Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

farukk

integrate tan^3 xsec x dx...!

  • one year ago
  • one year ago

  • This Question is Closed
  1. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits \tan^3 x secx dx\]

    • one year ago
  2. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    what to do?

    • one year ago
  3. experimentX
    Best Response
    You've already chosen the best response.
    Medals 1

    \[ \tan^3 x \sec x = \tan x \sec x ( \sec^2 x - 1)\] seems like it will get the same

    • one year ago
  4. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah ..next step

    • one year ago
  5. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    note that d(sec x) =sec x tan x dx

    • one year ago
  6. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    yes all right

    • one year ago
  7. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    what's next..

    • one year ago
  8. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    let u = sec x then proceed. du= sec x tan x dx so it all becomes \(\int (u^2 - 1) du\)

    • one year ago
  9. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    dear are you solving integral by parts?

    • one year ago
  10. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    or by substituion?

    • one year ago
  11. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    it will become like this i guess u^3/3 - u +c

    • one year ago
  12. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    \( \int (\sec^2-1) \tan x \sec x dx\) =\( \int (\sec^2-1) d(\sec x)\) =\( \int (u^2-1) du\), where u=\sec x\) by substitution.

    • one year ago
  13. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    yes next step..

    • one year ago
  14. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    eh? \(\int u^n du= \frac{u^{n+1}}{n+1} +C\)

    • one year ago
  15. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    after applying we ll get as i above wrote ?

    • one year ago
  16. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    you'll get the answer....from integrating the above eq.

    • one year ago
  17. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    wait let me write what i am getting.

    • one year ago
  18. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{ \sec^3x }{ 3 }- secx +c = answer ???\]

    • one year ago
  19. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    it should be, yeah. :) you can always check your answers with wolfram.

    • one year ago
  20. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    wolfram.?

    • one year ago
  21. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    http://www.wolframalpha.com/input/?i=integrate%20tan%5E3%20x%20sec%20x%20dx&t=crmtb01

    • one year ago
  22. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    but answer is differnet in my book?

    • one year ago
  23. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\frac{ 1 }{ 3 }(secxtan^2x-2secx)+c =answer ( book)\]

    • one year ago
  24. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    @Shadowys

    • one year ago
  25. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    just take sec x out. and also, the integral, \(\int du=u\)

    • one year ago
  26. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    did't get..

    • one year ago
  27. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    \(\int (u^2-1) du = \int u^2 du - \int du\) following the integral, it becomes, \(\frac{u^3}{3} - u+C\)

    • one year ago
  28. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    i have already written this.Scroll up a bit

    • one year ago
  29. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    i just wanna get the same answer as in my book...:)

    • one year ago
  30. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    oh. unfortunately, either your book's wrong, or the computer integration is wrong. because wolfram agrees with you....lol

    • one year ago
  31. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah i have seen there but what you think about book's anwer is that wrong,there is really less possibilit though and yes lolz?

    • one year ago
  32. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    i have three books with same answer(:

    • one year ago
  33. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    lol i dun think wolfram's wrong, in anycase....lol

    • one year ago
  34. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    if we solve this by ''integration by parts'' rather tha by substituion?

    • one year ago
  35. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits uvdx= u \int\limits vdx - \int\limits(\int\limits vdx) u'dx\]

    • one year ago
  36. Shadowys
    Best Response
    You've already chosen the best response.
    Medals 3

    same way, but this time i still let du=d sec x tan x dx. and v=sec^2 -1 sorry, gtg, but i think you'll still get the same answer...(or that's what my calc tells me)

    • one year ago
  37. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    @Shadowys okay i think my all books are wrong this time.(there is no benifit or edge having more than one books) :)!

    • one year ago
  38. farukk
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks i took your time

    • one year ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.