The value of `int_0^1tan^(-1)((2x-1)/(1+x-x^2))dx ,\ ` is `1` b. `-1` c. `0` d. `pi//4`

Explanation

`0`


`text { Let } I=int_{0}^{1} tan ^{-1} frac{2 x-1}{1+x-x^{2}} d x ldots ldots (i) `

`=int_{0}^{1} tan ^{-1} frac{2(1-x)-1}{1+(1-x)-(1-x)^{2}} d x `

`=int_{0}^{1} tan ^{-1} frac{1-2 x}{2-x-1-x^{2}+2 x} d x `

`=int_{0}^{1} tan ^{-1} frac{1-2 x}{1+x-x^{2}} d x `

`=-int_{0}^{1} tan ^{-1} frac{2 x-1}{1+x-x^{2}} d x ldots . ldots . (ii)`


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