What is the integral from 0 to x of xe^x ?

The integral from 0 to x of xe^x is e^xx-e^x+1

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integral from 0 to x of xe^x

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

e^{x} x - e^{x} + 1

Solution steps

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

Apply Integration By Parts

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

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

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

Compute the boundaries:

e^{x} x - e^{x} + 1

= e^{x} x - e^{x} + 1

What is the integral from 0 to x of xe^x ?
The integral from 0 to x of xe^x is e^xx-e^x+1