What is the integral of 7+5t+(3t^2)/2 ?

The integral of 7+5t+(3t^2)/2 is 7t+(5t^2)/2+(t^3)/2+C

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integral of 7+5t+(3t^2)/2

\int 7 + 5 t + \frac{3 t ^{2}}{2} d t

7 t + \frac{5 t ^{2}}{2} + \frac{t ^{3}}{2} + C

Solution steps

\int 7 + 5 t + \frac{3 t ^{2}}{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 7 d t + \int 5 t d t + \int \frac{3 t ^{2}}{2} d t

\int 7 d t = 7 t

\int 5 t d t = \frac{5 t ^{2}}{2}

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

= 7 t + \frac{5 t ^{2}}{2} + \frac{t ^{3}}{2}

Add a constant to the solution

= 7 t + \frac{5 t ^{2}}{2} + \frac{t ^{3}}{2} + C

What is the integral of 7+5t+(3t^2)/2 ?
The integral of 7+5t+(3t^2)/2 is 7t+(5t^2)/2+(t^3)/2+C