What is expand ((x^2)/2+x)xe^{2x} ?

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

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expand ((x^2)/2+x)xe^{2x}

expand

(\frac{x ^{2}}{2} + x) x e^{2 x}

\frac{e ^{2 x} x ^{3}}{2} + e^{2 x} x^{2}

Solution steps

(\frac{x ^{2}}{2} + x) x e^{2 x}

= e^{2 x} x (\frac{x ^{2}}{2} + x)

Apply the distributive law:

a (b + c) = ab + a c

a = x e^{2 x}, b = \frac{x ^{2}}{2}, c = x

= x e^{2 x} \frac{x ^{2}}{2} + x e^{2 x} x

= e^{2 x} \frac{x ^{2}}{2} x + e^{2 x} xx

Simplify

e^{2 x} \frac{x ^{2}}{2} x + e^{2 x} xx : \frac{e ^{2 x} x ^{3}}{2} + e^{2 x} x^{2}

= \frac{e ^{2 x} x ^{3}}{2} + e^{2 x} x^{2}

\frac{d}{d x} ((x^{2} - a) e^{x}) + b x

(5 y - 6 i)^{2}

\frac{38.8}{( x ^{2} + 4 ) \cdot ( x + 5.2 )}

(6 z - 5 i)^{2}

- \frac{4}{( s + 2 ) ( s ^{2} + 4 s + 8 )}

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