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