|
|
|
|
|
|
Integral of $$$\frac{\sin{\left(x \right)}}{x}$$$
The calculator will find the integral/antiderivative of $$$\frac{\sin{\left(x \right)}}{x}$$$, with steps shown.
Related calculator: Integral Calculator
Solution
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: $$$\int{\frac{\sin{\left(x \right)}}{x} d x}=\operatorname{Si}{\left(x \right)}+C$$$