What is the integral from 0 to 1 of x(e^x) ?

The integral from 0 to 1 of x(e^x) is 1

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integral from 0 to 1 of x(e^x)

\int_{0}^{1} x (e^{x}) d x

1

Solution steps

\int_{0}^{1} x e^{x} d x

Apply Integration By Parts

= [e^{x} x - \int e^{x} d x]_{0}^{1}

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

= [e^{x} x - e^{x}]_{0}^{1}

Compute the boundaries:

1

= 1

What is the integral from 0 to 1 of x(e^x) ?
The integral from 0 to 1 of x(e^x) is 1