the Taylor series expansion about the origin in the region $|x| < 1$ for the given function Write down the Taylor series expansion about the origin in the region $|x| < 1$ for the function
$$f(x)=x\tan^{-1}x-\frac{1}{2}\log(1+x^2)$$

I cant find the general formula for $f^{(n)}(x)$.an I get some help?

Hint:


*

*Write down the standard expansion of $\arctan x$. Multiply term by term by $x$.

*Write down the standard expansion of $\ln(1+t)$. Replace $t$ everywhere by $x^2$.  Multiply term by term by $-\frac{1}{2}$.

*Add the results of (1) and (2),  collecting the coefficients of like powers of $x$ together. 
Remark: If you do not know the power series expansion of $\arctan x$, you can probably write down the power series expansion of $\frac{1}{1-u}$, and hence of $\frac{1}{1+t^2}$. Then use the fact that
$$\arctan x=\int_0^x \frac{dt}{1+t^2}\,dt,$$
integrating the series for $\frac{1}{1+t^2}$ term by term.
If you do not know the power series expansion of $\ln(1+t)$, integrate the power series expansion of $\frac{1}{1+u}$ term by term from $0$ to $t$. 
