What is the integral of ((t^2)/2+4t^3) ?

The integral of ((t^2)/2+4t^3) is (t^3)/6+t^4+C

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integral of ((t^2)/2+4t^3)

\int (\frac{t ^{2}}{2} + 4 t^{3}) d t

\frac{t ^{3}}{6} + t^{4} + C

Solution steps

\int \frac{t ^{2}}{2} + 4 t^{3} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{t ^{2}}{2} d t + \int 4 t^{3} d t

\int \frac{t ^{2}}{2} d t = \frac{t ^{3}}{6}

\int 4 t^{3} d t = t^{4}

= \frac{t ^{3}}{6} + t^{4}

Add a constant to the solution

= \frac{t ^{3}}{6} + t^{4} + C

What is the integral of ((t^2)/2+4t^3) ?
The integral of ((t^2)/2+4t^3) is (t^3)/6+t^4+C