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Integral de $$$\frac{1}{\cos^{2}{\left(\theta \right)}}$$$
Calculadora relacionada: Calculadora de integrales definidas e impropias
Tu entrada
Halla $$$\int \frac{1}{\cos^{2}{\left(\theta \right)}}\, d\theta$$$.
Solución
Reescribe el integrando en términos de la secante:
$${\color{red}{\int{\frac{1}{\cos^{2}{\left(\theta \right)}} d \theta}}} = {\color{red}{\int{\sec^{2}{\left(\theta \right)} d \theta}}}$$
La integral de $$$\sec^{2}{\left(\theta \right)}$$$ es $$$\int{\sec^{2}{\left(\theta \right)} d \theta} = \tan{\left(\theta \right)}$$$:
$${\color{red}{\int{\sec^{2}{\left(\theta \right)} d \theta}}} = {\color{red}{\tan{\left(\theta \right)}}}$$
Por lo tanto,
$$\int{\frac{1}{\cos^{2}{\left(\theta \right)}} d \theta} = \tan{\left(\theta \right)}$$
Añade la constante de integración:
$$\int{\frac{1}{\cos^{2}{\left(\theta \right)}} d \theta} = \tan{\left(\theta \right)}+C$$
Respuesta
$$$\int \frac{1}{\cos^{2}{\left(\theta \right)}}\, d\theta = \tan{\left(\theta \right)} + C$$$A