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** Step-by-step Solution **

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Expand the integral $\int\left(3t^2+\frac{t}{2}\right)dt$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

Learn how to solve integrals of polynomial functions problems step by step online.

$\int3t^2dt+\int\frac{t}{2}dt$

Learn how to solve integrals of polynomial functions problems step by step online. Integrate int(3t^2+t/2)dt. Expand the integral \int\left(3t^2+\frac{t}{2}\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int3t^2dt results in: t^{3}. The integral \int\frac{t}{2}dt results in: \frac{1}{4}t^2. Gather the results of all integrals.

** Final Answer

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