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

Popular >

integral of (-e^{-x})

\int (- e^{- x}) d 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

= - \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

\frac{d}{d x} (\frac{x ^{2} - 4}{x ^{2} - 3})

i = 0 \sum \infty (\frac{1}{3})^{i}

\frac{\partial}{\partial x} (\frac{1}{1 + x ^{2} + y ^{2}})

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

x \to 2 lim (x^{2} + 3 x - 1)