Average velocity in a turbulent flow tube

[Est120]

TL;DR

obtaining the average speed using the logarithmic profile

hi guys
I'm really struggling to get the expression for average speed in turbulent flow

The book explains absolutely nothing about how the integration is carried out, in addition to the fact that the logarithmic term becomes undefined when r = R what I did was carry out the integration up to 0.9999999R in order to obtain a numerical result equal to the one that I could have obtained integrating up to R even so, the expression I got is not the one shown in the book

 

[boneh3ad]

It would help if you cited the book you are using.

But for starters, are you not missing an $r$ in your denominator to go along with the $d\theta$?

 

[Est120]

It would help if you cited the book you are using.

But for starters, are you not missing an $r$ in your denominator to go along with the $d\theta$?

i already solved the problem i was supposed to integrate up to 0.9999999999...99999 R (integral in numerator) so i get the equation of the book, the book is Bird's Transport Phenomena