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thomas5267

  • 3 years ago

@Callisto Can you give me some more examples of doing integration "your way"?

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  1. Callisto
    • 3 years ago
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    \[\int tanx dx\]

  2. Callisto
    • 3 years ago
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    \[=\int \frac{sinx}{cosx}dx\]\[=-\int \frac{1}{cosx}d(cosx)\]\[=-\ln|cosx|+C\] Try: \[\int cotx dx\]

  3. thomas5267
    • 3 years ago
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    \[ \begin{align*} &\int\cot(x)\,dx\\ =&\int\frac{1}{\tan(x)}\,dx\\ =&\int\frac{\cos(x)}{\sin(x)}\,dx\\ =&\int\frac{1}{\sin(x)}\,d(\sin(x))\\ =&\int\ln(\sin(x)) \end{align*} \] Seems legit...

  4. Callisto
    • 3 years ago
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    No int for the last line \[=\int\frac{1}{sinx}d(sinx)\]\[=ln|sinx|+C\]

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