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$$$\sin{\left(x^{2} \right)}$$$ 的积分
您的输入
求$$$\int \sin{\left(x^{2} \right)}\, dx$$$。
解答
该积分（菲涅耳正弦积分）没有闭式表达式：
$${\color{red}{\int{\sin{\left(x^{2} \right)} d x}}} = {\color{red}{\left(\frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}\right)}}$$
因此，
$$\int{\sin{\left(x^{2} \right)} d x} = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}$$
加上积分常数：
$$\int{\sin{\left(x^{2} \right)} d x} = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2}+C$$
答案
$$$\int \sin{\left(x^{2} \right)}\, dx = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} x}{\sqrt{\pi}}\right)}{2} + C$$$A
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