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

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

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integral of (x^2-x+1)

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

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

Solution steps

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

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

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

\int 1 d x = x

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

Add a constant to the solution

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

\int \frac{6}{x ^{2} x ^{2} + 16} d x

x \to 2 lim (x + 1)

\int_{0}^{\infty} sin (2 x) d x

x \to 2 lim (\frac{3 x + 1}{x + 2})

\frac{d}{d t} (0.00225 t e^{- 0.0467 t})

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