The original poster is working on finding the antiderivative of the function 1/((x(lnx)^3), which involves the use of u-substitution where u = lnx. The problem is situated within the context of calculus, specifically focusing on integration techniques.
The discussion is ongoing, with participants providing guidance on the substitution process and clarifying the transformation of the integrand. There is recognition of the need to correctly handle the powers involved in the integration, and some participants are exploring the implications of their findings.
There is a focus on ensuring all components of the integral are correctly transformed during the substitution process. Participants are navigating the complexities introduced by the third power in the integrand.
When you make a substitution, replace everything. Here you still have a factor of x remaining. If u = ln(x), what is x in terms of u? Also, and this is related, did you replace dx by its appropriate expression involving du?stau40 said:It would be 1/(x(u)^3)
stau40 said:Ok, it should be the antiderivative of du/(u^3) but I still don't understand how to work thru the third power. If I solve for the antiderivative and end up with u^4 I would need (1/4) in front of u and that gets me to the wrong result.