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

The integral of ((arcsin(x))^3)/(sqrt(1-x^2)) is (arcsin^4(x))/4+C

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integral of ((arcsin(x))^3)/(sqrt(1-x^2))

\int \frac{( arcsin ( x ) ) ^{3}}{1 - x ^{2}} d x

\frac{arcsin ^{4} ( x )}{4} + C

Solution steps

\int \frac{( arcsin ( x ) ) ^{3}}{1 - x ^{2}} d x

Simplify

= \int \frac{arcsin ^{3} ( x )}{1 - x ^{2}} d x

Apply u-substitution

: \int u^{3} d u

= \int u^{3} d u

Apply the Power Rule

: \frac{u ^{4}}{4}

= \frac{u ^{4}}{4}

Substitute back

u = arcsin (x)

= \frac{arcsin ^{4} ( x )}{4}

Add a constant to the solution

= \frac{arcsin ^{4} ( x )}{4} + C

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What is the integral of ((arcsin(x))^3)/(sqrt(1-x^2)) ?
The integral of ((arcsin(x))^3)/(sqrt(1-x^2)) is (arcsin^4(x))/4+C