What is the integral of (6x)/(e^x) ?

The integral of (6x)/(e^x) is 6(-x/(e^x)-1/(e^x))+C

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integral of (6x)/(e^x)

\int \frac{6 x}{e ^{x}} d x

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

Solution steps

\int \frac{6 x}{e ^{x}} d x

Take the constant out:

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

= 6 \cdot \int \frac{x}{e ^{x}} d x

Apply Integration By Parts

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

= 6 (- \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x)

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

= 6 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})

Add a constant to the solution

= 6 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}) + C

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What is the integral of (6x)/(e^x) ?
The integral of (6x)/(e^x) is 6(-x/(e^x)-1/(e^x))+C