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

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

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

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

arcsin (r) + C

Solution steps

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

Use the common integral:

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

= arcsin (r)

Add a constant to the solution

= arcsin (r) + C

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