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

The integral of (x/2+3/2)^2 is (x^3}{12}+\frac{3x^2)/4+9/4 x+C

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

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

\frac{x ^{3}}{12} + \frac{3 x ^{2}}{4} + \frac{9}{4} x + C

Solution steps

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

Simplify

(\frac{x}{2} + \frac{3}{2})^{2} : \frac{x ^{2}}{4} + \frac{3 x}{2} + \frac{9}{4}

= \int \frac{x ^{2}}{4} + \frac{3 x}{2} + \frac{9}{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 \frac{x ^{2}}{4} d x + \int \frac{3 x}{2} d x + \int \frac{9}{4} d x

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

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

\int \frac{9}{4} d x = \frac{9}{4} x

= \frac{x ^{3}}{12} + \frac{3 x ^{2}}{4} + \frac{9}{4} x

Add a constant to the solution

= \frac{x ^{3}}{12} + \frac{3 x ^{2}}{4} + \frac{9}{4} x + C

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What is the integral of (x/2+3/2)^2 ?
The integral of (x/2+3/2)^2 is (x^3}{12}+\frac{3x^2)/4+9/4 x+C