The integral `int_(2)(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx` is equal toA. `2`B. `4`C. `1`D. `6`

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

1.	The integral `int_(2)(4)(logx^(2))/(logx^(2)+log(36-12x+x^(2))) dx` is equal toA. `2`B. `4`C. `1`D. `6`
Answer» Correct Answer - 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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