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

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

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

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

t^{3} + \frac{t ^{2}}{4} + C

Solution steps

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

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

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

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

Add a constant to the solution

= t^{3} + \frac{t ^{2}}{4} + C

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