What is the integral of 25x^2-10x+1 ?

The integral of 25x^2-10x+1 is (25x^3)/3-5x^2+x+C

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integral of 25x^2-10x+1

\int 25 x^{2} - 10 x + 1 d x

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

Solution steps

\int 25 x^{2} - 10 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 25 x^{2} d x - \int 10 x d x + \int 1 d x

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

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

\int 1 d x = x

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

Add a constant to the solution

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

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What is the integral of 25x^2-10x+1 ?
The integral of 25x^2-10x+1 is (25x^3)/3-5x^2+x+C