Question Number 196436 by RoseAli last updated on 24/Aug/23
$$\int\frac{{dx}}{{x}\left({x}^{{n}} −\mathrm{1}\right)} \\ $$
Answered by MM42 last updated on 24/Aug/23
$$\int\frac{{x}^{{n}} −\mathrm{1}+{x}^{{n}} }{{x}\left({x}^{{n}} −\mathrm{1}\right)}=\int\left(\frac{\mathrm{1}}{{x}}+\frac{{x}^{{n}−\mathrm{1}} }{{x}^{{n}} −\mathrm{1}}\right){dx} \\ $$$$={lnx}+\frac{\mathrm{1}}{{n}}{ln}\left({x}^{{n}} −\mathrm{1}\right)+{c} \\ $$