A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 4 years ago

please integrate this. =) sqr (x^2 - 1)dx /x

  • This Question is Closed
  1. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits \sqrt{x^2 - 1} dx / x\]

  2. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Put x^2 -1 = t^2 2xdx=2tdt dx=tdt/x it becomes integral of t/(t^2+1)

  3. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh sorry it becomes t^2/(t^2+1)

  4. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now can you do it?

  5. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yeah, i'll try my best. i'll do it first. :D

  6. anonymous
    • 4 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Try : sqrt(x^2-1)/x substitute x = sec(u) and dx = tan(u) sec(u) du. Then sqrt(x^2-1) = sqrt(sec^2(u)-1) = tan(u) and u = sec^(-1)(x) And now your integrand becomes tan^2(u) du which is nothing but tan(u)-u+constant.Now just put u = sec^(-1)(x) back to get : I = sqrt(x^2-1)-sec^(-1)(x)+constant And if you put some restrictions on x you get : sqrt(x^2-1)+tan^(-1)(1/sqrt(x^2-1))+constant. And you are done!

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

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

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.