What is the integral of e^{x/4} ?

The integral of e^{x/4} is 4e^{x/4}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of e^{x/4}

\int e^{\frac{x}{4}} d x

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

Solution steps

\int e^{\frac{x}{4}} d x

Apply u-substitution

: \int e^{u} \cdot 4 d u

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

Take the constant out:

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

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

Use the common integral:

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

= 4 e^{u}

Substitute back

u = \frac{x}{4}

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

Add a constant to the solution

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

y^{^{'}} - 2 y = e^{3 x}

n \to 1 lim (\frac{( - \frac{1}{5} ) ^{n}}{n})

\frac{d y}{d x} = \frac{y}{x ln ( x )}

\int \frac{3}{2 x} d x

\int \frac{1}{2 ^{n}}