What is the integral of (e^x+1/(4x)) ?

The integral of (e^x+1/(4x)) is e^x+1/4 ln|x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (e^x+1/(4x))

\int (e^{x} + \frac{1}{4 x}) d x

e^{x} + \frac{1}{4} ln ∣ x ∣ + C

Solution steps

\int e^{x} + \frac{1}{4 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

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

\int \frac{1}{4 x} d x = \frac{1}{4} ln ∣ x ∣

= e^{x} + \frac{1}{4} ln ∣ x ∣

Add a constant to the solution

= e^{x} + \frac{1}{4} ln ∣ x ∣ + C

What is the integral of (e^x+1/(4x)) ?
The integral of (e^x+1/(4x)) is e^x+1/4 ln|x|+C