What is the integral of x/(e^{-2x)} ?

The integral of x/(e^{-2x)} is 1/2 e^{2x}x-1/4 e^{2x}+C

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integral of x/(e^{-2x)}

\int \frac{x}{e ^{- 2 x}} d x

\frac{1}{2} e^{2 x} x - \frac{1}{4} e^{2 x} + C

Solution steps

\int \frac{x}{e ^{- 2 x}} d x

Apply Integration By Parts

: \frac{1}{2} e^{2 x} x - \int \frac{1}{2} e^{2 x} d x

= \frac{1}{2} e^{2 x} x - \int \frac{1}{2} e^{2 x} d x

\int \frac{1}{2} e^{2 x} d x = \frac{1}{4} e^{2 x}

= \frac{1}{2} e^{2 x} x - \frac{1}{4} e^{2 x}

Add a constant to the solution

= \frac{1}{2} e^{2 x} x - \frac{1}{4} e^{2 x} + C

\int \frac{1}{u ^{2} + 2} d u

\int_{0}^{1} e^{s} sin (t - s) d s

f (x) = x^{3} - 9 x, at x = (- 3)

f (x) = 2 x - \frac{1}{x}, at x = 0.5

x \to 1 + lim (\frac{5}{x - 1})

What is the integral of x/(e^{-2x)} ?
The integral of x/(e^{-2x)} is 1/2 e^{2x}x-1/4 e^{2x}+C