Question

Integration help!

integral of sec^5 x dx

Answer 1

/barf im guessing u sub will help you here

Answer 2

Integration by parts!

Answer 3

Whoops, I misread.

Answer 4

yes integration by parts

Answer 5

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

Answer 6

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

Answer 7

red formula will work if you have it

Answer 8

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

Answer 9

sec^2x = 1 + tan ^2

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

derive tan x = sec^2x

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

or wat to do?

Answer 19

hang on...

Answer 20

im a little rusty

Answer 21

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

Answer 22

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

Answer 23

this IS a reduction formula for powers of sec.

Answer 24

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

Answer 25

then again do u mind tellin me wat that is

Answer 26

or how to use it

Answer 27

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

Answer 28

cool i will prob understand that if u explain

Answer 29

the trig solution i mean

Answer 30

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

Answer 31

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

Answer 32

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

Answer 33

a=1

Answer 34

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)

Answer 35

where do u go on from there

Answer 36

omg i havent done definite integrals!

Answer 37

no, I mistyped

Answer 38

∫sec^5dx=1/4sec^3xtanx+3/4∫sec^3xdx

Answer 39

no definite integrals here

Answer 40

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

Answer 41

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

Answer 42

im confused how u got the previous step thou

Answer 43

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

Answer 44

i mean teh 1/4 sec part im confused about

Answer 45

in the reduction formula it 1/(a(n-1)

n=5, the power of secant
a = 1

Answer 46

ok so now how did u get 3/4?

Answer 47

from the reduction formula: (n-2)/(n-1)

again n = 5, the power of the secant

Answer 48

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

Answer 49

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

Answer 50

yea the trigonometric integrals take practice( obviously )

Answer 51

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

Answer 52

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

Answer 53

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

Answer 54

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

Answer 55

right ( n-2)/(n-1)

this time the formula will end with \[\int\limits \sec x dx\]

Answer 56

wait but isnt is half secant

Answer 57

so how is teh integral jsut sec

Answer 58

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

Answer 59

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

Answer 60

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

Answer 61

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!

Answer 62

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

Answer 63

SRY TAHTS SUPPOOSED TO be ln not tn

Answer 64

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?

Answer 65

let me check now

Answer 66

"table of integrals"

Answer 67

under wat heading shud i looj for te hreduction formulas

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

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

Answer 72

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

Answer 73

there might be one for ∫sec^n (ax)dx

Answer 74

might not

http://integral-table.com/

Answer 75

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

Answer 76

i guess tahts anoterh form of te one u showed me

Answer 77

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 ;) )

Answer 78

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

Answer 79

peace

Answer 80

ii imma go study sum more

Answer 81

gnite