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

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].

Is there an error in this question or solution?
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#### APPEARS IN

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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