What is the integral of (3x^2+5x-6) ?

The integral of (3x^2+5x-6) is x^3+(5x^2)/2-6x+C

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integral of (3x^2+5x-6)

\int (3 x^{2} + 5 x - 6) d x

x^{3} + \frac{5 x ^{2}}{2} - 6 x + C

Solution steps

\int 3 x^{2} + 5 x - 6 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 5 x d x - \int 6 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 6 d x = 6 x

= x^{3} + \frac{5 x ^{2}}{2} - 6 x

Add a constant to the solution

= x^{3} + \frac{5 x ^{2}}{2} - 6 x + C

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What is the integral of (3x^2+5x-6) ?
The integral of (3x^2+5x-6) is x^3+(5x^2)/2-6x+C