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Integral de $$$\frac{1}{\sqrt{1 - y^{2}}}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{1}{\sqrt{1 - y^{2}}}\, dy$$$.
Solución
La integral de $$$\frac{1}{\sqrt{1 - y^{2}}}$$$ es $$$\int{\frac{1}{\sqrt{1 - y^{2}}} d y} = \operatorname{asin}{\left(y \right)}$$$:
$${\color{red}{\int{\frac{1}{\sqrt{1 - y^{2}}} d y}}} = {\color{red}{\operatorname{asin}{\left(y \right)}}}$$
Por lo tanto,
$$\int{\frac{1}{\sqrt{1 - y^{2}}} d y} = \operatorname{asin}{\left(y \right)}$$
Añade la constante de integración:
$$\int{\frac{1}{\sqrt{1 - y^{2}}} d y} = \operatorname{asin}{\left(y \right)}+C$$
Respuesta
$$$\int \frac{1}{\sqrt{1 - y^{2}}}\, dy = \operatorname{asin}{\left(y \right)} + C$$$A