What is the integral of arcsin(y) ?

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

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integral of arcsin(y)

\int arcsin (y) d y

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

Solution steps

\int arcsin (y) d y

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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