What is the integral of (arccos(y))^2 ?

The integral of (arccos(y))^2 is yarccos^2(y)-2(arccos(y)sqrt(1-y^2)+y)+C

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integral of (arccos(y))^2

\int (arccos (y))^{2} d y

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

Solution steps

\int (arccos (y))^{2} d y

Simplify

= \int arccos^{2} (y) d y

Apply Integration By Parts

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

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

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

= y arccos^{2} (y) - 2 (arccos (y) 1 - y^{2} + y)

Add a constant to the solution

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

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What is the integral of (arccos(y))^2 ?
The integral of (arccos(y))^2 is yarccos^2(y)-2(arccos(y)sqrt(1-y^2)+y)+C