Primitive of x over x squared plus a squared/Corollary

Theorem

 * $\ds \int \frac {x \rd x} {a^2 + b^2 x^2} = \frac 1 {2 b^2} \map \ln {a^2 + b^2 x^2} + C$

where $a$ is a non-zero constant.

Proof
Let $z = b x$.

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

Hence: