$($a$)$ Determine the following integrals, make a direct substitution and change of limit where necessary:

$($i$)$ Z

x

$$

x

$2+3$dx $(3)$

$($ii$)$ Z

$2$ sin x

cos x $(1+2$ ln cos x$)$

dx $(3)$

$($iii$)$ Z

x

$24$

x $+2$

dx $(3)$

$($iv$)$ Z $\backslash$pi

$3$

$0$