What is the integral of 8+6x+24x^2 ?

The integral of 8+6x+24x^2 is 8x+3x^2+8x^3+C

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integral of 8+6x+24x^2

\int 8 + 6 x + 24 x^{2} d x

8 x + 3 x^{2} + 8 x^{3} + C

Solution steps

\int 8 + 6 x + 24 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 8 d x + \int 6 x d x + \int 24 x^{2} d x

\int 8 d x = 8 x

\int 6 x d x = 3 x^{2}

\int 24 x^{2} d x = 8 x^{3}

= 8 x + 3 x^{2} + 8 x^{3}

Add a constant to the solution

= 8 x + 3 x^{2} + 8 x^{3} + C

\frac{d}{d x} (\frac{9 e ^{x} x ^{\frac{7}{2}}}{2} + e^{x} x^{\frac{9}{2}})

\frac{\partial}{\partial x} (\frac{4 x + 9}{3 y + 1})

f (x) = 4 x^{2} + 5 x + 3

\int (x^{3} + 3 x)^{32} (3 x^{2} + 3) d x

x \to \infty lim (1 + \frac{1}{x})

What is the integral of 8+6x+24x^2 ?
The integral of 8+6x+24x^2 is 8x+3x^2+8x^3+C