$(2)$ Determine each integrah is converget or divergint

$($a$){\displaystyle \underset{1}{\overset{}{}}}\frac{x}{1+x^2}dx$

$($b$){\displaystyle \underset{-}{\overset{1}{}}}x{e}^{-2x}dx$

$(3)$ Find a formula for general terms an For $-\frac{2}{3}*\frac{3}{9}*-\frac{4}{27}+$cdotsdots

$(4)$ Express $9.13$ as artion of integors