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{\partial}{\partial x} (ln (1 + (x - 1)^{4} \cdot y^{2}))

\frac{\partial}{\partial y} (3 e^{x} sin (y))

\frac{d}{d x} (\frac{1 - x}{x})

\int \frac{1}{x ^{2} - 2 x + 101} d x

\int sec^{5} (4 x) d x

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