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x-2-1-x-2-1-dx-




Question Number 79398 by ubaydulla last updated on 24/Jan/20
((x^2 −1)/(x^2 +1))dx
$$\frac{{x}^{\mathrm{2}} −\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$
Commented by john santu last updated on 24/Jan/20
∫ ((x^2 +1−2)/(x^2 +1)) dx = ∫ 1 dx−∫((2dx)/(x^2 +1))  = x −2 tan^(−1) (x)+c
$$\int\:\frac{{x}^{\mathrm{2}} +\mathrm{1}−\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx}\:=\:\int\:\mathrm{1}\:{dx}−\int\frac{\mathrm{2}{dx}}{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$=\:{x}\:−\mathrm{2}\:\mathrm{tan}^{−\mathrm{1}} \left({x}\right)+{c} \\ $$

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