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

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

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

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

\frac{\partial}{\partial x} (\frac{e ^{x z + y}}{z ^{2} + w})

\frac{d}{d x} (\frac{1}{( x + 9 ) ^{2}})

\frac{\partial}{\partial x} ((- x^{4} + 7 y^{2} + 3 y)^{6})

\int 1 + \frac{1}{2 x} d x

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = 3, y^{^{'}} (0) = 2

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