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

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

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

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

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

Solution steps

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

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

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

\int 5 d x = 5 x

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

Add a constant to the solution

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

\int 2 (sin (x) - cos (x) + 1) d x

\frac{d y}{d t} + y = cos (2 t), y (0) = 5

\frac{d y}{d x} = \frac{1}{x y}

f (x) = x x^{3} - 6

y = 2 x^{2} 2 - x

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