Question

Determine the series of the function:

Answer 1

\[g(x) = \arctan( x/\sqrt8)\]I know:\[g ^\prime (x) = \sqrt8/(8 +x^2)\]I can write this as a power series and integrate it to arrive back the equivalent of g(x).
\[\sqrt8/8*\int\limits_{}^{}\sum_{n=0}^{\infty}(-1)^n(x^2/8)^n dx \]After integrating I have this:\[\sqrt8/8*\sum_{n=0}^{\infty}((-1)^n(x^2/8)^n(x^2/8))/(n+1) + C\]Am I doing this right so far?