What is the integral of 20x^3+12x^2+8 ?

The integral of 20x^3+12x^2+8 is 5x^4+4x^3+8x+C

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integral of 20x^3+12x^2+8

\int 20 x^{3} + 12 x^{2} + 8 d x

5 x^{4} + 4 x^{3} + 8 x + C

Solution steps

\int 20 x^{3} + 12 x^{2} + 8 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 20 x^{3} d x + \int 12 x^{2} d x + \int 8 d x

\int 20 x^{3} d x = 5 x^{4}

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

\int 8 d x = 8 x

= 5 x^{4} + 4 x^{3} + 8 x

Add a constant to the solution

= 5 x^{4} + 4 x^{3} + 8 x + C

2 x^{2} - 5 x

\frac{d}{d x} ((5 x^{6} + 2 x^{3})^{4})

\frac{d}{d x} (3 x sin (y) + ln (y^{2}))

x \to 3 - lim (x - 3)

\frac{\partial}{\partial x} (y ln (x z^{2}))

What is the integral of 20x^3+12x^2+8 ?
The integral of 20x^3+12x^2+8 is 5x^4+4x^3+8x+C