5.5 The Substitution Rule/41

$\int {\frac {1}{{\sqrt {1-x^{2}}}\arcsin {x}}}$

${\begin{aligned}u&=\arcsin {x}\\[2ex]du&={\frac {1}{\sqrt {1-x^{2}}}}\;dx\\[2ex]\end{aligned}}$

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} \int (\frac{1}{\sqrt{1-x^{2}}}\c* \frac{1}{\arcsin {x}})\;dx &= \int \frac{1}{u}\;du \\[2ex] &= \ln |u| +c \\[2ex] &= \ln |\arcsin {x}| + c \\[2ex] \end{align} }