What is the integral of (x-1/2)^2 ?

The integral of (x-1/2)^2 is 1/24 (2x-1)^3+C

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integral of (x-1/2)^2

\int (x - \frac{1}{2})^{2} d x

\frac{1}{24} (2 x - 1)^{3} + C

Solution steps

\int (x - \frac{1}{2})^{2} d x

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{u ^{3}}{3}

Substitute back

u = x - \frac{1}{2}

= \frac{( x - \frac{1}{2} ) ^{3}}{3}

Simplify

\frac{( x - \frac{1}{2} ) ^{3}}{3} : \frac{1}{24} (2 x - 1)^{3}

= \frac{1}{24} (2 x - 1)^{3}

Add a constant to the solution

= \frac{1}{24} (2 x - 1)^{3} + C

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What is the integral of (x-1/2)^2 ?
The integral of (x-1/2)^2 is 1/24 (2x-1)^3+C