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

The integral of (arcsin(x))/(sqrt(1-x)) is -2arcsin(x)sqrt(1-x)+4sqrt(1+x)+C

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

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

- 2 arcsin (x) 1 - x + 4 1 + x + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{2 1 - x}{1 - x ^{2}} d x = - 4 1 + x

= - 2 arcsin (x) 1 - x - (- 4 1 + x)

Simplify

= - 2 arcsin (x) 1 - x + 4 1 + x

Add a constant to the solution

= - 2 arcsin (x) 1 - x + 4 1 + x + C

f (x) = ln (ln (3 x))

\frac{d}{d x} (\frac{x ^{2}}{x + 7})

n = 1 \sum \infty sin (\frac{1}{n})

\frac{\partial}{\partial x} (y^{2} sin (x z))

x \to 4 + lim (\frac{1}{x ^{3} - 64})

What is the integral of (arcsin(x))/(sqrt(1-x)) ?
The integral of (arcsin(x))/(sqrt(1-x)) is -2arcsin(x)sqrt(1-x)+4sqrt(1+x)+C