What is the integral from-1 to 1 of x*e^x ?

The integral from-1 to 1 of x*e^x is 2/e

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integral from-1 to 1 of x*e^x

\int_{- 1}^{1} x \cdot e^{x} d x

\frac{2}{e}

Decimal

0.73575 \dots

Solution steps

\int_{- 1}^{1} x e^{x} d x

Apply Integration By Parts

= [e^{x} x - \int e^{x} d x]_{- 1}^{1}

\int e^{x} d x = e^{x}

= [e^{x} x - e^{x}]_{- 1}^{1}

Compute the boundaries:

\frac{2}{e}

= \frac{2}{e}

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What is the integral from-1 to 1 of x*e^x ?
The integral from-1 to 1 of x*e^x is 2/e