What is the integral of 2x^2-x+100 ?

The integral of 2x^2-x+100 is (2x^3)/3-(x^2)/2+100x+C

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integral of 2x^2-x+100

\int 2 x^{2} - x + 100 d x

\frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} + 100 x + C

Solution steps

\int 2 x^{2} - x + 100 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 2 x^{2} d x - \int x d x + \int 100 d x

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

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

\int 100 d x = 100 x

= \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} + 100 x

Add a constant to the solution

= \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} + 100 x + C

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What is the integral of 2x^2-x+100 ?
The integral of 2x^2-x+100 is (2x^3)/3-(x^2)/2+100x+C