What is the integral of 5xe^{x+4} ?

The integral of 5xe^{x+4} is 5(e^{4+x}x-e^{4+x})+C

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integral of 5xe^{x+4}

\int 5 x e^{x + 4} d x

5 (e^{4 + x} x - e^{4 + x}) + C

Solution steps

\int 5 x e^{x + 4} 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 + 4} d x

Apply Integration By Parts

: e^{4 + x} x - \int e^{4 + x} d x

= 5 (e^{4 + x} x - \int e^{4 + x} d x)

\int e^{4 + x} d x = e^{4 + x}

= 5 (e^{4 + x} x - e^{4 + x})

Add a constant to the solution

= 5 (e^{4 + x} x - e^{4 + x}) + C

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What is the integral of 5xe^{x+4} ?
The integral of 5xe^{x+4} is 5(e^{4+x}x-e^{4+x})+C