Question Number 25224 by kshreyasingh200@gmil.com last updated on 06/Dec/17
$$\int\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{{x}×{x}−{x}+\mathrm{1}\:\:\:{dx}} \\ $$
Answered by prakash jain last updated on 06/Dec/17
$$\int\left(\mathrm{2}{x}−\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{1}}\:{dx} \\ $$$${x}^{\mathrm{2}} −{x}+\mathrm{1}={u} \\ $$$$\left(\mathrm{2}{x}−\mathrm{1}\right){dx}={du} \\ $$$$\int\sqrt{{u}}\:{du} \\ $$$$=\frac{\mathrm{2}}{\mathrm{3}}{u}^{\mathrm{3}/\mathrm{2}} +{C} \\ $$$$=\frac{\mathrm{2}}{\mathrm{3}}\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)^{\mathrm{3}/\mathrm{2}} +{C} \\ $$