Primitive of x over x squared plus a squared/Proof 2

Theorem

 * $\displaystyle \int \frac {x \ \mathrm d x} {x^2 + a^2} = \frac 1 2 \ln \left ({x^2 + a^2}\right) + C$

where $a$ is a non-zero constant.

Proof
From Primitive of Power of x less one over Power of x plus Power of a:
 * $\displaystyle \int \frac {x^{n - 1} \ \mathrm d x} {x^n + a^n} = \frac 1 n \ln \left\vert{x^n + a^n}\right\vert + C$

So: