What is the integral of e^{-(2x)/3} ?

The integral of e^{-(2x)/3} is -3/2 e^{-(2x)/3}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{-(2x)/3}

\int e^{- \frac{2 x}{3}} d x

- \frac{3}{2} e^{- \frac{2 x}{3}} + C

Solution steps

\int e^{- \frac{2 x}{3}} d x

Apply u-substitution

= \int - \frac{3}{2} e^{u} d u

Take the constant out:

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

= - \frac{3}{2} \cdot \int e^{u} d u

Use the common integral:

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

= - \frac{3}{2} e^{u}

Substitute back

u = - \frac{2 x}{3}

= - \frac{3}{2} e^{- \frac{2 x}{3}}

Add a constant to the solution

= - \frac{3}{2} e^{- \frac{2 x}{3}} + C

What is the integral of e^{-(2x)/3} ?
The integral of e^{-(2x)/3} is -3/2 e^{-(2x)/3}+C