What is the integral of 5(t^2-5t-2) ?

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

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integral of 5(t^2-5t-2)

\int 5 (t^{2} - 5 t - 2) d t

5 (\frac{t ^{3}}{3} - \frac{5 t ^{2}}{2} - 2 t) + C

Solution steps

\int 5 (t^{2} - 5 t - 2) d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int t^{2} - 5 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

= 5 (\int t^{2} d t - \int 5 t d t - \int 2 d t)

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

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

\int 2 d t = 2 t

= 5 (\frac{t ^{3}}{3} - \frac{5 t ^{2}}{2} - 2 t)

Add a constant to the solution

= 5 (\frac{t ^{3}}{3} - \frac{5 t ^{2}}{2} - 2 t) + C

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