Question

Can someone help me with Calculus 2 material?

Answer 1

Am I approaching this right?:

find the series of f(x):

\[f (x)=\tan^{-1} (x/\sqrt8)\]
I know that
\[f^\prime(x)= \sqrt8/(x^2+8)\]this can be expressed as a power series and I can integrate the series to arrive back to an expression that is equivalent to f(x).
\[\int\limits\limits_{}^{}\sqrt8/(x^2 +8) dx = \int\limits\limits_{}^{}\sum_{n=0}^{\infty} \sqrt8/8(-1)^n(x^2/8)^ndx\]which is equal to:\[\sum_{n=0}^{\infty}\sqrt8/8(-1)^n ((x^2/8)^n(x^2/8)/(n+1)) +C\]is this correct so far?