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

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

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

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

ln ∣ arcsin (x) ∣ + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = arcsin (x)

= ln ∣ arcsin (x) ∣

Add a constant to the solution

= ln ∣ arcsin (x) ∣ + C

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