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

Explanation

`int_{0}^{1} cot ^{-1}(1-x+x^{2}) d x `


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


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


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


`=int_{0}^{1}[tan ^{-1} x+tan ^{-1}(1-x)] d x`



Use `(1-{x})={t}`


...