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

The integral of (x/2)^2 is (x^3)/4-(x^3)/6+C

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integral of (x/2)^2

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

\frac{x ^{3}}{4} - \frac{x ^{3}}{6} + C

Solution steps

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

Apply Integration By Parts

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

\int \frac{x ^{2}}{2} d x = \frac{x ^{3}}{6}

= \frac{x ^{3}}{4} - \frac{x ^{3}}{6}

Add a constant to the solution

= \frac{x ^{3}}{4} - \frac{x ^{3}}{6} + C