What is the integral of x/(x(x^2+1)) ?

The integral of x/(x(x^2+1)) is arctan(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\int \frac{x}{x ( x ^{2} + 1 )} d x

arctan (x) + C

Solution steps

\int \frac{x}{x ( x ^{2} + 1 )} d x

Cancel the common factor:

x

= \int \frac{1}{x ^{2} + 1} d x

Use the common integral:

\int \frac{1}{x ^{2} + 1} d x = arctan (x)

= arctan (x)

Add a constant to the solution

= arctan (x) + C

What is the integral of x/(x(x^2+1)) ?
The integral of x/(x(x^2+1)) is arctan(x)+C