|
Integral de $$$\frac{1}{\sqrt{1 - x^{2}}}$$$
Calculadora relacionada: Calculadora de integrais definidas e impróprias
Sua entrada
Encontre $$$\int \frac{1}{\sqrt{1 - x^{2}}}\, dx$$$.
Solução
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,
$$\int{\frac{1}{\sqrt{1 - x^{2}}} d x} = \operatorname{asin}{\left(x \right)}$$
Add the constant of integration:
$$\int{\frac{1}{\sqrt{1 - x^{2}}} d x} = \operatorname{asin}{\left(x \right)}+C$$
Answer: $$$\int{\frac{1}{\sqrt{1 - x^{2}}} d x}=\operatorname{asin}{\left(x \right)}+C$$$