Help in integrating an expression

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DM
DM on 25 Oct 2014
Answered: Roger Stafford on 25 Oct 2014
My question is regarding integral in MATLAB. Please don't be scared by the complicated notation. They are almost all constants. I have the following function to integrate
syms v
syms gamma2
syms s
lambdav= (14679452516410005*exp(-(3*5^(1/2)*v^(1/4))/25))/(9223372036854775808*v^(1/2)) + (7339726258205003*exp(-(2*v^(1/4))/5))/(4611686018427387904*v^(1/2));
fun2=lambdav* (1./(1+s.*v^(-1)));
B=int(fun2,v,gamma2,+inf);
I would like the answer to be only in terms of gamma2 and s. The problem is MATLAB doesnt perform the integration and I get the following
int(((14679452516410005*exp(-(3*5^(1/2)*v^(1/4))/25))/(9223372036854775808*v^(1/2)) + (7339726258205003*exp(-(2*v^(1/4))/5))/(4611686018427387904*v^(1/2)))/(s/v + 1), v, gamma2, Inf)
which is basically the function I wrote meaning that MATLAB wasnt able to resolve it.
Can anyone help me understand how to perform the integration?

Accepted Answer

Roger Stafford
Roger Stafford on 25 Oct 2014
If 'int' is unable to integrate your function, you may have to resign yourself to using numerical integration for which you would have to supply actual values for the parameters gamma2 and s. Of course this is less convenient, but it may well be the only possible way you can proceed.
As an undergraduate student in calculus I learned the hard way that the formulas we were given to solve integrals covered only a small fraction of all the possible integrands we might think up. A friend of mine and I once devoted several weeks trying to integrate x^x but finally gave up on it. The truth is that in most cases these integrals are functions that have never been studied by mathematicians as yet because they are so numerous and diverse in nature and cannot be expressed in terms of the known elementary functions.

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