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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of sqrt(e^{x+3)}

\int e^{x + 3} d x

2 e e^{1 + \frac{x}{2}} + C

Solution steps

\int e^{x + 3} d x

e^{x + 3} = e^{3} e^{x}

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

Take the constant out:

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

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

e^{3} = e e

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

Apply radical rule:

n a^{m} = a^{\frac{m}{n}},

assuming

a \geq 0

= e e \cdot \int e^{\frac{x}{2}} d x

Apply u-substitution

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

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

Take the constant out:

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

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

Use the common integral:

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

= e e \cdot 2 e^{u}

Substitute back

u = \frac{x}{2}

= e e \cdot 2 e^{\frac{x}{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e e^{\frac{x}{2}} = e^{1 + \frac{x}{2}}

= 2 e e^{1 + \frac{x}{2}}

Add a constant to the solution

= 2 e e^{1 + \frac{x}{2}} + C

\int \frac{2 x ^{\frac{1}{2}} + 3 x ^{2}}{x ^{3}} d x

\int csc (4 x) cot (4 x) + \frac{13}{x ^{2} + 16} d x

\int e^{- 7 x} sin (x) d x

\int - 2 e^{x} e^{x} d x

\int t cos (k wt) d t

What is the integral of sqrt(e^{x+3)} ?
The integral of sqrt(e^{x+3)} is 2sqrt(e)e^{1+x/2}+C