Question Number 131919 by Algoritm last updated on 09/Feb/21
Answered by Dwaipayan Shikari last updated on 09/Feb/21
$${x}={u}^{\mathrm{6}} \\ $$$$=\mathrm{6}\int\frac{{u}^{\mathrm{5}} }{{u}^{\mathrm{2}} +{u}^{\mathrm{3}} }{du}=\mathrm{6}\int\frac{{u}^{\mathrm{3}} }{{u}+\mathrm{1}}{du}=\mathrm{6}\int\left({u}^{\mathrm{2}} −{u}+\mathrm{1}\right){du}−\mathrm{6}{log}\left({u}\right) \\ $$$$=\mathrm{2}{u}^{\mathrm{3}} −\mathrm{3}{u}^{\mathrm{2}} +\mathrm{6}{u}−\mathrm{6}{log}\left({u}\right)+{C} \\ $$$$=\mathrm{2}\sqrt{{x}}−\mathrm{3}\sqrt[{\mathrm{3}}]{{x}}+\mathrm{6}\sqrt[{\mathrm{6}}]{{x}}−{log}\left({x}\right)+{C} \\ $$