Tentukanlah integral tak tentu berikut dengan integral parsial ∫ײ e¹⁻ˣ dx =

[tex]\displaystyle \int x^2e^{1-x}\,dx=x^2\int e^{1-x}\,dx-2x\iint e^{1-x}\,dx+2\iiint e^{1-x}\,dx\\\int x^2e^{1-x}\,dx=x^2(-e^{1-x})-2x\int -e^{1-x}\,dx+2\iint -e^{1-x}\,dx\\\int x^2e^{1-x}\,dx=-x^2e^{1-x}-2x( e^{1-x})+2\int e^{1-x}\,dx\\\int x^2e^{1-x}\,dx=-x^2e^{1-x}-2xe^{1-x}-2e^{1-x}+C\\\boxed{\boxed{\int x^2e^{1-x}\,dx=-e^{1-x}(x^2+2x+2)+C}}[/tex]