Re: thank you

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: : : : How do I integrate this? : : : : dx/(a+Sqrt(x)) : : : : Can someone explain the technique please? : : : : I don't need the actual answer, just help with the approach. : : : : I can do dx/Sqrt(x) fine (2Sqrt(x)) but this seems to be a beast of another nature... : : : First of all, T.Gracken's approach is correct -- and very courageous! : : : I assumed he'd already tried Substitution and didn't try it until just now. : : : And when I did -- WOW! : : : Let sqrt(x) = u : : : Then: x = u^2 : : : And: dx = 2u du : : : Substitute: INT 2u/(u+a) du : : : Divide: 2 INT [1 - a/(u+a)] du : : : There! : : : : Thank you! : : I sometimes get tunnel vision and just go with it. For some reason I thought a basic substitution would have already been attempted and did not even consider a simple substitution (and manipulating the fraction by "adding zero to the numerator"). : One of my favorite tricks is "adding zero", : 'though I've never heard that phrase before. : I like it! (Funny that it didn't occure me - : I've been "multiplying by one" for years.) : : I should be severly whipped for all that extra crap I did. : Naw - I think the overheard snickering (whether : real or imagined) is punishment enough. : : ...I think I've been teaching too many developmental classes of late. : I know THAT feeling, too! : A long story - maybe you'll feel better, TG. : A colleague (working on his MS in math) asked for : help with a Diff.Equation. He had tried various : techinques: Homogenous, Cauchy, Integrating : Factors, Method of Operators, etc. : I worked on it for an hour and finally consulted : a reference book. There I found an obscure : theorem which solved the DE. I proudly showed : John my work; he thanked me and left for his : evening DE course. : Some time later, I looked again and saw that the : very complicated solution simplified drastically : - SO drastically that I was sure I had overlooked : something. I looked again... : Oh, no! It was VARIABLES SEPARABLE! : Talk about "tunnel vision"! : Luckily, I was able to phone John and tell him - : before he showed our intricate (and egregiously : stupid) solution to anyone. : That was twenty years ago. : I'm recovering nicely now, thank you for asking.

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