What is the integral of 8e^{3x} ?

The integral of 8e^{3x} is 8/3 e^{3x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 8e^{3x}

\int 8 e^{3 x} d x

\frac{8}{3} e^{3 x} + C

Solution steps

\int 8 e^{3 x} d x

Take the constant out:

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

= 8 \cdot \int e^{3 x} d x

Apply u-substitution

= 8 \cdot \int e^{u} \frac{1}{3} d u

Take the constant out:

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

= 8 \cdot \frac{1}{3} \cdot \int e^{u} d u

Use the common integral:

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

= 8 \cdot \frac{1}{3} e^{u}

Substitute back

u = 3 x

= 8 \cdot \frac{1}{3} e^{3 x}

Simplify

8 \cdot \frac{1}{3} e^{3 x} : \frac{8}{3} e^{3 x}

= \frac{8}{3} e^{3 x}

Add a constant to the solution

= \frac{8}{3} e^{3 x} + C