What is the integral of arcsin(x/2) ?

The integral of arcsin(x/2) is xarcsin(x/2)+sqrt(4-x^2)+C

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integral of arcsin(x/2)

\int arcsin (\frac{x}{2}) d x

x arcsin (\frac{x}{2}) + 4 - x^{2} + C

Solution steps

\int arcsin (\frac{x}{2}) d x

Apply Integration By Parts

: x arcsin (\frac{x}{2}) - \int \frac{x}{4 - x ^{2}} d x

= x arcsin (\frac{x}{2}) - \int \frac{x}{4 - x ^{2}} d x

\int \frac{x}{4 - x ^{2}} d x = - 4 - x^{2}

= x arcsin (\frac{x}{2}) - (- 4 - x^{2})

Simplify

= x arcsin (\frac{x}{2}) + 4 - x^{2}

Add a constant to the solution

= x arcsin (\frac{x}{2}) + 4 - x^{2} + C

\frac{d y}{d x} = x^{2} x - 9

x \to 0 lim (ln (1 - 2 x))

\int e^{5 x} cos (2 x) d x

\int (x cos (y)) d y

\frac{\partial}{\partial x} (y - x)

What is the integral of arcsin(x/2) ?
The integral of arcsin(x/2) is xarcsin(x/2)+sqrt(4-x^2)+C