Answer :

Let


Put t=x2


dt=2xdx


Now putting,


A(t+1)+B(t-1) = t


Putting t+1=0,


t=-1


A(0)+B(-1-1)=-1



Putting t-1=0,


t=1


A(1+1)+B(0)=1



From equation(1),we get,






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