What is the integral of x^2-10x+25 ?

The integral of x^2-10x+25 is (x^3)/3-5x^2+25x+C

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integral of x^2-10x+25

\int x^{2} - 10 x + 25 d x

\frac{x ^{3}}{3} - 5 x^{2} + 25 x + C

Solution steps

\int x^{2} - 10 x + 25 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 10 x d x + \int 25 d x

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

\int 10 x d x = 5 x^{2}

\int 25 d x = 25 x

= \frac{x ^{3}}{3} - 5 x^{2} + 25 x

Add a constant to the solution

= \frac{x ^{3}}{3} - 5 x^{2} + 25 x + C

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What is the integral of x^2-10x+25 ?
The integral of x^2-10x+25 is (x^3)/3-5x^2+25x+C