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