5.5 The Substitution Rule/21: Difference between revisions
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<math> | <math> | ||
\int \frac{\cos{(\sqrt{t})}}{\sqrt{t}} dt | \int \frac{\cos{(\sqrt{t})}}{\sqrt{t}}\;dt | ||
</math> | </math> | ||
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u &= \sqrt{t} \\[2ex] | u &= \sqrt{t} \\[2ex] | ||
du &= \frac{1}{2}\ \frac{1}{\sqrt{t}} dt \\[2ex] | du &= \frac{1}{2}\ \frac{1}{\sqrt{t}}\;dt \\[2ex] | ||
2du &= \frac{1}{\sqrt{t}} dt | 2du &= \frac{1}{\sqrt{t}}\;dt | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
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\begin{align} | \begin{align} | ||
\int \frac{\cos{(\sqrt{t})}}{\sqrt{t}} dt &= 2\int \cos {u} du \\[2ex] | \int \frac{\cos{(\sqrt{t})}}{\sqrt{t}} dt &= 2\int \cos {u}\;du \\[2ex] | ||
&= 2 \sin{u}+c \\[2ex] | &= 2 \sin{u}+c \\[2ex] | ||
&= 2 \sin(\sqrt{t}) + c \\[2ex] | &= 2 \sin(\sqrt{t}) + c \\[2ex] | ||
Revision as of 23:17, 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{\cos{(\sqrt{t})}}{\sqrt{t}}\;dt }
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 &= \sqrt{t} \\[2ex] du &= \frac{1}{2}\ \frac{1}{\sqrt{t}}\;dt \\[2ex] 2du &= \frac{1}{\sqrt{t}}\;dt \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{(\sqrt{t})}}{\sqrt{t}} dt &= 2\int \cos {u}\;du \\[2ex] &= 2 \sin{u}+c \\[2ex] &= 2 \sin(\sqrt{t}) + c \\[2ex] \end{align} }