Find the position vector for a particle with acceleration, initial velocity, and initial position given below.

vec$(a)(t)=($:$5t,3sin(t),cos(3t)$:$)$

vec$(v)(0)=($:$0,1,-3$:$)$

vec$(r)(0)=($:$-2,-5,-5$:$)$

vec$(r)(t)=$