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Integral de $$$- \sec^{2}{\left(x \right)}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \left(- \sec^{2}{\left(x \right)}\right)\, dx$$$.
Solución
Aplica la regla del factor constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ con $$$c=-1$$$ y $$$f{\left(x \right)} = \sec^{2}{\left(x \right)}$$$:
$${\color{red}{\int{\left(- \sec^{2}{\left(x \right)}\right)d x}}} = {\color{red}{\left(- \int{\sec^{2}{\left(x \right)} d x}\right)}}$$
La integral de $$$\sec^{2}{\left(x \right)}$$$ es $$$\int{\sec^{2}{\left(x \right)} d x} = \tan{\left(x \right)}$$$:
$$- {\color{red}{\int{\sec^{2}{\left(x \right)} d x}}} = - {\color{red}{\tan{\left(x \right)}}}$$
Por lo tanto,
$$\int{\left(- \sec^{2}{\left(x \right)}\right)d x} = - \tan{\left(x \right)}$$
Añade la constante de integración:
$$\int{\left(- \sec^{2}{\left(x \right)}\right)d x} = - \tan{\left(x \right)}+C$$
Respuesta
$$$\int \left(- \sec^{2}{\left(x \right)}\right)\, dx = - \tan{\left(x \right)} + C$$$A