply u-substitution

: \int - 5 e^{u} d u

= \frac{1}{5} \cdot \int - 5 e^{u} d u

Take the constant out:

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

= \frac{1}{5} (- 5 \cdot \int e^{u} d u)

Use the common integral:

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

= \frac{1}{5} (- 5 e^{u})

Substitute back

u = - \frac{x}{5}

= \frac{1}{5} (- 5 e^{- \frac{x}{5}})

Simplify

\frac{1}{5} (- 5 e^{- \frac{x}{5}}) : - e^{- \frac{x}{5}}

= - e^{- \frac{x}{5}}

Add a constant to the solution

= - e^{- \frac{x}{5}} + C

\int (2 + tan^{2} (x)) d x

x \to 0 + lim (L (x))

\frac{d ^{2} x}{d t ^{2}} + 4 x = cos (3 t)

x \to 2 lim (4 - a \cdot x)

What is the integral of 1/5 e^{-x/5} ?
The integral of 1/5 e^{-x/5} is -e^{-x/5}+C