What is the integral of 3-1(x^3-2x^2+x+1) ?

The integral of 3-1(x^3-2x^2+x+1) is -(x^4)/4+(2x^3)/3-(x^2)/2+2x+C

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integral of 3-1(x^3-2x^2+x+1)

\int 3 - 1 (x^{3} - 2 x^{2} + x + 1) d x

- \frac{x ^{4}}{4} + \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} + 2 x + C

Solution steps

\int 3 - 1 \cdot (x^{3} - 2 x^{2} + x + 1) d x

Simplify

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

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

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What is the integral of 3-1(x^3-2x^2+x+1) ?
The integral of 3-1(x^3-2x^2+x+1) is -(x^4)/4+(2x^3)/3-(x^2)/2+2x+C