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

The integral of sqrt(2e^{2t)} is sqrt(2)e^t+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(2e^{2t)}

\int 2 e^{2 t} d t

2 e^{t} + C

Solution steps

\int 2 e^{2 t} d t

Apply u-substitution

: \int \frac{1}{2} e^{\frac{u}{2}} d u

= \int \frac{1}{2} e^{\frac{u}{2}} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int e^{\frac{u}{2}} d u

Apply u-substitution

: \int e^{v} \cdot 2 d v

= \frac{1}{2} \cdot \int e^{v} \cdot 2 d v

Take the constant out:

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

= \frac{1}{2} \cdot 2 \cdot \int e^{v} d v

Use the common integral:

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

= \frac{1}{2} \cdot 2 e^{v}

Substitute back

= \frac{1}{2} \cdot 2 e^{\frac{2 t}{2}}

Simplify

\frac{1}{2} \cdot 2 e^{\frac{2 t}{2}} : 2 e^{t}

= 2 e^{t}

Add a constant to the solution

= 2 e^{t} + C

\frac{d}{d x} ((x^{2} + 2 x)^{4} (x^{2} + 3 x^{2} + 7)^{3})

y = x^{2} - 5 x + 3, (2, - 3)

\int x \cdot x^{2} - 1 d x

\int \frac{225 - x ^{2}}{x} d x

\int (\frac{1 + x}{x})^{2} d x

What is the integral of sqrt(2e^{2t)} ?
The integral of sqrt(2e^{2t)} is sqrt(2)e^t+C