What is the integral of (12x^2-7x+2) ?

The integral of (12x^2-7x+2) is 4x^3-(7x^2)/2+2x+C

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integral of (12x^2-7x+2)

\int (12 x^{2} - 7 x + 2) d x

4 x^{3} - \frac{7 x ^{2}}{2} + 2 x + C

Solution steps

\int 12 x^{2} - 7 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 7 x d x + \int 2 d x

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

\int 7 x d x = \frac{7 x ^{2}}{2}

\int 2 d x = 2 x

= 4 x^{3} - \frac{7 x ^{2}}{2} + 2 x

Add a constant to the solution

= 4 x^{3} - \frac{7 x ^{2}}{2} + 2 x + C

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What is the integral of (12x^2-7x+2) ?
The integral of (12x^2-7x+2) is 4x^3-(7x^2)/2+2x+C