- #1

Mr Davis 97

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## Homework Statement

##\displaystyle \int \frac{\ln x}{x(1 + \ln x)} dx##

## Homework Equations

## The Attempt at a Solution

[/B]

Let ##u = 1 + \ln x##, then ##\ln x = u - 1##

##\displaystyle du = \frac{1}{x}dx##

Thus, ##\displaystyle \int \frac{\ln x}{x(1 + \ln x)} dx = \int \frac{u - 1}{u} du= \int 1 - u^{-1} du = u - \ln u + C = 1 + \ln x - \ln \left | \ln x + 1\right | + C##

However, this is the wrong answer. What am I doing wrong?