January 16th, 2013, 09:38 AM  #1 
Senior Member Joined: Oct 2012 Posts: 460 Thanks: 0  integrals
[color=#0000FF]Dear All! Please, does anyone have an idea how to solve: the result is ment to be: Many thanks![/color] 
January 16th, 2013, 10:26 AM  #2 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: integrals
Use the substitution t = arcsin(x) ,

January 16th, 2013, 09:25 PM  #3 
Newbie Joined: Jan 2013 Posts: 13 Thanks: 0  Re: integrals
Interesting problem. It's just a usub as zaida mentioned. Split the into if you don't see the cancelling. Jc 
January 19th, 2013, 07:57 AM  #4 
Senior Member Joined: Oct 2012 Posts: 460 Thanks: 0  Re: integrals
[color=#0000FF]Thank you! now I have the integral of a rational function! what now? http://integraltable.com/integraltabl ... 0000000000 nth frm this goes well with...??? [/color] 
January 20th, 2013, 02:54 PM  #5  
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: integrals Quote:
 
January 21st, 2013, 06:16 AM  #6 
Senior Member Joined: Oct 2012 Posts: 460 Thanks: 0  Re: integrals
[color=#0000FF]Thank U, HallsofIvvy! (Well, be honest and admit it is not that easy!) [/color] 
January 21st, 2013, 06:28 AM  #7 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,929 Thanks: 1124 Math Focus: Elementary mathematics and beyond  Re: integrals 
January 21st, 2013, 06:37 AM  #8 
Senior Member Joined: Oct 2012 Posts: 460 Thanks: 0  Re: integrals [color=#0000FF] I dont get this... we dont know what is cosy? how do we know that it is 1?[/color] 
January 23rd, 2013, 10:14 AM  #9 
Senior Member Joined: Oct 2012 Posts: 460 Thanks: 0  Re: integrals
[color=#0000FF]Hello! Now I have: what shoud I do now? many thanks! Not finding the idea at: http://integraltable.com/ [/color] 
January 23rd, 2013, 01:20 PM  #10 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: integrals
I believe you have done this same thing repeatedly and been told, repeatedly, that you cannot do it! You cannot replace part of the function so that it is in terms of "u" while leaving the rest in terms of "x". That was the whole point in suggesting the substitution u= arcsin(x). Differentiating both sides, . You have put that in backwards, writing it as if it were . Instead write the integral as . 

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