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}

Decimal

0.14849 \dots

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}

\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}

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