Primitive of Reciprocal of x squared by a squared minus x squared

Theorem

 * $\displaystyle \int \frac {\d x} {x^2 \paren {a^2 - x^2} } = \frac {-1} {a^2 x} + \frac 1 {2 a^3} \map \ln {\frac {a + x} {a - x} } + C$

for $x^2 < a^2$.

Also see

 * Primitive of $\dfrac 1 {x^2 \paren {x^2 - a^2} }$