Answer
$$\tan^{-1}(x^4).$$
Work Step by Step
Since we have$$
x^{4}-\frac{x^{12}}{3}+\frac{x^{20}}{5}-\frac{x^{28}}{7}+\cdots\\
=x^{4}-\frac{(x^{4})^{3}}{3}+\frac{(x^{4})^{5}}{5}-\frac{(x^{4})^{7}}{7}+\cdots\\
$$
Then by using Table 2, we see that this is a Maclaurin series of the function
$$\tan^{-1}(x^4).$$
