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

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

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

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

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

Solution steps

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

Apply Integration By Parts

= \frac{x ^{5}}{4} - \int x^{4} d x

\int x^{4} d x = \frac{x ^{5}}{5}

= \frac{x ^{5}}{4} - \frac{x ^{5}}{5}

Add a constant to the solution

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

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