caseclosed Posted May 9, 2006 Share Posted May 9, 2006 This integral Tan(x)^3+Tan(x) doing it by hang gives Tan(x)^2/2 Mathematica gives Sec(x)^2/2 so why the difference, are both correct, how to get the mathematica answer by hand? Link to comment Share on other sites More sharing options...
Tartaglia Posted May 9, 2006 Share Posted May 9, 2006 Since sec^2(X) = tan^2(x) + 1, the only difference will be in the integration constant Link to comment Share on other sites More sharing options...
caseclosed Posted May 9, 2006 Author Share Posted May 9, 2006 I see, I hope the exam does not give mathematica answer as the chice because I have absolutely no clue how to get sec(x)^2/2, anyone know how to get that? Link to comment Share on other sites More sharing options...
ydoaPs Posted May 9, 2006 Share Posted May 9, 2006 tartaglia already said....... tan2(x)+1=sec2(x) Link to comment Share on other sites More sharing options...
caseclosed Posted May 10, 2006 Author Share Posted May 10, 2006 ok, now I understand it, basically constant can be thrown out. Link to comment Share on other sites More sharing options...
ydoaPs Posted May 10, 2006 Share Posted May 10, 2006 there's still a constant, it is just a different one. you get .5tan2(x)+C. they get .5sec2(x)+C'. the answers are identicle. C and C' differ by .5. Link to comment Share on other sites More sharing options...
matt grime Posted May 10, 2006 Share Posted May 10, 2006 one observation: sec^2=tan^2+1 has been used to explain how to translate between the two answers, after the integration, but it can be used bbefore hand too. use it in the original expression and you just get tan(x)sec^2(x) to integrate, which is sin(x)/cos^3(x), and that is integrable by inspection as 1/2cos^2(x) = sec^2(x). Link to comment Share on other sites More sharing options...
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