To integrate the given expression, we first simplify it:
S(3t^2 + t^2/2)dx
= S(3t^2)dx + S(t^2/2)dx
= 3S(t^2)dx + (1/2)S(t^2)dx
= (3 + 1/2)S(t^2)dx
= (7/2)S(t^2)dx
Now, we can integrate the simplified expression:
S(7/2 * t^2) dx
= (7/2) * S(t^2)dx
= (7/2) * (t^3/3) + C
= (7/6) * t^3 + C
Therefore, the integral of the given expression is (7/6) * t^3 + C.
S(3t^2+t^2/2)dx
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