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

Simplify

= \int e^{- \frac{x}{4}} x 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{d}{d x} (\frac{x ^{5} - 4 x ^{2}}{x ^{3}})

cos ((ln (x + 1))^{2} - e^{x^{2}})

\int \frac{10}{x ^{2} + 16} d x

\frac{d}{d x} (\frac{1}{15} cos^{3} (x) (3 cos^{2} (x) - 5))

\int_{4}^{e^{5}} \frac{1}{x} d x

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