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Question
Evaluate:
Solution
\[\int\frac{e\log\sqrt{x}}{x}dx\]
\[ = \int\frac{\sqrt{x}}{x}dx\]
\[ = \int\frac{1}{\sqrt{x}} dx\]
\[ = \int x^{- \frac{1}{2}} dx\]
\[ = \left[ \frac{x^{- \frac{1}{2} + 1}}{- \frac{1}{2} + 1} \right] + C\]
\[ = 2\sqrt{x} + C\]
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