What is the integral of xe^{-x/4} ?

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

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integral of xe^{-x/4}

\int x 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

x + \frac{1}{x}, at x = 4

\int ln^{2} (c) os x tan (x)

\frac{d y}{d x} + y = x y^{3}

x \to 22 lim (2 x^{2} - 3 x - 5)

n = 1 \sum \infty \frac{3}{3 ^{n}}

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