Primitive of Reciprocal of a squared minus x squared/Logarithm Form 1

Theorem

 * $\displaystyle \int \frac {\d x} {a^2 - x^2} = \begin {cases} \dfrac 1 {2 a} \ln \size {\dfrac {a + x} {a - x} } + C & : \size x < a\\

& \\ \dfrac 1 {2 a} \ln \size {\dfrac {x + a} {x - a} } + C & : \size x > a \\ & \\ \text {undefined} & : x = 0 \end {cases}$

Also see

 * Primitive of Reciprocal of $x^2 + a^2$
 * Primitive of Reciprocal of $x^2 - a^2$: Logarithm Form