What is the integral of ((x^2)/4+2x+3) ?

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

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integral of ((x^2)/4+2x+3)

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

\frac{x ^{3}}{12} + x^{2} + 3 x + C

Solution steps

\int \frac{x ^{2}}{4} + 2 x + 3 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 \frac{x ^{2}}{4} d x + \int 2 x d x + \int 3 d x

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

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

\int 3 d x = 3 x

= \frac{x ^{3}}{12} + x^{2} + 3 x

Add a constant to the solution

= \frac{x ^{3}}{12} + x^{2} + 3 x + C

\frac{d}{d x} (\frac{ln ( 6 x )}{6 x})

\frac{d y}{d x} = 5 y \cdot e^{x + 6}

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

(x^{2} + 2 x y - 4 y^{2}) d x - (x^{2} - 8 x y - 4 y^{2}) d y = 0

y = \frac{f ( x )}{x ^{9}}

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