# Find the area bounded by $y = \ln(x)$, $y = 1$, the x-axis and the y-axis

The answer in the book is $e-1$, and but I can't figure out how to go from $x(\ln(x) - 1)$ to that answer...

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Your area is nothing but $\displaystyle \int_{y=0}^{y=1} x dy$ where $x = e^y$. Plug this in to get the answer.
$$\int_{y=0}^{y=1} e^y \ dy$$ which is
$$e-1$$