Here's the question you clicked on:
duff44
find the integral of 1/x sqrt(5-x^2) not sure how to do an identity with the 5 in there
What would you do if it were a '1', rather than a '5'?
|dw:1359690189282:dw| hmm let me think for a sec
well if it was a 1 I could use a^2-x^2 as the identity for sin but I dont think taking sqrt of 5 is the way to go.
You didn't quite answer my question. What substitution would you actually use if it were a 1?
assume x=sqrt(5)*sinp ...
I would make x=sin theta so|dw:1359690857236:dw|
Perfect. So, \(1 - x^{2}\) leads to \(x = \sin(\theta)\). You already suggested that \(a^{2} - x^{2}\) leads to \(x = a\cdot\sin{\theta}\). Why would \(5 - x^{2}\) lead to anything but \(x = \sqrt{5}\cdot\sin(\theta)\)?
|dw:1359691617818:dw| then just plug back in x for theta?