First, we can rewrite the integral as:
$$\int \frac{t^{3}+\sqrt[3]{t}}{t^{2}} dt = \int \frac{t^{3}}{t^{2}} dt + \int \frac{\sqrt[3]{t}}{t^{2}} dt$$
Now, we can simplify the terms inside the integrals:
$$\int \frac{t^{3}}{t^{2}} dt + \int \frac{\sqrt[3]{t}}{t^{2}}
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