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Write a Value of ∫ Log E X D X

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Question

Write a value of\[\int \log_e x\ dx\].

 

Sum
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Solution

\[\int\]loge x dx
` ∫   1_{II} . log_{e_I   \text{ x   dx } `
 =  \[\log_e x\int1 \text{ dx} - \int\left\{ \frac{d}{dx}\left( \log_e x \right)\int1 \text{ dx} \right\}dx\]
\[\int\]= loge  x   \[\int\] 1 . dx  \[\int\] \[\frac{1}{x} \times x   .   dx\]
= loge x × x – ​\[\int\]dx
=​ x loge x – x + C
=​ x loge x – x + C
= x (loge x – 1) + C
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Chapter 18: Indefinite Integrals - Very Short Answers [Page 197]

APPEARS IN

R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 18 Indefinite Integrals
Very Short Answers | Q 20 | Page 197

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