Primitive of Square of Arccosine of x over a

Theorem

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

Proof
Let:

Then:

Also see

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