What is the integral from 2 to 5 of xe^x ?

The integral from 2 to 5 of xe^x is 4e^5-e^2

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integral from 2 to 5 of xe^x

\int_{2}^{5} x e^{x} d x

4 e^{5} - e^{2}

Decimal

586.26358 \dots

Solution steps

\int_{2}^{5} x e^{x} d x

Apply Integration By Parts

= [e^{x} x - \int e^{x} d x]_{2}^{5}

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

= [e^{x} x - e^{x}]_{2}^{5}

Compute the boundaries:

4 e^{5} - e^{2}

= 4 e^{5} - e^{2}

What is the integral from 2 to 5 of xe^x ?
The integral from 2 to 5 of xe^x is 4e^5-e^2