Integrating 1/xlnx by parts...
Find the integral of 1/xlnx
The question asks to solve by substitution, which I can do and results in ln(ln(x)) + c
It then asks to compute using integration by parts, and then to explain how it can be true (because it will compute something different to substitution).
The Attempt at a Solution
I = uv - int (v dU)
let u= 1/lnx du = 1/x(lnx)^2
let dv = 1/x, v = lnx
Sub into the parts formula
I = lnx* 1/lnx - int (lnx/x(lnx)^2)
I = lnx/lnx - int (1/xlnx) <--- what we started with
I = 1 - int (1/xlnx) This is 1 - I, the integral we began with...
I've bene shown this trick where you can go..
I = 1- I
2I = 1
I = 1/2
I'm not sure if this is correct, but I would appreciate any help