What is expand 3/2 (e^x-1/9 (e^{3x}*3x-e^{3x})+C) ?

The solution to expand 3/2 (e^x-1/9 (e^{3x}*3x-e^{3x})+C) is 3/2 e^x-(e^{3x}x)/2+(e^{3x})/6+(3C)/2

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expand 3/2 (e^x-1/9 (e^{3x}*3x-e^{3x})+C)

expand

\frac{3}{2} (e^{x} - \frac{1}{9} (e^{3 x} \cdot 3 x - e^{3 x}) + C)

\frac{3}{2} e^{x} - \frac{e ^{3 x} x}{2} + \frac{e ^{3 x}}{6} + \frac{3 C}{2}

Solution steps

\frac{3}{2} (e^{x} - \frac{1}{9} (e^{3 x} \cdot 3 x - e^{3 x}) + C)

= \frac{3}{2} (e^{x} - \frac{1}{9} (3 e^{3 x} x - e^{3 x}) + C)

Distribute parentheses

= \frac{3}{2} e^{x} + \frac{3}{2} (- \frac{1}{9} (e^{3 x} \cdot 3 x - e^{3 x})) + \frac{3}{2} C

Apply minus-plus rules

+ (- a) = - a

= \frac{3}{2} e^{x} - \frac{3}{2} \cdot \frac{1}{9} (3 e^{3 x} x - e^{3 x}) + \frac{3}{2} C

Simplify

\frac{3}{2} e^{x} - \frac{3}{2} \cdot \frac{1}{9} (3 e^{3 x} x - e^{3 x}) + \frac{3}{2} C : \frac{3}{2} e^{x} - \frac{e ^{3 x} x}{2} + \frac{e ^{3 x}}{6} + \frac{3 C}{2}

= \frac{3}{2} e^{x} - \frac{e ^{3 x} x}{2} + \frac{e ^{3 x}}{6} + \frac{3 C}{2}

- (\frac{5}{14} lo g_{2} (\frac{5}{14}) + \frac{9}{14} lo g_{2} (\frac{9}{14}))

x - 2

(2 y^{2} + 3 x) d x + (2 x y) d y

\frac{d}{d x} ((3 x - 3 x^{2} - 3) 6) - 12

(8 x^{2} - 6 x + 3) (8 x^{2} - 6 x + 3)^{'}

What is expand 3/2 (e^x-1/9 (e^{3x}*3x-e^{3x})+C) ?
The solution to expand 3/2 (e^x-1/9 (e^{3x}*3x-e^{3x})+C) is 3/2 e^x-(e^{3x}x)/2+(e^{3x})/6+(3C)/2