What is the integral of 118-(3x^2+10x+30) ?

The integral of 118-(3x^2+10x+30) is -x^3-5x^2+88x+C

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integral of 118-(3x^2+10x+30)

\int 118 - (3 x^{2} + 10 x + 30) d x

- x^{3} - 5 x^{2} + 88 x + C

Solution steps

\int 118 - (3 x^{2} + 10 x + 30) d x

Simplify

= \int - 3 x^{2} - 10 x + 88 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

= - \int 3 x^{2} d x - \int 10 x d x + \int 88 d x

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

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

\int 88 d x = 88 x

= - x^{3} - 5 x^{2} + 88 x

Add a constant to the solution

= - x^{3} - 5 x^{2} + 88 x + C

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What is the integral of 118-(3x^2+10x+30) ?
The integral of 118-(3x^2+10x+30) is -x^3-5x^2+88x+C