anonymous
  • anonymous
\[\int tanxdx\] integration by parts
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
i integrate it twice; but i dont know why it failed
anonymous
  • anonymous
separate them into tanx and dx
anonymous
  • anonymous
i did\[(tanx)(x) - \int\limits xsec^{2}dx \]

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hartnn
  • hartnn
integral sin x /cos x put t= cos x
anonymous
  • anonymous
i know..but i want to do it by parts
mayankdevnani
  • mayankdevnani
- ln |cos x| + C proof int tan x dx = int sinx/cos x set u=cosx then we find du=-sinx dx substitute du=-sin x, u=cos x int sinx/cos x= - int of (-1) sin x dx / cosx =- int of du/u Solve the integral = - ln |u| + C substitute back u=cos x = - ln |cos x| + C
mayankdevnani
  • mayankdevnani
ok @Omniscience
anonymous
  • anonymous
i know u-sub i want to do it by parts
mayankdevnani
  • mayankdevnani
http://wiki.answers.com/Q/Integration_by_parts_of_x_tanx
mayankdevnani
  • mayankdevnani
i think it will help you!!!
anonymous
  • anonymous
that's \(xtanx\)
mayankdevnani
  • mayankdevnani
oh!!! sorry
anonymous
  • anonymous
maybe you could try converting tan x to sinx/cosx. then integrate sinxsecx by parts?
anonymous
  • anonymous
ok i will try it
anonymous
  • anonymous
wait. is the ans ln|secx|?
anonymous
  • anonymous
-ln(cosx)
anonymous
  • anonymous
looks the same lol
anonymous
  • anonymous
sec x is (cosx)^-1 bring the -1 to the front
anonymous
  • anonymous
yup thats the answer
anonymous
  • anonymous
ok thanks

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