Methods of integration

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Question

$\int \frac{\log x}{{(1 + \log x)}^{2}} d x =$

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Solution

$\begin{array}{l} Let \log x = t \Rightarrow x = e^{t} \\ \int e^{t} [\frac{1}{1 + t} + \frac{- 1}{{(1 + t^{})}^{2}}] d t \\ f (t) = \frac{1}{1 + t} \\ = e^{t} \frac{1}{1 + t} + c = \frac{x}{1 + \log x} + c \end{array}$

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