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Factorization under the square root won't help you a bit, but completing the square beneath it will........I think the u=lnx substitution is quite obvious, I mean the 1/x factor is right there.
After you use the substituion, the 1/x factor will go away and you can factorize that junk in the root sign, I think you can take it from there.
No, you haven't.thank you all but ive tried it all...
And, for the last time:what execises? Im new here and I have no idea what your talking about. believe me I know a thing or two in math and this integral i couldnt solve so dont call me laze because Ive tried for 5 hours befor I decided to ask for help. you can see that it is my first post
At this stage, I'd look to recast the denominator into a single trig ratio in the form of ##R\sin(\theta  \phi)## and integrate the cosecant term. But halfangles are fine also. Not sure which approach is more work when you "unfurl" all the substitutions back to the original variable.Correct!
Now, we multiply that cosine factor into the parenthesis, and we get the integral:
[tex]\int\frac{dv}{\sqrt{3}\sin(v)\cos(v)}[/tex]
Well, I haven't bothered to check. They'll differ by at most a wellhidden constant.At this stage, I'd look to recast the denominator into a single trig ratio in the form of ##R\sin(\theta  \phi)## and integrate the cosecant term. But halfangles are fine also. Not sure which approach is more work when you "unfurl" all the substitutions back to the original variable.
No, at most two constants. The domain of the integrand is disconnected ## x \in (0,1)\cup(1,\infty)##. It's possible to have one constant for the first connected component and a different constant for the other.Well, I haven't bothered to check. They'll differ by at most a wellhidden constant.