5.5 The Substitution Rule/13: Difference between revisions
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\int \frac{dx}{5-3x} &= -\frac{1}{3}\int \left(\frac{1}{u}\right)du \\[2ex] | \int \frac{dx}{5-3x} &= -\frac{1}{3}\int \left(\frac{1}{u}\right)du \\[2ex] | ||
&=-\frac{1}{3}\ln{ | &=-\frac{1}{3}\ln{|u|} du \\[2ex] | ||
&=-\frac{1}{3}\ln{|5-3x|}+C | &=-\frac{1}{3}\ln{|5-3x|}+C | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 19:53, 22 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{dx}{5-3x} \text{,} \quad u=5-3x }
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 &=5-3x \\[2ex] du &=-3dx \\[2ex] -\frac{1}{3}du &=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{dx}{5-3x} &= -\frac{1}{3}\int \left(\frac{1}{u}\right)du \\[2ex] &=-\frac{1}{3}\ln{|u|} du \\[2ex] &=-\frac{1}{3}\ln{|5-3x|}+C \end{align} }