Integrating a Function with Constants: A Physics Perspective

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tade
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Mathematical expression: cos[D · (√(c² + (b − x)²) − √(c² + (b + a)²))], a cosine of D times the difference of two square-root terms in x.

I would like to integrate w.r.t. x, the rest are constants.

This is not homework; it is related to a physics problem regarding single-slit diffraction.
 
I guess there's a couple of ideas to consider:

1) Did you correctly derive the integral from your physics problem?

2) Did the Prof say it should be integrable?

3) Its not in my integral tables book so I'm not sure how to solve it which isn't saying much for me but perhaps you'll need to numerically solve it.

4) Have you plotted the integrand to see what kind of curve it is?