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

The integral of ((2x)/(e^x)) is 2(-x/(e^x)-1/(e^x))+C

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integral of ((2x)/(e^x))

\int (\frac{2 x}{e ^{x}}) d x

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int_{0}^{\frac{π}{2}} sin (2 x - π) d x

k = 1 \sum \infty \frac{1}{k !}

y = \frac{5}{( 2 x ^{3} )} + 2 cos (x)

\int \frac{ln ( x ^{9} )}{x} d x

\frac{d y}{d x} - e^{4 x + y} = 0

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