My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 9th, 2009, 09:17 AM   #1
Newbie
 
Joined: Dec 2009

Posts: 12
Thanks: 0

Need help for an integration

Can anyone help me solve this integration below?

Integral of square root of (4+x^2) divided by x^5 dx. Thanks.
xujack88 is offline  
 
December 9th, 2009, 04:20 PM   #2
Math Team
 
Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Need help for an integration

Hello, xujack88!

I made some substitutions, but I really don't want to finish it . . .


Quote:


[color=beige].v . [/color]






[color=beige]. . [/color]









[color=beige]. . [/color]



You go on ahead . . . I'll wait in the car.
[color=beige] .[/color]
soroban is offline  
December 9th, 2009, 06:04 PM   #3
Senior Member
 
Joined: Feb 2009
From: Adelaide, Australia

Posts: 1,519
Thanks: 3

Re: Need help for an integration

There is no need for the introduction of u; the denominator (sec≤ ? - 1)≥ is equal to (tan≤ ?)≥. So you can turn the integrand into powers of csc ? and use a reduction formula.



It might be tricky rewriting the answer in terms of x.
aswoods is offline  
December 11th, 2009, 12:47 PM   #4
Global Moderator
 
Joined: Dec 2006

Posts: 20,469
Thanks: 2038

Let u = ?(4 + x), so u = 4 + x and udu = xdx.

?u/(u - 4) du = ?(1/(u + 2) - 1/(u - 2) + 2/(u + 2) + 2/(u - 2) + 8/(u - 2) - 8/(u + 2))/128 du, which is straightforward. Your final answer (in terms of x) can be written as a logarithmic term and another term. Post your working if you want it checked.
skipjack is offline  
December 11th, 2009, 01:17 PM   #5
Newbie
 
Joined: Dec 2009

Posts: 12
Thanks: 0

Re: Need help for an integration

Thank you all guys. I learned two methods to solve this, one is by using partial fractions, the other is reduction formula. This question is actually on my final, it's kinda time-consuming to finish it.
xujack88 is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
integration



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
integration rose Calculus 8 October 25th, 2017 01:08 AM
Integration LousInMaths Calculus 10 September 27th, 2012 02:26 AM
integration of S1-2 (x^2-x)^(1/2)dx gelatine1 Calculus 5 September 26th, 2012 06:38 PM
Integration fantom2012 Calculus 3 June 11th, 2012 05:49 PM
integration rose Calculus 7 April 11th, 2010 12:51 AM





Copyright © 2019 My Math Forum. All rights reserved.