Question

Evaluate the following indefinite integral using the appropriate techniques of integration.

Answer 1

Given:

`\int x^3e^(-x)dx`

Required:

To integrate given equation

Step-by-step explanation:

`\int x^3e^{-xdx\text{ }}\text{ let u=x}^(-3),v=e^(-x),\text{ then v =-e}^(-x)`
`\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}`
`\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}`
`=-x^3e^(-x)-3x^2e^(-x)-6xe^(-x)+\int6e^(-x)dx`
`=-x^3e^(-x)-3x^2e^(-x)-6xe^(-x)-6e^(-x)+c\text{ C}\in R`

Required answer:

Above explanation