en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

integral of (3+x)/x

Solution

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

Solution

3 ln ∣ x ∣ + x + C

Solution steps

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

Expand

\frac{3 + x}{x} : \frac{3}{x} + 1

= \int \frac{3}{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{3}{x} d x + \int 1 d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 1 d x = x

= 3 ln ∣ x ∣ + x

Add a constant to the solution

= 3 ln ∣ x ∣ + x + C

Graph

Popular Examples

integral of 1/(sin^2(x))

integral of (cos(pi/(x^{47)}))/(x^{48)}

integral of (4-x^2)^{-3/2}

integral of cos^3(5x)sin(5x)

integral of \sqrt[3]{sin(x)}*cos(x)

Frequently Asked Questions (FAQ)

What is the integral of (3+x)/x ?
The integral of (3+x)/x is 3ln|x|+x+C