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

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

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

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

- \frac{1}{2 arcsin ^{2} ( x )} + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{3}} d u

= \int \frac{1}{u ^{3}} d u

Apply the Power Rule

: - \frac{1}{2 u ^{2}}

= - \frac{1}{2 u ^{2}}

Substitute back

u = arcsin (x)

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

Add a constant to the solution

= - \frac{1}{2 arcsin ^{2} ( x )} + C

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