What is the integral of 53-(3x^2+2x+20) ?

The integral of 53-(3x^2+2x+20) is -x^3-x^2+33x+C

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integral of 53-(3x^2+2x+20)

\int 53 - (3 x^{2} + 2 x + 20) d x

- x^{3} - x^{2} + 33 x + C

Solution steps

\int 53 - (3 x^{2} + 2 x + 20) d x

Simplify

= \int - 3 x^{2} - 2 x + 33 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 2 x d x + \int 33 d x

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

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

\int 33 d x = 33 x

= - x^{3} - x^{2} + 33 x

Add a constant to the solution

= - x^{3} - x^{2} + 33 x + C

What is the integral of 53-(3x^2+2x+20) ?
The integral of 53-(3x^2+2x+20) is -x^3-x^2+33x+C