What is the integral of e^{x-2x} ?

The integral of e^{x-2x} 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-2x}

\int e^{x - 2 x} d x

- e^{- x} + C

Solution steps

\int e^{x - 2 x} d x

Simplify

= \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}

Add a constant to the solution

= - e^{- x} + C

x \to \infty lim ((x - 1) \cdot e^{\frac{1}{x - 1}})

x \to 1 lim (\frac{2 - 2 x}{x - 1})

\int \frac{1}{x x ^{2} + 5} d x

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