What is the integral from 0 to 2 of x*e^x ?

The integral from 0 to 2 of x*e^x is e^2+1

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integral from 0 to 2 of x*e^x

\int_{0}^{2} x \cdot e^{x} d x

e^{2} + 1

Decimal

8.38905 \dots

Solution steps

\int_{0}^{2} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{2}

= [e^{x} x - \int e^{x} d x]_{0}^{2}

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

= [e^{x} x - e^{x}]_{0}^{2}

Compute the boundaries:

e^{2} + 1

= e^{2} + 1

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What is the integral from 0 to 2 of x*e^x ?
The integral from 0 to 2 of x*e^x is e^2+1