Primitive of Square of Arcsine of x over a

Theorem

 * $\displaystyle \int \left({\arcsin \frac x a}\right)^2 \ \mathrm d x = x \left({\arcsin \frac x a}\right)^2 - 2 x + 2 \sqrt{a^2 - x^2} \arcsin \frac x a + C$

Proof
Let:

Then:

Also see

 * Primitive of $\left({\arccos \dfrac x a}\right)^2$