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$$$\frac{1}{x^{2} + 1}$$$ 的积分
您的输入
求$$$\int \frac{1}{x^{2} + 1}\, dx$$$。
解答
$$$\frac{1}{x^{2} + 1}$$$ 的积分为 $$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}$$$:
$${\color{red}{\int{\frac{1}{x^{2} + 1} d x}}} = {\color{red}{\operatorname{atan}{\left(x \right)}}}$$
因此，
$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}$$
加上积分常数：
$$\int{\frac{1}{x^{2} + 1} d x} = \operatorname{atan}{\left(x \right)}+C$$
答案
$$$\int \frac{1}{x^{2} + 1}\, dx = \operatorname{atan}{\left(x \right)} + C$$$A
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