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Question

[f(x)g(x)+g(x)f(x)]f(x).g(x)[log f(x)+log g(x)] dx is equal to

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

The correct option is B 12[logf(x)g(x)]2+C
[f(x)g(x)+g(x)f(x)]f(x).g(x) [log f(x)+log g(x)] dx=[f(x)g(x)+g(x)f(x)]f(x).g(x) [log f(x) g(x)] dx=log tt dt [putting f(x).g(x)=t[f(x)gx+g(x)f(x)dx=dt]=12(log t)2+C=12[log f(x).g(x)]2+C

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