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Question

5101x-1x-2dx=


A

log2732

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B

log3227

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C

log89

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D

log34

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Solution

The correct option is B

log3227


Explanation for the correct option:

Finding the value for the given integral:

Let I=5101x-1x-2dxi

Consider 1x-1x-2=Ax-1+Bx-2 integrationbyparts

1x-1x-2=Ax-2+Bx-1x-1x-2

1=Ax-2A+Bx-B

1=A+Bx+-2A-B

A+B=0ii

-2A-B=1ii

on solving the equation ii and (iii) we get

A=-1

B=1

Therefore i becomes

I=510-1x-1+1x-2dx

=-logx-1+logx-2510

=logx-2x-1510

=log10-210-1-log5-25-1

=log89-log34

=log3227

Thus, option B is the correct answer.


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