What is the integral of xe^{1+x} ?

The integral of xe^{1+x} is e^{1+x}x-e^{1+x}+C

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integral of xe^{1+x}

\int x e^{1 + x} d x

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

Solution steps

\int x e^{1 + x} d x

Apply Integration By Parts

: e^{1 + x} x - \int e^{1 + x} d x

= e^{1 + x} x - \int e^{1 + x} d x

\int e^{1 + x} d x = e^{1 + x}

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

Add a constant to the solution

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

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What is the integral of xe^{1+x} ?
The integral of xe^{1+x} is e^{1+x}x-e^{1+x}+C