What is the integral of e^{x/3} ?

The integral of e^{x/3} is 3e^{x/3}+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/3}

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

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

Solution steps

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

Apply u-substitution

: \int e^{u} \cdot 3 d u

= \int e^{u} \cdot 3 d u

Take the constant out:

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

= 3 \cdot \int e^{u} d u

Use the common integral:

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

= 3 e^{u}

Substitute back

u = \frac{x}{3}

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

Add a constant to the solution

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

ln (x + 1 + x^{2} + 2 x), 1

\int_{- 6}^{- 1} 8 d x

\int (x + 4)^{2} (x - 4) d x

x^{2}

e^{t}