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Evaluate : \[\Int\Frac{1}{X(1 + \Log X)} Dx\] - Mathematics

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Question

Evaluate : \[\int\frac{1}{x(1 + \log x)} \text{ dx}\]

Sum

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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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Evaluation of Simple Integrals of the Following Types and Problems

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Chapter 19: Indefinite Integrals - Very Short Answers [Page 198]

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RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Very Short Answers | Q 62 | Page 198

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