Question

${\int }_0^{1}x{e}^{x}dx$

Answer 1

${\int }_0^{1}x{e}^{x}dx$

Integrating by parts

$\Rightarrow x\int e^{x}dx-\int 1.e^{x}dx=x.e^x-e^x={\left[e^x\right(x-1\left)\right]}_0^1=e(1-1)-1(0-1)=0+1=1$