5.5 The Substitution Rule/37: Difference between revisions
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\begin{align} | \begin{align} | ||
\int \frac{\cos(x)}{\sin(x)}dx &= \int \frac{1}{\ | \int \frac{\cos(x)}{\sin(x)}dx &= \int \frac{1}{\sin(x)}\cos(x)\;dx = \int \frac{1}{\sin(x)}(\cos(x)\;dx) \\[2ex] | ||
&= | &= \int \frac{1}{{u}}(du) \\[2ex] | ||
&= \ | &= \left| \ln(u) \right| + C \\[2ex] | ||
&= \ | &= \left| \ln(\sin(x)) \right| + C \\[2ex] | ||
\end{align} | \end{align} | ||
</math> | </math> | ||
Latest revision as of 19:18, 20 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 \cot(x)dx = \int \frac{\cos(x)}{\sin(x)}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 &= \sin(x) \\[2ex] du &= \cos(x)\;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 \frac{\cos(x)}{\sin(x)}dx &= \int \frac{1}{\sin(x)}\cos(x)\;dx = \int \frac{1}{\sin(x)}(\cos(x)\;dx) \\[2ex] &= \int \frac{1}{{u}}(du) \\[2ex] &= \left| \ln(u) \right| + C \\[2ex] &= \left| \ln(\sin(x)) \right| + C \\[2ex] \end{align} }