What is expand 1/6 (1+e^{2x})^3 ?

The solution to expand 1/6 (1+e^{2x})^3 is 1/6+1/2 e^{2x}+1/2 e^{4x}+1/6 e^{6x}

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expand 1/6 (1+e^{2x})^3

expand

\frac{1}{6} (1 + e^{2 x})^{3}

\frac{1}{6} + \frac{1}{2} e^{2 x} + \frac{1}{2} e^{4 x} + \frac{1}{6} e^{6 x}

Solution steps

\frac{1}{6} (1 + e^{2 x})^{3}

(1 + e^{2 x})^{3} = 1 + 3 e^{2 x} + 3 e^{4 x} + e^{6 x}

= \frac{1}{6} (3 e^{2 x} + 3 e^{4 x} + e^{6 x} + 1)

Distribute parentheses

= \frac{1}{6} \cdot 1 + \frac{1}{6} \cdot 3 e^{2 x} + \frac{1}{6} \cdot 3 e^{4 x} + \frac{1}{6} e^{6 x}

= 1 \cdot \frac{1}{6} + 3 \cdot \frac{1}{6} e^{2 x} + 3 \cdot \frac{1}{6} e^{4 x} + \frac{1}{6} e^{6 x}

Simplify

1 \cdot \frac{1}{6} + 3 \cdot \frac{1}{6} e^{2 x} + 3 \cdot \frac{1}{6} e^{4 x} + \frac{1}{6} e^{6 x} : \frac{1}{6} + \frac{1}{2} e^{2 x} + \frac{1}{2} e^{4 x} + \frac{1}{6} e^{6 x}

= \frac{1}{6} + \frac{1}{2} e^{2 x} + \frac{1}{2} e^{4 x} + \frac{1}{6} e^{6 x}

(1 + 5 sin (t)) \cdot (5 cos (t))

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\frac{1}{( x ) ( x + 1 )}

\frac{3 x ^{3} - 18 x ^{2} + 29 x - 4}{( x + 1 ) ( x - 2 ) ^{3}}

What is expand 1/6 (1+e^{2x})^3 ?
The solution to expand 1/6 (1+e^{2x})^3 is 1/6+1/2 e^{2x}+1/2 e^{4x}+1/6 e^{6x}