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

The integral of e^{(-x)/2} is -2e^{-x/2}+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)/2}

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

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

Solution steps

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

Simplify

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

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= - 2 e^{u}

Substitute back

u = - \frac{x}{2}

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

Add a constant to the solution

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

cot (x^{5})

5^{3^{x^{2}}}

x^{2} y^{^{'}} + 2 x y = 5 cos^{2} (x)

\frac{d}{d x} (x e^{\frac{- x}{2}})

y = \frac{6 x ^{2} + 6 x + 4}{x}