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Question

0f(x+1x)lnxxdx

A
is equal to zero
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B
is equal to one
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C
is equal to 12
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D
can not be evaluated
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Solution

The correct option is B is equal to zero
I=0f(x+1x)lnxxdx

Substitute x=1tdx=1t2dt

I=0f(t+1t)ln(1/t)1/t.dtt2

=0f(t+1t)lnttdt

=0f(x+1x)lnxxdx=I

2I=0I=0

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