Solution
= Solution
Since the <derivative> of the <arctangent> is $1/(1+x^2)=1-x^2+O(x^4)$ near zero, termwise <integration> gives
$$
\boxed{\arctan x=x-\frac{x^3}{3}+O(x^5).}
$$
The integration constant is zero because $\arctan0=0$.
= Solution
Since the <derivative> of the <arctangent> is $1/(1+x^2)=1-x^2+O(x^4)$ near zero, termwise <integration> gives
$$
\boxed{\arctan x=x-\frac{x^3}{3}+O(x^5).}
$$
The integration constant is zero because $\arctan0=0$.