Primitive of Arctangent Function

Theorem

 * $\ds \int \arctan x \rd x = x \arctan x - \frac {\map \ln {x^2 + 1} } 2 + C$

Proof
From Primitive of $\arctan \dfrac x a$:
 * $\ds \int \arctan \frac x a \rd x = x \arctan \frac x a - \frac a 2 \map \ln {x^2 + a^2} + C$

The result follows by setting $a = 1$.

Also see

 * Primitive of $\arcsin x$
 * Primitive of $\arccos x$
 * Primitive of $\arccot x$