Question: How do I deal with a chimera?

Frequently a variable appears in an expression but not in the result, e.g., there is no x in int(sin(x),x=0..3). How do I tell that to Maple? I am trying to solve (numerically) an ODE of the form
x^2 y'' + alpha(x) y' +   beta(y) = 0. However, alpha(x) has an integral in its defintion whose upper limit is x. Maple demands that I list the dummy variable of the integral as a parameter. How do I deal with that? BTW, Maple has no problem with plot (alpha(x), x=0..6) for example.

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