Primitive of Reciprocal of x by x fourth minus a fourth

Theorem

 * $\ds \int \frac {\d x} {x \paren {x^4 - a^4} } = \frac 1 {4 a^4} {\ln \size {\frac {x^4 - a^4} {x^4} } } + C$

Proof
From Primitive of $\dfrac 1 {x \paren {x^n - a^n} }$:
 * $\ds \int \frac {\d x} {x \paren {x^n - a^n} } = \frac 1 {n a^n} \ln \size {\frac {x^n - a^n} {x^n} } + C$

Setting $n = 4$:


 * $\ds \int \frac {\d x} {x \paren {x^4 - a^4} } = \frac 1 {4 a^4} \ln \size {\frac {x^4 - a^4} {x^4} } + C$

directly.