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integration question


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#1 paddyb67

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Posted 12 October 2007 - 03:40 PM

integrate with respect to x: (x^(1/2))/(1+x)


cheers

#2 weerydo

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Posted 12 October 2007 - 07:11 PM

ok you need to bring the (1+x) up 2 the top so the second line would be.

(x^1/2)(1+x)^-1


then use the chain rule...if you need any more help message me - better letting you try it for yourself from there



#3 ad absurdum

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Posted 14 October 2007 - 12:17 PM

QUOTE(weerydo @ Oct 12 2007, 08:11 PM) View Post
ok you need to bring the (1+x) up 2 the top so the second line would be.

(x^1/2)(1+x)^-1


then use the chain rule...if you need any more help message me - better letting you try it for yourself from there
I can't see where this is going? I think you might be trying to differentiate this by mistake.

Paddy, try the substituion x=\tan^2 u. I end up with 2\sqrt{x} - 2arctan(\sqrt{x}) + C
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#4 madman69

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Posted 17 October 2007 - 04:32 PM

An easier substitution would be x=u^2. While using tan^2 x is more intuitive, it wastes a lot of effort since you have to substitute twice to get it in to a form where you can integrate to obtain a tan^(-1) function.

#5 paddyb67

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Posted 14 November 2007 - 04:01 PM

cheers guys, i think for forms like that you're just meant to fire in a tan substitution (half angle mainly). like madman said its not always the easiest but apparently it always works.





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