What is the integral of 12x^2-5x+4 ?

The integral of 12x^2-5x+4 is 4x^3-(5x^2)/2+4x+C

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integral of 12x^2-5x+4

\int 12 x^{2} - 5 x + 4 d x

4 x^{3} - \frac{5 x ^{2}}{2} + 4 x + C

Solution steps

\int 12 x^{2} - 5 x + 4 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 12 x^{2} d x - \int 5 x d x + \int 4 d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

\int 4 d x = 4 x

= 4 x^{3} - \frac{5 x ^{2}}{2} + 4 x

Add a constant to the solution

= 4 x^{3} - \frac{5 x ^{2}}{2} + 4 x + C

\int_{- 2}^{2} \frac{1}{x ^{2} + 4} d x

\frac{d}{d x} (e^{2 x + 5} + \frac{1}{e ^{x^{2}}})

\frac{\partial}{\partial x} (7 x cos (5 x y))

x y y^{^{'}} = 4 x^{2} + 2 y^{2}

\frac{d}{d x} (x \cdot y^{2})

What is the integral of 12x^2-5x+4 ?
The integral of 12x^2-5x+4 is 4x^3-(5x^2)/2+4x+C