What is the integral of arctan(x) ?

The integral of arctan(x) is xarctan(x)-1/2 ln|x^2+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of arctan(x)

\int arctan (x) d x

x arctan (x) - \frac{1}{2} ln x^{2} + 1 + C

Solution steps

\int arctan (x) d x

Apply Integration By Parts

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

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

= x arctan (x) - \frac{1}{2} ln x^{2} + 1

Add a constant to the solution

= x arctan (x) - \frac{1}{2} ln x^{2} + 1 + C

y \to \infty lim (\frac{y ^{2} + 2}{5 y - 6})

\int 3 e d x

\frac{\partial}{\partial x} (sin^{4} (x - 7 y))

\int 5 x d x

4 d y + y d x = x^{2} d y

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