integrate the followingintegral of logx\\x^2.dxon (0,infinity)

Since you should be doing such question once you know the concept, I will skip the solution here and just give the steps.

Put logx = t

Therefore dx/x = dt and x = exp(t) Limits will change accordingly.

Now substitute all of the above in the integral.

Use method of integration by parts. (that is the u,v integral method)

You will get the integral's answer in terms of t, in which you substitute the new limits and get the answer.

Note : Answer is 1.