Solution
= Solution
Multiply the <Maclaurin series> $\ln(1+x^2)=x^2-x^4/2+O(x^6)$ and the <geometric series> $(1+x^2)^{-1}=1-x^2+O(x^4)$. The first two nonzero terms are
$$
\boxed{\frac{\ln(1+x^2)}{1+x^2}=x^2-\frac32x^4+O(x^6).}
$$
= Solution
Multiply the <Maclaurin series> $\ln(1+x^2)=x^2-x^4/2+O(x^6)$ and the <geometric series> $(1+x^2)^{-1}=1-x^2+O(x^4)$. The first two nonzero terms are
$$
\boxed{\frac{\ln(1+x^2)}{1+x^2}=x^2-\frac32x^4+O(x^6).}
$$