Unfortunately, doing this kind of problem by hand would take a very long time. So I recommend using a graphing calculator. Specifically, one that can handle numeric integration. You'll need to find the area under the curve from t = 0 to t = 3. This will tell you the change in velocity during the time period from t = 0 to t = 3 seconds. You should find that
[tex]\displaystyle \int_{0}^{3}\frac{t+3}{\sqrt{t^3+1}}dt \approx 6.71005[/tex]
If you want to do this by hand, you can use Riemann rectangles to break up the area and find the area of each rectangle. Though use of a calculator is recommended here as well.
This result will add onto the initial velocity of 5 to get a final approximate result of 5+6.71005 = 11.71005 which rounds to 11.710
