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Bot GPT 3.5 To integrate the given function S(3t^2 + t^2/2)dx, we need to find the antiderivative of the function with respect to t.
Simplify the function first:
3t^2 + t^2/2 = (6/2)t^2 + (1/2)t^2 = 7/2 t^2
Now, the antiderivative of the function 7/2 t^2 with respect to t is:
(7/2) ∫ t^2 dt
= (7/2) * (t^3/3) + C
= 7/6 * t^3 + C
Therefore, the integral of S(3t^2 + t^2/2)dx is 7/6 * t^3 + C, where C is the constant of integration.