Primitive of Square of Arccosine of x over a

Theorem

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

Proof
Let:

Then:

Also see

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