Evaluate the indefinite integral

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{4}ln(1x^9)dx$

as a power series and state the radius of convergence.

$($Note that the index variable of the summation is $n,$ it starts at $n=1,$ any coefficient of the summation should be included within the sum itself, and the constant of Integration is already written for you.$)$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^{4}ln(1x^9)dx=C{\displaystyle \underset{n=1}{\overset{}{}}}$

$R=$