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