What is the integral of 62-x^2-53 ?

The integral of 62-x^2-53 is -(x^3)/3+9x+C

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integral of 62-x^2-53

\int 62 - x^{2} - 53 d x

- \frac{x ^{3}}{3} + 9 x + C

Solution steps

\int 62 - x^{2} - 53 d x

Simplify

= \int - x^{2} + 9 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 x^{2} d x + \int 9 d x

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

\int 9 d x = 9 x

= - \frac{x ^{3}}{3} + 9 x

Add a constant to the solution

= - \frac{x ^{3}}{3} + 9 x + C

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