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

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

integral of (arccos(x))^2

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

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

Solution steps

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

Simplify

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

Apply Integration By Parts

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

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

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

Add a constant to the solution

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

d er i v a t i v e y = x^{2} 16 - x^{2}

\int_{0}^{\frac{π}{6}} 6 sec^{3} (x) d x

l a pl a ce t r an s f or m sin (6 (t - \frac{π}{6}))

n = 0 \sum \infty \frac{1}{( 4 n + 3 ) ^{2}}

\frac{d}{d x} ((x + 3)^{\frac{1}{2}})

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