February 16th, 2008, 01:55 PM  #1 
Newbie Joined: Feb 2008 Posts: 13 Thanks: 0  Stuck on an Integration problem
I am not sure how to do this problem, here it is. int 1/sqrt((x6)(10x)) I think the answer is something with arcsine but I am not sure how to get it. 
February 16th, 2008, 04:04 PM  #2 
Global Moderator Joined: Dec 2006 Posts: 19,505 Thanks: 1741 
You're right: arcsin((x âˆ’ 8)/2) + C. Differentiate that to see why.

February 16th, 2008, 06:53 PM  #3 
Newbie Joined: Feb 2008 Posts: 13 Thanks: 0 
Ahhh, but what is the first step I should do to integrate?

February 16th, 2008, 07:54 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 19,505 Thanks: 1741 
The first step is called "completing the square", but you wouldn't be asking about that if, as I suggested, you'd verified the answer by differentiating it.

February 16th, 2008, 08:28 PM  #5  
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0  Quote:
?? 1/?((x6)(10x)) dx = ? 1/?(2²  (x8)²) dx (? 1/?(a²  u²) du = arcsin(u/a) + C, in general) = arcsin((x  8)/2) + C Hence solved.  
February 17th, 2008, 07:30 AM  #6 
Newbie Joined: Feb 2008 Posts: 13 Thanks: 0 
Ooh that is really simple, I forgot about completing the square. Thanks 

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