Posted by T.Gracken on September 04, 2002 at 19:56:01:
In Reply to: Re: integration help posted by Soroban on September 04, 2002 at 18:41:39:
: : 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
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").
I should be severly whipped for all that extra crap I did.
...I think I've been teaching too many developmental classes of late.
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