What is the integral of cos^{-1}(x) ?

The integral of cos^{-1}(x) is xarccos(x)-sqrt(1-x^2)+C

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integral of cos^{-1}(x)

\int arccos (x) d x

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

Solution steps

\int arccos (x) d x

Apply Integration By Parts

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

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

= x arccos (x) - 1 - x^{2}

Add a constant to the solution

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

What is the integral of cos^{-1}(x) ?
The integral of cos^{-1}(x) is xarccos(x)-sqrt(1-x^2)+C