What is expand (e^{3x})(x+Ce^{-x}+Ce^{-3x}) ?

The solution to expand (e^{3x})(x+Ce^{-x}+Ce^{-3x}) is e^{3x}x+e^{2x}C+C

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expand (e^{3x})(x+Ce^{-x}+Ce^{-3x})

expand

(e^{3 x}) (x + C e^{- x} + C e^{- 3 x})

e^{3 x} x + e^{2 x} C + C

Solution steps

(e^{3 x}) (x + C e^{- x} + C e^{- 3 x})

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

Distribute parentheses

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

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

Simplify

x (e^{3 x}) + e^{- x} C (e^{3 x}) + e^{- 3 x} C (e^{3 x}) : e^{3 x} x + e^{2 x} C + C

= e^{3 x} x + e^{2 x} C + C

(a - b) (a - b)

- \frac{( 2 - x ) ^{3}}{3}

(3 + x - 4)^{2}

\frac{6 ( - x + 3 )}{( x - 1 ) ^{3}}

(\frac{2 x ^{2}}{y} + \frac{y ^{2}}{x})^{4}

What is expand (e^{3x})(x+Ce^{-x}+Ce^{-3x}) ?
The solution to expand (e^{3x})(x+Ce^{-x}+Ce^{-3x}) is e^{3x}x+e^{2x}C+C