Given:
[tex]\int x^3e^{-x}dx[/tex]
Required:
To integrate given equation
Explanation:
[tex]\int x^3e^{-xdx\text{ }}\text{ let u=x}^{-3},v=e^{-x},\text{ then v =-e}^{-x}[/tex][tex]\begin{gathered} =x^3(-e^{-x})-\int(-e^{-x}).bx\text{ -}\int(-e^{-x}).bdx \\ \\ \\ =x^3(-e^{-x})-(e^{-x}.3x^2-\int e^{-x}.bx\text{ dx} \end{gathered}[/tex][tex]\begin{gathered} =-x^3(-e^{-x})-(3e^{-x}x^2-((-e^{-x)}.bdx \\ \\ =-x^3.e^{-x}-3e^{-x}x^2+(-6xe^{-x}-\int-6e^{-x}dx)) \end{gathered}[/tex][tex]=-x^3e^{-x}-3x^2e^{-x}-6xe^{-x}+\int6e^{-x}dx[/tex][tex]=-x^3e^{-x}-3x^2e^{-x}-6xe^{-x}-6e^{-x}+c\text{ C}\in R[/tex]
Required answer:
Above explanation
