What is the integral of (5xe^x) ?

The integral of (5xe^x) is 5(e^xx-e^x)+C

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integral of (5xe^x)

\int (5 x e^{x}) d x

5 (e^{x} x - e^{x}) + C

Solution steps

\int 5 x e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int x e^{x} d x

Apply Integration By Parts

= 5 (e^{x} x - \int e^{x} d x)

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

= 5 (e^{x} x - e^{x})

Add a constant to the solution

= 5 (e^{x} x - e^{x}) + C