Answer
$$\sec v + 1$$
Work Step by Step
$$\eqalign{
& f\left( v \right) = \sec v\tan v \cr
& {\text{find an antiderivative of }}f\left( t \right) \cr
& F\left( v \right) = \sec v + C \cr
& {\text{using the initial condition }}F\left( 0 \right) = 2 \cr
& 2 = \sec 0 + C \cr
& 2 = 1 + C \cr
& C = 1 \cr
& {\text{so}}{\text{,}} \cr
& = \sec v + 1 \cr} $$
