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

The integral of xe^{x/5} is 5e^{x/5}x-25e^{x/5}+C

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integral of xe^{x/5}

\int x e^{\frac{x}{5}} d x

5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}} + C

Solution steps

\int x e^{\frac{x}{5}} d x

Apply Integration By Parts

= 5 e^{\frac{x}{5}} x - \int 5 e^{\frac{x}{5}} d x

\int 5 e^{\frac{x}{5}} d x = 25 e^{\frac{x}{5}}

= 5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}}

Add a constant to the solution

= 5 e^{\frac{x}{5}} x - 25 e^{\frac{x}{5}} + C

What is the integral of xe^{x/5} ?
The integral of xe^{x/5} is 5e^{x/5}x-25e^{x/5}+C