Integrate dx/(xlogx): Limits 1 to n - Result

[prasoonsaurav]

Is there any way to integrate
$$\int dx/(xlogx)$$

within the limits 1 and n?

If yes what is the result?

 

[darkSun]

Assuming that log x means ln x (if not a constant is just introduced), if you make the substitution u= ln x the integrand simplifies to du/u. However the limits are 0 to ln n, and so ln u would have to be evaluated at 0, which means the integral does not converge.

 

[srijithju]

Yes the integral doesn not converge . This can be seen without integrating - the function 1 / (x * ln x) goes to infinity at x = 1 , and also func is continuous in the interval .. so the area under the curve is infinite