A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

integrate 1/((x^5)*sqrt(9*x^2-1))

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

    I've gotten pretty far I think, set x= 1/3 sec(U)

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

    then I got to the point where I had \[81 \int\limits_{}^{} (\cos(x))^4 dx\]

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

    the I apply the reduction formula twice and sub back in values for x to get (81/4)*(1/(3*x))^(3)*((sqrt(9 x^2-1))/(3*x))+243/(8)*(1/(3*x))*((sqrt(9 x^2-1))/(3*x))+243

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

    |dw:1327038086064:dw|

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

    maple and wolfram tell me that there is supposed to be an arctan in there somehow. But I can't figure out where it would get added in.

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

    I can show more steps in between, but what I have there matches maple except for the last term 243/8 is multiplied by -arctan(1/(sqrt(9 x^2-1))) for some reason.

  7. Mr.Math
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    It seems like if you have made a mistake when substituting back for x.

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

    I did this |dw:1327038548902:dw|

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

    I know I've done it correctly right up until the substitution

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

    |dw:1327038727194:dw| then all I did was substitute the values for sin and cos I found from the triangle

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

    oops that last term should be over 8

  12. Mr.Math
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    There's more than a way to substitute back, seems to me like wolfarm did this \[\tan{u}=\sqrt{9x^2-1} \implies u=\tan^{-1}{\sqrt{9x^2-1}}.\]

  13. Mr.Math
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    There should be a term in the form \(ku\) in your integral, k is a constant.

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

    Back in the step where you had \[81\int\limits_{}^{}\cos ^{4}(u) du\] did you consider substituting \[\cos^{2}u = (1 + \cos2u) / 2\] and solving from there?

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

    is the integral |dw:1327039058333:dw|

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

    I think that's where my missing term might be

  17. Mr.Math
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Yeah.

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

    ok because I had it set to 1. Then I will do the tan substitution you mentioned before and it should work out

  19. Mr.Math
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    And this is the term where the arctan came from, because \(u=\tan^{-1}{\sqrt{9x^2-1}}\).

  20. Mr.Math
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Exactly.

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

    Yeah, thanks a lot for your help!

  22. Mr.Math
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    You're welcome.

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

    If you guys are still online I ran into problems with how this was working out.

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

    I somehow need u= -arctan(1/sqrt(9x^2−1))

  25. Mr.Math
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 2

    Why would you need that?

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

    |dw:1327040345712:dw|

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

    that is what it's telling me I'm missing from the end

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

    |dw:1327040463342:dw|

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

    any ideas where this would come from. It's confusing since my first substitutions look right, but the u one isn't consistent with the same triangle

  30. 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.