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How can I simplify:

((-I)*Integrate[E^((I*Pi*(f*(x^2 - 2*x*x0 + y*(y - 2*y0)) - (x0^2 + y0^2)*zR))/
  (f*(f + zR)*λ))*P[x0, y0], y0, {x0, -Infinity, Infinity}])/((f + zR)*λ)

to turn it into: (where k = 2 Pi / λ)

1/(I λ (f + zR)) Exp[I k/(2 (f + zR))(x^2 + y ^2)] Integrate[P[x0, y0]*
  Exp[-I k/(2 f) zR/(f + zR)(x0^2 + y0^2)] Exp[-I 2 Pi/(λ(f + zR))*
  (x x0 + y y0)], y0, {x0, -Infinity, Infinity}]

Where I is the complex number i and P[x0, y0] is a function.

What I want to do is to pull expressions that are independent of the variables of integration outside of that integral. How can I simply get Mathematica to do that for me?"

Bill
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Marina Nebot
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    Please, look at what you have posted and realize that it is illegible. Understand that no one can help if this cannot be read to see what the problem is. What it would be better to do is to right-click, copy as... and select InputForm. Kindly, update your question with a more legible version. It will also be helpful to use the code block formatting available with markdown here. – CA Trevillian Apr 07 '21 at 14:57
  • Done, thank you. – Marina Nebot Apr 07 '21 at 15:09
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    I am only guessing, but I think you might have a better chance of getting a satisfactory answer if you reworded your question to be something more like "I have a complicated integral, a mixture of definite and indefinite and including an undefined function. What I want to do is to pull expressions that are independent of the variables of integration outside of that integral. How can I simply get Mathematica to do that for me?" That seems like it tries to highlight the essential part of your question. – Bill Apr 07 '21 at 16:31
  • The expression (f + zR)[Lambda] looks like a syntactic error in Mathematica. What did you want to express by it? Further, it would be reasonable to explain the variables, such as IPi and others, and specify if they are positive, real, complex, and so on. The same concerns the function P[x0,y0]. – Alexei Boulbitch Apr 08 '21 at 07:34
  • I is the complex number i. I just need to know how can I simplify an integral by pulling out the constant terms, the ones that are independent of the variable of integration. – Marina Nebot Apr 08 '21 at 07:51

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