What is the integral of arccos(2x) ?

The integral of arccos(2x) is xarccos(2x)-1/2 sqrt(1-4x^2)+C

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integral of arccos(2x)

\int arccos (2 x) d x

x arccos (2 x) - \frac{1}{2} 1 - 4 x^{2} + C

Solution steps

\int arccos (2 x) d x

Apply Integration By Parts

: x arccos (2 x) - \int - \frac{2 x}{1 - 4 x ^{2}} d x

= x arccos (2 x) - \int - \frac{2 x}{1 - 4 x ^{2}} d x

\int - \frac{2 x}{1 - 4 x ^{2}} d x = \frac{1}{2} 1 - 4 x^{2}

= x arccos (2 x) - \frac{1}{2} 1 - 4 x^{2}

Add a constant to the solution

= x arccos (2 x) - \frac{1}{2} 1 - 4 x^{2} + C

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What is the integral of arccos(2x) ?
The integral of arccos(2x) is xarccos(2x)-1/2 sqrt(1-4x^2)+C