Primitive of Reciprocal of Root of 1 minus x squared/Arcsine Form/Proof 1

Corollary to Primitive of $\frac 1 {\sqrt {a^2 - x^2} }$: Arcsine Form

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

Proof

From Primitive of $\dfrac 1 {\sqrt {a^2 - x^2} }$: Arcsine Form:

$\ds \int \frac {\d x} {\sqrt {a^2 - x^2} } = \arcsin \frac x a + C$

The result follows by setting $a = 1$.

$\blacksquare$