Integral of $$$\frac{\cos{\left(x \right)}}{x}$$$

Find $$$\int \frac{\cos{\left(x \right)}}{x}\, dx$$$.

This integral (Cosine Integral) does not have a closed form:

$${\color{red}{\int{\frac{\cos{\left(x \right)}}{x} d x}}} = {\color{red}{\operatorname{Ci}{\left(x \right)}}}$$

Therefore,

$$\int{\frac{\cos{\left(x \right)}}{x} d x} = \operatorname{Ci}{\left(x \right)}$$

Add the constant of integration:

$$\int{\frac{\cos{\left(x \right)}}{x} d x} = \operatorname{Ci}{\left(x \right)}+C$$

$$$\int \frac{\cos{\left(x \right)}}{x}\, dx = \operatorname{Ci}{\left(x \right)} + C$$$A