What is the integral of x/(e^{8x)} ?

The integral of x/(e^{8x)} is -1/8 e^{-8x}x-1/64 e^{-8x}+C

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integral of x/(e^{8x)}

\int \frac{x}{e ^{8 x}} d x

- \frac{1}{8} e^{- 8 x} x - \frac{1}{64} e^{- 8 x} + C

Solution steps

\int \frac{x}{e ^{8 x}} d x

Apply Integration By Parts

: - \frac{1}{8} e^{- 8 x} x - \int - \frac{1}{8} e^{- 8 x} d x

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

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

= - \frac{1}{8} e^{- 8 x} x - \frac{1}{64} e^{- 8 x}

Add a constant to the solution

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

\int x^{2} a^{x} d x

\int \frac{ln ( 2 x )}{x ln ( 4 x )} d x

\int \frac{ln ( ln ( 3 x ) )}{x ln ( 3 x )} d x

2 x^{2}

\int \frac{1}{1 - \frac{x ^{2}}{64}} d x

What is the integral of x/(e^{8x)} ?
The integral of x/(e^{8x)} is -1/8 e^{-8x}x-1/64 e^{-8x}+C