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Question

f(x)g(x)f(x)g(x)f(x)g(x)[log(g(x))log(f(x))]dx=

A
log(g(x)f(x))+C
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B
12[log(g(x)f(x))]2+C
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C
(g)xf(x)log(g(x)f(x))+C
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D
log[g(x)f(x)]g(x)f(x)+C
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Solution

The correct option is D 12[log(g(x)f(x))]2+C
I=f(x)g(x)f(x)g(x)f(x)g(x)[log(g(x))log(f(x))]dx
Put log(g(x))log(f(x))=t
g(x)g(x)f(x)f(x)dx=dt
f(x)g(x)f(x)g(x)f(x)g(x)dx=dt
I=f(x)g(x)f(x)g(x)f(x)g(x)[log(g(x))log(f(x))]dx
I=tdt
I=t22
Subsituting t, we get
I=[log(g(x))log(f(x))]22
This is same as option B.

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