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Evaluate: ∫ E Log √ X X D X - Mathematics

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Question

Evaluate:

\[\int\frac{e\log \sqrt{x}}{x}dx\]

Sum

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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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Evaluation of Definite Integrals by Substitution

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Chapter 19: Indefinite Integrals - Exercise 19.01 [Page 4]

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RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.01 | Q 6 | Page 4

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