Integration help! integral of sec^5 x dx

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Integration help! integral of sec^5 x dx

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/barf im guessing u sub will help you here
Integration by parts!
Whoops, I misread.

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yes integration by parts
(sec^2x)(sec^2)(sec x)
I read it as sec^5(x)x for a moment there. Hmm, in this case, you have to use a reduction formula.
red formula will work if you have it
well i havent learned taht so is tehre anoterh way to do it by parts
sec^2x = 1 + tan ^2
( 1 + tan ^2 x ) ( 1 + tan^2 x ) (sec x )
I had to look it up\[\frac{\sin(x)\sec^{m-1}(x)}{m-1}+\frac{m+2}{m-1}\int\sec^{m-2}(x)dx\]
this is wat i have so far: \[\int\limits_{}^{}\sec^3 x (\sec^2 dx)\] \[\int\limits_{}^{}\sec^3 x (1+\tan^2 x dx)\] \[\int\limits_{}^{}(\sec^3 x +\sec^3 x \tan^2 x )dx\]
derive tan x = sec^2x
so do a u sub with u = tan x , du = sec^2 x dx
\[\int\limits_{}^{}(\sec^3 x) + \int\limits_{}^{}(\sec^3 x \tan^2 x) dx\] can i use u sub after this step
you will prolly end up with a ( 1 + u ) ^(to some power ) then it a simple integration
can u show me the steps after the one i just did
or wat to do?
hang on...
im a little rusty
ughh i hate problems liek this!! XD...requires too much work
yea, it may have to be broken up into parts I cant get rid of one of the sec^x check out: http://www.wolframalpha.com/input/?i=integrate+sec^5+x
this IS a reduction formula for powers of sec.
i did n idont understand it b.c it uses smthng i didnt leard which is teh reduction formula thing
then again do u mind tellin me wat that is
or how to use it
yea, your instructor may not accept a reduction formula answer, it the quick way, but there is a trigonometric solution for this.
cool i will prob understand that if u explain
the trig solution i mean
there is an identity that will lead to an integral of u. anywa here is a like with the reduction formula for secant, and others http://www.sosmath.com/calculus/integration/moretrigpower/moretrigpower.html
as a matter of fact I bet your textbook has a table of integrals for integrals of powers of secant
what is the dffnce between sex^n (x) and sec^n (ax)
a=1
i wud use the first formula right? sec^5 (x) = sec ^5-2 (x) sec^2(x) = sec^3 (tan^2 x * sec^2 x -1)
where do u go on from there
omg i havent done definite integrals!
no, I mistyped
∫sec^5dx=1/4sec^3xtanx+3/4∫sec^3xdx
no definite integrals here
hmm how did u get 1/4 sec ...etc
then apply the reduction formula ( or integrate ) \[\int\limits \sec ^ 3 x dx\]
im confused how u got the previous step thou
its from the reduction formula, it ends with an integral of ∫sec^3xdx
i mean teh 1/4 sec part im confused about
in the reduction formula it 1/(a(n-1) n=5, the power of secant a = 1
ok so now how did u get 3/4?
from the reduction formula: (n-2)/(n-1) again n = 5, the power of the secant
you instructor will be either impressed or put off that you are using the integral tables. :)
lol...he will b impressed hopefully...i have a test 2mm n im trying to udnerstand probs idk
yea the trigonometric integrals take practice( obviously )
srry this is new to me so after taht step wat do u do..u still have a integral of sec^3 dx to deal with
right! so integrate the sec^x or use the formula again, but this time with n = 3, see?
sec^x is short, but it indefinite integral has many parts.
so after using n=3 do u get 1/2 sec x dx
right ( n-2)/(n-1) this time the formula will end with \[\int\limits \sec x dx\]
wait but isnt is half secant
so how is teh integral jsut sec
no the formula will end ith ∫secxdx, integrate that and you are done.
\[\int\limits \sec x dx = \ln ( \sec x +tanx ) + C\]
so teh final answer is: 1/4 sec^3 x tanx + 3/4 ...idk teh rest
1/4 sec^3 x tanx + 3/4∫sec^3xdx then apply the formula again for ∫sec^3xdx that answer will end with ∫sec xdx integrate ∫secxdx, done!
so the final asnwer is: 1/4 sec^3 x tanx + 3/8 sec x tanx + tn (secx+tanx) + C
SRY TAHTS SUPPOOSED TO be ln not tn
right, distribute the 3/4, I didnt work it all out but it looks right. Those tables are in you textbook right, in the appendix?
let me check now
"table of integrals"
under wat heading shud i looj for te hreduction formulas
i see basic forms, forms invlving sqrt of (a^2+u^2, forms involving (a^2 - u^2), forms involvung sqrt of (u^2 - a^2), forms involving a+bu, trig forms, inverse trig forms, exp and log forms, hyperbolic forms
Tables of integrals, Lists of Integrals usually in the appendix, could be on the inside covers.
yeah i see them in the appenxix...jsut under wat heading of integrals will i fimd teh reduction formulas
or wher u jsut letting me know taht tehre was a table of integrtals
that really what we were using, an integration formula, so you can integrate by parts or look up the formula.
there might be one for ∫sec^n (ax)dx
might not http://integral-table.com/
ths is wat is in my bk...sec^n du = 1/n tan u sec^n-2 + (n-2/n-1) *integral of sec^n-2 u du
i guess tahts anoterh form of te one u showed me
right that one dont account for a coefficient on x. so, yea, you seem to have it. Im out. ( gotta brush up on my integrals ;) )
THANK U SOOOOO MUCH!!! PLUS THE WEBSITE LOOKS SUPER HELPFUL =)
peace
ii imma go study sum more
gnite

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