What is the integral of x^3-3x^2+3x+0.25 ?

The integral of x^3-3x^2+3x+0.25 is 0.25x^4-x^3+1.5x^2+0.25x+C

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integral of x^3-3x^2+3x+0.25

\int x^{3} - 3 x^{2} + 3 x + 0.25 d x

0.25 x^{4} - x^{3} + 1.5 x^{2} + 0.25 x + C

Solution steps

\int x^{3} - 3 x^{2} + 3 x + 0.25 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^{3} d x - \int 3 x^{2} d x + \int 3 x d x + \int 0.25 d x

\int x^{3} d x = \frac{x ^{4}}{4}

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

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

\int 0.25 d x = 0.25 x

= \frac{x ^{4}}{4} - x^{3} + \frac{3 x ^{2}}{2} + 0.25 x

Simplify

= 0.25 x^{4} - x^{3} + 1.5 x^{2} + 0.25 x

Add a constant to the solution

= 0.25 x^{4} - x^{3} + 1.5 x^{2} + 0.25 x + C

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What is the integral of x^3-3x^2+3x+0.25 ?
The integral of x^3-3x^2+3x+0.25 is 0.25x^4-x^3+1.5x^2+0.25x+C