What is the integral of-10-5x^2 ?

The integral of-10-5x^2 is -5(2x+(x^3)/3)+C

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integral of-10-5x^2

\int - 10 - 5 x^{2} d x

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

Solution steps

\int - 10 - 5 x^{2} d x

- 10 - 5 x^{2} = (- 5) (2 + x^{2})

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

\int 2 d x = 2 x

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

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

Add a constant to the solution

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