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

The integral of x/(e^{4x)} is -1/4 e^{-4x}x-1/16 e^{-4x}+C

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integral of x/(e^{4x)}

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

- \frac{1}{4} e^{- 4 x} x - \frac{1}{16} e^{- 4 x} + C

Solution steps

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

Apply Integration By Parts

: - \frac{1}{4} e^{- 4 x} x - \int - \frac{1}{4} e^{- 4 x} d x

= - \frac{1}{4} e^{- 4 x} x - \int - \frac{1}{4} e^{- 4 x} d x

\int - \frac{1}{4} e^{- 4 x} d x = \frac{1}{16} e^{- 4 x}

= - \frac{1}{4} e^{- 4 x} x - \frac{1}{16} e^{- 4 x}

Add a constant to the solution

= - \frac{1}{4} e^{- 4 x} x - \frac{1}{16} e^{- 4 x} + C

n = 1 \sum \infty \frac{2}{9 ^{n}}

3 x - 2 x^{2}

x \to 0 lim ((e^{- \frac{1}{x}})^{x})

\frac{d y}{d t} + t y = t y^{2}

\int x e^{2 x y} d y

What is the integral of x/(e^{4x)} ?
The integral of x/(e^{4x)} is -1/4 e^{-4x}x-1/16 e^{-4x}+C