What is the integral of arcsin(x) ?

The integral of arcsin(x) is xarcsin(x)+sqrt(1-x^2)+C

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integral of arcsin(x)

\int arcsin (x) d x

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

Solution steps

\int arcsin (x) d x

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

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