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

= 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

\frac{d}{d x} (ln (\frac{( x - 3 )}{x - 1}))

\frac{d}{d x} (sin (a t))

\frac{\partial}{\partial x} (5 x e^{x y})

x \to - 1 lim (\frac{x ^{4} - 1}{x - 1})

2^{3 x^{2}}

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