5.5 The Substitution Rule/31: Difference between revisions
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\int \frac{\cos{(x)}}{\sin^2{(x)}}dx &= \int\frac{1}{u^2}du = \int u^-2du \\[2ex] | \int \frac{\cos{(x)}}{\sin^2{(x)}}dx &= \int\frac{1}{u^2}du = \int u^-2du \\[2ex] | ||
&= u^-1 + C | &= u^-1 + C \\[2ex] | ||
&= \frac{-1}{\sin{(x)}} + C | &= \frac{-1}{\sin{(x)}} + C | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Revision as of 15:51, 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 (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}u&=\sin {(x)}\\[2ex]du&=\cos {(x)}dx\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{\cos{(x)}}{\sin^2{(x)}}dx &= \int\frac{1}{u^2}du = \int u^-2du \\[2ex] &= u^-1 + C \\[2ex] &= \frac{-1}{\sin{(x)}} + C \end{align} }