I think you probably meant to say v(1) = 6?
dv = 9*sqrt(t)*dt = 9*t^1/2*dt
integrate both sides with respect to t and remembering the formula for integrating a power,
v = 9*t^(3/2)/(3/2) + C
don't for get the C as we are dealing with an indefinite integral here.
reducing gives v = 6*t^(3/2) + C
to solve for C, we use the initial conditions. Put t = 1 and v = 6 gives, 6 = 6*1 + C. This gives C = 0 and the solution of the problem is,
v = 6*t^(3/2)