Question Number 189382 by TUN last updated on 15/Mar/23
Answered by Ar Brandon last updated on 15/Mar/23
$$\mathrm{Use}\:\mathrm{integration}\:\mathrm{by}\:\mathrm{parts}\:\mathrm{with}; \\ $$$${a}.\:\mathrm{u}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{1}\:\mathrm{and}\:\mathrm{v}'\left({x}\right)={e}^{\mathrm{3}{x}−\mathrm{2}} \\ $$$${b}.\:\mathrm{u}\left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} −{x}+\mathrm{2}\:\mathrm{and}\:\mathrm{v}'\left({x}\right)={e}^{{x}−\mathrm{2}} \\ $$$${c}.\:\mathrm{u}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{2}{x}\:\mathrm{and}\:\mathrm{v}'\left({x}\right)=\mathrm{sin}\left(\mathrm{3}−{x}\right) \\ $$$${d}.\:\mathrm{u}\left({x}\right)=\mathrm{cos}\left(\pi{x}\right)\:\mathrm{and}\:\mathrm{v}'\left({x}\right)={e}^{\mathrm{2}{x}} \\ $$