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

The integral of (e^{2x})^2 is 1/4 e^{4x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

\frac{1}{4} e^{4 x} + C

Solution steps

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

Simplify

(e^{2 x})^{2} : e^{4 x}

= \int e^{4 x} d x

Apply u-substitution

: \int e^{u} \frac{1}{4} d u

= \int e^{u} \frac{1}{4} d u

Take the constant out:

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

= \frac{1}{4} \cdot \int e^{u} d u

Use the common integral:

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

= \frac{1}{4} e^{u}

Substitute back

u = 4 x

= \frac{1}{4} e^{4 x}

Add a constant to the solution

= \frac{1}{4} e^{4 x} + C

\int (2 + 2 cos (x))^{2} d x

\int_{0}^{π} 9 sin (x) d x

\frac{d}{d x} (\frac{x ^{12}}{x ^{2}})

y^{^{'}} = x^{2} \cdot (1 + y)

n = 1 \sum \infty n (\frac{1}{2})^{n}