What is the integral from 0 to 1 of y/(e^{5y)} ?

The integral from 0 to 1 of y/(e^{5y)} is -6/(25e^5)+1/25

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integral from 0 to 1 of y/(e^{5y)}

\int_{0}^{1} \frac{y}{e ^{5 y}} d y

- \frac{6}{25 e ^{5}} + \frac{1}{25}

Decimal Notation

0.03838 \dots

Solution steps

\int_{0}^{1} \frac{y}{e ^{5 y}} d y

Apply Integration By Parts

: [- \frac{1}{5} e^{- 5 y} y - \int - \frac{1}{5} e^{- 5 y} d y]_{0}^{1}

= [- \frac{1}{5} e^{- 5 y} y - \int - \frac{1}{5} e^{- 5 y} d y]_{0}^{1}

\int - \frac{1}{5} e^{- 5 y} d y = \frac{1}{25} e^{- 5 y}

= [- \frac{1}{5} e^{- 5 y} y - \frac{1}{25} e^{- 5 y}]_{0}^{1}

Compute the boundaries:

- \frac{6}{25 e ^{5}} + \frac{1}{25}

= - \frac{6}{25 e ^{5}} + \frac{1}{25}

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What is the integral from 0 to 1 of y/(e^{5y)} ?
The integral from 0 to 1 of y/(e^{5y)} is -6/(25e^5)+1/25