What is the integral from-infinity to 0 of y^3e^y ?

The integral from-infinity to 0 of y^3e^y is -6

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integral from-infinity to 0 of y^3e^y

\int_{- \infty}^{0} y^{3} e^{y} d y

- 6

Solution steps

\int_{- \infty}^{0} y^{3} e^{y} d y

Compute the indefinite integral:

\int y^{3} e^{y} d y = y^{3} e^{y} - 3 (y^{2} e^{y} - 2 (e^{y} y - e^{y})) + C

Compute the boundaries:

\int_{- \infty}^{0} y^{3} e^{y} d y = - 6 - 0

= - 6 - 0

Simplify

= - 6

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What is the integral from-infinity to 0 of y^3e^y ?
The integral from-infinity to 0 of y^3e^y is -6