The Taylor series expansion of a function $f(x)$ about $x=a$ is given by:
\[f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \frac{f'''(a)}{3!}(x-a)^3 + \cdots\]
For the function $\ln(1+x^2)$, the Taylor series expansion about $x=0$ up to the sixth degree
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