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

= 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

\frac{\partial}{\partial x} (4 \frac{y}{x})

\frac{d}{d y} (x y)

y = (x)

y = 4 x - 16, y^{2} = 4 x + 4

y = arctan (7 x^{2} - 1)

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