What is the integral of (3x)/(e^x) ?

The integral of (3x)/(e^x) is 3(-x/(e^x)-1/(e^x))+C

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integral of (3x)/(e^x)

\int \frac{3 x}{e ^{x}} d x

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

Solution steps

\int \frac{3 x}{e ^{x}} d x

Take the constant out:

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

= 3 \cdot \int \frac{x}{e ^{x}} d x

Apply Integration By Parts

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

= 3 (- \frac{x}{e ^{x}} - \int - \frac{1}{e ^{x}} d x)

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

= 3 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}})

Add a constant to the solution

= 3 (- \frac{x}{e ^{x}} - \frac{1}{e ^{x}}) + C

\frac{d}{d x} (x^{2} sin (\frac{1}{a x}))

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

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

x \to 4 lim (x^{2} + 9)

f (x) = (5 + x^{4})^{3 x}

What is the integral of (3x)/(e^x) ?
The integral of (3x)/(e^x) is 3(-x/(e^x)-1/(e^x))+C