What is the integral of \sqrt[7]{e^x} ?

The integral of \sqrt[7]{e^x} is 7e^{x/7}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of \sqrt[7]{e^x}

7 e^{\frac{x}{7}} + C

Solution steps

Apply radical rule:

assuming

a \geq 0

= \int e^{\frac{x}{7}} d x

Apply u-substitution

: \int e^{u} \cdot 7 d u

= \int e^{u} \cdot 7 d u

Take the constant out:

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

= 7 \cdot \int e^{u} d u

Use the common integral:

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

= 7 e^{u}

Substitute back

u = \frac{x}{7}

= 7 e^{\frac{x}{7}}

Add a constant to the solution

= 7 e^{\frac{x}{7}} + C

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

y = (1 + sin (7 t))^{- 6}

\frac{d y}{d t} = \frac{t e ^{t}}{y 9 + y ^{2}}

\frac{d}{d x} (y^{2} e^{x y - 3})

f (x) = 4 x y

What is the integral of \sqrt[7]{e^x} ?
The integral of \sqrt[7]{e^x} is 7e^{x/7}+C