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

The integral of 1/(arcsin(x)) is \Ci(arcsin(x))+C

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integral of 1/(arcsin(x))

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

Ci (arcsin (x)) + C

Solution steps

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

Apply Integration By Parts

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

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

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

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

Simplify

= Ci (arcsin (x))

Add a constant to the solution

= Ci (arcsin (x)) + C

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What is the integral of 1/(arcsin(x)) ?
The integral of 1/(arcsin(x)) is \Ci(arcsin(x))+C