duff44 2 years ago find the integral of 1/x sqrt(5-x^2) not sure how to do an identity with the 5 in there

1. tkhunny

What would you do if it were a '1', rather than a '5'?

2. Goten77

|dw:1359690189282:dw| hmm let me think for a sec

3. duff44

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.

4. tkhunny

You didn't quite answer my question. What substitution would you actually use if it were a 1?

5. matricked

assume x=sqrt(5)*sinp ...

6. duff44

I would make x=sin theta so|dw:1359690857236:dw|

7. tkhunny

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 $$x = \sqrt{5}\cdot\sin(\theta)$$?

8. duff44

|dw:1359691617818:dw| then just plug back in x for theta?