Menu Close

2x-3-1-x-4-x-dx-




Question Number 144792 by imjagoll last updated on 29/Jun/21
 ∫ ((2x^3 −1)/(x^4 +x)) dx ?
$$\:\int\:\frac{\mathrm{2x}^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}}\:\mathrm{dx}\:? \\ $$
Answered by liberty last updated on 29/Jun/21
 Ω=∫ ((2x^3 −1)/(x^4 +x)) dx = ∫ ((2x−x^(−2) )/(x^2 +x^(−1) )) dx  Ω = ∫ ((d(x^2 +x^(−1) ))/(x^2 +x^(−1) ))  Ω = ln ∣x^2 +(1/x)∣ + c . ⧫
$$\:\Omega=\int\:\frac{\mathrm{2x}^{\mathrm{3}} −\mathrm{1}}{\mathrm{x}^{\mathrm{4}} +\mathrm{x}}\:\mathrm{dx}\:=\:\int\:\frac{\mathrm{2x}−\mathrm{x}^{−\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{−\mathrm{1}} }\:\mathrm{dx} \\ $$$$\Omega\:=\:\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{−\mathrm{1}} \right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{−\mathrm{1}} } \\ $$$$\Omega\:=\:\mathrm{ln}\:\mid\mathrm{x}^{\mathrm{2}} +\frac{\mathrm{1}}{\mathrm{x}}\mid\:+\:\mathrm{c}\:.\:\blacklozenge \\ $$

Leave a Reply

Your email address will not be published. Required fields are marked *