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

a⃗(t)=⟨2t,2sin⁡(t),cos⁡(6t)⟩\displaystyle \vec{{a}}{\left({t}\right)}={\left\langle{2}{t},{2}{\sin{{\left({t}\right)}}},{\cos{{\left({6}{t}\right)}}}\right\rangle}

v⃗(0)=⟨−4,−5,0⟩\displaystyle \vec{{v}}{\left({0}\right)}={\left\langle-{4},-{5},{0}\right\rangle}

r⃗(0)=⟨−2,5,−5⟩\displaystyle \vec{{r}}{\left({0}\right)}={\left\langle-{2},{5},-{5}\right\rangle}

r⃗(t)=\displaystyle \vec{{r}}{\left({t}\right)}=
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