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Question

Evaluate: e1lnxx2dx

A
1 2e
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B
2e1
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C
e1e
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D
1+2e
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Solution

The correct option is C 1 2e
e1lnxx2dx

Let z=lnx dz=1x and x=ez

When x=1,z=0 and when x=e,z=1, hence integration becomes:-

e11xlnxdxx

=10ez.zdz

Using integration by parts:-

=[zezez]10

=(e1e1)(1)=2e1+1

=12e

Hence, answer is option-(A).

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