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