How do you find the integral of (x^2)(e^(-x))(x2)(e−x)?

1 Answer
Dharma R.
Sep 23, 2015

x^2e^(-x)-2xe^(-x)+2e^(-x)+cx2e−x−2xe−x+2e−x+c

Explanation:

intx^2e^(-x)dx∫x2e−xdx
if f(x)=x^2e^(-x) let u(x)=x^2 and v(x)=e^(-x)
using integration by parts
x^2e^(-x)dx=x^2e^(-x)/-1-int2x*e^(-x)/-1=x^2e^(-x)+2intxe^(-x)dx=x^2e^(-x)+2[xe^(-x)/-1-e^(-x)/-1]=x^2e^(-x)-2xe^(-x)+2e^(-x)+cx2e−xdx=x2e−x−1−∫2x⋅e−x−1=x2e−x+2∫xe−xdx=x2e−x+2[xe−x−1−e−x−1]=x2e−x−2xe−x+2e−x+c

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