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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 5e^{-x}

\int 5 e^{- x} d x

- 5 e^{- x} + C

Solution steps

\int 5 e^{- x} d x

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= 5 (- e^{u})

Substitute back

u = - x

= 5 (- e^{- x})

Simplify

= - 5 e^{- x}

Add a constant to the solution

= - 5 e^{- x} + C