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