The integral of a vector

Starting from rest, a flying saucer of mass m is observed to vary its propulsion with mathematical precision according to the equation

(The aliens inform us that the numbers 42 and 137 have a special religious significance for them.) Find the saucer's velocity as a function of time.

From the given force, we can easily find the acceleration

The velocity vector v is the integral with respect to time of the acceleration,

and integrating component by component gives

where we have omitted the constants of integration, since the saucer was starting from rest.