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x-1-x-3-dx-




Question Number 35290 by Fiko Jean last updated on 17/May/18
∫((x+1)/x^3 )dx
$$\int\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}} }{dx} \\ $$
Commented by abdo mathsup 649 cc last updated on 17/May/18
∫ ((x+1)/x^3 )dx = ∫ (dx/x^2 )  + ∫   (dx/x^3 ) = −(1/x)  + (1/(−3+1))x^(−3+1)  +c  =−(1/x) −(1/(2x^2 ))  +c .
$$\int\:\frac{{x}+\mathrm{1}}{{x}^{\mathrm{3}} }{dx}\:=\:\int\:\frac{{dx}}{{x}^{\mathrm{2}} }\:\:+\:\int\:\:\:\frac{{dx}}{{x}^{\mathrm{3}} }\:=\:−\frac{\mathrm{1}}{{x}}\:\:+\:\frac{\mathrm{1}}{−\mathrm{3}+\mathrm{1}}{x}^{−\mathrm{3}+\mathrm{1}} \:+{c} \\ $$$$=−\frac{\mathrm{1}}{{x}}\:−\frac{\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} }\:\:+{c}\:. \\ $$

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