Integral von $$$\frac{\sin{\left(y \right)}}{y}$$$

Bestimme $$$\int \frac{\sin{\left(y \right)}}{y}\, dy$$$.

Dieses Integral (Sinusintegral) besitzt keine geschlossene Form:

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

Daher,

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

Fügen Sie die Integrationskonstante hinzu:

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

$$$\int \frac{\sin{\left(y \right)}}{y}\, dy = \operatorname{Si}{\left(y \right)} + C$$$A