Integral de $$$\frac{\cos{\left(c \right)}}{x^{2}}$$$ em relação a $$$x$$$

Encontre $$$\int \frac{\cos{\left(c \right)}}{x^{2}}\, dx$$$.

Aplique a regra do múltiplo constante $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ usando $$$c=\cos{\left(c \right)}$$$ e $$$f{\left(x \right)} = \frac{1}{x^{2}}$$$:

$${\color{red}{\int{\frac{\cos{\left(c \right)}}{x^{2}} d x}}} = {\color{red}{\cos{\left(c \right)} \int{\frac{1}{x^{2}} d x}}}$$

Aplique a regra da potência $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$ com $$$n=-2$$$:

$$\cos{\left(c \right)} {\color{red}{\int{\frac{1}{x^{2}} d x}}}=\cos{\left(c \right)} {\color{red}{\int{x^{-2} d x}}}=\cos{\left(c \right)} {\color{red}{\frac{x^{-2 + 1}}{-2 + 1}}}=\cos{\left(c \right)} {\color{red}{\left(- x^{-1}\right)}}=\cos{\left(c \right)} {\color{red}{\left(- \frac{1}{x}\right)}}$$

Portanto,

$$\int{\frac{\cos{\left(c \right)}}{x^{2}} d x} = - \frac{\cos{\left(c \right)}}{x}$$

Adicione a constante de integração:

$$\int{\frac{\cos{\left(c \right)}}{x^{2}} d x} = - \frac{\cos{\left(c \right)}}{x}+C$$

$$$\int \frac{\cos{\left(c \right)}}{x^{2}}\, dx = - \frac{\cos{\left(c \right)}}{x} + C$$$A