Question Number 212896 by MrGaster last updated on 26/Oct/24
$$\int\frac{{dx}}{{x}^{\mathrm{5}} −\mathrm{1}} \\ $$
Commented by Frix last updated on 26/Oct/24
$${x}^{\mathrm{5}} −\mathrm{1}=\left({x}−\mathrm{1}\right)\left({x}^{\mathrm{2}} +\frac{\mathrm{1}−\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right)\left({x}^{\mathrm{2}} +\frac{\mathrm{1}+\sqrt{\mathrm{5}}}{\mathrm{2}}{x}+\mathrm{1}\right) \\ $$$$\mathrm{You}\:\mathrm{must}\:\mathrm{decompose},\:\mathrm{then}\:\mathrm{it}'\mathrm{s}\:\mathrm{easy}. \\ $$
Commented by MrGaster last updated on 27/Oct/24
Understood, sir