What is the integral of (arccos^2(x))/(sqrt(1-x^2)) ?

The integral of (arccos^2(x))/(sqrt(1-x^2)) is -(arccos^3(x))/3+C

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integral of (arccos^2(x))/(sqrt(1-x^2))

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

- \frac{arccos ^{3} ( x )}{3} + C

Solution steps

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

Apply u-substitution

: \int - u^{2} d u

= \int - u^{2} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= - \frac{u ^{3}}{3}

Substitute back

u = arccos (x)

= - \frac{arccos ^{3} ( x )}{3}

Add a constant to the solution

= - \frac{arccos ^{3} ( x )}{3} + C

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What is the integral of (arccos^2(x))/(sqrt(1-x^2)) ?
The integral of (arccos^2(x))/(sqrt(1-x^2)) is -(arccos^3(x))/3+C