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Expand the integral $\int_{1}^{2}\left(4\sqrt[3]{t}+t\left(t^2+1\right)^3\right)dt$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
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$\int_{1}^{2}4\sqrt[3]{t}dt+\int_{1}^{2} t\left(t^2+1\right)^3dt$
Learn how to solve problems step by step online. Integrate the function 4t^1/3+t(t^2+1)^3 from 1 to 2. Expand the integral \int_{1}^{2}\left(4\sqrt[3]{t}+t\left(t^2+1\right)^3\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{1}^{2}4\sqrt[3]{t}dt results in: \frac{383}{84}. The integral \int_{1}^{2} t\left(t^2+1\right)^3dt results in: \frac{609}{8}. Gather the results of all integrals.