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Date: Around 1993


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!



Replies:
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.


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


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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