Find a power series representation for the function.

Question

f(x)= x²arctan(x³)

Answer 1

The Maclaurin series for Arctanx is x - x³/3 + x⁵/5 - x⁷/7 + ...

So, x²Arctan(x³) = x² [ (x³) - (x³)³/3 + (x³)⁵/5 - (x³)⁷/7 + ...] = x⁵ - x¹¹ / 3 + x¹⁷ / 5 - x²³ / 7 + ...