A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

compute the indefinite integral. \[\int\limits (dx) /(x^2+4)^{5/2} \]

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

    I don't have heaps of time, but I can get you started. Make a substitution,\[x=2\tan \theta\]Then\[dx=2\sec ^2 \theta d \theta\]and your integral becomes,\[\int\limits_{}{}\frac{dx}{(x^2+4)^{5/2}}=\int\limits_{}{}\frac{2\sec^2 \theta }{(4+4\tan^2 \theta)^{5/2}}d \theta =\int\limits_{}{}\frac{2\sec^2 \theta }{2^5(1+\tan^2 \theta)}d \theta\]\[=\int\limits_{}{}\frac{2\sec^2 \theta }{2^5(\sec^2 \theta)^{5/2}}d \theta=\frac{1}{2^4}\int\limits_{}{}\frac{d \theta }{\sec^3 \theta}=\frac{1}{2^4}\int\limits_{}{}\cos^3 \theta d \theta\]

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

    The denominator on the third integral in the firs line should be raised to the power of 5/2

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

    You can solve this now using a reduction formula on cos^3(theta), or by using integration by parts on cos^3(theta) a couple of times. Once you have your answer, remember to undo your substitution; that is\[\theta = \tan^{-1}\frac{x}{2}\]and add a constant. If I didn't have to rush off, I'd finish it. I'll look in later to see how you went. Good luck :)

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

    \[{1\over12 }\left( \dfrac {x}{(x^2+4)^{3/2}}+\tan^{-1}(\dfrac{x}{2})\right)\]

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

    thank you so much guys!

  6. 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.