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

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

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

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

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

Solution steps

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

Simplify

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

Apply u-substitution

: \int \frac{1}{u ^{2}} d u

= \int \frac{1}{u ^{2}} d u

Apply the Power Rule

: - \frac{1}{u}

= - \frac{1}{u}

Substitute back

u = arcsin (x)

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

Add a constant to the solution

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

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