What is the integral of (2x^3+5x^2-2x+1) ?

The integral of (2x^3+5x^2-2x+1) is (x^4)/2+(5x^3)/3-x^2+x+C

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integral of (2x^3+5x^2-2x+1)

\int (2 x^{3} + 5 x^{2} - 2 x + 1) d x

\frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + x + C

Solution steps

\int 2 x^{3} + 5 x^{2} - 2 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 2 x^{3} d x + \int 5 x^{2} d x - \int 2 x d x + \int 1 d x

\int 2 x^{3} d x = \frac{x ^{4}}{2}

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

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

\int 1 d x = x

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + x

Add a constant to the solution

= \frac{x ^{4}}{2} + \frac{5 x ^{3}}{3} - x^{2} + x + C

x (x + 1)^{- 1}

e^{e^{x}} \to 0 + lim (\frac{e ^{e^{x} - 2}}{2})

\frac{d}{d x} (cot (6 x - x^{2}))

x \cdot sin (\frac{1}{x})

y = x^{3} - 11 x^{2} + 30 x, y = - x^{3} + 11 x^{2} - 30 x

What is the integral of (2x^3+5x^2-2x+1) ?
The integral of (2x^3+5x^2-2x+1) is (x^4)/2+(5x^3)/3-x^2+x+C