$($a$)$ Find the position vector of a particle that has the given acceleration and the specified initial velocity and position.

a$($t$)=5$t$$i $+$ et$$j $+$ e$$t$$k$,$v$(0)=$ k$,$r$(0)=$ j $+$ k

r$($t$)=$

$56$t$3$i$+($et$$t$)$j$+($e$$t$+2$t$+2)$k