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

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

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

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

arcsin (x) + C

Solution steps

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

Use the common integral:

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

= arcsin (x)

Add a constant to the solution

= arcsin (x) + C

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