What is the integral of 3x^2+8x-2 ?

The integral of 3x^2+8x-2 is x^3+4x^2-2x+C

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integral of 3x^2+8x-2

\int 3 x^{2} + 8 x - 2 d x

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

Solution steps

\int 3 x^{2} + 8 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 3 x^{2} d x + \int 8 x d x - \int 2 d x

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

\int 8 x d x = 4 x^{2}

\int 2 d x = 2 x

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

Add a constant to the solution

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

\frac{\partial}{\partial t} (t^{4} cos (s))

csc^{3} (5 x^{2} + 1)

y^{^{'}} + \frac{2 y}{x} = - \frac{2}{x}

\frac{d ^{2} y}{d x ^{2}} + \frac{d y}{d x} - 6 y = 0

\frac{d}{d x} (\frac{x - y}{2 x + 4 y})