Final Answer
$\frac{t^{3}}{6}+t^{4}+C_0$
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Step-by-step Solution
Problem to solve:
$\int\left(\frac{t^2}{2}+4t^3\right)dt$
Choose the solving method
1
Expand the integral $\int\left(\frac{t^2}{2}+4t^3\right)dt$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
$\int\frac{t^2}{2}dt+\int4t^3dt$
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$\int\frac{t^2}{2}dt+\int4t^3dt$
Learn how to solve integrals of polynomial functions problems step by step online. Find the integral int((t^2)/2+4t^3)dt. Expand the integral \int\left(\frac{t^2}{2}+4t^3\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{t^2}{2}dt results in: \frac{t^{3}}{6}. The integral \int4t^3dt results in: t^{4}. Gather the results of all integrals.
Final Answer
$\frac{t^{3}}{6}+t^{4}+C_0$