Primitive of x over Root of a squared minus x squared

Theorem

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

Proof
Let:

Also see

 * Primitive of $\dfrac x {\sqrt {x^2 + a^2} }$
 * Primitive of $\dfrac x {\sqrt {x^2 - a^2} }$