$($A$3)[4$ pts each$]$ The acceleration of a particle as a function of time is given by

$a(t)=($:$9e^{3t}+2,-\frac{{}^2}{4}sin(\frac{}{2}t),-\frac{1}{(t+1{)}^2}$:$).$

a$.$ Given that $v(0)=($:$3,\frac{}{2},1$:$),$ find $v(t),$ the velocity of the particle.

b$.$ Use your answer in part a and the fact that $r(0)=($:$0,0,0$:$)$ to find the exact value of $r(1).$ Do not give decimal approximations. Note: $r(t)$ represents the position of the particle.