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

The integral of 1/((arcsin(y))sqrt(1-y^2)) is ln|arcsin(y)|+C

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

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

ln ∣ arcsin (y) ∣ + C

Solution steps

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = arcsin (y)

= ln ∣ arcsin (y) ∣

Add a constant to the solution

= ln ∣ arcsin (y) ∣ + C

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