5.5 The Substitution Rule/41: Difference between revisions
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<math> | <math> | ||
\begin{align} | \begin{align} | ||
\int \frac{1}{\sqrt{1-x^{2}}} \frac{1}{\arcsin {x} | \int \frac{1}{\sqrt{1-x^{2}}} \frac{1}{\arcsin {x}} | ||
&= \int \frac{1}{u} du \\[2ex] | &= \int \frac{1}{u} du \\[2ex] | ||
&= \ln |u| +c \\[2ex] | &= \ln |u| +c \\[2ex] | ||
Revision as of 23:13, 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 (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\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{aligned}}}