What is the integral of (12t^7-t^2-t+3) ?

The integral of (12t^7-t^2-t+3) is (3t^8)/2-(t^3)/3-(t^2)/2+3t+C

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integral of (12t^7-t^2-t+3)

\int (12 t^{7} - t^{2} - t + 3) d t

\frac{3 t ^{8}}{2} - \frac{t ^{3}}{3} - \frac{t ^{2}}{2} + 3 t + C

Solution steps

\int 12 t^{7} - t^{2} - 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 12 t^{7} d t - \int t^{2} d t - \int t d t + \int 3 d t

\int 12 t^{7} d t = \frac{3 t ^{8}}{2}

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

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

\int 3 d t = 3 t

= \frac{3 t ^{8}}{2} - \frac{t ^{3}}{3} - \frac{t ^{2}}{2} + 3 t

Add a constant to the solution

= \frac{3 t ^{8}}{2} - \frac{t ^{3}}{3} - \frac{t ^{2}}{2} + 3 t + C

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What is the integral of (12t^7-t^2-t+3) ?
The integral of (12t^7-t^2-t+3) is (3t^8)/2-(t^3)/3-(t^2)/2+3t+C