I What is the benefit of differentiation under the integral sign?

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From website https://math.stackexchange.com/questions/43203/integrate-int-fracz-rur2-z2-2rzu3-2-du
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QuantumQuest said:
It's differentiation under the integral sign. See Wikipedia here.
What is the benefit of it?
 
Another said:
What is the benefit of it?

Under fairly loose conditions on the function being integrated, differentiation under the integral sign allows one to interchange the order of integration and differentiation. In many cases where the integration is otherwise impossible or is significantly more complex differentiation under the integral sign is able to provide solution.
 

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