What is the integral of (x^2)/2-8x+30 ?

The integral of (x^2)/2-8x+30 is (x^3)/6-4x^2+30x+C

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integral of (x^2)/2-8x+30

\int \frac{x ^{2}}{2} - 8 x + 30 d x

\frac{x ^{3}}{6} - 4 x^{2} + 30 x + C

Solution steps

\int \frac{x ^{2}}{2} - 8 x + 30 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 \frac{x ^{2}}{2} d x - \int 8 x d x + \int 30 d x

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

\int 8 x d x = 4 x^{2}

\int 30 d x = 30 x

= \frac{x ^{3}}{6} - 4 x^{2} + 30 x

Add a constant to the solution

= \frac{x ^{3}}{6} - 4 x^{2} + 30 x + C

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What is the integral of (x^2)/2-8x+30 ?
The integral of (x^2)/2-8x+30 is (x^3)/6-4x^2+30x+C