find the velocity vector for an object having

$\displaystyle \vec a(t) = e^t \hat{j} -32 \hat{k} $

if

$\displaystyle v(0) = 3 \hat{i} - 2 \hat{j} + \hat{k}$

Im not sure how to proceed. Would i integrate? How to handle the v(0) has me confused!

$\displaystyle v(t) = \int e^t \hat{j} -32 \hat{k}\ dt$

$\displaystyle v(t) = e^t j -32t k + c$

Im not sure if i am doing this correctly?