5.5 The Substitution Rule/41: Difference between revisions
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<math> | <math> | ||
\int \frac{1}{\sqrt{1-x^{2}}} = \int \frac{1}{u} du = \ln u +c = \ln |\arcsin {x}| + c | \int \frac{1}{\sqrt{1-x^{2}} \arcsin {x}} | ||
</math> | |||
<math> | |||
\begin{align} | |||
u &= \arcsin {x} | |||
\\[2ex] | |||
du &= \frac{1}{\sqrt{1-x^2}}\;dx \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
\int (\frac{1}{\sqrt{1-x^{2}}}\frac{1}{\arcsin {x}})\;dx | |||
&= \int \frac{1}{u}\;du \\[2ex] | |||
&= \ln |u| +c \\[2ex] | |||
&= \ln |\arcsin {x}| + c \\[2ex] | |||
\end{align} | |||
</math> | </math> | ||
Latest revision as of 23:19, 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}})\;dx &= \int \frac{1}{u}\;du \\[2ex] &= \ln |u| +c \\[2ex] &= \ln |\arcsin {x}| + c \\[2ex] \end{align} }