What is the integral of 3x^2-24x+48 ?

The integral of 3x^2-24x+48 is x^3-12x^2+48x+C

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integral of 3x^2-24x+48

\int 3 x^{2} - 24 x + 48 d x

x^{3} - 12 x^{2} + 48 x + C

Solution steps

\int 3 x^{2} - 24 x + 48 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 24 x d x + \int 48 d x

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

\int 24 x d x = 12 x^{2}

\int 48 d x = 48 x

= x^{3} - 12 x^{2} + 48 x

Add a constant to the solution

= x^{3} - 12 x^{2} + 48 x + C

\frac{d}{d x} (3 x^{4} - 8 x^{3} + 2)

d er i v a t i v e lo g_{6} (x)

y^{^{''}} + 2 t = 0

\int_{- 1}^{2} - x^{2} + x + 2 d x

t an g e n t f (x) = (2 x + 4)^{\frac{1}{5}}, at x = 1

What is the integral of 3x^2-24x+48 ?
The integral of 3x^2-24x+48 is x^3-12x^2+48x+C