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

The integral of xe^{x/a} is ae^{x/a}x-a^2e^{x/a}+C

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integral of xe^{x/a}

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

a e^{\frac{x}{a}} x - a^{2} e^{\frac{x}{a}} + C

Solution steps

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

Apply Integration By Parts

: a e^{\frac{x}{a}} x - \int a e^{\frac{x}{a}} d x

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

\int a e^{\frac{x}{a}} d x = a^{2} e^{\frac{x}{a}}

= a e^{\frac{x}{a}} x - a^{2} e^{\frac{x}{a}}

Add a constant to the solution

= a e^{\frac{x}{a}} x - a^{2} e^{\frac{x}{a}} + C

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What is the integral of xe^{x/a} ?
The integral of xe^{x/a} is ae^{x/a}x-a^2e^{x/a}+C