(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Integrating 1/xlnx by parts...

2. Relevant equations

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).

3. 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

Thank you

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Integrating 1/xln(x) using integration by parts

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