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$$$\sin{\left(t^{2} \right)}$$$ 的積分
您的輸入
求$$$\int \sin{\left(t^{2} \right)}\, dt$$$。
解答
此積分（菲涅耳正弦積分）不存在閉式表示：
$${\color{red}{\int{\sin{\left(t^{2} \right)} d t}}} = {\color{red}{\left(\frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} t}{\sqrt{\pi}}\right)}{2}\right)}}$$
因此，
$$\int{\sin{\left(t^{2} \right)} d t} = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} t}{\sqrt{\pi}}\right)}{2}$$
加上積分常數：
$$\int{\sin{\left(t^{2} \right)} d t} = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} t}{\sqrt{\pi}}\right)}{2}+C$$
答案
$$$\int \sin{\left(t^{2} \right)}\, dt = \frac{\sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2} t}{\sqrt{\pi}}\right)}{2} + C$$$A
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