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

Find $$$\int \frac{\cos{\left(t \right)}}{t}\, dt$$$.

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

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

Therefore,

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

Add the constant of integration:

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

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