5.5 The Substitution Rule/7: Difference between revisions
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<math> | <math> | ||
\int\ | \int x\sin{(x^{2})}dx | ||
</math> | </math> | ||
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u &=x^{2} \\[2ex] | u &=x^{2} \\[2ex] | ||
du &=2xdx \\[2ex] | du &=2xdx \\[2ex] | ||
\frac{1}{2}du=dx | \frac{1}{2}du &=dx \\[2ex] | ||
\end{align} | \end{align} | ||
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\begin{align} | \begin{align} | ||
\int\ | \int x\sin{(x^{2})}dx &=\frac{1}{2}\int\sin{(u)}du \\[2ex] | ||
&= -\frac{1}{2}\cos{(u)}+C \\[2ex] | |||
&= -\frac{1}{2}\cos{(x^{2})}+C | |||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 20:02, 7 September 2022
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \int x\sin {(x^{2})}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 &=x^{2} \\[2ex] du &=2xdx \\[2ex] \frac{1}{2}du &=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 x\sin{(x^{2})}dx &=\frac{1}{2}\int\sin{(u)}du \\[2ex] &= -\frac{1}{2}\cos{(u)}+C \\[2ex] &= -\frac{1}{2}\cos{(x^{2})}+C \end{align} }