What is the integral of (2x)/(e^{8x)} ?

The integral of (2x)/(e^{8x)} is 2(-1/8 e^{-8x}x-1/64 e^{-8x})+C

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integral of (2x)/(e^{8x)}

\int \frac{2 x}{e ^{8 x}} d x

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

Solution steps

\int \frac{2 x}{e ^{8 x}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \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

= 2 (- \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}

= 2 (- \frac{1}{8} e^{- 8 x} x - \frac{1}{64} e^{- 8 x})

Add a constant to the solution

= 2 (- \frac{1}{8} e^{- 8 x} x - \frac{1}{64} e^{- 8 x}) + C

y = - 3 x^{2} - x

\frac{d ^{2}}{d x ^{2}} (\frac{1}{ln ( x )})

\frac{d}{d y} (y^{2})

x \to \infty lim (\frac{1}{( 2 + x ^{2} ) ^{\frac{1}{x}}})

f (x) = arctan (2 x)

What is the integral of (2x)/(e^{8x)} ?
The integral of (2x)/(e^{8x)} is 2(-1/8 e^{-8x}x-1/64 e^{-8x})+C