$$$\frac{\sin{\left(x \right)}}{x}$$$の積分
入力内容
$$$\int \frac{\sin{\left(x \right)}}{x}\, dx$$$ を求めよ。
解答
この積分(正弦積分)には閉形式はありません:
$${\color{red}{\int{\frac{\sin{\left(x \right)}}{x} d x}}} = {\color{red}{\operatorname{Si}{\left(x \right)}}}$$
したがって、
$$\int{\frac{\sin{\left(x \right)}}{x} d x} = \operatorname{Si}{\left(x \right)}$$
積分定数を加える:
$$\int{\frac{\sin{\left(x \right)}}{x} d x} = \operatorname{Si}{\left(x \right)}+C$$
解答
$$$\int \frac{\sin{\left(x \right)}}{x}\, dx = \operatorname{Si}{\left(x \right)} + C$$$A
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