Primitive of Square of Arcsine of x over a

Theorem

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

Proof
Let:

Then:

Also see

 * Primitive of $\paren {\arccos \dfrac x a}^2$