Written Problems

W$1.$ Evaluate the following integrals, if they converge, or show that they diverge.

$($a$){\displaystyle \underset{0}{\overset{}{}}}\frac{1}{4+x^2}dx$

$($b$){\displaystyle \underset{-}{\overset{}{}}}\frac{e^y}{1+e^{2y}}dy$

$($c$){\displaystyle \underset{6}{\overset{24}{}}}\frac{1}{t\sqrt[\phantom{2}]{t^2-36}}dt$

$($d$){\displaystyle \underset{0}{\overset{4}{}}}\frac{3}{x^2-x-2}dx$