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

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

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integral from-infinity to 2 of xe^x

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

e^{2}

Decimal

7.38905 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= e^{2} - 0

Simplify

= e^{2}

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