Ask A Scientist Mathematics Archive

Question: Hey, I am new on this system and am not yet familiar with the 
commands.  Please respond via e-mail.  I am having a problem with an integral 
that I think will be some trig function.  Am I overlooking something simple?  
Anyway, here goes: integral of (E+k/x)^(-1/2) dx where the variable is x, E 
and k are constant.  Thanks for any replies!  
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If I remember my rules of integration correctly, you should be 
able to take E and k outside the integral if they are constants.  Take (E+k)^-
1/2 outside the integral leaving (1/x)^-1/2 dx.  (1/x)^-1/2 is also x^1/2 
which is an easy integral to do.  I hope this has helped.
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As stated, E+k is not factorable since E+k/x is not (E+k)/x given 
the standard hierarchy of operations.  The substitution given by x/(xE+k) = 
t^2 will convert the integral to one that has a rational integrand in variable 
t.  I get the integrand to be the quotient of 2kt^2 by (1-Et^2)^2.  Reference: 
Tables of Integrals, Series, and Products by Gradshteyn & Ryzhik, Academic 
Press, 1965, pp 70-1.
Tom Elsner
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I stand corrected.  I thought that looked too easy.  I did not 
even think that it was E+(k/x) and not (E+k)/x.  Thanks for correcting me.
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