Expert: Paul Klarreich - 10/16/2011

Question
Hi Sir it is Ghutty here again.I do first year Calculus.

I am completely stuck on the following question:
Determine Integral of 4/[x(4lnx+1)] dx

I am not sure how to apply the substitution.

Thanks again.

Answer
Questioner:Ghutty
Country:Eastern Cape, South Africa
Category:Calculus
Private:No
Subject:Integration by substitution
Question:
Hi Sir it is Ghutty here again.I do first year Calculus.

I am completely stuck on the following question:
Determine Integral of 4/[x(4lnx+1)] dx

I am not sure how to apply the substitution.

Thanks again.
.............................
What substitution are you not sure how to apply?  I think that for:
   4 dx
-------------
x (4 ln x + 1)

using:

u = 4 ln x + 1

should do it nicely.

The Integrator, at integrals.wolfram.com/index.jsp

gives:

Log[1 + 4 Log[x]]