Evaluate the following $($definite and indefinite$)$ integrals

$($a$)$

$($

ex $+1$

x

$)$

dx

$($b$)$

$2$

$1$

$(3$u $2)($u $+1)$du

$($c$)$

$$

cos$3($$)$ sin$($$)$d

$($d$)$

$3$

$1$

$(1$

z$2+1$

$($z$)3$

$)$

dz