A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
find the integral of tan^5(x)sec^3(x) dx
how do I do this? thank you!
anonymous
 one year ago
find the integral of tan^5(x)sec^3(x) dx how do I do this? thank you!

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1442281422437:dw

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Since the powers are both you can strip one tangent or one secant and use the trig identity \[\tan^2x+1=\sec^2x\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay!! so what happens next? :/

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5You can make a u substitution, have you tried anything?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so u = tan^5(x)sec^3(x) and dv = dx ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh okay so what would be my next step? :/ sorry, integrals confuse me a lot :(

beginnersmind
 one year ago
Best ResponseYou've already chosen the best response.0You'll need to remember that (secx)' = secxtanx

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5You should try messing with it yourself @iheartfood

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5lets do u = secx then du = secxtanxdx better to do this \[\int\limits \tan^4xsec^2x secxtanx dx\]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Save some time this way

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yea astrophysics your second way is better.... then invert the relationship you gave to put it all in terms of sec(x)

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Yup, it just goes to show, there's many ways to approach these :P

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1\[ \int\tan^5(x)\sec^3(x)\,dx\\ \tan^2(x)+1=\sec^2(x)\\ \int\left(\sec^2(x)1\right)^2(x)\sec^3(x)\tan(x)\,dx\\ u=\sec(x)\\ du=\sec(x)\tan(x)\,dx\\ \int\left(u^21\right)u^2\,du \] A bit late lol.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ooh okay haha thank you both!! and so would i sub in now?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[ \int tan^4(x)sec^2(x) sec(x)tan(x)dx = \int tan^4(x)sec^2(x) d(sec(x)= \int (1sec^2(x))^2sec^2(x) d(sec(x) \] Then change variables to u=sec(x) \[ \int (1u^2)^2u^2du\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Darn it got cut off... well the only change between the second and third step was subbing in the fact that tan^4=(tan^2)^2 and then tan^2=1sec^2

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5You can integrate it now from \[\int\limits (u^21)^2 u^2 du\]

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1Either integration by parts or multiply the whole thing out.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i get integral of (u^41)(u^2)du > integral of u^6u^2 du so then i get ((u^7)/7)  ((u^3)/3) du ?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Hard to tell what you're doing \[\int\limits (u^21)^2u^2 du \implies \int\limits (u^42u^2+1)u^2 du\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes the equations form is by far superior... btw can I get one medal pretty please though astro deserves the rest since he is finishing it off

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Equations *button* form :D

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5I gave you one, sorry thomas took one from you so everyone would have one haha :P

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohhh :O wait so do i distribute next?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Yes, there still is the u^2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh wow I didnt see Thomas had beaten me to the punch he does deserve the medal there... I was posting in another problem

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so then i get integral of u^6  2u^4 + u^2 du ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay! and so i integrate and get this? dw:1442282862540:dw

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5You drop the integral sign and du when you integrate, now you can plug back your u substitution and add a +C

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ohh okay i see so i would end up with this? dw:1442282938959:dw

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5\[\large \checkmark\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ooh yay! and so I'm done? :O

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yay!! thank you so much!!:D

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5Np @thomas5267 and @PlasmaFuzer did great work to, collaborative, which makes it funner!

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1So Mr Astrophysics has beaten me has beaten PlasmaFuzer? An ordering on OpenStudy lol?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Haha makes sense @thomas5267 sorry for trying to steal your thunder im bouncing around in too many questions I guess

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Definitely agree @Astrophysics... Its also more fun to do harder problems :D

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1Sometimes it is really fun to race with others and spit out the correct answer fastest!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yea totally agree it adds to the excitement since many questions can be fairly dull

thomas5267
 one year ago
Best ResponseYou've already chosen the best response.1Most question here are quite dull. However I am not that good to answer questions on Math StackExchange.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.5There can be good questions, it's just hard to find the ones you're interested in, and most other sites I've encountered aren't as kind as the people here, very discouraging at times.
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.