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Question Number 69167 by rajesh4661kumar@gmail.com last updated on 21/Sep/19

Answered by petrochengula last updated on 21/Sep/19

$$from{tan}^{-1}\left(\frac{x+y}{1-xy}\right)={tan}^{-1}x+{tan}^{-1}y$$$${tan}^{-1}\left(\frac{2x-1}{1+x-x^2}\right)={tan}^{-1}\left(\frac{x+x-1}{1-x(x-1)}\right)={tan}^{-1}x+{tan}^{-1}(x-1)$$$$I={\int }_0^1{tan}^{-1}xdx+{\int }_0^1{tan}^{-1}(x-1)dx$$$$usethecomceptofintegrationbyparts$$

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