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integrate tan^3 xsec x dx...!

Mathematics
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\[\int\limits \tan^3 x secx dx\]
what to do?
\[ \tan^3 x \sec x = \tan x \sec x ( \sec^2 x - 1)\] seems like it will get the same

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Other answers:

yeah ..next step
note that d(sec x) =sec x tan x dx
yes all right
what's next..
let u = sec x then proceed. du= sec x tan x dx so it all becomes \(\int (u^2 - 1) du\)
dear are you solving integral by parts?
or by substituion?
it will become like this i guess u^3/3 - u +c
\( \int (\sec^2-1) \tan x \sec x dx\) =\( \int (\sec^2-1) d(\sec x)\) =\( \int (u^2-1) du\), where u=\sec x\) by substitution.
yes next step..
eh? \(\int u^n du= \frac{u^{n+1}}{n+1} +C\)
after applying we ll get as i above wrote ?
you'll get the answer....from integrating the above eq.
wait let me write what i am getting.
\[\frac{ \sec^3x }{ 3 }- secx +c = answer ???\]
it should be, yeah. :) you can always check your answers with wolfram.
wolfram.?
http://www.wolframalpha.com/input/?i=integrate%20tan%5E3%20x%20sec%20x%20dx&t=crmtb01
but answer is differnet in my book?
\[\frac{ 1 }{ 3 }(secxtan^2x-2secx)+c =answer ( book)\]
just take sec x out. and also, the integral, \(\int du=u\)
did't get..
\(\int (u^2-1) du = \int u^2 du - \int du\) following the integral, it becomes, \(\frac{u^3}{3} - u+C\)
i have already written this.Scroll up a bit
i just wanna get the same answer as in my book...:)
oh. unfortunately, either your book's wrong, or the computer integration is wrong. because wolfram agrees with you....lol
yeah i have seen there but what you think about book's anwer is that wrong,there is really less possibilit though and yes lolz?
i have three books with same answer(:
lol i dun think wolfram's wrong, in anycase....lol
if we solve this by ''integration by parts'' rather tha by substituion?
\[\int\limits uvdx= u \int\limits vdx - \int\limits(\int\limits vdx) u'dx\]
same way, but this time i still let du=d sec x tan x dx. and v=sec^2 -1 sorry, gtg, but i think you'll still get the same answer...(or that's what my calc tells me)
@Shadowys okay i think my all books are wrong this time.(there is no benifit or edge having more than one books) :)!
thanks i took your time

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