Primitive of x by Arcsine of x over a/Proof 1

Theorem

 * $\displaystyle \int x \arcsin \frac x a \ \mathrm d x = \left({\frac {x^2} 2 - \frac {a^2} 4}\right) \arcsin \frac x a + \frac {x \sqrt {a^2 - x^2} } 4 + C$

Proof
Let:

Then: