What is the integral of (arcsin(y))/2 ?

The integral of (arcsin(y))/2 is 1/2 (yarcsin(y)+sqrt(1-y^2))+C

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integral of (arcsin(y))/2

\int \frac{arcsin ( y )}{2} d y

\frac{1}{2} (y arcsin (y) + 1 - y^{2}) + C

Solution steps

\int \frac{arcsin ( y )}{2} d y

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int arcsin (y) d y

Apply Integration By Parts

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

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

\int \frac{y}{1 - y ^{2}} d y = - 1 - y^{2}

= \frac{1}{2} (y arcsin (y) - (- 1 - y^{2}))

Simplify

= \frac{1}{2} (y arcsin (y) + 1 - y^{2})

Add a constant to the solution

= \frac{1}{2} (y arcsin (y) + 1 - y^{2}) + C

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What is the integral of (arcsin(y))/2 ?
The integral of (arcsin(y))/2 is 1/2 (yarcsin(y)+sqrt(1-y^2))+C