Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

sirm3d

  • one year ago

integral problem. i have seen one solution in full. Maybe i can get another solution here.

  • This Question is Closed
  1. Spacelimbus
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\Large \int \frac{x}{\sqrt{x^2+x+1}}dx  \]?

  2. sirm3d
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\Large \int \frac{\mathrm dx}{x\sqrt{x^2+x+1}}\]

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

    ah, I see.

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

    This integral is frustrating...

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

    \[\Huge \checkmark \]

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

    What did you try @TuringTest, completing the square and then a trig substitution?

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

    That's what I did, and I did end up with an integral that is optically neater, integration wise still as bad

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

    yep, exactly. then I wound up with\[2\int\frac{\sec\theta d\theta}{\sqrt3\tan\theta-1}\]at which point I'm stuck

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

    From there I tried some difference of squares voodoo, but that only serves to complicate things it seems :p

  10. sirm3d
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    it's the same solution i had. \[2\frac{\sec \theta}{\sqrt 3 \tan \theta -1}=\frac{1}{\tfrac{\sqrt 3}{2} \sin \theta -\tfrac{1}{2}\cos \theta}=\frac{1}{\sin(\theta-\pi/6)}\] which can be integrated easily but the return to the variable \(x\) is the frustrating part.

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

    this might work ... http://en.wikipedia.org/wiki/Euler_substitution this is uglier than weirstrass substitution.

  12. sirm3d
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 2

    i found another solution. \[\frac{1}{x\sqrt{x^2+x+1}}=\frac{1}{\displaystyle x^2\sqrt{1+\frac{1}{x}+\frac{1}{x^2}}}=\frac{1}{\displaystyle x^2\sqrt{\left(\frac{\sqrt 3}{2}\right)^2+\left(\frac{1}{2}+\frac{1}{x}\right)^2}}\] let \[y=\frac{1}{2} + \frac{1}{x}\\\mathrm dy=-\frac{1}{x^2}\mathrm dx\]

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

    • Attachments:

Ask your own question

Ask a Question
Find 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
  • 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.