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$$$\frac{1}{y^{2} + 1}$$$ 的積分
您的輸入
求$$$\int \frac{1}{y^{2} + 1}\, dy$$$。
解答
$$$\frac{1}{y^{2} + 1}$$$ 的積分是 $$$\int{\frac{1}{y^{2} + 1} d y} = \operatorname{atan}{\left(y \right)}$$$：
$${\color{red}{\int{\frac{1}{y^{2} + 1} d y}}} = {\color{red}{\operatorname{atan}{\left(y \right)}}}$$
因此，
$$\int{\frac{1}{y^{2} + 1} d y} = \operatorname{atan}{\left(y \right)}$$
加上積分常數：
$$\int{\frac{1}{y^{2} + 1} d y} = \operatorname{atan}{\left(y \right)}+C$$
答案
$$$\int \frac{1}{y^{2} + 1}\, dy = \operatorname{atan}{\left(y \right)} + C$$$A
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