Find a power series representation for ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x}{1+8x^3}dx$

${\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n{8}^n\frac{x^{3n+2}}{3n+2}+C$

${\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n{8}^{n+1}{x}^{3n+1}+C$

${\displaystyle \underset{n=0}{\overset{}{}}}(-1{)}^n{8}^n{x}^{3n+1}+C$

${\displaystyle \underset{n=1}{\overset{}{}}}{8}^n\frac{x^{3n+2}}{3n+2}+C$

${\displaystyle \underset{n=0}{\overset{}{}}}{8}^n\frac{x^{3n+1}}{3n+1}+C$