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

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

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

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

arcsin (x) + C

Solution steps

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

Simplify

\frac{1 - x ^{2}}{1 - x ^{2}} : \frac{1}{1 - x ^{2}}

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

Use the common integral:

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

= arcsin (x)

Add a constant to the solution

= arcsin (x) + C

\int \frac{1}{x} arcsin (x) d x

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