Arctan[Tan[x]]

Input

tan^(-1)(tan(x))

Plot

Plot
Plot

Roots

x = π n, n element Z

Integer root

x = 0

Series expansion at x=0

x + O(x^13)
(Taylor series)

Derivative

d/dx(tan^(-1)(tan(x))) = (sec^2(x))/(tan^2(x) + 1)

Indefinite integral

integral tan^(-1)(tan(x)) dx = x tan^(-1)(tan(x)) - x^2/2 + constant