Primitive of Arcsine Function

Theorem

 * $\ds \int \arcsin x \rd x = x \arcsin x + \sqrt {1 - x^2} + C$

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

The result follows by setting $a = 1$.

Also see

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