What is the integral of arcsin(w) ?

The integral of arcsin(w) is warcsin(w)+sqrt(1-w^2)+C

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integral of arcsin(w)

\int arcsin (w) d w

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

Solution steps

\int arcsin (w) d w

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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