Q$2.[5$ marks$]$ Write ${\displaystyle \underset{-\frac{1}{2}}{\overset{0}{}}}x{e}^{x^3}dx$ as an infinite series. $[\text{'}$Solutions$\text{'}$ such as ${\displaystyle \underset{-\frac{1}{2}}{\overset{0}{}}}x{e}^{x^3}dx=$

$({\displaystyle \underset{-\frac{1}{2}}{\overset{0}{}}}x{e}^{x^3}dx)+0+0+0+$cdots, while both highly amusing and technically correct,

will earn $0.]$