5.5 The Substitution Rule/53: Difference between revisions
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<math> | <math> | ||
&= u=1+2x^3\end{align | \int_{0}^{1}x^2(1+2x^3)^5dr | ||
</math> | |||
<math> | |||
\begin{align} | |||
u &=1+2x^3 \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
du &=6x^2dx \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
\int_{1}^{3} u^5 | |||
\frac{1}{6} du \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
&= \frac{1}{6} \int_{1}^{3} u^5 du \\[2ex] | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
&= \frac{1}{36} (1+2x^3)^6 | |||
\end{align} | |||
</math> | |||
<math> | |||
\begin{align} | |||
&= \frac{181}{9} \\[2ex] | |||
\end{align} | |||
</math> | </math> | ||
Latest revision as of 03:26, 23 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_{0}^{1}x^2(1+2x^3)^5dr }
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 &=1+2x^3 \\[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} du &=6x^2dx \\[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_{1}^{3} u^5 \frac{1}{6} du \\[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} &= \frac{1}{6} \int_{1}^{3} u^5 du \\[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} &= \frac{1}{36} (1+2x^3)^6 \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} &= \frac{181}{9} \\[2ex] \end{align} }