Primitive of Arcsine of x over a/Proof 2

Theorem

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

Proof
With a view to expressing the primitive in the form:


 * $\displaystyle \int u \frac {\d v} {\d x} \rd x = u v - \int v \frac {\d u} {\d x} \rd x$

let:

and let:

Then: