What is the integral of (x^2-2x+5) ?

The integral of (x^2-2x+5) is (x^3)/3-x^2+5x+C

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integral of (x^2-2x+5)

\int (x^{2} - 2 x + 5) d x

\frac{x ^{3}}{3} - x^{2} + 5 x + C

Solution steps

\int x^{2} - 2 x + 5 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 2 x d x + \int 5 d x

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

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

\int 5 d x = 5 x

= \frac{x ^{3}}{3} - x^{2} + 5 x

Add a constant to the solution

= \frac{x ^{3}}{3} - x^{2} + 5 x + C

\int_{- 8}^{8} (e^{x} - e^{- x})^{2} d x

\int_{0}^{2} x + 1 d x

\frac{\partial}{\partial x} (4 x^{\frac{2}{3}} y^{\frac{1}{3}})

t (e^{t} + e^{2 t})^{2}

\frac{d}{d x} (0.5 e^{\frac{x}{3}} - sin (x))

What is the integral of (x^2-2x+5) ?
The integral of (x^2-2x+5) is (x^3)/3-x^2+5x+C