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

= \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

\frac{\partial}{\partial x} (x^{2} + x y + y^{2} + 2 x - y)

\frac{d}{d t} (- cos (2 t))

y = x^{8} e^{- x}, (1, \frac{1}{e})

\int (2 x^{4} - 8 x^{3}) \cdot e^{- 3 x} d x

\frac{d}{d x} (\frac{2 cos ( x )}{sec ( x )})

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