What is the integral of (4x^3-2x+2) ?

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

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integral of (4x^3-2x+2)

\int (4 x^{3} - 2 x + 2) d x

x^{4} - x^{2} + 2 x + C

Solution steps

\int 4 x^{3} - 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 4 x^{3} d x - \int 2 x d x + \int 2 d x

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

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

\int 2 d x = 2 x

= x^{4} - x^{2} + 2 x

Add a constant to the solution

= x^{4} - x^{2} + 2 x + C

x \to \infty lim (\frac{5}{2 x})

\frac{d}{d x} (cos (3 x^{2} + 1))

\int_{0}^{\infty} \frac{1}{x ^{2} + 1} d x

\frac{d y}{d x} = 29 - y

(1 + 4 x)^{\frac{3}{2}}, at x = 2

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