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Question

Evaluate : 13coslogxxdx


A

1

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B

coslog3

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C

sinlog3

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D

π4

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Solution

The correct option is C

sinlog3


Evaluating the given integral

I=13coslogxxdx

Let logx=t

Differentiating with respect to x

1xdx=dt

if x=1 then t=0

if x=3 then t=log3⁠⁠⁠⁠⁠⁠

Thus, We have :

I=0log3costdt

=sint0log3

=sinlog3-sin0

I=sinlog3

Hence, Option C is the correct answer


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