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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of-e^{-x}

integral

- e^{- x}

e^{- x} + C

Solution steps

\int - e^{- x} d x

Take the constant out:

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

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

Apply u-substitution

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

Take the constant out:

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

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

Use the common integral:

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

= - (- e^{u})

Substitute back

u = - x

= - (- e^{- x})

Simplify

= e^{- x}

Add a constant to the solution

= e^{- x} + C

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

\int r e^{k r} d r

\int 6 cos (x) sin (x) d x

\int (x^{5} + 3 x^{2}) d x

\int \frac{x ^{7}}{( 4 - x ^{8} ) ^{2}} d x