What is the integral of (12x^2-8x+2) ?

The integral of (12x^2-8x+2) is 4x^3-4x^2+2x+C

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integral of (12x^2-8x+2)

\int (12 x^{2} - 8 x + 2) d x

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

Solution steps

\int 12 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 12 x^{2} d x - \int 8 x d x + \int 2 d x

\int 12 x^{2} d x = 4 x^{3}

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

\frac{d y}{d x} = \frac{( x - 1 )}{y}

\frac{d}{d x} (7 arcsin (x^{2}))

y = 1 x, (0, 4)

t \frac{d y}{d t} + 9 y = \frac{1}{t}

\int \frac{2 y ^{2} - 3}{y ^{2}} d y

What is the integral of (12x^2-8x+2) ?
The integral of (12x^2-8x+2) is 4x^3-4x^2+2x+C