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

\int \frac{6 + t + t ^{2}}{t} d t

\frac{\partial}{\partial x} (\frac{2 x}{x ^{2} + y ^{2}})

x^{6}, x^{3}

\frac{d}{d x} (x^{2} - \frac{8}{x ^{3}})

\frac{d}{d x} (1. 4^{x} - 2.7)

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