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