Question

help on integration....??
so basically if i am having equation...as
dx/x=dy
so if we integrate both sides what we are doing..i mean with respect to what variable we are integrating...whether x or y..
1) if x be taken as factor wrt which integration is done then
integral(dx/x,x)=integral(dy,x)
2) or wrt to y then..
integral(dx/x,y)=integral(dy,y)
both cases could be possible...but why did we try to do integral (dx/x,x)=integral(dy,y)
to get log x =y this could be only possible if we do integrate wrt to different variables left wrt x and right wrt y....??

Answer 1

what i mean to say is it true that we can't integrate the left side of equation wrt to x and right side of equation wrt y......??