Question

determine the series of the given function:

Answer 1

determine the series of the given function:
\[f(x) = \arctan(x/\sqrt8)\]
I know that:
\[\int\limits\limits\limits_{}^{} 1/(1+(x^2/8)) dx = \sqrt8 *\arctan(x/\sqrt8)\]and the right side of the equation can be written as a power series:

\[1/\sqrt8*\int\limits\limits_{}^{}\sum_{n=0}^{\infty} (-1)^n(x^2/8)^n dx = \arctan(x/\sqrt8)\]which i can then integrate:\[1/\sqrt8*\sum_{n=0}^{\infty}((-1)^n(x^2/8)^n(x^2/8))/(n+1) + C\]am I on the right track so far?