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The integral int(2)^(4)(logx^(2))/(logx^...

The integral `int_(2)^(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx` is equal to

A

`2`

B

`4`

C

`1`

D

`6`

Text Solution

Verified by Experts

The correct Answer is:
C
`I=int_(2)^(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))dx`
`I=2/2 int_(2)^(4)(log|x|)/(log|x|+log||6-x|)dx` ……….i
`I=int_(2)^(4)(log|6-x|)/(log|6-x|+log|x|) dx{int_(a)^(b)f(x)dx=int_(1)^(b)f(a+b-x)dx}` ……ii
Adding i and ii
`2I=int_(2)^(4)(log|x|+log|6-x|)/(log|x|+log|6-x|)dx=int_(2)^(4)dx=2`
Hence `I=1`
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