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Evaluate: int(-1/2)^(1/2)cosxlog((1-x)/(...

Evaluate: `int_(-1/2)^(1/2)cosxlog((1-x)/(1+x))dx`

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Given:`int_(-1/2)^(1/2)cosxlog((1-x)/(1+x))dx`
`I=int_(-1/2)^(1/2)cosxlog((1-x)/(1+x))dx.....(i)`
As we know `int_a^b f(x)dx=int_a^b f(a+b-x)dx`
Then
`I=int_(-1/2)^(1/2)cos(-x)log((1-x)/(1+x))dx......(ii)`
Now add (i) and (ii) we get
`2I=int_(-1/2)^(1/2) 0dx`
`I=0`
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