Choose the correct options from the given alternatives : ∫log(3x)xlog(9x)⋅dx = - Mathematics and Statistics

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MCQ

Choose the correct options from the given alternatives :

`int (log (3x))/(xlog (9x))*dx` =

Options

  • log (3x) – log (9x) + c·

  • log (x) – (log 3) · log (log 9x) + c

  • log 9 – (log x) · log (log 3x) + c

  • log (x) + (log 3) · log (log 9x) + c

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Solution

log (x) – (log 3) · log (log 9x) + c

[ Hint : `int (log3x)/(xlog(x))*dx = int (log((9x)/3))/(xlog(9x))*dx`

= `int (log (9x) - log3)/(xlog(9x))*dx`

= `int[1/x- (log3)/(xlog(9x))]*dx`

= `int 1/x*dx - (log3) int ((1/x))/(log (9x))*dx`

= log (x) – (log 3) · log (log 9x) + c].

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Chapter 3: Indefinite Integration - Miscellaneous Exercise 3 [Page 148]

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Balbharati Mathematics and Statistics 2 (Arts and Science) 12th Standard HSC Maharashtra State Board
Chapter 3 Indefinite Integration
Miscellaneous Exercise 3 | Q 1.03 | Page 148

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