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Question
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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