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. 
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]  
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 (sec² ?  1)³ is equal to (tan² ?)³. 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. 
December 11th, 2009, 12:47 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,747 Thanks: 2133 
Let u = ?(4 + x²), so u² = 4 + x² and udu = xdx. ?u²/(u²  4)³ du = ?(1/(u + 2)  1/(u  2) + 2/(u + 2)² + 2/(u  2)² + 8/(u  2)³  8/(u + 2)³)/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. 
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 timeconsuming to finish it. 

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