What is the integral from 0 to 1 of ue^u ?

The integral from 0 to 1 of ue^u is 1

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integral from 0 to 1 of ue^u

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

1

Solution steps

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

Apply Integration By Parts

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

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

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

Compute the boundaries:

1

= 1

What is the integral from 0 to 1 of ue^u ?
The integral from 0 to 1 of ue^u is 1