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That is, curlA=B?

Griffiths goes through a systematic development to show that we may make sure that div A=0 to make life easy.But in our exam the question appeared assuming the vector potential's form:[1/4 pi]int{J dV/|r-r'|},prove that divA=0.Is it justified?Howeevr,I know there is another method to reach the form of vector potential where an additional term (grad phi) appears.And we make it zero.Please help.