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May 20th, 2013, 06:57 PM  #1 
Member Joined: Apr 2012 Posts: 72 Thanks: 3  What is the final solution and the way to solve the integral 
May 20th, 2013, 08:05 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 465 Math Focus: Calculus/ODEs  Re: What is the final solution and the way to solve the inte
We are given: Let: and we have: Now, continue substituting in the same way, and you should see a pattern develop... 
May 20th, 2013, 08:11 PM  #3 
Member Joined: Apr 2012 Posts: 72 Thanks: 3  Re: What is the final solution and the way to solve the inte
Thanks! Is there any trick or shortcut? 
May 20th, 2013, 08:19 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 465 Math Focus: Calculus/ODEs  Re: What is the final solution and the way to solve the inte
Once you see the pattern (which you can see even from the first substitution) you will know the result without having to go through then entire process...

May 20th, 2013, 08:52 PM  #5 
Member Joined: Apr 2012 Posts: 72 Thanks: 3  Re: What is the final solution and the way to solve the inte
Sorry but I could not solve it. Could you please show the simplest way?

May 20th, 2013, 09:08 PM  #6 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 465 Math Focus: Calculus/ODEs  Re: What is the final solution and the way to solve the inte
Let's look first at: Now, consider: Let and we have: Next, consider: Let and we have: Now we know from the previous integral we may write: Do you see the pattern? 

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