Primitive of Reciprocal of a squared minus x squared/Logarithm Form 2/Corollary

Theorem
Let $a \in \R_{>0}$ be a strictly positive real constant.

Let $x \in \R$ such that $\size x \ne a$.


 * $\ds \int \frac {\d x} {a^2 - b^2 x^2} = \dfrac 1 {2 a b} \ln \size {\dfrac {a + b x} {a - b x} } + C$

Proof
Let $z = b x$.

Then:
 * $\dfrac {\d x} {\d z} = \dfrac 1 b$

Hence: