I have noticed is that when a problem is thorny using classical methods

True but Niharika's question was not that thorny

]]>Here is the problem:

and we are asked to solve for a,b,c,d,f.

Whatever those coefficients are they might just work for definite integrals too. This reduces the problem to solving a 6 x 6 simultaneous set of linear equations and to the numerical evaluation of 6 integrals. This of course is generally a trivial matter to almost all the software out there.

We obtain the six integrals using Gaussian or Romberg integration.

If we call the RHS of 1) g(x) we have:

We know from calculus that

We can now easily follow the pattern and generate the 6 simultaneous equations.

Solving for a,b,c,d,f we get:

a = -4

b = -12

c = -20

d = 0

f = 32

More to come...

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