See, I want to say you some generalised idea about how to integrate such kind of composite functions where you have two kind of functions. In this question you have one logarithmic function and another algebraic function(1/x). In this kind of problem you do use a formula called ILATE: I is for Inverse, L for logarithm, A for algebraic, T for trigonometric and E for exponential functions. Just choose the first function depending upon the sequence from the start. Then move on to integrate as following
Suppose consider the integral as I1 and then you can write
I1=first function * (integration of 2nd function)- integration of ((derivative of the first function)*(integration of second function))
This way you can solve most of the questions like this.
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