Arcsine as Integral

Theorem

 * $\ds \map \arcsin x = \int_0^x \frac {\d x} {\sqrt {1 - x^2} }$

Lemma 2

 * $\ds \map \arcsin x = \map {\arcsin_A} x = \map {\arcsin_G} x = \int_0^x \frac {\d x} {\sqrt {1 - x^2} }$

Also see

 * Primitive of Reciprocal of Root of a squared minus x squared/Arcsine Form