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}{( x ^{2} + b ^{2} ) ^{\frac{3}{2}}} d x

x \to (- 1 + 1) lim (\frac{1}{x - 2})

y = 2 x^{3} - 2 x, (- 1, 0)

\int x cos (x) + cos (x) - 1 d x

\int cos^{2} (x) - sin^{2} (x) d x

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