What is the integral of arcsin(x)) ?

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

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integral of arcsin(x))

\int d (arcsin (x)) d x

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

Solution steps

\int d arcsin (x) d x

Take the constant out:

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

= d \cdot \int arcsin (x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

Add a constant to the solution

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

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