What is the integral of t*arctan(t) ?

The integral of t*arctan(t) is 1/2 t^2arctan(t)-1/2 (-arctan(t)+t)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of t*arctan(t)

\int t \cdot arctan (t) d t

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

Solution steps

\int t arctan (t) d t

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

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