What is the integral from 1 to 3 of xe^x ?

The integral from 1 to 3 of xe^x is 2e^3

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integral from 1 to 3 of xe^x

\int_{1}^{3} x e^{x} d x

2 e^{3}

Decimal Notation

40.17107 \dots

Solution steps

\int_{1}^{3} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{1}^{3}

= [e^{x} x - \int e^{x} d x]_{1}^{3}

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

= [e^{x} x - e^{x}]_{1}^{3}

Compute the boundaries:

2 e^{3}

= 2 e^{3}

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What is the integral from 1 to 3 of xe^x ?
The integral from 1 to 3 of xe^x is 2e^3