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Question
Evaluate : \[\int\frac{1}{x(1 + \log x)} \text{ dx}\]
Solution
I = \[\int\frac{1}{x\left( 1 + \log x \right)} \text{ dx }\]
Let (1 + log x) = t
or,\[ \frac{1}{x}dx = dt\]
\[ \Rightarrow I = \int\frac{1}{t}dt\]
\[\Rightarrow I = \text{ log }\left| t \right| + C\]
\[ \therefore I = \text{ log}\left| 1 + \log x \right| + C\]
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