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

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

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

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

\frac{arcsin ^{3} ( x )}{3} + C

Solution steps

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

Apply u-substitution

: \int u^{2} d u

= \int u^{2} d u

Apply the Power Rule

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

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

Substitute back

u = arcsin (x)

= \frac{arcsin ^{3} ( x )}{3}

Add a constant to the solution

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

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