What is the integral of 1/(sqrt(4-x^2)arcsin(x/2)) ?

The integral of 1/(sqrt(4-x^2)arcsin(x/2)) is ln|arcsin(x/2)|+C

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integral of 1/(sqrt(4-x^2)arcsin(x/2))

\int \frac{1}{4 - x ^{2} arcsin ( \frac{x}{2} )} d x

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

Solution steps

\int \frac{1}{4 - x ^{2} arcsin ( \frac{x}{2} )} d x

Apply u-substitution

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

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

Apply u-substitution

: \int \frac{1}{v} d v

= \int \frac{1}{v} d v

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

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

Add a constant to the solution

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

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

What is the integral of 1/(sqrt(4-x^2)arcsin(x/2)) ?
The integral of 1/(sqrt(4-x^2)arcsin(x/2)) is ln|arcsin(x/2)|+C