Question Number 164686 by Zaynal last updated on 20/Jan/22
$$\int\mathrm{36}\boldsymbol{{x}}^{\mathrm{2}} \:\left(\mathrm{2}\boldsymbol{{x}}+\mathrm{3}\right)^{−\mathrm{7}} \:\boldsymbol{{dx}} \\ $$$$\: \\ $$
Answered by Ar Brandon last updated on 20/Jan/22
$$=\mathrm{36}\int\frac{{x}^{\mathrm{2}} }{\left(\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{7}} }{dx}=\mathrm{9}\int\frac{\left(\mathrm{2}{x}+\mathrm{3}−\mathrm{3}\right)^{\mathrm{2}} }{\left(\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{7}} }{dx} \\ $$$$=\mathrm{9}\int\left(\frac{\mathrm{1}}{\left(\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{5}} }−\frac{\mathrm{6}}{\left(\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{6}} }+\frac{\mathrm{9}}{\left(\mathrm{2}{x}+\mathrm{3}\right)^{\mathrm{7}} }\right){dx} \\ $$