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

The integral of e^{-2x} is -1/2 e^{-2x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{-2x}

\int e^{- 2 x} d x

- \frac{1}{2} e^{- 2 x} + C

Solution steps

\int e^{- 2 x} d x

Apply u-substitution

: \int - \frac{1}{2} e^{u} d u

= \int - \frac{1}{2} e^{u} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{1}{2} e^{u}

Substitute back

u = - 2 x

= - \frac{1}{2} e^{- 2 x}

Add a constant to the solution

= - \frac{1}{2} e^{- 2 x} + C

\frac{d y}{d t} + y = t

\int 18 cos (x) d x

\frac{df}{d x} = 4 x^{2} - 5 x + lo g_{10} (x)

\int \frac{2 x}{x - 1} d x

x \to 0 + lim (9)