Question

hey can somone please help me with this question.
intergral =tan(x)^3*secx^(5) dx

Answer 1

its using trig identities

Answer 2

notice that \[\frac d{dx} \sec x=\sec x\tan x\]strip that out and see what you have to work with

Answer 3

in cases like these it is nice to shoot for even powers in the integrand so we can apply trig identities

Answer 4

\[\int\tan^3x\sec^5xdx=\int\tan^2\sec^4\cdot\tan x\sec xdx\]this should give you some ideas

Answer 5

i have done that far. and differentiated it. but i dont know where to subsitute the trig identity.

Answer 6

doesn't it look like \(\tan x\sec x\) will be our \(du\) ?
If that is the case, what is our \(u\) ?

Answer 7

try this alternate approach too :)

write
\(\Large \tan^2 x = \sec^2 x-1\)
and then
plug in u = sec x

Answer 8

oh, Turing is going with that approach only!

Answer 9

I was getting there @hartnn :P

Answer 10

lol

Answer 11

\[\int\limits_{}^{}(\sec ^{2}x-1)\sec x^{4}.\tan x^{}\sec x^{} dx\]

Answer 12

looking good, now simplify and u-sub

Answer 13

\[dx = du/secxtanx\]

Answer 14

yes

Answer 15

do i cancel secxtanx

Answer 16

I like to think of it like\[du=\sec x\tan xdx\]and then substituting for \(\sec x\tan x\), but your "cancellation" method will have the exact same result; it's just different logic

Answer 17

i see

Answer 18

so i have to integate u^5(u^2-1)

Answer 19

yep

Answer 20

er u^4(u^2-1)

Answer 21

I = secx^7/7 - secx^5/5 + C

Answer 22

sounds correct, let's double check with the wolf

Answer 23

the wolf agrees:
http://www.wolframalpha.com/input/?i=intergral%20tan(x)%5E3*secx%5E(5)%20dx&t=crmtb01

Answer 24

do u stoll need help