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

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

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

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

Therefore,

$$\int{\frac{\sin{\left(x \right)}}{x} d x} = \operatorname{Si}{\left(x \right)}$$

Add the constant of integration:

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

Answer: $$$\int{\frac{\sin{\left(x \right)}}{x} d x}=\operatorname{Si}{\left(x \right)}+C$$$