What is the integral of x/(e^{5x)} ?

The integral of x/(e^{5x)} is -1/5 e^{-5x}x-1/25 e^{-5x}+C

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integral of x/(e^{5x)}

\int \frac{x}{e ^{5 x}} d x

- \frac{1}{5} e^{- 5 x} x - \frac{1}{25} e^{- 5 x} + C

Solution steps

\int \frac{x}{e ^{5 x}} d x

Apply Integration By Parts

: - \frac{1}{5} e^{- 5 x} x - \int - \frac{1}{5} e^{- 5 x} d x

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

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

= - \frac{1}{5} e^{- 5 x} x - \frac{1}{25} e^{- 5 x}

Add a constant to the solution

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

\frac{x ^{3}}{6} + \frac{1}{2 x}

\int e^{2 x} cos (1 - x) d x

y^{^{'}} = y^{2} - 2

y = (4 x - x^{2})^{3}

\frac{d}{d x} (\frac{4 x}{( x ^{2} + 1 ) ^{2}})

What is the integral of x/(e^{5x)} ?
The integral of x/(e^{5x)} is -1/5 e^{-5x}x-1/25 e^{-5x}+C