What is the integral of x*e^{x/4} ?

The integral of x*e^{x/4} is 4e^{x/4}x-16e^{x/4}+C

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integral of x*e^{x/4}

\int x \cdot e^{\frac{x}{4}} d x

4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}} + C

Solution steps

\int x e^{\frac{x}{4}} d x

Apply Integration By Parts

= 4 e^{\frac{x}{4}} x - \int 4 e^{\frac{x}{4}} d x

\int 4 e^{\frac{x}{4}} d x = 16 e^{\frac{x}{4}}

= 4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}}

Add a constant to the solution

= 4 e^{\frac{x}{4}} x - 16 e^{\frac{x}{4}} + C

What is the integral of x*e^{x/4} ?
The integral of x*e^{x/4} is 4e^{x/4}x-16e^{x/4}+C