How to find the Taylor series of $f(x)=\arctan x$. I want to find the Taylor series of $f(x)=\arctan x,\; x\in[-1,1],\;\xi=0$.
That's what I have tried do far:
$$f'(x)=\frac{1}{1+x^2}=\frac{1}{1-(-x^2)}=\sum_{n=0}^{\infty} (-x^2)^n.$$
How can I continue?

Thus, we have 
$$f(x)=\int f'(x)\,dx=\int\sum_{n\ge 0}(-1)^nx^{2n}\,dx\ =\\
=\ \sum_{n\ge 0}(-1)^n\frac{x^{2n+1}}{2n+1}\ +C$$
Then find $C$ by plugging in $x=0$.
What will you get if you plug in $x=1$?
