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