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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