What is the integral of-3x^2-12x+15 ?

The integral of-3x^2-12x+15 is -x^3-6x^2+15x+C

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integral of-3x^2-12x+15

\int - 3 x^{2} - 12 x + 15 d x

- x^{3} - 6 x^{2} + 15 x + C

Solution steps

\int - 3 x^{2} - 12 x + 15 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 12 x d x + \int 15 d x

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

\int 12 x d x = 6 x^{2}

\int 15 d x = 15 x

= - x^{3} - 6 x^{2} + 15 x

Add a constant to the solution

= - x^{3} - 6 x^{2} + 15 x + C

\int_{0}^{1} \frac{3}{x ^{5}} d x

\int (e^{x} + sin (x) + x) d x

x \to 0 lim (\frac{2 x}{x ^{2}})

x \to 0 lim (- cos (x))

\int 6 x - x^{2} d x

What is the integral of-3x^2-12x+15 ?
The integral of-3x^2-12x+15 is -x^3-6x^2+15x+C