Question: inconsistent output - what am I missing?

Hi,

I'm new to these forums. I'm using Maple 17. What am I missing about the odd behaviour exhibited below? (the code can be copy pasted into Maple)

Suppose I define m,n,p,q as integers and x as real, then define the function h(x,m,n,p,q) below.

assume(m::integer, n::integer, p::integer, q::integer, x::real);
h:=(x,m,n,p,q)->-(1/8*I)*(exp((2*I)*Pi*x)-1)^2*(exp(-(2*I)*Pi*x*(n-q+2))-exp(-(2*I)*Pi*x*(n-q+1)))/(Pi^3*x*(m-x)*(p-x));

If I do:

int(h(x, m, n, p, q), x = -infinity .. infinity)

It says it's 0, but that's not true. The integral is not always 0 but depends on m,n,p,q ... and even Maple acknowledges this. If I do:

int(h(x, 1, 1, 1, 1), x = -infinity .. infinity)

I get -(1/2*I)/Pi ... so clearly not 0.

Also, if I do:

int(h(x, m, n, m, n), x = -infinity .. infinity)

I get -(1/2*I)/(m*Pi) ... again, not 0.

What am I missing? How can I correct this and obtain the analytic expression for int(h(x, m, n, p, q), x = -infinity .. infinity)?

Trying without the assume() causes Maple to run into issues not knowing anything about m,n,p,q.

[ Edit: I finally solved the integral on paper, see my post below if you're curious. The Maple inconsistency and wrong result explained above are still there though ]

Any help would be greatly appreciated.

Regards,

Alex.