∫ 1 1 − x 2 = ∫ 1 u d u = ln | u | + c = ln | arcsin x | + c {\displaystyle \int {\frac {1}{\sqrt {1-x^{2}}}}=\int {\frac {1}{u}}du=\ln |u|+c=\ln |\arcsin {x}|+c}
u = arcsin x d u = 1 2 1 t d x 2 d u = 1 t d x {\displaystyle {\begin{aligned}u&=\arcsin {x}\\[2ex]du&={\frac {1}{2}}\ {\frac {1}{\sqrt {t}}}dx\\[2ex]2du&={\frac {1}{\sqrt {t}}}dx\end{aligned}}}
![{\displaystyle {\begin{aligned}u&=\arcsin {x}\\[2ex]du&={\frac {1}{2}}\ {\frac {1}{\sqrt {t}}}dx\\[2ex]2du&={\frac {1}{\sqrt {t}}}dx\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a5c84e8063fd702744415887e1cb1347363c66b5)