Quantcast

A community for students. Sign up today!

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

mony01

  • 9 months ago

Anyone know how to do this integral?

  • This Question is Closed
  1. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits \frac{ x ^{2} +x+1}{ (x ^{2}+1)^{2} }dx\]

  2. wio
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Play around with the fraction.

  3. wio
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Maybe partial fraction decomposition

  4. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    did you try a trig sub i think that would work just fine

  5. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    you think i can try sin?

  6. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I think you can try tan

  7. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the hint was the x^2+1 on bottom

  8. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    tan^2(theta)+1=sec^2(theta)

  9. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    would the set up be integral x^2+x+1/sex^2 theta

  10. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    well you have to replace all the x's and the dx

  11. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and also you are leaving off the square on bottom

  12. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x=\tan(\theta) => dx=\sec^2(\theta) d \theta \] Replace all the x's with tan(theta) Replace the dx with sec^2(theta) d theta

  13. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it integral tan^2theta+tan theta+1/sec^2 theta d (theta)

  14. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If I think what you wrote is what I think then yes. You mean the following I assume: integral of (tan^2(theta)+tan(theta)+1)/sec^2(theta) d(theta)

  15. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\int\limits_{}^{}\frac{\tan^2(\theta)}{\sec^2(\theta)} d \theta +\int\limits_{}^{}\frac{\tan(\theta)}{\sec^2(\theta)} d \theta +\int\limits_{}^{} \frac{1}{\sec^2(\theta) }d \theta \]

  16. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Look at them three separately

  17. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 4

    \[\int\limits_{}^{}(\frac{ x^2+1 }{ (x^2+1)^2 } +\frac{ x }{ (x^2+1)^2 })*dx\]

  18. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 4

    \[\int\limits_{}^{}\frac{ dx }{ x^2+1 } +\int\limits_{}^{}\frac{ x }{ (x^2+1)^2 }\]

  19. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 4

    first one is standard formula

  20. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how can i figure out the answer?

  21. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 4

    \[\int\limits_{}^{}\frac{ x }{ (x^2+1)^2 } *dx\] for this x^2+1=t 2xdx=dt xdx=dt/2

  22. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 4

    \[\int\limits_{}^{} \frac{ dt }{ 2*t^2 }\]

  23. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 4

    \[\int\limits_{}^{}\frac{ dx }{ x^2+1 } +\int\limits_{}^{}\frac{ dt }{ 2t^2 }\]

  24. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 4

    can u solve it @mony01

  25. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is it sec^2 (theta)/2(x^2+1)^2

  26. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I do like gorv's way. But either way is fine. gorv's is simpler though.

  27. gorv
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 4

    actual its less calculative...both ways anns will be same

  28. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    how can i solve the rest of it?

  29. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What question on what part do you have?

  30. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[\int\limits \frac{ dx }{ x ^{2}+1}+\int\limits \frac{ dt }{ 2t ^{2} }\]

  31. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the first integral is just remembering that it is acran(x) the second one 1/2 is a constant multiple and you should know how to integrate t^(-2) at this point in calculus

  32. mony01
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 0

    is the answer arctan(x)-1/2(x^2+1)+C

  33. myininaya
    • 9 months ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes that's right you mean arctan(x)- 1/[2(x^2+1)] +C good job

  34. 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.