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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. We can solve the integral \int t\left(t^2+1\right)^3dt by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dt, we need to find the derivative of t. We need to calculate dt, we can do that by deriving the equation above. Substituting in the original integral, we get.