Question Number 145723 by madwdah last updated on 07/Jul/21
Answered by bramlexs22 last updated on 07/Jul/21
$$\int\:\mathrm{x}.\mathrm{e}^{\mathrm{2x}} \:\mathrm{dx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{xe}^{\mathrm{2x}} −\frac{\mathrm{1}}{\mathrm{2}}\int\mathrm{e}^{\mathrm{2x}} \:\mathrm{dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{e}^{\mathrm{2x}} \left(\mathrm{2x}−\mathrm{1}\right)+\mathrm{c} \\ $$