What is the integral from-infinity to 0 of x^2*e^x ?

The integral from-infinity to 0 of x^2*e^x is 2

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integral from-infinity to 0 of x^2*e^x

\int_{- \infty}^{0} x^{2} \cdot e^{x} d x

2

Solution steps

\int_{- \infty}^{0} x^{2} e^{x} d x

Compute the indefinite integral:

\int x^{2} e^{x} d x = x^{2} e^{x} - 2 (e^{x} x - e^{x}) + C

Compute the boundaries:

\int_{- \infty}^{0} x^{2} e^{x} d x = 2 - 0

= 2 - 0

Simplify

= 2

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What is the integral from-infinity to 0 of x^2*e^x ?
The integral from-infinity to 0 of x^2*e^x is 2