What is the integral from 0 to 1 of (x/(e^{2x)}) ?

The integral from 0 to 1 of (x/(e^{2x)}) is -3/(4e^2)+1/4

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integral from 0 to 1 of (x/(e^{2x)})

\int_{0}^{1} (\frac{x}{e ^{2 x}}) d x

- \frac{3}{4 e ^{2}} + \frac{1}{4}

Solution steps

\int_{0}^{1} \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]_{0}^{1}

= [- \frac{1}{2} e^{- 2 x} x - \int - \frac{1}{2} e^{- 2 x} d x]_{0}^{1}

\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}]_{0}^{1}

Compute the boundaries:

- \frac{3}{4 e ^{2}} + \frac{1}{4}

= - \frac{3}{4 e ^{2}} + \frac{1}{4}

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What is the integral from 0 to 1 of (x/(e^{2x)}) ?
The integral from 0 to 1 of (x/(e^{2x)}) is -3/(4e^2)+1/4