Integrate the following functions w.r.t. x : 1x.logx.log(logx). - Mathematics and Statistics

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Sum

Integrate the following functions w.r.t. x : `(1)/(x.logx.log(logx)`.

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Solution

Let I = `int (1)/(x.logx.log(logx)).dx`

= `int(1)/log(logx).(1)/(x.logx).dx`

Put log(log x) = t

∴ `(1)/logx.(1)/x.dx` = dt

∴ `(1)/(x.logx).dx` = dt

∴ I = `int (1)/t dt = log|t| + c`

= log|log (logx)| + c.

  Is there an error in this question or solution?
Chapter 3: Indefinite Integration - Exercise 3.2 (A) [Page 110]

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Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Exercise 3.2 (A) | Q 1.25 | Page 110

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