how do you integrate...
Posted 14 November 2007 - 09:48 PM
i swear iv gone brain dead in the last 4 hours
Posted 27 November 2007 - 06:01 PM
Let rearrange it first
1/(1+cosx) = 1/( 1 + 2cos2(x/2)-1) cosx = 2cos2 (x/2)-1
= 1/ 2 cos2 (x/2)
=1/2 sec2 (x/2)
From now, if I werenít wrong, integrate sec2 (x/2), we get tan (x/2) + C !!!
So the answer is 1/2 tan (x/2) + C
Posted 27 November 2007 - 09:30 PM
Just to clarify your solution, it relies on the identity , i.e. . So in the denominator, we have the LHS with . So we can replace it using the identity:
Note that the answer isn't - you can see this just by differentiating, as the chain rule comes in to play.
Another possible method is to use the " substitution". I vaguely recalled this from 1st year at uni (!) but didn't have time to hunt out my notes. There's a relevant bit on Wikipedia.
Basically, we can let and do a substitution. The hardest bit is getting that , and ; then you get:
Notice that I've left out some lines of working there; it's just manipulating the fractions to get a lot of cancellation.
Posted 28 November 2007 - 01:01 PM
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