A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 5 years ago
compute the indefinite integral.
\[\int\limits (dx) /(x^2+4)^{5/2} \]
anonymous
 5 years ago
compute the indefinite integral. \[\int\limits (dx) /(x^2+4)^{5/2} \]

This Question is Closed

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I 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,\[\int\limits_{}{}\frac{dx}{(x^2+4)^{5/2}}=\int\limits_{}{}\frac{2\sec^2 \theta }{(4+4\tan^2 \theta)^{5/2}}d \theta =\int\limits_{}{}\frac{2\sec^2 \theta }{2^5(1+\tan^2 \theta)}d \theta\]\[=\int\limits_{}{}\frac{2\sec^2 \theta }{2^5(\sec^2 \theta)^{5/2}}d \theta=\frac{1}{2^4}\int\limits_{}{}\frac{d \theta }{\sec^3 \theta}=\frac{1}{2^4}\int\limits_{}{}\cos^3 \theta d \theta\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The denominator on the third integral in the firs line should be raised to the power of 5/2

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You 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 :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0\[{1\over12 }\left( \dfrac {x}{(x^2+4)^{3/2}}+\tan^{1}(\dfrac{x}{2})\right)\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you so much guys!
Ask your own question
Sign UpFind 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
 Engagement 19 Mad Hatter
 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.