Primitive of x squared over a squared minus x squared/Inverse Hyperbolic Tangent Form

Theorem

 * $\displaystyle \int \frac {x^2 \ \mathrm d x} {a^2 - x^2} = -x + a \tanh^{-1} \frac x a + C$

for $x^2 < a^2$.

Proof
Let: