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x-3-x-1-x-2-1-dx-




Question Number 31543 by Cheyboy last updated on 09/Mar/18
∫((x^3 +x+1)/(x^2 +1)) dx
$$\int\frac{{x}^{\mathrm{3}} +{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{dx} \\ $$$$ \\ $$$$ \\ $$
Commented by prof Abdo imad last updated on 10/Mar/18
I=∫ ((x(x^2 +1) +1)/(x^2  +1))dx= ∫ xdx +∫  (dx/(x^2 +1))  =(x^2 /2) +arctanx +λ  .
$${I}=\int\:\frac{{x}\left({x}^{\mathrm{2}} +\mathrm{1}\right)\:+\mathrm{1}}{{x}^{\mathrm{2}} \:+\mathrm{1}}{dx}=\:\int\:{xdx}\:+\int\:\:\frac{{dx}}{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$$=\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:+{arctanx}\:+\lambda\:\:. \\ $$
Commented by Cheyboy last updated on 10/Mar/18
Thank you sir
$${Thank}\:{you}\:{sir} \\ $$

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