Integration help!
integral of sec^5 x dx

- anonymous

Integration help!
integral of sec^5 x dx

- chestercat

I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your **free** account and access **expert** answers to this

and **thousands** of other questions

- anonymous

/barf im guessing u sub will help you here

- across

Integration by parts!

- across

Whoops, I misread.

Looking for something else?

Not the answer you are looking for? Search for more explanations.

## More answers

- anonymous

yes integration by parts

- anonymous

(sec^2x)(sec^2)(sec x)

- across

I read it as sec^5(x)x for a moment there. Hmm, in this case, you have to use a reduction formula.

- anonymous

red formula will work if you have it

- anonymous

well i havent learned taht so is tehre anoterh way to do it by parts

- anonymous

sec^2x = 1 + tan ^2

- anonymous

( 1 + tan ^2 x ) ( 1 + tan^2 x ) (sec x )

- across

I had to look it up\[\frac{\sin(x)\sec^{m-1}(x)}{m-1}+\frac{m+2}{m-1}\int\sec^{m-2}(x)dx\]

- anonymous

this is wat i have so far:
\[\int\limits_{}^{}\sec^3 x (\sec^2 dx)\]
\[\int\limits_{}^{}\sec^3 x (1+\tan^2 x dx)\]
\[\int\limits_{}^{}(\sec^3 x +\sec^3 x \tan^2 x )dx\]

- anonymous

derive tan x = sec^2x

- anonymous

so do a u sub with u = tan x , du = sec^2 x dx

- anonymous

\[\int\limits_{}^{}(\sec^3 x) + \int\limits_{}^{}(\sec^3 x \tan^2 x) dx\]
can i use u sub after this step

- anonymous

you will prolly end up with a ( 1 + u ) ^(to some power ) then it a simple integration

- anonymous

can u show me the steps after the one i just did

- anonymous

or wat to do?

- anonymous

hang on...

- anonymous

im a little rusty

- anonymous

ughh i hate problems liek this!! XD...requires too much work

- anonymous

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

- anonymous

this IS a reduction formula for powers of sec.

- anonymous

i did n idont understand it b.c it uses smthng i didnt leard which is teh reduction formula thing

- anonymous

then again do u mind tellin me wat that is

- anonymous

or how to use it

- anonymous

yea, your instructor may not accept a reduction formula answer, it the quick way, but there is a trigonometric solution for this.

- anonymous

cool i will prob understand that if u explain

- anonymous

the trig solution i mean

- anonymous

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

- anonymous

as a matter of fact I bet your textbook has a table of integrals for integrals of powers of secant

- anonymous

what is the dffnce between sex^n (x) and sec^n (ax)

- anonymous

a=1

- anonymous

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)

- anonymous

where do u go on from there

- anonymous

omg i havent done definite integrals!

- anonymous

no, I mistyped

- anonymous

∫sec^5dx=1/4sec^3xtanx+3/4∫sec^3xdx

- anonymous

no definite integrals here

- anonymous

hmm how did u get 1/4 sec ...etc

- anonymous

then apply the reduction formula ( or integrate ) \[\int\limits \sec ^ 3 x dx\]

- anonymous

im confused how u got the previous step thou

- anonymous

its from the reduction formula, it ends with an integral of ∫sec^3xdx

- anonymous

i mean teh 1/4 sec part im confused about

- anonymous

in the reduction formula it 1/(a(n-1)
n=5, the power of secant
a = 1

- anonymous

ok so now how did u get 3/4?

- anonymous

from the reduction formula: (n-2)/(n-1)
again n = 5, the power of the secant

- anonymous

you instructor will be either impressed or put off that you are using the integral tables. :)

- anonymous

lol...he will b impressed hopefully...i have a test 2mm n im trying to udnerstand probs idk

- anonymous

yea the trigonometric integrals take practice( obviously )

- anonymous

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

- anonymous

right! so integrate the sec^x or use the formula again, but this time with n = 3, see?

- anonymous

sec^x is short, but it indefinite integral has many parts.

- anonymous

so after using n=3 do u get 1/2 sec x dx

- anonymous

right ( n-2)/(n-1)
this time the formula will end with \[\int\limits \sec x dx\]

- anonymous

wait but isnt is half secant

- anonymous

so how is teh integral jsut sec

- anonymous

no the formula will end ith ∫secxdx, integrate that and you are done.

- anonymous

\[\int\limits \sec x dx = \ln ( \sec x +tanx ) + C\]

- anonymous

so teh final answer is: 1/4 sec^3 x tanx + 3/4 ...idk teh rest

- anonymous

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!

- anonymous

so the final asnwer is:
1/4 sec^3 x tanx + 3/8 sec x tanx + tn (secx+tanx) + C

- anonymous

SRY TAHTS SUPPOOSED TO be ln not tn

- anonymous

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?

- anonymous

let me check now

- anonymous

"table of integrals"

- anonymous

under wat heading shud i looj for te hreduction formulas

- anonymous

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

- anonymous

Tables of integrals, Lists of Integrals usually in the appendix, could be on the inside covers.

- anonymous

yeah i see them in the appenxix...jsut under wat heading of integrals will i fimd teh reduction formulas

- anonymous

or wher u jsut letting me know taht tehre was a table of integrtals

- anonymous

that really what we were using, an integration formula, so you can integrate by parts or look up the formula.

- anonymous

there might be one for ∫sec^n (ax)dx

- anonymous

might not
http://integral-table.com/

- anonymous

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

- anonymous

i guess tahts anoterh form of te one u showed me

- anonymous

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 ;) )

- anonymous

THANK U SOOOOO MUCH!!! PLUS THE WEBSITE LOOKS SUPER HELPFUL =)

- anonymous

peace

- anonymous

ii imma go study sum more

- anonymous

gnite

Looking for something else?

Not the answer you are looking for? Search for more explanations.