What is the integral of (x^2-5x+9) ?

The integral of (x^2-5x+9) is (x^3)/3-(5x^2)/2+9x+C

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integral of (x^2-5x+9)

\int (x^{2} - 5 x + 9) d x

\frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 9 x + C

Solution steps

\int x^{2} - 5 x + 9 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 5 x d x + \int 9 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 9 d x = 9 x

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 9 x

Add a constant to the solution

= \frac{x ^{3}}{3} - \frac{5 x ^{2}}{2} + 9 x + C

(2 x^{3} - y) d x + x d y = 0

\frac{\partial}{\partial x} (y^{2} + x^{2} (1 - x y)^{- 2})

\frac{\partial}{\partial x} (y^{2} - y)

f (r) = π r^{2}

\frac{d}{d x} (e^{c x})

What is the integral of (x^2-5x+9) ?
The integral of (x^2-5x+9) is (x^3)/3-(5x^2)/2+9x+C