What is the integral of 1/(2sqrt(1-x^2)) ?

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

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integral of 1/(2sqrt(1-x^2))

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

\frac{1}{2} arcsin (x) + C

Solution steps

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

Take the constant out:

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

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

Use the common integral:

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

= \frac{1}{2} arcsin (x)

Add a constant to the solution

= \frac{1}{2} arcsin (x) + C

y^{^{''}} + 4 y^{^{'}} + 4 y = 2 e^{- 2 t}

x - 1, 0

x \to 0 lim (\frac{2}{3 + 4 ^{\frac{1}{0}}})

y = \frac{16 x}{x ^{2} + 16}, (- 2, - \frac{8}{5})

y^{^{''}} - 9 y = 0, y (0) = 7

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