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int ((f (x) g' (x) -f' (x) g (x))/(f (x)...

`int ((f (x) g' (x) -f' (x) g (x))/(f (x) g(x)))(log (g(x )) - log (f(x)))dx `is equal to:

A

`f(x)g (x)log{f(x)g(x)}+C`

B

`(1)/(2)[log{f(x)g(x)}]^(2)+C`

C

`[log{f(x)g(x)}]^(2)+C`

D

`log{f(x)g(x)}+C`

Text Solution

Verified by Experts

The correct Answer is:
b
Let `I=int(f(x)g'(x)+f'(x)g(x))/(f(x)g(x)){logf(x)+log(x)}dx`
`rArr I=intlog{f(x)g(x)}xx(1)/(f(x)g(x))d{f(x)g(x)}`
`rArr I=intlog{f(x)g(x)}d[log{f(x)}]`
`rArrI=(1)/(2)[log{f(x)g(x)}]^(2)+C`
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OBJECTIVE RD SHARMA ENGLISH-INDEFINITE INTEGRALS-Solved Example
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