en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (4+x)/x

Solution

\int \frac{4 + x}{x} d x

Solution

4 ln ∣ x ∣ + x + C

Solution steps

\int \frac{4 + x}{x} d x

Expand

\frac{4 + x}{x} : \frac{4}{x} + 1

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

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int 1 d x = x

= 4 ln ∣ x ∣ + x

Add a constant to the solution

= 4 ln ∣ x ∣ + x + C

Graph

Popular Examples

integral of r/(sqrt(1-r^2))

integral of (3x^{1/2}-x^{(-2)/3}+7)

integral of arcsin(x-1)

integral of (2+sin^2(x))/(cos^2(x))

integral of y/((y^2+1))

Frequently Asked Questions (FAQ)

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