Question Number 164682 by Zaynal last updated on 20/Jan/22
$$\int\mathrm{27}\boldsymbol{{x}}^{\mathrm{2}} \:\sqrt{\mathrm{3}\boldsymbol{{x}}−\mathrm{2}}\:\boldsymbol{{dx}} \\ $$
Answered by Ar Brandon last updated on 20/Jan/22
$$=\mathrm{3}\int\left(\mathrm{3}{x}−\mathrm{2}+\mathrm{2}\right)^{\mathrm{2}} \sqrt{\mathrm{3}{x}−\mathrm{2}}{dx} \\ $$$$=\mathrm{3}\int\left(\left(\mathrm{3}{x}−\mathrm{2}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} +\mathrm{4}\left(\mathrm{3}{x}−\mathrm{2}\right)^{\frac{\mathrm{3}}{\mathrm{2}}} +\mathrm{4}\left(\mathrm{3}{x}−\mathrm{2}\right)^{\frac{\mathrm{1}}{\mathrm{2}}} \right){dx} \\ $$