In this problem, we will find the integral

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x}{1+x^4}dx$

To receive full credit, your solution must include:

A$)$ An explanation of why you choose the method you did from among: $1)$ known integral, $2)$ algebraic simplification, $3)$ substitution, and $4)$ integration by parts.