What is the integral of-2+30x-12x^2 ?

The integral of-2+30x-12x^2 is -2x+15x^2-4x^3+C

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integral of-2+30x-12x^2

\int - 2 + 30 x - 12 x^{2} d x

- 2 x + 15 x^{2} - 4 x^{3} + C

Solution steps

\int - 2 + 30 x - 12 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 2 d x + \int 30 x d x - \int 12 x^{2} d x

\int 2 d x = 2 x

\int 30 x d x = 15 x^{2}

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

= - 2 x + 15 x^{2} - 4 x^{3}

Add a constant to the solution

= - 2 x + 15 x^{2} - 4 x^{3} + C

x \to 0 lim ((1 + 4 x)^{\frac{3}{x}})

\int (\frac{tan ( u )}{4} - \frac{4}{7} u^{6} - \frac{2}{u}) d u

x \to a lim (\frac{1}{2})

f (x) = (5 x + 4)^{3}

\frac{x cos ( x ) - sin ( x )}{7 x ^{2}}

What is the integral of-2+30x-12x^2 ?
The integral of-2+30x-12x^2 is -2x+15x^2-4x^3+C