Question Number 226554 by Spillover last updated on 03/Dec/25
Answered by peace2 last updated on 03/Dec/25
$$=\frac{\mathrm{1}}{{n}}\int\frac{{nx}^{{n}−\mathrm{1}} {dx}}{{x}^{{n}} \left(\mathrm{1}+{x}^{{n}} \right)}=\frac{\mathrm{1}}{{n}}\int\frac{{dy}}{{y}\left(\mathrm{1}+{y}\right)}=\frac{\mathrm{1}}{{n}}\int\frac{\mathrm{1}}{{y}}−\frac{\mathrm{1}}{\mathrm{1}+{y}}{dy} \\ $$$$=\frac{\mathrm{1}}{{n}}{ln}\left(\frac{{y}}{\mathrm{1}+{y}}\right)+\mathrm{c};{y}={x}^{{n}} \\ $$
Answered by Spillover last updated on 04/Dec/25
Answered by Spillover last updated on 04/Dec/25
