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

The integral of arccos(x/2) is xarccos(x/2)-sqrt(4-x^2)+C

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integral of arccos(x/2)

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

x arccos (\frac{x}{2}) - 4 - x^{2} + C

Solution steps

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

Apply Integration By Parts

= x arccos (\frac{x}{2}) - \int - \frac{x}{4 - x ^{2}} d x

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

= x arccos (\frac{x}{2}) - 4 - x^{2}

Add a constant to the solution

= x arccos (\frac{x}{2}) - 4 - x^{2} + C

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