# Integral of $\frac{1}{\sqrt{1 - x^{2}}}$

The calculator will find the integral/antiderivative of $\frac{1}{\sqrt{1 - x^{2}}}$, with steps shown.

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Find $\int \frac{1}{\sqrt{1 - x^{2}}}\, dx$.

### Solution

The integral of $\frac{1}{\sqrt{1 - x^{2}}}$ is $\int{\frac{1}{\sqrt{1 - x^{2}}} d x} = \operatorname{asin}{\left(x \right)}$:

$${\color{red}{\int{\frac{1}{\sqrt{1 - x^{2}}} d x}}} = {\color{red}{\operatorname{asin}{\left(x \right)}}}$$

Therefore,

$$\int{\frac{1}{\sqrt{1 - x^{2}}} d x} = \operatorname{asin}{\left(x \right)}$$

$$\int{\frac{1}{\sqrt{1 - x^{2}}} d x} = \operatorname{asin}{\left(x \right)}+C$$
Answer: $\int{\frac{1}{\sqrt{1 - x^{2}}} d x}=\operatorname{asin}{\left(x \right)}+C$