Why some functional integral(in QTF theo)of a product equal product of two the integr

[ndung200790]

Please teach me this:
In section 11.4 chapter 11 of QTF theory book of Peskin&Schroeder,computing Effective Action,they calculate a functional integral of product of two exponentials of ''exact'' Lagrangian and ''counterterm'' Lagrangian with the same variable of integral(value of field).I do not understand why they can calculate the integral by integrating separately the two exponentials.Why the integral of the product of two exponentials equals the two integrals of each exponential?(That is (11.57),(11.59),(11.62) chapter 11).
Thank you very much for your kind helping.

 

[ndung200790]

Now,I am thinking that it is possible,because the freely choosing the value of counterterms.Is it correct?

 

[ndung200790]

Sorry,I had misunderstood the authors,because the product of the two integrals adding connected diagrams is equal the functional integral of product of the two factors.