Question Number 164685 by Zaynal last updated on 20/Jan/22
$$\int\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} \:\left(\mathrm{1}−\boldsymbol{{x}}\right)^{\mathrm{3}} \:\boldsymbol{{dx}} \\ $$
Answered by Ar Brandon last updated on 20/Jan/22
![=4∫(1−x−1)^2 (1−x)^3 dx =4∫[(1−x)^5 −2(1−x)^4 +(1−x)^3 ]dx](https://www.tinkutara.com/question/Q164694.png)
$$=\mathrm{4}\int\left(\mathrm{1}−{x}−\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{1}−{x}\right)^{\mathrm{3}} {dx} \\ $$$$=\mathrm{4}\int\left[\left(\mathrm{1}−{x}\right)^{\mathrm{5}} −\mathrm{2}\left(\mathrm{1}−{x}\right)^{\mathrm{4}} +\left(\mathrm{1}−{x}\right)^{\mathrm{3}} \right]{dx} \\ $$