Evaluate: `int_0^1cot^(-1)(1-x+x^2)dx`

Explanation

Let I= `int_0^1cot^(-1)(1-x+x^2)dx`

= `int_0^1tan^(-1)1/(1-x+x^2)dx`

= `int_0^1tan^(-1)1/(1-x(1-x))dx`

= `int_0^1[tan^(−1)x+tan^(−1)(1−x)]dx`

Let (1−x)=t

`-dx=dt`

Also,`x→0 to 1
⇒t→1 to 0`

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