Question Number 40965 by Glorious Man last updated on 30/Jul/18
Answered by tanmay.chaudhury50@gmail.com last updated on 30/Jul/18
$${t}={x}^{\mathrm{5}} −{x}^{\mathrm{3}} \:\:\:{dt}=\mathrm{5}{x}^{\mathrm{4}} \:−\mathrm{3}{x}^{\mathrm{2}} \:\:{dx} \\ $$$$=−\mathrm{2}\int\frac{\mathrm{5}{x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{2}} \:{dx}}{{x}^{\mathrm{5}} −{x}^{\mathrm{3}} \:} \\ $$$$=−\mathrm{2}\int\frac{{d}\left({x}^{\mathrm{5}} −{x}^{\mathrm{3}} \right)}{{x}^{\mathrm{5}} −{x}^{\mathrm{3}} } \\ $$$$=−\mathrm{2}{ln}\left({x}^{\mathrm{5}} −{x}^{\mathrm{3}} \right)+{c} \\ $$