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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (e^{4x})/(4x)

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

\frac{1}{4} Ei (4 x) + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

Use the nonelementary integral:

\int \frac{e ^{x}}{x} d x = Ei (x)

= \frac{1}{4} Ei (u)

Substitute back

u = 4 x

= \frac{1}{4} Ei (4 x)

Add a constant to the solution

= \frac{1}{4} Ei (4 x) + C

What is the integral of (e^{4x})/(4x) ?
The integral of (e^{4x})/(4x) is 1/4 \Ei(4x)+C