Find the most general antiderivative of the function. (Check your answer by differentiation. Use $C$ for the constant of the antiderivative.) \[ g(t)=\frac{9+t+t^{2}}{\sqrt{t}} \] \[ G(t)= \]

Step 1 ：Rewrite the given function as a sum of simpler functions: \(g(t) = 9t^{-1/2} + t^{1/2} + t^{3/2}\)

Step 2 ：Find the antiderivative of each of these functions using the power rule for integration, which states that the integral of \(t^n\) is \(\frac{1}{n+1}t^{n+1}\), plus a constant.

Step 3 ：The antiderivative of \(9t^{-1/2}\) is \(18t^{0.5}\)

Step 4 ：The antiderivative of \(t^{1/2}\) is \(\frac{2}{3}t^{1.5}\)

Step 5 ：The antiderivative of \(t^{3/2}\) is \(\frac{2}{5}t^{2.5}\)

Step 6 ：Combine these to find the most general antiderivative of the function \(g(t)\)

Step 7 ：\(\boxed{G(t) = 18t^{0.5} + \frac{2}{3}t^{1.5} + \frac{2}{5}t^{2.5} + C}\), where \(C\) is the constant of the antiderivative.