What is the integral from 0 to 1 of y/(e^{8y)} ?

The integral from 0 to 1 of y/(e^{8y)} is -9/(64e^8)+1/64

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integral from 0 to 1 of y/(e^{8y)}

\int_{0}^{1} \frac{y}{e ^{8 y}} d y

- \frac{9}{64 e ^{8}} + \frac{1}{64}

Decimal Notation

0.01557 \dots

Solution steps

\int_{0}^{1} \frac{y}{e ^{8 y}} d y

Apply Integration By Parts

: [- \frac{1}{8} e^{- 8 y} y - \int - \frac{1}{8} e^{- 8 y} d y]_{0}^{1}

= [- \frac{1}{8} e^{- 8 y} y - \int - \frac{1}{8} e^{- 8 y} d y]_{0}^{1}

\int - \frac{1}{8} e^{- 8 y} d y = \frac{1}{64} e^{- 8 y}

= [- \frac{1}{8} e^{- 8 y} y - \frac{1}{64} e^{- 8 y}]_{0}^{1}

Compute the boundaries:

- \frac{9}{64 e ^{8}} + \frac{1}{64}

= - \frac{9}{64 e ^{8}} + \frac{1}{64}

\int \frac{ln ( 7 x )}{x} d x

\frac{3 s ^{2}}{( s + 2 ) ( s + 5 )}

\frac{d}{d x} (3 x^{3} - 2 x^{2})

f (x) = (4 x + 3)^{2}

x \to 0 lim (tan^{x} (x))

What is the integral from 0 to 1 of y/(e^{8y)} ?
The integral from 0 to 1 of y/(e^{8y)} is -9/(64e^8)+1/64