What is the integral of 4x^2-2x-2 ?

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

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integral of 4x^2-2x-2

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

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

6 x e^{5 x}

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

x \to 1 + lim (\frac{6}{x ^{3} - 1})

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

\int_{0}^{1} x^{3} e^{x^{2}} d x

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