5.5 The Substitution Rule/31: Difference between revisions
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u &=\sin{(x)} \\[2ex] | u &=\sin{(x)} \\[2ex] | ||
du &= \cos{(x)}dx | du &= \cos{(x)}dx | ||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
\int \frac{\cos{(x)}}{\sin^2{(x)}}dx &= \int\frac{1}{u^2}du = \int u^-2du \\[2ex] | |||
&= u^-1 + C | |||
&= \frac{-1}{\sin{(x)}} + C | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 15:50, 4 October 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{\cos{(x)}}{\sin^2{(x)}}dx }
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 &=\sin{(x)} \\[2ex] du &= \cos{(x)}dx \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{\cos{(x)}}{\sin^2{(x)}}dx &= \int\frac{1}{u^2}du = \int u^-2du \\[2ex] &= u^-1 + C &= \frac{-1}{\sin{(x)}} + C \end{align} }