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

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

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

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

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

Solution steps

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

Take the constant out:

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

= 5 \cdot \int x^{2} - 5 x - 2 d x

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 x^{2} d x - \int 5 x d x - \int 2 d x)

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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