inkyvoyd
  • inkyvoyd
Can anyone explain how to find the integral of sec(x) or csc(x) with respect to x?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
lalaly is the integral master today
lalaly
  • lalaly
\[\int\limits{secxdx}=\int\limits{secx \times \frac{secx+tanx}{secx+tanx}}dx\]\[=\int\limits{\frac{\sec^2 x+secxtanx}{secx+tanx}dx}\] let u=secx+tanx so the integration becomes \[\int\limits{\frac{du}{u}}=\ln|u|+C\]\[=\ln|secx+tanx|+C\]
lalaly
  • lalaly
same for csc(x) but u multiply by (cscx+cotx)/(cscx+cotx)

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lalaly
  • lalaly
lol satelite:)
inkyvoyd
  • inkyvoyd
Holy crap, no wonder I couldn't figure it out on my own. Are there any other cases where we do this?
anonymous
  • anonymous
lalaly is correct
anonymous
  • anonymous
here is another version. apparently this was a big deal in the 17th century http://en.wikipedia.org/wiki/Integral_of_the_secant_function

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