October 14th, 2012, 11:18 PM  #1 
Senior Member Joined: Jul 2011 Posts: 399 Thanks: 15  Indefinite Integration 
October 15th, 2012, 12:08 AM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 464 Math Focus: Calculus/ODEs  Re: Indefinite Integration
This is not expressible in elementary terms.

October 15th, 2012, 03:26 AM  #3  
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: Indefinite Integration Quote:
Let x = ((t^4)1)^( 1/4) Bring it back into the integal. This leads to an integral easy to express in terms of usual functions.  
October 15th, 2012, 05:37 AM  #4 
Senior Member Joined: Jul 2011 Posts: 399 Thanks: 15  Re: Indefinite Integration
Thanks JJacquelin and Markfl My solution:: [attachment=0:1705p6tf]Integral......gif[/attachment:1705p6tf] 
October 15th, 2012, 06:14 AM  #5 
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: Indefinite Integration
Your transformation is not completed yet because there is still (x^4) remainings at denominator. No x must remain in the integral. This is an integral with only t. 
October 15th, 2012, 12:32 PM  #6  
Senior Member Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0  Re: Indefinite Integration Quote:
@panky That is the substitution that came into my mind too! Regards, Rejjy 16Oct2012 01:02 IST  
October 15th, 2012, 12:41 PM  #7 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Indefinite Integration
Hi guys .. This substitution is giving me a headache .. There is something wrong with it ! I agree With Mark 
October 15th, 2012, 01:17 PM  #8  
Senior Member Joined: Aug 2011 Posts: 334 Thanks: 8  Re: Indefinite Integration Quote:
It remains only to find the primitives of tē/((t^4)1), which is not too difficult.  
October 16th, 2012, 02:36 AM  #9  
Senior Member Joined: Aug 2012 From: New Delhi, India Posts: 157 Thanks: 0  Re: Indefinite Integration Quote:
Here are my initial steps which prompted me of the substitution. Regards, Rejjy 16Oct2012 15:02 IST  
October 16th, 2012, 03:14 AM  #10 
Math Team Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions  Re: Indefinite Integration
You are right guys ,,, I agree with you


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