5.5 The Substitution Rule/41: Difference between revisions
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u &= \arcsin {x} | u &= \arcsin {x} | ||
\\[2ex] | \\[2ex] | ||
du &= \frac{1}{\sqrt{1-x^2}} dx \\[2ex] | du &= \frac{1}{\sqrt{1-x^2}}\;dx \\[2ex] | ||
\end{align} | \end{align} | ||
Revision as of 23:15, 13 September 2022
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 \int \frac{1}{\sqrt{1-x^{2}} \arcsin {x}} }
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}{\sqrt{1-x^2}}\;dx \\[2ex] \end{align} }
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}}} \frac{1}{\arcsin {x}} &= \int \frac{1}{u} du \\[2ex] &= \ln |u| +c \\[2ex] &= \ln |\arcsin {x}| + c \\[2ex] \end{align} }