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




Question Number 106010 by bemath last updated on 02/Aug/20
∫ ((1+x+x^2 )/(x^2 (x+1))) dx
$$\int\:\frac{\mathrm{1}+{x}+{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}\:{dx}\: \\ $$
Answered by Dwaipayan Shikari last updated on 02/Aug/20
∫((1+x)/(x^2 (x+1)))+(x^2 /(x^2 (x+1)))  ∫(1/x^2 )+∫(1/(x+1))  log(x+1)−(1/x)+C
$$\int\frac{\mathrm{1}+{x}}{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)}+\frac{{x}^{\mathrm{2}} }{{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)} \\ $$$$\int\frac{\mathrm{1}}{{x}^{\mathrm{2}} }+\int\frac{\mathrm{1}}{{x}+\mathrm{1}} \\ $$$${log}\left({x}+\mathrm{1}\right)−\frac{\mathrm{1}}{{x}}+{C} \\ $$

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