5.5 The Substitution Rule/41

$\int {\frac {1}{\sqrt {1-x^{2}}}}=\int {\frac {1}{u}}du=\ln |u|+c=\ln |\arcsin {x}|+c$

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} u &= \arcsin {x} \\[2ex] du &= \frac{1}{2}\ \frac{1}{\sqrt{t}} dx \\[2ex] 2du &= \frac{1}{\sqrt{t}} dx \end{align} }