Find the MacLaurin Series

Question

Find the MacLaurin Series of f(x) = x³sin(x)

Answer 1

The MacLaurin series of sin(x) is ∑_n=0^∞ (-1)ⁿ x²ⁿ⁺¹/(2n+1)!, so the series for x³sin(x) is

∑_n=0^∞ (-1)ⁿ x²ⁿ⁺⁴/(2n+1)!

It converges everywhere.