What is the integral of 3+xe^{x-1} ?

The integral of 3+xe^{x-1} is 3x+e^{x-1}x-e^{x-1}+C

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integral of 3+xe^{x-1}

\int 3 + x e^{x - 1} d x

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

Solution steps

\int 3 + x e^{x - 1} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 d x + \int x e^{x - 1} d x

\int 3 d x = 3 x

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

= 3 x + e^{x - 1} x - e^{x - 1}

Add a constant to the solution

= 3 x + e^{x - 1} x - e^{x - 1} + C

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What is the integral of 3+xe^{x-1} ?
The integral of 3+xe^{x-1} is 3x+e^{x-1}x-e^{x-1}+C