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

The integral of (e^{3x})^2 is 1/6 e^{6x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\int (e^{3 x})^{2} d x

\frac{1}{6} e^{6 x} + C

Solution steps

\int (e^{3 x})^{2} d x

Simplify

(e^{3 x})^{2} : e^{6 x}

= \int e^{6 x} d x

Apply u-substitution

= \int e^{u} \frac{1}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{6} e^{u}

Substitute back

u = 6 x

= \frac{1}{6} e^{6 x}

Add a constant to the solution

= \frac{1}{6} e^{6 x} + C