What is the integral of x/(e^{7x)} ?

The integral of x/(e^{7x)} is -1/7 e^{-7x}x-1/49 e^{-7x}+C

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integral of x/(e^{7x)}

\int \frac{x}{e ^{7 x}} d x

- \frac{1}{7} e^{- 7 x} x - \frac{1}{49} e^{- 7 x} + C

Solution steps

\int \frac{x}{e ^{7 x}} d x

Apply Integration By Parts

: - \frac{1}{7} e^{- 7 x} x - \int - \frac{1}{7} e^{- 7 x} d x

= - \frac{1}{7} e^{- 7 x} x - \int - \frac{1}{7} e^{- 7 x} d x

\int - \frac{1}{7} e^{- 7 x} d x = \frac{1}{49} e^{- 7 x}

= - \frac{1}{7} e^{- 7 x} x - \frac{1}{49} e^{- 7 x}

Add a constant to the solution

= - \frac{1}{7} e^{- 7 x} x - \frac{1}{49} e^{- 7 x} + C

x \to 1 lim (\frac{2}{5} x + 7)

\int ln (3)

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\int \frac{1}{x ^{2} x ^{2} - 144} d x

What is the integral of x/(e^{7x)} ?
The integral of x/(e^{7x)} is -1/7 e^{-7x}x-1/49 e^{-7x}+C