What is the integral of sqrt(arcsin(x)) ?

The integral of sqrt(arcsin(x)) is xsqrt(arcsin(x))-sqrt(pi/2)\S(sqrt(2/pi)sqrt(arcsin(x)))+C

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integral of sqrt(arcsin(x))

\int arcsin (x) d x

x arcsin (x) - \frac{π}{2} § (\frac{2}{π} arcsin (x)) + C

Solution steps

\int arcsin (x) d x

Apply Integration By Parts

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

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

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

= x arcsin (x) - \frac{π}{2} § (\frac{2}{π} arcsin (x))

Add a constant to the solution

= x arcsin (x) - \frac{π}{2} § (\frac{2}{π} arcsin (x)) + C

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What is the integral of sqrt(arcsin(x)) ?
The integral of sqrt(arcsin(x)) is xsqrt(arcsin(x))-sqrt(pi/2)\S(sqrt(2/pi)sqrt(arcsin(x)))+C