What is the integral of x/(e^{3x)} ?

The integral of x/(e^{3x)} is -1/3 e^{-3x}x-1/9 e^{-3x}+C

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integral of x/(e^{3x)}

\int \frac{x}{e ^{3 x}} d x

- \frac{1}{3} e^{- 3 x} x - \frac{1}{9} e^{- 3 x} + C

Solution steps

\int \frac{x}{e ^{3 x}} d x

Apply Integration By Parts

: - \frac{1}{3} e^{- 3 x} x - \int - \frac{1}{3} e^{- 3 x} d x

= - \frac{1}{3} e^{- 3 x} x - \int - \frac{1}{3} e^{- 3 x} d x

\int - \frac{1}{3} e^{- 3 x} d x = \frac{1}{9} e^{- 3 x}

= - \frac{1}{3} e^{- 3 x} x - \frac{1}{9} e^{- 3 x}

Add a constant to the solution

= - \frac{1}{3} e^{- 3 x} x - \frac{1}{9} e^{- 3 x} + C

\int ln (x) x^{- 3} d x

\frac{\partial}{\partial x} (x^{2} - 6 y)

(- ln (2 x))^{^{'}}

f (x) = x^{2} + 1, at x = 2

\int 12 - x d x

What is the integral of x/(e^{3x)} ?
The integral of x/(e^{3x)} is -1/3 e^{-3x}x-1/9 e^{-3x}+C