问题
通过凑微分，如何计算 [$\textcolor{Orange}{\int \frac{f(\arcsin x)}{\sqrt{1-x^{2}}} \mathrm{d} x}$] ?选项
[A]. $\int$ $\frac{f(\arcsin x)}{\sqrt{1-x^{2}}}$ $\mathrm{d} x$ $=$ $\int$ $f(\arcsin x)$ $\mathrm{d}$ $(\arcsin x)$[B]. $\int$ $\frac{f(\arcsin x)}{\sqrt{1-x^{2}}}$ $\mathrm{d} x$ $=$ $\int$ $f(\arcsin x)$ $\mathrm{d}$ $(\arctan x)$
[C]. $\int$ $\frac{f(\arcsin x)}{\sqrt{1-x^{2}}}$ $\mathrm{d} x$ $=$ $- \int$ $f(\arcsin x)$ $\mathrm{d}$ $(\arcsin x)$
[D]. $\int$ $\frac{f(\arcsin x)}{\sqrt{1-x^{2}}}$ $\mathrm{d} x$ $=$ $\int$ $f(\arcsin x)$ $\mathrm{d} x$
$$\int \textcolor{Red}{\frac{f(\arcsin x)}{\sqrt{1-x^{2}}}} \mathrm{d} \textcolor{Yellow}{x} =$$ $$\int \textcolor{Red}{f(\arcsin x)} \mathrm{d} (\textcolor{Yellow}{\arcsin x})$$