What is the integral of (3x^2-x+1) ?

The integral of (3x^2-x+1) is x^3-(x^2)/2+x+C

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integral of (3x^2-x+1)

\int (3 x^{2} - x + 1) d x

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

Solution steps

\int 3 x^{2} - x + 1 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 x d x + \int 1 d x

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

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

\int 1 d x = x

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

Add a constant to the solution

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

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What is the integral of (3x^2-x+1) ?
The integral of (3x^2-x+1) is x^3-(x^2)/2+x+C