Answer :



For x=1, equation: 0 = A+B


For x=1/e, equation: -1 = B i.e. B = -1


So, A = 1




The given equation becomes




Tip – If f1(x) and f2(x) are two functions, then an integral of the form can be INTEGRATED BY PARTS as


where f1(x) and f2(x) are the first and second functions respectively.


Taking f1(x) = 1/(1+logx) and f2(x) = 1in the second integral and keeping the first integral intact,





, where c is the integrating constant


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